Answer:
A
[tex]h = -16t^2 + 192t[/tex]
B
Vertex=(6,576)
Step-by-step explanation:
The problem gives us the following data:
[tex]v_o=192\ ft/s,\ h_o=0[/tex]
A.
Thus the function is
[tex]h = -16t^2 + 192t[/tex]
The graph of h has the shape of an inverted parabola. Recall if the coefficient of the quadratic term is negative, the parabola is concave down, so it has a maximum value.
Part B
Let's take the function of h
[tex]h = -16t^2 + 192t[/tex]
Factoring by -16
[tex]\displaystyle h = -16(t^2 - 12t)[/tex]
Completing squares
[tex]\displaystyle h = -16(t^2 - 12t+36-36)[/tex]
[tex]\displaystyle h = -16(t^2 - 12t+36)+576[/tex]
Factoring
[tex]\displaystyle h = -16(t-6)^2+576[/tex]
Rearranging
[tex]\displaystyle h -576= -16(t-6)^2[/tex]
We can get the coordinates of the vertex from this standard form of the parabola.
Vertex=(6,576)
The maximum value means that at t=6 seconds, the firework will be 576 feet high and then it will start falling back to the ground.
Joe wants to build a doll house for his daughter. He wants the doll house to look just like his house. His house is 28 feet wide and 36 feet tall at the highest point of the roof. If the dollhouse will be 2.5 feet wide, how many feet will its highest point be?
The highest point for the dollhouse will be 3.12 feet
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
His house is 28 feet wide and 36 feet tall at the highest point of the roof.
And, The dollhouse will be 2.5 feet wide.
Now,
Let the highest point for the dollhouse = x
So, By definition of proportion, we get;
⇒ 28 / 36 = 2.5 / x
Solve for x as;
⇒ x = 2.5 × 36/28
⇒ x = 3.12 feet
Thus, The highest point for the dollhouse = 3.12 feet
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Given f(x) = 3x - 1 and g(x)= -x + 6, find f(-2) + g(5).
answer choices are:
-6
6
8
Answer:
-6Step-by-step explanation:
f(x)=3x-1 g(x)=-x+6f(-2)=3*(-2)-1 g(5)=-5+6f(-2)=-7 g(5)=1 f(-2)+g(5)=-7+1=-6Researchers at Gallup were interested in whether there was a decrease in the proportion of nonretirees (in other words, people who are not yet retired) who did not believe that the U.S. Social Security program will be able to pay them a retirement benefit when they retire. In the summer of 2010, the Gallup poll found that 60% of nonretirees thought that Social Security would not be able to pay a benefit. Five years later in the summer of 2015, Gallup asked the same question to 1,282 nonretirees and found that 51% of respondents did not think that Social Security would be able to pay a retirement benefit by the time that they retire. We would like to test the hypothesis that in 2015 there is a lower proportion of nonretirees who do not think that Social Security will be able to pay them a benefit. A z-test for the population proportion showed that z = -4.29, p < 0.001.
Which of the following is the best conclusion based on the output?
A. We have extremely strong evidence to reject H0.
B. We have extremely strong evidence to reject Ha.
C. We have moderately strong evidence to reject H0.
D. There is a probability of 0 that H0 is correct.
E. There is a probability of 0 that Ha is correct.
Answer:
A. We have extremely strong evidence to reject H0.
Step-by-step explanation:
Let P be the proportion of non-retirees in 2015 who did not think that Social Security would be able to pay a retirement benefit by the time that they retire.
According to the data null and alternative hypotheses should be:
[tex]H_{0}[/tex]: P=0.60[tex]H_{a}[/tex]: P<0.60Test statistics is -4.29 and p-value of the statistics is p<0.001
At every significance levels higher than 0.001, we can reject the null hypothesis since p<0.001.
an automobile 16 feet long overtakes a truck that is 28 feet long and is traveling 30 mph. At what rate must the automobile travel to pass the truck in 4 seconds?
Step-by-step explanation:
Length of automobile = 16 feet = 4.88 m
Length of truck = 28 feet = 8.53 m
Speed of truck = 30 mph = 48 km/h = 13.33 m/s
Time in which automobile to pass truck = 4 s
Distance traveled by truck in 4 seconds = 4 x 13.33 = 53.33 m
Distance which need to cover by automobile in 4 seconds to pass truck is the sum of length of automobile, length of truck and distance traveled by truck in 4 seconds.
