Answer:
length = 17; breadth = 9
Step-by-step explanation:
Let x = area of rectangle; a = length; b = breadth.
+) a × b = x (1)
+) (a - 5) × (b + 3) = x - 9 => x = ab + 3a - 5b - 15 + 9 (2)
+) (a + 3) × (b + 2) = x + 67 => x = ab + 2a + 3b + 6 - 67 (3)
Replace (1) into (2) & (3):
[tex]\left \{ {{3a - 5b=6} \atop {2a+3b=61}} \right. = > \left \{ {{a=17} \atop {b=9}} \right.[/tex]
Please help me solve and show my work
The degree measure of the angles are;
1. 5π/3 = 300°
2 3π/4 = 135°
3. 5π/6 = 150°
4. -3π/2 = 90°
What is degree and radian?A degree is a unit of measurement which is used to measure circles, spheres, and angles while a radian is also a unit of measurement which is used to measure angles.
A circle has 360 degrees which are its full area while its radian is only half of it which is 180 degrees or one pi radian.
therefore π = 180°
1. 5π/ 3 = 5×180/3 = 300°
2. 3π/4 = 3× 180/4 = 540/4 = 135°
3. 5π/6 = 5×180/6 = 150°
4. - 3π/2 = -3 × 180/2 = -270° = 90°
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Given F(x) = 4x - 8 and g(x) = -3x + 1, what is (f - g)(x)?
A) 7x-9
B) 7x - 7
C) x-9
D) x - 7
Therefore, the answer is (A) 7x-9 when it is given that function F(x) = 4x - 8 and g(x) = -3x + 1.
What is function?In mathematics, a function is a relationship between two sets of values, where each input (or domain element) is associated with a unique output (or range element). In other words, a function is a rule or a process that takes an input (or inputs) and produces a corresponding output. Functions can be expressed using various mathematical notations, such as algebraic formulas, graphs, tables, or even verbal descriptions. They are widely used in many fields of mathematics, science, engineering, economics, and computer science, to model and solve problems that involve relationships between variables or quantities.
Here,
To find (f - g)(x), we need to subtract g(x) from f(x), so we get:
(f - g)(x) = f(x) - g(x)
Substituting the given functions, we get:
(f - g)(x) = (4x - 8) - (-3x + 1)
Simplifying the expression by distributing the negative sign, we get:
(f - g)(x) = 4x - 8 + 3x - 1
Combining like terms, we get:
(f - g)(x) = 7x - 9
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Oliver and Mike each place some apples and oranges into the same bowl.
• The ratio of apples to oranges Oliver places in the bowl is 2:3
• The ratio of apples to oranges Mike places in the bowl is 1:2
• They each place 6 oranges in the bowl.
Write the total number of apples and oranges they place in the bowl.
Answer: 5 * 5 = 20
20 divided by 1 = 20
If there are 5 apples with an apple:orange ratio of 1:4, there are 20 oranges.
You take out a loan in the amount of your tuition and fees cost $70,000. The loan has a monthly interest rate of 0.25% and a monthly payment of $250. How long will it take you to pay off the loan? Use the formula N= (-log(1-i*A/P))/(log(1+i)) to determine the number of months it will take you to pay off the loan. Let N represent the number of monthly payments that will need to be made, i represent the interest rate in decimal form, A represent the amount owed (total amount of the loan), and P represent the amount of your monthly payment. Be sure to show your work for all calculations made.
Therefore, it will take 173 months to pay off the loan, or approximately 14 years and 5 months.
What is percentage?A percentage is a way of expressing a number as a fraction of 100. The symbol for a percentage is "%". For example, 50% is the same as 50/100 or 0.5 as a decimal. Percentages are often used to express a portion or share of a whole. For instance, if you scored 90% on a test, it means you got 90 out of 100 possible points. In finance, percentages are commonly used to express interest rates, returns on investments, or changes in stock prices.
First, we need to convert the monthly interest rate from a percentage to a decimal by dividing by 100.
0.25% / 100 = 0.0025
Now we can plug in the values into the formula:
N= (-log (1-0.0025*70000/250))/ (log (1+0.0025))
Simplifying the equation in the parentheses:
N= (-log (1-175))/ (log (1.0025))
N= (-log (0.9964))/ (0.002499)
N= 172.9
Rounding up to the nearest whole number since we can't make partial payments:
N= 173
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Given that sin 0 = 20/29 and that angle terminates in quadrant III, then what is the value of tan 0?
The value of Tanθ is 20/21.
What is Pythagorean Theorem?
A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Here, we have
Given: sinθ = -20/29 and that angle terminates in quadrant III.
