Data
Milk drank = 1 1/2 twice a day
Volume in a container = 15 cups
Number of days the contaier will be empty = ?
Procedure
To solve this problem just divide the volume of the container by the milk drank by the child.
As the child drinks 1 1/2 twice a day, the total milk drank in a day will be = 2 x 1 1/2 = 3
Division 15/3 = 5
Solution: The container will be empty in 5 days
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Identify an equation in point slope form for the line perpendicular to y=1/4 x-7that passes through -2,-6
The equation in the point slope form for the line perpendicular to y = (1/4)x-7 that passes through the point (-2,-6) is y+6 = -4(x+2)
The given equation of the perpendicular line
y = (1/4)x -7
The equation is in the slope intercept form of the line
y = mx+b
Where m is the slope of the line
By comparing the given equation with the slope intercept form
The slope of the line m = 1/4
The slope of its perpendicular line = -1/m
= -4
The point slope form is
[tex](y-y_1)=m(x-x_1)[/tex]
The point is given that (-2,-6)
Substitute these values in the equation
(y-(-6) = -4(x-(-2)
y+6 = -4(x+2)
Hence, the equation in the point slope form for the line perpendicular to y = (1/4)x-7 that passes through the point (-2,-6) is y+6 = -4(x+2)
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Laura, a sandwich maker, produces 80 sandwiches on average per day. How many sandwiches will she produce in pdays?Number of sandwiches =
Number of sandwiches = 80p
Explanation:Given:
Laura produces 80 sandwiches per day
To find:
The number of sandwiches that will be produced in p days
1 day = 80 sandwiches
p days = 80 × p
p days = 80p
This means that she will produce 80p number of sandwiches in p days
Solve y^3= −125.
y = −5
y = ±5
y = −25
y = ±25
Answer:
A. y=-5Step-by-step explanation:
Use the order of operations.
PEMDAS stands for:
ParenthesesExponentsMultiplyDivideAddSubtractDo exponents first.
[tex]\sf{y^3=-125}[/tex]
[tex]\sf{x=\sqrt[3]{f\left(a\right)},\:\sqrt[3]{f\left(a\right)}\dfrac{-1-\sqrt{3}i}{2},\:\sqrt[3]{f\left(a\right)}\dfrac{-1+\sqrt{3}i}{2}}}[/tex]
[tex]\rightarrow \sf{y=\sqrt[3]{-125},\:y=\sqrt[3]{-125}\dfrac{-1+\sqrt{3}i}{2},\:y=\sqrt[3]{-125}\dfrac{-1-\sqrt{3}i}{2}}[/tex]
[tex]\sf{\sqrt[3]{-125}=\boxed{\sf{-5}}}[/tex]
Therefore, the correct answer is y=-5.
I hope this helps, let me know if you have any questions.
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{y^3 = -125}[/tex]
[tex]\large\text{Solve/take the cube root}[/tex]
[tex]\mathsf{(-125)^{^\dfrac{1}{3}}}\mathsf{ = y}[/tex]
[tex]\mathsf{y = (-125)^{^\dfrac{1}{3}}}[/tex]
[tex]\large\text{Simplify it}[/tex]
[tex]\mathsf{y = -5}[/tex]
[tex]\huge\text{Therefore, your answer is: \boxed{\mathsf{y = -5\ (\rm \bold{O}ption\ A.)}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Collinear points are two or more points that lie on the sameA. planeB. angleC. lineD. space
Collinear points are two or more points that lie on the same line.
For Example:
Point A, B and C
Andrew constructed a triangle so that the measurement of 1 and 2 were congruent. if angle 3 measured 70 degrees, what is the measure of angle 1?
Andrew constructed a triangle such that the measurements of angles m<1 and m<2 are congruent.
The above statement can be inferred from concept of congruency of triangles. The oppsoite sides of the two congruent angles in a traingles are also equal.
