Order the numbers from least to greatest. ___ 45 11 , 4.5, √ ___ 20 , √ ___ ___ 45 4

Answer:

10. x=3 and y=0

11. Infinitely many solutions.

12. No solutions.

13. x=3/2 and y=-12

14. Infinitely many solutions

15. x=0 and y=−2

Step-by-step explanation:

I just solved them by solving the top part first then the bottom part, I can not put in the actual steps because it takes up way to much space

Answer:

kitchen scaleuwueieie

The shopping times were recorded for 64 randomly selected customers from a local supermarket. The average and variance of the 64 shopping times were 33 minutes and 256, respectively.

Estimate the true average shopping time per customer, with a confidence coefficient of 1- = 0.90.

x-bar = 33 min

ME = 1.645 = 3.29

90% CI: 33-3.29 < u < 33+3.29

Population Means – You can use this calculator to find the confidence interval for your sample mean if you are estimating the mean of a population trait (e.g., the mean blood pressure of a group of patients).

The estimate is your "best guess" at the unknown mean, and the confidence interval displays how reliable the estimate is. You may determine a range of values within which the population mean is expected to fall using the confidence interval.

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The 90% confidence interval is ( 992.053088, 1119.946912 ).

Mean is defined as the average of given numbers i.e. sum of all numbers divided by the total number of numbers. The Mean is denoted as m or μ. Standard deviation is the measure which it shows the variation from the mean exists or not. The standard deviation is denoted as σ. The subset chosen from the larger set to make assumptions is known as a random sample. A range of values is a confidence interval.

As per the question,

⇒  degree of freedom ( df )   =   n - 1

                                                =   64 - 1

                                        df   =   63

⇒ α   =   0.05

⇒ t    =   1.998341 ( Calculated using excel functions )

At 90% confidence, the confidence interval is

( μ - t ) ( s / √n )  ≤  x  ≤  ( μ + t ) ( s / √n )

( 33 - 1.998341 ) ( 256 / √64 )  ≤  x  ≤  ( 33 + 1.998341 ) ( 256 / √64 )

( 31.001659 ) ( 256 / 8 )  ≤  x  ≤  ( 34.998341 ) ( 256 / 8 )

( 31.001659 ) ( 32 )  ≤  x  ≤  ( 34.998341 ) ( 32 )  

992.053088   ≤  x  ≤    1119.946912

Therefore, ( 992.053088   ≤  x  ≤    1119.946912 ) is the 90% confidence interval for the true population mean.

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Answer:

Step-by-step explanation:

The digit in the ones place is 7

The digit in the tenths place is 0

The digit in the tens place is 5

Answer:

\(x^4+2x^3-4x-8\)

Step-by-step explanation:

\((x^3-4)(x+2)\\\\(x^3)(x)+(x^3)(2)+(-4)(x)+(-4)(2)\\\\x^4+2x^3-4x-8\)

The volume of the cylinder is given as 3053.63 cubic units

V=πr²h

Where the V = volume

r = radius

h = height

We have to apply the values to the formula

In this case, the radius (r) is 9, and the height (h) is 12.

Now, we can plug the radius and height into the volume formula:

Volume = π * (9)² * 12 ≈ 3.1416 * 81 * 12

3053.63 cubic units

The volume of the cylinder is given as 3053.63 cubic units

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Answer:

x²+8x+16

Step-by-step explanation:

f(x) = (x+4)²

= (x+4)(x+4)

= x² + 4x + 4x + 16

= x² + 8x + 16

The equation which represents the given situation as described about snow depths in the task content is; 4 + 3x = 1 + 5x and the solution is; x = 1 and a half hours.

It follows from the task content that the time at which the snowfall in the towns in discuss will be equal be determined.

According to.the word phrases given;

A town has accumulated 4 inches of snow and the snow depth is increasing by 3 inches every hour. Hence, we have;

4 + 3x.