We have to find the value of tanθ.
Using the definition of sine to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.
Sinθ = Perpendicular/hypotenuse
Find the adjacent side of the unit circle triangle. Since the hypotenuse and opposite sides are known, use the Pythagorean theorem to find the remaining side.
Adjacent = - √Hypotenuse² - perpenducualr²
Replace the known values in the equation.
Adjacent = -√29² - (-20)²
Adjacent = -21
Find the value of tangent.
Tanθ = Perpendicular/base
Tanθ = -20/(-21)
Hence, the value of Tanθ is 20/21.
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how am i supposed to prove that theyre collinear
Answer:
They are collinear if they are on the same line
14. The local credit union is offering a special student checking account. The monthly cost of the account is $15. The first 10 checks are free, and each additional check costs $0.75. You search
the Internet and find a bank that offers a student checking account with no monthly charge. The first 10 checks are free, but each additional check costs $2.50.
a. Assume that you will be writing more than 10 checks a month. Let n represent the number of checks written in a month. Write a function rule for the cost c of each account in terms of n.
b. Write an inequality to determine what number of checks in the bank account would be more expensive than the credit union account.
c. Solve the inequality in part b.
Answer: a. c(n) = 15 + 0.75(n - 10)
b. 15 + 0.75(n - 10) = 2.50(n - 10)=
Simplifying and solving for n, we get:
n = 50
c. n > 50
Step-by-step explanation:
a. The cost c of the credit union account in terms of the number of checks written n can be expressed as:
c(n) = 15 + 0.75(n - 10)
The first term, 15, represents the monthly cost of the account, and the second term represents the additional cost per check beyond the first 10 free checks.
The cost c of the bank account in terms of the number of checks written n can be expressed as:
c(n) = 2.50(n - 10)
The first term, 0, represents the monthly cost of the account, and the second term represents the additional cost per check beyond the first 10 free checks.
b. We want to find the number of checks for which the bank account is more expensive than the credit union account. Let x be the number of checks that makes the cost of the two accounts equal. Then we have:
15 + 0.75(n - 10) = 2.50(n - 10)
Simplifying and solving for n, we get:
n = 50
So if the number of checks written in a month is greater than 50, the bank account will be more expensive than the credit union account.
c. The solution to the inequality is:
n > 50
This means that the number of checks written in a month must be greater than 50 for the bank account to be more expensive than the credit union account.
Naya has a pitcher that contains 3 cups of salted lassi, a yogurt drink with sait and sites. She pours 6 fluid ounces of lassi into each glass. If she uses all of the lassi, how many glasses does Naya use?
A. 2
B. 4
C. 16
D. 18
After 6 fluid ounces , Naya uses 4 glasses as a result.
Define ounces?A unit of weight is an ounce. There are various kinds of ounces, including avoirdupois, troy, and fluid ounces. One sixteenth of a pound is equivalent to one avoirdupois ounce . A troy ounce, often known as an apothecaries' measure, is equivalent to 480 grains or one-twelfth of a pound. A volume unit is a fluid ounce. 1/8 of a cup, 2 tablespoons, or 6 teaspoons make to one fluid ounce
In Naya's pitcher, there are three glasses of salted lassi.
She fills each glass with six fluid ounces of lassi.
By translating cups to fluid ounces and dividing the entire amount of lassi by the amount put into each glass, we can determine how many glasses Naya uses if she consumes all of the lassi.
8 fluid ounces make constitute a cup.
Consequently, 3 cups equal 24 fluid ounces (3 x 8).
24 divided by 6 results in:
4 glasses are equal to 24/6.
Naya uses four glasses as a result.
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Suppose that the function h is defined as follows.
if
-2
-1
h(x)= 0
1
2
Graph the function h.
-3.5
if-2.5
if-1.5
if -0.5
if 0.5 ≤x≤1.5
+
X
Ś
The required graph of the function given; h (x) has been attached.
Define a graph?In mathematics, graph theory is the study of graphs, which are mathematical structures used to represent pairwise interactions between objects. In this definition, a network is made up of nodes or points called vertices that are connected by edges, also called links or lines. In contrast to directed graphs, which have edges that connect two vertices asymmetrically, undirected graphs have edges that connect two vertices symmetrically. Graphs are one of the primary areas of study in discrete mathematics.
Here as per the question the graph of the function, h (x) has been attached.
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The five number summary of a dataset was found to be:
45, 52, 56, 63, 66
An observation is considered an outlier if it is below:
An observation is considered an outlier if it is above:
An observation is considered an outlier if it is below 35.5 or above 79.5 in this dataset.
