The stronger flavor of grape is in Tia's glass.
Given,
Martin's glass of grape drink has weaker tasting grape flavor
Tia's glass of grape drink has stronger tasting grape flavor
3 ounces of water is added to Martin's glass
One table spoon of grape mix is added to Tia's glass
We have to find the glass which contain the stronger grape flavor
Already in Martin's glass flavor is low. When we add water again to his glass, the flavor will again dissolves with water.
In Tia's glass grape flavor is stronger. By adding one tablespoon of grape mix the flavor will become more stronger.
That is,
The stronger flavor of grape is in Tia's glass.
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if the flow rate in an artery has been reduced to 8.5% of its normal value by a blood clot and the average pressure difference has increased by 20.5%, what percent of the original is the radius of the reduced artery?
Percent of the original is the radius of the reduced artery is 0.070 times the original radius.
Given that,
A blood clot has lowered the flow rate in an artery to 8.5% of its usual value, and the average pressure difference has increased by 20.5%.
p1 = 8.5 % ,
p2 = 20.5 %
The equation is using here is From Poiseuille's equation
Q = \Delta p \pi r4 / 8 \eta L
now
Q1 = \Delta p1\pi r14 / 8 \eta L
and
Q2 = \Delta p2\pi r24 / 8 \eta L
Q1 = \Delta p1\pi r14 / 8 \eta L / Q2 = \Delta p2\pi r24 / 8 \eta L
Q1 / Q2 = \Delta p1 ro4 / \Delta p2 r24
r24 = ( 0.085 Q1 / Q1 ) ( \Delta p1 / \Delta p1 + 0.20 \Delta p1 ) ro4
r24 = 0.085 X ( 1 / ( 1 + 0.20 ) ro4
r2 = 0.070 ro
As a result, the shortened artery's radius is 0.070 times its original radius, or percent of the original.
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The quantities xxx and yyy are proportional.
xxx yyy
222 222222
777 777777
999 999999
The value of y when x is 9 for the proportional relationship between is 31.5.
What is constant of proportionality?The constant of proportionality is used to show the proportional relationship between the numbers given.
In this case, when x is 2, y is 7. This will be illustrated thus:
y = kx
7 = 2k
Divide
k = 7/2
k = 3.5
Therefore, when x is 9, the value of y will be:
y = kx
y = 3.5 × 9
y = 31.5
Therefore, y is 31.5.
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A rectangular garden has a length that is 3 feet longer than its width. Let represent the width of the garden, in feet. The entire garden is surrounded by a 2-foot wide cement walkway. What does the algebraic expression ( w + 4) (w + 7) represent in this context?
HIghschool Alegbra 1
Expression ( w+4)(w + 7) represent the total area of the garden and walkway.
What is Area of Rectangle?The area of Rectangle is length times of width.
Given that the width of the garden, in feet be w.
The length is 3 feet longer than its width, hence: w + 3
The entire garden is surrounded by a 2-foot-wide cement walkway. Therefore:
garden and walkaway length= (w + 3) + 2 + 2 = w + 7
garden and walkaway width = w + 2 + 2 = w + 4
The area of garden and walkaway
= length times of width
=Length × Width
= (w + 7)(w + 4)
Hence expression ( w+4)(w + 7) represent the total area of the garden and walkway
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Please help ASAP, I am in a super big hurry and have no idea what I’m doing! Please help!
Given the function:
h(x)=-6/7x+8/9
Find the following values.
a) h(1)
h(1)=
b) h(2)
h(2)=
c) h (-1/2)
h(-1/2)=
Answer: [tex]2/63, -52/63, 83/63[/tex]
Step-by-step explanation:
[tex]h(1)=-\frac{6}{7}(1)+\frac{8}{9}=\frac{2}{63}\\\\h(2)=-\frac{6}{7}(2)+\frac{8}{9}=-\frac{52}{63}\\\\h(-1/2)=-\frac{6}{7}(-1/2)+\frac{8}{9}=\frac{83}{63}[/tex]
angles in a triangle
Answer:
i = 74
j = 47
Step-by-step explanation:
to find "i" add 16 & 90 which is 106. subtract 106 from 180 to get 74.
