This figure is made up of two rectangular prisms.
What is the volume of the figure?
Enter your answer in the box.

Answer:

The answer is 100. One way to find it out is 1600/16, and then you get 100.

Answer:

$\(45\)

Step-by-step explanation:

\(30\)% \(\mathrm{of}\) $\(150\)

\(=\frac{30}{100}\times 150\\\)

\(=\) $\(45\)

Answer:

100.8 cm squared

Step-by-step explanation:

a right triangle is half a rectangle so multiply base x height then divide by 2

12.6x16=201.6

201.6/2=100.8

Answer:

105.84

Step-by-step explanation:

Multiply the height of the triangle (in this case 12.6) by the base (16.8) then divide by 2.

Answer: f(3) = g(6)

Step-by-step explanation: if you plug them in we see that f of 3 on the y axis intercept g of x so we then go up and see that g of 6 intercepts f of 3 so therefore that is the answer

While both groups have the same average height, group B is more likely to have better basketball players due to their smaller standard deviation, which suggests that the heights of the students in this group are more tightly clustered around the mean.

Standard deviation is a measure of how spread out a set of data is. A smaller standard deviation means the data points are more tightly clustered around the mean, while a larger standard deviation means the data points are more spread out.

Now, let's consider the advantage of height in basketball. Taller players have a better advantage in reaching the basket, blocking shots, and rebounding the ball. Therefore, a group of taller players is more likely to have better basketball players.

Since the standard deviation of group B is smaller, it is more likely that the heights of the students in this group are more tightly clustered around the mean, with more students closer to the average height of five-feet, six-inches.

This suggests that group B is more likely to have more students who are taller than average and therefore more likely to have better basketball players.

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Answer:

(x+24)(x-2)=0

Step-by-step explanation:

2*-24=-48

factorise -48 to get 24 and -2 (which will add up to 22)

Answer: 3131,64$ will be in the account in 12 years

Answer:

x = 45

y = 7

Step-by-step explanation:

To obtain the value of x and y, do the following:

√7 – 3√5

Rearrange

– 3√5 + √7

Multiply through by –1

3√5 – √7 ... (1)

Express 3√5 as a single surd

3√5 = √(3 × 3 × 5)

3√5 = √45

Replace 3√5 with √45 in equation 1

3√5 – √7

√45 – √7

Comparing

√45 – √7 and √x – √y i.e

√45 – √7 = √x – √y

x = 45

y = 7

The vector v+w has a magnitude of 2√2 and its direction is along the positive x-axis.

What is meant by vector?

A vector is a quantity that has both magnitude and direction. It is represented as an arrow with its length representing the magnitude and its direction representing the direction of the quantity.

What is meant by the x-axis?

The x-axis is the horizontal line on a coordinate plane that is used as a reference for plotting and describing the positions of points in two-dimensional space. It is often referred to as the "horizontal axis" or the "abscissa".

According to the given information

Here the vector v has a magnitude of 2 and a direction of 45° so the components of vector v are:

v_x = 2 cos 45° = √2

v_y = 2 sin 45° = √2

Vector w has a magnitude of 2 and a direction of 45° South of East. This means that the angle between vector w and the positive x-axis is 45°, and the angle between vector w and the negative y-axis is 45°. Therefore, the components of vector w are:

w_x = 2 cos 45° = √2

w_y = -2 sin 45° = -√2

Now we can add the components of vectors v and w to find the components of the vector v+w:

(v+w)_x = v_x + w_x = √2 + √2 = 2√2

(v+w)_y = v_y + w_y = √2 - √2 = 0

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The variable t becomes the subject of the equation c=t³ - 8v by adding 8v to both sides and taking the cube root, giving t = ∛(c + 8v).

We need to make t the subject of the equation c=t³ - 8v. To do this, we first add 8v to both sides of the equation to isolate t³ on one side, giving us t³ = c + 8v. We then need to take the cube root of both sides to solve for t. Hence, t = ∛(c + 8v). Now, t is the subject of the equation.

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Answer:

C.

Step-by-step explanation:

A. 4 - 2 = 2    not zero

B.

$50 in 1 account

$50 in another account

Not zero

C.

6 deg - 6 deg = 0 deg

This is zero

D.

$8 - $3 = $5

Not zero

Answer:

c

Step-by-step explanation:

ANSWER

2

To find 1% of something (1/100 of something), divide by 100.

1% of 200 is 2.

Answer : 12%

explanation :

Let the sum of money be P(which is the principal value) and rate of interest be R.

According to the question,

Amount (principal +simple interest) = 8P/5

Time (T) = 5 years

Simple interest (SI) = PRT/100

SI = 5PR/100

Amount = P +SI

8P/5 = P+(5PR/100)

8P/5 = P(100+5R)/100

160 = 100 +5R

5R =60

R = 12

Therefore, rate of interest = 12% p.a.

The perimeter of the given shape as represented in the task content is; 29 cm.

It follows from the task content that the perimeter of the given shape on the centimeter grid as required is to be determined.

Since each grid line has 1cm as it's length;

The perimeter of the shape is the sum of all side lengths of the shape;

Perimeter, P = 6+2+3+2+2+1+3+2+2+2+2+1

P = 29 cm

Hence, the perimeter of the shape is; 29 cm.

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Answer:

Step-by-step explanation:

All it's saying is that the 12% of the people are 35 and the 82% of people who did not submitted data is 175 people

The calculated test statistic (2.08) is greater than the critical value (1.96), we reject the null hypothesis and conclude that there is evidence to suggest that the contest has increased participation in the box tops for education program.

To determine if the contest has increased participation in the box tops for the education program, we need to conduct a hypothesis test.

We will use a significance level of 0.05, which means we are willing to accept a 5% chance of making a Type I error (rejecting the null hypothesis when it is actually true).

Null Hypothesis: The proportion of students submitting box tops for education is still 12% (or has decreased) after the contest.

Alternative Hypothesis: The proportion of students submitting box tops for education has increased after the contest.

To test this hypothesis, we will use a one-sample proportion test. We will use the sample proportion, p' = 35/210 = 0.1667, as an estimate of the population proportion, p. The test statistic is calculated as:

z = (p' - p) / √(p x (1-p)/n)

where n is the sample size.

Under the null hypothesis, the expected value of the test statistic is 0, and the standard deviation of the test statistic is sqrt(p*(1-p)/n).

Using p = 0.12 and n = 210, we have:

z = (0.1667 - 0.12) / √(0.12 x 0.88/210) ≈ 2.08

The critical value for a significance level of 0.05 and a two-tailed test is ±1.96.

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Answer:

11.

Step-by-step explanation:

\( \cos(42) = x \div 15\)

\(15 \cos(42) = x\)

x=11.147

Answer:

11

Step-by-step explanation:

cos(42)=x÷15

15 \cos(42) = x15cos(42)=x

x=11.147

The associative property is a property that happnes with some operators in which the rearrengements of the perenthesis don't alter the result.

With this in mind, the alternatives that don't have any parenthesis can be excluded already.

Now, the same goes for the alternatives that have only parenthesis in one of the sides.

This excludes alternatives 1, 2 and 4.

The third alternative is:

Notice that the only difference between the two sides are the position of the parenthesis, and this doesn't alter the result, so the third is the correct alternative.

Answer:

167.42

Step-by-step explanation:

p = 1/q²

22 = k* 1/8² .........k is the constant which we re finding now

k = 1408

p = 1408/2.9²

= 167.42

\(\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ h=8\\ r=12 \end{cases}\implies V=\cfrac{\pi (12)^2 (8)}{3} \\\\\\ V=384\pi \implies \stackrel{using~\pi =3.14 }{V=1206}~cm^3\)

Answer:

(a) An expression for the number n of bacteria after t hours is n(t)=700*\(3^{t}\)

(b) The rate of growth of the bacteria population after 1.5 hours is 3,996 number of bacteria per hour.

Step-by-step explanation:

An exponential function is one in which the independent variable x appears in the exponent and has a constant a as its base. Its expression is:

f(x)=aˣ

being a real positive.

When 0 <a <1, then the exponential function is a decreasing function and when a> 1, it is an increasing function.

An exponential function allows us to refer to phenomena that grow faster and faster, such as population growth.

In that case, the formula used to model the growth of a population is given by:

P(t)=P0*\(a^{t}\)

where the function P (t) grows exponentially and represents the quantity of the population at time t; a represents the constant of growth or decrease and P0 represents the initial population at time zero.

In this case:

Replacing, you get:

P(t)=700*\(3^{t}\)

An expression for the number n of bacteria after t hours is n(t)=700*\(3^{t}\)

The derivative of this function P (t) is:

n'(t)=700*ln(3)*\(3^{t}\)

and reflects the growth rate of the bacteria population.

So, the rate of growth of the bacteria population after 1.5 hours is:

n(1.5)=700*ln(3)*\(3^{1.5}\)

Solving, you get:

n(1.5)≅ 3,996

The rate of growth of the bacteria population after 1.5 hours is 3,996 number of bacteria per hour.

Answer:5

Step-by-step explanation:

5098

Answer:

Step-by-step explanation:

Given the system of equation  x−3y=−3 and x+y=5, we can solve for x and y by solving the equation simultaneously using the substitution method.

x−3y=−3_____________ 1

x+y=5 ______________2

From equation 2; x = 5- y ________ 3

Substitute equation 3 into equation 1

Since x - 3y = -3

(5-y)-3y = -3

5-y-3y = -3

5-4y = -3

Subtract 5 from both sides of the equation

5-4y-5 = -3-5

-4y = -8

Divide both sides by -4

-4y/-4 = -8/-4

y = 2

Substitute y = 2 into equation 2 to get the value of y;

From equation 2, x+y = 5

x+2 = 5

Subtract 2 from both sides of the equation

x+2-2 = 5-2

x = 3

Hence the value of x and y from the graph will be 3 and 2 respectively.

Based on the information provided, the missing number would be number 6.

When it comes to finding missing numbers, the first step is to decipher or identify the pattern. This can be either a sequence of numbers or the application of a specific mathematical operation such as subtraction or addition.

In this case, we can see there is a sequence of numbers that seems to go from 1 to 9. However, if you check carefully, the number 6 is missing, which is the number you need to add.

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Answer:

15/17

Step-by-step explanation:

sine is opposite/hypotenuse

Using proportions, the amounts are given as follows:

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using operations such as multiplication or division.

One example of application is for percentage problems, as the equivalent amount can be found multiplying the equivalent decimal by the total amount.

The amount of Federal Income Tax Withholding each month is given by:

0.2 x 3500 = $700.

The amount of State Income Tax Withholding each month is given by:

0.12 x 3500 = $420.

The amount of Social Security Tax Withholding each month is given by:

0.0825 x 3500 = $288.75.

The amount contributed to the 401k each month is:

0.04 x 3500 = $140.

The take-home pay for the month is the $3,5500 subtracted by all the with holdings, hence:

3500 - (700 + 420 + 288.75 + 140) = $1,951.25.

A year has 12 months, hence the take-home pay for the year is given by:

12 x 1951.25 = $23,415.

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Step-by-step explanation:

7! = 5040 ways

The probability of selecting a biography or a mystery is 0.8

We assume that all the books have the same probability of being randomly selected.

The probability of getting a particular type of book is given by the quotient between the number of these books and the total number of books.

Here we want to find the probability of selecting a biography or a mystery, there are 9 mysteries and 7 biographies, and a total of 20 books in the shelf, so the probability is:

P = (7 + 9)/20 = 16/20 = 4/5 =0.8

The probability is 0.8

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The correct question is;

A string is stretched and fastened to two points distance l apart. Motion is started by displacing the string into the form y = k(lx - x²),from which it is released at time t = 0. Which are the correct conditions?

Answer:

The boundary conditions are listed below.

Step-by-step explanation:

The displacement y(x,t) will be given by the equation;

d²y/dt² = a²(d²y/dx²)

Thus, the boundary conditions will be as follows;

1) y(0,t) = 0 ; for values of t ≥ 0

2) y(l,t) = 0 ; for values of t ≥ 0

3) y(x,0) = 0 ; for 0 ≤ x ≤ l

4) dy/dt (at t = 0) = kx(l - x) ; for 0 ≤ x ≤ l