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The linear equation that shows a proportional relationship is y = 1/4x.

A proportional relationship is one in which there is a constant ratio between the values of two variables.

In the given options, the linear equation that shows a proportional relationship is:

y= 1/4 (x- 5) and y = -1/4x

In this equation, the coefficient of x is 1/4, indicating that for every increase or decrease in x, y will change in proportion to that change.

Now, y= 1/4x

In a proportional relationship, the ratio of y to x remains constant. In this equation, y is directly proportional to x with a constant of proportionality of 1/4. This means that as x increases or decreases, y will also increase or decrease by a quarter of the amount.

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Answer:

3(x + y + z) = k

z = k\/3 - x - y

-k + 3 x + 3 y + 3 z = 0

The value of k that makes the equation 3x + 3y + 3z = k equal to 42 is k = 14. When you substitute k = 14 into the equation, you get 3x + 3y + 3z = 42, which satisfies the condition.

To find the value of k that makes the equation 3x + 3y + 3z = k equal to 42, you need to solve for k.

The equation is:

3x + 3y + 3z = k

Now, we want this equation to equal 42, so we substitute 42 for k:

3x + 3y + 3z = 42

Next, we can simplify the equation by factoring out the common factor of 3 on the left side:

3(x + y + z) = 42.

Now, we have a simpler equation:

x + y + z = 42 / 3

Divide both sides by 3:

x + y + z = 14

So, to make the equation 3x + 3y + 3z = k equal to 42, k should be equal to 14.

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The size of the land that Muya's son and daughter received is [tex]1\frac{11}{12}[/tex] hectares.

We can see that, Muya started with a [tex]6\frac{2}{3}[/tex] hectares piece of land, which we can write as an improper fraction i.e.:

[tex]6\frac{2}{3}[/tex] = (6 × 3 + 2) / 3 = [tex]\frac{20}{3}[/tex] hectares

The Muya donated [tex]\frac{7}{8}[/tex] hectares to a school and [tex]1 \frac{1}{2}[/tex] hectares to a children's home. The total amount of land he donated is:

[tex]= \frac{7}{8}+ \frac{11}{2} \\\\= \frac{7}{8} + \frac{3}{2} \\\\= \frac{14}{8} + \frac{12}{8} \\\\= \frac{26}{8} \\\\= \frac{13}{4} hectares[/tex]

The size of the land left is:

[tex]\frac{20}{3} - \frac{13}{4} = (\frac{80}{12}) - (\frac{39}{12}) = \frac{41}{12} hectares[/tex]

Muya's son and daughter share this remaining land equally, so each of them gets:

[tex](\frac{41}{12}) / 2 = \frac{20.5}{12} = 1 \frac{11}{12} hectares[/tex]

Therefore, the size of the land that Muya's son and daughter received is 1 11/12 hectares.

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Answer:

D

Step-by-step explanation:

Answer:

True

False
True

The probability that a student takes a history class given that the student is taking a science class is 0.59 to the nearest hundredth.

The probability that a student takes a history class given that the student is taking a science class is a conditional probability.

Assuming;

P(H) = Probability of taking a history class

P(S) = Probability of taking a science class

P(H ∩ S) = Probability of taking both a history class and a science class

Given data:

P(H ∩ S) = 0.48

P(S) = 0.82

Solving for P(H | S) using the formula for conditional probability:

P(H | S) = P(H ∩ S) / P(S)

P(H | S) = 0.48 / 0.82

P(H | S) ≈ 0.59

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To write the ratio of 2/3 to 8 as a fraction in simplest form, we need to divide the numerator and denominator by their greatest common factor (GCF).The GCF of 2 and 8 is 2.So, we divide both the numerator and denominator by 2:2/3 ÷ 8/1 = (2/3) ÷ (8/1) = 2/3 x 1/8 = (2 x 1) / (3 x 8) = 2/24Now, we can simplify the fraction by dividing the numerator and denominator by their greatest common factor again.The GCF of 2 and 24 is 2.So, we divide both the numerator and denominator by 2:2/24 ÷ 2/2 = (2/24) ÷ (2/2) = 2/24 x 1/2 = (2 x 1) / (24 x 2) = 1/12Therefore, the ratio of 2/3 to 8 as a fraction in simplest form is 1/12.