to find "j" add 43 & 90 which is 133. subtract 133 from 180 to get 47
If triangle ABD = triangle CBD,
angle ABD = 99° and angle CBD = 9x - 9
Answer:
x = 12
Step-by-step explanation:
since the triangles are congruent then corresponding angles are congruent, so
∠ CBD = ∠ ABD , that is
9x - 9 = 99 ( add 9 to both sides )
9x = 108 ( divide both sides by 9 )
x = 12
-5x - 7<3 and -5x-7> -42
Answer:
x<-2, x>-7
Step-by-step explanation:
1st one
add 7 to 3 =10
-5 divide by 10 = -2
2nd one
add 7 to -42 = -35
-35 divided by 5 = -7
Before a piece of steel can be sold for its maximum price, it must be 35 feet long with an absolute error of 1 foot. Find the range of acceptable heights for steels that are to be sold at full price by writing an absolute value inequality to represent this situation then solving it.
Let's call x to the height. The inequality that represents an acceptable range is:
|x - 35| ≤ 1
Solving it, we get:
x - 35 ≤ 1 or x - 35 ≥ -1
x ≤ 1 + 35 x ≥ -1 + 35
x ≤ 36 x ≥ 34
which is equivalent to 34 ft ≤ x ≤ 36 ft
Question 2(Multiple Choice Worth 5 points)
(03.05 LC)
Which of the following is the equation of the ellipse with a vertical major axis, center at (1, -3), a = 7, and b = 5?
○ (x-1)²+(y+32²-1
25
49
0 (x+12+(y-32²-1
25
49
O(y-322²(x+12²
49
25
O(y+32 (x-12
49
25
+
1
-1
The equation of the the ellipse with a vertical major axis, center at (1, -3), a = 7, and b = 5 is [tex]\frac{(x-1)^2}{49}+\frac{(y+3)^2}{25}[/tex]
Equation of the ellipses:
The Equation of the ellipse with center at (h, k)
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}[/tex]
where,
a = length of semi-major axis
b = length of semi-minor axis
Given,
Here we have the value of center as (1, -3) and the values of a = 7 and b = 5.
Here we need to find the equation of the ellipse.
According to the formula we we have the following values are given,
We know the value of center of ellipses is written as,
(h, k) = (1, -3)
And the values of
a = 7 and b = 5
Therefore, when we apply the values on the formula then we get,
[tex]\frac{(x-1)^2}{7^2}+\frac{(y-(-3))^2}{5^2}[/tex]
When we simplify the term then we get,
[tex]\frac{(x-1)^2}{49}+\frac{(y+3)^2}{25}[/tex]
Therefore, the equation of the ellipse is [tex]\frac{(x-1)^2}{49}+\frac{(y+3)^2}{25}[/tex].
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Multiply. [−3⋅914]⋅[(−0.1)⋅(−28)]
The solution to the given expression is 7,677.6.
This is a question of multiplication.
Multiplication
In mathematics, multiplication is used as a method of finding the product of two or more numbers. It is one of the arithmetic operations, like addition, subtraction and division that we use in everyday life. The major application we can see in multiplication tables.
In arithmetic, the multiplication of two numbers is represented by the repeated addition of one number with respect to another.
Given expression:-
[−3*914]*[(−0.1)*(−28)]
We have to find the solution of the given expression.
We have,
-3*914 = -2742
(-0.1)*(-28) = 2.8
Hence, we can write,
[−3*914]*[(−0.1)*(−28)] = (-2742)*(2.8)
(-2742)*(2.8) = 7,677.6
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PLEASEE HELPPP!!! 30 POINTSSS
Create a system of equations and use algebra
To write a quadratic equation for each set of three points that lie on a parabola.
(5-6), (-2,8), (3,4)
(1,17), (-1,-9), (2,105)

The system of quadratic equations obtained on solving general equation of parabola are
a. 5=36a - 6b +c
-2=64a+8b+c
3=16a+4b+c
b. 1=289a+17b+c
-1=81a-9b+c
2=11025a+105b+c
the equation parabola
the general equation of Parabloa is written as-
y=a[tex]x^{2}[/tex]+bx+c
if the parabola passes through the point. then this point must satisfy the equation of the parabola. so, by putting the value of points we get a set equations-
5=a[tex]6^{2}[/tex]+b(-6)+c
5=36a - 6b +c
and for other two points we get equations
-2=64a+8b+c
and 3=16a+4b+c
and for other three points we get the equations
1=289a+17b+c
-1=81a-9b+c
2=11025a+105b+c
so on solving we get these three set of quadratic equations.
