Chloe has already read 50 pages of a book and reads 40 additional pages per hour. Write the equation of the line that represents the number of pages read y in x hours. Plus sign Minus sign Multiplication sign Division sign Big fraction Superscript (Ctrl+Up) Square root Root Equals sign Not equal to Less-than sign Greater-than sign Less-than or equal to Greater-than or equal to Parentheses Pi

David can best improve his investigation by including a control group. A control group is a group that does not receive any treatment or intervention and is used as a benchmark to compare the results of the experimental group. In this case, the control group would be a third young elm tree that is planted near the other two but does not receive any water or fertilizer. David can measure the height and trunk girth of the control tree every week for a year as well.

In scientific research, it is important to include a control group to ensure that the results of the experimental group are due to the treatment or intervention and not due to other factors. In this case, David is investigating the factors that affect plant growth, and he is manipulating the amount of water and fertilizer that the two elm trees receive. However, there could be other factors that affect plant growth, such as soil quality, sunlight exposure, temperature, and pests. If David only measures the height and trunk girth of the two elm trees that receive water and fertilizer, he cannot be sure if any changes in their growth are due to the treatment or due to other factors.

To improve his investigation, David can plant a third young elm tree near the other two and not give it any water or fertilizer. This third tree will serve as the control group, and David can measure its height and trunk girth every week for a year as well. By comparing the growth of the experimental group (the two elm trees that receive water and fertilizer) to the growth of the control group (the third elm tree that receives nothing), David can be more confident that any changes in the growth of the experimental group are due to the treatment and not due to other factors.

David can best improve his investigation by including a control group, which will serve as a benchmark to compare the results of the experimental group. The control group should be a third young elm tree that is planted near the other two but does not receive any water or fertilizer. David can measure the height and trunk girth of the control tree every week for a year as well. By comparing the growth of the experimental group (the two elm trees that receive water and fertilizer) to the growth of the control group (the third elm tree that receives nothing), David can be more confident that any changes in the growth of the experimental group are due to the treatment and not due to other factors.

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The true proportion of people who prefer dark chocolate (p) likely falls within the range of 0.205 to 0.255 (0.23 ± 0.025) based on the poll results.

To describe the conclusion about the proportion of people who like dark chocolate more than milk chocolate, denoted as "p," using an absolute value inequality, we can consider the margin of error.

Let's assume that p represents the true proportion of people who prefer dark chocolate. The poll results indicate that the sample proportion of people who like dark chocolate more than milk chocolate is 23%, with a margin of error of 2.5%.

The margin of error represents the maximum likely deviation between the sample proportion and the true population proportion. It is typically expressed as a positive value. In this case, the margin of error is 2.5%, which can be written as 0.025.

Using an absolute value inequality, we can write the conclusion as:

| p - 0.23 | ≤ 0.025

This inequality states that the difference between the true population proportion (p) and the observed sample proportion (0.23) is less than or equal to 0.025, which represents the margin of error.

In other words, the absolute value of the difference between p and 0.23 is less than or equal to 0.025, indicating that the true proportion of people who prefer dark chocolate (p) likely falls within the range of 0.205 to 0.255 (0.23 ± 0.025) based on the poll results.

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To complete the square for the equation x2 - 16x + 60 = -12, add 64 to each side of the equation. This will give us x2 - 16x + 124 = 52.

Then, factor out the coefficient of x2 (1) and the coefficient of x (16). This will give us (x - 8)2 = 52. Finally, subtract 52 from both sides to get (x - 8)2 = 0. Solving for x yields x = 8.

Equations are mathematical statements that express the equality of two expressions. They involve one or more unknowns that are represented by variables and involve numbers, constants, and operators. An equation states that the expressions on either side of the equal sign have the same value.

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Answer:

-5x + 7y

Step-by-step explanation:

2x - 7x = -5x

8y - y = 7y

The probability that a randomly selected barista has a salary less than $13 thousand is approximately 0.0228.

In this scenario, we are given that the salaries of coffee shop baristas follow a normal distribution with a mean of $16 thousand per year and a standard deviation of $1 thousand. To find the probability of a randomly selected barista earning less than $13 thousand, we need to calculate the area under the normal distribution curve to the left of $13 thousand. By standardizing the value using the z-score formula and referring to a standard normal distribution table or using statistical software, we find that the probability is approximately 0.0228. This means there is a 2.28% chance that a randomly selected barista earns less than $13 thousand.