Answer:

How to find Ratio?

Ratios compare two numbers, usually by dividing them. If you are comparing one data point (A) to another data point (B), your formula would be A/B. This means you are dividing information A by information B. For example, if A is five and B is 10, your ratio will be 5/10

In order to find the ratio of a certain number to another number or the relation of each other, we also need to know the concept of fraction and percentage.

1/12 or 1 to 12

The ratio is 2/3*8=23⋅8=2/24=1/12

So it is 1 to 12

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The exponential model for the given data is:

f(x) = abˣ + k = 14.85 + 18.638(0.169)ˣ

Let's choose the points (-4, 138.6) and (-3, 23.4):

[tex]f(-4) = ab^{(-4)} + k = 138.6\\f(-3) = ab^{(-3)} + k = 23.4[/tex]

Now we can subtract the second equation from the first equation to eliminate k:

[tex]f(-4) - f(-3) = ab^{(-4)} - ab^{(-3)}[/tex]

Simplifying this equation gives:

[tex]138.6 - 23.4 = a(b^{(-3)} - b^{(-4)})\\115.2 = a(b^{(-3)} - b^{(-4)})[/tex]

Next, we can divide the second equation by the first equation to eliminate a:

[tex]\dfrac{f(-3)}{f(-4)} = (ab^{(-3)} + k)/(ab^{(-4)} + k)\\\dfrac{23.4}{138.6} = b^1[/tex]

Solving for b gives:

[tex]b = (23.4/138.6)^{(1/1)}\\b = 0.169[/tex]

Now that we have found b, we can use one of the original equations to solve for a. Let's use the equation f(1) = ab¹ + k:

f(1) = ab¹ + k

-14.85 = a(0.169) + k

Solving for a gives:

a = (-14.85 - k)/(0.169)

To find k, we can substitute the value of a and b into any of the original equations. Let's use the equation f(0) = ab⁰ + k:

f(0) = ab⁰ + k

-14.4 = a(1) + k

-14.4 = a + k

Substituting the value of a into this equation gives:

-14.4 = (-14.85 - k)/(0.169) + k

-14.4 = -88.157 + 5.988k

k = 18.638

Therefore, the exponential model for the given data is:

f(x) = abˣ + k = 14.85 + 18.638(0.169)ˣ

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Answer:

20 quartesrs

Step-by-step explanation:

20 quarters

The volume of the cylinder is approximately 1335.7 cm³.

To find the volume of a cylinder, we can use the formula:

Volume =[tex]\pi \times r^2 \times h[/tex]

Where π is a constant approximately equal to 3.14159, r is the radius of the cylinder, and h is the height or length of the cylinder.

Given that the diameter of the cylinder is 11 cm, we can find the radius by dividing the diameter by 2:

Radius = 11 cm / 2 = 5.5 cm

The length or height of the cylinder is given as 14 cm.

Now we can plug these values into the volume formula:

Volume = [tex]\pi \times (5.5 cm)^2 \times 14 cm[/tex]

Calculating this equation, we get:

Volume ≈ 3.14159 [tex]\times[/tex] [tex](5.5 cm)^2 \times[/tex] 14 cm

≈ 3.14159 [tex]\times[/tex] 30.25 [tex]cm^2 \times[/tex] 14 cm

≈ 1335.727 [tex]cm^3[/tex]

Therefore, the volume of the cylinder is approximately 1335.7 cm³.

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Answer:

2

Step-by-step explanation:

First, we need to arrange the data in order. We can convert the mixed numbers to improper fractions for ease of comparison:

1/3, 2/1, 4/1, 1/1, 7/3, 4/5, 5/2

Now, let's arrange them in ascending order:

1/3, 4/5, 1, 7/3, 2, 5/2, 4

The median is the middle value in the data set. Since we have an odd number of values, the median is the middle value when the data is arranged in order. Therefore, the median is:

median = 2

Therefore, the correct option is C

Answer:

1.5

Step-by-step explanation:

1/3    2    4    1    7    2/3    4/5    5/2

Write the numbers in ascending order.