Distance which need to cover by automobile in 4 seconds = 4.88 + 8.53 + 53.33
Distance which need to cover by automobile in 4 seconds = 66.74 m
Distance = Speed x Time
66.74 = Speed x 4
Speed = 16.69 m/s = 60 km/h = 96 mph
Automobile must travel at 96 mph to pass the truck in 4 seconds.
Madison spent 3 times as long on her social project as she did on her other project. If she spent a total of 8 hours on he projects how long did she spend on her social project
Answer:
6 hours
Step-by-step explanation:
Suppose Madison spent x hours on her social project,
then the number of hours spent on other project will be 1/3 of x=x/3
Total hours spend on all projects will be the addition of hours spent on social project and hour spent on other project, i.e
x + x/3 = 4x/3
It si given that this is 8 hours, therefore
4x/3=8
Multiplying both sides by 3:
4x=24
Dividing across board by 4:
x= 6 hours
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A function is shown: f(x) = 16x2 − 1. Choose the equivalent function that best shows the x-intercepts on the graph.
A. f(x) = (4x + 1)(4x − 1)
B. f(x) = (8x + 1)(8x − 1)
C. f(x) = 4(x2 + 1)
D. f(x) = 8(x2 − 1)
Answer:
it is option a
Step-by-step explanation:
. f(x) = (4x + 1)(4x − 1) is the correct answer overall you have the check it and just make sure you fully to your capability of those steps
The equivalent function that best shows the x-intercepts on the graph is f(x)=(4x-1)(4x+1).
What is a Function?
A function assigns the value of each element of one set to the other specific element of another set.
As the function is given to us that f(x)=16x²-1, therefore, the equivalent function that best shows the x-intercepts on the graph can be written as,
[tex]f(x)= 16x^2-1\\\\f(x)=16x^2-1^2\\\\f(x)=(4x-1)(4x+1)[/tex]
If we solve the roots of the given function,
(4x-1)=0
x = 1/4 = 0.25
(4x+1)=0
x = -1/4 = -0.25
Thus, the x-intercept of the function is 0.25 or -0.25.
Thus, the equivalent function that best shows the x-intercepts on the graph is f(x)=(4x-1)(4x+1).
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Given: ∆AKM, R = 2, m∠A = 33°, O∈ AM . Find: perimeter of ∆AKM
Answer:
∆AKM is a right triangle for it is inscribed in semicircle O.
AM = diameter of semi-circle O = 2R = 2(2) = 4
%22AK%22%2F%22AM%22=cos%2833%5Eo%29
AK+=+AM%2Acos%2833%5Eo%29
AK+=+4cos%2833%5Eo%29
%22KM%22%2F%22AM%22=sin%2833%5Eo%29
KM+=+AM%2Asin%2833%5Eo%29
KM+=+4sin%2833%5Eo%29
The perimeter of a triangle is the sum of the three sides.
perimeter=AK%2BKM%2BAM
perimeter=4cos%2833%5Eo%29%2B4sin%2833%5Eo%29%2B4
Approximately 9.533238412
Step-by-step explanation:
Answer:
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Step-by-step explanation:
A fried chicken franchise finds that the demand equation for its new roast chicken product, "Roasted Rooster," is given by p = 45 / q 1.5
where p is the price (in dollars) per quarter-chicken serving and q is the number of quarter-chicken servings that can be sold per hour at this price.
1) Express q as a function of p.
2) Find the price elasticity of demand when the price is set at $4.00 per serving.
Answer:
1. [tex]q=(\dfrac{45}{p})^{\frac{2}{3}}[/tex]
2. [tex]E_d=-\dfrac{2}{3}[/tex]
Step-by-step explanation:
The given demand equation is
[tex]p=\dfrac{45}{q^{1.5}}[/tex]
where p is the price (in dollars) per quarter-chicken serving and q is the number of quarter-chicken servings that can be sold per hour at this price.
Part 1 :
We need to Express q as a function of p.
