Drag each label to the correct location on the table. Match each equation with its number of unique solutions. y = -52 – 41 +7 y = –202 + 91 - 11 y = 3.12 – 61 + 3 Two Real Solutions One Real Solution One Complex Solution Two Complex Solutions Reset Next reserved

Answer:

7/6 feet

Step-by-step explanation:

The board is 3 and 1/2 feet long, so it is 3+(1/2) feet long.

3 + 1/2 = ?

3/1 + 1/2 = ?

6/2 + 1/2 = ?

(6 + 1)/2 = ?

= 7/2

3 + 1/2 = 7/2

In other words, the board is 7/2 feet long.

Now we have to divide by 3 since Andrea is cutting the board in three pieces.

So:

(7/2)/3       or        (7/2) ÷ 3       or        [tex]\frac{\frac{7}{2}}{3}[/tex]        or     (7/2) × (1/3)

= 7/(2×3)

= 7/6

So we found that each piece (after cutting the board into three pieces) is 7/6 feet long.

Answer:

14.7 times bigger is (1.176 x 10¹) than (8 × 10-¹) if the numbers are  (1.176 x 10¹) than (8 × 10-¹).

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

To compare numbers this way, we divide.

(1.76 × 10^1) / (8 × 10^-1) =

= 1.76/8 × 10^1 / 10^-1

= 0.22 × 10^(1 - (-1))

= 0.22 × 10^2

= 22

Answer:Answer: number 2 is correct

We will have the following:

When we solve for x we will have

So, x is equal or grater than -5.

The approximate air distance from La Sarre to Lebel-sur-Quevillon is 167.71 km.

To determine the air distance from La Sarre to Lebel-sur-Quevillon, analyze the path she has traveled.

When she drove east and drove another north, the total path she ave traveled is similar to the sides of a right triangle, where the distance from the start and end point is the hypotenuse. (see photo attached)

Using Pythagorean theorem, solve the distance from La Sarre to Lebel-sur-Quevillon.

c² = a² + b²

where a = 150 km and b = 75 km

distance² = 150² + 75²

distance² = 22500 + 5625

distance² = 28125

distance = 167.71 km

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Answer:

y=[tex]\frac{3}{2}[/tex]x - [tex]\frac{5}{2}[/tex]

Step-by-step explanation:

To get slope intercept form (y=mx+b), simplify and solve for y.

y+1=[tex]\frac{3}{2}[/tex](x-1)

Simplify

y+1=[tex]\frac{3}{2}[/tex]x - [tex]\frac{3}{2}[/tex]

Solve for y

y=[tex]\frac{3}{2}[/tex]x - [tex]\frac{5}{2}[/tex]

The answer for the equation:

7x+31 = 8x -1/3(27x+3) is x=-4

The width of the cooling tower at the base of the structure is (D) 40 meters.

Now, calculate the cooling tower's width:

Equation: x2/400 given (y-90)

Calculating the width:

Therefore, the width of the cooling tower at the base of the structure is (D) 40 meters.

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The area of the figure given below is 56.6 units² .

In the question ,

a figure is given

where there is one rectangle and two semicircles .

the length of the rectangle is given as 11 units

and the breadth of the rectangle is = 4 units

we know that the area of the rectangle is = length × breadth

on substituting the values ,

we get

area = 11 × 4

area = 44 units²

the radius of the semicircle = 2 units

the are of the semi circle = (1/2)*π*r²

since there are two semicircle , the area of the two semi circle will be

= 2 * (1/2)πr²

= π*r²

On substituting , the value of radius = 2 ,

we get the area is = 3.14*(2)² = 12.56       using π = 3.14

so the area of the complex figure is = 44 + 12.56 = 56.56

≈ 56.6

Therefore , The area of the figure given below is 56.6 units²  .

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The length of the rectangular pegboard is 80 inches

A rectangle is a polygon with four sides in which two opposite sides are parallel and equal

Since Vince is cutting a rectangular piece of pegboard to use in his garage for organization. The width of the pegboard is 8 inches less than half the length. The perimeter of the pegboard is 224 inches.

Let

Since the width of the pegboard is 8 inches less than half the length, we have that

W = L/2 - 8

Also, since the pegboard is a rectangle, its perimeter, P = 2(L + W)

Now, its perimeter P = 224 inches.

So, 2(L + W) = 224

L + W = 112

Now, substituting the width, W into the equation, we have

L + W = 112

L + L/2 - 8 = 112

L + L/2 = 112 + 8

L + L/2 = 120

3L/2 = 120

L = 120 × 2/3

L = 240/3

L = 80 inches

So, the length of the pegboard is 80 inches

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We have the next function

First we need to make h(x)=y

Then we make x=y and y=x

Then we isolate the y

Therefore the inverse function is

The 80th percentile for the number of hours spent studying each day is 7.07 hours.

A data set with a normal distribution has the majority of its values clustered in the middle of the range, while the remainder taper off symmetrically toward either extreme. The term "standard deviation" refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are dispersed when the standard deviation is high.

The percentage of scores below a given value is shown by percentiles. They provide information about how a score compares to other scores.

Given Data :

Mean time (u) = 6.4 hour

Standard Deviation = 0.80 hour

It is given that the probability distribution is normal.

The formula for the z-score is z =( x- mean)/standard deviation

For the 80th percentile,  the z value from the z table is 0.842.

We have,

0.842 = (x - 6.4)/0.8

0.842*0.8 = x - 6.4

0.6736 =x - 6.4

x = 0.6736 + 6.4

x = 7.0736

x = 7.07

Hence, the 80th percentile for the number of hours spent studying each day is 7.07 hours.