Also, a nearby town has accumulated 1 inch and the depth is increasing by 5 inches every hour. Hence ,we have;

1 + 5x

Consequently, when the snowfalls are equal, we have;

4 + 3x = 1 + 5x

3 = 2x

x = 3/2.

x = 1 and a half hours.

Ultimately, the equation which represents the given situation as described about snow depths in the task content is; 4 + 3x = 1 + 5x and the solution is; x = 1 and a half hours.

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There are 7920 ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

In this problem, we want to find the number of ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

Since every man must be diametrically opposite a woman, we can pair each man with one woman. There are 5 men and 9 women, so there are 5 pairs. We need to find the number of ways to seat these 5 pairs of people in a circle.

To do this, we can first seat one pair in any position. Then, we can seat the second pair anywhere but opposite the first pair. This gives us 11 positions for the second pair. Continuing in this way, we see that there are 11 * 6 * 5 * 4 * 3 = 7920 ways to seat the 5 pairs of people in a circle.

So, there are 7920 ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

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Assuming 14 people, 5 men and 9 women, how many ways can they sit in a circle such that every man is diametrically opposite a woman?

Answer: x = 29; RZ = 60, SW = 120

Step-by-step explanation:

If you look at the lines, RZ is half the value of SW. Knowing this, we can set up an equation like this:

2(RZ) = SW

2(2x+2) = 5x-25

By plugging in the values for RZ and SW, we can set them equal to each other and find x.

2(2x+2) = 5x-25

4x+4 = 5x-25

4 = x-25

x = 29

I think you only needed the variable, but I can provide the measures of the line, just in case:

RZ = 2x+2 ; 2(29)+2 = 60

SW = 5x-25 ; 5(29)-25 = 120

Since RZ is half of SW, we can tell we correctly determined x. Hope this helps!

Answer:

I think its 7% but I could be wrong

The probability of event A given event B, denoted as P(A | B), is 0.750. The probability of event B given event A, denoted as P(B | A), is 0.900. A and B are not independent events because the conditional probabilities P(A | B) and P(B | A) are not equal to the marginal probabilities P(A) and P(B), respectively.

To find P(A | B), we use the formula:

P(A | B) = P(A ∩ B) / P(B)

In this case, P(A ∩ B) = 0.45 and P(B) = 0.60.

Plugging these values into the formula, we get

P(A | B) = 0.45 / 0.60 = 0.750.

To find P(B | A), we use the formula:

P(B | A) = P(A ∩ B) / P(A)

Here, P(A ∩ B) = 0.45 and P(A) = 0.50.

Substituting the values, we find

P(B | A) = 0.45 / 0.50 = 0.900.

A and B are not independent because the probabilities of A and B are affected by each other. If A and B were independent, then P(A | B) would be equal to P(A), and P(B | A) would be equal to P(B). However, in this case, both P(A | B) and P(B | A) differ from their respective marginal probabilities. Therefore, A and B are dependent events.

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Notice that the angles UWV and YWX are vertical angles. Then, they have the same measure.

Additionally, the angles VUW and XYW are specified to have the same measure, as well as the sides VW and WX. Then, the pair of triangles UVW and YXW have two angles in common as well as one side.

Then, the congruence theorem that can be used to identify that ΔUVW ≅ ΔYXW is:

Answer:

62x^2 + 16x + 1

Step-by-step explanation:

The area of a square is Side times Side.

One of the sides is (8x + 1). So the equation is,

(8x + 1) * (8x + 1)

62x^2 + 16x + 1

Answer:

$50.00

Step-by-step explanation:

Answer:

The correct answer is: 49.82

Step-by-step explanation:

First, you have to turn 6% into a decimal.

6%=0.06 (6/100)

Then, you multiply 6% by $53.00

0.06*53=3.18

Finally, you subtract the sales tax ($3.18) from the total paid ($53.00)

53-3.18=49.82

Hope this helps!

344865

Explanation

Use the following formula:

In this case, n=830, thus you get your answer by entering 830 in the formula like this:

so, the answer is

344865

The decimal number system uses nine different symbols is False as the decimal number system actually uses ten different symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. These ten symbols, also known as digits, are used to represent all possible numerical values in the decimal system.

