Which of the following are solutions to the equation

Answer:

64 im pretty cxsure

Step-by-step explanation:

The test statistic: X² = 42.620, Critical values: X²=38.932.

What are critical values?

A critical value is one that can be used to compare the test statistic to determine if the null hypothesis can be rejected or not.

Here, we have

Given: In one town, monthly incomes for men with college degrees are found to have a standard deviation of $650. A random sample of 22 men without college degrees resulted in incomes with a standard deviation of $926.

s = 926, n = 22

The null and alternative hypotheses:

H₀ : σ = 650; H₁ : σ > 650

Test statistic:

X² = (n-1)s²/σ²

X² = (22-1)926²/650²

x = 42.62

Critical values:

X² = X²a(n-1)

X² = X²(0.01)(21)

X² = 38.932.

Hence, the test statistic: X² = 42.620, Critical values: X²=38.932.

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Answer:

The correct answer would be option (A).

Step-by-step explanation:

Answer: 5

Step-by-step explanation:

length = x

Width=x-2
Area=lw

15=(x)(x-2)

15=x^2-2x

0=x^2-2x-15

Quadratic formula:

X=-15

X=5

the length is 5 because the length can’t be negative

The expression 75 + 1.45x represents the total cost of a training session with Terrell

Let x be the distance (in miles) that Terrell must drive to and from the training session.

Then the total cost C of the training session, in dollars, can be expressed as:

C = 75 + 1.45x

Therefore, the expression 75 + 1.45x represents the total cost of a training session with Terrell, including both the base fee and the additional cost for driving.

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In the bridge, when the south has 13 points and 3 clubs and bids 1 club, the north responding with 3 clubs means that the North has a strong hand with six or more clubs.

In the game of bridge, bidding is a method of indicating the strength of a player's hand, which is the number of tricks that they believe they can win if they become the declarer. Every player has to declare their abilities based on the bid of the previous player when it is their turn to bid.

The bidding starts with the dealer and proceeds in a clockwise direction. The players can either make a bid or pass. The following are the four basic bids in Bridge:

When South has 13 points and 3 clubs, he makes a 1 Club bid. This bid can be interpreted as follows:

South has a strong hand with five or more clubs and 13 to 21 high card points. When South bids 1 Club, he implies that he has a balanced hand, which means that he has four cards in each suit, or an unbalanced hand, which means that he has a long suit, a singleton, or a void in some other suit.

When North responds with 3 Clubs, it means that he has a strong hand with six or more clubs. North has understood that South has five or more clubs and therefore responds with the number of clubs that he has in his hand to show that he is strong enough to support South's suit. Thus, North is trying to force South to become the declarer in clubs.

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Lisa would need to serve 12 customers to attain the projected income if Daisy calls in sick that day

What is linear function ?

A linear function is a mathematical function that can be represented by a straight line on a graph. It has the form of:

y = mx + b

where m is the slope of the line, which determines how steeply the line rises or falls, and b is the y-intercept, which is the point where the line crosses the y-axis.

According to the question:
If Daisy calls in sick, then Lisa will be the only stylist at the salon, and all customers will go to her. Let's use x to represent the number of Lisa's customers. Then the income generated by Lisa's customers can be represented by the equation:

18x = projected income

We can solve for x by dividing both sides of the equation by 18:

x = projected income / 18

Substituting the given projected income of $216, we get:

x = 216 / 18 = 12

Therefore, Lisa would need to serve 12 customers to attain the projected income if Daisy calls in sick that day.

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Step-by-step explanation:

We can also solve the equation x² + 4x + 4 = 8 by rearranging the terms and using the quadratic formula:

x² + 4x + 4 - 8 = 0

x² + 4x - 4 = 0

Applying the quadratic formula, we have:

x = (-b ± √(b² - 4ac)) / 2a

where a = 1, b = 4, and c = -4. Substituting these values, we get:

x = (-4 ± √(4² - 4(1)(-4))) / 2(1)

x = (-4 ± √32) / 2

Simplifying the square root of 32, we get:

x = (-4 ± 4√2) / 2

x = -2 ± 2√2

Therefore, the solutions to the equation x² + 4x + 4 = 8 are x = -2 + 2√2 and x = -2 - 2√2.

For the number of miles driven, Company A will charge less than Company B if x<y, where x is the number of miles driven for Company A and y is the number of miles driven for Company B. Therefore, the inequality is x<y.

When comparing two companies for their charges for a specific service, it is necessary to obtain a basic understanding of the charges for each company. You can make use of the inequality operator to check when one company will charge less than the other company.

To use the inequality operator, you'll need to calculate the differences between the two companies for the specific mileage. Let's assume that the mileage is represented by "m" and that the charge for company A is "cA" and the charge for company B is "cB".

If the question only provides specific numerical values for these variables, you can substitute them into the inequality formula. If you're given algebraic expressions, you'll need to simplify them before substituting them into the inequality formula.

The inequality formula for comparing the charges is as follows: cA < cB.

To use this formula, substitute the expression for each variable.

For example: 4m + 20 < 3.5m + 35 Now, you'll need to simplify the inequality by performing algebraic operations on both sides of the inequality. Begin by subtracting 3.5m from both sides of the inequality: 0.5m + 20 < 35.

Next, subtract 20 from both sides of the inequality: 0.5m < 15 Finally, divide both sides of the inequality by 0.5: m < 30

Therefore, Company A will charge less than Company B for any mileage less than 30.

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Tom will pay a total of $13,424.20 in interest over the term of the loan.

The formula to calculate the monthly payment for an amortized loan is given by:  `P = r(PV) / [1 - (1 + r)^(-n)]`Where P is the monthly payment, r is the interest rate per month, PV is the present value of the loan, and n is the number of payments or the total number of months.

Substituting the given values, we get:P = 0.0052083333 × 44,000 / [1 - (1 + 0.0052083333)^(-7×12)]P = 632.32Therefore, Tom's monthly payment is $632.32 (rounded to the nearest cent).b. Since Tom pays the monthly payment each month for the full term, his total amount to repay the loan is equal to the present value of the loan.

Therefore, the total amount to repay the loan is $44,000 (rounded to the nearest cent).c. The total amount of interest paid over the term of the loan can be calculated as the difference between the total amount repaid and the principal amount of the loan.

Therefore, the total interest paid is: Total interest paid = Total amount repaid - Principal amount of the loan Total interest paid = $57,424.20 - $44,000Total interest paid = $13,424.20

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If at a school of 550 children 80% walk to school, the 110 children come to school by other means.

If 80% of the children walk to school, then the remaining 20% of children must arrive at school by other means (such as being driven by a parent, taking public transportation, etc.).

To find out how many children come to school by other means, we can use the following formula:

Number of children who come to school by other means = Total number of children x Percentage who don't walk to school

In this case, we have:

Number of children who come to school by other means = 550 x 20% = 110

Therefore, 110 children come to school by other means.

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The given question is incomplete, the complete question is:

At a school of 550 children 80% walk to school, how many comes in other way ?

Answer: 40

Step-by-step explanation:

25/100 x ? = 10

multiply both sides by 100/25

x= 10 x 100/25

x=10

In Linear equation, 260.2 would they each earn if they divided their earnings equally.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

                                         Equations with variables of power 1 are referred to be linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

three friends earned $359 in August, $522 in July, and $420 in September

                = $359 + $522 $ 420  

                = 1301/5 = 260.2

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The solution (16, 2) is a feasible production plan that satisfies all the constraints of the problem.

Inequality is a mathematical statement that compares two values or expressions, indicating whether they are equal or not equal, greater than or less than, greater than or equal to or less than or equal to each other, using mathematical symbols such as "<", ">", "<=", ">=", and "≠".

