29. The area of a rectangle is given by the expression +7x² + 11x + 2) in². The length of the rectangle is given by the expression (x + 2) in. What is an expression for the width of the rectangle?​

If Cara's calculation of the sum of the squared differences i.e. 1370 from the mean is incorrect, that would be the first error she made in computing the variance.

As the steps for finding the variance are not provided, it is difficult to determine the first error Cara made.

However, the formula for calculating the variance is:

Variance = (sum of the squared differences from the mean) / (number of observations)

The first error Cara may have made is in calculating the sum of the squared differences from the mean.

The correct steps to find the variance are:

Find the mean:

Mean = (87 + 46 + 90 + 78 + 89) / 5 = 78

Calculate the differences from the mean for each observation:

87 - 78 = 9

46 - 78 = -32

90 - 78 = 12

78 - 78 = 0

89 - 78 = 11

Square each difference:

[tex]9^2 = 81[/tex]

[tex](-32)^2 = 1024[/tex]

[tex]12^2 = 144[/tex]

[tex]0^2 = 0[/tex]

[tex]11^2 = 121[/tex]

Find the sum of the squared differences:

81 + 1024 + 144 + 0 + 121 = 1370

Divide the sum of squared differences by the number of observations:

Variance = 1370 / 5 = 274.

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Original number = $\frac{3}{4}$. The original number expressed as a common fraction is $\frac{3}{4}$.

1. Reciprocal: This is the result of switching the numerator and denominator of a fraction (or dividing 1 by a whole number).
2. Original number: This is the number we're trying to find.
3. Common fraction: This is a fraction where the numerator and denominator are both integers (whole numbers).

Step 1: Set up the equation using the given information.

One more than the reciprocal of the original number is $\frac{7}{3}$. We can express this as an equation:

Reciprocal of the original number + 1 = $\frac{7}{3}$

Step 2: Solve for the reciprocal of the original number.

Reciprocal of the original number = $\frac{7}{3}$ - 1

Step 3: Simplify the equation.

Reciprocal of the original number = $\frac{7}{3}$ - $\frac{3}{3}$

Reciprocal of the original number = $\frac{4}{3}$

Step 4: Find the original number.

Since we have the reciprocal of the original number, we can find the original number by taking the reciprocal of this value:

Original number = $\frac{1}{(\frac{4}{3})}$

Step 5: Simplify the expression.

Original number = $\frac{1}{1} \times \frac{3}{4}$

Original number = $\frac{3}{4}$

The original number expressed as a common fraction is $\frac{3}{4}$.

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If you choose not to make a payment during the 24-month period, your balance at the end of the promotion will be $3,637.16.

Explain month

A month is a unit of time equal to one-twelfth of a year, or approximately 30.44 days. It is often used to represent periodic phenomena, such as interest rates or seasonal trends, and to calculate the duration between two dates. The number of months between two dates is calculated by dividing the difference in days by 30.44.

According to the given information

If you do not make any payments during the 24-month period, your balance will increase each month due to the interest that accrues. After 24 months, your balance will be:

$2299.99 * (1 + 0.020825)²⁴ = $3,637.16

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the new club sent out 50 coupons to existing members and 150 coupons to potential members to boost sales for next year's memberships.

How to solve the question?

Let x be the number of coupons sent to existing members. Then the number of coupons sent to potential members is 3x, as they provided 3 times as many coupons to potential members than to existing members.

According to the problem, the total number of coupons sent is 200. Therefore, we can write the following equation:

x + 3x = 200

Simplifying this equation, we get:

4x = 200

Dividing both sides by 4, we get:

x = 50

Therefore, the number of coupons sent to existing members is 50, and the number of coupons sent to potential members is 3 times as many, or 150.

In conclusion, the new club sent out 50 coupons to existing members and 150 coupons to potential members to boost sales for next year's memberships.

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Answer:

Step-by-step explanation:

Answer:

9) Keep the denominators the same, and subtract the numerators. Then simplify if necessary.

