Multiply a Polynomial by a Monomial
In the following exercises, multiply.
236. (8b − 1)b

Answer:

Answer is 382.5 square inch

Step-by-step explanation:

calculate all the area of the surface

Answer is 382.5 square inch

The surface area of the prism is given by the equation A = 382.5 inches²

The surface area of the prism is calculated as

The formula for the surface area of a prism is SA=2B+ph, where B, is the area of the base, p represents the perimeter of the base, and h stands for the height of the prism

Surface Area of the prism = 2B + ph

The area of the triangular prism is A = ph + ( 1/2 ) bh

Given data ,

Let the surface area of the prism be represented as A

Now , the prism consists of 2 right angled triangles and 3 faces of rectangles

So , the base of the triangle b = 9 inches

The height of the triangle h = 10 inches

So , the area of the 2 triangles = 2 ( bh ) / 2

On simplifying the equation , we get

The area of 2 triangles = 9 x 10 = 90 inches²

The area of first rectangle = 9 x 10 = 90 inches²

The area of second rectangle = 9 x 9 = 81 inches²

The area of third rectangle = 13.5 x 9 = 121.5 inches²

So , the area of the prism = area of 2 triangles + area of first rectangle + area of second rectangle + area of third rectangle

Substituting the values in the equation , we get

The area of the prism A = 90 + 90 + 81 + 121.5

The area of the prism A = 382.5 inches²

Hence , the surface area of prism is 382.5 inches²

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The equation would be 5(x + 3) = 45

To solve:

1) Distribute 5 to x and then 5 to 3

2) That gives you this equation: 5x + 15 = 45

3) Then subtract 15 from both sides

4) You should get this: 5x = 30

5) Then divide 5/5 and 30/5 to isolate the x

6) The answer should be: x = 6

Have a good day/night :)

Answer:

x=4

x=64

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

i can not really tell what letters are on the picture but i think it is 9

The trigonometric ratios for each triangles are:

Please note that all angles B are the right angle, then:

cos B = 1; sin B = 0; tan B = -

The trigonometric ratio of sin, cos, tan, can be formulated as:

(please refer to the attached triangle below for reference)

cos A = side adjacent to A / Hypotenuse

Cos A = b/c

Sin A = side opposite to A / Hypotenuse

Sin A = a/b

Tan A = Side opposite to A / Side adjacent to A

Tan A = a/b

From these formulas, we can find that:

Triangle 1

Cos A = 40/50 = 4/5

Sin A = 30/50 = 3/5

Tan A = 30/40 = 3/4

Cos C = 30/50 = 3/5

Sin C = 40/50 = 4/5

Tan C = 40/30 = 4/3

Triangle 2

Cos A = 27/45 = 3/5

Sin A = 36/45 = 4/5

Tan A = 36/27 = 4/3

Cos C = 36/45 = 4/5

Sin C = 27/45 = 3/5

Tan C= 27/36 = 3/4

Triangle 3

Cos A = 15/17

Sin A = 8/15

Tan A = 8/15

Cos C = 8/17

Sin C = 15/17

Tan C = 15/8

Please note that all angle B on the three triangles are all a right angle, then:

Cos B = 1

Sin B = 0

Tan B = -

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Mandy will catch up Rita at 0.5 hour after they start walking.

As per data given are Mandy start = 1, Rita start = 2, Mandy speed = 5 and Rita speed = 2. Based on this explanation we can determine the formula for Mandy time to catch up Rita as follow

s1 = s2

Rita start + Rita speed x t = Mandy start + Mandy speed x t

2 +3 x t = 1 + 5 x t

2 + 3t = 1 + 5t

2 - 1 = 5t - 3t

1 =  2t

t = 0.5 h

Hence, Mandi will catch up with Rita at 0.5h after start.

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Answer:

-3 x 10

Step-by-step explanation:

the first one is 5

Answer:

Ummmm... Both?