The solution (16, 2) represents that Wanda can produce 16 small pairs of gloves and 2 large pairs of gloves, and this production plan satisfies all the given constraints.

To see why, let's substitute x=16 and y=2 in the two inequalities:

Therefore, the solution (16, 2) is a feasible production plan that satisfies all the constraints of the problem.

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Answer:

k - 6

Step-by-step explanation:

I'm not sure if this is a mistake or not, or if you pressed enter a little too early, but for example:

let k = 16

6 [the number provided] less than 16 [k] is not 6 - 16, as that would be 16 less than 6. You can read the math problem from right to left, and 16 - 6 would read out as "six less than sixteen".

Honestly, you don't really need this, and it isn't a good way to do it, there are many better ways.

You have a 4/12 probability.

Answer:

13 - The first option

11 - (x+1)

16 - first option

Step-by-step explanation:

The probability that a flight between New York City and Chicago is less than 64 minutes is 0.28, or 28%.

Since the time to fly between New York City and Chicago is uniformly distributed between 50 and 100 minutes, we can use the formula for the uniform probability density function (PDF) to find the probability that a flight is less than 64 minutes:

f(x) = 1 / (b - a), for a ≤ x ≤ b

where a = 50 and b = 100 are the minimum and maximum times, respectively.

To find the probability that a flight is less than 64 minutes, we need to integrate the PDF from a to 64:

P(X < 64) = [tex]\int\limits^{64}_{50}[/tex] f(x) dx = [tex]\int\limits^{64}_{50}\\[/tex](1 / 50) dx = (1 / 50) * [x]|₅₀ ⁶⁴

= (1 / 50) * (64 - 50) = 0.28

This means that approximately 28% of flights will arrive in less than 64 minutes.

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The vertices of the image of QRTW for a dilation with center (0, 0) and a scale factor of 1/4 include the following:

Q' (-0.5, 0.75).

R' (-0.75, 0.25).

T' (0.5, -0.25).

W' (0.25, 1).

In Mathematics and Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape.

Next, we would have to dilate the coordinates of the pre-image by using a scale factor of 1/4 centered at the origin (0, 0) as follows:

Ordered pair Q (-2, 3) → Ordered pair Q' (-2 × 1/4, 3 × 1/4) = (-0.5, 0.75).

Ordered pair R (-3, 1) → Ordered pair R' (-3 × 1/4, 1 × 1/4) = (-0.75, 0.25).

Ordered pair T (2, -1) → Ordered pair T' (2 × 1/4, -1 × 1/4) = (0.5, -0.25).

Ordered pair W (2, 4) → Ordered pair W' (2 × 1/4, 4 × 1/4) = (0.25, 1).

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In conclusion, the power series converges absolutely over an interval given by [tex]\left|x-7\right|>\frac{\left|a_n+1\right|}{\left|a_n\right|}\;\;\;\forall\;\;\;n\in\mathbb{N}\;\;\;\text{and}\;\;\;n>N, where N\in\mathbb{N}[/tex]is a natural number.

The interval over which the power series converges absolutely is given by [tex]\left|x-7\right|>\frac{\left|a_n+1\right|}{\left|a_n\right|}\;\;\;\forall\;\;\;n\in\mathbb{N}\;\;\;\text{and}\;\;\;n>N, where N\in\mathbb{N}[/tex] is a natural number.

In other words, for any given N, the series will converge absolutely over the interval \left|x-7\right|>\frac{\left|a_n+1\right|}{\left|a_n\right|}\;\;\;\forall\;\;\;n>N.

This means that the series will converge absolutely over a larger interval as N increases, since the terms \frac{\left|a_n+1\right|}{\left|a_n\right|} get closer to 1 for larger values of n.

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On a control chart, Control limits separates common from assignable causes of variation option C.