The given equation can be rewritten as
[tex]q^{1.5}=\dfrac{45}{p}[/tex]
Using the properties of exponent, we get
[tex]q=(\dfrac{45}{p})^{\frac{1}{1.5}}[/tex] [tex][\because x^n=a\Rightarrow x=a^{\frac{1}{n}}][/tex]
[tex]q=(\dfrac{45}{p})^{\frac{2}{3}}[/tex]
Therefore, the required equation is [tex]q=(\dfrac{45}{p})^{\frac{2}{3}}[/tex].
Part 2 :
[tex]q=(45)^{\frac{2}{3}}p^{-\frac{2}{3}}[/tex]
Differentiate q with respect to p.
[tex]\dfrac{dq}{dp}=(45)^{\frac{2}{3}}(-\dfrac{2}{3})(p^{-\frac{2}{3}-1}})[/tex]
[tex]\dfrac{dq}{dp}=(45)^{\frac{2}{3}}(-\dfrac{2}{3})(p^{-\frac{5}{3}})[/tex]
[tex]\dfrac{dq}{dp}=(45)^{\frac{2}{3}}(-\dfrac{2}{3})(\dfrac{1}{p^{\frac{5}{3}}})[/tex]
Formula for price elasticity of demand is
[tex]E_d=\dfrac{dq}{dp}\times \dfrac{p}{q}[/tex]
[tex]E_d=(45)^{\frac{2}{3}}(-\dfrac{2}{3})(\dfrac{1}{p^{\frac{5}{3}}})\times \dfrac{p}{(45)^{\frac{2}{3}}p^{-\frac{2}{3}}}[/tex]
Cancel out common factors.
[tex]E_d=(-\dfrac{2}{3})(\dfrac{1}{p^{\frac{5}{3}}})\times \dfrac{p}{p^{-\frac{2}{3}}}[/tex]
Using the properties of exponents we get
[tex]E_d=-\dfrac{2}{3}(p^{-\frac{5}{3}+1-(-\frac{2}{3})})[/tex]
[tex]E_d=-\dfrac{2}{3}(p^{0})[/tex]
[tex]E_d=-\dfrac{2}{3}[/tex]
Therefore, the price elasticity of demand is -2/3.
To address the question, q as a function of p is q = (45/p)^(2/3), and the price elasticity of demand when p is $4 can be found by taking the derivative of q with respect to p and substituting the given values in the elasticity formula.
Explanation:The student has asked to express q as a function of p and to find the price elasticity of demand when the price is set at $4.00 per serving for a new roast chicken product. The given equation is p = 45 / q1.5.
To find q as a function of p, we rearrange the equation: q = (45/p)1/1.5 or q = (45/p)2/3.To find the price elasticity of demand, we use the formula Ed = (dq/dp) × (p/q). First, we calculate the derivative dq/dp of the function q(p), and then substitute p=4 to find Ed at that price.The derivative of q with respect to p is dq/dp = -2/3 × (45/p4/3). Substituting p=4, we get the quantity q = (45/4)2/3. Plugging these values into our elasticity formula gives us the price elasticity of demand at p=$4.00.
Sheila predicts that 480 people will attendthe fall concert. There was an actual total of 350 people who attended the fall concert. What is the percent error?
Final answer:
To calculate the percent error, subtract the actual attendance from the predicted attendance, take the absolute value, divide by the actual attendance, and multiply by 100%. Sheila's prediction has a percent error of 37.14%.
Explanation:
The question is asking for the calculation of the percent error between Sheila's prediction for concert attendance and the actual attendance. To find the percent error, you subtract the actual value from the predicted value, take the absolute value of the difference, divide by the actual value, and then multiply by 100 to convert it to a percentage.
Steps to Calculate Percent Error
Subtract the actual number of attendees (350) from the predicted number (480) to get the difference: 480 - 350 = 130.Take the absolute value of the difference: |130| = 130.Divide the absolute difference by the actual number of attendees: 130 / 350 = 0.3714.Multiply by 100 to get the percent: 0.3714 * 100 = 37.14%.The percent error in Sheila's prediction is 37.14%.
Write an equation for the line that is parallel to y = −2x and passes through the point (0,7).
A. y=2x–7
B. y=-2x + 7
C. y=-2x-7
D. y=2x+7
Answer:
B. [tex]\displaystyle y = -2x + 7[/tex]
Step-by-step explanation:
The y-intercept is given to us, which is [tex]\displaystyle [0, 7],[/tex]and Parallel Lines have SIMILAR RATE OF CHANGES [SLOPES], so −2 remains the way it is.