Each digit's position in a number determines its value, and the combination of digits creates unique numbers. This system is widely used in everyday life and forms the basis for arithmetic operations and mathematical calculations. Thus, the decimal number system consists of ten symbols, not nine.

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To find next year's population in one step, the current population should be multiplied by 0.962. This value is obtained by subtracting 3.8% from 100% (1) and converting it to a decimal form (0.962).

1. Multiplying the current population by this factor accounts for the decrease of 3.8% and gives an estimate of the population for the next year.

2. To calculate next year's population in one step, we need to consider the decrease of 3.8% per year. When a population decreases by a certain percentage, we can express it as a decimal value by subtracting that percentage from 100%. In this case, subtracting 3.8% from 100% gives us 96.2%. To convert this to a decimal form, we divide it by 100, resulting in 0.962.

3.By multiplying the current population by 0.962, we take into account the decrease of 3.8% and estimate the population for the next year. This approach assumes a consistent decrease rate over time. For example, if the current population is 100, multiplying it by 0.962 would yield an estimated next year's population of 96.2.

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Answer:

Step-by-step explanation:

-1 = 7 - x

On this case, what you want to achieve is for all the constants to go to one side of the equation and all the variables would be on the other side of the equation. Let us transpose 7 to the left side of the equation.

subtract 7 on both sides

-1 = 7 - x

-1 - 7 = 7 - 7 - x

Simplify

-8 = -x

Divide both sides by -1

-8/-1 = -x/-1

8 = x

The answer to the question is x=8. It is an example of a linear equation.

A linear equation is an algebraic equation that represents a straight line when graphed on a coordinate plane. It consists of variables, constants, and coefficients, with the variables raised to the power of 1 (i.e., they are not squared or cubed).

A general form of a linear equation with one variable, let's say x, is:

ax + b = 0

Here, 'a' and 'b' are constants, and 'x' is the variable. The coefficient 'a' represents the slope or gradient of the line, while the constant term 'b' represents the y-intercept, which is the point where the line crosses the y-axis.

In this question,

-1 = 7-x (Given)

so, x = 7+1

        =8

Therefore, the solution to the equation is x=8.

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To determine whether there is a decrease in voter support for the candidate after the scandal, we can test the hypothesis using the proportions of the two polls. The first poll showed 54% support among 630 randomly selected voters, while the second poll showed 51% support among 1010 voters. By conducting a hypothesis test, we can determine if the difference in proportions is statistically significant.

To test the hypothesis, we can use the two-sample z-test for proportions. The null hypothesis (H0) assumes no difference in voter support, while the alternative hypothesis (H1) assumes a decrease in support. We can calculate the test statistic using the formula:

z = (p1 - p2) / √[(p(1 - p) / n1) + (p(1 - p) / n2)]

where p1 and p2 are the proportions from the two samples, and n1 and n2 are the respective sample sizes. p is the pooled proportion, calculated as (x1 + x2) / (n1 + n2), where x1 and x2 are the respective number of successes (votes for the candidate) in each sample.

By calculating the z-value, we can compare it to the critical value for the desired significance level (e.g., α = 0.05). If the z-value exceeds the critical value, we reject the null hypothesis in favor of the alternative hypothesis, indicating a statistically significant decrease in voter support.

After performing the calculations, if the z-value exceeds the critical value, we can conclude that there is evidence to support the claim of a decrease in voter support for the candidate after the scandal. Conversely, if the z-value does not exceed the critical value, we fail to reject the null hypothesis, suggesting that there is insufficient evidence to conclude a significant decrease in support.

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Answer:

12 is the slope.

Step-by-step explanation:

This is because in the equation y = mx + b, m is the slope.

Hope this helps!

Answer:

The equation of required line is: \(\mathbf{x+y=5}\)

Step-by-step explanation:

We need to find an equation of the line that passes through the point (2,3) and is parallel to the line x+y=4

For finding an equation of line, we need to find slope and y-intercept of the line.

