Mrs. Carter baked a cake that was in the shape of a rectangular prism. The cake was 24 inches long, 15 inches wide and 3 inches high. She spread frosting on all four sides and the top. How many square inches of frosting did she use?
477 inches squared
594 inches squared
954 inches squared
1080 inches squared
Answers
Mrs. Carter used 954 square inches of frosting.
To find the surface area of the rectangular prism cake, we need to find the area of all six sides and then subtract the bottom since frosting was not applied to it.
The area of the top and bottom sides is 24 x 15 = 360 square inches each.
The area of the two side faces is 24 x 3 = 72 square inches each.
The area of the two end faces is 15 x 3 = 45 square inches each.
So, the total surface area of the cake is:
2(360) + 2(72) + 2(45) = 720 + 144 + 90 = 954 square inches.
Since frosting was applied to all sides, including the top, we use this surface area to find the amount of frosting used.
Therefore, Mrs. Carter used 954 square inches of frosting.
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Related Questions
A car traveling at a rate of 54 miles per hour. What is the car's rate in feet per secondHow many fect will the car travel in 2 seconds? In your computations use the fact that mile equal to 5280 feet. Do not round your answers
Answers
The car's speed in feets per second is 79.2, Hence, it will cover a distance of 158.4 feets in 2 seconds.
Car's speed in miles per hour = 54 miles per hour
Recall :
1 mile = 5280 feets 1 hour = 3600 secondsCar's rate in feet per second
54 miles per hour = (54 × 5280 × 1/3600) feet per second = 79.2 feets per second. Distance in 2 seconds :Distance = speed × time Distance = 79.2 × 2 = 158.4 feetsTherefore, the car will cover a distance of 158.4 feets in 2 seconds.
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christina, a restaurant manager, would like to make the claim that the average number of customers that her restaurant serves per hour is more than 57. christina samples 29 hours over the course of a week and records the number of customers served and obtains a sample mean of 62 customers per hour.at the 2.5% significance level, should christina reject or fail to reject the null hypothesis given the sample data below?
Answers
Reject the null hypothesis because \($p$\)-value \($=0.0045$\) is less than the Significance level x=0.025.
What is Null Hypothesis ?The null hypothesis is a widely used statistical theory that states that for any given single observable variable, there is no statistical relationship or significance between any two sets of observed data and measured events.
According to the given information
\(& H_0: \mu=57 \\\)
\(& H_a ; \mu > 57 \\\)
\(& \alpha=0.025 \\\)
\(& \text { Test Statistic }=2.61\)
So,
This is right tailed test
\(& \text { Using } z \text { table } \\\)
\(& p(z > 2.61) \\\)
\(&= 1-p(z < 2.61) \\\)
\(&= 1-0.9955 \\\)
\(& p \text {-value }= 0.0045\)
Reject the null hypothesis because \($p$\)-value \($=0.0045$\) is less than the Significance level x=0.025.
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A) Find the constant of proportionality ( K )K =B) Find the equation Y = ____X
Answers
N 7
Part A
In a direct variation
k=y/x
take one point from the graph
(2,4)
k=4/2
k=2Part B
In a direct variation, the equation is
y=kx
we have
k=2
therefore
y=2xsomeone please explain
Answers
Explain what? What would you like help with? :)
Answer:
whats ur question
Step-by-step explanation:
Karen lee, a 63-year old woman, has osteoarthritis. what nonpharmacologic treatment should be considered? select the best answer.
Answers
For nonpharmacologic treatment, tropical non-steroidal anti-inflammatory drugs (NSAIDs) should be considered.
What is Non-pharmacological Treatment?Non-pharmacological pain therapy refers to interventions that do not involve the use of medications to treat pain. The goals of non-pharmacological interventions are to decrease fear, distress, and anxiety, and reduce pain and provide patients with a sense of control.Non-pharmacological interventions manage pain, reduce stress, encourage positive changes in mood, reduce depression, and increase awareness of self and environment. Some of the different types of non-pharmacological interventions are support groups, family support, and music therapy.Therefore option (A) Topical non-steroidal anti-inflammatory drugs (NSAIDs) is the correct answer.
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The complete question is:
Karen Lee, a 63-year-old woman, has osteoarthritis. What nonpharmacologic treatment should be considered? Select the best answer.