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When Felix started his paper route, he had 25 customers. Every second week he gained 2 new customers. Every third week he lost a customer. How many customers did he have in the seventh week? pls help
The number of customers he would have in the seventh week is 37.
How many customers would there by in the seventh week?The customers of Felix grow at a linear rate. A linear growth rate is when a value increases a constant rate. The customers would increase by 2 each week.
The linear equation that represents the number of customers in the seventh week:
Initial number of customers + [ rate of increase x (number of weeks - 1)]
25 + [2 x (7 - 1)]
25 + (2 x 6)
25 + 12 = 37
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Simplify the following expressions by combining like terms, if possible.
20 + xy - 3 + 4y^2 + 10 - 2y^2
(20 - 3 + 10) + (4y^2 - 2y^2) + xy
27 + 2y^2 + xy
PLSSSSSSSSS HELP DUE SOON!!!
Answer:
option 4
Step-by-step explanation:
let c represent the old amount , then twice the old amount is 2c.
1.5 less than twice the old amount is 2c - 1.5 , so
2c - 5 = 6
Determine whether the table of values represents a linear function. If so, write the function.
PLEASE HELP!!
What is 42/80 as a whole number ?
Answer:
it can't be in a whole number since it is a fraction and will go in decimals
PLEASE HELP GIVE BRAINLIST Exterior Angle
Theorem
On a triangle ABC
Why is A+B=D
Not D=A+B I wrote it backwards
Angle d is exterior angle . and an exterior angle is equal to addition of two interior angles .
What is the formula for the exterior angle theorem?
The exterior angle that results from the creation of a triangle side is equal to the product of the two opposite internal angles.Two inside opposite angles that are not adjacent add up to the external angle. A triangle's outer angle is the product of its two inner, diagonally opposing angles.In this figure,
Angle d is exterior angle . and an exterior angle is equal to addition of two interior angles .
So, According to Exterior Angle Theorem,
∠D = ∠A + ∠B
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Answer:
See explanation below.
Step-by-step explanation:
There is a theorem about the sum of the measures of the angles of a triangle.
In this case, with the interior angle measures called a, b, and c, the theorem states:
Theorem:
The sum of the measures of the interior angles of a triangle is 180°.
a + b + c = 180°
Now we will prove the theorem and answer why a + b = d.
Look at angles c and d. They form a linear pair. Angles that form a linear pair are supplementary angles. By the definition of supplementary angles, the sum of the measures of angles c and d is 180°.
We have
c + d = 180° Eq. 1
By the theorem above, we have
a + b + c = 180° Eq. 2
Let's subtract Eq. 1 from Eq. 2:
a + b + c = 180°
- c + d = 180°
------------------------------
a + b - d = 0
a + b - d = 0
Add d to both sides.
a + b = d
That is a proof of the Exterior Angle Theorem.
each year, nordstrom sets up a gift-wrapping station to assist its customers with holiday shopping. preliminary observations of one worker at the station produced the following sample time (in minutes per package): 3.5, 3.2, 4.1, 3.6, 3.9. based on this small sample, what number of observations would be necessary to determine the true cycle time with a 95% confidence level and an accuracy of ? [px]
Number of observations would be necessary to determine the true cycle time with a 95% confidence level and an accuracy are 16.
Sample timings as observed are 3.5, 3.1, 4.0, 3.5, and 3.9.
Sample-time average (X) = (3.5+3.1+4+3.5+3.9)/5
The average sample time (X) is 3.6.
Observed time (T) Mean (X) (X - T) (X - T)^2
3.5 3.6 0.1 0.01
3.1 3.6 0.5 0.25
4.0 3.6 -0.4 0.16
3.5 3.6 0.1 0.01
3.9 3.6 -0.3 0.09
Allow Standard deviation to be S.
2 in (X-T) - 1 n
[tex]S=\sqrt{\frac{0.52}{4}}[/tex]
S = 0.3605
Considering that (h) = 0.05,
Given that 95% of the time,
Z value at 95% confidence interval = 1.96
Let N be the number of observations.