To delve deeper into the topic of probability and normal distribution, it's useful to understand how z-scores are calculated and applied. Z-scores are a way to standardize values in a normal distribution, allowing us to compare and calculate probabilities. By subtracting the mean from the observed value and dividing it by the standard deviation, we obtain the z-score. This score tells us how many standard deviations away from the mean a particular value is. Using z-scores, we can refer to a standard normal distribution table or use statistical software to determine probabilities accurately.

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Answer:

Work:

Hence, the solution to the problem is 11/5.

Hoped this helped.

\(BrainiacUser1357\)

Answer:

x = 53

Step-by-step explanation:

The angle labeled with the expression "2x - 20 " and the angle with the measure of 86 degrees are opposite interior angles.

Opposite interior angles are congruent

This means that 2x - 20 = 86

This is our equation.

We now solve for x using basic algebra

2x - 20 = 86

step 1 add 20 to each side

-20 + 20 cancels out

86 + 20 = 106

now we have 2x = 106

step 2 divide each side by 2

2x / 2 = x

106 / 2 = 53

we're left with x = 53

hope it helps you

can you brainlest me

The data includes a concave mirror with a radius of curvature of +31.5 cm and magnification of m = 3.40. The formula for magnification is m = v/u, and the focal length is f = r/2. Substituting the values, we get u = v/m, and using the mirror formula, the distance of the object from the mirror is 10.15 cm.

Given data: Radius of curvature of a concave mirror, r = +31.5 cm Magnification produced by the mirror, m = 3.40

We know that the formula for magnification is given by:

m = v/u where, v = the distance of the image from the mirror u = the distance of the object from the mirror We also know that the formula for the focal length of the mirror is given by :

f = r/2where,f = focal length of the mirror

Using the mirror formula:1/f = 1/v - 1/u

We know that a concave mirror has a positive focal length, so we can replace f with r/2.

We can now simplify the equation to get:1/(r/2) = 1/v - 1/u2/r = 1/v - 1/u

Also, from the given data, we have :m = v/u

Substituting the value of v/u in terms of m, we get: u/v = 1/m

So, u = v/m Substituting the value of u in terms of v/m in the previous equation, we get:2/r = 1/v - m/v Substituting the given values of r and m in the above equation, we get:2/31.5 = 1/v - 3.4/v Solving for v, we get: v = 22.6 cm Now that we know the distance of the image from the mirror, we can use the mirror formula to find the distance of the object from the mirror.1/f = 1/v - 1/u

Substituting the given values of r and v, we get:1/(31.5/2) = 1/22.6 - 1/u Solving for u, we get :u = 10.15 cm

Therefore, the distance of the mirror from the face is 10.15 cm. The units are centimeters (cm).Answer: 10.15 cm.

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$54.25 are required for the second purchase of lace.

Mixed numbers are formed by combining three parts: An integer, a numerator, and a denominator. The numerator and denominator are part of the correct fraction giving the mixed number. A fraction represented by a quotient and a remainder is a mixed number. For example, 2 1/3 is a mixed fraction, 2 is the quotient, and 1 is the remainder. A mixed number has a combination of an integer and a proper fraction.

Cost of each yd of lace:

= 5.60 ÷ (4/5)

= 5.60 × 5/4

= $7

Now for the cost of second purchase:

Total yd of lace to be purchased = 7 3/4 yd            [mixed fraction]

= 31/4 yd                                                                     [improper fraction]

Cost of 1 yd of lace = $7

Total cost of second purchase = (31/4) × 7

= $54.25

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All the elements of the product CD are,

The inverse function of a function f in mathematics is a function that reverses the operation of f. If the inverse of f exists, it is shown by the displaystyle f-1. The inverse of f exists if and only if f is bijective.

Given that;

C and D are inverses of one another.

And, CD = \(\left[\begin{array}{ccc}e1&e2\\e3&e4\\\end{array}\right]\)

Now,

Since, C and D are inverses of one another.

Hence, The multiplication of C and D are equal to identity.

So, We get;

⇒ CD = \(\left[\begin{array}{ccc}1&0&\\0&1\\\end{array}\right]\)

By comparing, we get;

All the elements of the product are,

⇒ e₁ = 1

⇒ e₂ = 0

⇒ e₃ = 0

⇒ e₄ = 1

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C and D are inverses of one another.

