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A race car drove around a circular track that was 0.4 mile. If 1 mile = 5,280 feet, what is the radius of the track, in feet? Use π = 3.14 and round to the nearest hundredth.

107.11 feet
214.21 feet
336.31 feet
672.61 feet

The system of inequalities is y < x + 2 and 5y ≤ -2x + 10

From the question, we have the following parameters that can be used in our computation:

The blue and the red lines

For the blue line, we have the following points

(0, 2) and (-2, 0)

The equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 2

Using the points, we have

-2m + 2 = 0

m = 1

So, we have

y = x + 2

The lower part is shaded and the line is a dotted line

So, we have

y < x + 2

For the red line, we have the following points

(0, 2) and (5, 0)

The equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 2

Using the points, we have

5m + 2 = 0

m = -2/5

So, we have

y = -2/5x + 2

The lower part is shaded and the line is a shaded line

So, we have

y ≤ -2/5x + 2

Multiply through by 5

5y ≤ -2x + 10

Hence, the system is y < x + 2 and 5y ≤ -2x + 10

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The weight of the kitten is expected to rise by 0.2 ounces for every extra day after birth. The correct answer is B.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

For the first three months following birth, data on kitten weight (in ounces) was gathered. A line of fit was constructed through the scatter plot with the equation w = 2.75 + 0.2d, where w is the kitten's weight in ounces and d is the kitten's age in days.

For each additional day after the kitten is born, its weight is predicted to increase by 0.2 ounces. Then the correct option is B.

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This could result in one, two, or multiple points of intersection, depending on the specific values of the deposits and the rates of increase.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

we can assume that the graph of Cera's and Bethany's savings accounts will show the total amount of money in their accounts after a certain number of weeks.

Since both Cera and Bethany deposit the same amount of money and make the same additional deposits each week, their savings will increase at the same rate. Therefore, the graph will likely show two parallel lines that start at $20 and increase by $15 per week.

The number of solutions modeled by the graph will depend on whether the two lines ever intersect. If the lines do not intersect, then there is no solution to the system of equations that model the two savings accounts. In other words, there is no point at which the total amount of money in both accounts is the same.

On the other hand, if the lines do intersect, then there is at least one solution to the system of equations. In this case, the point of intersection represents the week at which the total amount of money in both accounts is the same.

To change the situation so that the graphs model a different number of solutions, we could change the initial deposit or the amount of money deposited each week for one or both of the savings accounts. For example, if Cera starts with a higher initial deposit than Bethany, or if Cera deposits more money each week, then their savings will increase at different rates and the lines on the graph will not be parallel.

Therefore, This could result in one, two, or multiple points of intersection, depending on the specific values of the deposits and the rates of increase.

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The gym fee increases by $6 for each additional class taken. The average rate of change in cost per class is equal to the slope of the linear function, which is $6 per class.

What is average rate ?

Average rate refers to the rate of change of a quantity over a given period of time. It is calculated by dividing the change in the quantity by the time period over which the change occurs.

To find the average rate of change in cost per class, we need to calculate the slope of the linear function that relates the gym fee to the number of classes taken.

Let x be the number of classes taken, and y be the gym fee. We can use the two data points given to find the equation of the line:

When x = 6, y = 43

When x = 11, y = 73

The slope of the line passing through these two points can be calculated as follows:

slope = (change in y) / (change in x)

slope = (73 - 43) / (11 - 6)

slope = 30 / 5

slope = 6

Therefore, the gym fee increases by $6 for each additional class taken.

The average rate of change in cost per class is equal to the slope of the linear function, which is $6 per class.

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The second bar represents the price range from $2.51 to $5.00, so the data set includes the value of 4.53 and the value of 5.00 the correct answer is {0.50, 2.00, 2.52, 3.37, 4.53, 5.00, 8.99}

A histogram is a graph used to represent the frequency distribution of a few data points of one variable. Histograms often classify data into various “bins” or “range groups” and count how many data points belong to each of those bins.