Finding slope:

If the lines are parallel their slope is same

We are given: x+y=4

Writing in slope-intercept form: \(y=mx+b\) where m is slope and b is y-intercept

\(x+y=4\\y=-x+4\)

Comparing \(y=-x+4\) with \(y=mx+b\) the slope m is -1

So, slope of given line is -1

It is parallel with required line, so they have same slope.

The slope of required line is m=-1

Finding y-intercept

Using slope m=-1 and point(2,3) we can find y-intercept

Using slope-intercept form: \(y=mx+b\)

\(y=mx+b\\3=-1(2)+b\\3=-2+b\\b=3+2\\b=5\)

So, y-intercept is: b=5

The equation of required line having slope m=-1 and y-intercept b = 5 is

\(y=mx+b\\y=-1x+5\\y=-x+5\\x+y=5\)

So, equation of required line is: \(\mathbf{x+y=5}\)

The equation of the line that passes through the point (2,3) and is parallel to the line x+y=4 is y  =  -x  +  5

Two equations are parallel if they have equal slope

For the equation x + y = 4

Rewrite the equation in the form y = mx + c

y  =  -x  +  4

Compare y = -x + 4 with y = mx + c

The slope, m = -1

The equation parallel to x + y = 4 will also have a slope, m = -1

The line passes through the point (2, 3)

That is, x₁ = 2, y₁ = 3

The point-slope form of the equation of a line is:

y - y₁  =  m(x  -  x₁)

Substitute x₁ = 2, y₁ = 3 into y - y₁  =  m(x  -  x₁)

y - 3 = -1(x  - 2)

y - 3 = -x + 2

y  =  -x  +  2  +  3

y  =  -x  +  5

The equation of the line that passes through the point (2,3) and is parallel to the line x+y=4 is y  =  -x  +  5

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Step-by-step explanation:

Let's call the shorter base of the trapezoid "b1", the longer base "b2", and the height "h". We can use the formula for the surface area of a right prism to set up an equation:

Surface area of prism = 2(base area) + (lateral area) = 1280

The base area is the area of the trapezoid, which is given by:

(base area) = (1/2)(b1 + b2)h

The lateral area is the area of the four rectangular faces of the prism, which are all congruent. Each face has an area equal to the product of the height and the length of one of the legs of the trapezoid, so the lateral area is:

(lateral area) = 4hl

where l is the length of one of the legs of the trapezoid.

Substituting these expressions into the formula for the surface area of the prism, we get:

2[(1/2)(b1 + b2)h] + 4hl = 1280

Simplifying and rearranging, we get:

h(b1 + b2) + 2hl = 1280

We also know that the sum of the lengths of the legs of the trapezoid is 52 feet, which means:

l1 + l2 = 52

But we can express l1 and l2 in terms of b1 and b2 using the formula for the area of a trapezoid:

(base area) = (1/2)(b1 + b2)h = (1/2)(l1 + l2)h

Simplifying, we get:

b1 + b2 = (l1 + l2)h

Substituting this into the previous equation, we get:

h[(l1 + l2)h] + 2hl = 1280

Simplifying, we get:

h^2(l1 + l2) + 2hl = 1280

Substituting l1 + l2 = 52, we get:

h^2(52) + 2hl = 1280

This is a quadratic equation in h. We can solve it using the quadratic formula:

h = [-2l ± sqrt(4l^2 + 4h^2(52)(1280 - 2hl))] / 2(52)

Simplifying and factoring out a 2, we get:

h = [-l ± sqrt(l^2 + h^2(1280 - 2hl))] / 52

We have two possible solutions for h, but one of them is negative, which doesn't make sense in the context of the problem. So we can discard the negative solution and focus on the positive one:

h = [-l + sqrt(l^2 + h^2(1280 - 2hl))] / 52

We don't know the exact value of h yet, but we can use this equation to set up a system of equations that we can solve for h. Specifically, we can use the fact that the legs of the trapezoid add up to 52 feet to solve for l in terms of b1 and b2:

l = 52 - (b1 + b2)