1/3    2/3    4/5    1    2    5/2    4    7

The median is the middle value if there is an odd number of numbers.

If there is an even number of numbers, the median is the mean of the middle two numbers.

Here, there are 8 values, so we do the mean of the middle 2 values.

median = (1 + 2)/2

median = 1.5

Answer:

2csc(2x)

Step-by-step explanation:

When simplifying the given expression, we can start by finding a common denominator for the fractions. The common denominator for sin x and cos x is cos x * sin x.

Rewriting the expression using the common denominator, we have:

(sin x * sin x)/(cos x * sin x) + (cos x * cos x)/(sin x * cos x)

Simplifying the fractions, we get:

sin^2(x)/(cos x * sin x) + cos^2(x)/(sin x * cos x)

Now, let's simplify each fraction individually:

sin^2(x)/(cos x * sin x) can be simplified to (sin x / cos x)

cos^2(x)/(sin x * cos x) simplifies to (cos x / sin x)

Now, combining the simplified fractions, we have:

(sin x / cos x) + (cos x / sin x)

To combine these fractions, we need a common denominator, which is cos x * sin x:

[(sin x * sin x) + (cos x * cos x)] / (cos x * sin x)

Using the Pythagorean identity sin^2(x) + cos^2(x) = 1, we can simplify the numerator:

(1) / (cos x * sin x)

Therefore, the simplified form of the expression is 1 / (cos x * sin x), or 2csc(2x)

Answer:

18. The probability of rolling a number less than five or an odd number

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Please Brainiest

12/70 is the probability of getting a point in the triangle.

From the dimension given in the figure,

height of the triangle  = 6 cm

base of the triangle  = 4 cm

width of the rectangle = 7 cm

length of  the rectangle = 10 cm

From the general formula of the area of a triangle and a rectangle,

The area of the triangle = 1/2*base*height

in a given case,

Area of triangle = 1/2*4*6=12 cm²

The area of the rectangle = length * width

in the given case,

Area of the rectangle = 7*10=70 cm²

So the probability of randomly choosing a point in the triangle:

Probability =Area of triangle/area of the rectangle

probability = 12/70

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Based on the given data, the probabilities of the spinner landing on each color are approximately:

Red: 0.3469

Blue: 0.2449

Green: 0.0816

Yellow: 0.2449

Purple: 0.0816

To calculate the probability of the spinner landing on a specific color, we need to divide the frequency of that color by the total number of spins.

Given the spinner results:

Color Frequency

Red 17

Blue 12

Green 4

Yellow 12

Purple 4

To find the probability of landing on a specific color, we divide the frequency of that color by the total number of spins:

Probability (Red) = Frequency (Red) / Total Spins

= 17 / (17 + 12 + 4 + 12 + 4)

= 17 / 49

= 0.3469 (rounded to four decimal places)

Probability (Blue) = Frequency (Blue) / Total Spins

= 12 / 49

= 0.2449 (rounded to four decimal places)

Probability (Green) = Frequency (Green) / Total Spins

= 4 / 49

= 0.0816 (rounded to four decimal places)

Probability (Yellow) = Frequency (Yellow) / Total Spins

= 12 / 49

= 0.2449 (rounded to four decimal places)

Probability (Purple) = Frequency (Purple) / Total Spins

= 4 / 49

= 0.0816 (rounded to four decimal places)

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Answer:

Step-by-step explanation:

150 mile length. We can make an inequality for this with him riding on his bike for r and walking for w.
40r + 4w = 150

r + w = 6

Then we get

r = 7/2

w = 5/2

The equation that passes through the point (4, -3) and has a slope of 4 is option A: 5x + 4y = 8.

To determine which equation passes through the point (4, -3) and has a slope of 4, we can substitute the values of x and y into each equation and check if the resulting equation is true.

