Find the volume of a right prism with height h=10 cm, if the base is a trapezoid with height htr = 3 cm and bases of 2 cm and 5cm

Therefore, the speed of the car in m/s is [tex]\frac{75000}{3600}[/tex] m/s i.e., option (B) is correct.

What is the equation?

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Here given that,

A car is traveling at a speed of [tex]75[/tex] km/h.

As we know,

[tex]1km=1000m[/tex]

[tex]1h=60s[/tex]

So,

[tex]75[/tex] km/h=[tex]\frac{75(1000)}{3600}[/tex] m/s

[tex]=\frac{75000}{3600}\\\\[/tex]

Hence, the speed of the car in m/s is [tex]\frac{75000}{3600}[/tex] m/s i.e., option (B) is correct.

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The linear function that represents this graph is given by:

y = 300 - 0.6667x.

A linear function is modeled by:

y = mx + b

In which:

From the graph, when x = 0, y = 300, hence the y-intercept is of b = 300. The amount decays to 0 when the x-intercept is of x = 450, hence the slope is given by:

m = -300/450 = -0.6667.

Which means that the equation is:

y = 300 - 0.6667x.

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Answer:

is greater for data set 2 ; is greater for data set 2

Step-by-step explanation:

The range is found by subtracting the highest and lowest value.  The range of the first plot would be

34-21 = 13.

The range of the second plot would be

36-12 = 24.

The mean is found by adding together all of the data points and dividing by the number of data points.  For the first plot, the sum of the data is 274 and there are 10 data points; this makes the mean 274/10 = 27.4.

For the second plot, the sum of the data is 280.5 and there are 10 data points; this makes the mean 280.5/10 = 28.05.

The range is greater for data set 2.

Then mean is greater for data set 2.

Mean of a set of data is defined as the average of all the values. It gives the exact middle point of the data set.

Consider the data plot for 13 to 15 years olds.

Mean = Average of the values

          = (21 + 24 + 26 + 27 + 27 + 28 + 28 + 28 + 31 + 34) / 10

          = 27.4

Range = Maximum value - Minimum value

           = 34 - 21

          = 13

Consider the data plot for 16 to 18 years olds.

Mean = Average of the values

          = (12 + 21 + 28 + 28 + 28 + 28 + 30.5 + 34 + 35 + 36) / 10

          = 28.05

Range = Maximum value - Minimum value

           = 36 - 12

          = 24

Hence the range and mean are greater for data set 2.

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(a) All the possible outcomes of the compound event are {(1, A), (1, B), (2, A), (2, B), (3, A), (3, B)}

(b) Probability is 2/3.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

Given that,

At a fair, each person can spin two wheels of chance.

The first wheel has the numbers 1, 2, and 3.

The second wheel has the letters A and B.

(a) 1 can be followed by A and B, 2 can be followed by A and and B and so is 3.

Possible outcomes = {(1, A), (1, B), (2, A), (2, B), (3, A), (3, B)}

(b) Total possible outcomes = 6

Number of outcomes which has either 1 or A = 4

Probability = 4/6 = 2/3

Hence the required probability is 2/3.

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It says "No more than 8 books are in your bag". Here "Not more than" a specific number would be a set of all values that are "less than or equal" to given number.  

So let's consider 'n' represents the number of books in the bag and we know this number can not be a negative value i.e. n is "greater than or equal" to 0.

Also n is "less than or equal" to 8 as given in the question.

Hence, the inequality would be 0 ≤ n ≤ 8.

y = 5 is the equation of the horizontal line that passes through the point (-2,5).

Mathematically, an equation is a statement that two expressions are equal. The expressions on either hand of the equals sign are termed the left-hand side and the right-hand side of the equation. The equals sign is perused as" is equal to" or" equals".

An equation comprises variables, numbers and comparison sign.

As the ordinate of the given point is 5 then y = 5 is the horizontal line that passes through (-2,5).

Thus, the equation that passes through the point (-2,5) and is the horizontal line is y = 5.

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To determine how much hardener is required for 16 containers of resin, multiply 55 mL by 16 to get 880 mL, and then convert this to liters by dividing by 1,000, resulting in 0.88 liters of hardener needed.

To determine how much hardener should be added to 16 containers of resin, we must multiply the amount needed for one container by the number of containers. The formula given states that 55 mL of hardener is required for each container of resin. To find the total amount for 16 containers, we perform the following multiplication:

Therefore, 0.88 liters of hardener should be added to 16 containers of resin.

Final answer:

To determine the amount of hardener needed for 16 containers of resin, multiply 55 mL by 16 to get 880 mL and then convert that to liters, resulting in 0.88 liters of hardener.

Explanation:

To find out how much hardener should be added to 16 containers of resin, where each container requires 55 mL of hardener, you need to do a simple multiplication operation. Multiply the amount of hardener needed for one container by the number of containers:

Therefore, you should add 0.88 liters of hardener to the 16 containers of resin.

How far are 27 and -54 apart on the number line?

Solution:

If we see on the number line , 27 is 27 units apart from 0 and it is 27 units to the right of 0

And, -54 is 54 units apart from 0 and it is 54 units to the left of 0. So, -54 is in opposite direction with respect to 27.

So, To find how far is 27 from -54 we must add 27 and 54

As, 27+54=81

So, -54 and 27 are 81 units away from each other.

Answer:81 units

Please see the number line attached.

Answer:

Option A. [tex]cot\theta = -1[/tex]

Step-by-step explanation:

[tex]\frac{tan^{3}\theta -1}{tan\theta -1}-sec^{2}\theta +1=0[/tex]

we have to the value of [tex]cot\theta[/tex]

We further solve the equation

[tex]\frac{(tan\theta -1)(tan^{2}\theta +1+tan\theta )}{(tan\theta -1)}-sec^{2}\theta+1=0[/tex]         [a³- b³= (a-b)(a² + b²+ ab)]

[tex]sec^{2}\theta +tan\theta -sec^{2}\theta +1=tan\theta +1=0[/tex]

[tex]\frac{1}{cot\theta }=-1[/tex]

[tex]cot\theta = -1[/tex]

Therefore Option A. [tex]cot\theta = -1[/tex] is the answer.

The number of the times cube is rolled for getting less than three is 8.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability of getting less than three = 2 / 6 = 1 / 3

The number of the times cube rolled is,

Pn = ( 1 / 3 ) x 24 = 8

Therefore, the number of the times cube is rolled for getting less than three is 8.

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The experimental probability of Brandy rolling a strike in the first frame of the next game is 1/2.

To find the experimental probability that Brandy will roll a strike in the first frame of the next game, we need to divide the number of times Brandy rolled a strike in the first frame by the total number of frames. In this case, Brandy rolled a strike in 5 out of 10 frames, so the experimental probability is 5/10, which simplifies to 1/2.

1. The probability P of an event and its complement P' are mutually exclusive and add up to 1

2.  If the probability of an event is 0.3, then the probability of its complement is 0.7.   (1 - 0.3 = 0.7)