Identifying the outliers in the summaryTo determine the outliers in a dataset using the five-number summary, we need to calculate the interquartile range (IQR), which is the difference between the third quartile (Q3) and the first quartile (Q1).
IQR = Q3 - Q1
Where
Q1 = 52
Q3 = 63
So, we have
IQR = 63 - 52
IQR = 11
An observation is considered an outlier if it is:
Below Q1 - 1.5 × IQR
Above Q3 + 1.5 × IQR
Substituting the values, we get:
Below 52 - 1.5 × 11 = 35.5
Above 63 + 1.5 × 11 = 79.5
Therefore, an observation is considered an outlier if it is below 35.5 or above 79.5 in this dataset.
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solve the equation
a) y''-2y'-3y= e^4x
b) y''+y'-2y=3x*e^x
c) y"-9y'+20y=(x^2)*(e^4x)
Answer:
a) To solve the differential equation y''-2y'-3y= e^4x, we first find the characteristic equation:
r^2 - 2r - 3 = 0
Factoring, we get:
(r - 3)(r + 1) = 0
So the roots are r = 3 and r = -1.
The general solution to the homogeneous equation y'' - 2y' - 3y = 0 is:
y_h = c1e^3x + c2e^(-x)
To find the particular solution, we use the method of undetermined coefficients. Since e^4x is a solution to the homogeneous equation, we try a particular solution of the form:
y_p = Ae^4x
Taking the first and second derivatives of y_p, we get:
y_p' = 4Ae^4x
y_p'' = 16Ae^4x
Substituting these into the original differential equation, we get:
16Ae^4x - 8Ae^4x - 3Ae^4x = e^4x
Simplifying, we get:
5Ae^4x = e^4x
So:
A = 1/5
Therefore, the particular solution is:
y_p = (1/5)*e^4x
The general solution to the non-homogeneous equation is:
y = y_h + y_p
y = c1e^3x + c2e^(-x) + (1/5)*e^4x
b) To solve the differential equation y'' + y' - 2y = 3xe^x, we first find the characteristic equation:
r^2 + r - 2 = 0
Factoring, we get:
(r + 2)(r - 1) = 0
So the roots are r = -2 and r = 1.
The general solution to the homogeneous equation y'' + y' - 2y = 0 is:
y_h = c1e^(-2x) + c2e^x
To find the particular solution, we use the method of undetermined coefficients. Since 3xe^x is a solution to the homogeneous equation, we try a particular solution of the form:
y_p = (Ax + B)e^x
Taking the first and second derivatives of y_p, we get:
y_p' = Ae^x + (Ax + B)e^x
y_p'' = 2Ae^x + (Ax + B)e^x
Substituting these into the original differential equation, we get:
2Ae^x + (Ax + B)e^x + Ae^x + (Ax + B)e^x - 2(Ax + B)e^x = 3xe^x
Simplifying, we get:
3Ae^x = 3xe^x
So:
A = 1
Therefore, the particular solution is:
y_p = (x + B)e^x
Taking the derivative of y_p, we get:
y_p' = (x + 2 + B)e^x
Substituting back into the original differential equation, we get:
(x + 2 + B)e^x + (x + B)e^x - 2(x + B)e^x = 3xe^x
Simplifying, we get:
-xe^x - Be^x = 0
So:
B = -x
Therefore, the particular solution is:
y_p = xe^x
The general solution to the non-homogeneous equation is:
y = y_h + y_p
y = c1e^(-2x) + c2e^x + xe^x
c) To solve the differential equation y" - 9y' + 20y = x^2*e^4x, we first find the characteristic equation:
r^2 - 9r + 20 = 0
Factoring, we get:
(r - 5)(r - 4) = 0
So the roots are r = 5 and r = 4.
The general solution to the homogeneous equation y" - 9y' + 20y = 0 is:
y_h = c1e^4x + c2e^5x
To find the particular solution, we use the method of undetermined coefficients. Since x^2*e^4x is a solution to the homogeneous equation, we try a particular solution of the form:
y_p = (Ax^2 + Bx + C)e^4x
Taking the first and second derivatives of y_p, we get:
y_p' = (2Ax + B)e^4x + 4Axe^4x
y_p'' = 2Ae^4x +
I need helppp!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
The distance formula is
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
x1 is a,
x2 is 0,
y1 is 0 and
y2 is b. Fitting those into the formula where they belong:
[tex]d=\sqrt{(0-a)^2+(b-0)^2}[/tex] and
[tex]d=\sqrt{(-a)^2+(b)^2}[/tex]
Since a negative squared is a positive, then
[tex]d=\sqrt{a^2+b^2}[/tex]
which is the second choice down.