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Two roads that cross at right angles are used as coordinate axes for a map. A library is located at point L . Use the drop-down menus to complete the statements about the location of the library.
The question is incomplete. Here is the complete question:
Two roads that cross at right angles are used as coordinate axes for a map. A library is located at point L.
Use the drop-down menus to complete the statements about the location of the library.
(a) The library is located at point (_,_).
(b) The library is __ miles from Road X and __ miles from Road Y.
Answer:
(a) The library is located at point (3.25, -1.5).
(b) The library is 1.5 miles from Road X and 3.25 miles from Road Y
Step-by-step explanation:
Given:
The roads are at right angles to each other. Point 'L' is the location of the library.
(a)
From the graph, we can conclude that,
The length of each square in the graph is 0.5 miles. So,
The coordinates of point L are (3.25, -1.5).
The 'x' value is 3.25 and the 'y' value is -1.5.
Since the point 'L' is the location of library, therefore, the library is located at point (3.25,-1.5).
(b)
The distance of point L from road X is obtained by moving vertically up from point L till we reach the road X. In other words, the perpendicular distance between point L and horizontal x axis is the required distance.
The perpendicular distance is the absolute value of the y-coordinate of point L. The absolute value of 'y' of point L is |-1.5| = 1.5 miles.
Hence, the library is 1.5 miles from road X.
Similarly, the distance of point L from road Y is the perpendicular distance of point L to the road Y.
The perpendicular distance is the absolute value of the x-coordinate of point L. The absolute value of 'x' of point L is |3.25| = 3.25 miles.
Therefore, the library is 3.25 miles from road Y.
So, the library is 1.5 miles from Road X and 3.25 miles from Road Y
The number of stamps that Kaye and Alberto had were in the ratio 5 : 3, respectively. After Kaye gave Alberto 10 of her stamps, the ratio of the number Kaye had to the number Alberto had was 7 : 5. As a result of this gift, Kaye had how many more stamps than Alberto?
A. 20
B. 30
C. 40
D. 60
E. 90
Answer:
D.
Step-by-step explanation:
Let the number of stamps Kaye had be k and that of Alberto be a. Then we know that are in a ratio of 5 to 3.
Hence, k : a = 5:3
or 3k = 5a
Then Kaye gave Alberto 10 of her stamp to make the ratio 7:5
k - 10/a + 10 = 7/5
Cross multiply:
5(k - 10) = 7(a + 10)
5k - 50 = 7a + 70
5k - 7a = 120
Let us now solve the last equation simultaneously with the equation 3k = 5a
5k - 7a = 120
3k - 5a = 0
Multiply equation 1 by 3 and equation 2 by 5
15k - 21a = 360
15k - 25a = 0
Subtract 1 from 2, 4a = 360
and thus a = 90
We know 3k = 5a
3k = 5 * 90
k = 450/3 = 150
Now if we subtract 90 from 150, this yields 60
JUST ONE MORE I NEED HELP ON HW IM STRUGGLING 15pts
A pilot was scheduled to depart at 4:00 pm, but due to air traffic, her departure has been delayed by 16 minutes. Air traffic control approved a new flight plan that will allow her to arrive four times faster than she calculated in her original flight plan. Let x represent the time, in minutes, of her original flight. Create an equation that can be used to predict the number of minutes after 4:00 pm she will arrive at her destination.
y equals one fourth times x minus 16
y = 4x − 16
y equals one fourth times x plus 16
y = 4x + 16
Answer:
y equals one fourth times x minus 16
y = 4x − 16
Step-by-step explanation:
this is because you're taking the time it took to get there minus 16 because of the delay
Answer:
Answer is three because it is one fourth of the time don't listen to the other person's.
Step-by-step explanation:
Let f(x) = x³+6x²+6x and let c be the number that satisfies the Mean Value Theorem for f on the interval [-6,0].Find the Mean Value Theorem.