A) Topical non-steroidal anti-inflammatory drugs (NSAIDs)
B) Exercise
C) Intra-articular glucocorticoid injections
D) Acetaminophen
Stock Repurchase [LO4] Awake Corporation is evaluating an extra dividend ver- sus a share repurchase. In either case, $17,500 would be spent. Current earnings are $1.89 per share, and the stock currently sells for $64 per share. There are 2.000 shares outstanding. Ignore taxes and other imperfections in answering the first two questions. Evaluate the two alternatives in terms of the effect on the price per share of the stock and shareholder wealth. What will be the effect on the company's EPS and PE ratio under the two different scenarios
Answers
The effect under the scenarios are:
Choosing the extra dividend option would result in a decrease in the stock price per share and a decrease in the PE ratio.Choosing the share repurchase option would result in a lower stock price per share,The extra dividendTotal Dividend = $17,500
Dividend per Share = Total Dividend / Number of Shares
= $17,500 / 2,000
= $8.75 per share
Effect on Share Price:
Typically, when a dividend is paid, the stock price tends to decrease by the amount of the dividend. Therefore, the stock price per share would decrease by the dividend per share:
New Stock Price per Share = Current Stock Price - Dividend per Share
= $64 - $8.75
= $55.25
New Shares Outstanding = Current Shares Outstanding - Number of Shares Repurchased
= 2,000 - 273.44
= 1,726.56 shares
New Stock Price per Share = Total Amount Spent / New Shares Outstanding
= $17,500 / 1,726.56
= $10.14
EPS = Earnings / Number of Shares
= $1.89 / 2,000
= $0.000945
The PE (Price-to-Earnings) ratio is calculated by dividing the stock price per share by the EPS. Let's calculate the PE ratio under each scenario:
PE Ratio before the decision = Stock Price / EPS
= $64 / $0.000945
= 67772.49
PE Ratio with Extra Dividend = New Stock Price per Share / EPS
= $55.25 / $0.000945
≈ 58413.92
PE Ratio with Share Repurchase = New Stock Price per Share / EPS
= $10.14 / $0.000945 ≈ 10727.51
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Which segment is skew to AB?
Answers
Answer:
bh
Step-by-step explanation:
Answer
BC sorry this is a year late mate
Marquis has 7 cups of yogurt. He gives his sister 3 3
5 cups of the yogurt, how much of
Marquis’s yogurt remains?
Answers
Answer:
He has 3,65 cups of yogurt left.
Step-by-step explanation:
7 - 3,35 = 3,65
The graph shows a scatter plot for a set of data.
image of a scatter plot with Money Saved on the x axis and Money Earned on the y axis, with points 1 comma 20, 3 comma 19, 5 comma 15, 7 comma 11, 9 comma 9, 11 comma 5 and 15 comma 3
Which of the following equations is the best model for a line of fit for the data?
ŷ = −1.34x + 21.5
ŷ = 1.34x + 21.5
ŷ = −0.75x + 17
ŷ = 0.75x + 17
Answers
The equations that best model to fit the scatter plot will be; ŷ = −1.34x + 21.5. The correct option is A.
What is a scatter plot?A scatter plot is a type of graph that is used to represent the values of two variables graphically, with the resulting points indicating any association (correlation) between the data set.
We are Given that the graph shows a scatter plot for a set of data. A scatter plot with Money Saved on the x-axis and Money Earned on the y-axis, with points (1,20),(3,19),(5,15),(7,11),(9,9), and (11,5).
The model of the equation best fit for the plot will be;
ŷ = −1.34x + 21.5
At point (1,20)
ŷ = −1.34x + 21.5
20 = ( -1.34 x 1 ) + 21.5
20 ≈ 20.15
At point (3,19),
ŷ = −1.34x + 21.5
19 = (-1.34 x 3) + 21.5
19 ≈17.45
At point (5,15),
ŷ = −1.34x + 21.5
15 = (-1.34 x 5 ) + 21.5
15 ≈ 14.75
The model A ŷ = −1.34x + 21.5 gives the best estimation.
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x-intercept of 2x+4y=8
Answers
Answer:
-39/2
substitute 0 for y to find this in the future.
