Find the volume of this prism.

Answer:

7 and 7x

Step-by-step explanation:

We distributing these factors are the only that can make sense

D. The length is 18 inches and the width is 9 inch

What is a scale factor?

A scale factor resembles a unit scale in several ways. It is a ratio that assesses the relationship between scale and real dimensions. Because it doesn't provide any specified units, it differs.

It is given that the scale factor of the gardener is 1:15.

The dimensions of his drawing are 6 inches long by 3 inches wide.

Therefore the original dimensions are 6*15= 90 inches.

3*15= 45 inches.

The scale of his partner is 1:5.

So, we have to divide the original dimensions by 5.

The dimensions of the scale drawing are 90/5= 18 inches long

45/5=9 inches wide.

Therefore length is 18 inches and the width is 9 inches.

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Answer: B

Step-by-step explanation:

if r is close to 1 (or -1) it means the relationship is strong, -0.2041 is really close to 0 so the data is most likely scattered and the association is weak

Answer:

Strong

Step-by-step explanation:

edge 2023

Answer:-3

Step-by-step explanation: -7 -4

The time at which the rocket reaches its maximum height is 3.5 seconds. Therefore, b. is the correct answer.

An equation describing the relationship between the input (x) and the output (f(x)) is called the function f(x). Any equation that represents the connection between an input x and an output f is referred to as the function f(x) (x).

A function can be expressed as a graph or table in addition to the standard form of an equation. Functions can be stated using symbols and phrases in addition to equations. A function could be expressed, for instance, as "the square of x" or "f of x equals x squared."

Whatever form a function takes, it's critical to keep in mind that the input (x) always yields the same result (f(x)).

In the given question,

The maximum height of the rocket is achieved at the point when the velocity of the rocket is 112 feet. This can be determined by taking the derivative of the function S(t).

S'(t) = 112

Therefore, when S'(t) = 112, t = 3.5.

This means that the rocket reaches its maximum height at t = 3.5 seconds.

Therefore, the time at which the rocket reaches its maximum height is 3.5 seconds.

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Answer:

7 traders sell oranges and mangoes alone.

Step-by-step explanation:

(21 + 4 + 5 + 10 + x + 35 – x + 32 – x = 100)

(107 – x = 100)

(x = 107 – 100 = 7)

Therefore, 7 traders sell oranges and mangoes alone.

(b) (312_{four} + 52_{x} = 96_{ten})

(312_{4} = 3 times 4^{2} + 1 times 4^{1} + 2 times 4^{0})

= (48 + 4 + 2 = 54_{10})

(52_{x} = 5 times x^{1} + 2 times x^{0})

= ((5x + 2)_{10})

(therefore 54 + (5x + 2) = 96)

(56 + 5x = 96 implies 5x = 96 – 56 = 40)

(x = 8)

(therefore 312_{4} + 52_{8} = 96_{10})

Answer: No

Step-by-step explanation:

Valid only for numbers less than 40.

P(40) = 412 which is not a prime number

The binomial (x+5) is a factor of x² + 8x + 15 then the other factor is x+3.

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

Given that binomial  (x+5) is a factor of x² + 8x + 15.

We need to find the other factor.

Let us solve x² + 8x + 15=0

x² + 5x +3x+ 15=0

x(x+5)+3(x+5)=0

(x+3)(x+5)

So the other binomial factor is x+3.

Hence, the binomial (x+5) is a factor of x² + 8x + 15 then the other factor is x+3.

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A. Circle

B. Ellipse (which can resemble an oval)

Answer:

Step-by-step explanation:

Find the GCF:

12, 24, 36

8, 16, 24, 32

GCF is 24

The lowest amount of boxes the teacher could buy would be 2 boxes of Rulers and 3 boxes of Protractors. I hope this helped

Answer:

The statement "A = (1/2) (B)(B + 5)" represents the area of a triangle, where B is the base of the triangle and (B + 5) is the height. This formula is used by the carpenter to calculate the area of a triangle with a given base and height.

