Vertically stretching the equation[tex]Y=x^3[/tex] by a factor of 4 results in the equation [tex]Y=4x^3[/tex]. This means that the value of the function increases four times for every x. Visually, the stretched function appears steeper along the y-axis.
Explanation:The equation represents[tex]Y=x^3[/tex] a cubic function. When you vertically stretch a function by a factor of 4, this means you multiply the output (Y-values) of the function by 4. Therefore, to vertically stretch Y=x3 by a factor of 4, you will multiply the entire function by 4. The final equation would look like [tex]Y=4x^3[/tex]
To clarify, the 'stretch' implies that for each x, the value of the function increases four times. This change can is noticeable graphically as the function will look 'steeper' or 'more stretched out' along the y-axis.
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In winter, the price of apples suddenly went up by \$0.75$0.75dollar sign, 0, point, 75 per pound. Sam bought 333 pounds of apples at the new price for a total of \$5.88$5.88dollar sign, 5, point, 88.
Write an equation to determine the original price per pound (p)(p)left parenthesis, p, right parenthesis.
Your formula would be 3(p+0.75)=5.88
Because you have 3 pounds and 0.75 for each.
Solving the equation by distributing, you will get P=1.21
Hope this helps!
The equation will be 3 (p + 0.75) = 5.88. Then the original price per pound p will be 1.21.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
In winter, the price of apples suddenly went up by a $0.75 dollar sign per pound. Sam bought 3 pounds of apples at the new price for a total of $5.88 dollar sign.
The original price per pound p will be
3 (p + 0.75) = 5.88
p + 0.75 = 1.96
p = 1.96 - 0.75
p = 1.21
The equation will be 3 (p + 0.75) = 5.88. Then the original price per pound p will be 1.21.
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The Kendal Company manufactures automobile engine parts. Running the manufacturing operations requires 12 watts (units of electricity per hour). The amount of electricity required to run the manufacturing operations and lighting the facility is given by y = 12x + 24, where x is the number of hours of manufacturing and y is the amount of electricity expended. How much electricity is used on a day when no parts are manufactured? (x 0, y 0)
Answer:
The answer is 24 watts.
Step-by-step explanation:
Running the manufacturing operations requires 12 watts (units of electricity per hour).
The amount of electricity required to run the manufacturing operations and lighting the facility is given by [tex]y=12x+24[/tex]
Here x is the number of hours of manufacturing and y is the amount of electricity expended.
When there are no parts manufactured, then x = 0
[tex]y=12(0)+24[/tex] = 24.
what is 3(7x-6)<-81?
Natalia is making gift bags for her son's birthday party. Each bag costs $3.24 to make and she needs to make 15 bags. How much will the 15 bags cost?
A.) $48.60
B.) $47.40
C.) $486.00
D.) $4.74
Answer:
48.60
Step-by-step explanation:
The answer is $48.60 you just have to multiply the amount of bags times the cost of each bag to get your amount so
15 x 3.24 =48.60
The Hamptons family has a fish tank holding 10,450 ml of water. The water is leaking at a rate of 270 ml per minute. Define the input and output in the given scenario
The input is any variable which goes into the system. In this case there is no input.
While the output is any variable going out of the system. In this case the output is the amount of water which leaked out.
Answer:
The number of minutes represents input and remaining water represents output.
Step-by-step explanation:
Given,
The original quantity of the water in the tank = 10,450 ml,
Also, the quantity of the water leaked per minute = 270 ml,
Thus, the quantity water leaked in x minutes = 270x
∵ Remaining water in the tank ( say y ) = Original water - leaked water
⇒ y = 10450 - 270x,
Which is the equation that shows the given scenario.
In this equation, x represents the input value and y represents the output value,
Hence, the number of minutes represents input and remaining water represents output.
About 36,100,000 households in the U.S. have cats and about 43,300,000 households have dogs. About how may more households dogs and cats
I thought of a number, multiplied it by 2 1/2 , divided the result by 1 1 /5 , subtracted 7/18 from it, and got 1 5/6 . What was my number?
The student's original number was 1 3/45. This was obtained by reversing the processes described in the problem and applying them to the final number.
Explanation:
To solve this problem, we basically need to reverse the operations given in the problem and perform them on the final answer 1 5/6. Let's start:
Add 7/18 to 1 5/6. The sum is 2. Multiply 2 by 1 1/5. The product is 2 2/5. Finally, divide 2 2/5 by 2 1/2. The quotient, which is the number the student originally thought of, is 48/45 or 1 3/45.
So the student's original number was 1 3/45.
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Mark draws one card from a standard deck of 52. he receives $ 0.35 for a heart, $ 0.55 for a jack and $ 0.85 for the jack of hearts. how much should he pay for one draw
To find out how much Mark should pay for one draw, calculate the expected value by multiplying the payouts for a heart, a jack, and the jack of hearts by their respective probabilities. Sum these values to find the amount Mark should pay per draw to make the game fair, which is $0.135.
To determine how much Mark should pay for one draw from the deck of 52 cards, we need to calculate the expected value (EV) of one draw. The EV is calculated by multiplying each outcome by its probability and summing these products.
The deck has 13 hearts, so the probability of drawing a heart (excluding the jack of hearts) is 12/52 or 3/13. Drawing any jack other than the jack of hearts has 3 possible outcomes in the remaining 51 cards; the probability is 3/52. The jack of hearts is a single card with a probability of 1/52. The remaining 36 cards are neither hearts nor jacks and yield no payout.