CD = [e1 e2

e3 e4]

Find the elements of the product.

e1 =

e2 =

e3 =

e4 =

First, lets draw a graph of some function that has this properties:

in our case, we know that if our function is a polynomial and has a bounce in some point, that means that the point that its bounces is a even degree root, wich means that is a double root, or a fouth root...

So, if we construct a polinomial with the form:

Is a polynomial that has roots in x=3, x=-2 and double root in x=5, meaning that bounces in x=5.

Given data ; Initial distance between cars, d = 960m Speed of Car A, vA = 50 m/sSpeed of Car B, vB = 30 m/sSpeed of sound, vS = 340 m/s

Let's solve the parts given in the question;

a) Find vAB; Relative speed, \(vAB = vA + vBvAB = 50 m/s + 30 m/svAB = 80 m/s\)

b)Let t be the time until the two cars collide.In time t, the distance traveled by Car A = vA0t

The distance traveled by Car B = vBt

The total distance covered by both cars is d:

Therefore, \(vAt + vBt = dd/t = (vA + vB)t = 960 mt = d / (vA + vB)t = 960 / 80t = 12 s\)

Let ΔsSound be the displacement of the sound during that time.

Distance traveled by Car \(A = vA x t = 50 m/s x 12 s = 600 mDistance traveled by Car B = vB x t = 30 m/s x 12 s = 360 m\)

Therefore, the distance between the cars will be \(960 - (600 + 360) = 0 m.\) So, the sound wave will have traveled the displacement of 4080 m from Car B to Car A.

Hence, ΔsSound = 4080 m.

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The fact that may countries have a lot of processes involved in the purchase of a house makes the process last about 60-90 days.

Buying a house is a very serious investment in so many countries. As a result of the process that are involved in buying the house, it may take about 60 - 90 days in order to complete the process of acquisition.

On the other hand, a car can be out rightly bought as it does not involve a lot of procedure.

Thus, the fact that may countries have a lot of processes involved in the purchase of a house makes the process last about 60-90 days.

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the rate of change of the radius at the instant the volume equals 36π cm³ is 7 / (36π) cm/sec.

The volume V of a sphere with radius r is given by the formula V = (4/3)πr³. We are given that the rate of change of the volume is 7 cm³/sec. Differentiating the volume formula with respect to time, we get dV/dt =(4/3)π(3r²)(dr/dt), where dr/dt represents the rate of change of the radius with respect to time.

We are looking for the rate of change of the radius, dr/dt, when the volume equals 36π cm³. Substituting the values into the equation, we have: 7 = (4/3)π(3r²)(dr/dt)

7 = 4πr²(dr/dt) To find dr/dt, we rearrange the equation: (dr/dt) = 7 / (4πr²) Now, we can substitute the volume V = 36π cm³ and solve for the radius r: 36π = (4/3)πr³

36 = (4/3)r³

27 = r³

r = 3  Substituting r = 3 into the equation for dr/dt, we get: (dr/dt) = 7 / (4π(3)²)

(dr/dt) = 7 / (4π(9))

(dr/dt) = 7 / (36π)

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The expression that represents the perimeter, in centimeters, of the triangle is (7m - 2) + (9m - 5) + (6n - 1).

The perimeter of a triangle is the sum of the lengths of its sides. Therefore, to find the perimeter of the triangle with side lengths (7m - 2) cm, (9m - 5) cm, and (6n - 1) cm, we need to add these lengths together.

Thus, the expression that represents the perimeter of the triangle is (7m - 2) cm + (9m - 5) cm + (6n - 1) cm.

Simplifying this expression, we get 16m + 6n - 8 cm, which is the final answer. Therefore, the perimeter of the triangle is 16m + 6n - 8 cm.

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The Measure of angle A is 120°, Measure of angle C = 120° and the Measure of angle D is 60°

In a parallelogram, opposite angles are congruent. Therefore, if the measure of angle A is 120°, then the measure of angle C is also 120°.

Since angle A and angle C are opposite angles, their adjacent angles are also congruent. This means that the measure of angle B is equal to the measure of angle Z.

Now, let's consider angle D. In a parallelogram, the sum of the measures of adjacent angles is always 180°. Since angle C is 120°, the adjacent angle D must be:

180° - 120°

= 60°.

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The area of the triangle is approximately 36.83 square units.

To find the area of a triangle using calculus, we can use the formula:

A = (1/2) ∫(x2 - x1)dy

Where x1 and x2 are the x-coordinates of the vertices, and dy is the change in the y-coordinate.

