A right triangular prism is constructed so that its height is equal to the leg length of the base.

A right triangular prism is shown. The right triangles have 2 sides with a length of x. The length of the hypotenuse is unknown. The height of the prism is x.

What expression represents the volume of the prism, in cubic units?


a. One-halfx3

b. One-halfx2 + x

c. 2x3

d. 2x2+ x

Final answer:

Option D, with scores of 100, 87, 94, 94, and 81, yields the highest average when calculated using the mean, making it the best choice for the student seeking the highest test average.

Explanation:

The question asks which set of test scores will give the highest average if calculated using the mean. To find the answer, we calculate the mean of each set of scores:

A: (95+82+76+95+96)/5 = 88.8

B: (79+80+91+83+80)/5 = 82.6

C: (65+84+75+74+65)/5 = 72.6

D: (100+87+94+94+81)/5 = 91.2

Among the options, option D has the highest mean.

Therefore, the student with test scores of 100, 87, 94, 94, and 81 will have the highest average when using the mean to calculate.

Answer: True

Explanation: To add mixed numbers, first add the fractions.

So here, we have 4/9 + 6/9 which is 10/9.

Then add the whole numbers.

So we have 1 + 2 which is 3.

So our answer is 3 and 10/9.

But notice, that since 10/9 is an improper fraction,

our answer is not in lowest terms.

10/9 can be rewritten as the mixed number 1 and 1/9.

So 3 and 10/9 is the same as 3 + 1 and 1/9 which is 4 and 1/9.

Since 4 and 1/9 is in lowest terms, this is our final answer.

So we can say that 1 and 4/9 + 2 and 6/9 is 4 and 1/9.

Answer:

3/10

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

Answer:

422.389 cm

Step-by-step explanation:

First you have to find the area of the circle then subtract it by the area of the rectangle. To find the area of the circle you have to square the radius then multiply it by 3.14.(12×12=144, 144× 3.14=452.389) Therefore 452.389 cm is the area of the circle. Area of the rectangle 30cm.

452.389 -30=422.389

Answer:

The answer to your question is   b = 11.31 cm  or   8[tex]\sqrt{2}[/tex] cm

Step-by-step explanation:

Data

hypotenuse = 18 cm

one leg = 14 cm

second leg = ?

Process

1.- Use the Pythagorean Theorem to solve this problem

                 c² = a² + b²

c = hypotenuse

a = longer leg

b= shorter leg

2.- Substitution

                        18² = 14² + b²

-Solve for b

                         b² = 18² - 14²

-Simplify

                         b² = 324 - 196

                         b² = 128

-Find the prime factors of 128

                          128   2

                            64  2

                             32  2

                             16  2

                              8  2

                              4  2

                              2  2

                               1

          128 = 2⁶2¹                                    

-Result

                         b = 11.31   or   8[tex]\sqrt{2}[/tex]

Answer:

21.32 Cm

Step-by-step explanation:

Add up the centiminer

Answer:

A and C

Step-by-step explanation:

I did the assignment

The width of the computer monitor is 22 inches

What is a Rectangle?

In a Rectangle

The diagonal equals the square root of the width squared plus the height squared

Given data ,

Let the Width of the rectangle be W

Diagonal of the rectangle = 27 inches

Height of the rectangle = 15 inches

D² = L² + W²

W² = D² - L²

W² = ( 27 )² - ( 15 )²

     = 729 - 225

     = 504

Therefore , Width W = √504

                                  ≈ 22.45 inches

                                  ≈ 22 inches

Hence , the width of the computer monitor is 22 inches

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Answer: Hannah blew 1 bubble

Step-by-step explanation:

Mean * number of gum chewers= total bubbles

4*4=16

Let’s add up the numbers of bubbles that we do know.

4+5+6=15

16-15=1

Hannah blew 1 bubble

The number of bubbles Hannah blew can be expressed as 1

The study of variables and the formula manipulation principles is known as algebra. Its roots lie in the computation methods of ancient Babylonia, but now it is a mode of thinking that permeates practically all branches of mathematics.

Let number of bubbles Hannah blew =x

Then we can set up the equation as

[tex]\frac{1}{4} (4+5+6+x)=4[/tex]

15+x=16

x=16-15

x=1

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As supply rises, prices decrease.

And The average rate of change describes how much a quantity changes as prices increases

As supply decreases, prices increase. It seems logical but I'm not 100% positive on the last one. I know the first 2 are right.

The statements that are true as they relate to supply and demand are: as supply rises, prices generally decrease; as demand decreases, prices generally increase; as supply decreases, prices increase.

Supply and demand are fundamental concepts in economics. The law of supply states that as supply increases, prices generally decrease. This is because when there is a higher quantity supplied, producers compete to sell their products, leading to lower prices. On the other hand, the law of demand states that as demand decreases, prices generally decrease. When there is lower demand for a product, sellers may lower prices to attract more buyers.