Answer:
c = 0 or c = -4
Step-by-step explanation:
According to the Mean Value Theorem
[tex]f^{'}(c) = \frac{f(0) - f(-6)}{0 - (-6)} = \frac{0 - (-6)^3 - 6*(-6)^2 - 6*(-6)}{6} = 36 - 36 + 6 = 6[/tex]
By taking the first derivative of f
[tex]f^{'}(x) = 3x^2 + 12x + 6[/tex]
Since[tex]f^{'}(c) = 6[/tex]
We can solve for c
[tex]3c^2 + 12c + 6 = 6[/tex]
[tex]3c^2 + 12c = 0[/tex]
[tex]c(c + 4) = 0[/tex]
c = 0 or c = -4
Charlie and his friend Jay went to the fair. They were having a sale and the admission was 25% off. The regular ticket price was $9.00 and the tax is 6%. What would Charlie's total be?
Answer:
The Total of Charlie's will be $7.16.
Step-by-step explanation:
Given:
Charlie and his friend Jay went to the fair. They were having a sale and the admission was 25% off.
Price of regular ticket = $9.00.
tax = 6%.
We need to find Charlie’s total.
So we will first find the price of regular ticket with 25% off.
25% percent of regular ticket = [tex]\frac{25}{100}\times 9 = \$2.25[/tex]
Discounted Price of regular ticket will be equal to Price of regular ticket minus Discounted amount.
Discounted Price of regular ticket = 9 - 2.25 = $6.75
Now, including tax :
Tax paid will be on discounted amount.
Hence Amount paid in tax = [tex]6\% \times 6.75= \frac{6}{100}\times 6.75 = \$0.405[/tex]
Total amount paid by charlie is equal to sum of Discounted Price of regular ticket and Amount paid in tax
Total Amount paid by charlie = [tex]6.75+0.405 =\$7.155 \approx \$7.16[/tex]
Therefore, the total of Charlie's will be $7.16.
help me on this question please
Answer:
Step-by-step explanation:
The diameter equals the side length of the outer square. The radius of the circle is √2. The diameter of the circle would be
2 × radius = 2 × √2 = 2√2
The area of a square is expressed as length^2. This means that the area of the outer square would be
( 2√2)^2 = 4×2 = 8
The area of the circle is expressed as πr^2. Therefore, the area of the circle would be
π×√2^2 = 2π = 2×3.14 = 6.28
Looking at the inner square, to find the length of the base, we would apply Pythagoras theorem.
√2^2 = base^2 + 1^2
2 = base^2 + 1
base^2 = 2 -1 = 1
base = √1
Area of the inner square would be
√1^2 = 1
Total shaded area would be
6.28 - 1 = 5.28
The probability that the dart will land on the shaded area is
5.28/8 = 0.66
What is the vertex of the graph of y = -2|x-4|+ 11?
Please show work on how to get the answer. Thanks!
Answer:
The vertex is the point [tex](4,11)[/tex]
Step-by-step explanation:
we know that
The equation of the absolute value in vertex form is equal to
[tex]y=a\left|x-h\right|+k[/tex]
where
a is a coefficient
(h,k) is the vertex
In this problem we have
[tex]y=-2\left|x-4\right|+11[/tex]
so
[tex]a=-2[/tex] ---> the vertex represent a maximum
[tex]h=4[/tex]
[tex]k=11[/tex]
therefore
The vertex is the point [tex](4,11)[/tex]
Find the coordinates of the midpoint of a segment having the given endpoints.
Q(0.3, 1.8), R(2.7, 3.9)
(1.5, 2.85)
O (1.05, 3.3)
(-1.2, -1.05)
O(-2.4, -2.1)
Answer:
[tex](1.5,2.85)[/tex]
Step-by-step explanation:
we know that
The formula to calculate the midpoint between two points is equal to
[tex]M(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
we have the endpoints:
Q(0.3, 1.8), R(2.7, 3.9)
substitute in the formula
[tex]M(\frac{0.3+2.7}{2},\frac{1.8+3.9}{2})[/tex]
[tex]M(\frac{3}{2},\frac{5.7}{2})[/tex]
[tex]M(1.5,2.85)[/tex]
AB = x + 4 DC = 12 AD = x + 2 BC = ? Quadrilateral ABCD is a parallelogram if both pairs of opposite sides are congruent. Show that quadrilateral ABCD is a parallelogram by finding the lengths of the opposite side pairs. What is the length of BC?
