Answer:
A 2.5 years
Step-by-step explanation:
When the dimensions of a cube are reduced by 4 inches on each side, the surface area of the new cube is 864 square inches. What where the dimensions of the original cube?
Answer:
The dimensions of the original cube are 16 in x 16 in x 16 in
Step-by-step explanation:
Let
x ----> the length side of the original cube
The surface area of the cube is equal to
[tex]SA=6b^2[/tex]
where
b is the length side of the cube
we know that
The dimensions of a cube are reduced by 4 inches on each side and the surface area of the new cube is 864 square inches
so
The length side of the new cube is
[tex]b=(x-4)\ in[/tex]
substitute in the formula of surface area
[tex]SA=6(x-4)^2[/tex]
[tex]SA=864\ in^2[/tex]
so
[tex]6(x-4)^2=864[/tex]
Simplify
[tex](x-4)^2=144[/tex]
take square root both sides
[tex](x-4)=(+/-)12[/tex]
[tex]x=4(+/-)12[/tex]
[tex]x=4(+)12=16\ in[/tex]
[tex]x=4(-)12=-8\ in[/tex] ----> the length side cannot be a negative number
therefore
The dimensions of the original cube are 16 in x 16 in x 16 in
To find the dimensions of the original cube, set up an equation using the surface area of the new cube and solve for the original side length.
Explanation:To find the dimensions of the original cube, we need to work backwards.
First, let's find the surface area of the original cube. If we reduce each side of the cube by 4 inches, the new side length would be 'x-4'. The surface area of the new cube is given as 864 square inches. So we have the equation: (x-4)^2 = 864 Solving this equation, we find that the side length of the original cube is 22 inches.
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is 5.871 greater than or equal to 5.781
the ratio of boys to girls in a class is 5:4 there are 36 students in the class how many students are girls
Final answer:
To find the number of girls in the class, you calculate the value of each part of the ratio by dividing the total number of students by the sum of the ratio parts, and then multiply the result by the number of parts for girls, which gives us 16 girls.
Explanation:
The question involves finding the number of girls in a class where there is a given ratio of boys to girls and a total number of students. In this case, the ratio of boys to girls is 5:4, and there are 36 students in the class. To solve for the number of girls, we can use the concept of ratios. First, combine the parts of the ratio to find the total parts in the ratio, which is 5 + 4 = 9 parts. Each part is then equal to the total number of students divided by the total parts, which is 36 students \/ 9 parts = 4 students per part. Since the ratio of boys to girls is 5:4, we know that girls constitute 4 parts of the total. Thus, the number of girls can be calculated by multiplying 4 (the number of parts for girls) by 4 students per part, resulting in 16 girls in the class.
Steven has a rectangular closet the length is 10 feet and the width is 48 inches determine the area of the closet in square feet.
The directions on a seed packet day to plant the seeds 1 7/8 inches apart. What is the decimal equivalent of this mixed number.
Answer:
1.875 inches
Step-by-step explanation:
We are given that the direction on a seed packet day to plant the seeds apart=[tex]1\frac{7}{8}[/tex] inches
We have to find the decimal equivalent to given fraction.
In order to find the value of given fraction in decimal we will convert mixed fraction into simple fraction.
[tex]1\frac{7}{8}\; inches=\frac{15}{8}[/tex] inches
Now, divide 15 by 8
Then, we get [tex]\frac{15}{8}=1.875[/tex]
Therefore, the value of given fraction =1.875 inches
Your sports drink bottle is 5/6 full. After practice, the bottle is 3/8 full. Write the difference of the amounts after practice and before practice. Write your answer as a fraction in simplest form.
Answer:
its -11/24
Step-by-step explanation:
how does understanding place value help you to subtract across zeros
Marisol plans to make 9 mini-sandwiches for every 2 people attending her party. Write a ratio that is equivalent to marisol's ratio.
Solve for e. 9e-7=7e-11
The value of e is -2.
To solve the equation 9e - 7 = 7e - 11, follow these steps:
Move all terms involving e to one side of the equation:
9e - 7e = -11 + 7
Combine like terms:
2e = -4
Divide both sides by 2 to solve for e:
e = -2
Thus, the value of e is -2.
HELP ME PLEASE!! MATHEMATICS
The school gym can hold no more than 650 people. The bleachers will seat 176 people. The PTA is setting up 25 rows of chairs for their meeting. At most, how many chairs can be in each row? A) 18 B) 19 C) 26 D) 27
Answer A (18
Step-by-step explanation:
Solve for s. 23s+56s=21 Enter the answer, as a whole number or as a fraction in simplest form, in the box.
Choose the correct simplification of the expression (7ab3)2.
Answer:
[tex]49a^2b^6[/tex]
Step-by-step explanation:
The given expression is:
[tex](7ab^3)^2[/tex]
Now, squaring the above expression, we get
=[tex](7)^2(a)^2(b^3)^2[/tex]
=[tex]49(a^2b^6)[/tex]
=[tex]49a^2b^6[/tex]
which is the required simplification of the given expression.
Thus, the correct simplification of the expression [tex](7ab^3)^2[/tex] is [tex]49a^2b^6[/tex].
If one side of a square is 8 inches, what is the perimeter of the square?