Step-by-step explanation:

The value of (f - g)(-1) is 5.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = -5x³ - 8x² - 4x + 3

g(x) = 3x³ - 2x² - 8x - 4

Now,

(f - g)(x)

= f(x) - g(x)

= -5x³ - 8x² - 4x + 3 - (3x³ - 2x² - 8x - 4)

= -5x³ - 8x² - 4x + 3 - 3x³ + 2x² + 8x + 4

= -8x³ - 6x² + 4x + 7

Now,

(f - g) (-1)

Substitute x = -1.

= -8(-1)³ - 6(-1)² + 4(-1) + 7

= -8 x -1 - 6 - 4 + 7

= 8 - 6 - 4 + 7

= 8 - 10 + 7

= 15 - 10

= 5

Thus,

(f - g)(-1) = 5

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If 5 1/2 ounce of mango has 17 1/2 grams of sugar and 4 ounces of pineapple has 25 grams of sugar, We will be having 7 grams of sugar for one ounce of mango and 6 1/4 grams of sugar for one ounce of pineapple.

The problem states that we have 5 1/2 ounces of mango with 17 1/2 grams of sugar, and 4 ounces of pineapple with 25 grams of sugar. We are asked to determine the grams of sugar per ounce for each type of food. To determine the grams of sugar per ounce for each type of food, we can use the following calculations:

For mango: 5 1/2 ounces is equivalent to 11/2 + 1/2 = 2 ounces + 1 ounce/2, so we have 17 1/2 grams of sugar in 2 1/2 ounces of mango. To find the grams of sugar per ounce, we can divide 17 1/2 by 2 1/2, which gives us 7 grams of sugar per ounce of mango.

For pineapple: 4 ounces of pineapple has 25 grams of sugar. To find the grams of sugar per ounce, we can divide 25 by 4, which gives us 6 1/4 grams of sugar per ounce of pineapple.

Therefore, the grams of sugar per ounce for mango and pineapple are 7 and 6 1/4, respectively.

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Complete question is:

5 1/2 ounce of mango has 17 1/2 grams of sugar and 4 ounces of pineapple has 25 grams of sugar. Determine the grams of sugar for ounce for each type of food​.

The length of the third side of a triangle with perimeter 9x + 6 and measures of other two sides of the triangle is equal to option a. x + 13.

Perimeter of the triangle is equal to

= 9x + 6

First side of the triangle = 5x

Second side of the triangle = 3x - 7

Let 'n' be the third side of the triangle

perimeter of the triangle = 9x + 6

⇒ 5x + 3x - 7 + n = 9x + 6

⇒ n + 8x - 7 = 9x + 6

⇒ n = 9x -8x + 6 + 7

⇒ n = x + 13

Therefore, the third side of the triangle with given perimeter of the triangle is equal to option a. x + 13.

The above question is incomplete , the complete question is :

A triangle has a perimeter of 9x + 6. the first side of the triangle has a length of 5x, and the second side has a length of 3x − 7. what is the length of the third side of the triangle?

a. x + 13       b. x − 1            c. 8x − 7         d. 17x − 1

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Answer:

it will be £960

Step-by-step explanation:

first £800×20/100

simplify £8×20

£160= VAT

Total cost=VAT+ normal cost

£160+£800

=£960

The equation of the quadratic function is x² + x - 6

Note that functions are equations, laws or expressions showing the relationship between two variables.

These variables are;

From the information given, we have that;

x = 2 and  = -3 are the roots

Then,

(x -2)(x + 3)

expand the bracket, we get;

x² + 3x - 2x - 6

collect the like terms, we have;

x² + x - 6

Hence, the equation is x² + x - 6 = 0

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The probability that a randomly selected worker lives more than 5 miles from work and rides their bicycle is 57%.

To calculate the probability that a randomly selected worker lives more than 5 miles from work and rides their bicycle, we need to use the data from the survey. Let's assume that the survey results are summarized in the following table (attached) :

From this table, we can see that the probability of a worker living more than 5 miles from work is 35%. We can also see that the probability of a worker riding their bicycle is 50%, and the probability of a worker living more than 5 miles from work and riding their bicycle is 20%.

To calculate the probability that a randomly selected worker lives more than 5 miles from work and rides their bicycle, we can multiply the probabilities of these two events:

P(Lives > 5 miles and Rides Bicycle) = P(Lives > 5 miles) x P(Rides Bicycle | Lives > 5 miles)

= 35% x (20%/35%)

= 0.5714 or 57% (rounded to the nearest whole percent)

Therefore, the probability that a randomly selected worker lives more than 5 miles from work and rides their bicycle is 57%.

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Answer:

Step-by-step explanation:

7/x^-8 = 7x^8

The ordered pairs from the graph of quadratic and linear equations are (-2, 7) and (2, -1)

A graph of a quadratic equation is a parabolic curve that opens up or down, depending on the sign of the coefficient of the squared term. A general form of a quadratic equation is given by:

y = ax^2 + bx + c,

where a, b, and c are constants. The graph of this equation can be plotted by choosing a range of values for x and calculating the corresponding values of y.

A graph of a linear equation is a straight line. A general form of a linear equation is given by:

y = mx + b,

where m is the slope of the line and b is the y-intercept.

In this problem, the ordered-pairs will be the point in which they intersect with each other.

Looking carefully at the graph, the ordered pair will be at points

A = (-2, 7)

B = (2, -1)

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The number of different necklaces that Ginger can make, with the same ratio of pink to white beads is 5 necklaces.

To find the number of necklaces, find the smallest equivalent ratio of pink to white beats used to make the necklace.

Pink beads : White beads

30 : 35

( 30 / 5 ) : ( 35 / 5 )

6 : 7

To find the find the number of beads, divide the number of pink beads available by the number of pink beads in the ratio:

= 30 / 6

= 5 necklaces

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The dimensions are 5 units each

The area of the rectangle is 25 units

It is important to note that algebraic expressions are defined as expressions that are composed of variables, terms, cofficients, constants and factors.

They are also described as expressions with mathematical operations.

From the information given, we have that;

x² - 5x + 3x - 15

To solve the quadratic equation, let us use the factorization method

Group the values in pairs

(x² - 5x) + (3x - 15)

factor the terms

x(x -5) +3(x - 5)

Then, x + 3 = 0

x = -3

And x - 5 = 0

x =5

But area of a rectangle is;

= Length× width

= 5 × 5

= 25 square units

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P(A)=1/5, P(B)=7/20, P(A and B)= 7/100. The events A and B are independent.

Two events are independent if the occurrence of one event does not affect the chances of the occurrence of the other event. The mathematical formulation of the independence of events A and B is the probability of the occurrence of both A and B being equal to the product of the probabilities of A and B (i.e., P(A and B).

1) P(A)=1/5, P(B)=7/20, P(A and B)= 7/100

Here, P(A and B)= P(A)×P(B)

= 1/5 × 7/20

= 7/100

So, the events A and B are independent.

2) P(A)=13/20, P(B)=13/20, P(A and B)= 169/400

Here, P(A and B)= P(A)×P(B)

= 13/20 × 13/20

= 169/400

So, the events A and B are independent.

3) P(A)=7/10, P(B)=2/5, P(A and B)= 21/100

Here, P(A and B)= P(A)×P(B)

= 7/10 × 2/5

= 14/50

So, the events A and B are not independent.

2) P(A)=1/5, P(B)=1/5, P(A and B)= 1/25

Here, P(A and B)= P(A)×P(B)

= 1/5 × 1/5

= 1/25

So, the events A and B are independent.

Therefore, options 1, 2 and 4 are correct answers.

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The correct statements are:

The length of the other leg is 6√2 feet.

The length of the hypotenuse is 12 feet.

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

Given:

One leg of an isosceles triangle is 6√2 feet.

As, we know isosceles triangle two of its sides equal in length then the other side can be  6√2 feet.