Substituting this into the equation for h, we get:

h = [-l + sqrt(l^2 + h^2(1280 - 2hl))] / 52

h = [-52 + (b1 + b2) + sqrt((52 - (b1 + b2))^2 + h^2(1280 - 2h(b1 + b

Answer: The formula to calculate simple interest is:

I = P * r * t

where:

- I is the interest earned

- P is the principal amount (the initial investment)

- r is the annual interest rate (as a decimal)

- t is the time in years

- To calculate the total amount in the account after the interest is earned, you need to add the interest earned to the principal amount.

So for Mrs. Baxter's investment, the calculation would be:

P = 2000 (the principal)

r = 0.05 (the annual interest rate as a decimal)

t = 8 (the time in years)

I = P * r * t = 2000 * 0.05 * 8 = 800

The interest earned over the 8-year period is $800.

The total amount in the account after 8 years would be the principal plus the interest earned:

A = P + I = 2000 + 800 = 2800

So Mrs. Baxter's investment would be worth $2,800 after 8 years.

Step-by-step explanation:

The amount after 8 years with the rate of interest as 5% simple interest is $2800.

What is meant by simple interest?

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Unlike compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant. Simple interest is a quick and simple approach to figuring out how much money has accrued interest. Interest is always applied to the original principal amount and is calculated at the same rate for each period of time.

Given,

The principal amount P = $2000

The rate of interest r = 5% = 5/100 = 0.05

The time period t = 8 years.

We have to find the amount after 8 years using simple interest formula.

Amount A = P(1+rt) = 2000(1+0.05 * 8)

                              = 2000 * 1.4 = $2800.

Therefore the amount after 8 years with the rate of interest as 5% simple interest is $2800.

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Answer: A

Step-by-step explanation:

The segment passes through the center of the circle, O, and its endpoints lie on the circumference of the circle.

The segment ZX is the diameter of the circle O. Then the correct option is A.

It is the center of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

The diameter of the circle is the longest chord that is passing through the center of the circle.

The segment ZX is the diameter of the circle O.

Then the correct option is A.

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There are 10 students in the class who are not enrolled in either music or art.

To solve this problem, we can use the inclusion-exclusion principle.

The total number of students in the class who take music or art is given by:

18 + 26 - 2 = 42

However, this counts the 2 students who take both art and music twice, so we need to subtract them once to get the total number of students who take either music or art but not both:

42 - 2 = 40

So, 40 students in the class take either music or art.

To find the number of students who are not enrolled in either music or art, we subtract this from the total number of students in the class:

50 - 40 = 10

Therefore, there are 10 students in the class who are not enrolled in either music or art.

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Answer:

A

Step-by-step explanation:

A.

at 1.5 seconds

h=-16(1.5)²+30(1.5)+6

=-16×2.25+45+6

=-36+45+6

=15 ft

which is correct.

B.

h=-16(t²-30/16 t)+6

=-16(t²-30/16t+(15/16)²-(15/16)²)+6

=-16(t-15/16)²-16(-225/256)+6

=-16(t-15/16)²+225/16 +6

=-16(t-15/16)²+(225+96)/16

=-16(t-15/16)²+321/16

it is at maximum height when t=15/16 seconds

so B is not true.

C.

when t=15/16 seconds

h=321/16 ft=20 1/16 ft

height of fence=20 ft

so it will clear the fence.

C is not true.

D.

when h=0

-16t²+30t+6=0

8t²-15t-3=0

\(t=\frac{15\pm\sqrt{225-4 \times 8 \times (-3)} }{2 \times 8} \\=\frac{15 \pm \sqrt{225+96} }{16} \\=\frac{15\pm \sqrt{321} }{16} \\rejecting~negative~sign\\t=\frac{15+\sqrt{321}}{16} \approx. 2.057 seconds\)

it hits the ground in 2.057 seconds

so D is not true.

Answer:

y = \(\frac{2}{5}\) x - 9

Step-by-step explanation: