Determine which statement completes each open sentence:

32+8+1
15 (1+2)
4²
4.2
3(x - 4 + x)
when x = 4
111
3(x-4 + x)
when x = 2
32-1
15 +1 +2
3x4+x
3x4+x
1. is equal to
2. is NOT equal to

Answer: The answer is 1013, it is already rounded as much as it can go.

Step-by-step explanation:

Given data:

The given expression for height is h=3t+2.

Substitute 30 for t in the above expression.

Thus, the height of the balloon after 30 seconds is 92 ft, so option (C) is correct.

Answer: A. 3(2x−1)(x+2)

The solution of the inequality (x-3)(x-5) ≥ 0 is union of two intervals

 (-∞,3] or  [5,∞) that is x ≥5 or x≤3

An inequality is a statement that compares two expressions using ≤, ≥, <, > .

We can solve an inequality by adding same number to both sides or by subtracting same number from both side. While adding or subtracting the sign of the inequality will not change.

Given inequality (x-3)(x-5) ≥ 0

It generates two cases either case1 is true or case 2.

Case1.   (x-3)(x-5) ≥ 0 when (x-3) ≥0 and (x-5)≥0

       ⇒(x-3) ≥0 and (x-5)≥0

     ⇒ x ≥ 3 and x ≥ 5

     ⇒ x ∈ [3,∞) and x∈ [5,∞)

    ⇒  x ∈ [3,∞) ∩[5,∞)

    ⇒ x ∈ [5,∞)

∴ x is greater than or equal to 5

Case 2: (x-3)(x-5) ≥ 0 when (x-3) ≤0 and (x-5)≤0

      ⇒(x-3) ≤0 and (x-5)≤0

     ⇒ x ≤3 and x ≤ 5

     ⇒ x ∈ (-∞,3] and x∈ (-∞,5]

    ⇒  x ∈ (-∞,3] ∩ (-∞,5]

    ⇒ x ∈  (-∞,3]

∴ x is less than or equal to 3

Solution of the given inequality is case 1 or case 2

⇒  x ∈ [5,∞) or  x ∈  (-∞,3]

⇒ x  x ∈  (-∞,3] ∪ [5,∞)

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The correlation for r = -0.009 is B. weak negative.

The Pearson correlation coefficient (r) is the most commonly used metric for determining a linear relationship. It is a number ranging from -1 to 1 that indicates the strength and direction of a link between two variables. When one variable shifts, the other shifts in the same way.

Positive correlation is graded on a scale of 0.1 to 1.0. Weak positive correlation would be between 0.1 and 0.3, moderate positive correlation between 0.3 and 0.5, and strong positive correlation between 0.5 and 1.0. The stronger the positive correlation, the more probable the equities will move in unison. Having a minus means it's negative correlation.

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Answer:

If you’re in the mood for a scary movie, you may want to check out one of the five most popular horror movies of all time—I am Legend, Hannibal, The Ring, The Grudge, and The Conjuring. Figure 1 shows the amount, in dollars, each of those movies grossed when they were released as well as the ticket sales for horror movies in general by year. Notice that we can use the data to create a function of the amount each movie earned or the total ticket sales for all horror movies by year. In creating various functions using the data, we can identify different independent and dependent variables, and we can analyze the data and the functions to determine the domain and range. In this section we will investigate methods for determining the domain and range of functions such as these.

Step-by-step explanation:

Answer:

the anwser is 180

Step-by-step explanation:

Answer:

Step-by-step explanation:

answer is the first one: square root property of equality

BTS zzz

Answer:

Reflexive property of equality

Step-by-step explanation:

look at the image

Answer:

BC = 10

Step-by-step explanation:

given CD ≅ BC , then

BC = CD , that is

3x + 1 = 13 - x ( add x to both sides )

4x + 1 = 13 ( subtract 1 from both sides )

4x = 12 ( divide both sides by 4 )

x = 3

Then

BC = 3x + 1 = 3(3) + 1 = 9 + 1 = 10

Let's use the variable x to represent the length of the paper and y to represent the width of the paper.

If there are margins of 1 inch along the sides and 3 inches along the top and bottom, and the area with printer matter is 27 in², we can write the equation:

Solving for x, we have:

Then, the equation that we want to minimize is the area equation, so:

The critical points of this function are:

y = 0 (one of the roots)

y = -15/2 (one of the roots)

y = 6 (function is not defined)

Answer:

Solutions Below.

Step-by-step explanation:

These questions test on the concept of Functions Substitution.

