A 90% confidence interval for the mean of a population is computed to be 135 to 160. Which one of the following claims would the interval tend to refute?
A. The population mean is more than 110.
B. The population mean is less than 150.
C. The population mean is between 140 and 150.
D. The population mean is more than 140.
E. The population mean is less than than 125.

The possible dimensions of the skateboard park are (x + 9) by (x + 6), where x > -6.

The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.

The area of a rectangular skateboard park can be expressed as the product of its length and width. Therefore, we need to factor the quadratic expression x² + 15x + 54 to determine its possible dimensions.

x² + 15x + 54 factors into (x + 9)(x + 6).

So, the possible dimensions of the park are x + 9 and x + 6.

Note that since x represents a length, the dimensions of the park must be positive. Therefore, x + 9 and x + 6 must both be greater than zero.

Solving for x, we get:

x + 9 > 0

x > -9

x + 6 > 0

x > -6

Since x must be greater than both -9 and -6, the possible values of x are x > -6.

Therefore, the possible dimensions of the skateboard park are (x + 9) by (x + 6), where x > -6.

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The value of the side q is 2.2

To determine the value, we need to take note of the properties of an isosceles triangle. They include;

Using the Pythagorean theorem stating that the square of the longest sides of the triangle is equivalent to the sum of the square of the opposite sides as well as the square of the adjacent side.

From the information given, we have;

q² = 2² + 1²

Find the squares

q² = 4 + 1

Add the values, we get;

q² = 5

Find the square root of both sides, we have;

q = 2.2 cm

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Kayla has read more pages than Bilquis after 4 days, so she is farther along in the book.

The equation to represent the situation of Bilquis would be B = 23 + 7t

The equation to represent the situation of Kayla would be K = 2 + 14t

For Bilquis, the equation to represent the situation would be B = 23 + 7t, where B is the page of the book that Bilquis is on at the end of t days into the month.

For Kayla, the equation to represent the situation would be K = 2 + 14t, where K is the page of the book that Kayla is on at the end of t days into the month.

The equations help us to calculate the page number of each reader at any given point in time. Bilquis starts at page 23 and reads 7 pages a day, so we add 7t to her starting point. Kayla starts at page 2 and reads 14 pages a day, so we add 14t to her starting point. By comparing their page numbers after a certain number of days, we can determine which reader is farther along in the book.

After 4 days,

Bilquis would be on page = 23 + 7(4) = 51

Kayla would be on page = 2 + 14(4) = 58.

Therefore, Kayla would be farther along in the book after 4 days with a gap of 7 pages with Bilquis.  

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The values of y When x = -2, 0 and 2 are:

At x = -2, y = -12

At x = 0, y = -8

At x = 2, y = -4

The general form of the equation of a straight line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

Let us rewrite the given equation in slope intercept form to get:

y = 2x - 8

Thus, from the table, we want to find y when x = -2, 0 and 2

When x = -2, we have:

y = 2(-2) - 8

y = -12

When x = 0, we have:

y = 2(0) - 8

y = -8

When x = 2, we have:

y = 2(2) - 8

y = -4

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Answer:

x=-5,-6

Step-by-step explanation:

x²+11x+30=0

(x+5)(x+6)=0

The conclusion about QR and NP is 2QR = NP; x = 3

From the question, we have the following parameters that can be used in our computation:

RQ and RS are midsegments of ANOP,

This means that

2QR = NP

So, we have

2 * (3x + 2) = 2x + 16

6x + 4 = 2x + 16

Evaluate the like terms

4x = 12

Divide

x = 3

Hence, the value of x is 3

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Answer: 5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

The high R-squared value indicates that time is a strong predictor of the number of married people in the United States, it is important to consider the limitations of the equation and the uncertainty in the prediction.

First, let's talk about the R-squared value of your trendline equation.

Now, let's talk about your belief that there will never be a time when we have zero married people. This belief is not accounted for in your trendline equation, as it is purely based on your personal belief rather than any data or statistical analysis.

When it comes to confidence level, we need to consider the uncertainty in the prediction. Since we know that there will likely always be some people who want to get married, we can say with a high level of confidence that the number of married people will never actually reach zero.

In mathematical terms, we can use the equation for the confidence interval to determine the range of values within which we can be confident the true value will fall.

This equation takes into account the standard error of the estimate (the degree of variability in the data) and the desired level of confidence (typically 95% or 99%). However, since we know that the true value will never be zero, this equation is not particularly useful in this case.

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When the experimenter fails to reject the null hypothesis when the null hypothesis is really true, the option (c) type II error is made.

When conducting a hypothesis test, there are two possible errors that can occur: type I and type II errors. Type I error is the rejection of a true null hypothesis, while type II error is the failure to reject a false null hypothesis. In other words, a type II error occurs when the experimenter accepts the null hypothesis when it should have been rejected.

This can lead to a false conclusion that there is no significant difference or effect when there actually is. It is important to minimize both types of errors in hypothesis testing, but the type II error can be particularly dangerous as it can lead to missed opportunities for important discoveries.

