The equation [tex]p^{2} =5a[/tex] represents the perimeter, p, of a square with an area, A, a square stained glass had an area of 20ft. What is the perimenter of the window?

Answer:

a=3 d=6 n=45

A45= 3+44×6=267

Step-by-step explanation:

i hope you find it helpful

Given the first three terms of the sequence to be

[tex]3,9,15,...[/tex]

It is observed that each successive term of the sequence is obtained by the addition of 6 to the preceding term.

Thus, the sequence is an arithmetic sequence.

The nth term of an arithmetic sequence is given as

[tex]a_n=ar^{r-1}[/tex]

Thus, from the given sequence,

               [tex]a=3[/tex]

[tex]d=9-3=6 \ \text{OR} \ 15-9=6[/tex]

              [tex]n=45[/tex]

[tex]T_{45} \ \text{is thus evaluated as}[/tex]

     [tex]T_{45}=3+(45-1)6[/tex]

    [tex]T_{45}=3+(44\times6)[/tex]

        [tex]T_{45}=3+264[/tex]

             [tex]T_{45}=267[/tex]

The 45th term of the sequence is thus 267

The center of dilation, point C, is located at (4, 3/2). The center of dilation, point C, is the point of intersection of the lines joining each vertex of the original triangle to the corresponding vertex of the dilated triangle.

Since triangle XYZ is dilated by a scale factor of 0.5, each point of the dilated triangle is located halfway between the corresponding point of the original triangle and the center of dilation, point C.

Therefore, to find the location of point C, we need to find the midpoint of each line segment joining the corresponding vertices of the original and dilated triangles.

Plotting the vertices of the original triangle at points X(2, 4), Y(6, 2), and Z(3, 5) on the coordinate plane, we can use the midpoint formula to find the midpoint of each segment.

Midpoint of segment XX' = (2 + 6)/2, (4 + 2)/2 = (4, 3)

Midpoint of segment YY' = (6 + 18)/2, (2 + 4)/2 = (12, 3)

Midpoint of segment ZZ' = (3 + 9/2)/2, (5 + 7/2)/2 = (15/4, 11/4)

The point of intersection of the lines joining the original vertices to the dilated vertices is point C(4, 3/2).

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Answer:

256[tex]\pi[/tex]

Step-by-step explanation:

The Area of a circle --> A =[tex]\pi*r^{2}[/tex]

Radius = 16 ft,

[tex]16^{2} = 256[/tex], so instead of then multiplying this number by [tex]\pi[/tex], Just leave it as,

256[tex]\pi[/tex]

The value for theta is 16.7 degrees and that of alpha is 73.3 degrees.

Trigonometric functions are also known as Circular Functions can be simply defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle are given by these trig functions

The tangent function is the ratio of the length of the opposite side to that of the adjacent side. It should be noted that the tan can also be represented in terms of sine and cos as their ratio.

To find alpha, we can take the inverse tangent of both sides of the equation:

tan α = 10/3

tan⁻¹(tan α) = tan⁻¹(10/3)

α = tan⁻¹(10/3)

Using a calculator, we get:

α ≈ 73.3 degrees (rounded to one decimal place)

Therefore, the value of alpha is approximately 73.3 degrees.

To find theta, we can take the inverse tangent of both sides of the equation:

tan θ = 3/10

tan⁻¹(tan θ) = tan⁻¹(3/10)

θ = tan⁻¹(3/10)

Using a calculator, we get:

θ ≈ 16.7 degrees (rounded to one decimal place)

Therefore, the value of theta is approximately 16.7 degrees.\

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If the money box has 600 coins that consist of 20 cents and 50 cents, the total amount of cents in the money box is 24,000 cents.

To determine the total amount of cents in Thabang's money box, we need to know how many of the 600 coins are 20 cents and how many are 50 cents. Let's use variables to represent these quantities.

Let x be the number of 20 cent coins, and y be the number of 50 cent coins. We know that the total number of coins is 600, so we have:

x + y = 600

We also know that the value of each 20 cent coin is 20 cents, and the value of each 50 cent coin is 50 cents. So the total value of the coins in the money box is:

20x + 50y

To find the total amount of cents in the money box, we need to simplify and solve for the value of the expression above. We can do this by using the equation we have for x and y and substituting y = 600 - x:

20x + 50(600 - x) = 20x + 30000 - 50x = -30x + 30000

So the total value of the coins in the money box is -30x + 30000 cents. We don't know the value of x yet, but we know that x and y must be non-negative integers and x + y = 600.

We can solve for x by trying different values of x until we find one that satisfies these conditions. For example, if we set x = 200, then y = 400 and the conditions are satisfied. Therefore, the total amount of cents in the money box is:

-30x + 30000 = -30(200) + 30000 = 24000

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For the equation [tex]F(x) = x^2 - 3x + 9[/tex], when x = 2, F(x) = 5. For the equation f(x) = kx + 1, when x > 2, F(x) = kx + 1. For the two equations to be continuous at x = 2, k must equal 4. Yes, f(x) is continuous at x = 2.