HELP RAAHHHH
1. During halftime of a football game, a sing shot launches T-shirts at the crowd
A T-shirt is launched from a height of 4 feet with an intal upward velocity of 72 feet per second
The T-shirt is caught 42 feet above the field
How long will take the T-shirt to reach its maximum height? What is the maximum height? What is the range of the function that models the height of the T-shirt over time?
2. During halftime of a football game, a sing shot launches T-shirts at the crowd
A T-shirt is launched from a height of 3 feet with an intal upward velocity of 80 feet per second
The T-shirt is caught 36 feet above the field
How long will take the T-shirt to reach its maximum height? What is the maximum height? What is the range of the function that models the height of the T-shirt over time?
Answer:
1. Using the kinematic equation h(t) = -16t^2 + v0t + h0, where h0 is the initial height, v0 is the initial velocity, and t is time, we have:
h(t) = -16t^2 + 72t + 4
To find the maximum height, we need to find the vertex of the parabolic function h(t). The t-coordinate of the vertex is given by t = -b/2a, where a = -16 and b = 72:
t = -b/2a = -72/(2(-16)) = 2.25 seconds
To find the maximum height, we substitute t = 2.25 seconds into the equation for h(t):
h(2.25) = -16(2.25)^2 + 72(2.25) + 4 = 82 feet
The range of the function h(t) is [4, 82], since the T-shirt starts at a height of 4 feet and reaches a maximum height of 82 feet before falling back to the ground.
2. Using the same kinematic equation as before, we have:
h(t) = -16t^2 + 80t + 3
To find the maximum height, we again need to find the vertex of the parabolic function h(t). The t-coordinate of the vertex is given by t = -b/2a, where a = -16 and b = 80:
t = -b/2a = -80/(2(-16)) = 2.5 seconds
To find the maximum height, we substitute t = 2.5 seconds into the equation for h(t):
h(2.5) = -16(2.5)^2 + 80(2.5) + 3 = 80 feet
The range of the function h(t) is [3, 80], since the T-shirt starts at a height of 3 feet and reaches a maximum height of 80 feet before falling back to the ground.
Step-by-step explanation:
7. A group of students wants to demonstrate that sunlight provides the energy for plants to grow. What is
the control group for the experiment?
A. Some plants will receive less water
B. Some plants will receive fertilizer
C. Some plants will receive no sunlight
D. Some plants will receive no water
I
The control group for the experiment would be option C: some plants will receive no sunlight.
What is control group for experiment ?The control group in an experiment is the group that does not receive the treatment or intervention being tested, so that the effects of the treatment can be compared to a baseline or reference point. In this experiment, the treatment being tested is the provision of sunlight as an energy source for plant growth.
Therefore, the control group should not receive sunlight, so that the effects of sunlight can be compared to the baseline of plant growth without sunlight.
Therefore, the control group for the experiment would be option C: some plants will receive no sunlight.
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. Bert has a well-shuffled standard deck of 52 cards, from which he draws one card; Ernie has a 12-sided die, which he rolls at the same time Bert draws a card. Compute the probability that:
a. Bert gets a Jack and Ernie rolls a five.
b. Bert gets a heart and Ernie rolls a number less than six.
c. Bert gets a face card (Jack, Queen or King) and Ernie rolls an even number.
d. Bert gets a red card and Ernie rolls a fifteen.
e. Bert gets a card that is not a Jack and Ernie rolls a number that is not twelve.
Therefore , the solution of the given problem of probability comes out to be a)1/78 ,b)65/624 ,c)1/4 ,d)0 and e)12/13.
What is probability, exactly?The basic goal of any considerations technique is to assess the probability that a statement is accurate or that a specific incident will occur. Chance can be represented by any number range between 0 and 1, where 0 normally indicates a percentage but 1 typically indicates the level of certainty. An illustration of probability displays how probable it is that a specific event will take place.
Here,
a.
P(Bert gets a Jack and Ernie rolls a five) = P(Bert gets a Jack) * P(Ernie rolls a five)
= (4/52) * (1/12)
= 1/78
b.
P(Bert gets a heart and Ernie rolls a number less than six) = P(Bert gets a heart) * P(Ernie rolls a number less than six)
= (13/52) * (5/12)
= 65/624
c.
P(Bert gets a face card and Ernie rolls an even number) = P(Bert gets a face card) * P(Ernie rolls an even number)
= (12/52) * (6/12)
= 1/4
d.
P(Bert gets a red card and Ernie rolls a fifteen) = 0
e.
Ernie rolls a number that is not twelve, and Bert draws a card that is not a Jack:
A regular 52-card deck contains 48 cards that are not Jacks,
so the likelihood that Bert will draw one of those cards is 48/52, or 12/13.
On a 12-sided dice with 11 possible outcomes,
Ernie rolls a non-12th-number (1, 2, 3, etc.).
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Given the expression 3x+2 evaluate the expression for the given values of x when x=(-2)
Answer:
...............................
LOOK AT THE PHOTO PLS
The next entry on the long division would be 0.054, and 0.0054
How to perform long divisionLong division is a method of dividing two numbers using a step-by-step process. Here's how to perform long division:
Step 1: Write the dividend (the number being divided) and the divisor (the number you're dividing by) in the long division format, with the dividend inside the division symbol and the divisor outside.
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Complete the truth table for (A ⋁ B) ⋀ ~(A ⋀ B).
The truth table for (A ⋁ B) ⋀ ~(A ⋀ B) is:
A B (A ⋁ B) ⋀ ~(A ⋀ B)
0 0 0
0 1 0
1 0 0
1 1 0
The truth table is what?A truth table is a table that displays all possible combinations of truth values (true or false) for one or more propositions or logical expressions, as well as the truth value of the resulting compound proposition or expression that is created by combining them using logical operators like AND, OR, NOT, IMPLIES, etc.
The columns of a truth table reflect the propositions or expressions themselves as well as the compound expressions created by applying logical operators to them. The rows of a truth table correspond to the various possible combinations of truth values for the propositions or expressions.
To complete the truth table for (A ⋁ B) ⋀ ~(A ⋀ B), we need to consider all possible combinations of truth values for A and B.
A B A ⋁ B A ⋀ B ~(A ⋀ B) (A ⋁ B) ⋀ ~(A ⋀ B)
0 0 0 0 1 0
0 1 1 0 1 0
1 0 1 0 1 0
1 1 1 1 0 0
So, the only case where the expression is true is when both A and B are true, and for all other cases it is false.
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Is each number rounded correctly to the nearest hundred thousand?
yes is answer for all option .we can check it by rules of rounding off numbers .
what is rounding ?
Rounding is the process of approximating a number to a nearby value that is easier to work with or more appropriate for a given context. When rounding, we take a number with many decimal places or significant figures and adjust it to a simpler or more convenient value with fewer decimal places or significant figures.
In the given question,
Yes, each number is rounded correctly to the nearest hundred thousand based on the rules of rounding.
To round to the nearest hundred thousand, we look at the digit in the hundred thousand place and the digit to its right (i.e., in the ten thousand place).
If the digit in the ten thousand place is 5 or greater, we round up the digit in the hundred thousand place by adding 1.
If the digit in the ten thousand place is less than 5, we leave the digit in the hundred thousand place as it is.
Using these rules, we can see that:
350000 rounded to the nearest hundred thousand is 400000 because the digit in the ten thousand place is 5, so we round up the digit in the hundred thousand place.
555555 rounded to the nearest hundred thousand is 560000 because the digit in the ten thousand place is 5, so we round up the digit in the hundred thousand place.
137998 rounded to the nearest hundred thousand is 200000 because the digit in the ten thousand place is 7, so we round up the digit in the hundred thousand place.
792314 rounded to the nearest hundred thousand is 800000 because the digit in the ten thousand place is 3, so we leave the digit in the hundred thousand place as it is.
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The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for 35 minutes of calls is $16.83 and the monthly cost for 52 minutes is $18.87. What is the monthly cost for 39 minutes of calls?
Answer: We can use the two given points to find the equation of the line and then plug in 39 for the calling time to find the corresponding monthly cost.
Let x be the calling time (in minutes) and y be the monthly cost (in dollars). Then we have the following two points:
(x1, y1) = (35, 16.83)
(x2, y2) = (52, 18.87)
The slope of the line passing through these two points is:
m = (y2 - y1) / (x2 - x1) = (18.87 - 16.83) / (52 - 35) = 0.27
Using point-slope form with the first point, we get:
y - y1 = m(x - x1)
y - 16.83 = 0.27(x - 35)
Simplifying, we get:
y = 0.27x + 7.74
Therefore, the monthly cost for 39 minutes of calls is:
y = 0.27(39) + 7.74 = $18.21
Step-by-step explanation:
Write an equation for the polynomial graphed below
The polynomial in factor form is y(x) = - (1 / 6) · (x + 3) · (x + 1) · (x - 2) · (x - 3).
