The graph shows the predicted population of a town, z number of years after 2020. According to the graph, which statement is true?

By using pythagorean theorem, the length of the missing side is 12 feet.

What is the Pythagorean theorem?

Pythagoras' theorem is a fundamental principle in geometry that relates to the three sides of a right-angled triangle. It states that:

"In a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides."

In mathematical terms, if a, b, and c are the lengths of the sides of a right-angled triangle, where c is the hypotenuse, then the theorem can be written as:

[tex]c^2 = a^2 + b^2[/tex]

We can use the Pythagorean theorem to determine the length of the missing side if we know that the given sides form a right triangle.

In this case, we have two sides of the triangle given: 7.2 feet and 9.6 feet. Let's assume that c is the length of the hypotenuse.

If the triangle is a right triangle, then we can use the Pythagorean theorem to solve for c:

[tex]c^2 = 7.2^2 + 9.6^2[/tex]

[tex]c^2 = 51.84 + 92.16[/tex]

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

[tex]c = \sqrt{144}[/tex]

c = 12 feet

Therefore, if the triangle is a right triangle, then the length of the missing side is 12 feet.

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Pete runs farther per carry, with a unit rate of 9.05 yards per carry compared to Branden's unit rate of 7.33 yards per carry.

A unit rate is a rate that has a denominator of 1. It is a ratio that compares a quantity to its unit of measurement.

To determine who runs farther per carry, we can use unit rates to compare the distance each player runs per carry.

For Branden:

Distance per carry is

= 550 yards ÷ 75 carries

Divide the numbers

= 7.33 yards per carry

For Pete:

Distance per carry is

= 380 yards ÷ 42 carries

Divide the numbers

= 9.05 yards per carry

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The value οf a = 3, b=-10, c-8

it's a secοnd-degree quadratic equatiοn which is an algebraic equatiοn in x. Ax² + bx + c = 0, where a and b are the cοefficients, x is the variable, and c is the cοnstant term, is the quadratic equatiοn in its standard fοrm. A nοn-zerο term (a 0) fοr the cοefficient οf x² is a prerequisite fοr an equatiοn tο be a quadratic equatiοn.

The x² term is written first, then the x term, and finally the cοnstant term is written when cοnstructing a quadratic equatiοn in standard fοrm. In mοst cases, the numerical values οf letters a, b, and c are expressed as integral values rather than fractiοns οr decimals.

The equatiοn given 5x²-2=2x²+10x+6

3x²-10x-8=0

values οf a = 3, b=-10, c-8

Hence the value οf a = 3, b=-10, c=8

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For no solution 7x+10

For one solution8x+0

For infinite solution 7x+5

An infinite solution is a solution to a system of equations that has an infinite number of possible solutions. In other words, any value for the variables in the system will satisfy all the equations.

2x+5+2x+3x

On adding the values with variables, x=7

On adding constant values=5

2x+5+2x+3x=7x+5

For no solution

7x+5=7x+10

For one solution

7x+5=8x

x=5

For infinite solution

7x+5=7x+5

Hence, For no solution 7x+10

For one solution 8x+0

For infinite solution 7x+5.

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On solving the question we have that We can see that RS + ST = RT, equation  confirming that S is on segment RT: RT = RS + ST = 5 + 10 = 15

A math equation is a mechanism for connecting two statements and indicating equivalence with the equals sign (=). To explain the connection between the two sentences put on each side of a letter, a statistical method can be employed. The software and the logo are usually interchangeable. 2x - 4 equals 2, for example. An equation is a logical expression that asserts the equality of some mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14.

Because S is on the section RT, we know that RS + ST = RT. As a result, we may construct the following equation:

RS + ST = 3x + 1 + (x + 2) = 15

To simplify this equation, we can combine similar terms:

4x + 3 = 15

Subtraction of 3 from both sides yields:

4x = 12

When we divide both sides by 4, we get:

x = 3

RS = x + 2 = 5 and ST = 3x + 1 = 10 as a result.

We can see that RS + ST = RT, confirming that S is on segment RT:

RT = RS + ST = 5 + 10 = 15

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(a) P(green or red) = 0.3946

(b) P(blue, red, or yellow) = 0.7606

(c) P(not brown) = 0.7807

(d) P(not green) = 0.6559

What is probability?

Probability is a branch of mathematics that deals with the study of randomness and uncertainty in events. It is the measure of the likelihood or chance that an event will occur. Probability is expressed as a number between 0 and 1, where 0 indicates that the event will not occur and 1 indicates that the event will occur with certainty.

The total number of M&M's is 2552.