Step-by-step explanation:

66k+9 OR 3(22K+3)

Answer:

k>10

k>-4

Step-by-step explanation:

-10k<-100

k>10

you flip the sign when dividing by a negative

-8k<32

k>-4

Answer:

x= 6/7 - 2y/7

y= 3 - 7x/2

Step-by-step explanation:

I said so

a) If N is the population of the city and is the time in years, N expressed as a function of t is; N(t) = N₀*e^(kt)

b) The population 2 years from now will be; 25198 people

The general formula for exponential growth model is;

N(t) = N₀*e^(kt)

where;

f(x) is exponential growth function

N₀ is initial amount

t is time

k is constant

a) We are told that;

N is the population of the city.

t is the time in years

Thus, N expressed as a function of t is;

N(t) = N₀*e^(kt)

b) We are told that the population doubled in size over an 18-month

period . Thus, the equation would now be;

N(t) = N₀*2^(t/18)

Thus,  if the current population is 10000, then it means that 2 years from now, we will have;

N(2) = 10000 * 2^(24/18)

I used 24 because 2 years is 24 months

Thus;

N(2) ≈ 25198 people

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To find the length of the curve y = 1 - cos x from x = 0 to x = 4π, we can use the arc length formula:

Arc length = ∫[sqrt(1 + (dy/dx)^2)] dx from a to b

First, find the derivative of y with respect to x:
dy/dx = d(1 - cos x)/dx = sin x

Now, substitute into the arc length formula:
Arc length = ∫[sqrt(1 + sin^2(x))] dx from 0 to 4π

This integral doesn't have an elementary function as its antiderivative, but we can use the elliptic integral of the second kind to evaluate it.

Arc length = 4 * E(4π, k) where E is the elliptic integral of the second kind and k = 1 (since k = sin^2(x) in our case).

Using a calculator, we find that E(4π, 1) ≈ 3.8202. So, the arc length is approximate:
Arc length ≈ 4 * 3.8202 ≈ 15.2808

Hence, the correct answer is B) 15.281.

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The given equation is:

It is required to solve for x.

Distribute 6 into the expression in parentheses:

Add 12 to both sides of the equation:

Divide both sides of the equation by 6:

Hence, the correct answer is 3) x=2 2/3.

The correct option is 3.

Jamal would need approximately 7.9 gallons of gas to travel 296.25 miles.

We can use the concept of direct variation to solve this problem. Direct variation means that two quantities are related by a constant ratio. In this case, the number of miles driven is directly proportional to the number of gallons used.

To find the constant of proportionality, we can use the given data. From the table, we can see that when Jamal used 14 gallons, he drove 525 miles. So we can write:

14/525 = k

where k is the constant of proportionality.

Solving for k, we get:

k = 14/525

Now we can use this value of k to find how many gallons Jamal would need to travel 296.25 miles. Let x be the number of gallons he would need. Then we can write:

x/296.25 = k

Substituting the value of k, we get:

x/296.25 = 14/525

Solving for x, we get:

x = (296.25 × 14) / 525

x ≈ 7.9

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Answer:

x = 60

Step-by-step explanation:

Answer:

abc is a triangle so ,

a is ( 9,6 )

b is ( 9,3 )

and c is ( 3,3 )

Answer:

Yes its a function....good job!!!

Step-by-step explanation:

Answer:

-1/3, -1/7, -2/3, -2/5, -2/7, 1/3, 2/3, 2/5, 9/8

Step-by-step explanation:

I hope this helps!

Answer:

30

Step-by-step explanation:

A)an = 2*2^(n-1)`. B) `The sum of the first n fractions is `2*(2^n - 1)`.

a. The sequence is a geometric sequence with the first term `a1 = 2` and common ratio `r = 2`.Therefore, the nth term `an` is given by:`an = a1*r^(n-1)`

Substituting `a1 = 2` and `r = 2`, we have:`an = 2*2^(n-1)`

b. To find the sum of the first n terms, we use the formula for the sum of a geometric series:`S_n = a1*(1 - r^n)/(1 - r)

`Substituting `a1 = 2` and `r = 2`, we have:`S_n = 2*(1 - 2^n)/(1 - 2)

`Simplifying:`S_n = 2*(2^n - 1)

`The sum of the first n fractions is `2*(2^n - 1)`.As `n` gets larger and larger, the sum approaches `infinity`.

Thus, the sum is getting closer and closer to infinity.

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the value of the given logarithmic function \(\log_ba + \log_bd\) will be  \(\log_b(a*d)\).

The opposite of an exponential function is a logarithmic function. A log function and an exponential function both use the same base. An exponent is a logarithm. f(x) = bˣ is how the exponential function is expressed. The formula for the logarithmic function is f(x) = log base b of x.

Given a function of log such as:

\(\log_ba + \log_bd\)

From the general addition and subtraction properties of a log:

\(\log_mx + \log_my = \logm(x *y)\\\log_mx - \log_my = \logm(x /y)\)

Thus,

From the above Formulas, we can determine the values of the asked logarithmic function:

=> \(\log_ba + \log_bd\)

=> \(\log_b(a*d)\)

Therefore, the value of the given logarithmic function will be  \(\log_b(a*d)\).

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The probability that the date sara chose is a prime number is 0.2.

Given that, sara chose a date from the calendar.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.

Here, total number of outcomes = 30

Number of favourable outcomes = 6

Now, probability = 6/30

= 1/5

= 0.2

Therefore, the probability that the date sara chose is a prime number is 0.2.

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To find a 95% confidence interval for the difference in fuel efficiencies between city and highway driving,The Confidence interval = 7.29 ± (1.96 * (2.53 / √(608))).

Confidence interval = mean difference ± (t-value * standard error)

First, we need to calculate the standard error. The standard error is the standard deviation divided by the square root of the sample size:

Standard error = standard deviation / √(sample size)

In this case, the mean difference in fuel efficiencies is 7.29 mpg, and the standard deviation is 2.53 mpg. The sample size is 608 vehicles. Let's calculate the standard error:

Standard error = 2.53 / √(608)

Next, we need to find the t-value for a 95% confidence level. Since the sample size is large (608), we can approximate the t-value using a normal distribution. For a 95% confidence level, the t-value is approximately 1.96.

Now, we can calculate the confidence interval:

Confidence interval = 7.29 ± (1.96 * standard error)

Substituting the values we calculated:

Confidence interval = 7.29 ± (1.96 * (2.53 / √(608)))

Simplifying this expression will give us the confidence interval.

To interpret the confidence interval in context, we can say:

We are 95% confident that the true mean difference in fuel efficiencies between city and highway driving for the population of vehicles lies within the calculated confidence interval. This means that, on average, we expect the difference in fuel efficiencies between city and highway driving to be between [lower bound] mpg and [upper bound] mpg.

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Answer:34 13

Step-by-step explanation:

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Cost of tjhe donut: D

Cost of the large coffee: C

On Monday Harold picked up six donuts and two large coffees for the office staff, he paid $5.80:

On Tuesday, Melinda picked up four donuts and 5 large coffees for the office staff. She paid $7.02:

Use the next system of linear equations to find the value of D and C:

1. Solve D in the first equation:

2. Substitute the D in the second equation by the equation you get in step 1:

3. Solve C:

4. Use the value of C=0.86 to find D;

The solution fot the system is:

False. The expected cell frequency in statistical analysis, specifically in the context of contingency tables and chi-square tests, is not based on the researcher's opinion. Instead, it is determined through mathematical calculations and statistical assumptions.

In contingency tables, the expected cell frequency refers to the expected number of observations that would fall into a particular cell if the null hypothesis of independence is true (i.e., if there is no relationship between the variables being studied). The expected cell frequency is calculated based on the marginal totals (row totals and column totals) and the overall sample size.

The expected cell frequency is computed using statistical formulas and is not influenced by the researcher's opinion or subjective judgment. It is a crucial component in determining whether the observed frequencies in the cells significantly deviate from what would be expected under the null hypothesis.

By comparing the observed cell frequencies with the expected cell frequencies, statistical tests like the chi-square test can assess the association or independence between categorical variables in a data set.

Thus, the statement "the expected cell frequency is based on the researcher's opinion" is false. The expected cell frequency is derived through statistical calculations and is not subject to the researcher's subjective input.

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The rate of change (slopes) and initial value (y-intercepts) are as follows:

A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.

A line of best fit is also referred to as a trend line and it can be defined as a statistical (analytical) tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association (correlation) between a data.

By critically observing the graph which models the given data, we can logically deduce the following rate of change (slopes) and initial value (y-intercepts):

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The best point estimate for the mean GPA for all residents of the local apartment complex would be 1.6.

Given, the mean GPA for the 127 residents of the local apartment complex is 1.6.

The mean or sample mean is used as a point estimate for the population mean or population parameter when the value of the mean of the sample is unbiased and accurately represents the mean of the population.

Here, we are given the mean GPA of 127 residents of the local apartment complex, which is 1.6.

Therefore, the best point estimate for the mean GPA for all residents of the local apartment complex would be 1.6.

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Answer:

$19.8

Step-by-step explanation:

To find the answer, find the  ratio.

Answer: 1980

Step-by-step explanation:

Set yp a proportion

5.60dollars=56texts

----------------   ----------

198dollars=    x

Then you cross multiply the 198 with the 56

then you divide the 5.60

Answer:The answer is It has no slope because x2 - x1 in the formula m=y2-y1-x2-x1 is zero, and the denominator of a fraction cannot be zero

Step-by-step explanation:

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