a. Starting with the number 10, build a sequence of 5 numbers.

It would be expected to be correct approximately 14.82 times over the next 38 years, based on the 39% accuracy of Groundhog Day predictions.

The expected value, also known as the mathematical expectation, is a key concept in probability theory and statistics.

Here,
Groundhog Day predictions have a 39% accuracy, so on average, 39% of the predictions made on Groundhog Day are correct.

To find the expected number of correct predictions over the next 38 years, we can multiply the accuracy of the predictions (39%) by the number of predictions made (38),

39% * 38 = 14.82

So, we would expect to be correct approximately 14.82 times over the next 38 years, based on the 39% accuracy of Groundhog Day predictions.

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The equation of the total cost is C = 3 + 5x and the amount earned after 5 hours is $28.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

Let us suppose the number of hours = x.

The cost of additional hour is $5.

The cost of x hours is 5x.

Given that, Nicole charges a flat fee of $3, plus $5 per hour.

C = 3 + 5x

If she baby sits for 5 hours, that is x = 5, then:

C = 3 + 5(5)

C = 3 + 25

C = $28

Hence, the equation of the total cost is C = 3 + 5x and the amount earned after 5 hours is $28.

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The conclusion is that there is sufficient evidence at the 0.01 level to support the mayor's claim that under 51% of the residents favor construction of the bridge.

The mayor rejects the null hypothesis at the 0.01 level, which means that the results from the hypothesis test show that the actual proportion of residents who favor construction is less than 51%. The alternative hypothesis would be that the true proportion is less than 51%. After gathering information from 380 voters, the results of the hypothesis test were used to make a decision on whether to reject or fail to reject the null hypothesis.

If the hypothesis test showed that the null hypothesis could be rejected at the 0.01 level, it means that there was sufficient evidence to support the mayor's claim that less than 51% of the residents favor the bridge construction. However, it's important to note that hypothesis testing is not a perfect method and other factors such as sample size and sampling method should also be considered when interpreting the results.

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Solution of given inequality is x < -12.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values.

Given inequality

- (1/2)x > 6
Multiplying with 2 on both sides

- (2/2)x > 6×2

- x > 12

Multiplying with -1 on both sides

x < -12

Hence, x < -12 is the solution of given inequality.

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The two numbers are 3 and 11 respectively

From the information given, we have that

The first number is x

The second number is y

Also,

2x - y = -5

x + y = 14

Make 'x' the subject from equation 2

x = 14 - y

Make 'x' the subject

2(14-y) - y = -5

28 - 2y - y= -5

collect like terms

-3y = -33

y = 11

Substitute the values

x = 3

Hence, the values are 3 and 11

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The solution to the system of linear equations associated with the reduced row-echelon form matrix is (0, 0). This indicates that both variables, x and y, have a value of zero.

The reduced row-echelon form of a matrix is the simplest way to represent the solution to a system of linear equations. In the case of a matrix with two rows and two columns, a solution is produced when the matrix is in its reduced row-echelon form. Specifically, for the given matrix, 0 0, the solution to the corresponding system of linear equations is (0, 0). This indicates that both variables, x and y, have a value of zero. This is because the reduced row-echelon form is the simplest way to represent the solution to a system of linear equations. In this form, all the leading entries are ones and all the other entries are zero. Since the matrix is 0 0, this indicates that the solution is (0, 0). This solution can be seen as an ordered pair, where the first value represents the solution for the x variable, and the second value represents the solution for the y variable. In this case, both values are zero, which means that the solution to the system of linear equations is (0, 0).

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The complete question is

The matrix 1 −1 ]5 0 0 ]0 is in reduced row-echelon form. Determine the solution of the corresponding system of linear equations. Write the solution as an ordered pair. For parametric solutions use either x = t or y = t as the parameter form matrix(0,0).

Answer:

if it's parallel isn't the slope the same?

The measure of ∠A is 53.

The measure of ∠B is 37.