The histogram shows the number of items sold at various price ranges, and the heights of the bars indicate the number of items sold within each price range.

The data set that is represented in the histogram is:

{0.50, 2.00, 2.52, 3.37, 4.53, 5.00, 8.99}

This is because the histogram has four bars with heights of 2, 4, 0, and 1, which correspond to the number of items sold in each of the four price ranges shown.

The values in the data set correspond to the boundaries of these price ranges. For example, the first bar represents the price range from $0.00 to $2.50, so the data set includes the value 2.00 (which is within this range) and the value 2.52 (which is just outside this range).

Similarly, the second bar represents the price range from $2.51 to $5.00, so the data set includes the value of 4.53 (which is within this range) and the value of 5.00 (which is the upper boundary of this range).

Therefore, the second bar represents the price range from $2.51 to $5.00, so the data set includes the value of 4.53 and the value of 5.00 the correct answer is {0.50, 2.00, 2.52, 3.37, 4.53, 5.00, 8.99}

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Answer:

Step-by-step explanation:

The length of a rectangular picture frame is 3 inches longer than it's width. If the perimeter of the picture frame is 38 Inches, what is the length and width ?

Given :

Perimeter of rectangle is 38 Inches

lenght is 3 inches more than the breadth.

let, width be x, and length be x+3

So, Breadth is 8 inches and length is 8+3= 11 inches.

Let's verify ::

Thus Solved !!

The answer to the probabilities are: (a) 0.8,  (b)  0.2  (c)  0.3  (d)  0.7

Probability is a branch of mathematics used to measure how likely something is to happen. It is calculated by taking into account the chance that a given event will occur, as well as taking into account an exhaustive set of equally likely outcomes

The percentage of married women is 80%

the number of women is 10

The probability that all of them dislike their mother in-laws is

P(x) = Number of required outcome/Number of possible outcomes

80/100 * 10  = 8 women

a)  P(All of them dislike their mother in-law is 8/10 = 0.8

b)  P(none of them dislike their mother-in-law is

P(x) = 1 0.8 = 0.2

c)  P(At least eight of them dislike their mother-in-law)

P(x) = 8, 9, 10 = 3

Therefore,  the probability is 3/10 = 0.3

d) P(no more than seven dislike their mother in-law

1,2,3,4,5,6,7 = 7

P(x) = 7/10 = .0.7

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The equation of line is y = ( -6/5 )x + 2 , where the slope is m = ( -6/5 )

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( -6/5 )

The y intercept of the line is b = 2

So , equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

On simplifying , we get

y = ( -6/5 )x + 2

Hence , the equation of line is y = ( -6/5 )x + 2 and the graph is plotted

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Answer:

-1/3

Step-by-step explanation:

When adding or subtracting fractions, you don't add or subtract the denominators.

So, Start by subtracting the numerators

3/9 - 6/9 = -3/9

you can simplify this fraction by dividing both the numerator and denominator by 3

-3 ÷ 3 = -1

9 ÷ 3 = 3

So, the answer is:

-1/3

Hope this helps!

Answer:

3×1×1.

Step-by-step explanation:

The restaurant gives us an Italian bread, a whole wheat role and a wrap:

Counted together that's 3.

Then they let us choose one type of meat:

Counted that's only 1.

Finally, they let us choose one type of cheese:

Counted that's also 1.

Together that makes 3×1×1.

Answer: it is 4:2

Step-by-step explanation: because it is a ratio, both sides can be divided by the same number and still have the same meaning. btw in this case both divided by 2

Answer:

1. 6/18 = 1/3

  9/21 = 3/7

2. 4/6 = 2/3

   2/4 = 1/2

3. 6/12 = 1/2

   8/12 = 2/3

4. 2/8 = 1/4

   3/6 = 1/2

5. 7/21 = 1/3

   8/10 = 4/5

6. 9/12 = 3/4

   12/20 = 3/5

7. 8/16 = 1/2

   10/25 = 2/5

Answer:

the output is −16

Step-by-step explanation:

x=-1

9·x-7

9·-1-7

-9-7

-16

The logical form of this argument is -

Denying the Antecedent.