Consider m=[5 6; 7 8; 9 10]; What is the result of the following expression ? sum(sum( m([true false true], [false true]) ))
Answers
The result of the expression sum(sum(m([true false true], [false true]))) for the given matrix m is 16.
To find the result of the expression sum(sum(m([true false true], [false true]))), consider the matrix m=[5 6; 7 8; 9 10]. Follow these steps:
Apply the logical indexing m([true false true], [false true]): This selects the rows 1 and 3 and the second column.
The result is a new matrix:
[6; 10]
Calculate the sum of this new matrix using sum(): This will sum the elements in each column, resulting in:
[16]
Finally, apply sum() to this result: This sums the elements in the resulting array, giving the final answer:
16
So, the result of the expression sum(sum(m([true false true], [false true]))) for the given matrix m is 16.
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Write the equation of a line that passes through the point (4, 2) and is parallel to the line graphed below.
Answers
Answer:
Step-by-step explanation:
(-2, 2) (2, -3)
(-3 - 2)/(2 + 2)
-5/4 the slope
y - 2 = -5/4(x + 2)
y - 2 = -5/4x - 5/2
y- 4/2 = -5/4x - 5/2
y = -5/4x - 1/2
P= 3in
a) find the length of each side of the square
b) find the area of the square
Answers
Step-by-step explanation:
what does P mean ?
I assume it is perimeter ?
what is the perimeter of a square ?
come on, there is practically nothing in math that is easier to solve.
a square has 4 equal sides.
so, to go one time around the whole square, we have to go along every one of its 4 sides (which are all of equal length).
so, when I get the perimeter number, I know this is the result of all 4 sides added together.
and how can we express having 4 times the same number ? exactly how we say it in English : 4 times the number.
therefore
P = 4 × side length
and from there we can immediately deduct
side length = P / 4 = 3/4 in
now we know how long the sides of the square are.
what is the area of the square ?
like for any rectangle the area is length×width. just that length=width, so that we end up with length×length = length².
therefore, the area is
3/4 × 3/4 = (3/4)² = 9/16 in²
this is important : a length is measured e.g. in inches (in). an area is then measured in square-inches = in²
jon and alex play a game where they each need to kick a ball into a net. they will each kick 11 balls, but alex has a slight edge, with a 60% chance of scoring to jon's 40%. what is the probability that jon will score exactly 8 times?
Answers
The probability of scoring a goal exactly 8 times by Jon is given by 0.0234. It is obtained using the prerequisite knowledge of binomial distribution and probability.
What is Binomial Distribution in Probability?
When each trial has a probability of occurring equally likely, then the number of trials or observations is outlined using the binomial distribution. The chance of observing a specific number of successful outcomes in a specific number of trials is determined by using the binomial distribution.
Calculation of the probability of the given event
Total no. of possible outcomes, n = 11
The probability that Jon will kick the ball in the net, p(x) = 0.4
The probability that Alex will kick the ball in the net, q(x) = 0.6
Using Binomial Distribution, we get,
P(x = r) = C(n,r) × (p)r × q(n - r)
where x is the score made by Joe
P(x = 8) = C(11,8) × (0.4)8 × (0.6)3
= 0.0234
Hence, the probability that Jon will score exactly 8 times is 0.0234.
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William got scores of q sub 1, , and q sub 3 on three quizzes.
a. Write a formula for the average x of all three quizzes.
b. William got an 85 and an 88 on the first two quizzes. What formula can William use to determine the score he needs on the third quiz to get an average of 90? What score does he need?
Answers
Answer:
a. The average is =(++) .
b. He can use the formula =−− q sub 3 , equals 3 x minus , q sub 1 , minus , q sub 2. He will need a score of =()−−= q sub 3 , equals 3 open 90 close minus 85 minus 88 equals 97 on his third quiz.
Step-by-step explanation:
You found that x = -4 is the boundary point. That is the point that separates numbers that are solutions from numbers that are not solutions. What is the solution to the inequality?
-2x>8
x__-4
< > \(\leq \geq\)
Answers
The solution to the inequality -2x > 8, with the boundary point at x = -4, is x < -4.