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

[tex] = \frac{3x + 2 - (2x - 3)}{x + 5} [/tex]

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

[tex] \frac{x + 5}{x + 5} = 1[/tex]

10) Find the LCD. Rewrite each rational expression as an equivalent expression with the LCD as the denominator. Add the numerators and write the sum over the LCD. Then simplify if necessary.

[tex] \frac{4x}{x - 2} + \frac{x - 4}{x - 5} [/tex]

[tex] = \frac{4x(x - 5) + (x - 4)(x - 2)}{(x - 2)(x - 5)} [/tex]

[tex] = \frac{4 {x}^{2} - 20x + {x}^{2} - 6x + 8 }{(x - 2)(x - 5)} [/tex]

[tex] = \frac{5 {x}^{2} - 26x + 8}{(x - 2)(x - 5)} [/tex]

[tex] = \frac{5 {x}^{2} - 26x + 8 }{ {x}^{2} - 7x + 10} [/tex]

Answer:

15 1/2

Step-by-step explanation:

hope this helped

After solving equation , the plumber put in 3.1 hours of work (or 3 hours, 6 minutes).

A mathematical assertion that demonstrates the equality of two expressions is called an equation The equals symbol (=) is used to denote the separation of two phrases. Numerous mathematical ideas and relationships, including linear functions, quadratic functions, and trigonometric functions, can be represented by equations.

Let's use the letter 'h' to indicate how many hours the plumber put in.

The plumber costs $35 to come to Jerald's residence and $50 for every hour they work. If Jerald is charged a total of $190 by the plumber, the following equation can be written:

$50h + $35 = $190

To solve for 'h,' we obtain:

$50h = $190 - $35

$50h = $155

h = 155 / 50

h = 3.1

Consequently, the plumber put in 3.1 hours of work (or 3 hours, 6 minutes).

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The point of tangency is (-3, -2).

To find the point of  tangency , we really want to find the convergence point between the line and the circle. We can begin by tracking down the situation of the circle with focus (- 1,2).

A circle's equation for its center (a,b) and radius (r) is as follows:

[tex](x - a)^2 + (y - b)^2 = r^2[/tex]

Plugging in the values for the center and solving for r, we get:

[tex](x + 1)^2 + (y - 2)^2 = r^2[/tex]

Now we need to find the intersection point between this circle and the line 2x+3y=-22. We can do this by substituting y = (-2/3)x - (22/3) into the equation of the circle:

[tex](x + 1)^2 + ((-2/3)x - (16/3))^2 = r^2[/tex]

Expanding and simplifying, we get:

[tex]10x^2 + 24x + 44 = 9r^2[/tex]

Next, we can make use of the fact that the line intersects the circle at a tangent. This indicates that the distance between the intersection point and the center of the circle is the same as its radius. The distance between the center of the circle and the line can be determined using the distance formula:

distance = [tex]|2x + 3y - (-22)\sqrt{2^2 + 3^2}| = |2x + 3y + 22| \sqrt(13)[/tex]

Setting this equal to the radius r, we get:

[tex]|2x + 3y + 22| \sqrt{13} = \sqrt{10x^2 + 24x + 44} / 3[/tex]

Squaring both sides and simplifying, we get:

[tex]36(2x + 3y + 22)^2 = 13(10x^2 + 24x + 44)[/tex]

Expanding and simplifying, we get:

[tex]26x^2 + 36xy + 45y^2 + 52x + 132y + 240 = 0[/tex]

Now we can use the quadratic formula to solve for x:

x = (-18y - 13 ± [tex]\sqrt{169 - 720y^2[/tex])) / 13

Substituting this into the equation for the line, we get:

2(-18y - 13 ± [tex]\sqrt{169 - 720y^2))[/tex] / 13 + 3y = -22

Simplifying, we get:

y = -2

Substituting y = -2 into the equation for x, we get:

x = -3

Therefore, the point of tangency is (-3, -2).

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The score to be made on the 4th quiz in order to have a mean quiz score of exactly 90 is equal to 88.

Let us consider the score that Tim needs to get on his fourth quiz be x.