An expression contains one variable or more than one variable with addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

∠A and ∠B are complementary.

This means,

∠A + ∠B = 90

Now,

∠A = 7x + 4

∠B = 4x + 9

7x + 4 + 4x + 9 = 90

11x + 13 = 90

11x = 90 - 13

11x = 77

x = 7

Now,

∠A = 7x + 4 = 7 x 7 + 4 = 49 + 4 = 53

∠B = 4x + 9 = 4 x 7 + 9 = 28 + 9 = 37

Thus,

∠A = 53

∠B = 37

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Step-by-step explanation:

50

because 50*(30/100)=1500/100

then it gives 15

so the 30 percent of a number is 15 that number is 50.

The requried, 30 percent of 50 is 15, as of the given condition.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

We can use algebra to solve the problem.

Let's call the number we're looking for "x". Then we can translate the problem statement into an equation:

30% of x is 15:

0.3x = 15

To solve for x, we can divide both sides of the equation by 0.3:

x = 15 ÷ 0.3

x = 50

Therefore, 30 percent of 50 is 15.

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We are 90% confident that the true weekly return of the index portfolio is between 1.186% and 1.214%.

One important concept in statistics is a confidence interval, which is a range of values that is likely to contain the true value of a parameter, such as a population mean or proportion.

The analyst has a sample of 28 observations of the weekly return, which is assumed to be normally distributed. The sample mean is 1.2% and the sample variance is 0.00175. With this information, we can calculate the standard error of the mean, which measures the variability of the sample mean from one sample to another. The formula for the standard error is:

standard error = sample standard deviation / square root of sample size

In this case, the sample standard deviation is the square root of the sample variance, which is approximately 0.0418%. The square root of the sample size is 5.2915. Therefore, the standard error of the mean is:

standard error = 0.0418 / 5.2915 = 0.0079%

To construct a 90% confidence interval for the weekly return, we need to use the t-distribution, which is a probability distribution that takes into account the sample size and the level of confidence. The t-distribution has more variability than the normal distribution, which results in wider confidence intervals for smaller sample sizes.

The formula for a t-confidence interval is:

sample mean ± t-value x standard error

The t-value depends on the sample size and the level of confidence. For a sample size of 28 and a 90% confidence level, the t-value is 1.699. Therefore, the confidence interval is:

1.2 ± 1.699 x 0.0079 = [1.186%, 1.214%]

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Answer: The best graph to illustrate June's situation is a cost-volume-profit (CVP) graph, which shows the relationship between the revenue, cost, and volume of goods sold.

In June's case, her fixed costs (the cost of the sewing machine) are constant and do not change regardless of the number of quilts she makes and sells. Her variable costs (the raw materials) are directly proportional to the number of quilts she makes and sell. Her revenue is directly proportional to the number of quilts she sells.

The CVP graph will show a line representing fixed costs, a line representing variable costs, and a line representing revenue. The point at which the total costs (fixed costs + variable costs) equal the revenue represents the break-even point, at which June neither makes a profit nor incurs a loss. Beyond this point, June will make a profit, and before this point, she will incur a loss.

The CVP graph can be used to determine the break-even point and to make predictions about the future financial performance of a business, based on changes in volume, costs, or price.

Step-by-step explanation:

The surface area not covered by the sticker on the spherical toy is approximately 5614.1 cm².

CLAIM: The surface area not covered by the sticker on the spherical toy is approximately 5614.1 cm².

EVIDENCE: The total surface area of the spherical toy can be calculated using the formula A = 4πr², where r is the radius of the sphere. Since the diameter of the sphere is given as 75 cm, the radius is half of the diameter, which is 37.5 cm. Therefore, the total surface area of the spherical toy is:

A = 4π(37.5)²

A = 4π(1406.25)

A ≈ 17593.29 cm²

The surface area covered by the triangular sticker can be calculated by finding the area of the triangle, which is given by the formula A = 1/2 bh, where b is the base and h is the height. Therefore, the surface area covered by the sticker is:

A = 1/2 (10)(12)

A = 60 cm²

The surface area not covered by the sticker is the difference between the total surface area of the spherical toy and the surface area covered by the sticker:

A_not_covered = A - A_sticker

A_not_covered ≈ 17593.29 - 60

A_not_covered ≈ 17533.29 cm²

Therefore, the surface area not covered by the sticker on the spherical toy is approximately 5614.1 cm².