The EV is calculated as follows:
(12/52 × $0.35) for a heart
(3/52 × $0.55) for a jack
(1/52 × $0.85) for the jack of hearts
Adding these up we get: (3/13 × $0.35) + (3/52 × $0.55) + (1/52 × $0.85) = $0.13538. To ensure the game is fair and the host neither loses nor gains money in the long term, Mark should pay $0.135 per draw.
An arithmetic sequence with a thrid term of 8 and constant difference of 5
A crane cable can support a maximum load of 20,000 kg. If a bucket has a mass of 4,000 kg and gravel has a mass of 1,500 kg for every cubic meter, how many cubic meters of gravel (g) can be safely lifted by the crane?
Answer:
10.67 kg of gravel can be safely lifted by the crane
Step-by-step explanation:
Maximum load that a crane can support = 20000 kg.
Bucket has a mass = 4000 kg
Gravel has a mass = 1500 kg for every cubic meter.
Let the volume of gravel is = g cubic meter
Therefore, mass of the gravel = 1500g kg
Now we form an equation to show the weight that the crane cable can support
Mass of Bucket + mass of Gravel = Total mass that a lift can support
4000 + 1500g = 20000
1500g = 20000 - 4000
1500g = 16000
[tex]g=\frac{16000}{1500}[/tex]
g = 10.67 kg
Therefore, 10.67 kg of gravel can be safely lifted by the crane.
Stan and hilda can mow the lawn in 35 min if they work together. if hilda works twice as fast as stan, how long would it take stan to mow the lawn alone?
Grandpa Schmidt is 75 years old this is nine years less than seven times the age of Junior submit how old is Junior
what is the measure of an angle that turns through 1/12 of a circle
The measure of an angle that turns through 1/12 of a circle is 30 degree.
What is Angle?A pair of rays (half-lines) with a shared terminal are combined to form an angle. The latter is referred to as the angle's vertex, and the rays are sometimes referred to as the angle's legs and other times as its arms.
We know the complete is 360 degree.
Then, to turn 1/12 of circle
= 360 x 1/2
= 360 / 12
= 30 degree
Thus, the measure of angle is 30 degree.
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What is the distributive property of 60 - 50?
what is( ×+4 /6)=(18/12)
The store keeper sold 9 1/4 yards from a piece of material containing 53 yards. How much was left in the original piece?
Find the inverse of f(x)= -x + 3
The square root of 2.25 is
A.15
B.1.5
C.0.15
D.irrational
Is it possible for two different numbers, when squared, to give the same result? What does this result tell you about solving an equation when the variable is squared? How many solutions will an equation like this have? Will there always be the same number of solutions for any equation with a squared variable? Explain.
At the half ime show, a marching band marched in formation. the lead drummer started at a point with coordinates (–2, –5) and moved 3 steps up and 1 step right.
a. write a rule to describe the translation.
b. what were the coordinates of the drummer's final position?
how would you translate this into an equation
"one less than the product of number and 3 is 5 more than the number itself "
Thirty-five states in a country have four-star hotels. Assume the country has 50 states. (a) What fraction of the states can claim at least one four-star hotel? (b) How many states do not have a four-star hotel? (c) Write the fraction of states without a four-star hotel.
a. The fraction of states with a four-star hotel ........ (Simplify your answer.)
The fraction of states with at least one four-star hotel is 7/10, 15 states do not have a four-star hotel, and the fraction of states without a four-star hotel is 3/10.
Answer to Student's Question
(a) To find the fraction of states with at least one four-star hotel, we divide the number of states with a four-star hotel by the total number of states. Therefore, the fraction is 35/50, which simplifies to 7/10.
(b) To determine how many states do not have a four-star hotel, we subtract the number of states with a four-star hotel from the total number of states: 50 - 35 = 15. So, there are 15 states without a four-star hotel.
(c) Finally, the fraction of states without a four-star hotel is the number of states without such hotels divided by the total number of states. This is 15/50, which can be simplified to 3/10.
Find an equation of the sphere with points p such that the distance from p to a(−3, 6, 4) is twice the distance from p to b(5, 3, −2).
Find a linear function that gives the cost in dollars of buying
Pop tarts on sale two boxes cost four dollars four boxes cost six dollars
x + y = 12
x - y = 10
What is the value of the x-determinant for the system shown?
(A.) -22
(B.) -12
(C.) -2
Final answer:
The value of the x-determinant for the system of equations is (C) -2, which is found by evaluating the determinant of the system's coefficient matrix.
Explanation:
To find the x-determinant for the system of equations given below:
x - y = 10
We can set up the coefficient matrix for these equations:
Matrix [A] =
| 1 1 |
| 1 -1 |
The determinant of this matrix is calculated by multiplying the diagonal elements and then subtracting the product of the off-diagonal elements. Hence, the determinant (det A) = (1)(-1) - (1)(1) = -1 - 1 = -2.
Therefore, the value of the x-determinant is (C) -2.
Let point C be between V and W on VW. Given that VW = 61, VC = z + 13, and CW = z + 8, solve for z. A. 18 B. 19 C. 20 D. 21
Only individuals over the age of 60 need to create an estate plan? True or False
Answer: False
Step-by-step explanation: People of any age over 21 need to complete an estate plan or a will. If you don't complete an estate plan or a will, anything you have could be left to the government. Regardless of your age or income, you always want to have a plan to distribute your money should you die unexpectedly.
How many ways are there to separate these 10 people into two groups, if no group can have less than 2 people?
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A soccer player runs 1 5/6 miles during the first half of a match and 2 1/2 miles during the second half. How many miles does he run during the match in total?