From the above statement we can deduce the type of a triangle that Andrew drew as follows:
[tex]\text{Andrew drew a isoceles triangle}[/tex]An isoceles triangle has two equal sides and angles i.e congruent sides and interior angles. Hence,
[tex]m\angle1\text{ = m}\angle2\ldots\text{ Eq1}[/tex]The following information is given for the third interior angle m<3 of the isoceles triangle:
[tex]m\angle3\text{ = 70 degrees}[/tex]We need determine the angle measure of the angle 1. Recall that the sum of interior angles of a triangle is given as follows:
[tex]m\angle1\text{ + m}\angle2\text{ + m}\angle3\text{ = 180 degrees }\ldots\text{ Eq2}[/tex]Substitute Eq1 into Eq2 as follows:
[tex]\begin{gathered} m\angle1\text{ + m}\angle1\text{ + m}\angle3\text{ = 180} \\ \\ 2\cdot m\angle1\text{ + m}\angle3\text{ = 180} \end{gathered}[/tex]Substitute the angle measurement of angle ( 3 ) in the expression above and solve for angle ( 1 ) as follows:
[tex]\begin{gathered} 2\cdot m\angle1\text{ + 70 = 180} \\ 2\cdot m\angle1\text{ = 110} \\ m\angle1\text{ = }\frac{110}{2} \\ \\ m\angle1\text{ = 55 degrees }\ldots\text{ Answer} \end{gathered}[/tex]PLSSS HELPPPPPthe number of stores opened by a coffee company can be modeled by the exponential function graphed on the grid. Based on the graph, which statement does not appear to be true.
Let's analyze the statements to see which one is not true.
Statement F. The coffee shop company had opened 400 stores by the end of 1992.
The horizontal axis on the graph (the x-axis) represents the number of years that have passed since 1992, thus the year 1992 is at x=0 on the graph.
The vertical axis (the y-axis) represents the number of stores.
As we can see in the following diagram, the red point represents the number of stores at x=0 (at the year 1992):
it is true that the coffee shop had 400 stores by the end of 1992.
Statement G. The coffee shop opened 100 stores in 1 year.
To see if this is true, we look at x=1, which represents 1 year, and check for the number of stores corresponding to 1 year:
This point is at (1,500) --> After 1 year there were 500 stores.
Since they started with 400 stores, this means that it is true that they opened 100 stores in 1 year.
Statement H. Every year the number of stores the coffee company opened increased by 25%.
We can find if this is true just by looking at the form of the graph. This graph has an exponential curve which means that the growth increases at every step. Thus there is an increase in the coffee shop that they open every year. This statement is true.
Statement J. Since 1992 the coffee shop company has opened 250 stores each year.
As we saw with the previous statement, the number of shops opened every year is not constant, it increases with time. Thus, since they do not open the same amount of shops every year, this option the one that is not true.
Answer: Statement J
Give a number in scientific notation that isbetween the two numbers on a number line.71 X 103 and 71,000,000
For this problem we have the following two numbers
[tex]71x10^3[/tex][tex]71000000[/tex]Let's convert the two numbers with scientific notation
[tex]71x10^3=71000=7.1x10^4[/tex][tex]71000000=7.1x10^7[/tex]Now we just need to find a number between the two given we know that:
[tex]7.1x10^4<7.1x10^7[/tex]The final answer for this case would be any number between these two numbers and it could be:
[tex]7.1x10^6[/tex]also it could be:
[tex]9.5x10^5[/tex]Or any number between the two given
Answer:
The answer is B,D, And F
Step-by-step explanation:
7.1 × 103 = 7,100
7.1 × 105 = 710,000
Because 7,100 < 710,000 < 71,000,000 then 7.1 × 105 falls between 7.1 × 103 and 71,000,000
Use the graph of f to describe the transformation that results in the graph of g. Then sketch the graphs of g and f.
EXPLANATION
Since we have the function:
[tex]f(x)=(\frac{1}{3})^x[/tex]Graphing this an the transformation into a graph calculator we have:
We can see that the transformated function is translated 2 units to the right, and that It is also translated 4 units down.
Thus, the transformations are the following:
g(x) is the graph of f(x) translated 2 units to the right and 4 units down.
Given four numbers P, Q, R and S. The first three numbers form an arithmetic sequence while the last three form a geometric sequence. If the sum of the first and the fourth number is 16 and the sum of the second and the third number is 12, find these four numbers.
The most appropriate choice for arithmetic and geometric series will be given by-
P = 0, Q = 4 , R = 8, S = 16 or P = 15, Q = 9, R = 3, S = 1 are the required numbers
What is arithmetic and geometric series?
Arithmetic series are those series whose difference between two consecutive terms are same.
Geometric series are those series whose ratio between two consecutive terms are same.
Here,
P, Q and R forms an Arithmetic sequence
Let P = a - d , Q = a, R = a + d, Where a is the first term of the Arithmetic sequence and d is the common difference of the sequence.