For the equation [tex]F(x) = x^2 - 3x + 9[/tex], when x = 2, [tex]F(x) = 2^2 - 3(2) + 9 = 4 + (-6) + 9 = 5.[/tex]

For the equation f(x) = kx + 1, when x > 2, F(x) = kx + 1. We must find the value of k such that F(x) is continuous at x = 2. To do this, we must set F(2) = f(2).

5 = 4k + 1

4k = 4

k = 1

Therefore, for the two equations to be continuous at x = 2, k must equal 1. Yes, f(x) is continuous at x = 2.

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Answer:

a) Given two perpendicular sides of a square (as given in the diagram), we can construct two more perpendicular lines that are parallel to the initial two (since we are given their slopes). The intersection of these two lines is the unknown point.

b) From points A and C we can construct lines perpendicular from the lines coming out of point B. The intersections of these lines will be our unknown point.

The value οf x frοm the given diagram is 36°

A functiοn with οne οr twο variables and nο expοnents is referred tο as a linear functiοn. It is a functiοn with a straight line as its graph.

The sum οf angles οn a straight line.

The sum οf angles οn a straight line is 180°.

In this scenariο, the sum οf angles οn the straight line: AOB is 180°.

Therefοre, we have

3x + x + x = 180°

5x = 180

x = 36°

Hence, The value οf x frοm the given diagram is 36°

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Complete Question:

The probability that Ben will make three out of his next five free throws is approximately 0.3456

Assuming that each free throw attempt is independent of the others, we can use the binomial distribution to calculate the probability of Ben making three out of his next five free throws.

The probability of making a free throw is 0.6, so the probability of missing a free throw is 0.4. Let X be the number of successful free throws out of 5 attempts. Then X follows a binomial distribution with n = 5 and p = 0.6.

The probability of making three out of five free throws can be calculated as follows

P(X = 3) = (5 choose 3) × (0.6)^3 × (0.4)^2

where (5 choose 3) = 10 is the number of ways to choose 3 successful free throws out of 5 attempts.

Using a calculator, we get

P(X = 3) = 0.3456

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The measure of angle subtended by the arc CEB is 210⁰.

The value of m∠CDB is 30⁰.

The measure of angle subtended by the arc CEB is calculated by applying the following formula.

The sum of angles in a circle = 360⁰, so the value of arc CEB is calculated as;

arc CEB = 360 - 150⁰

arc CEB = 210⁰

Based on the angle of intersecting chord theorem, we will have the following equation to determine the value of m∠CDB.

m∠CDB = ¹/₂ (210 - 150)

m∠CDB = 30⁰

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Answer: 5

Step-by-step explanation:

Substitute the values:

A(1) + 2(2) = 9

A + 4 = 9

A = 9 - 4

A = 5

The sampling distribution of the proportion of people who respond "yes" in samples of 4 individuals is not binomial. This is because the binomial distribution has specific requirements that must be met, including a fixed number of trials, independent outcomes, and a constant probability of success. the probability of observing a sample proportion of 0.75 or higher is approximately 0.16.        

Assuming that the sample size is sufficiently large and the proportion of people who respond "yes" in the population is not too close to 0 or 1, the sampling distribution of the proportion of people who respond "yes" in samples of 4 individuals can be approximated by a normal distribution using the Central Limit Theorem. This means that the distribution of the sample proportion will be approximately normal with a mean equal to the population proportion and a standard deviation equal to the square root of [p(1-p)/n], where p is the population proportion and n is the sample size.

For example, let's say that we know that 60% of the population believes that gun laws should be more stringent. If we take samples of 4 individuals and calculate the proportion of people who respond "yes" in each sample, the sampling distribution of these proportions can be approximated by a normal distribution with a mean of 0.6 and a standard deviation of sqrt[(0.6)(0.4)/4] = 0.15.

Using this normal approximation, we can calculate probabilities and confidence intervals for the sample proportion. For example, if we take a sample of 4 individuals and find that 3 of them respond "yes," the sample proportion is 0.75. We can calculate the probability of observing a sample proportion of 0.75 or higher by standardizing the sample proportion using the mean and standard deviation of the sampling distribution:

z = (0.75 - 0.6)/0.15 = 1

Using a standard normal distribution table or calculator, we can find that the probability of observing a standard normal random variable greater than or equal to 1 is approximately 0.16. This means that the probability of observing a sample proportion of 0.75 or higher is approximately 0.16.

In summary, while the sampling distribution of the proportion of people who respond "yes" in samples of 4 individuals is not binomial, it can be approximated by a normal distribution using the Central Limit Theorem under certain conditions. This approximation allows us to calculate probabilities and confidence intervals for the sample proportion, even when the exact distribution is unknown.