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To solve an inequation for x you have to follow the same procedure you follow when solving equations, with exception that when you multiply/divide by a negative number the direction of the inequality gets inverted.

So to solve the given inequelity for x, you have to pass "+49" to the other side of the expression. To do so, subtract it from both sides of the expression:

The result of the inequality is x > -21

Given data:

The given amount of equipment purchased by the Sandra is A=$1,200.

Answer:

x>-2

Step-by-step explanation:

3 times five is fifteen, which is larger than 12, so all x needs to be is be bigger negative 2.

Compound interest: $8,765.58

We need to know how to read a graph inorder to solve the problem. At the end of 6 weeks, Lorena will have more money, she will have $8 more than Benita.

We know that Lorena started with $40 and she added $8 every week. We need to find out the final amount she has at the end of 6 weeks. For Benita, we can see from the graph that she started with $50, since the graph starts from $50, and if we observe the amount after every week we can see that she adds $5 every week to the savings. We can directly say from the graph that the final amount Benita has after 6 weeks is $80.

amount Lorena has after 6 weeks = 40+ (6x8)=40+48=$88

Therefore we can see that Lorena will have more money after 6 weeks and she has $8 more than Benita.

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The proportion of these banks that had an interest rate less than 2.5 percent is 0.724.

For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

First, solve for the z-score using the formula below.

z-score = (x – μ) / σ

where x = individual data value = 2.5

μ = mean = 2.28

σ = standard deviation = 0.37

z-score = (2.5 - 2.28) / 0.37

z-score = 0.22 / 0.37

z-score = 0.5946

To get the proportion, find the probability that corresponds to the z-score in the z-table. (see attached images)

z-score = 0.5946

By interpolating the values,

probability = 0.724

proportion = 0.724

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The percentage of young adults who send fewer than 218 text messages is 99.87%.

For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

First, solve for the z-score using the formula below.

z-score = (x – μ) / σ

where x = individual data value = 218

μ = mean = 128

σ = standard deviation = 30

z-score = (218 - 128) / 30

z-score = 90 / 30

z-score = 3

Find the probability that corresponds to the z-score in the z-table. (see attached images)

z-score = 3

probability = 0.9987

To get the percentage, multiply the probability by 100.

percentage = probability x 100

percentage = 0.9987 x 100

percentage = 99.87%

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The cost of the total bill for the friends is $154.665.

This implies a levy that's paid to the government by individuals and firms.

From the information, the.group of friends’ dinner bill before tax is $122.75, sales tax rate is 8% and they want to leave an 18% tip after tax.

The total bill will be:

= Cost of food + Tax + Tip

= $122.75 + (8% × $122.75) + (18% × $122.75)

= $122.75 + $9.82 + $22.095

= $154.665

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⇒For perpendicular lines when their gradients are multiplied they have to give -1, in this case we are given a line with gradient [tex]\frac{1}{2}[/tex] meaning the gradient of the line perpendicular to it will be -2 since

[tex]-2*\frac{1}{2} =-1[/tex]  this means that the gradient of the new line will be -2

⇒Now we have a point and  gradient.

⇒And we know that the general equation for a straight line is y=mx+c

[tex]3=-2(0)+c\\3=c\\c=3[/tex]

The equation of the line perpendicular to the given one is

y=-2x+3

GOODLUCK!!

Given that;

Line a and b are two straight lines cut by two transversal lines l and m.

The tranversal line l shows that;

But also;

Thus,

Then, if two lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel.

Thus, line l is parallel to m

The sampling distribution for is normal (or approximately normal) and give its mean and standard deviation is  the mean is $28520 and its standard deviation is $762.5.

The notion of mean is crucial in both mathematics and statistics. The mean is the average or most frequent value among a set of numbers. It is a statistical measure used to determine the median and mode of a probability distribution's central tendency. It's also known as an expected value. Sum of all observations divided by the total observations equals the mean. The term "standard deviation" refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.  

Given information :

Mean annual income = $28540

Standard Deviation = $5000

Given sample size is n = 43

Sample size doesn't affect the mean, hence the mean remains the same

New mean = $28540

New standard Deviation = Standard Deviation / n^1/2 = 5000/ (43)^1/2

New standard Deviation = 5000/6.5574 = $762.5

Hence, The mean is $28520 and its standard deviation is $762.5

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Answer:

can't answer the first two questions as figure is not mentioned in picture

3. -3

4. 6

5. 3/4

6. -3

7. 5

8. 3

Step-by-step explanation:

Mathematics → Solid Figures → Volume

The volume of a cylinder is:

In this question,

r = 2 ft (4/2 =2)

h = 5 ft

Then, the volume of the cylinder is (Vc):

Using π = 3:

The volume of a rectangular prism (Vr) is:

In this question:

l = 9 ft

w = 5 ft

h = 5 ft

Then, the volume of the rectangular prism is:

The volume of the object (V) is the sum of the volumes:

Answer: 285 ft³.

Explanation:

Take any two whole numbers you want. Multiplying them together always result in some (other) whole number.

Examples:

In other words,

(whole number)*(whole number) = whole number

This is why we consider the set closed under multiplication.

The equation of the line is found as y = -x/2 + 9/2.

For the given question;

The equation of the perpendicular line is given as;

y = 2x - 7

Compare the equation with the standard form of slope intercept.

y = mx + c

m = slope and c is the y intercept.

m1 = 2

Now, the line is perpendicular, thus the relation between both slopes is;

m1 × m2 = -1

m2 = -1/2

The passing coordinates of the line is (1. 4).

Find the equation using formula.

y - y1 = m2(x - x1)

y - 4 = (-1/2) (x - 1)

Simplifying,

y = -x/2 + 9/2

Thus, the equation of the line is found as y = -x/2 + 9/2.

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