By using the concept of volume of a sphere, the result obtained is
Radius of the tennis ball = 1.35 inch
What is Volume of a sphere?
Volume of the sphere is the total space taken by the sphere.
If r is the radius of the sphere, then the volume of the sphere is given by the formula
V = [tex]\frac{4}{3}\pi r^3[/tex]
Let the radius of the ball be r inch
Volume of the ball = [tex]\frac{4}{3}\pi r^3[/tex]
= [tex]\frac{4}{3} \times 3.14 \times r^3[/tex]
By the problem,
[tex]\frac{4}{3} \times 3.14 \times r^3 = 10.31\\r^3 = \frac{10.31 \times 3}{4 \times 3.14}\\r^3 = 2.46\\r = \sqrt[3]{2.46}\\ r = 1.35\ in[/tex]
Radius of the tennis ball = 1.35 inch
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Question 5 (1 point)
What is the area of the figure?
5 cm
11.0 cm
20.0 cm
1 cm
2cm
3 cm
The area of the given figure is 25cm².
Area of rectangle
Area = length x width
Perimeter of rectangle
Perimeter = length + length + width + width
Hence, we have
length = 5cm
width = 5cm
then, by applying the Area of the rectangle, we get
Area = length x width
Area = 5 x 5
= 25cm²
Hence, The area of the given figure is 25cm².
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A university reported that its enrollment increased from 11,937 students in 2005-2006 to 12,256 students in 2006-2007.
a. What is the ratio of the number of students in 2006-2007 to the number of students in 2005-2006?
b. From your result in part a, determine the growth factor. Write it in decimal form to the nearest thousandth.
c. By what percent did the enrollment increase?
a.
The ratio of the number of students in 2006-2007 to the number of students in 2005-2006 is = 12,256 : 11,937
b.
Growth factor = (12256-11937)/11937
= 0.02672.
c.
Increase in percent = 100* (12256 - 11937)/11937
= 100 * 0.02672
= 2.672%
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BD = 3x, CD = x + 16
what does X =
Answer:
x = 8Step-by-step explanation:
from the figure we understand that it is an isosceles triangle, therefore 2 sides and two congruent angles, BD and CD are congruent, therefore 3x = x + 16.
let's solve
3x = x + 16
2x = 16
x = 8
-----------------------------
check
3 × 8 = 8 + 16
24 = 24
thee answer is good
Use the definition of exponents as repeated multiplication to simplify. Enter only the simplified expression (2/3)^2
The expression (2/3)² when simplified by repeated multiplication is 4/9
How to evaluate the expression?From the question. the expression is given as
(2/3)²
We start by rewriting the expression using repeated multiplication
This in other words means that:
We rewrite the (2/3)² as repeated multiplication
To do this, we apply the exponent rule of indices
This rule states that:
a^m = a * a * a .... in m places
So, we have
(2/3)² = (2/3) x (2/3)
Evaluate the products
(2/3)² = 4/9
Hence, the equivalent expression is 4/9
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Simplify.
2x-4
²-8+12
O
O
O
-6
x+6
x-6
-
x-2
²-82+12
The simplified value of (2x - 4)² is 4x² - 16x + 16.
First, let us understand the algebraic identities;
Algebraic identities are equations in which the left hand side of the equation is identically equal to the right hand side of the equation.
Some of the identities are:
(a + b)² = a² + 2ab + b²(a - b)² = a² - 2ab + b², etc.We are given (2x - 4)².
Use the identity (a - b)² = a² - 2ab + b² to expand to the given expression.
So, a = 2x and b = 4.
Put it into the identity, we will get;
Therefore,
(2x - 4)² = (2x)² - 2 * 2x * 4 + (4)² = 4x² - 16x + 16
Thus, the simplified value of (2x - 4)² is 4x² - 16x + 16.
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PLS HELP! 30 POINTS!!!!!
A Linear equation in standard form is
2x + y = -4
slope of the function = -2
the perpendicular line equation in standard form -x + 2y = -6
How to find slope of linear equationA standard equation is of the form Ax + By = C
A = 2
B = 1
C = -4
Rearranging the equation to the slope intercept form of the form as
y = mx + c
where
m = slope
c = intercept
x = input variables
y = output variables
Ax + By = C
By = -Ax + C
y = -Ax/B + C
calculation of slope
m = -A/B
substituting the values of A and B
m = - 2/1
m = -2
a new perpendicular slope, m' is given by
m' = -1/m
plug in the value of m
m' = -(1/-2)
m' = 1/2
new equation passing through point (8, 1)
(y - y₁) = m' (x - x₁)
y - 1 = 1/2(x -8)
y - 1 = x/2 - 4
y = x/2 - 3
writing in standard form
y = x/2 - 3
2y = x - 6
-x + 2y = -6
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Sophie determine that the function describing the cost of dinner is linear if you order X eggrolls your dinner will cost 1.50x + $10 what is the per egg roll fee?