Score he needs to get in order to have a mean quiz score of 90,

Set up an equation using the formula for the mean ,

(mean score) = (sum of scores) / (number of scores)

If Tim wants his mean quiz score to be 90, then we have,

⇒ 90 = (86 + 92 + 94 + x) / 4

Multiplying both sides by 4, we get,

⇒360 = 86 + 92 + 94 + x

Simplifying this equation, we get,

⇒ x = 360 - 272

⇒ x = 88

Therefore, Tim needs to get a score of 88 on his fourth quiz in order to have a mean quiz score of exactly 90.

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Answer: y=1/2x-3

Step-by-step explanation:

I'm assuming you're trying to find it in slope intercept form!

y=mx+b

y=1/2x-3

easy

If you are trying to determine if an input variable may affect your key characteristic (output variable) by examining the

correlation between variables, you should use the tool: D. Scatter plot diagram. therefore, option D.Scatter plot

diagram is correct.

A scatter plot diagram is a graphical representation of the relationship between two variables. It can help you visualize

the correlation between the input and output variables, making it easier to determine if there is a potential cause-and-

effect relationship.

The tool that you should use to examine the correlation between variables is D. Scatter plot diagram.

A scatter plot diagram is a graphical representation that displays the relationship between two variables.

The x-axis represents the input variable, while the y-axis represents the output variable.

By plotting the data points on the scatter plot diagram, you can visually analyze the correlation between the variables.

If there is a strong positive or negative correlation between the variables, it suggests that the input variable may affect

the key characteristic (output variable).

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D. Scatter plot diagram is the tool that should be used to examine the correlation between variables to determine if an input variable may affect your key characteristic (output variable).

The scatter plot diagram is a graphical representation that displays the relationship between two variables, and it is commonly used to identify patterns, trends, and correlations between variables. By examining the scatter plot diagram, you can determine whether there is a positive, negative, or no correlation between the variables, which can help you to identify potential cause-and-effect relationships.
 To determine if an input variable may affect your key characteristic (output variable) by examining the correlation between variables, you should use:

A scatter plot diagram is a graphical tool that helps visualize the relationship between two variables, allowing you to identify any correlation between the input and output variables.

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The rate of change of the area is 20π square inches per second.

The area of the shaded region can be calculated as the difference between the areas of the outer circle and the inner circle:

A = πr^2 - πr'^2

where r is the radius of the outer circle, r' is the radius of the inner circle, and π is the constant pi.

To find the rate of change of the area, we can take the derivative of both sides of the equation with respect to time t:

dA/dt = d/dt (πr^2) - d/dt (πr'^2)

Using the chain rule, we can express the derivatives in terms of the rates of change of the radii:

dA/dt = 2πr (dr/dt) - 2πr' (dr'/dt)

Substituting the given values at the instant when r=4 inches and r'=3 inches, we have:

dA/dt = 2π(4)(2) - 2π(3)(-1) = 20π

Therefore, the rate of change of the area is 20π square inches per second.

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Duri can make 72 cupcakes on his own and Habib can make 36 cupcakes on her own, assuming they have enough of all the other ingredients.

To determine how many cupcakes each person can make on their own, we need to check if they have enough of all the other ingredients required to make 12 cupcakes.

Terrance has 1 cup of flour and 6 eggs, which is not enough to make 12 cupcakes.

Duri has 12 cups of flour and 1000 grams of butter, which is more than enough to make 12 cupcakes. However, the recipe requires 3/4 cup of sugar, 2 eggs, and 3/4 cup of milk, which we do not know if Duri has enough of.

Habib has 3 cups of milk and 6 cups of sugar, which is enough to make 12 cupcakes.

Anika has 1 cup of sugar and 4 cups of milk, which is not enough to make 12 cupcakes.

Therefore, only Duri and Habib have enough ingredients to make 12 cupcakes on their own.

To determine how many cupcakes they can make, we need to calculate how much of each ingredient is required for one cupcake and then divide the available ingredients by that amount.