Let S = b
Q, R and S forms a Geometric sequence
[tex]\frac{a + d}{a} = \frac{b}{a +d}[/tex]
[tex](a + d)^2 = ab\\a^2 + d^2 + 2ad = ab\\[/tex] ............... (1)
Now the sum of first and fourth number is 16
a - d + b = 16
b = 16 - a + d
Putting the value of b in (1),
[tex]a^2 + d^2 + 2ad = a(16 - a +d)\\a^2 + d^2 + 2ad = 16a -a^2+ad\\a^2+a^2 + d^2+2ad - ad - 16a = 0\\2a^2 + ad+d^2 -16a = 0[/tex]............ (2)
Sum of second and third number is 12
[tex]a + a + d = 12\\2a +d = 12\\d = 12-2a[/tex]
Putting the value of d in (2)
[tex]2a^2 + a(12 - 2a)+(12 - 2a)^2-16a = 0\\2a^2 + 12a - 2a^2+144-48a+4a^2 - 16a = 0\\4a^2-52a+144=0\\4(a^2-13a+36)=0\\a^2 -13a+36=0\\a^2-9a-4a+36=0\\a(a - 9)-4(a-9)=0\\(a-4)(a-9) = 0\\[/tex]
[tex]a - 4 = 0[/tex] or [tex]a - 9 = 0[/tex]
[tex]a = 4[/tex] or [tex]a = 9[/tex]
When a = 4,
[tex]d = 12 - 2\times 4\\d = 12 - 8\\d = 4[/tex]
[tex]b = 16 - 4+4\\b = 16[/tex]
P = 4 - 4 = 0
Q = 4
R = 4 + 4 = 8
S = 16
When a = 9,
[tex]d = 12 - 2\times 9\\d = 12 - 16\\d = -6[/tex]
[tex]b = 16 - 9-6\\b = 1[/tex]
P = 9 - (-6) = 15
Q = 9
R = 9 + (-6) = 3
S = 1
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For the parabola given by 4y – 9 = x2 – 6x, find the vertex and focus.
Solution
Gievn the equation below
[tex]4y-9=x^2-6x[/tex]To find the vertex and focus of the given equation, we apply the parabola standard equation which is
[tex]4p(y-k)=(x-h)^2[/tex]Where p is the focal length and the vertex is (h,k)
Rewriting the equation in standard form gives
[tex]\begin{gathered} 4y-9=x^2-6x \\ 4y=x^2-6x+9 \\ 4y=x^2-3x-3x+9 \\ 4y=x(x-3)-3(x-3) \\ 4y=(x-3)^2 \\ 4(1)(y-0)=(x-3)^2 \end{gathered}[/tex]Relating the parabola standard equation with the given equation, the vertex of the parabola is
[tex]\begin{gathered} x-3=0 \\ x=3 \\ y-0=0 \\ y=0 \\ (h,k)\Rightarrow(3,0) \\ p=1 \end{gathered}[/tex]Hence, the vertex is (3,0)
The focus of the parabola formula is
[tex](h,k+p)[/tex]Where
[tex]\begin{gathered} h=3 \\ k=0 \\ p=1 \end{gathered}[/tex]Substitute the values of h, k and p into the focus formula
[tex](h,k+p)\Rightarrow(3,0+1)\Rightarrow(3,1)[/tex]Hence, the focus is (3, 1)
Express 1.27times 10^3 in decimal notation
1.27 x 10^3
10^3 is 1000
1.27 x 10^3 = 1.27 x 1000 = 1270
[tex]1.27x10^3\text{ = 1.27}x1000\text{ = 1270}[/tex]Answer:
1270
what's the answer?[tex] - 4 \sqrt{15 \times - \sqrt{3} } [/tex]
In decimal form this is equal to -17.22.
18
If p percent of an adult's daily allowance of
potassium is provided by x servings of Crunchy
Grain cereal per day, which of the following
expresses p in terms of x ?
Express p in terms of x : p = 5x
What is Percent?
A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a measurement system.
If 5% of an adult's daily potassium requirement is provided by each serving of Crunchy Grain cereal, then x servings will offer x times 5%.
Five times as many servings, or p, of potassium are required for an adult's daily requirement.
As a result,
p = 5x can be used to describe the proportion of potassium in an adult's daily allotment.
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Choose SSS, SAS, or neither to comparethese two triangles.A) SSSB) SASC) neither
Answer:
C. Neither
Explanation:
The SSS Congruence Rule states that if the three sides of a triangle are equal to the three sides of another triangle, then the two triangles are congruent.