Answer:
AB = DC = 12
AD = BC = 10
Step-by-step explanation:
For ABCD to be a parallelogram, opposite side pairs must be congruent. That will be the case when ...
AB = DC
x+4 = 12 . . . . substitute expressions for length
x = 8 . . . . . . . subtract 4
Then the lengths of AD and BC must be ...
BC = AD = x+2 = 8+2 = 10
___
The figure will be a parallelogram when x=8 and sides have lengths ...
AB = DC = 12
AD = BC = 10
_____
Comment on the problem
Of course, if x ≠ 8, or BC ≠ AD, the figure will not be a parallelogram. You are asked to show the figure IS a parallelogram, but all you can really show is that the figure CAN BE a parallelogram. In order to do anything useful with the given expressions for side lengths, you must assume the figure is a parallelogram.
Twenty years ago, you began investing $3,000 a year. Because your investments earned an average of 8 percent a year, your investment portfolio has a current dollar value of $92,000. How much did you earn on your investments over the 20-year period of time? a.) $40,000
b.) $132,000
c.) $92,000
d.) $52,000
e.) $2,000
Answer:
$32,000
Step-by-step explanation:
Yearly investment = $3,000
Number of years = 20
Investments earned an average of 8 percent a year.
Total invested amount = $3,000 × 20 = $60,000
Current value of investment = $92,000.
We need to find the total earnings on the investment.
Earnings = Current value of investment - Total invested amount
Earnings = $92,000 - $60,000
Earnings = $32,000
Therefore, the total earnings is $32,000.
To find out how much was earned on the investments over a 20-year period, we subtract the total amount invested ($60,000) from the final value of the portfolio ($92,000), yielding $32,000 as the total earnings. However, this option is not offered in the question.
Explanation:This type of question is typically encountered in personal finance or mathematics related to investment portfolios. The total amount invested over twenty years is calculated by multiplying the yearly investment by the number of years, so $3,000 * 20 years = $60,000. This is the amount you've put in from your own pocket. The value of the investment portfolio now is given as $92,000, which is the sum of your investment and the earnings. So to calculate your earnings alone, you subtract the total amount you invested from the current value of your portfolio: $92,000 (total value) - $60,000 (your total investment) = $32,000. So the amount you earned on your investments over this 20-year period is not given in the question as none of the options match our calculation of $32,000.
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Given a positive integer N, find all of the positive integers from 1 to N that can be written as a sum of 2 cubic numbers (also have to be positive) in two different ways.
Answer:
There are infinite such positive integers which can be written as a sum of cubes of two positive integers. Some of them are written below:
1³+12³=9³+10³=17292³+24³=18³+20³=1383210³+27³=19³+24³=2068315³+945³=744³+756³=843912000Hence it is not possible to write all such numbers which can be written in this format. Though some of them can be enlisted if the value of maximum integer "N" is given.
A firm is hiring labor and capital in the cost-minimizing combination. Which of the following would cause the firm to increase hiring capital and decrease hiring of labor?
The productivity of labor increases by 5% would cause the firm to increase hiring capital and decrease hiring of labor
Step-by-step explanation:
A company can convert input data to output data. So, it gets divided the data into broad categories called production factors. Productivity variations, or more precisely the marginal products of labour, work in the same way as differences in real wages. Remember that marginal prices depend on both - real wages and the productivity.
If in case, productivity increases, perhaps because the company has increased its capital base, thereby marginal costs will decrease. Companies will produce more products and employ more employees. Conversely, if productivity drops, companies will produce less and destroy jobs.
When a firm faces union demands for higher wages, they may increase hiring of capital and decrease hiring of labor. This can result in increased labor productivity. In the United States in the 1970s, firms shifted towards more capital and less labor due to union demands for higher wages.
Explanation:When a firm is confronted with union demands for higher wages, they may choose to increase hiring of capital and decrease hiring of labor. This is because using more physical capital and less labor can result in increased labor productivity.
For example, if the cost of machines increases relative to labor, the firm may shift towards using less capital and more labor to minimize costs. In this situation, the firm would hire more capital and decrease hiring of labor.
In the United States in the 1970s, this situation occurred where firms faced union demands for higher wages, causing a shift towards more capital and less labor in production methods.
A 4-inch tall box with a square base is constructed in order to hold a set of 16 identical cupcakes, each with a diameter of 2 inches. What is the area of the base, in square inches, of the smallest box that can hold the cupcakes?