2 N= Z.S hX
[tex]N=(\frac{1.96X0.3605}{0.05X3.6})[/tex]
N = 15.4
N = 16 (rounded off to next whole number) (rounded off to next whole number)
Consequently, 16 observations are required.
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Answer:
Step-by-step explanation:
Number of observations would be necessary to determine the true cycle time with a 95% confidence level and an accuracy of 16.
Sample-time average (X) = (3.5+3.1+4+3.5+3.9)/5
The average sample time (X) is 3.6. Observed time (T) Mean (X) (XT) (X-T)^2
3.5 3.6 0.1 0.01
3.1 3.6 0.5 0.25
4.0 3.6 -0.4 0.16
3.5 3.6 0.1 0.01
3.9 3.6-0.3 0.09
Allow Standard deviation to be S.
2 in (X-T) - 1n
S=√0.52/4
S=0.3605
Considering that (h) = 0.05,
Given that 95% of the time,
Z value at 95% confidence interval = 1.96 Let N be the number of observations.
2 N=Z.S hx
N=(1.96X0.3605)÷(0.05×3.6)
N = 15.4
N = 16 (rounded off to next whole number) (rounded off to next whole number) Consequently, 16 observations are required.
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PLEASE HELP ME ASAP!!!
Answer:
1256
Step-by-step explanation:
A=3.14*20^2
=400*3.14
=1256
If F(x) = 5x + 4, which of the following is the inverse of F(x)? A. F-1(x) = 4 – 5x B. F-1(x) = C. F-1(x) = D. F-1(x) = 5x – 4
Answer:
5x-4
Step-by-step explanation:
one student from the school will be selected at random. what is the probability that the student is in the age-group of 6 to 8 years given that the selected student responded joy?
Given that the chosen kid gave a joy response, the probability that the student belongs to the age range of 6 to 8 years is 28/89.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.So, the likelihood that a pupil is between the ages of 6 and 8 can be calculated using the techniques below:
Step 1: 89 pupils out of a possible 200 answered with joy, as shown in the table.Step 2 - It is also stated that there were a total of 28 students in the age range of 6 to 8 years who answered positively.Step 3 - Accordingly, the likelihood that the pupil belongs to the 6 to 8-year-old age range is:P = 28/89
Therefore, given that the chosen kid gave a joy response, the probability that the student belongs to the age range of 6 to 8 years is 28/89.
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The complete question is given below:
Students at a local elementary school were shown a painting and asked which emotion—joy, happiness, love, or anger—they felt by looking at the painting. The students were classified by their age. The following table summarizes the responses of the students by age group. One student from the school will be selected at random. What is the probability that the student is in the age group of 6 to 8 years given that the selected student responded with joy?
Hi Can someone help this is hard?
The domain is the set of all real numbers and the range is the set of all real numbers larger than -4, so the correct option is the third one.
How to get the domain and the range?For a function y = f(x) we define the domain as the set of the x-values (horizontal axis) and the range as the set of the y-values (vertical axis).
Here we have a parabola, in this case the domain is always the set of all real numbers, and the range is all the values above or equal to the vertex (in cases like this, where the parabola opens up).
We can see that the vertex is at y = -4
So the range is.
[-4, ∞]
So the correct option is 3.
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this sentence is false
Answer: what sentence ?
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
The sentence is true because if it is true, then the sentence is false.
You are asking if the sentence is false, and it is false, so the question you asked is true.
This is so confusing though...
A supermarket wants to find the percent of shoppers who use coupons. A manager interviews every shopper entering the greeting dard aisle. Identify the sampling method.convience samplesystematic sampleself-selected samplerandom sample
To determine the percet of shoppers that use coupons, the manager interviews every shopper thay enters the greeting aisle and records wether they use or not coupons.