Denying the antecedent, sometimes also called inverse error or fallacy of the inverse, is a formal fallacy of inferring the inverse from the original statement.

It is committed by reasoning in the form :

If P, then Q. Therefore, if not P, then not Q.

Given is the argument as -

"If seven clowns are squeezed into a small car, we are at the circus. Seven clowns are not squeezed into a small car. So, we are not at the circus"

The logical form of this argument is -

Denying the Antecedent

Therefore, the logical form of this argument is -

Denying the Antecedent.

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From the image given, inequality is -2≤x<8 from x≥-2, x<8. It serves as a concrete example of inequality.

Broadly speaking, a mathematical phrase that defines an order relationship between two integers equivalent algebraic expressions, showing whether one is bigger than, equal to, smaller than, or smaller than and equal to the other.

The sentence "5x - 4 > 2x + 3" seems like an equation because the mathematical sign for "equals" has indeed been replaced by an arrowhead. It serves as a concrete example of inequality. From the image given, inequality is -2≤x<8 from x≥-2, x<8.

Therefore, from the image given, inequality is -2≤x<8 from x≥-2, x<8.

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The area of the composite figure is equal to 63.270 square feet.

In this problem we need to compute the area of a composite figure, which is the result of adding the areas of a semicircle and a right triangle. The area formulas of the figures mentioned above are introduced below:

Semicircle

A = 0.5 · r²

Right triangle

A = 0.5 · b · h

Where:

If we know that r = 5 ft, b = 8 ft and h = 6 ft, then the area of the composite figure is:

A = 0.5π · (5 ft)² + 0.5 · (8 ft) · (6 ft)

A = 12.5π + 24 ft²

A = 63.270 ft²

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Answer:

864 sq cm

Step-by-step explanation:

Surface area of cube = 6 × (l)square units. = 6 × 12cm × 12cm = 6 × 144cm = 864cmsquare.

All the central angles are,

Red= 100°

blue= 150°

green= 50°

purple= 60°

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The data below shows the colors preferred by a group of people.

Cooler          Number of people

Red=                 20

blue=                 30

green=               10

purple=              12

Now, Total number of Peoples is,

⇒ 20 + 30 + 10 + 12

⇒ 72

Hence, We get;

Proportion of Red = 20/72 = 5/18 = 10/36

Central angle = 5/18 x 360 = 100°

Proportion of Blue = 30/72 = 15/36

Central angle = 15/36 x 360 = 150°

Proportion of Green = 10/72 = 5/36

Central angle = 5/36 x 360 = 50°

Proportion of Purple = 12/72 = 1/6 = 6/36

Central angle = 1/6 x 360 = 60°

Thus, All the central angles are,

Red= 100°

blue= 150°

green= 50°

purple= 60°

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The graph of the equation is added as an attachment

From the question, we have the following parameters that can be used in our computation:

y = 6x

The above expression is a linear equation that implies that

The product of 6 and x is equal to the the value of y

Note that:

A linear graph is a straight line on a two-dimensional coordinate plane that represents a linear equation

Where the equation is in the form y= mx + b, where m is the slope and b is the y-intercept.

This also means that

Next, we plot the graph

See attachment for the graph of the linear equation and few points on it

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A table that represents the function y = -3x/4 + 3 is: B. table B.

In order to use the given linear function to complete the table, we would have to substitute each of the values of x (x-values) into the linear function and then evaluate as follows;

When the value of x = -2, the linear function is given by;

y = -3x/4 + 3

y = -3(-2)/4 + 3

y = 9/2 (False).