Answer:
64 square inches
Step-by-step explanation:
The base is square, and there are 16 cupcakes, so there are 4 cupcakes along the width and 4 cupcakes along the length.
Each cupcake is 2 inches, so the base is 8 inches by 8 inches. Therefore, the area is 64 square inches.
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Answer:
c
Step-by-step explanation:
A pile of newspaper was 17 3/4 inches high. Each consecutive week for the next 5 weeks the height of pile increase by 8 7/12 inches. What is the height in inches, of the pile after 3 weeks?
Answer: the height in inches, of the pile after 3 weeks is 34 11/12 inches
Step-by-step explanation:
Each consecutive week for the next 5 weeks the height of pile increase by 8 7/12 inches. Converting 8 7/12 inches to improper fraction, it becomes 103/12 inches. The height is increasing in an arithmetic progression. The formula for determining the nth term of an arithmetic sequence is expressed as
Tn = a + (n - 1)d
Where
a represents the first term of the sequence.
d represents the common difference.
n represents the number of terms in the sequence.
From the information given,
a = 17 3/4= 71/4 inches
d = 103/12 inches
n = 3 weeks
the height in inches, of the pile after 3 weeks, T3. Therefore,
T3 = 71/4 + (3 - 1)103/12
T3 = 71/4 + 2 × 103/12 = 71/4 + 103/6
T3 = 419/12 inches = 34 11/12 inches
for which values of x and y is line p parallel to line q?
x=5, y=3
x=1, y=5
x=3, y=5
x=3, y=6
Answer:
x=3, y=5
Step-by-step explanation:
(16x+2) and (45x-5) are co-interior angles and they sum up to 180 degrees.
To find x
(16x+2)+(45x-5)=180
16x+45x-5+2=180
61x-3=180
61x=180+3
61x=183
x=3
(45x-5) and (26y) are corresponding angles so their values are equal
(45x-5)=(26y), x=3
(45 (3)-5)=(26y)
135-5=26y
130=26y
5=y
A long-distance phone company has a monthly fee of $7.95 and charges a rate of $0.05 per minute. Another long-distance company has a monthly fee of $9.95 and charges a rate of $0.03 per minute. At how many minutes would the two companies have equal charges?
Answer:
100 minutes
Step-by-step explanation:
Let the number of minutes required for the two Billings to be equal be x.
Now we write this in an equation form.
7.95 + 0.05x = 9.95 + 0.03x
0.05x - 0.03x = 9.95 - 7.95
0.02x = 2
x = 2/0.02 = 100 minutes
At the 100th minute, the amount of Billings would be equal
There are twelve shirts in your closet: five blue, four green, and three red. You randomly select one to wear. What is the probability it is blue or green?
A)
5
36
B)
11
12
C)
2
5
D)
3
4
Which expression is equivalent to (64 y Superscript 100 Baseline) Superscript one-half?
8y10
8y50
32y10
32y50
Answer:
[tex]8y^{50}[/tex]
Step-by-step explanation:
This expression is equal :
[tex]{(64y^{100})}^{\frac{1}{2}}[/tex]
Here we can use this rule :
[tex](a^mb^n)^y=a^{my}b^{ny}[/tex]
Now, 64 we can write like : [tex]8^2[/tex]
[tex](8^2y^{100})^{\frac{1}{2}}[/tex]
Now we can use our rule :
[tex]8^{2*\frac{1}{2}}y^{100*\frac{1}{2}[/tex]
When we simplify, we have :
8y^{50}
Answer:
b
Step-by-step explanation:
If the integers a and n are greater than 1 and the product of the first 8 positive integers is a multiple of a^n, what is the value of a?(1) a^n = 64(2) n=6
Answer:
a=2
Step-by-step explanation:
Well, first let us find product of the first 8 positive integers, which is 1*2*3*4*5*6*7*8=40320. It can also be written as 40320=[tex]2^{7}[/tex]*3²*5*7. From the formula above, it can be extracted that if a=2, n can be any number from 3 to 7 (considering that a and n are not equal and greater than 1).
In (1) a^n=64 and in (2) n=6 so it can be written as 2^6=64 so a=2 and n=6. So the value of a is 2. a=2