The SAS Congruence Rule states that if the two sides and the included angle of one triangle are equal to the two sides and the included angle of another triangle, then the two triangles are congruent.
Notice that in the given triangles, there are two congruent sides and a non-included angle, since this does not satisfy any of the rules stated above, SSS Congruence rule or SAS Congruence rule, we'll choose "neither" as the correct answer.
Lin is traveling from Japan to several other countries. The conversion table shows exchange rates between different currencies.
2,000 Yen 16 Euros
40 Euros = 3,125 Indian Rupees
What is the rate of yen per Indian rupee?
0.625
0.64
1.5625
1.6
The rate of yen per Indian rupee is 1.6
How do you convert currency to another currency?
Divide your current currency by the exchange rate if you are aware of it.
Assume, for instance, that you want to change 100 USD into EUR and the USD/EUR exchange rate is 0.631. Simply multiply 100 by 0.631 to do this, and the result is 63.10 EUR, which is the amount you will receive.
Given, 2000 Yen = 16 Euros
and, 40 Euros = 3,125 Indian Rupees
Find rate of yen per India rupee
1 Euro = 2000/16
1 Euro = 125 yen
And, 1 Euro = 3125/40
1 Euro = 78.125 India rupee
Now, find 1 yen = ? Indian rupee
we know, 1 Euro = 125 yen and 1 Euro = 78.125 India rupee
put the values of euro in India rupee in 1 Euro = 125 yen, we get
78.125 India rupee = 125 yen
1 India rupee = 125 / 78.125
1 Indian rupee = 1.6 Yen
Therefore, the rate of yen per Indian rupee is 1.6
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What is the range of the following numbers? 12, 20, 18, 25.6 OA. 5 O B. 167/ O C. 18 O D. 19 E. 25
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
12, 20, 18, 25 , 6
range = ?
We must order the data.
Step 02:
6 , 12 , 18 , 20 , 25
Range = 25 - 6 = 19
The answer is:
The range is 19
Solve for 5x - 3y = -45the equations beside it are the answer choices.
You have the following equation:
5x - 3y = -45
In order to solve the previous equation for y, you proceed as follow:
5x - 3y = -45 subtract 5x both sides
- 3y = -45 - 5x multiply by -1 both sides
(-1)(-3y) = (-1)(-45 - 5x)
3y = 45 + 5x divide by 3 both sides
y = 45/3 + 5/3 x order the right side
y = 5/3 x + 15
Hence, the solution for y is y = 5/3 x + 15
Find the length of the legs of a night triangle whose hypotenuse is 25cm and whose area is 84cm use phytagorean theorem.
Answer:
Explanation:
Here, we want to find the length of the legs of the right triangle given the area and the length of the hypotenuse
We have the sketch of the triangle as shown below:
According to Pythagoras' the square of the length of the hypotenuse equals the sum of the squares of the length of the two other sides
Thus, mathematically:
[tex]a^2\text{ + b}^2\text{ = 25}^2[/tex]Mathematically, we have the area calculated as:
[tex]\begin{gathered} A\text{ = }\frac{1}{2}\times b\times h \\ \\ 84\text{ = }\frac{1}{2}\times a\times b \\ \\ a\text{ = }\frac{168}{b} \end{gathered}[/tex]Now, we have two equations to solve simultaneously
Substitute equation ii into i
We have that as:
[tex][/tex]Consider the following algebraic expression:7s - 7Step 1 of 2: Identify the first term of the algebraic expression. Indicate whether the term is a variable term or a constant term. For avariable term, identify the variable and the coefficient of the term.
Given the algebraic expression below
[tex]7s-7[/tex]The first term of the algebraic expression is
[tex]7s[/tex]The first term "7s" is a variable term.
The variable of the first term is "s"
The coefficient of the variable term is 7
Henry had a batting average of 0.341 last season (out of 1000 at-bats, he had 341 hits). Given that thisbatting average will stay the same this year, answer the following questions. What is the probability that his first hit will not occur until his 5th at-bat? Answers. 0.64. 0.083. 0.129. 0.166
The probability of success (a hit) is given by:
p = 0.341
The complement (a failure) of this probability is:
q = 1 - 0.341 = 0.659
Then, we can construct a probability distribution for the first hit until his nth at-bat:
[tex]P(x=n)=p\cdot q^{n-1}[/tex]For his 5th at-bat, we have n = 5, then:
[tex]\begin{gathered} P(x=5)=0.341\cdot(0.659)^{5-1}=0.341\cdot0.659^4 \\ \\ \therefore P(x=5)=0.064 \end{gathered}[/tex]In ∆PQR, p=13 inches, q=18 inches and r= 12 inches. Find the area of ∆PQR to the nearest square inch.