REASONING: By calculating the total surface area of the spherical toy and subtracting the surface area covered by the triangular sticker, we can determine the surface area not covered by the sticker. Since the sticker covers a relatively small area compared to the total surface area of the sphere, the surface area not covered by the sticker is almost equal to the total surface area of the sphere, minus the area of the sticker.

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The only value of x from the set {7, 9, 36} that makes the inequality 2x < 18 true is x = 7.

We can use substitution to find which value of x makes the inequality 2x < 18 true by trying each value in the set {7, 9, 36} one by one.

Let's start with x = 7:

2x = 2(7) = 14

14 < 18 is true, so x = 7 satisfies the inequality.

Next, let's try x = 9:

2x = 2(9) = 18

18 < 18 is not true, so x = 9 does not satisfy the inequality.

Finally, let's try x = 36:

2x = 2(36) = 72

72 < 18 is not true, so x = 36 does not satisfy the inequality.

Therefore, the only value of x from the set {7, 9, 36} that makes the inequality 2x < 18 true is x = 7.

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The profit that they will make if they have 24 dogs for adoption is given as follows:

$160.

The profit is obtained with the subtraction of the revenue by the costs.

The revenue and the costs for this problem are obtained as follows:

Hence the profit made is obtained as follows:

Profit = 45 x 24 - 920

Profit = $160.

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Step-by-step explanation:

Let the distance between them be y

sin20° =

=> 0.342 =           [  sin20° = 0.342]

=> y =  33/ 0.342

=> y = 96.5 ft

So, the distance between them is 96.5 ft

Answer:

[tex]\sqrt{106}[/tex]

Step-by-step explanation:

Using the distance formula,

[tex]LM=\sqrt{(7-(-2))^2+(-1-4)^2}=\sqrt{106}[/tex]

Answer:

SSS

Step-by-step explanation:

Since [tex]\overline{AD} \cong \overline{AD}[/tex] by the reflexive property, there are three pairs of congruent sides.

With dilation at center (0,0) and a scale factor of 5, the coordinates as we can see from given graph are Q(-3,4), R(-2,-1), T(3,1), W(3,5).

What exactly is dilation?

Dilation is the process of modifying the size of an item or form by reducing or expanding its dimensions according to specific scaling variables. A circle of radius 10 unit, for example, is reduced to a circle with radius 5 unit. This approach is utilised in photography, arts and crafts, and the creation of logos, among other things. There are four primary types of transformations in geometry. They are as follows:

Dilation Properties

Some characteristics of forms that stay constant during dilation changes are:

Now,

As we can see from properties that the image does not change in dilation it stays same and angles are also same.

So, we can see coordinates from the given graph

hence,

         the coordinates as we can see from given graph are Q(-3,4), R(-2,-1), T(3,1), W(3,5).

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Using the diagram in the problem angle TQU is solved to be

The angle at U is 90 degrees, Using the concept of adjacent angles the three angles at U is solved

Using the trigonometry relations of right triangle we solve for angle PQT'

tan (angle PQT) = 1 / 3

angle PQT = arc tan (1 / 3)  

angle PQT = 18.43

angle PQT = angle UQS and

angle PQT + angle UQS  + angle TQU = 90 degrees adjacent angles

2 * 18.43 * angle TQU = 90

angle TQU = 90 - 2 * 18.43

angle TQU = 53.14 degrees

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The age of the jane is 565/48 years old.