A barrel holds 50L how many gallons is this
Joe has a savings account and a credit card. He has $422 saved in his savings account and has purchased $484 worth of merchandise on his credit card. Use positive and negative numbers to explain the sitiuation. Is Joe's overall balance represented by a positive or negative number? Justify your answer.
write an equation in function form 3x-y=7
One advantage of credit-card buying is the monthly list of expenditures you receive. True or False
Answer: False .
Step-by-step explanation:
False, it is not an advantage of credit-card buying to get the monthly list of expenditures.
As if we use credit card for every purchase, our liability would get increase, and to burden to pay off with interest will be increased as well.
So, it will be disadvantage instead of advantage to use credit card for every buying.
what is the measure of <rst
The measure of the angle ∠RST will be 81°. Then the correct option is B.
What is a circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
The central angle is double the angle at the periphery that was subtended by the same chords.
The measure of the central angle of the sector of the circle is 162°.
Then the measure of the angle ∠RST is half of the central angle. Then we have
∠RST = 162° / 2
∠RST = 81°
The measure of the angle ∠RST will be 81°. Then the correct option is B.
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Which inequality models this problem?
Miranda started a car-washing business. She spent $75 to purchase supplies to get started and she uses about $0.50 worth of supplies per car washed. Miranda charges $9 for each car washed. Let c represent the number of cars.
What is the minimum number of cars Miranda will need to wash to make a profit?
9c>75+0.5c
0.5c>75+9c
9c<75+0.5c
0.5c≥75+9c
Answer:
9c>75+0.5c Is your answer
Step-by-step explanation:
I took the test :3
Good luck
how do you find the power of 35,036 1/3
Final answer:
To find the power of 35,036 to the 1/3 exponent, you can use the formula (a^b)^c = a^(b*c). The cube root of 35,036 is approximately 32.41.
Explanation:
To find the power of 35,036 to the 1/3 exponent, you can use the formula (a^b)^c = a^(b*c). In this case, a = 35,036 and b*c = 1/3. So, the power of 35,036 to the 1/3 exponent is 35,036^(1/3).
Now, to evaluate this expression, you can find the cube root of 35,036 using a calculator. The cube root of 35,036 is approximately 32.41. Therefore, the power of 35,036 to the 1/3 exponent is approximately 32.41.
Danielle is saving to buy a flat screen television that cost $510. She wants to know how long it will take to save the money and writes the expression 510 ÷ [(35×11)]. Will Daniels expression help her find how long it will take to save the money she needs? Explain your answer.
Danielle's expression doesn't provide the correct time frame for saving unless $385 is her savings rate. She needs to divide the cost of the television by her regular savings amount to find the needed time to save.
Explanation:Danielle is trying to figure out how long it will take to save enough money to buy a flat screen television that costs $510. However, her expression 510 ÷ (35×11) will not accurately give her the information she needs unless $385 (which is 35×11) represents her monthly savings or some other specific saving interval. To determine how long it will take to save the money, Danielle would need to know her savings rate per week, month, or another interval of time and then divide the total cost of the television by that rate.
For example, if Danielle can save $50 each month, the correct expression would be $510 ÷ $50/month. This would yield 10.2 months, assuming she can save that amount consistently every month without any additional costs or interest. Budgeting and cutting unnecessary expenses can also help Danielle accelerate her savings plan. If she finds ways to increase her savings rate by reducing discretionary spending, she would be able to purchase her desire faster.
21 and 61 which is composite and which is prime
A popular chain of superstores made 3.0479×108 dollars in profit last year. One particular store in the chain made 2.102×106 dollars in profit last year. How many times greater is the profit made by the entire chain last year than by this particular store? Drag and drop the values into the boxes to represent the answer in scientific notation. 0.145
1.45
145
10²
10^14
10^48
find 1/2 of 5 less than 10
Which equation is equivalent to 2/3x - 5/6 = -5/12x + 1/4 ?
A. -5/6 = 1/4 X +1/4
B. 2/3 X = -5/12 X -7/12
C. 1/4 X-5/6 = 1/4
D. 2/3 X -13/12 = -5/12 x
Answer:
The answer is D
Step-by-step explanation:
2/3x-5/6=5/12x+1/4
x=1
the only option that x=1 is
2/3x-13/12=-5/12x
What is the best estimate for the following expression: 6.79 - (-3.2)?
10
9
4
1
Hiiiii pleaseeeee helppppp understand how to do this I want to understand.
Two bicyclists are 180 miles apart when they start racing towards each other. If their speeds are 14 mph and 16 mph respectively, how long will it be before they are twenty miles apart?
The table shows the number of flowers in four bouquets and the total cost of each bouquet.
What is the correlation coefficient for the data in the table?
–0.57
–0.28
0.28
0.57
we know that
The correlation coefficient is a number between [tex]-1[/tex] and [tex]+1[/tex] that represent the linear dependence of two variables or sets of data
Using the function CORREL in a excel tool, calculate the correlation coefficient (r)
see the attached table
the correlation coefficient for the data in the table is equal to [tex]0.28[/tex]
therefore
the answer is
[tex]0.28[/tex]
It should be noted that in the table, the correlation coefficient for the data is C. 0.28.
Correlation coefficient.It should be noted that a correlation coefficient simply means the number that's between -1 and +1.
It represents the linear dependence between the two variables. In this case, the correlation coefficient for the data is 0.28.
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