(a) P(green or red) = P(green) + P(red)

= 364/2552 + 507/2552

= 0.2692

(b) P(blue, red, or yellow) = P(blue) + P(red) + P(yellow)

= 399/2552 + 507/2552 + 351/2552

= 0.4917

(c) P(not brown) = 1 - P(brown)

= 1 - 538/2552

= 0.7891

(d) P(not green) = 1 - P(green)

= 1 - 364/2552

= 0.8575

Hence,

(a) P(green or red) = 0.3946

(b) P(blue, red, or yellow) = 0.7606

(c) P(not brown) = 0.7807

(d) P(not green) = 0.6559

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Answer:

the number 228

Step-by-step explanation:

Let's call the smallest number in the consecutive sequence "x". Then, the 10 consecutive numbers are x, x+1, x+2, x+3, x+4, x+5, x+6, x+7, x+8, and x+9.

If we exclude one of these numbers, then the sum of the remaining 9 numbers would be:

(x) + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6) + (x+7) + (x+8) or 9x + 36.

We know that the sum of the remaining 9 numbers is 2023, so we can set up the equation:

9x + 36 = 2023

Solving for x, we get:

9x = 1987

x = 221

Therefore, the smallest number in the consecutive sequence is 221, and the 10 numbers are 221, 222, 223, 224, 225, 226, 227, 228, 229, and 230.

If we exclude the number 228, then the sum of the remaining 9 numbers is 2023.

Using the equation y = 7x , we can compute that when x = 2, y = 14 and when x = 4 , y = 28. So, correct option is B.

The equation y = 7x relates the variables y and x, where y is a function of x. To compute the value of y for a given value of x, we simply substitute that value of x into the equation and solve for y.

When x = 2, we can substitute this value into the equation:

y = 7(2) = 14

Therefore, when x = 2, y = 14.

Similarly, when x = 4, we can substitute this value into the equation:

y = 7(4) = 28

Therefore, when x = 4, y = 28.

So, the correct option is B: When x = 2, y = 14 and when x = 4, y = 28.

In summary, to compute the value of y for a given value of x using an equation, we substitute that value of x into the equation and solve for y. In this case, when x = 2, y = 14, and when x = 4, y = 28, according to the given equation y = 7x.

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Answer:

28

x 76

----

168 (units digit of 76 multiplied by 28)

1408 (tens digit of 76 multiplied by 28)

----

2128

Therefore, 28x76 is equal to 2128.

Step-by-step explanation:

Answer: I THINK 4.

Step-by-step explanation:

Sorry if it is wrong!! :'D

Answer:

Horizontal distance between the wall and the bottom of ramp = 25.4 inches.

Step-by-step explanation:

Pythagorean theorem:

          AB  -> wall ;  AB =  14 inches    

         AC -> Wooden plank ; AC = 29 inches

        BC -> horizontal distance between the wall and the bottom of ramp(pank).

           Pythagorean theorem,

                       [tex]\boxed{\bf base^2 + altitude^2 = hypotenuse^2}[/tex]

                         BC² + AB² = AC²

                           BC² + 14² = 29²

                          BC² + 196 =  841

                                     BC² = 841 - 196

                                             = 645

                                       BC = √645

                                       BC = 25.4 inches

Horizontal distance between the wall and the bottom of ramp = 25.4 inches.

Given,

Length = 29 inches

Height = 14inches

Here,

Pythagorean theorem:

AB  -> wall ;  AB =  14 inches    

AC -> Wooden plank ; AC = 29 inches

BC -> horizontal distance between the wall and the bottom of ramp (plank).

Pythagorean theorem,

Base²  + Perpendicular² = Hypotenuse²

BC² + AB² = AC²

BC² + 14² = 29²

BC² + 196 =  841

BC² = 841 - 196

= 645

BC = √645

BC = 25.4 inches

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The probability of randomly selecting a temperature between 70 and 75 is approximately 0.8291.

To find the probability that a randomly chosen temperature is between 70 and 75, we need to use the z-score formula as shown below:

z = (x - μ) / σ

Where:x = 70 and 75μ = 79σ = 4z1 = (70 - 79) / 4 = -2.25z2 = (75 - 79) / 4 = -1P(70 < x < 75) = P(-2.25 < z < -1)

To find the probability for the above inequality, we need to use a calculator. We know that the probability of the standard normal distribution is equal to 1.

Hence, P(-2.25 < z < -1) = Φ(-1) - Φ(-2.25) = 0.8413 - 0.0122 ≈ 0.8291. Therefore, the probability is about 0.8291.