Problems on ages is a common topic from which questions are asked in almost all Government exams in the quantitative aptitude section.

in this the ages has been found by solving the relationship between the ages given in the question.

the age of rick is = 11 3/4 years old

= 47/4 years old

the age of the lane is 1 3/8 years older than rick

so we add 1 3/8 in the age of rick to find out the age of lane,

so, the age of Lane is = 47/4 + 1 3/8

= 47/4 + 11/8

= (94 + 11)/8

= 105/8 years old .

the age of the jane is 1 1/5 years older than Lane

so we add 1 1/5 in the age of lane to find out the age of jane,

so, the age of jane is = 105/8 + 1 1/5

= 105/8 + 6/5

= (525 + 40)/48

= 565/48 years old .

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The value of x is 7, therefore AC = 23 and BD = 23, which means diagonals AC = BD.

What is linear equations in two variables?

A linear equation in two variables is an equation that can be written in the form ax + by = c, where a, b, and c are constants, and x and y are variables. The graph of a linear equation in two variables is a straight line in the Cartesian coordinate system.

In a trapezium, the diagonals divide the trapezium into four triangles. The diagonals of a trapezium are also equal to the sum of the two parallel sides.

Let the two parallel sides of the trapezium be a and b. Then, we have:

8x - 33 = a + b ...(1)

37 - 2x = a + b ...(2)

We can solve for x by setting (1) and (2) equal to each other:

8x - 33 = 37 - 2x

10x = 70

x = 7

8(7) - 33 = 23

37 - 2(7)  = 23

Therefore, the value of x is 7.

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The value of x is approximately 0.8 cm when rounded to the nearest tenth.

A triangle is a two-dimensional geometric shape that has three sides and three angles. It is the simplest polygon and is a fundamental building block in many areas of mathematics and science.

The three sides of a triangle can have different lengths and can be of different types, such as equilateral, isosceles, or scalene. An equilateral triangle has three sides of equal length, while an isosceles triangle has two sides of equal length and a third side of a different length. A scalene triangle has all three sides of different lengths.

In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Thus, we have:

sin(IHJ) = IJ/IH

Taking the sine of both sides and substituting the given values, we get:

sin(23°) = x/2

Multiplying both sides by 2, we have:

x = 2*sin(23°)

Using a calculator, we get:

x ≈ 0.83

Therefore, the value of x is approximately 0.8 cm when rounded to the nearest tenth.

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Histogram 1 is positively skewed, and Histogram 2 is symmetric, which is a true statement about the distributions represented by the histograms.

An illustrated display of data points arranged into user-specified ranges is called a histogram. By taking several data points and organising them into logical ranges or bins, the histogram, which resembles a bar graph in appearance, condenses a data series into an easily understood graphic.

Among graphing tools, the histogram is widely used. It is utilised to encapsulate discrete or continuous data that is measured on an interval scale. It is frequently employed as a convenient way to highlight the key characteristics of the data distribution.

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Answer:

C) Histogram 1 is negatively skewed, and Histogram 2 is positively skewed.

Step-by-step explanation:

When most of the data on a histogram is gathered to the right, then the distribution is negatively skewed. If most of the data is gathered to the left, then the distribution is positively skewed.

Assuming you are going off of these Histograms:

C is the correct answer.

Applying the Two Tangents Exterior Angle Theorem, the value of x is: 12.

m(BD) = 120°

If you draw two tangents from a point outside a circle, the size of the angle they form is equal to half of the difference between the sizes of the two arcs they intercept inside the circle, based on the Two Tangents Exterior Angle Theorem.

Therefore, we have:

6x - 12 = 1/2[(-12 + 21x) - (12x - 24)] (according to the Two Tangents Exterior Angle Theorem)

Solve for x:

6x - 12 = 1/2[(-12 + 21x - 12x + 24)

2(6x - 12) = -12 + 21x - 12x + 24

12x - 24 = 9x + 12

12x - 9x = 24 + 12

3x = 36

x = 36/3

x = 12

m(BD) = 12x - 24 = 12(12) - 24

m(BD) = 120°

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8-3√11 is the expression which is equivalent to √11+√64-2√44.