For one cupcake, we need:

1/6 cups of flour

1/16 cup of sugar

1/6 eggs

1/16 cups of milk

125/12 grams of butter

Duri has 12 cups of flour and 1000 grams of butter, which is enough to make 72 cupcakes. Habib has 6 cups of sugar and 3 cups of milk, which is enough to make 36 cupcakes.

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The probability that a student who did not complete the homework passed the test is 0.25.

The bearing of C from A is 90 degrees when B is equidistant from A and C.

In navigation and geometry, bearing refers to the direction or angle between two points, measured clockwise from a fixed reference direction. Typically, bearings are measured in degrees, with 0 degrees indicating a direction due north, 90 degrees indicating a direction due east, 180 degrees indicating a direction due south, and 270 degrees indicating a direction due west. Bearings can be expressed as either magnetic bearings or true bearings, depending on the reference direction used.

Let's assume that the distance from B to A and from B to C is the same.

To find the bearing of C from A, we can use the fact that the interior angles of a triangle sum up to 180 degrees. Therefore, we can first find the bearing of A from C:

180 - 129 = 51

This means that the bearing of C from A is 51 degrees in the opposite direction of the bearing of A from C. Since the bearing of A from C is 219, the bearing of C from A is:

219 - 180 + 51 = 90 degrees

Therefore, the bearing of C from A is 90 degrees.

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Answer:

3(n + 6) = 2(n + 6) + (n + 6)

3(n + 6) = 3n + 18

The game owner should charge option (a) $0.55 to make it a fair game

To determine how much the game owner should charge to make it a fair game, we need to calculate the average value of each package. We can do this by finding the total value of all the packages and dividing it by the total number of packages.

The total value of the 30 packages worth $.65 each is:

30 x $.65 = $19.50

The total value of the 10 packages worth $.60 each is:

10 x $.60 = $6.00

The total value of the 15 packages worth $.30 each is:

15 x $.30 = $4.50

The total value of all the packages is

$19.50 + $6.00 + $4.50 = $30.00

The total number of packages is

30 + 10 + 15 = 55

The average value of each package is

$30.00 / 55 = $0.55

Therefore, the correct option is (a) $0.55

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The measure of angle I in the triangle HIJ using given measurements is equal to 46.05 degrees.

In the triangle HIJ,

The measure of angle J is equal to 90 degrees.

This implies ,

HI is the hypotenuse.

JH is the opposite side to angle I.

In triangle HIJ,

Using trigonometric ratio we get,

sin ∠I = Opposite side / Hypotenuse

Substitute the values we have,

⇒ sin ∠I = 4.8 / 6.7

⇒ sin ∠I = 0.72

Now , take sin⁻¹ both the side of the equation we get,

⇒sin⁻¹(sin ∠I) = sin⁻¹( 0.72 )

Here sin⁻¹(sin ∠I) = ∠I

⇒∠I = sin⁻¹( 0.72 )

⇒∠I = 46.05 degrees

Therefore, the measure of angle I is equal to 46.05 degrees.

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The compound interest investment earns more interest than the simple interest investment, and the difference becomes more significant over time.

After 10 years, the difference is relatively small, but after 20 years, the compound interest investment has earned over $3,700 more than the simple interest investment.

To calculate the amount after 10 and 20 years, we can use the following formulas:

Simple Interest: A = P * (1 + r * t)

Compound Interest: A = P * (1 + r/n)^(n*t)

Where:

Using these formulas and the information given in the table, we can calculate the amount after 10 years and 20 years for each type of investment.

For simple interest, the interest is not compounded, so we just add the interest to the principal:

Amount after 10 years: A = $50,000 * (1 + 0.0275 * 10) = $68,750

Amount after 20 years: A = $50,000 * (1 + 0.0275 * 20) = $87,500

For compound interest, we need to use the formula above with n=12 (since the interest is compounded monthly):

Amount after 10 years: A = $50,000 * (1 + 0.0275/12)^(12*10) = $68,704.23

Amount after 20 years: A = $50,000 * (1 + 0.0275/12)^(12*20) = $91,262.47

To compare the two investments, we can look at the difference between the amounts after 10 and 20 years:

Difference after 10 years: $68,750 - $68,704.23 = $45.77

Difference after 20 years: $87,500 - $91,262.47 = $3,762.47

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Answer:

Step-by-step explanation:

1 + 1 divided by 3 x 3.5 = 4.66 or 4 2/3

Answer:

In its simplest form, the ratios of the length of sides in a 45 45 90 special right angle triangles should be 1 : 1 : 2 1:1:\sqrt{2} 1:1:2on:

And because this is a 30-60-90 triangle, and we were told that the shortest side is 8, the hypotenuse must be 16 and the missing side must be 8 * 3 , or 8 3 . Our final answer is 8√3

The theoretical probability of the spinner not landing on red is 0.875.

The total number of sections on the spinner is 8, out of which only one section is red. Therefore, the probability of the spinner landing on red is:

P(Red) = 1/8

The probability of the spinner not landing on red would be the probability of landing on any other section, which is:

P(Not Red) = 1 - P(Red) = 1 - 1/8 = 7/8

Therefore, the theoretical probability of the spinner not landing on red is 7/8 or 0.875 in decimal form.

So, the correct answer is: 0.875.

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Answer:

D

Step-by-step explanation:

Answer: 64 sqaure centimetres.

Step-by-step explanation:

- Surface area means the area of all exterior sides of a 3D dimensional shape. This means we'll have to find the area of every face and then add them all together.

Top and Bottom

4 x 4 = 16

16 x 2 = 32

Both faces are the same so once we find the area of one, we can just double it.

North, South, East and West Side

4 x 2 = 8

8 x 4 = 32

All four remaining faces had the same dimensions, meaning that once you found one, you just had to multiply that answer by 4.

To find the overall surface area add all the areas you have.

32 + 32 = 64

or

16 +_16 + 8 + 8 + 8 + 8 = 64

Answer:

f(x + 1) + 2

Step-by-step explanation:

All the points are translated 1 unit to the left and 2 units up.
To write a translation along the x-axis, movement to the right would be written as f(x - a), where a is the amount translated, and movement to the left would be written as f(x + a). In this case, we would need to write the translation as f(x + 1), since it is moving 1 unit to the left.
As for translations along the y-axis, movement upward would be written as f(x) + a, and movement downward would be written as f(x) - a. Thus, the transformation rule to describe the path the pre-image made to arrive at the image would be f(x + 1) + 2.

P.S. I'm a bit rusty with this stuff, so I apologize in advance if I messed something up.

The height of the hill for the given angle of elevation through which the given condition is satisfied is 460.1 ft

What about angle of elevation?

The angle of elevation is the angle between the horizontal plane and the line of sight or the direction of the observer's line of sight above the horizontal plane. It is measured upwards from the horizontal plane to the object being viewed. The angle of elevation is typically used in trigonometry and geometry to calculate the height, distance, or length of an object or location.

According to the given information:

Given, The given angle of elevation from point A to the top of a hill is [tex]49^{0}[/tex].

As, we know tan (x) = [tex]\frac{perpendicular}{base}[/tex]

tan [tex]49^{0}[/tex] = [tex]\frac{unknown}{400}[/tex]

1.15 x 400 = unknown

So, the unknown = 460.1 ft

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Step-by-step explanation:

Volume of rect prism = L X W X H = 4 X 9 X 10 = 360 cm^3

Answer:

50 meters/21.91 seconds = 2.282 m/sec

The correct answer is option B. Translate 1 to the left, scale vertically by 1/2, then reflect over the y-axis.

The process of modifying the shape, location, or features of a graph is often referred to as graph transformation. Graphs are visual representations of mathematical functions or data point connections, often represented on a coordinate plane.

Translations, reflections, rotations, dilations, and other changes to the look of a graph are examples of graph transformations.

For the given problem, Transformation to get the desired result can be carried out as:

Hence, to convert the graph of "y = k(x)" to the graph of "y = -k(x + 1)," the correct sequence of transformations is to translate 1 unit to the left, scale vertically by 1/2, and then reflect across the y-axis, which is option B.

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