Sophie determine that the function describing the cost of dinner is linear if you order X eggrolls your dinner will cost 1.50x + $10 what is the per egg roll fee?
1.50x + $10
per egg roll fee is $1.50
(x^2+4)/(x^3+x^2+4x+4)=
The solution is 1/(x+1)
From the question, we have
(x^2+4)/(x^3+x^2+4x+4)
=(x^2+4)/(x^2 (x^3/x^2 +x^2/x^2 )+2^2 ((2^2⋅x)/2^2 +2^2/2^2 ) )
=(x^2+4)/(x^2 (x^(3-2)+1)+2^2 (x+1))
=(x^2+4)/(x^2 (x+1)+2^2 (x+1))
=(x^2+4)/((x+1)((x^2 (x+1))/(x+1)+(2^2 (x+1))/(x+1)) )
=(x^2+4)/((x+1)(x^2+2^2 ) )
=(x^2+4)/((x+1)(x^2+4) )
=1/(x+1)
The solution is 1/(x+1)
Divide:
Split is to divide into two or more equal sections, places, groupings, or divisions in its most basic form. To divide something simply means to provide it to a group in equal quantities or to cut it up into equal pieces. Let's imagine a diagonal divides a square into two triangles with equal areas. An integer may or may not be the result of a division operation. Sometimes the result will be expressed as decimal numbers.
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You can tell that is an irrational number because it has a what?
Answer:
Can't be written as fraction
Step-by-step explanation:
Irrational Numbers are Real Numbers which are not rational , which means that it can't be written as fraction
5 Math on the Spot Robin says, "I can find 6 × 9 by
multiplying 4 X 9 and doubling it." Does her statement
make sense? Justify your answer.
If Robin says, "I can find 6 × 9 by multiplying 4 X 9 and doubling it, her statement didn't make any sense because it is not possible.
What is distributive property?
The same outcome will be obtained by multiplying the sum of two or more addends by a number as it is by multiplying each addend separately by the number and then adding the resulting products.
A × (B + C) = AB + AC
A (B - C) = AB - AC
Here,
we can write 6 × 9 as,
= 6 × 9 = 6 × (6 + 3) = (6 × 6) + (6 × 3), by applying distributive property
Hence, If Robin says, "I can find 6 × 9 by multiplying 4 X 9 and doubling it, her statement didn't make any sense because it is not possible.
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Graph the line with slope 1/3 and y-intercept −2.
What is the sale price including tax to the nearest cent? $595 refrigerator, 20% discount; 9.25% tax
The sale price including tax for the refrigerator is $520.
How to calculate the price?From the information, the following can be deduced:
Refrigerator = $595
Discount = 20%
Tax = 9.25%
The sales price will be:
= Refrigerator price + Tax - Discount
= $595 + (9.25% × $595) - (20% × 650)
= $595 + $55 - $130
= $520
The price is $520.
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The Acme Candy Company claims that 60% of the jawbreakers it produces weigh more than 4 ounces. Suppose that 800 jawbreakers are selected at random from the production lines. Would it be unusual for this sample of 800 to contain 528 jawbreakers that weigh more than .4 ounces?
It would be unusual for this sample of 800 to contain 528 jawbreakers that weigh more than .4 ounces, using the binomial distribution, as 528 is more than 2.5 standard deviations above the mean.
What are unusual values in the binomial distribution?The binomial distribution gives the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The mean of the binomial distribution is of:
E(X) = np.
The standard deviation of the binomial distribution is of:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
The unusual measures are the ones that are more than 2.5 standard deviations from the mean.
The values of the parameters in this problem are given as follows:
p = 0.6, n = 800.
Hence the mean and the standard deviation are given as follows:
Mean: 800 x 0.6 = 480.Standard deviation: [tex]\sqrt{800 \times 0.6 \times 0.4} = 13.86[/tex]The upper bound of usual values is of:
480 + 2.5 x 13.86 = 514.65.
528 > 514.65, hence it is an unusual value.
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7/2a+4/2a^2 as a fraction
Answer:
1/2a (4a+7)
Step-by-step explanation:
First You Divide:7/2a+ 2a^2
Rearrange Terms: 2a^2+ 7/2a
Find the Common Factor: 1/2(4a^2+7a)
Rewrite in the Fraction Form: 1/2a (4a+7)
I know this is the right answer because I learned this in 5th grade.
Please mark me Brainliest!!!
Find the values of P and Q in the arithmetic progression: -12, P, Q, 18.
The value of P=2 and Q=8 as in AP, The difference in two terms is equal between all the terms.
What is Arithmetic Progression?A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. Sn = n/2[2a + (n 1) d] is the formula to determine the sum of an arithmetic progression. where an is the first term in the arithmetic progression, n is the total number of terms, and d is the common difference. If there is always the same difference between any two consecutive terms in a series of numbers, that progression is known as an arithmetic progression. Simply put, it means that the previous number in the series is added to determine the next number in the series.
Here,
18--12=30/3=10
P=-12+10
=-2
Q=-2+10
=8
P=2 and Q=8 as in AP, the difference between the two terms is equal for all terms.
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Find the slope and reduce.
P=(2, 3) Q=(9, 7)
Answer:
[tex]\frac{4}{7}[/tex]
Step-by-step explanation:
Slope = m
m = [tex]\frac{y_{2}- y_{1}}{x_{2}-x_{1}}[/tex]
m = [tex]\frac{7-3}{9-2}[/tex] = [tex]\frac{4}{7}[/tex]
The number of carbon atoms in a fossil is given by the function y = 51000(0.85), where t represents the number of
years since being discovered. What is the percent of change each year? Explain how you arrived at your answer.
The percent of change each year is 15%.
How to calculate percentage?
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
It is given that The number of carbon atoms in a fossil is given by the function y = [tex]51000(0.85)^t[/tex], where t represents the number of years since being discovered.
Here , y = [tex]51000(0.85)^t[/tex]
t = number of years
y = number of carbon atoms in a fossil.
For t = 1 year
y = 51000[tex](0.85)^1= 51000(0.85) = 43350[/tex]
For t = 2 years
y = 51000[tex](0.85)^2= 36847.5[/tex]
For t = 3 years
y = 51000[tex](0.85)^3=31320.375[/tex]
Percentage change in one year = [tex]\frac{36847.5-43350}{43350}[/tex] × 100 = -15%
Percentage change in second year = [tex]\frac{31320.375-36847.5}{36847.5}[/tex] × 100 = -15%
here, negative sign shows decrement. In this way, every year carbon atom in fossil decreases by 15%.
Therefore, the percent of change each year is 15%.
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Find the product. Simplify your answer
2x² (4x³+2y¹)
12x³y +6
08x5 +4y6
48x5y6
8x5 +8x²y¹
Answer: The answer is D bc i did the test before hope you have a great day:]
Step-by-step explanation:
8
x
5
−
6
x
4
+
12
x
3
Find the mean, μ, for the binomial distribution which has
the stated values of n and p. Round answer to the nearest
tenth.
n = 38; p = 0.2
Select one:
Ο Α. μ = 8.3
OB. μ = 7.9
Cu = 7.1
OD. μ = 7.6
The mean value is 7.6. Option (D) is the correct answer.
The number of successes in a sample of size n drawn with replacement from a population of size N is frequently modeled using the binomial distribution.
The mean value of a binomial distribution is,
[tex]\mu =np\\=38*0.2\\=7.6[/tex]
Multiplication:
In mathematics, multiplying two or more numbers yields the product of the numbers. It is one of the basic mathematical operations that we carry out on a regular basis. The most obvious application is using multiplication tables. The multiplication of two numbers in mathematics represents the repeated addition of one number in respect to another. These numbers can be natural numbers, whole numbers, fractions, integers, or other types of numbers. When m is multiplied by n, m is either multiplied by n times or added to itself n times.
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A cable TV company has 3400 customers paying $130 each month. If each $1 reduction in price attracts 50 new customers, find the price that yields maximum revenue.
The price that yields maximum revenue is equal to $99. Also, the maximum revenue is equal to $490,050.
How to determine the unit price that yields a maximum revenue?In order to determine the price that would yield the maximum revenue, we have to find the derivative of the revenue function R(p) by applying the Power Rule.
Mathematically, the revenue function, R(p) is given by this mathematical expression:
Revenue function, R(p) = NP
Where:
N represents the number of customersP represents the monthly price of the subscriptionLet the variable n represent the number of reductions in the price. Therefore, we have:
N = 3,400 + 50n ....equation 1.
P = 130 - n
n = 130 - P
From equation 1, we have:
N = 3,400 + 50(130 - P)
N = 3,400 + 6,500 - 50P
Next, we would re-write the revenue function R(p) as follows:
Revenue function, R(p) = (3,400 + 6,500 - 50P)P
Revenue function, R(p) = 3,400P + 6,500P - 50P²
Revenue function, R(p) = 9,900P - 50P²
Taking the derivative of R(p), we have:
R'(p) = 9,900 - 100P
100P = 9,900
Price, P = 9,900/100
Price, P = $99
For the the maximum revenue, we have:
Maximum revenue, R(p) = 9,900P - 50P²
Maximum revenue, R(p) = 9,900(99) - 50(99)²
Maximum revenue, R(p) = 980,100 - 490,050
Maximum revenue, R(p) = $490,050.
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Complete Question:
A cable TV company has 3400 customers paying $130 each month. If each $1 reduction in price attracts 50 new customers, find the price that yields maximum revenue. Find the maximum revenue.
Write the equation of the line that is perpendicular
to the y-axis and passes through the point (3, 12).
Answer:
[tex]y=12[/tex]
Step-by-step explanation:
The [tex]y[/tex]-axis has equation [tex]x=0[/tex], so the equation of a line perpendicular to the [tex]y[/tex]-axis would be of the form [tex]y=c[/tex].
The equation of this line given the point [tex](3,12)[/tex] is [tex]y=12[/tex].
10. Brock bought a bicycle that cost $40.00 when it was new. If he eventually sold it for 10%
of the original cost, how much was it sold for?
Answer:IT WOULD BE 60.00
Step-by-step explanation:
BC 40 = 60
What is the average hourly pay of someone making 45,000 per year? Assume a 40 hour workweek and a 52 week year.
The average hourly pay of person making 4500 per year is 21.63 per hour.
Given that,
we have to find what does a person making $45,000 a year make per hour on average, Assume a 52-week year and a 40-hour workweek.
To calculate this
The ratio of the sum of the values in a given set to all the values in the set is the mean value, which is the definition of the average.
We have to multiply 52-week year and a 40-hour work week.
40×52
2080
Now, divide 45000 by 2080
45000/2080
21.63
Therefore, The average hourly pay of person making 4500 per year is 21.63 per hour.
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If a=-1+2i and b=5, then find the value of the a^2b in fully simplified form.
The value of the algebraic expression is:
a^2*b = -15 + 20i
How to find the value of the expression?
Here we have the following expression:
a^2*b
And we want to use the values:
a = -1 + 2i
b = 5
Replacing these values in the expression we will get:
(-1 + 2i)^2*5
Expanding the first part we get:
(-1 + 2i)*(-1 + 2i) = (-1)*(-1) + (-1)*(2i) + (2i)*(-1) + (2i)*(2i)
= 1 - 2i - 2i - 4
= -3 + 4i
Replacing that in the expression we get:
(-1 + 2i)^2*5 = (-3 + 4i)*5 = -3*5 + 4i*5 = -15 + 20i
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4. Two card are down Randomly from well suffled deck of card without Replacement Find the probability by of getting both Face card at two succession tree diagram.
Answer:
[tex]\frac{11}{221}\approx{0.0498}\approx{4.98\%}[/tex]
Step-by-step explanation:
Two cards are drawn randomly from a well-shuffled deck of cards without replacement. Find the probability of getting both face cards in succession.
In a deck of 52 cards, there are three face cards (J, Q, and K) in each of four suits (clubs, diamonds, hearts, and spades). That means there are 12 face cards in total (J♣, Q♣, K♣, J♦, Q♦, K♦, J♥, Q♥, K♥, J♠, Q♠, K♠).
The probability of drawing a face card the first time, then, is 12 out of 52.
There is now one less face card in the deck, as well as one less card in the deck. Therefore, the probability of drawing a face card a second time is 11 out of 51.
The probability, then, of drawing two face cards in succession is:
[tex]\frac{12}{52}\times{\frac{11}{51}}=\frac{132}{2652}=\frac{11}{221}\approx{0.0498}\approx{4.98\%}[/tex]
What is the first step needed to solve 4 over 7 multiplied by x minus 5 equals negative 13 ? (1 point)
Group of answer choices
Add 5 to both sides
Multiply both sides by 4
Subtract 13 from both sides
Divide both sides by 7
Answer:add 5 to both sides
Step-by-step explanation:
The number of computer security breaches is expected to increase at a yearly rate of 86%
Use the exponential growth model to determine the equivalent monthly rate.
Enter the rate, to the nearest tenth of a percent, in the box.
____%
Answer:
The population is expected to grow at a rate of 1.36% each year. What is the population of the town in 2006? Round your answer to the nearest whole number.
Step-by-step explanation:
3/5 - 1/3 simplified
Answer:
4/15
Step-by-step explanation:
[tex]\frac{3}{5}=\frac{9}{15} \\ \\ \frac{1}{3}=\frac{5}{15} \\ \\ \frac{3}{5}-\frac{1}{3}=\frac{9}{15}-\frac{5}{15}=\frac{4}{15}[/tex]
Solve for j ??????????????????????????
Answer:
j=24
Step-by-step explanation:
j/8 - 2 = 1
j/8 - 2 + 2 = 1 + 2
j/8 = 3
8 * j/8 = 8 * 3
j=24
Consider the equation and the following ordered pairs: (1,y) and (x,−3).
6x+3y=15