Let's substitute x = 4 and y = -3 into each equation:

A. 5x + 4y = 8

Substituting x = 4 and y = -3:

5(4) + 4(-3) = 20 - 12 = 8

The equation is true for points (4, -3).

B. 5x - 4y = 8

Substituting x = 4 and y = -3:

5(4) - 4(-3) = 20 + 12 = 32

The equation is not true for points (4, -3).

C. 4x + 5y = 8

Substituting x = 4 and y = -3:

4(4) + 5(-3) = 16 - 15 = 1

The equation is not true for points (4, -3).

D. 4x - 5y = 8

Substituting x = 4 and y = -3:

4(4) - 5(-3) = 16 + 15 = 31

The equation is not true for points (4, -3).

Therefore, the equation that passes through the point (4, -3) and has a slope of 4 is option A: 5x + 4y = 8.

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Answer:

1/30

Step-by-step explanation:

All of the colours have the same probability of being spun. 5 colours.

So, P(spinning a green) = 1/5.

6-sided to a die.

So, P(rolling a 5) = 1/6

P(spinning a green AND rolling a 5) = (1/5) X (1/6) = 1/30

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Answer:

1/30

Step-by-step explanation:

i got this answer because the probability of spinning green is 1/5, as there are 5 colors including green.

The probability of rolling 5 is 1/6, as there are 6 numbers including 5.

However, the questions asks for the probability of green and rolling 5, so I simply multiplied 1/6 and 1/5 and got 1/30.

I apologize if I misunderstood the question and answered it wrong.

Since the difference between the areas of the two rectangles is 64 cm², it has been proven that it is equal to x² - 2x - 35 = 0.

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = LB

Where:

Area of rectangle M = L × B

Area of rectangle M = (x - 3) × (3x + 4)

Area of rectangle M = 3x² - 5x - 12

Area of rectangle N = L × B

Area of rectangle N = (x + 2) × (x - 3)

Area of rectangle N = x² - x - 6

Difference = Area of rectangle M - Area of rectangle N

Difference = 3x² - 5x - 12 - (x² - x - 6)

Difference = 3x² - 5x - 12 - x² + x + 6

64 = 2x² - 4x - 6

0 = 2x² - 4x - 6 - 64

0 = 2x² - 4x - 70

By dividing all through by 2, we have:

0 = x² - 2x - 35

x² - 2x - 35 = 0 (Proven).

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The number of jerseys that the senior class at Legion Academy can purchase for $430, using quadratic equation, is 190.

Quadratic equation is an algebraic equation of the second degree in x, represented in the form of ax²+bx+c=0.

In the quadratic equation, a, b, and c are known values but a ≠ 0 and x is unknown.

x = [-b ± √b² - 4ac]/2a

when ax^2 + bx + c = 0

C = 0 .1x² + 2.4x + 25, where C is the amount, it costs to buy x jerseys.

Simplifying the equation, we get:

x = 0.2 − 2.4 ± 40.4​

The two possible values of x are:

1) x = 0.2 − 2.4 + 40.4​ = 190

or

2) x = 0.2 − 2.4 − 40.4 ​= −214

The value of x cannot be negative, therefore, the class bought 190 jerseys for $430.

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Answer: 3 quarts is equivalent to 5 pints

The best equation that describes the lined graph is: C. y= -3x - 3

To determine the best description for the lined graph, we have to insert several values for x and see what that gives us as the value of y. After doing this, we will crosscheck against the values in the graph. First, at x = 0, the value of y = -3.

On the lined graph, we see that the values correspond. Also, at x = 1, the value of y becomes -6. On the lined graph, this also corresponds so, the selected equation matches the description of the lined graph.

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Answer: x<4

Step-by-step explanation:

If we break this down as

-2+4x<14 and we add 2 to both sides

4x+<16 and divide by 4

and you get x<4

This question involves using the binomial distribution.

Let X be the number of male high school lacrosse players who will play at the college level out of the 20 selected players . We can model X as a binomial random variable with parameters n=20 and p=0.128, where p is the probability of success (i.e., a player going on to play at the college level).