The combination of variables, numbers and operators is called as expression.

The given expression is √11+√64-2√44

Square root of 11 plus square root of sixty four minus two square root of forty four.

Let us find the equivalent expression of √11+√64-2√44

The expressions in which the expressions look different but have save same value are Equivalent

√11+√64-2√44

√11+8-2√4×11

√11+8-4√11

Combine like terms

8-3√11

Hence, 8-3√11 is the expression which is equivalent to √11+√64-2√44.

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Which expression is equivalent to √11+√64-2√44

A. 8-4√44

B. 5√3-4√11

C. 8-3√11

Answer:

The values of x for which f(x) = g(x) are:

Step-by-step explanation:

To find all the values of x for which f(x) = g(x), equate the given functions:

[tex]\implies f(x)=g(x)[/tex]

[tex]\implies -x^2+5=-2x+2[/tex]

Rearrange the equation so that it is in the quadratic form ax²+bx+c=0:

[tex]\implies -x^2+5+2x-2=0[/tex]

[tex]\implies -x^2+2x+3=0[/tex]

Divide both sides by -1:

[tex]\implies x^2-2x-3=0[/tex]

Factor the quadratic equation:

[tex]\implies x^2-3x+x-3=0[/tex]

[tex]\implies x(x-3)+1(x-3)=0[/tex]

[tex]\implies (x+1)(x-3)=0[/tex]

To solve for x, apply the zero-product property:

[tex](x+1)=0 \implies x=-1[/tex]

[tex](x-3)=0 \implies x=3[/tex]

Therefore, the values of x for which f(x) = g(x) are:

We can check the solutions by substituting each found value of x into the functions.

[tex]f(-1)=-(-1)^2+5=4[/tex]

[tex]g(-1)=-2(-1)+2=4[/tex]

[tex]f(3)=-(3)^2+5=-4[/tex]

[tex]g(3)=-2(3)+2=-4[/tex]

As f(-1) = g(-1) and f(3) = g(3), this proves that the values of x for which f(x) = g(x) are x = -1 or x = 3.

Equate Both equatios and find x

The points are -1,3

The barn with shadow height, 70 feet, having the the height which is equals to the 30 feet, that is barn is 30 feet tall.

The height of farmer Cole = 6 feet

The height of shadow of farmer Cole = 14 feet

The height of shadow of barn = 70 feet

Let the height of barn be ' x feet '. We have to determine the value of x. Now, we the above figure, AB and CD represents height of barn and Cole respectively. Similarly BE and CE represent the shadow height of barn and Cole respectively.

Let angle BAE made here be equals to θ. Also angle BAE = angle CDE = θ. Now, consider right angled triangle, CDE with sides. Using triganomertric functions, tanθ = height/base

=> tanθ = CE/CD = 14/6

simplify, tanθ = 7/3 --(1)

Also, consider right angled triangle ABE,

tanθ = height/base = BE/AB

=> tanθ = 70 / x

=> x tanθ = 70

from equation (1), x (7/3) = 70

=> 7x/3 = 70

=> 7x = 210

=> x = 210/7

=> x = 30

Hence, required value of x is 30 feet.

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The cost to wax the floor will be $2,184.03.

What is the area of any geometrical shape?

The area of a geometrical shape is a measurement of the extent of a two-dimensional surface. It is the measure of the amount of space inside the shape, which can be expressed in square units, such as square inches, square feet, or square meters.

Rectangle: area = length x width

Trapezoid: area = ((base1 + base2) / 2) x height

To find the area of the floor, we need to split the shape into two parts: a trapezoid on top and a rectangle on bottom.

The area of the trapezoid is: (33 + 19) / 2 * 14 = 385 square feet

The area of the rectangle is: 33 * 28 = 924 square feet

The total area is: 385 + 924 = 1309 square feet

Multiplying by the cost per square foot, we get:

1309 * 1.67 = 2184.03

Hence, the cost to wax the floor will be $2,184.03.

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