Function Substitution is about giving an input (domain) to a function to produce an output (range)

Example: f(x) = 9x , f(9) = 9(9) = 81

We are given the following function:

f(x) = 10x + 8, where we can express it as

y = 10x + 8

Now we can find the value of f(5) by substituting x = 5 into the function. (Meaning: Find the value of y when x = 5.)

f(5) = y = 10(5) + 8 = 50 + 8 = 58

Next, applying the same concept, we can find the value of f(-7) by substituting x = - 7 into the function. (Meaning: Find the value of y when x = -7.)

f(-7) = y = 10(-7) + 8 = -70 + 8 = - 62

This last question requires us to work in reverse, where we find the value of x when f(x) = y = 88.

f(x) = y = 10x + 8

10x + 8 = 88

10x = 88 - 8

10x = 80

x = 80 ÷ 10 = 8

The equation that passes through the given points is the 3 option which is y = -3/2 x + 5

A x + B y = C represents a two-variable linear equation in its standard form. As an illustration, the conventional form of the linear equation 2x + 3y = 5 It is rather simple to locate both intercepts when an equation is stated in this way (x and y). An algebraic equation with simply a constant and a first-order (linear) term, such as y = mx +b, where m is the slope and b is the y-intercept, is known as a linear equation. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times. Ax + b = 0, where a and b are two integers, and x is a variable, is an example of a linear equation with one variable. This equation has only one solution. 2x + 3 = 8, for instance.

According to the given points

x = -1

So

y = (-3/2)(-1) + 5

y = 6.5

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The proportion of elementary school children who get between 9 and 10 hours of sleep per night is 0.6367 or 63.67%.

The amount of sleep that elementary school children get per night  be denoted by X, X follows a Normal distribution with a mean of 9.5 hours and a standard deviation of 0.55 hours.

the proportion of elementary school children who get between 9 and 10 hours of sleep per night is equal to

P(9≤ X ≤ 10) = P((9 - 9.50)/0.55 ≤ Z ≤ (10 - 9.50)/0.55)

P(9≤ X ≤ 10) = P(-0.9091 ≤ Z ≤ 0.9091)

P(9≤ X ≤ 10) = 0.6367

P(X > 12) = P(Z>(12 - 9.50)/0.55)

P(X > 12) = P(Z>4.5455

P(X> 12) = 0.000

THere is zero possibility of student to get more than 12 houtrs of sleep

The proportion of elementary school children who get between 9 and 10 hours of sleep per night is 0.6367 or 63.67%.

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Answer:

Step-by-step explanation:

it would be a 20% tip

Answer:

3.75

Step-by-step explanation:

5% of 75 is 3.75

Answer:

2/5

Step-by-step explanation:

8+12=20

8/20 12/20

8 ÷ 4= 2

20÷4= 5

2/5

The number of the total students that are at the school is 570 if the ratio of boys to girls in a school is nine: ten and there are 300 girls at the school.

The ratio formula is given as a:b = a/b for any two quantities, let's say a and b.

Given that a and b are separate amounts for two quantities, the combined total quantity is denoted as (a + b).

Three steps are necessary to determine the ratio of three numbers:

Step 1: Add the ratio's numbers together to determine the total number of pieces.

Step 2: By dividing the given sum by the total number of parts, determine the value of each component in the ratio.

Step 3: Divide the original ratio by the sum of each component's values.

The ratio is given as 9:10 as boys to girls.

Number of girls = 300

Thus, girls will be 10x and boys will be 9x

then 10x = 300

⇒x = 30

Then we can calculate the number of boys as

9x = 9*30

=270

Thus, the total number of students in the school

= exact number of girls + exact number of boys

= 300 + 270

= 570

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√49 = +/- 7

√16 = +/- 4 as you calculated

Congrats, you did it!

Answer:

B. x = -3

Step-by-step explanation:

f(x) = y

or however the vertical axis is called.

that is just something you always have to consider.

so, for what value of x does the functional curve ever reach the result (y) value of 3 ?

imagine a horizontal line you put through y = 3.

at what points is the functional graph touching or intersecting this line ?

at exactly 1 point. and that is at x = -3.

In the graph given, the line of reflection for the triangle XYZ and triangle X'Y'Z' is x=2.

Given, the coordinates of the triangle XYZ are:

X = (4,5)

Y = (6,3)

Z = (3,2)

and the coordinates of the triangle X'Y'Z' are:

X' = (0,5)

Y' = (-2,3)

Z' = (1,2)

for image of the triangle XYZ to get reflected and become X'Y'Z',

reflection of axis takes place.