How to derive the equation of the polynomial
In this problem we find a representation of polynomial set on Cartesian plane, whose expression is described by the following formula in factor form:
y(x) = a · (x - r₁) · (x - r₂) · (x - r₃) · (x - r₄)
Where:
x - Independent variable.r₁, r₂, r₃, r₄ - Roots of the polynomial.a - Lead coefficient.y(x) - Dependent variable.Then, by direct inspection we get the following information:
y(0) = - 3, r₁ = - 3, r₂ = - 1, r₃ = 2, r₄ = 3
First, determine the lead coefficient:
- 3 = a · (0 + 3) · (0 + 1) · (0 - 2) · (0 - 3)
- 3 = a · 3 · 1 · (- 2) · (- 3)
- 3 = 18 · a
a = - 1 / 6
Second, write the complete expression:
y(x) = - (1 / 6) · (x + 3) · (x + 1) · (x - 2) · (x - 3)
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A partial table of nutrients and Daily Values (DVS)
based on a 2000-calorie diet is provided. The Sodium row and the Vitamin D row are completed, and each % of the DV is calculated.
Compare each amount with the amount on the given nutrition label. Now use the amount of
saturated fat on the nutrition label to calculate its
% of DV, X. Use the saturated fat amount on the nutrition label
to calculate the %DV for saturated fat.
Note that the %DV for saturated fat in this 2 tbsp serving size is approximately 18%.
What is the explanation for the above response?To calculate the %DV for saturated fat, we need to first calculate how many grams of saturated fat are in the 2 tablespoon (tbsp) serving size.
From the label, we see that the serving size contains 3.5g of saturated fat.
To calculate the %DV for saturated fat, we use the equation:
%DV = (amount of nutrient per serving / DV) x 100%
Plugging in the values for saturated fat, we get:
%DV = (3.5g / 19g) x 100%
%DV = 0.1842 x 100%
%DV ≈ 18%
Therefore, the %DV for saturated fat in this 2 tbsp serving size is approximately 18%.
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PLEASE HELP
Find the Area
2cm
___cm^2
Answer:
3.14 cm^2
Step-by-step explanation:
1. Find radius:
If diameter is 2, divide it by 2 to get radius = 1
2. Find formula:
A=πr^2
3. Plug in:
A = π(1)^2
4. Solve (multiply):
A = π(1)^2:
3.14159265359
Or
3.14 cm^2
Answer:
3.14 cm^2
Step-by-step explanation:
A=[tex]\pi[/tex]r^2
r=2
2/2=1
A=[tex]\pi[/tex](1)^2
=[tex]\pi[/tex]1
≈3.14x1
≈3.14cm^2
La Suma delos cuadrados de dos números naturales consecutivos es 181 halla dichos numeros
The two consecutive natural numbers whose sum of squares is 181 are 9 and 10
Let's assume that the two consecutive natural numbers are x and x+1. Then, we can write an equation based on the given information:
x² + (x+1)² = 181
Expanding the equation:
x² + x² + 2x + 1 = 181
Combining like terms:
2x² + 2x - 180 = 0
Dividing both sides by 2:
x² + x - 90 = 0
Now, we can use the quadratic formula to solve for x:
x = (-b ± √(b² - 4ac)) / 2a
where a = 1, b = 1, and c = -90
x = (-1 ± √(1 + 360)) / 2
x = (-1 ± √(361)) / 2
x = (-1 ± 19) / 2
We discard the negative value, as it does not correspond to a natural number:
x = 9
Therefore, the two consecutive natural numbers are 9 and 10, and their sum of squares is 81 + 100 = 181.
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0\left\{-10\le x\le10\right\}
Describe the transformations (vertical translation, horizontal translation, and dilation/reflection) from the parent function that happened to these formulas
The formula g(x) = 2 * 0{-10≤x+3≤10} represents a function that has been horizontally shifted left by 3 units, reflected about the y-axis, and vertically scaled by a factor of 2.
What is Function?A function is a mathematical rule that assigns each input from a set (domain) a unique output from another set (range), typically written as y = f(x).
The notation "0{-10≤x≤10}" typically represents the domain of a function or an inequality. It means that the function is defined only for the values of x that are between -10 and 10 (including -10 and 10).
Assuming that the function in question is a constant function equal to zero, the parent function is f(x) = 0.
To describe the transformations that happened to this function, we need more information about the specific formula. For example, if the formula is:
g(x) = 0{-10≤x≤10}
Then there are no transformations from the parent function. The function is simply a constant function that is equal to zero over the interval [-10, 10].
However, if the formula is something like:
g(x) = 2 * 0{-10≤x+3≤10}
Then we can describe the transformations as follows:
Horizontal translation: The function has been shifted horizontally to the left by 3 units. This means that the point (3, 0) on the parent function is now located at the origin (0, 0) on the transformed function.