Shewhart charts, after Walter A. Shewhart, are another name for control charts. It is a statistical process control tool that aids in tracking process advancements over time. For instance, hospital management decides to utilise a solution technique in order to shorten the time required to admit a patient.

The process flow diagram for how patients are admitted to the hospital is first created. The average amount of time it takes to admit a patient each day is then measured. Lastly, plot the process variables across time on a control chart.

This control chart's goals are to identify any "special" reasons of variation as well as to document any process improvements.

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Answer:

C. A limited government protects individual freedoms.

Step-by-step explanation:

There are more individual freedoms as opposed to the lifestyle of those who are under a monarchy

When the numerator of a certain fraction is a quarter of the value of the whole fraction, the value of the denominator of that fraction is four times the value of the numerator

The denominator of a certain fraction is a number that divides the numerator to produce a fraction. The fraction has two parts, the numerator, and the denominator. The numerator is the top part of a fraction, and the denominator is the bottom part of the fraction. When the numerator of a certain fraction is a quarter of the value of the whole fraction, the value of the denominator of that fraction can be calculated using a mathematical formula.

The mathematical formula for calculating the value of the denominator of a certain fraction is to divide the numerator by the quarter. This is because the numerator is a quarter of the value of the whole fraction. Therefore, the formula is represented as:D = N/1/4where D is the denominator, and N is the numerator of the fraction.To solve for D, we multiply both sides by the reciprocal of the fraction:1/4 = 4/1, so we have:D = N x 4/1D = 4N/

Therefore, the value of the denominator of the fraction is four times the value of the numerator. If the numerator of the fraction is 2, then the denominator of the fraction is 8. In summary, when the numerator of a certain fraction is a quarter of the value of the whole fraction, the value of the denominator of that fraction is four times the value of the numerator.

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The given statement "the sampling distribution becomes approximately normal, for all statistics, if there is a large enough sample size" is True as it is proved by the central limit theorem.

The central limit theorem (CLT) states that for large enough sample sizes, the distribution of the sample means approximates a normal distribution regardless of the shape of the initial population distribution.

It is a statistical theory that clarifies how the mean of a random sample of independent observations drawn from a non-normal population converges in distribution to a normal population.

According to this theory, the sample size should be at least 30 for the sample mean to have an approximately normal distribution. The following are the fundamental assumptions of the central limit theorem:

Therefore, we can say that the sampling distribution becomes approximately normal, for all statistics, if there is a large enough sample size. The statement is true.

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The two figures shown are made of unit squares. The positive difference of the perimeters, in units, is 8.

Perimeter is the total distance around the boundary of the shape. Since each square has a side length of 1 unit, the perimeter is equal to the number of sides.

1. Figure A: Counting the number of unit squares on the boundary of the shape, the perimeter of the first shape is:   8+4+4+4+4=24 units.

2. Figure B:Counting the number of unit squares on the boundary of the shape, the perimeter of the second shape is: 10+2+10+2=24 units.

The positive difference of the perimeters in units = |24 - 24| = 0 units. Therefore, the positive difference of the perimeters, in units is 0.

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The values of x is [tex]x < 39.5[/tex].

Given that the shopkeeper spends on rent and electricity is [tex]= 5x+14[/tex]

Spending of shopkeeper on rent [tex]= 3x-7[/tex]

So shopkeeper spends on electricity [tex]= (5x+14) - (3x-7) = 2x+21[/tex]

Given that amount the shopkeeper spends on electricity less than 100.

So suitable inequality,

[tex]2x+21 < 100[/tex]

[tex]2x < 100-21[/tex]

[tex]2x < 79[/tex]

[tex]x < 39.5[/tex]

All the values of [tex]x < 39.5[/tex].

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Only the final option, which is typical of a longitudinal study, calls for retesting the same set of individuals over a lengthy period of time.