Therefore, the correct option is (c) type II error.

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The time it will take for "scientist" to "travel-back" to "sea-level" with  submarine's maximum speed as 4.8 feet per second is 51.9 seconds.

We know a relationship that : Distance = Speed × time,

For the "First-Travel" :She travels "straight-down" for 90 seconds with speed of 3.5 feet per second,

So, Distance covered is = 90 × 3.5 = 315 ft,

For the Second travel :She then travels "directly-up" for 30 seconds with speed of 2.2 feet per second,

So, Distance covered is = 30 × 2.2 = 66 ft,

The "Net-Change" in position from "sea-level" is = 315 - 66 = 249 ft,

The Maximum speed of submarine is = 4.8 feet per second,

We know that, Time taken = Distance/speed,

⇒ Time taken = 249/4.8 = 51.875 seconds ≈ 51.9 seconds.

Therefore, it will take 51.9 seconds to return to sea level.

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Answer:

Step-by-step explanation:

D

If Joanna French's washing lines needs 16.11 metres of line to go around her garden three times, we can multiply 16.11 by three to get the length that one stretch. We get 5.37 metres as a result.

The lengths of the three portions of the line must be added up in order to determine the length across the backyard. The entire length of the path is 16.11 metres, which can be calculated by multiplying 5.37 by 3.

The 16.11 metres that separate Jo French's backyard are the result. This figure is predicated on the laundry line being strung across the garden in a straight path without sagging or curving.

It's crucial to keep in mind that the distance over the back yard may vary if the laundry line is not extended in a straight line. This estimate assumes that the laundry line is the only object using space in the backyard, therefore, the real length across the yard may differ if other items or impediments are present.

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The correct letter for each item are: a. variable, b. control group, c. experimental group, d. experimental group, e. control group, f. variable, g. variable

The answer to the different components of the experiment are listed below:

a. The cooking time is a variable

b. Group B is control group

c. The type of pizza crust is experimental group

d. The method for cooking the pizza experimental group

e. Group A is control group

f. The type of toppings is a variable

g. The chef who cooked the pizza is a variable

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Answer:

exchange 9 with 12

simplyfy both til 1/2*4/3

2/3 finally

The total amount purchased by Roger is

Calculating the sum of his purchase, Roger's total cost before any discounts or taxes amounted to:

4.50 + 12.00 = 16.50

Taking into account a ten percent discount on this total, the deduction was found to be:

0.10 * 16.50 = 1.65

where 10% = 0.1

Concluding, the total cost after the discount presented was:

16.50 - 1.65 = 14.85

Furthermore, 8.5% tax is determined of 14.85 equalling out to:

0.085 * 14.85 = 1.26

where 8.5% = 0.085

the final total cost for Roger's purchase is solved by addition of the amount after tac and amount after the discount:

14.85 + 1.26 = 16.11

Hence, the complete cost for Roger's acquisition totalled $16.11.

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For #3

A quadratic expression is in standard from when written as ax^2 + bx + c = 0. Where, a, b, and c are constants.

The only option that is written in the form above is option C. Where a=-1, b=-5, and c=7.

For #4

First how is 3x^2 in standard form?

Recall that the standard form of a quadratic is ax^2 + bx + c = 0. So lets alter 3x^2 a bit to show that it is in standard form.

3x^2 ==> 3x^2+0x+0

As you can see 3x^2 is in standard form, but the constants b and c are zero.

Second, how is 3x^2 in factored form?

Factored form is written as (a+x)(b+x). So let's alter 3x^2.

3x^2 ==> 3(0+x)(0+x)

3(0+x)(0+x) = 3(x)(x) which is 3x^2

Hence it can be said that 3x^2 is in both standard and factored form.

Answer:

25/32

Step-by-step explanation:

To evaluate the expression

[tex]\frac{x^{-2}y^{0} }{x^{3}y^{-2} }[/tex]

First we replace x and y by the given values

So x becomes 2 and y becomes 5

[tex]\frac{2^{-2}5^{0} }{2^{3}5^{-2} }[/tex]

Expressions with negative exponents in the numerator always go to the denominator with positive exponent and on the denominator goes to the numerator with positive exponent

[tex]\frac{5^{2}5^{0} }{2^{3} 2^{2} }[/tex]

Simplify

[tex]\frac{25*1 }{8*4 }[/tex]

Which is

[tex]\frac{25}{32}[/tex]

Answer:IQR=15

Step-by-step explanation:

Answer:

Step-by-step explanation:

A circle has a total angle measurement of 360 degrees.

To find the number of slices given a certain angle, simply perform

360/central angle.

For example, if the central angle is 180, you'll have two sections.

360/180 = 2.

Answer:

x = c-b

the easiest solution is this

The probability of picking up a ripe mango at random from a bag containing 12 mangoes is equal to 2 /3.

Total number of mangoes in the bag = 12

Total number of mangoes in the bag which are not ripe = 4

Then the number of ripe mangoes is equal to,

= 12 - 4

= 8

So, probability of picking a ripe mango at random can be calculated by dividing number of ripe mangoes by total number of mangoes.

This implies,

P(ripe mango)

= Number of ripe mangoes / Total number of mangoes

= 8 / 12

= 2 / 3

≈ 0.667

Therefore, the chance of picking at random a ripe mango is approximately 0.667 or 2/3.

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Answer:

[tex]\frac{4\sqrt{3} }{3}[/tex]

or

[tex]2.30940107[/tex]

Hope This Helps :)

Pls Brainliest...

To test the claim that the proportion of teenagers who receive all the recommended doses of the HPV vaccine is not equal to 0.50, we can use a hypothesis test.

Let p be the true proportion of teenagers who receive all the recommended doses of the HPV vaccine.

Our null hypothesis is that the true proportion is equal to 0.50, i.e. H0: p = 0.50. Our alternative hypothesis is that the true proportion is not equal to 0.50, i.e. Ha: p ≠ 0.50.

We can use a normal approximation to the binomial distribution to perform the hypothesis test. Under the null hypothesis, the sample proportion of teenagers who received all the recommended doses of the HPV vaccine follows a normal distribution with mean 0.50 and standard deviation σ = √((0.50)(1-0.50)/200) = 0.05.

Using the sample data, the test statistic is:

z = (p' - p) / σ = (0.55 - 0.50) / 0.05 = 1.00

where p' = 110/200 = 0.55 is the sample proportion.

The p-value for a two-sided test with a test statistic of 1.00 is approximately 0.32. Since the p-value is greater than the significance level of α = 0.05, we fail to reject the null hypothesis.

Therefore, we do not have sufficient evidence to conclude that the proportion of teenagers who receive all the recommended doses of the HPV vaccine is different from 0.50 at the 5% significance level.

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Answer:

The sum is 27,076.554.

Step-by-step explanation:

The sum of 27076, 0.55, and 0.004 is:

27076 + 0.55 + 0.004 = 27076.554

Therefore, the sum is 27,076.554.

If in triangle WXY, ∠W is 90° and ∠X is 12°, then the area of ΔWXY is approximately 38260.2 cm².

The measure of angle W is 90° and the measure of angle X is 12°,

So, By using concept of "angle-sum" property of triangle,

⇒ ∠X + ∠Y + ∠Z = 180°,

Substituting the values,

We get,

⇒ 90° + ∠Y + 12° = 180°,

⇒ ∠Y = 180° - (12° + 90°),

⇒ ∠Y = 180° - 102°,

⇒ ∠Y = 78°.

Next, we use the "Sine-Law" to find the length of WY(x),

The length of side "WX" = y = 600cm,

So, y/(SinY) = x/(SinX),         ,.....by Sine-Law

⇒ x = (y × SinX)/(SinY) ,

⇒ x = 127.533937..

The Area of the right triangle XYZ is = (1/2)×(WX)×(WY),

Substituting the values of "WX" and "WY",

We get,

⇒ Area = (1/2)×(600)×(127.533937),

⇒ Area = 38260.1811006...

⇒ Area ≈ 38260.2 cm².

Therefore, the required area is 38260.2 cm².

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Answer:

x= 68

Step-by-step explanation:

80+ 32+ x= 180

112 +x= 180

x= 180-112

x= 68

Answer:

68

Step-by-step explanation:

Since every single triangle is 180 degrees, we can add 32 + 80 and subtract that from 180 to get our answer.

[tex]32+80 = 112[/tex]

[tex]180-112=68[/tex]

You can check your work by:

[tex]32+80+68=180[/tex]

[tex]112+68=180[/tex]

[tex]180=180[/tex]

So your answer is 68.

Hope this helps!

The length of the straight line calculated between school and the fire station is equal to  4.6 miles ( nearest tenth ).

Location of town hall is 4.3 miles directly east of the middle school.

Location of fire station is 1.7 miles directly north of town hall.

To find the length of the straight line between the school and the fire station,

Apply the Pythagorean theorem,

Which states that in a right 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 this case, the distance between the school and Town Hall, and the distance between Town Hall and the fire station form a right triangle,

So, we can calculate the length of the hypotenuse as,

√(4.3² + 1.7²)

≈ √(18.49 + 2.89)

≈ √21.38

≈ 4.62

≈ 4.6 miles ( Rounding to the nearest tenth)

Therefore, the length of the straight line between the school and the fire station is approximately 4.6 miles.

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The above question is incomplete, the complete question is:

Town Hall is located 4.3 miles directly east of the middle school. The fire station is located 1.7 miles directly north of Town Hall. What is the length of a straight line between the school and the fire station? Round to the nearest tenth.

Step-by-step explanation:

The first one is a linear model    for each '1' change of x , the y value changes  -3    ( this would be the slope,m, of the linear equation)

 The others are not as regular or have two values for a given 'x'