Dilation/reflection: The function has been reflected about the y-axis and vertically scaled by a factor of 2. This means that the point (-1, 0) on the parent function is now located at (-4, 0) on the transformed function, and the point (1, 0) on the parent function is now located at (2, 0) on the transformed function.
Vertical translation: There is no vertical translation in this case, since the constant function is already centered at y = 0.
To summarize, the formula g(x) = 2 * 0{-10≤x+3≤10} represents a function that has been horizontally shifted left by 3 units, reflected about the y-axis, and vertically scaled by a factor of 2.
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The formula g(x) = 2 * 0{-10≤x+3≤10} represents a function that has been horizontally shifted left by 3 units, reflected about the y-axis, and vertically scaled by a factor of 2.
What is Function?A function is a mathematical rule that assigns each input from a set (domain) a unique output from another set (range), typically written as y = f(x).
The notation "0{-10≤x≤10}" typically represents the domain of a function or an inequality. It means that the function is defined only for the values of x that are between -10 and 10 (including -10 and 10).
Assuming that the function in question is a constant function equal to zero, the parent function is f(x) = 0.
To describe the transformations that happened to this function, we need more information about the specific formula. For example, if the formula is:
g(x) = 0{-10≤x≤10}
Then there are no transformations from the parent function. The function is simply a constant function that is equal to zero over the interval [-10, 10].
However, if the formula is something like:
g(x) = 2 * 0{-10≤x+3≤10}
Then we can describe the transformations as follows:
Horizontal translation: The function has been shifted horizontally to the left by 3 units. This means that the point (3, 0) on the parent function is now located at the origin (0, 0) on the transformed function.
Dilation/reflection: The function has been reflected about the y-axis and vertically scaled by a factor of 2. This means that the point (-1, 0) on the parent function is now located at (-4, 0) on the transformed function, and the point (1, 0) on the parent function is now located at (2, 0) on the transformed function.
Vertical translation: There is no vertical translation in this case, since the constant function is already centered at y = 0.
To summarize, the formula g(x) = 2 * 0{-10≤x+3≤10} represents a function that has been horizontally shifted left by 3 units, reflected about the y-axis, and vertically scaled by a factor of 2.
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6. Two out of every five Canadians read at least 10 books a year. What percent of Canadians read at least 10 books a year?
40% of Canadians read at least 10 books a year.
Define percentageA percentage is a way of expressing a portion or a part of a whole as a fraction of 100. It is represented by the symbol "%". Percentages are often used to compare different quantities or to describe how much of a total is made up by a specific amount or group. For example, if you score 80 out of 100 on a test, your score can be expressed as 80%, meaning you got 80 out of 100 possible points.
If two out of every five Canadians read at least 10 books a year, then we can write this as a fraction:
2/5
We can multiply this fraction by 100 to turn it to a percentage:
(2/5) x 100 = 40%
Therefore, 40% of Canadians read at least 10 books a year.
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The count in a bateria culture was initially 300, and after 35 minutes the population had increased to 1600. Find the doubling period. Find the population after 70 minutes. When will the population reach 10000?
Which graph represents the hyperbola x2/52-y2/42 = 1?
For the given equation we have horizontal length of 5 and vertical width of 4 units. The graph that depicts this hyperbola is: Option B.
What is a hyperbola?A hyperbola is a particular kind of conic section in mathematics, which is a curve created by the intersection of a cone and a plane. The collection of all points in a plane that have a constant difference between them and two fixed points, known as the foci, is referred to as a hyperbola. The distance between the foci is referred to as this consistent difference and is represented by the symbol 2a.
Two separate branches that are mirror reflections of one another make up a hyperbola. The vertices are the two locations where the two branches of a hyperbola are joined.
For the given equation of the parabola, the value of a and b = 5 and 4.
Thus, we have horizontal length of 5 and vertical width of 4 units
The graph that depicts this hyperbola is: Option B.
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The complete question is:
What are answers to these questions?
1. f is concave up on the intervals = ?
2. f is concave down on the intervals = ?
3. The inflection points occur at x = ?
f(x) is concave up on the interval (-∞, √(6/7)) U (√(6/7), ∞),f(x) is concave down on the interval (-√(6/7), √(6/7)) ,The inflection points occur at x = -√(6/7) and x = √(6/7).
What is inflection Point?An inflection point is a point on a curve where the concavity changes, from concave up to concave down or vice versa, indicating a change in the curvature of the curve.