We must isolate x on one side of the inequality in order to solve the inequality -2x > 8. We may achieve this by dividing both sides of the inequality by -2, but since we are doing so, we must also reverse the inequality's direction:
-2x > 8
x < -4
As a result, the boundary point for the inequality -2x > 8 is x = -4, and the solution is x -4. This shows that all numbers less than -4 are solutions to the inequality even while all numbers more than or equal to -4 are not. A visual illustration of this is shown below:
<====(o)
———|—————————->
zero to four infinite
As it is not less than -4, the circle at x = -4 denotes that this value is not a solution to the inequality, while the shaded area to the left of the circle depicts all the values that are.
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Solve this equation: 2b + 8 -5b + 3 = -13 + 8b -5
Answers
Answer: 2=6-8
Step-by-step explanation:-
Answer:
b=2.64
I think that's the answer
Step-by-step explanation:
combine like terms
-3b+11=-18+8b
move them
29=11b
divide
b=2.64
sam walks from home to his school which is 0.75 miles away in 12 minutes. how fast was he walking?
Answers
Answer:
3.75mph, or 0.0625 miles a minute
Step-by-step explanation:
12 times 5 is 60
.75 times 5 is 3.75
so he was walking mathematically 3.75 miles per hour
Answer:
3.75 mph
Step-by-step explanation:
12 minutes is 0.2 hours
0.75/0.2 = 3.75 mph
Joannie lent $200 to her sister. 4 years later, her sister repaid her in full with $228. What simple annual interest rate did joannies sister pay?
Answers
Answer:
$7/year
Step-by-step explanation:
228-200 = 28
divide by the 4 years : 28/4= 7
if ahmod has 2 times as many dimes as nickels and they have a combined value of 100 cents, how many of each coin does he have?
Answers
Finally ahmod will have 4 nickels and 10 dimes.
Ahmod has two times as many dimes as nickels.
They have a combined value of 100 cents.
Group all coins in sets by grouping each nickel with 2 dimes.
Each set, containing 1 nickel and 2 dimes, is worth 5 + 2*10 = 25 cents.
You will have 100/25 = 4 such groups
As we have 4 such groups at last ahmod will have 4 nickels and 10 dimes.
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Is 1.875 an rational or irrational number
Answers
Answer:
it is rational
Step-by-step explanation:
because our is a finite decimal which can be converted into a fraction
The formula t = 2 pi startroot startfraction l over 32 endfraction endroot relates the time, t, in seconds for a pendulum with the length, l, in feet, to make one full swing back and forth. what is the length of a pendulum that makes one full swing in 2.2 seconds? use 3.14 for pi. 2 feet 4 feet 11 feet 19 feet
Answers
The length of this pendulum that makes one full swing is 3.93 meters.
How to calculate the length of the pendulum?Mathematically, the time taken by this pendulum is given by this formula:
\(\rm T=2\pi \sqrt{\dfrac{L}{32}}\)
Making L the subject of the formula, we have:
\(\rm T=2\pi \sqrt{\dfrac{L}{32}}\\\\32T^2=4\pi ^2L\\\\L=\dfrac{32T^2}{4\pi ^2}\\\\\)
Substitute all the values in the formula
\(\rm L=\dfrac{32T^2}{4\pi ^2}\\\\ L = \dfrac{32 \times 2.2^2}{4 \times 3.14 ^2\\}\\\\ L =\dfrac{154.88}{39.43}\\\\L=3.93 \ m\)
Hence, the length of this pendulum that makes one full swing is 3.93 meters.
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Answer:
Basically if your coming from edge its 4 ft so B
Step-by-step explanation:
A student uses the equation tan theta= s^2/49 o represent the speed, s, in feet per second, of a toy car driving around a circular track having an angle of incline theta where sin theta =1/2
Answers
After finding the value of theta, the speed of the toy car driving around the circular track with an angle of incline theta, where sin(theta) = 1/2, is equal to √(7√3) feet per second.
The equation tan(theta) = s^2/49 represents the speed, s, in feet per second, of a toy car driving around a circular track with an angle of incline, theta, where sin(theta) = 1/2.
To solve this problem, we need to use the given information about sin(theta) to find the value of theta. Since sin(theta) = 1/2, we can determine that theta is equal to 30 degrees.