First, we need to find the equations of the lines that make up the sides of the triangle. The line between (0,0) and (6,1) has the equation y = (1/6)x. The line between (6,1) and (3,7) has the equation y = -2x + 13. The line between (3,7) and (0,0) has the equation y = (7/3)x.

Now we can use the formula to find the area of the triangle. We'll integrate from y = 0 to y = 1 for the first side, from y = 1 to y = 7 for the second side, and from y = 7 to y = 0 for the third side:

A = (1/2) ∫(x2 - x1)dy

= (1/2) ∫[(6x - 0) - (0 - 0)]dy from y = 0 to y = 1

+ (1/2) ∫[(13 - 2x) - (6x - 0)]dy from y = 1 to y = 7

+ (1/2) ∫[(0 - 0) - (7x/3 - 0)]dy from y = 7 to y = 0

= (1/2) ∫6xdy from y = 0 to y = 1

+ (1/2) ∫(13 - 8x)dy from y = 1 to y = 7

+ (1/2) ∫(-7x/3)dy from y = 7 to y = 0

= (1/2) [(3 - 0) + (49 - 8) + (-49/3 - 0)]

= (1/2) [(3) + (41) + (-49/3)]

= (1/2) [(147/3) + (123/3) + (-49/3)]

= (1/2) [(221/3)]

= 36.83

So the area of the triangle is approximately 36.83 square units.

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Answer:

7+4x=13+x

4x-x=13-7

3x=6

3 3

x =2

Step-by-step explanation:

because when 7 crosses the equal to sign it becomes negative and when the x from the other side crosses the equal sign it also will become negative which will become 4x-x=13-7

which is 3x=6 so u divide both sides by the coefficient of x which is three which will give u 2

Answer:

(x + 8)² = 36

Step-by-step explanation:

When you are trying to complete the square and the equation already has a constant, you add or subtract that value to the other side of the equation so you can cancel it out.

x² + 16x + 28 = 0

x² + 16x + 28 - 28 = 0 -28

x² + 16x = -28

Now, you find (\(\frac{b}{2}\))² (divide b by 2 and raise the quotient to the second power). Half of 16 is 8, and 8² is 64. Add 64 to both sides.

x² + 16x + 64 = -28 + 64

x² + 16x + 64 = 36

Now, you just factor the equation on the left. To factor it, you will always use the number you got to make the constant, which in this case is 8.

(x + 8)² = 36

Answer:

180-(65+57)=58

Step-by-step explanation:

Answer:

Step-by-step explanation:

There's only 1 angle to find.

45 + 57 + ? = 180                    All triangles have interior angles that add to 180.

102 + ? = 180                          Combined 45 and 57  Subtract 102 from both sides

? = 180 - 102                           Combine

? = 78

The correct statement is :David started at 0 instead of 2

A number line is a horizontal line that has equally spread number increments. The numbers included on the line will determine how the number on the line can be answered. The question that goes with the number determines how it will be used, for example, plotting a point.

Given here: In a number line the interval (-5,5) is marked and 2 to 5 is 3

The right steps are

Add 3 to 2 to obtain the required number as there are 3 spaces between 2 and 5

Thus 2+3=5 which is the required answer

but David addes 2-3=-1 which is incorrect.

Hence, David started at 0 instead of 2

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The average productivity of this production process is approximately 1.96 units per labor hour.

The average productivity, in terms of the average number of units per labor hour, for a production process can be determined using the expected value approach. In this case, the random variable X represents the number of units produced each week, with corresponding probabilities. The average production, or expected value, can be calculated by summing each production value multiplied by its probability. Finally, the productivity can be obtained by dividing the average production by the number of labor hours needed.

In this scenario, the production values are 99, 104, and 116, with corresponding probabilities of 0.1, 0.7, and 0.2, respectively. To find the average production, we multiply each production value by its probability and sum the results:

Average production = (99 * 0.1) + (104 * 0.7) + (116 * 0.2) = 9.9 + 72.8 + 23.2 = 105.9

Given that the number of labor hours needed is 54 units per labor hour, we can calculate the average productivity:

Productivity = Average production / Labor hours = 105.9 / 54 ≈ 1.96

The average productivity of this production process is approximately 1.96 units per labor hour.

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a. Approximately 20.33% of eggs are classified as medium.

b. The maximum weight of a small egg is approximately 89.05 grams.