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Answer:

each term is half the previous one. 1.6 *.5^(n-1). is a geometric sequence.

This is a geometric sequence with a common ratio of 1/2. Therefore, option B is correct.

A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a fixed constant called the common ratio (r).

In other words, if the first term of the sequence is "a", then the nth term of the sequence is given by:

an = a * r^(n-1)

where "n" is the position of the term in the sequence.

In this question:

To see why, notice that each term is half of the previous term:

0.8 is half of 1.6

0.4 is half of 0.8

0.2 is half of 0.4

In a geometric sequence, each term is obtained by multiplying the previous term by a fixed constant, which is called the common ratio. In this case, the common ratio is 1/2, because each term is half of the previous term.

So the sequence can be written as:

1.6, 0.8, 0.4, 0.2, …

or

a₁, a₁/2, a₁/4, a₁/8, …

where a₁ is the first term, which is 1.6 in this case.

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The models that represent a probability of 1/4 of pulling a red marble are given as follows:

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

After completing 12 trials, she pulled a red marble 3 times, hence the probability of pulling a red marble is given as follows:

3/12 = 1/4.

The other models with a probability of 1/4 are given as follows:

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In conclusion the value of a3 is 166.

How to solve and what does recursive mean?

We can use the given recursive formula to find the values of the sequence:

a1 = 4

a2 = (a1)²2 - 3 = 13

a3 = (a2)²2 - 3 = (13)²2 - 3 = 166

Therefore, the value of a3 is 166.

Recursive refers to a process or function that calls itself repeatedly until a specific condition is met. In mathematics, a recursive sequence or formula is a sequence that is defined in terms of its previous terms, such that the value of each term depends on the value of the previous term(s).

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Answer:

the answer for this question is A

Answer:

4

Step-by-step explanation:

Have a good day :-)

Answer:

y=12

Step-by-step explanation:

[tex]\frac{y}{24} =\frac{6}{y} \\y*y}= 6*24\\y^{2} =144\\y=12[/tex]

In the triangle the value of altitude y will be equal to 12 .

Proportion : y/24 = 6/y

Given,

Triangle.

Here,

First set up the proportions to solve for y,

Proportion : y/24 = 6/y

Now from the proportion solve for y,

y/24 = 6/y

y² = 144

y = √144

y = 12

Thus the value of y is 12 .

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Answer:

To multiply 9200 and 2.3 x 10^3 in scientific notation, we need to multiply their coefficients and add their exponents.

9200 x 2.3 x 10^3 = 21,160,000

Since the product is greater than 10, we need to adjust the coefficient and the exponent to express the number in scientific notation. We can move the decimal point to the left until there is only one digit to the left of the decimal point, and count how many places we moved the decimal point. In this case, we need to move the decimal point 7 places to the left:

2.116 x 10^7

Therefore, the product of 9200 and 2.3 x 10^3 expressed in scientific notation is 2.116 x 10^7.

A highway superintendent states that four bridges into a city are used in the ratio 2:3:3:4 during the morning rush hour.

A highway study of an SRS of 6000 cars indicates that main answer in 40 words and explanation in 140 words.According to the question, there are four bridges into the city, and they are used in the ratio of 2:3:3:4.

That means that for every 2 cars coming from the first bridge, there are 3 cars coming from the second and the third bridges and 4 cars coming from the fourth bridge.According to the SRS of 6000 cars, the total number of cars from the first bridge is: 2/12 * 6000 = 1000

The total number of cars from the second bridge is: 3/12 * 6000 = 1500The total number of cars from the third bridge is: 3/12 * 6000 = 1500The total number of cars from the fourth bridge is: 4/12 * 6000 = 2000

Therefore, the number of cars coming from the first, second, third, and fourth bridges are 1000, 1500, 1500, and 2000, respectively, during the morning rush hour.

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Answer:

Step-by-step explanation:

If the mother wants to get the amount of ice cream bars that will not contain any leftovers for her family of four, the least amount of boxes the mother could purchase to receive her goal is 2 boxes

MATH-

1 box= 6 bars

2 boxes= the bars(6)x2, which is equal to 12 ice cream bars

If you split 12 evenly between the members of her family which is 4 people,

12÷4=3 or 4x3=12

each family member would receive 3 ice cream bars each.

The additional variable used to determine the values of the original variables in the ordered pair of a system of equations whose solution is an infinite number of solution is called a parameter.

A parameter is an unknown variable that is not included in the original equations of a system of equations.

In algebra, a system of equations is a collection of two or more equations involving the same set of variables. The solution to a system of equations is the point or points at which the equations are true. A system of equations can have a unique solution, no solution, or an infinite number of solutions.