Now, using Pythagoras theorem

H² = P² + B²

H² = (6√2)² + (6√2)²

H² = 72 + 72

H² = 144

H= 12 units

The statements that applies here are:

The length of the other leg is 6√2 feet.

The length of the hypotenuse is 12 feet.

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Answer:

The answer is B and D

Step-by-step explanation:

I took the test.

let me know if you would like an explanation down in the comments!

To mode of given data set of number of days worked in october for 10 programmers of a software company is 7 and 14.

The mode of a data set is the value that appears most frequently. In this case, we can see that both 7 and 14 appear twice, while all other values appear only once. Therefore, there are two modes in this data set: 7 and 14.

To solve mathematically, we can use the mode formula:

mode = value with the highest frequency

In this case, we have two values with the highest frequency, which are 7 and 14. Therefore, the mode of given data set is 7 and 14.

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The roots of the quadratic equation are -

{x} = 4 ± i(√2/2)

The  general form of a quadratic equation is -

y = f(x) = ax² + bx + c

Given is the quadratic equation as -

f(x) = x² - 8x + 17

We can write the roots of the equation as -

x = {- b ± √(b² - 4ac)}/2a

x = {8 ± √(64 - 68)}/2

x = {8 ± i√2}/2

x = 4 ± i(√2/2)

Therefore, the roots of the quadratic equation are -

{x} = 4 ± i(√2/2).

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The blank in the statement should be filled in with "ΔVYZ." which is proven by the definition of congruence.

Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles. It is one of the fundamental shapes in geometry and is represented by the symbolΔ.

Since S, T, and U are midpoints in ΔVYZ, it follows that:

ST is a median of ΔVYZ, meaning it bisects the side VZ into two equal parts.

TU is a median of ΔVYZ, meaning it bisects the side VY into two equal parts.

SV is a median of ΔVYZ, meaning it bisects the side YZ into two equal parts.

Using the definition of congruence, two triangles are congruent if their corresponding sides are equal in length and their corresponding angles are equal in measure. Since medians bisect their corresponding sides, it follows that all three pairs of corresponding sides in ΔYST, ΔTUZ, and ΔSVU are equal in length.

Furthermore, since the medians divide the triangle into two smaller triangles that are similar to the original triangle, it follows that the corresponding angles in ΔYST, ΔTUZ, and ΔSVU are equal in measure.

Therefore, ΔYST ≅ ΔTUZ ≅ ΔSVU ≅ ΔVYZ.

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The solution of the function - 6x + 14 = - 2ˣ + 6 is 2. The required graphs are given below.  

We can solve the given function by adding or subtracting the same integer on both sides. Here adding or subtracting the same number on both sides doesn't change the condition of the function. In end-use trial and error mothed to find the value of the variable 'x'

Here we have

f(x) = - 6x + 14  and g(x) = - 2ˣ + 6  

The solution of - 6x + 14 = - 2ˣ + 6 can be calculated as follows

=> - 6x + 14 =  - 2ˣ + 6    

=> - 6x + 8 = - 2ˣ    

=> - 6x + 8 = - 2ˣ

=> - 6x + 2ˣ = - 8          

By using the trial and error method

At x = 2

=> - 6(2) + 2² = -8

=> - 12 + 4 = -8

Therefore,

The solution of the function - 6x + 14 = - 2ˣ + 6 is 2. The required graphs are given below.  

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The probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.

The number of possible subcommittees that contain only undergraduate students can be calculated by choosing 3 members from the 4 undergraduate students. This can be done in (4 choose 3) = 4 ways.

The total number of possible subcommittees of three students that can be formed from the 6 members of the committee can be calculated by choosing 3 members from the 6 students. This can be done in (6 choose 3) = 20 ways.

Therefore, the probability that there will be no graduate students on the subcommittee is:

Number of subcommittees with only undergraduate students / Total number of possible subcommittees

= 4 / 20

= 1/5

= 0.2

So, the probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.

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