When the value of x = -4, the linear function is given by;

y = -3x/4 + 3

y = -3(-4)/4 + 3

y = 6 (True).

When the value of x = 0, the linear function is given by;

y = -3x/4 + 3

y = -3(0)/4 + 3

y = 3 (True).

When the value of x = 4, the linear function is given by;

y = -3x/4 + 3

y = -3(4)/4 + 3

y = 0 (True).

When the value of x = 8, the linear function is given by;

y = -3x/4 + 3

y = -3(8)/4 + 3

y = -3 (True).

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The prove that triangle ABE is congruent to triangle CDE is given below

Generally, To prove that triangle ABE is congruent to triangle CDE, we need to show that they have the same size and shape.

First, we can see that angle AED and angle CEB are opposite angles and therefore congruent, since AB || DC.

Also, since line AB = line DC, we know that segment AE is congruent to segment CE and segment BE is congruent to segment DE.

Using these congruent sides and the congruent angle, we can apply the Side-Angle-Side (SAS) congruence criterion to conclude that triangle ABE is congruent to triangle CDE.

Therefore, we have proven that triangle ABE is congruent to triangle CDE.

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The price per pound of the carrots Dora bought is $0.80.

What is the unit rate?

Unit rate is a ratio that compares the amount of one unit of measure to the corresponding amount of another unit of measure. It is a special case of a ratio, in which the second term is always one. For example, if a car travels 120 miles in 2 hours, the unit rate of speed is 60 miles per hour, which means that the car travels 60 miles for every hour of driving.

Unit rate is commonly used in everyday life, such as in shopping (price per unit) or in cooking (ingredients per serving).

To find the price per pound of the carrots, we need to divide the total cost by the total weight.

First, we need to convert the mixed number 4 1/2 to an improper fraction:

4 1/2 = (4 x 2 + 1) / 2 = 9/2

Next, we divide the total cost by the total weight in pounds:

Price per pound = Total cost / Total weight

Price per pound = $3.60 / 4.5 pounds

Price per pound = $0.80

Therefore, the price per pound of the carrots Dora bought is $0.80.

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The maximum and minimum of the given function are 22 and -2, respectively

The system of inequalities is given as

y ≥ -x - 2

y ≥ 3x + 2

y ≤ x + 4

See attachment for the graph

From the graph, we have the following coordinates

(-1, -1), (-3, 1) and (1, 5)

Substitute (-1, -1), (-3, 1) and (1, 5) in f(x, y) = -3x + 5y

So, we have

f(-1, -1) = -3(-1) + 5(-1) = -2

f(-3, 1) = -3(-3) + 5(1) = 14

f(1, 5) = -3(1) + 5(5) = 22

Hence, the maximum is 22 and the minimum is -2

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a. The six trigonometric functions of the angle β are:

sin β = 7/25

cos β = 24/25

tan β = 7/24

csc β = 25/7

sec β = 25/24

cot β = 24/7

b. Using trigonometric identity, cos X + (sin X)(tan X) = 1

We can use the given value of cos β = 24/25 to find the other trigonometric functions of the angle β.

Let's draw a right triangle with angle β, adjacent side of length 24, and hypotenuse of length 25 (since cos β = adjacent/hypotenuse):

Using the Pythagorean theorem, we can find the opposite side:

Opposite side = sqrt(hypotenuse^2 - adjacent^2) = sqrt(25^2 - 24^2) = sqrt(49) = 7

So the triangle is:

Now we can find the other trigonometric functions:

sin β = opposite/hypotenuse = 7/25

cos β = adjacent/hypotenuse = 24/25

tan β = opposite/adjacent = 7/24

csc β = hypotenuse/opposite = 25/7

sec β = hypotenuse/adjacent = 25/24

cot β = adjacent/opposite = 24/7

2. We can use the trigonometric identity for tangent:

tan X = sin X / cos X

to rewrite the expression as:

cos X + (sin X)(sin X / cos X)