When a system of equations has an infinite number of solutions, it means that the equations are dependent on each other. This means that one of the equations can be expressed in terms of the other equation. The solution to the system of equations is then written in terms of the parameter, which is the variable that is not included in the original equations.

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The dimension of cone B is r = 4 and h = 9. Because the volume formula for a cone only considers the radius and height of the cone and not orientation, we know that cones B and A have the same volume.

The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

Many forms have various volumes. In 3D geometry, we have examined the numerous forms and solids such as cubes, cuboids, cylinders, cones, etc., that are specified in three dimensions. We will discover how to find the volume for each of these forms.

The volume of the cone is given by:

Volume = (1/3)πr²h

For cone B:

48π = (1/3)πr² * h

144 = r² * h

Suppose the r = 4 and h = 9:

144 = 4² * 9

144 = 144

True.

The possible dimension of cone B is r = 4 and h = 9.

Because the volume formula for a cone only considers the radius and height of the cone and not its shape or orientation, we know that cones B and A have the same volume. We utilised this rule to get the potential values for cone B: any two cones with the same volume must have the same product of radius and height.

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There is a potential association between hip fracture and active exercise, as a smaller proportion of women with hip fracture reported active exercise compared to the controls

Based on the provided information, we can say that there is a potential association between hip fracture and active exercise. The fact that a smaller proportion of women with hip fracture reported active exercise compared to the controls suggests that active exercise may have a protective effect against hip fracture.

However, it's important to note that this comparison alone does not establish a cause-and-effect relationship between active exercise and hip fracture. Other factors, such as age, bone density, and overall health status, may also play a role in the development of hip fractures.

To further evaluate the relationship between hip fracture and active exercise, additional research would be needed, including studies with larger sample sizes, more detailed information on exercise habits, and adjustments for potential confounding factors.

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1. The perimeter is 41.16 cm

2. The perimeter is 165.7 cm

Perimeter is a term used in geometry to describe the total length of the boundary or the distance around the edge of a two-dimensional shape.

1. Here, radius = 4cm,

Circumference of quarter circle = [tex]\frac{1}{4}[/tex] ×2πr = [tex]\frac{1}{4}[/tex] ×2×3.14×4 = 6.29 cm

Circumference of four quarters circle= 4×6.29 = 25.16 cm,

and 4 extra portion 4×4 = 16 cm

So, the Perimeter = 25.16 + 16 = 41.16 cm

2. The diameter = 40 cm then, Radius= 20 cm

here, 2 quarter circle and 1 half circle is equal to 1 complete circle.

Then circumference of circle equal to 2π r = 2×3.14×20 = 125.71,

So the perimeter = 125.71 + 20 + 20 = 165.7 cm

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  Slope = 8 is the value of  equation of Slope Intercept Form .

What does the Slope Intercept Form Equation stand for?

A straight line's slope and the location of its y-axis intersection are utilized to determine the general equation of the line using the slope intercept equation. Y = mx + b is the slope intercept form equation. One formula for figuring out a line's equation is the slope-intercept formula. Y = mx + b is the slope-intercept formula for a line with slope m and y-intercept b. Any point on the line is (x, y) in this case.

Y= 8x + 5

Compare the equation to the y = mx + c

       slope = 8

             c = 5

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If the population density for the area is 18.8 residents per square mile, to the nearest hundred, approximately 34,000 residents would be infected.

When a virus is accidentally released from a CDC lab, and it infects everyone within a 24-mile radius from the CDC lab, then if the population density for the area is 18.8 residents per square mile, to the nearest hundred, how many people were infected.

The number of people infected within the 24-mile radius from the CDC lab is calculated as follows:

The area of a circle with a radius of 24 miles is A = πr²,

which is A = π(24²) = 1,809.56 square miles, and the population density for the area is 18.8 residents per square mile.

Therefore, the number of people infected is calculated by multiplying the area by the population density:

Residents infected = area x population density

= 1,809.56 x 18.8 ≈ 34,037.

Approximating to the nearest hundred yields 34,000.

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The price rose by [tex]2.5\%[/tex]

A percentage is a number or ratio that represents a fraction of 100.

The change in price is

[tex]2.90 - 2.83 = 0.07[/tex]

The increase percentage is

[tex]\text{p}=\dfrac{0.07\times100}{2.83}[/tex]

[tex]\text{p}=2.473[/tex]

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The measure of angle ABD is 30 (optionD)

Angle addition postulate states that: The sum of the measure of two adjacent angles is equal to the measure of the angle formed by the non-common sides of the two adjacent angles.

angle ADB and DBC are adjascent angles. And the sum of the two adjascent angles is angle ABC

Therefore using angle addition postulate;

Angle ABC = < ABD + < DBC

70 = < ABD + 40

< ABD= 70 - 40

< ABD = 30°

therefore the measure of angle ABD = 30°

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