According to the given information:
To determine the intervals where f(x) is concave up or down, we need to find the second derivative of f(x) and determine its sign.
First, we find the first derivative of f(x):
f'(x) = (14x)/(7x²+6)²
Then, we find the second derivative of f(x):
f''(x) = [28(7x²+6)²- 28x(7x²+6)(4x)] / (7x²+6)^4
Simplifying the expression, we get:
f''(x) = 28(42x² - 72) / (7x^2+6)³
To determine where f(x) is concave up or down, we need to find the intervals where f''(x) is positive or negative, respectively.
Setting f''(x) = 0, we get:
42x² - 72 = 0
Solving for x, we get:
x = ±√(6/7)
These are the possible inflection points of f(x). To determine if they are inflection points, we need to check the sign of f''(x) on both sides of each point.
We can use a sign chart to determine the sign of f''(x) on each interval.
Intervals where f''(x) > 0 are where f(x) is concave up, and intervals where f''(x) < 0 are where f(x) is concave down.
Here is the sign chart for f''(x):
x | -∞ | -√(6/7) | √(6/7) | ∞
f''(x)| - | + | - | +
From the sign chart, we can see that:
a) f(x) is concave up on the interval (-∞, √(6/7)) U (√(6/7), ∞).
b) f(x) is concave down on the interval (-sqrt(6/7), √(6/7)).
c) The inflection points occur at x = -√(6/7) and x = √(6/7).
Therefore, the open intervals where f(x) is concave up are (-∞, -√(6/7)) and (√(6/7), ∞), and the open interval where f(x) is concave down is (-√(6/7), √(6/7)). The inflection points occur at x = -√(6/7) and x = √(6/7).
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The f(x) is concave up on the interval (-∞, √(6/7)) U (√(6/7), ∞),f(x) is concave down on the interval (-√(6/7), √(6/7)) ,The inflection points occur at x = -√(6/7) and x = √(6/7).
What is inflection Point?
An inflection point is a point on a curve where the concavity changes, from concave up to concave down or vice versa, indicating a change in the curvature of the curve.
According to the given information:
To determine the intervals where f(x) is concave up or down, we need to find the second derivative of f(x) and determine its sign.
First, we find the first derivative of f(x):
f'(x) = (14x)/(7x²+6)²
Then, we find the second derivative of f(x):
f''(x) = [28(7x²+6)²- 28x(7x²+6)(4x)] / (7x²+6)^4
Simplifying the expression, we get:
f''(x) = 28(4x² - 72) / (7x^2+6)³
To determine where f(x) is concave up or down, we need to find the intervals where f''(x) is positive or negative, respectively.
Setting f''(x) = 0, we get:
42x² - 72 = 0
Solving for x, we get:
x = ±√(6/7)
These are the possible inflection points of f(x). To determine if they are inflection points, we need to check the sign of f''(x) on both sides of each point.
We can use a sign chart to determine the sign of f''(x) on each interval.
Intervals where f''(x) > 0 are where f(x) is concave up, and intervals where f''(x) < 0 are where f(x) is concave down.
Here is the sign chart for f''(x):
x | -∞ | -√(6/7) | √(6/7) | ∞
f''(x)| - | + | - | +
From the sign chart, we can see that:
a) f(x) is concave up on the interval (-∞, √(6/7)) U (√(6/7), ∞).
b) f(x) is concave down on the interval (-sqrt(6/7), √(6/7)).
c) The inflection points occur at x = -√(6/7) and x = √(6/7).
Therefore, the open intervals where f(x) is concave up are (-∞, -√(6/7)) and (√(6/7), ∞), and the open interval where f(x) is concave down is (-√(6/7), √(6/7)). The inflection points occur at x = -√(6/7) and x = √(6/7).
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The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 0 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 10. There are two dots above 1 and 4. There are three dots above 2 and 5. There are 4 dots above 3.
Which of the following is the best measure of variability for the data, and what is its value?
The IQR is the best measure of variability, and it equals 3.
The IQR is the best measure of variability, and it equals 9.
The range is the best measure of variability, and it equals 3.
The range is the best measure of variability, and it equals 9.
The range is the best measure of variability for this data, and its value is 4.
Which of the following is the best measure of variability for the data, and what is its value?The line plot displays the number of roses purchased per day at a grocery store, with the data values ranging from 0 to 4 (since there are no dots above 4).
The best measure of variability for this data is the range, which is the difference between the maximum and minimum values in the data set. In this case, the minimum value is 0 and the maximum value is 4, so the range is:
Range = Maximum value - Minimum value = 4 - 0 = 4
Therefore, the range is the best measure of variability for this data, and its value is 4.
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