Multiplying through by cos X, we get:

(cos X)(cos X) + (sin X)(sin X)

Using the Pythagorean identity:

(sin X)^2 + (cos X)^2 = 1

we can simplify further:

1 - (cos X)^2 + (cos X)^2 = 1

So the final simplified expression is equal to 1

3. We can start with the left-hand side of the equation and manipulate it using the definitions of the trigonometric functions and the Pythagorean identity until we arrive at the right-hand side:

tan²α(csc²α - 1)

= (sin²α/cos²α)((1/sin²α) - 1)

= (sin²α/cos²α - sin²α/cos²α)

= 0

Now, let's look at the right-hand side:

1

We see that the left-hand side simplifies to 0, while the right-hand side is 1. Therefore, the identity is not true for all values of α.

We can see this more clearly by picking a specific value of α and evaluating both sides of the equation. For example, let's take α = 45°:

tan²45°(csc²45° - 1) = (1/1)((2/1) - 1) = 1

1 = 1

So the identity holds for α = 45°, but we have already shown that it does not hold for all values of α. Therefore, the identity is not true for all values of α.

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Answer:

Step-by-step explanation:

Square pyramid (since the base is a square)

Area base [tex]= 8^2=64mm^2[/tex]              (area of square)

Area each side [tex]= \frac{1}{2} base[/tex]×[tex]height[/tex]    (area triangle formula)

                          = [tex]\frac{1}{2}[/tex]×[tex]8[/tex]×[tex]10[/tex]

                          = [tex]40 mm^2[/tex]

Total area [tex]= 4triangles + square base[/tex]

                 [tex]=4[/tex]×[tex]40+64[/tex]

                 [tex]=224 mm^2[/tex]

Answer:

Step-by-step explanation:

We can start by setting up an equation to solve for x, the number of years it will take for the car to be worth $8,200:

8200 = 20000(0.8)^x

Dividing both sides by 20,000, we get:

0.41 = 0.8^x

Taking the logarithm of both sides (using any base, as long as we're consistent), we get:

log(0.41) = log(0.8^x)

Using the property of logarithms that allows us to bring down the exponent as a coefficient, we get:

log(0.41) = x log(0.8)

Dividing both sides by log(0.8), we get:

x = log(0.41) / log(0.8)

Using a calculator, we find:

x ≈ 5.92

Therefore, it will take about 5.92 years for the car to be worth $8,200.

(a) Commutative property of addition , (b) Distributive Property , (c) Associative Property of Multiplication , (d) Commutative property of multiplication and (e) Associative property of addition.

What is Associative Property ?

The associative property is a mathematical principle that states that the way in which factors are grouped in a multiplication or addition expression does not affect the final result. In other words, when using the associative property, we can add or multiply a group of numbers in any order we want, as long as we keep the order of the individual numbers the same.

(7 + 3) + 2 = 2 + (7 + 3)      Commutative property of addition

3(2x +4) = 6x + 12              Distributive Property

(9 * x) * 3 = 9 * (x * 3)         Associative Property of Multiplication

(8 * x * 2) = (8 * 2* x)          Commutative property of multiplication

(4 + 5) + 1 = 4 + (5 + 1)        Associative property of addition

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The equations that represent the plants' height after any given number of days are as follows;

y = 2x + 5

y = 3x + 3

The height of the first plant is 33 cm.

The height of the second plant is 48 cm.

Based on the information provided above, the first plant is 5 cm high and the plant grows 2 cm per day. Therefore, the total height, y, can be represented by this equation:

y = 2x + 5

where:

x represents the number of days.

For the second plant, we have:

y = 3x + 3

After 15 days, the total height of each plant is given by;

First plant, y = 2x + 5 = 2(15) + 3 = 33 cm.

Second plant, y = 3x + 3 = 3(15) + 3 = 48 cm.

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