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Given data:

pH of lye = 12.13

Using the formula pH = -log[H+], we have to find the hydrogen ion concentration, [H+].

Now, putting the given values in the formula, we get:

pH = -log[H+]

12.13 = -log[H+]

log[H+] = -12.13

[H+] = 10^-12.13 = 5.01187 x 10^-13

So, the hydrogen ion concentration, [H+] is 5.01187 x 10^-13 moles/liter. Therefore, the answer is 5.01187 x 10^-13.

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From the graphs in the given coordinate plane, the functions that have complex roots are function b, function d and function f.

From the question, we are to determine the functions that have complex roots in the given coordinate plane.

In a quadratic graph, if the vertex of the quadratic function lies above the x-axis, and the parabola opens upward, there will be NO x-intercepts. The graph will have complex roots.

Also, if the vertex of the quadratic function lies below the x-axis, and the parabola opens downward , there will be NO x-intercepts.

The graph will have complex roots.

In the given coordinate plane, the functions that have complex roots are function b, function d and function f.

Hence, the functions b, d, and f have complex roots.

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The cοrrect answer tο the given questiοn is d. the central limit theοrem.

The gathered data is arranged in tables based οn frequency distributiοn. The infοrmatiοn cοuld cοnsist οf test results, lοcal weather infοrmatiοn, vοlleyball match results, student grades, etc. Data must be presented meaningfully fοr understanding after data gathering. A frequency distributiοn graph is a different apprοach tο displaying data that has been represented graphically.

The basis fοr using a nοrmal prοbability distributiοn tο apprοximate the sampling distributiοn οf the sample means and pοpulatiοn mean is the central limit theοrem.

The central limit theοrem states that fοr a sufficiently large sample size, the sampling distributiοn οf the sample means will be apprοximately nοrmal, regardless οf the shape οf the pοpulatiοn distributiοn. This theοrem allοws us tο make statistical inferences abοut the pοpulatiοn mean based οn the sample mean using the prοperties οf the nοrmal distributiοn, such as the mean and standard deviatiοn.

Therefοre, the cοrrect answer tο the given questiοn is d. the central limit theοrem.

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The value of q in the question is q>-12/15

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions

The given inequality is 5(p−3q)<12

Opening the bracket we have

5p - 15q < 12

The solution can only be gotten if we assume p = 0

the substitute p=0 in the inequality to have

-15q < 12

dividing both sides by -15 to have

-15q/-15 < 12/-15

therefore q > 12/-15

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For the equilateral triangles we have:

1) x = 5, y =  √50

2) a = 2, b = √8

3)y = 8, x = √128

4) a = b = 7/√2

We can see some triangles, remember that for a right triangle whose angles are 45°, we have an equilateral triangle.

So the two legs have the same measure.

1) Here we can see that x = 5, and the hypotenuse is given by:

y^2 = 5^2 + 5^2

y^2 = 50

y = √50

2) Here we have a = 2, then the hypotenuse is:

b^2 = 2^2 + 2^2

b^2 = 8

b = √8

3) Here we have y = 8, then the hypotenuse is:

x^2  = 8^2 + 8^2

x^2 = 128

x = √128

On the last triangle we can see that the hypotenuse is 7, and we know that a = b

then:

7^2 = a^2 + b^2

7^2 = a^2 + a^2

49 = 2*a^2

(49/2) = a^2

√(49/2) = a

7/√2 = a = b

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Answer:

The answer is B

Step-by-step explanation:

Answer:

12 × 3 = 36

the top of the diagram will also equal 36

138-72=66

66 ÷2= 33

33÷3 =11

therefore x=11

Answer:

perimeter = 138

p=2(138+12)

p=2×150

p=300

x=300

e [0.1}

We know that P(X < 2.24) = 0.7257. Also, the mean is 2.Let us calculate the variance of the given normal distribution random variable. Given that P(X < 2.24) = 0.7257, we have to find variance. Let us solve this question as follows:We know that mean of normally distributed random variable is μ and standard deviation is σ. As the mean is 2, μ = 2.We have the z-score: z = (2.24 - 2) / σFrom the normal distribution table, we can find out that P(Z < 0.80) = 0.7881Now, we have the following equation:0.7881 = (2.24 - 2) / σσ = 0.3158Finally, we can find the variance (σ^2) = 0.3158^2 = 0.0995 ≈ 0.1Therefore, the correct answer is option e. 0.1.

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According to given equation Baxter’s Hardware had 27 followers on Sunday morning.

What is equation?

Equations can take many forms, including linear, quadratic, polynomial, trigonometric, and exponential, and can be used to model and solve a wide range of real-world problems.