(a) We know that a large egg weighs 90 grams or more. Since X follows a normal distribution with mean μ = 85 and variance σ^2 = o^2 = 36, we can find the probability that an egg weighs 90 grams or more as follows:

P(X ≥ 90) = P(Z ≥ (90 - μ)/σ)          [where Z is standard normal]

= P(Z ≥ (90 - 85)/6)

= P(Z ≥ 0.83)

Since the standard normal distribution is symmetric, we can use the property that P(Z ≥ z) = P(Z ≤ -z) to rewrite this as:

P(X ≥ 90) = P(Z ≤ -0.83)

Using a standard normal table or calculator, we can find that P(Z ≤ -0.83) ≈ 0.2033.

Therefore, the proportion of eggs that are classified as large is approximately 1 - 0.25 - 0.2033 = 0.5467.

Since the sum of the proportions of small, medium, and large eggs must equal 1, the proportion of eggs that are classified as medium is:

1 - 0.25 - 0.5467 = 0.2033

Therefore, approximately 20.33% of eggs are classified as medium.

(b) To find the maximum weight of a small egg, we need to find the 75th percentile of the distribution of X. Since X has a normal distribution with mean μ = 85 and variance σ^2 = o^2 = 36, we can find the 75th percentile using the standard normal distribution:

P(Z ≤ z) = 0.75

Using a standard normal table or calculator, we can find that z ≈ 0.6745.

Therefore,

z = (x - μ)/σ

0.6745 = (x - 85)/6

Solving for x, we obtain:

x = 89.05

Therefore, the maximum weight of a small egg is approximately 89.05 grams.

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Let a represent the volume of solution A. If it contains 2% of alcohol, then the amount of alcohol that A contains is 2/100 * a = 0.02a

If A = 200, then the amount of alcohol in A is 0.02 * 200 = 4

Let b represent the volume of solution B. If it contains 7% of alcohol, then the amount of alcohol that B contains is 7/100 * a = 0.07b

The total volume of solution A and B is (a + b)

If the volume of A = 200, then the total volume or resulting mixture is 200 + b

If the mixture contains 5% alcohol, the the amount of alcohol in the mixture is

5/100 * (200 + b)

0.05(200 + b)

By equating the concentrations, we have

4 + 0.07b = 0.05(200 + b)

4 + 0.07b = 10 + 0.05b

0.07b - 0.05b = 10 - 4

0.02b = 6

b = 6/0.02

b = 300

She needs to use 300 milliliters of solution B

The dilation will produce similar figures because the image and pre image will have congruent corresponding angles.

It should be noted that dilation simply means a transformation to resize an object

In this case, the dilation will produce similar figures because the image and pre image will have congruent corresponding angles.

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Answer:

The dilation will produce similar figures because the image and pre image will have congruent corresponding angles.

Step-by-step explanation:

Answer:

- 16

Step-by-step explanation:

following the rules as set out in PEMDAS

4² - 2(3 × 5 + 1) ← evaluate exponent term

= 16 - 2(3 × 5 + 1) ← evaluate multiplication inside parenthesis

= 16 - 2(15 + 1)

= 16 - 2(16) ← perform the multiplication

= 16 - 32 ← evaluate subtraction

= - 16

answer- the answer is c. 6

Step-by-step explanation:

\( \underline{ \underline{ \text{Given \: data}}} : \)

\( \underline{ \underline{ \text{Here :}}}\)

\( \underline{ \underline{ \text{To \: find}}} : \)

\( \underline{ \underline{ \text{Solution}}} : \)

\( \boxed{ \underline{ \tt{Mean = \frac{ \sum \: x}{n} }}}\)

⟶ \( \tt{ \frac{42}{7}} \)

⟶ \( \tt{6}\)

\( \pink{ \boxed{ \boxed{ \tt{Our \: final \: answer : \boxed{ \underline{ \: 6}}}}}}\)

Hope I helped ! ♡

Have a wonderful day / night ! ツ

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

The length of the radius AB is 6 units.

The angle ∠BAC is 90 degrees. The length of arc BC is 3π. The length of  

radius AB can be found as follows:

Hence,

length of arc = ∅ / 360 × 2πr

where

Therefore,

length of arc = 90 / 360 × 2πr

3π = 1 / 4 × 2πr

cross multiply

12π = 2πr

divide both sides by 2π

r = 6 units

Therefore,

radius AB = 6 units

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