Additionally, the statement that as supply decreases, prices increase is also true. When the quantity supplied decreases, the scarcity of the product can drive up prices as buyers are willing to pay more for limited supply. The average rate of change refers to how much a quantity changes as the price increases. It is not directly related to supply and demand dynamics, but rather focuses on the relationship between quantity and price. As demand rises, the price of a product generally increases. This is because as more people want to buy a product, sellers can charge higher prices since there is higher demand.

Answer:

10 combinations

Step-by-step explanation:

What we have to do is calculate the number of combinations of 3 in 5.

The formula for the combinations is:

nCr = n!/r!(n-r)!

in this case n = 5 and r = 3

replacing

5C3 = 5!/3!(5-3)! = 5!/(3!*2!)

5C3 = 10

So there are 10 combinations in which Erika can enjoy the books on her trip

Answer:

The number of different combinations of 3 books that Erika can take on a trip if she has 5 books is 10

Step-by-step explanation:

Here we have the formula for combination given as follows;

[tex]\binom{n}{r} = \frac{n!}{r!(n-r)!}[/tex]

Where n is the number of set  elements = 5 and

r = Number of subset elements = 3

Therefore, plugging the values, we have;

[tex]\binom{5}{3} = \frac{5!}{3!(5-3)!} = \frac{120}{6(2)} = 10[/tex]

Therefore, the number of different combinations of 3 books that Erika can take on a trip if she has 5 books = 10.

Answer:

-p - 30

Step-by-step explanation:

4p−5(p+6)

Distribute:

=4p+(−5)(p)+(−5)(6)

=4p+−5p+−30

Combine Like Terms

=4p+−5p+−30

=(4p+−5p)+(−30)

=−p+−30

=−p−30

Answer:

behaviour

Step-by-step explanation:

80 feet per second

Step-by-step explanation:

just divide the amount he fell by the amount of time it took so you would take 400/5 and get the answer

Answer:

80

Step-by-step explanation:

If it took him 5 seconds to drop 400 feet then you have to divide it by 5 to determine the rate he can drop a certain amount of feet per second.

Answer:

-0.555

Step-by-step explanation:

The terminal point of the vector in this problem is

(-2,-3)

So, it is in the 3rd quadrant.

We want to find the angle [tex]\theta[/tex] that gives the direction of this vector.

We can write the components of the vector along the x- and y- direction as:

[tex]v_x = -2\\v_y = -3[/tex]

The tangent of the angle will be equal to the ratio between the y-component and the x-component, so:

[tex]tan \theta = \frac{v_y}{v_x}=\frac{-3}{-2}=1.5\\\theta=tan^{-1}(1.5)=56.3^{\circ}[/tex]

However, since we are in the 3rd quadrant, the actual angle is:

[tex]\theta=180^{\circ} + 56.3^{\circ} = 236.3^{\circ}[/tex]

So now we can find the cosine of the angle, which will be negative:

[tex]cos \theta = cos(236.3^{\circ})=-0.555[/tex]

Answer: The probability of being chosen by a wand made of holly or a wand made of dragon scale core is 0.4 or 40%

Step-by-step explanation: What we have are probabilities of two events. The first is the probability that Harry Potter is chosen by a wand made of Holly which is P(A). The other event is the probability that Harry is chosen by a wand with a dragon scale which is P(B).

In other to calculate P(A), there is a total of four possibilities, (that is holly, elm, maple and wenge). Therefore, the probability is derived as;

P(A) = Number of required outcomes/Number of all possible outcomes

P(A) = 1/4 or (0.25)

To calculate P(B), there is a total of five possibilities (that is phoenix feather, unicorn hair, dragon scale, raven feather and thestral tail). Therefore the probability is derived as;

P(B) = Number of required outcomes/Number of all possible outcomes

P(B) = 1/5 or (0.20)

However, the question requires the probability of P(A or B).

First we derive the probability of being chosen by a wand made of holly AND one made of a dragon scale core. In other words we shall calculate the probability of P(A and B) which is derived as;

P(A and B) = P(A) x P(B)

P(A and ) = 1/4 x 1/5

P(A and B) = 1/20 (0.05)

The probability of P(A or B) can now be calculated as follows;

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = (0.25 +0.20) - 0.05

P(A or B) = 0.45 - 0.05

P(A or B) = 0.40

Therefore the probability that Harry Potter is chosen by a wand made of Holly or a wand with Dragon scale core is 0.4 or 40%

Answer: P( A or B) = 2/5

Step-by-step explanation:

Answer:

10 feet

Step-by-step explanation:

The height of the ball after it hits the floor and rebound is defined by the recursive formula:

[tex]a_n = 0.85a_{n-1}[/tex]

This is an example of a geometric sequence in which the next term is gotten by multiplication of the previous term by 0.85.

If the ball is dropped from a height of 10 feet, the first term is 10.