Now that we know the value of theta, we can substitute it into the equation tan(theta) = s^2/49. Plugging in 30 degrees for theta, the equation becomes tan(30) = s^2/49.
The tangent of 30 degrees is equal to √3/3. So, we have √3/3 = s^2/49.
To solve for s, we can cross multiply and solve for s^2. Multiplying both sides of the equation by 49 gives us 49 * (√3/3) = s^2.
Simplifying, we get √3 * 7 = s^2, which becomes 7√3 = s^2.
To find the value of s, we take the square root of both sides. So, s = √(7√3).
Therefore, the speed of the toy car driving around the circular track with an angle of incline theta, where sin(theta) = 1/2, is equal to √(7√3) feet per second.
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Add. Write your answer as a fraction or as a whole or mixed number.4 7/11 + 7 8/11
Answers
11 15/11 = 12 4/11
Answer:
The answer is12 4/11
Step-by-step explanation:
4+7=11 7/11+8/11
= (7+8)/11
= 15/11
= 1 4/11
=11+1 4/11
=12 4/11
Determine if the given relation is function or not. Give its domain and
range.
{(1, 6), (2, 7), (3, 8), (4, 9)}
Answers
Answer:
YesStep-by-step explanation:
According to definition of the function, it should have one-to-one relation.
We can see all pairs are unique, no repeated ranges for same domain.
Yes, this is a function.
Given relationship
(1,6)(2,7)(3,8)(4,9)Domain:-
{1,2,3,4}Range:-
{6,7,8,9}As every domain has an unique range it's a function
solve x and y simultaneously if:
\(y + 7 = 2x\)
\( {x}^{2} - xy + {3y}^{2} = 15\)
Answers
Answer:
make Y the subject in eqn........ 1
y + 7 = 2x
y = 2x - 7...........eqn 3
put y = 2x - 7 into eqn 2
x² - xy + 3y² = 15
x² - x(2x - 7) + 3(2x - 7)(2x - 7) = 15
x² - 2x² + 7x + 3(4x² + 14x -14x + 21) = 15
x² - 2x² + 7x + 12x² + 42x - 42x + 63 = 15
x² - 2x² + 7x + 12x² + 63 = 15
x² - 2x² + 12x² + 7x + 63 = 15
11x² + 7x + 63 - 15 = 0
11x² + 7x + 48 = 0
11x² + 7x = - 48
11x²/11 + 7x/11 = - 48/11
x² + 7x
The number of fish caught on a fishing trip varies directly as the number of boats that are fishing. There are 800 fish caught when 16 boats are fishing. How many fish will be caught if 6 boats are fishing? 300
Answers
Answer:
300 fish
Step-by-step explanation:
First you divide the 800 by 16 then you get 50
Next you multiply the 50 by 6
Finally you get the answer 300 fish
Sectionalism:Question 10
What was the main reason that most northerners were opposed to the
new Fugitive Slave Act created by the Compromise of 1850?
Answers
Answer:
They felt it gave the commissioners too much power and was unfair to slaves by giving them a trail without injury
5-(-5) please i need a answer ASAP
Answers
Answer:
10.
Step-by-step explanation:
If you're subtraction a negative number, you are basically adding a positive number. 5-(-5) = 5+5.
Hey there!
GUIDE:
2 negatives = positive
2 positives = positive
1 negative & 1 positive = negative
1 positive & 1 negative = negative
Negatives are BELOW 0 and they are to the LEFT of 0
Positives are ABOVE 0 and they are to the RIGHT of 0
ANSWERING the QUESTION
5 - (-5)
= 5 + 5
= 10
Therefore, your answer is: 10
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Kiran has 10 1/2 feet of lumber and wants to make a bookshelfKiran needs two side panels that are each 5 2/3 feet. How much more lumber does Kiran need in order to make the side panels?
Answers
Total height of lumber, H = 10 1/2 feet = 21/2 feet .
Height of side panel, h = 5 2/3 feet = 17/3 feet .
Now,
Extra lumber required, L = 2 × Height of side panel - Total height of lumber
\(L=[2\times (\dfrac{17}{3})]-\dfrac{21}{2}\\\\L = \dfrac{5}{6}\ feet\)
Therefore, extra lumber required is \(\dfrac{5}{6}\) feet.
Hence, this is the required solution.