Since he does not take any measures, nor divide the shopers into groups or, for example, interviews one every k number of shoppers, the sampling method he used is the most simple and common one, named
"Simple random sample" or "random sample"
Find the surface area of the triangular prism Formula: SA= p * h + 2 * b
ANSWER:
139 square yards
STEP-BY-STEP EXPLANATION:
We have that the formula for the surface area of a triangular prism is the following:
[tex]A=p\cdot h+2b[/tex]Where p, is the perimeter is the base and h is the height, while b is the area of the base, we replace and calculate the area like this:
[tex]\begin{gathered} p=4+4+5=13 \\ A=13\cdot9.5+2\cdot7.75 \\ A=123.5+15.5 \\ A=139 \end{gathered}[/tex]The area is 139 square yards
The hospital is 3.1 miles west of the fire station. What is the length of a straight line between the school and the hospital? Round to the nearest tenth. Enter your answer in the box.
Using the Pythagorean Theorem, it is found that:
A. The straight line distance between the school and the fire station is of 4.62 miles.
B. The distance between the school and the hospital is of 2.08 miles.
Pythagorean TheoremThe Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the following rule:
[tex]h^2 = l_1^2 + l_2^2[/tex]
In the context of this problem, the distance between the school and the fire station is the hypotenuse of a right triangle with sides 4.3 and 1.7, hence:
d² = 4.3² + 1.7²
d = sqrt(4.3² + 1.7²)
d = 4.62 miles.
The hospital is 3.1 miles west of the fire station, hence the distance between the school and the hospital is the hypotenuse of a right triangle of sides 1.7 and 4.3 - 3.1 = 1.2, hence:
d² = 1.2² + 1.7²
d = sqrt(1.2² + 1.7²)
d = 2.08 miles.
Missing informationThe complete problem is given by the image at the end of the answer.
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528 = 14y + 10
y =
Stuck again
Which is the polynomial for the given graph?
a) P(x) = (x + 2)(x + 8)(x-1)(x-4)
b) P(x)=(x-2)(x + 1)²(x+4)
c) P(x) = (x-2)(x-8)(x + 1)(x+4)
d) P(x) = (x + 2)(x-1)²(x-4)
The polynomial for the given graph is P(x) = (x+2)(x+8)(x-1)(x-4)
Define polynomial.A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x2 4x + 7 is an illustration of a polynomial with a single indeterminate x. In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable.
Given,
The polynomial for the given graph is:
P(x) = (x+2)(x+8)(x-1)(x-4)
Each non-zero term in a polynomial function is made up of a number, known as the term's coefficient, and a variable raised to a non-negative integer power. A polynomial function can be either zero or the sum of a finite number of non-zero terms.
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PLEASE HELP
Which transformation represents a reflection over the x-axis?
Answer: E
Step-by-step explanation:
Option A is a reflection over the y-axis.
Option B is a rotation of 180 degrees about the origin followed by a dilation.
Option C is a reflection over the line y=x.
Option D is a reflection over the y-axis.
Option E is a reflection over the x-axis.
a tank contains 200 liters of fluid in which 30 grams of salt is dissolved. brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 4 l/min; the well-mixed solution is pumped out at the same rate. find the number a(t) of grams of salt in the tank at time t.
The quantity of salt in the tank at period t equivalents A(t) = 200 - 130 e(-t/40).
Initially, the tank has A(0) = 50 g of salt.
The rate of salt entryway is (1 g/L) × (5 L/min) = 5 g/min
And a rate of (A(t) ÷ 200 g/L) × (5 L/min) = (A(t) ÷ 40) g/min,
As an outcome, the quantity of salt in the tank modifications as
A'(t) = (5 - A(t)) ÷ 40.
Solve ODE for A(t):
A'(t) + (A(t) ÷ 40) = 4
[tex]e^{\frac{(t)}{40} }[/tex] A'(t) + ([tex]e^{\frac{(t)}{40} }[/tex] ÷ 40 A(t)) = 4[tex]e^{\frac{(t)}{40} }[/tex]
([tex]e^{\frac{(t)}{40} }[/tex] A(t))' = 4[tex]e^{\frac{(t)}{40} }[/tex]
[tex]e^{\frac{(t)}{40} }[/tex] A(t) = 160[tex]e^{\frac{(t)}{40} }[/tex] + C
A(t) = 160 + C[tex]e^{\frac{(t)}{40} }[/tex]
Given A(0) = 30, conclude that
30 = 160 + C
C = -130,
This denotes that the quantity of salt in the tank at period t equivalents
A(t) = 200 - 130 e(-t ÷ 40).
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