It is a numerical value that runs from 0 to 1, with 0 denoting the impossibility of an event and 1 denoting its certainty. The probability of an event A is expressed mathematically as P(A), where P(A) is the number of possible ways that event A could happen divided by the total number of outcomes.

given

The final choice is the long-term study: "An intelligence test is given to a class of kindergarteners. During 30 years, they are retested every other year."

In a longitudinal study, a group of individuals are followed over a lengthy period of time, frequently years or even decades. A longitudinal study's goal is to look at how people change or grow over time and to pinpoint any potential contributing elements.

Only the final option, which is typical of a longitudinal study, calls for retesting the same set of individuals over a lengthy period of time.

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The greatest possible integer value of the radius of the circle is 7 inches.

The area of a circle is given by the equation[tex]$A = \pi r^2$[/tex]. We know that the area is less than [tex]$60\pi$[/tex] square inches, so the equation can be written as [tex]$60\pi > \pi r^2$[/tex]. We can solve for the radius by dividing both sides by [tex]$\pi$[/tex], which gives us [tex]$60 > r^2$[/tex]. Taking the square root of both sides gives us [tex]$r < \sqrt{60}$[/tex], which is approximately 7.74 inches. Therefore, the greatest possible integer value of the radius of the circle is 7 inches.

To explain this further, we can start with the equation for the area of a circle, which is[tex]$A = \pi r^2$[/tex]. Since the area is less than [tex]$60\pi$[/tex]square inches, this equation can be rewritten as[tex]$60\pi > \pi r^2$[/tex]. We can then divide both sides by [tex]$\pi$[/tex] to get [tex]$60 > r^2$[/tex]. Taking the square root of both sides gives us [tex]$r < \sqrt{60}$[/tex]. This result can then be rounded down to the nearest integer, which is 7. Therefore, the greatest possible integer value of the radius of the circle is 7 inches.

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The pizza would be covered by approximately 100.48 centimeters of the pizza cutter if it is rotated exactly 4 times.

The circumference of a circle can be calculated using the formula:

circumference = π x diameter

where π is approximately equal to 3.14.

Given that the diameter of the pizza cutter is 8 centimeters, we can calculate its circumference as:

circumference = π x diameter

circumference = 3.14 x 8

circumference = 25.12 centimeters

If the pizza cutter is rotated exactly 4 times, it will cover a distance equal to 4 times its circumference:

distance covered = 4 x circumference

distance covered = 4 x 25.12

distance covered = 100.48 centimeters

Therefore, approximately 100.48 centimeters of the pizza would be covered by the pizza cutter if it is rotated exactly 4 times.

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Complete question

The image shows a circular pizza cutter that has a diameter of 8 centimeters. Approximately how many centimeters would the pizza cutter cover if it is rotated exactly 4 times

The height of the BD for the house using Pythagorean theorem is obtained as: 4.23 m.

According to the Pythagorean Theorem, for any triangle which is a right triangle, the squares of the legs added together equal the square of the hypotenuse.

In the given triangle ABC.

AB = BC = 6 cm

So, ∠A = ∠C  (by isosceles triangle)

Then, AD = DC = 8.5/2

So, in right angles triangle ABD, applying Pythagorean theorem:

AB² = AD² + BD²

6² = (8.5/2)² + BD²

36 - 18.0625 = BD²

BD = √17.9375

BD =  4.23

Thus, the height of the BD for the house using Pythagorean theorem is obtained as: 4.23 m.

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The probability of red is 0.1724, given the following table.

The table provided is given in the form of a contingency table. It is used to display the relationship between two categorical variables or nominal data through frequency distribution. It is also referred to as a two-way frequency table.

The table has "Yes" and "No" categories in the rows and "Red" and "Blue" categories in the columns.

The probability of Red can be calculated using the formula;

P(Red) = (Frequency of Red) / (Total Frequency)

Using the values provided in the table

,P(Red) = 15/87P(Red) = 0.1724

Hence, the probability of red is 0.1724.

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