But the images are not identical and symmetrical, so the reflection is not about y axis.

we check for x=2

hence reflection of axis when x=a is :

P(x,y) →x'(2a-x , y)

therefore use the above formula and check the coordinates of the reflected image.

X(4,5) → X'(2(2)-4 , 5)

x(4,5) → X'(0,5)

Y(6,3) → Y'(2(2)-6 , 3)

Y(6,3) → Y'(-2,3)

Z(3,2) → Z'(2(2)-3 , 2)

Z(3,2) → Z'(1,2)

hence x=2 is the reflection of triangle XYZ and X'Y'Z'.

Therefore we get the requires answer.

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Answer:

x = 200

Step-by-step explanation:

a) Simplify both sides of the equation.

1/5x - 2/3(15) = 30

1/5x + -10 = 30

1/5x - 10 = 30

b) Add 10 to both sides.

1/5x - 10 + 10 = 30 + 10

1/5x = 40

c) Multiply both sides by 5.

5 * (1/5x) = (5) * (40)

x = 200

The shape comprises a semicircle, rectangle, and a trapezoid

A) The shape below will illustrate how the side length of the rectangle will be calculated

Part I is the semicircle of diameter

From the diagram above

To find the missing side length of the rectangle , we will use the relation below

Where.

By substituting the values, we will have

The missing side length of the rectangle is = 4.5 cm

Hence,

The rectangle can be represented below as

The formula for the area of the rectangle is

By substituting the values, we will have

Hence,

The Area of the rectangle = 36cm²

B) To calculate the area of the semicircle, we will use the formula below

By substituting the values , we will have

Hence,

The area of the semicircle = 25.13 cm²

To calculate the area of the trapezoid, we will use the formula below

The diagram below represents the trapezoid

By substituting the values, we will have

Hence,

The area of the trapezoid is = 40.25cm²

To calculate the total area of the shape, we will use the formula below

By substituting the values, we will have

Hence,

The Total Area of the composite shape = 101.38cm²

Answer:

a.) x = 5

b.) x = 35/2 = 17.5

Step-by-step explanation:

In both problems, we are trying to solve for x, which means we need to isolate it on one side of the equation.

a.) 5/2 x + 1 = 11

5/2 x = 10

Now to divide by a fraction is the same as multiplying by the reciprocal.

x = 10 * 2/5 = 4

b.) 2/7 x - 3 = 2

2/7 x = 5

To divide by a fraction is the same as multiplying by the reciprocal.

x = 5 * 7/2 = 35/2 = 17.5

Answer: (-3, 0)

Step-by-step explanation: Isolate the y variable, so you get 15y = 15 + 5x, then divide by 15, y = 1 + 1/3x. To get the x intercept, the y has to be equal to 0, so we get 0 = 1 + 1/3x.

0 = 1+1/3x

-1 = 1/3x

-3 = x

Answer:

x = - 3

Step-by-step explanation:

To get the x intercept, y has to be equal to 0.

- 5·x + 15·y = 15

- 5·x + 15·0 = 15

- 5·x = 15

x = 15/(- 5)

x = - 3

The formula for Permutation is,

The expression given is,

Given:

Plug in n = 9, r = 4

Simplify

Hence, the answer is 3,024.

Angles supplementary to ∠3 are ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, and ∠7.

So, angles supplementary to ∠3:

(Refer to the image attached below)

Therefore, angles supplementary to ∠3 are ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, and ∠7.

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Answer:

8n+16

Explanation:

Given the expressions:

First, distribute 8 over the terms in the bracket:

Finally, collect like terms and simplify:

An equivalent expression is 8n+16.

An equation represents proportional relationship when dividing the quantities of the equation results in a quotient that is always the same.

Equation: y = mx and m is a constant value, which means is the same.

A. Equation: 120 - x = L

Equation from alternative A is NOT proportional since the division of the quantities doesn't result in a constant.

B. Equation: 1.08p = t

Dividing total cost per item's price, will always give the sales tax, which is constant. So, this equation IS proportional.

t/p=1.08

C. Equation: x=m/4

This equation is proportional because dividing marbles per how much each sister gets, always gives the number of sisters:

m/x=4

D. Equation: V= 12s^2

This equation is NOT proportional because side length is squared, so it is not constant linearly.

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SOLUTION

From the diagram at the right of the question, a right-angle has been formed already. So we will use SOHCAHTOA to find angle A. Looking at angle A, the opposite side is 140 ft and the adjacent side is 173 ft.

Using TOA, we have

Hence the answer is 39 degrees

Answer: Reduce 12/28 to the lowest terms The simplest form of 12 28 is 3 7.

Step-by-step explanation: I hope this helps!