The probability of exactly 4 players playing at the college level is given by the formula:

P(X=4) = (20 choose 4) * (0.128)^4 * (1-0.128)^(20-4)

Using a calculator, we can evaluate this expression to find:

P(X=4) = 0.155

Therefore, the probability that exactly four of the 20 male high school lacrosse players selected at random will end up playing at the college level is 0.155, or between C and 1 (inclusive).

Note that we rounded to three decimal places as requested .

Answer

Hi!, if you need help right away, chat with a tutor!

Step-by-step explanation:

Answer:

(a) width = 71 ft; (b) length = 77 ft

Step-by-step explanation:

(a) The formula for area of a rectangle is

A = lw, where

Because we're already given the area and length, we can find the width by plugging everything into the formula and solve for width, w:

6319 = 89w

71 ft = w

(b) The formula for perimeter of a rectangle is

P = 2l + 2w, where

Since we're given the perimeter and width this time, we can plug everything into the formula and solve for l:

272 = 2l + 2(59)

272 = 2l + 118

154 = 2l

77 ft = l

We can check our answers for (a) and (b) by plugging in the length and width for (a) into the area formula and seeing whether we get 6319 and plugging in the length and width for (b) into the perimeter formula and seeing whether we get 272

Checking answers for (a):

6319 = 89 * 71

6319 = 272

Checking answers for (b):

272 = 2(77) + 2(59)

272 = 154 + 118

272 = 272

number 4

studied this before if no correct must be a error

Finance and Financial Planning companies are not really looking for employees who are innovators or think outside the box: False.

Financial planning skills can be defined as the ability of an individual such as an employee, to determine the most appropriate (best) financing and investing activities for himself or herself, or a business firm after analyzing and evaluating all available financial options.

In this context, we can reasonably infer and logically deduce that financial planning skills ultimately enables an individual such as an employee, to prepare and plan for the future.

In conclusion, most finance and financial planning companies require employees who are innovators and can think outside the box.

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The graph of the function |x| + 1 < 3 is plotted and attached

The graph is an absolute value graph merged with inequality. hence the attributes of inequality which involves shading of the graph will be seen in the graph

To create a table of values for the inequality |x| + 1 < 3, we can evaluate the inequality for each value of x within that range.

For x = -2:

|(-2)| + 1 < 3

2 + 1 < 3

3 < 3

This inequality is not true for x = -2.

For x = -1:

|(-1)| + 1 < 3

1 + 1 < 3

2 < 3

This inequality is true for x = -1.

For x = 0

|(0)| + 1 < 3

0 + 1 < 3

1 < 3

This inequality is true for x = 0.

For x = 2:

|(2)| + 1 < 3

2 + 1 < 3

3 < 3

This inequality is not true for x = 2.

Therefore, the values of x  that satisfy the inequality |x| + 1 < 3 are: x = -1 and x = 0.

the graph is attached

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Answer:

Step-by-step explanation:

B

Activity: "Percentage Analysis in Real-Life Situations"

Objective: The objective of this activity is to help learners recognize the practical application of percentages in various social situations. It aims to develop their critical awareness of how percentages are used in real-life contexts and their significance in social, environmental, cultural, and economic relations.

Procedure:

1. Provide learners with a set of real-life scenarios, such as a discount sale, population growth, or budget allocations.

2. Ask them to identify the relevant information and calculate percentages based on the given data.

3. In small groups, learners discuss and analyze the implications of these percentages in the given social situations.

4. Encourage learners to think critically about how percentages impact decision-making, resource allocation, and understanding social phenomena.

5. Have groups present their findings and engage in a class discussion about the significance of percentages in these scenarios.

Teaching and Learning Approach:

This activity promotes an active learning approach by engaging learners in real-life problem-solving. It helps them recognize the practical relevance of percentages and fosters critical thinking skills.

By connecting mathematical concepts to social situations, learners develop a deeper understanding of how percentages are utilized in various aspects of their lives.

The teacher's role is to facilitate discussions, provide guidance, and encourage learners to articulate their understanding of the connections between mathematics and real-world contexts.

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