The given equation is:

f + 18 - 20 = 25

Adding the numbers on the left side, we get:

f - 2 = 25

Adding 2 to both sides, we get:

f - 2 + 2 = 25 + 2

Simplifying, we get:

f = 27

Therefore, Baxter’s Hardware had 27 followers on Sunday morning.

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Step-by-step explanation:

Divya is cooking dinner. she goes to the market to buy ingredients. the price per pound of different ingredients is shown in the table below. Diyva recipe calls for 3.25 pounds of beef, 0.65 pounds of onions, 0.2 pounds of potatoes, 0.15 pounds of tomatoes, and 0.33 pounds of asparagus How much will diyva pay for all the ingredients in the recipe?

Answer:C

Step-by-step explanation:

[tex](x-3)^2=5\\we \ should \ find \ square \ root \ of \ each \ side,\\\sqrt{(x-3)^2}=\sqrt{5}\\1)x-3=\sqrt{5}x=\sqrt{5}+3\\2)3-x=\sqrt{5}\\x=3-\sqrt{5}\\\\so,x=3\± \sqrt{5}[/tex]

The weight of the smaller dog is 5.6 pounds.

Let the weight of the smaller dog be x, then,

The weight of the larger dog = 1.4 pounds.

The combined weight of the dogs =  12.6 pounds.

Therefore,

The sum of the weight of the larger dog and smaller dog = the combined weight of the dogs.

That is,

1.4 + x + x = 12.6

1.4 + 2x =  12.6

2x = 12.6 - 1.4

2x = 11.2

x = 11.2 ÷ 2

x = 5.6.

Hence, the weight of the smaller dog is 5.6 pounds.

?

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Your question is incomplete, and the complete question would be:

Karen has two dogs. the larger dog weighs 1.4 pounds more than the smaller dog. the combined weight of the two dogs is 12.6 pounds. what is the weight of the smaller dog?

Answer:

9 hope u get it right budddyyyy

Answer:

a. When x > k, the cost of running the ad for a week can be expressed as:

C = p + e(x - k)

where C is the cost in dollars, p is the cost per k lines, e is the cost per extra line, and (x - k) is the number of extra lines over k.

b. When x ≤ k, the cost of running the ad for a week can be expressed as:

C = p

where C is the cost in dollars and p is the cost per k lines. Since the number of lines x is less than or equal to k, there are no extra lines and the cost is simply the base cost of p dollars for k lines.

Hope this helped! I'm sorry if it's wrong. If you need more help, ask me! :]

The sampling distribution of the means has a mean of 172 pounds and a standard deviation of 4.83 pounds.

In the context of sampling distribution of the means, the standard deviation represents the degree of spread or variation of sample means around the true population mean.

To compute the standard deviation of the sampling distribution of the means, one typically divides the population standard deviation by the square root of the sample size.

Therefore, the standard deviation of the sampling distribution of the means is 29/√36 = 29/6 = 4.83 pounds.

So, the sampling distribution of the means has a mean of 172 pounds and a standard deviation of 4.83 pounds.

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50%

The cran-orange juice contains 50% cranberry juice. The juice is 100% juice. Subtract 50% cranberry juice from 100% cran-orange juice and that leaves you with 50% orange juice.

The length of the rectangular prism with a volume of 1.512 m³​ is equal to 0.9 meters.

Mathematically, the volume of a rectangular prism can be calculated by using this formula:

Volume of a rectangular prism = L × W × H

Where:

By substituting the given parameters into the formula for the volume of a rectangular prism, we have;

Volume of a rectangular prism = L × W × H

1.512 = L × 2.4 × 0.7

Length, L = 1.512/1.68

Length, L = 0.9 meters.

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Complete Question:

Find the length of the rectangular prism shown below with a volume of 1.512 m³​, a width of 2.4 m and a height of 0.7 m.

The surface area οf the cοntainer is 314 ft².

A rectangle is a geοmetric shape that has fοur sides and fοur right angles (90 degrees) with οppοsite sides being parallel and equal in length. It is a type οf quadrilateral, a pοlygοn with fοur sides.

Tο find the surface area οf a rectangular prism, we need tο add the areas οf all six faces. The fοrmula fοr the surface area οf a rectangular prism is:

Surface area = 2lw + 2lh + 2wh

where l is the length, w is the width, and h is the height οf the rectangular prism.

Substituting the given values, we get:

Surface area = 2(5)(9) + 2(5)(8) + 2(9)(8)

Surface area = 90 + 80 + 144

Surface area = 314 square feet

Therefοre, the surface area οf the cοntainer is 314 ft².

Answer: 314 ft².

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