Its Initial height, [tex]a_1=10 \:feet[/tex]

Answer:

s=-8

Step-by-step explanation:

Answer:

68 tickets

Step-by-step explanation:

This is a problem that involves a system of equations, the first step is to define your variables and write equations to represent the situation.

x = number of advance tickets

y = number of door tickets

x + y = 184

3x + 5y = 688

Next, you need to solve for one variable, based on how these equations are written, the best method would be to solve by multiplication.

-3(x + y = 184) (multiply equation by -3)

-3x - 3y = -552

Now we need to combine the two equations together

3x + 5y = 688

-3x - 3y = -552

From here we can eliminate the x variable when subtracting the equations, this results in:

2 y = 136

y = 68

Therefore, 68 tickets were sold at the door.

Answer:

tbh im not sure but i think the answer is 30 ft

Step-by-step explanation:

Answer:

1633.3 meters

Step-by-step explanation:

-Given the angle of depression is 31°, and the plane's height above the ground is 1400m.

-We use the Law of Sines to determine the distance between the plane and the rock.

-The angle of elevation from the rock to the plane is(corresponds to the plane's altitude):

[tex]\angle elevation=90-31\\=51\textdegree[/tex]

#Now, using Sine Law;

[tex]\frac{a}{Sin \A}=\frac{b}{Sin \ B}\\\\\\\frac{1400}{Sin \ 59}=\frac{d}{Sin \ 90}\\\\\\\\=1633.287\approx 1633.3\ m[/tex]

Hence, the direct distance between the plane and the rock is 1633.3 meters

false because it is formed wrong

Final answer:

The equation y = x^3 - 4 is not a linear equation because it contains a cubic term (x^3), which means the graph is a curve, not a straight line. Therefore, the correct answer is false.

Explanation:

The equation y = x3 − 4 is not a linear equation. A linear equation is one in which every term is either a constant or the product of a constant and the first power of a variable. In the given equation, the term x3 indicates that it is a cubic term because the value of x is raised to the power of three, suggesting that the graph of this equation would be a curve, not a straight line. Therefore, the correct answer is false.

Linear equations have the general form y = mx + b, where 'm' is the slope and 'b' is the y-intercept. Examples of linear equations include y = −3x, y = 0.2 + 0.74x, and y = −9.4 − 2x, which can all be graphed as straight lines. In contrast, an equation like y = x3 − 4 does not fit this form and therefore is not considered linear.

Answer:

this is to much work for me to do.

Step-by-step explanation:

Answer:

0.4444444

Step-by-step explanation:

2/3 x 2/3 = 0.4444 repeating!

Hope this helps!

Answer:

1 is c

2 is b

3 is d

4 is a

Step-by-step explanation:

Open circle is 'less than' or 'greater than'.

Closed (shaded) circle is 'less than or equal to' or 'greater than or equal to'.

Answer:

  yes

Step-by-step explanation:

The average weight of the three bags is ...

  (55 +51 +48)/3 = 154/3 = 51 1/3 . . . pounds

By removing 3 2/3 pounds of sand from the heaviest bag, adding 1/3 pound to the middle-weight bag, and the remaining 3 1/3 pounds to the lightest bag, Ortega can make all of the bags weigh the same: 51 1/3 pounds.

Answer:

The probability that he selects a raisin bagel and then a plain bagel is [tex]\frac1{11}[/tex].

Step-by-step explanation:

Probability:

The ratio of the number of outcomes of favorable event to total number of all possible outcomes is called probability of the favorable event.

[tex]Probability=\frac{\textrm{The number of favorable outcomes}}{\textrm{Total number of all possible}}[/tex]

Given that, there are 4 blueberry, 6 raisins and 2 plain bangles in a bag.

Total number of bangles= (4+6+2)

                                        = 12

The probability that he selects a raisin

[tex]=\frac{\textrm{Number of raisin bangles}}{\textrm{Total number of bangles}}[/tex]

[tex]=\frac{6}{12}[/tex]

[tex]=\frac12[/tex]

Total number of remaining bagels is =(12-1)=11

After selecting a raisin  bagel,the probability that he selects a plain bangle is

[tex]=\frac{\textrm{Number of plain bangles}}{\textrm{Total number of bangles}}[/tex]

[tex]=\frac{2}{11}[/tex]

Selecting of a raisin bangle and a plain bangle are both independent event.

The probability that he selects a raisin bagel and then a plain bagel is

[tex]=\frac{1}2\times\frac{2}{11}[/tex]

[tex]=\frac1{11}[/tex]

Answer:

Grows, Factor of 2

Step-by-step explanation:

The relationship between the elapsed time, t, in years, since Takumi started studying his tree, and the total  number of its branches, N(t), is modeled by the function:

[tex]N(t) = 63. 2^t[/tex]

For illustration, let us take the growth for the first three years after he started studying the number of branches.

[tex]When \:t=1, N(1) = 63. 2^1=126\\When \:t=2, N(2) = 63. 2^2=252\\When \:t=3, N(3) = 63. 2^3=504\\504\div 252=252\div 126=2[/tex]

We notice that for each subsequent year, the number of branches doubles.

Therefore:

Every year, the number of branches  grows by a factor of 2.