Given data:
The first side of the triangle is p=13 inches.
The second side of the triangle is q=18 inches.
The third side of the triangle is r= 12 inches.
The semi-perimeter is,
[tex]\begin{gathered} s=\frac{p+q+r}{2} \\ =\frac{13\text{ in+18 in+12 in}}{2} \\ =21.5\text{ in} \end{gathered}[/tex]The expression for the area of the triangle is,
[tex]\begin{gathered} A=\sqrt[]{s(s-p)(s-q)(s-r)_{}} \\ =\sqrt[]{21.5\text{ in(21.5 in-13 in)(21.5 in-18 in)(21.5 in-12 in)}} \\ =\sqrt[]{(21.5\text{ in)(8.5 in)(3.5 in)(9.5 in)}} \\ =77.95in^2 \end{gathered}[/tex]Thus, the area of the given triangle is 77.95 sq-inches.
Select the correct answer.
What is the value of this logarithmic e ession?
log2 16 - log₂ 4
Answer:l og2(16)=x log 2 ( 16 ) = x in exponential form using the definition of a logarithm. If x x and b b are positive real numbers and b b does not equal ...
Step-by-step explanation:
Determine the measures of angles x, y, and z: x = 75°95°105°° y = 75°95°105°° z = 75°95°105°°
Consider the figure,
So, we have, Two angles are called complementary when their measures add to 90 degrees. Two angles are called supplementary when their measures add up to 180 degrees.
So, here, [tex]<\text{AHB}+z=180[/tex]
Therefore, z can be calculated as,
[tex]z=180-<\text{AHB}=180-105=75[/tex]Now, the angles DHC and
can someone please help me find the value of X?
Answer:
x = 100degrees
Explanation:
Using the theorem;
The angle at the vertex is the half of the difference of its intercepted arcs
Angle at the vertex = 15 degrees
angle at the intercepted arcs = 70degrees and x degrees
According to the theorem;
15 = 1/2(x-70)
Cross multiply
15 * 2 = x - 70
30 = x - 70
Add 70 to both sides
30 + 70 = x - 70 + 70
100 = x
Swap
x = 100degrees
Hence the value of x is 100degrees
which number of pounds of bananas and total cost of the bananas could be used as the missing values in the table
Given :
The table show a proportional relationship between the number of pounds and the total cost
so,
if a figure has four corners then it is a quadrilateral and figure has four corners therefore it is a quadrilateral which statement illustrate this to be true the large attachment account example the law of syllogism the law contrapositive
The given conditions are true:
law of contrapositive
Use the data below to complete the following calculationm=76,37,27
Answer:
Σmf = 23347
Σm²f = 1621631
(Σmf)² = 545082409
Explanation:
The symbol Σ means that we need to sum all the products of m and f.
So, Σmf is equal to:
Σmf =76(94) + 37(92) + 27(63) + 98(62) + 62(81)
Σmf = 7144 + 3404 + 1701 + 6076 + 5022
Σmf = 23347
Then, to find Σm²f, we need to find the square of m, so:
Σm²f = (76)²(94) + (37)²(92) + (27)²(63) + (98)²(62) + (62)²(81)
Σm²f = 5776(94) + 1360(92) + 729(63) + 9604(62) + 3844(81)
Σm²f = 542944 + 125948 + 45927 + 595448 + 311364
Σm²f = 1621631
Finally, (Σmf)² is equal to:
(Σmf)² = (23347)²
(Σmf)² = 545082409
Therefore, the answers are:
Σmf = 23347
Σm²f = 1621631
(Σmf)² = 545082409
The numerator of the sum 1+1/3+2 is (a) 1 (b) 2 (c) 5 (d) 6.
The expression is given as,
[tex]\frac{1}{2}+\frac{1}{3}[/tex]Note that the denominator of both the fractions are prime numbers. So their lowest common multiple, LCM(2,3) will be the product of the numbers,
[tex]undefined[/tex]y - y1 = m (x - x1 ) write an equation in point slope form given point ( 4, -3 ) and m = 1
The point-slope form of a line is:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope.
Replacing with m = 1 and the point (4, -3):
y - (-3) = 1(x - 4)
y + 3 = x - 4