Question 26 2 pts A century ago, the average height of adult women in the United States was 63 inches. Researchers believe that the average might be greater today. A random sample of 40 adult women was selected from the population. The sample had mean 64.2 inches and standard deviation 2.9 inches. Assuming all conditions for inference are met, the researchers will perform an appropriate hypothesis test to investigate their belief. Which of the following is the correct test statistic for the hypothesis test? 0.4137 0 -0.2617 O-0.4137 0.2617

Answer:x^2+12x-28=01. 12/2=62. (x+6)^2=x^2+12x+363. If we subtract 64 from this expression it becomesx^2+12x+36-64=x^2+12x-28 and so equals 0We now have (x+6)^2-64=0This is our old friend a^2-b^2=(a+b)(a-b)(x+6)^2-8^2=(x+6+8)(x+6-8)=(x+14)(x-2)=0 and so x=-14 or x=2

Step-by-step explanation:

Answer:

To simplify (1/2)³x(1/2)², we can multiply the coefficients and add the exponents with the same base:

(1/2)³x(1/2)² = (1/2)^(3+2) = (1/2)^5

Therefore, (1/2)³x(1/2)² simplified is equal to (1/2)^5, which can also be written as 1/32 in fraction form.

Step-by-step explanation:

In order to multiply we use the formula for indices' multiplication that is

[tex] {n}^{a} \times {n}^{b} = {n}^{a + b} [/tex]

Hence,

[tex]{( \frac{1}{2} )}^{3}( { \frac{1}{2}}^{2}) = {( \frac{1}{2} )}^{5} [/tex]

[tex] ( \frac{{1}^{5} }{{2}^{5} } ) = {2}^{ - 5} [/tex]

Collecting data on 83,359 grade-point averages would be a significant undertaking and a 99% confidence level, especially if the data had to be collected in a short amount of time or if there were limited resources available for data collection.

To determine the sample size needed to estimate the population mean within a certain margin of error, we can use the formula:

[tex]n = (Z^2 * sigma^2) / E^2[/tex]

where n is the sample size, Z is the Z-score for the desired confidence level (in this case, 2.576 for a 99% confidence level), sigma is the population standard deviation (in this case, estimated as 1.25 using the range rule of thumb), and E is the desired margin of error (in this case, 0.01).

Plugging in the values, we get:

[tex]n = (2.576^2 * 1.25^2) / 0.01^2 = 83,358.08[/tex]

So we would need a sample size of at least 83,359 to estimate the population mean with a margin of error of 0.01 and a 99% confidence level.

However, this sample size may not be practical depending on the resources available. Collecting data on 83,359 grade-point averages would be a significant undertaking, especially if the data had to be collected in a short amount of time or if there were limited resources available for data collection.

In practice, researchers often use statistical software to calculate sample sizes based on the desired margin of error, confidence level, and population standard deviation. This allows them to determine a more realistic sample size based on the specific context of their study.

In summary, while the formula for determining sample size can provide an estimate of the number of observations needed to estimate the population mean with a certain level of precision, other factors such as the availability of resources must also be considered when determining a practical sample size.

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Answer:

Step-by-step explanation:The sum of the measures of the angles in a triangle is always 180 degrees. So, we can set up an equation and solve for x:

36 + (6x+3) + 87 = 180

Combine like terms:

126 + 6x = 180

Subtract 126 from both sides:

6x = 54

Divide both sides by 6:

x = 9

Therefore, the value of x is 9.

Answer:

3x + 18

Step-by-step explanation:

3 ( x + 6 )

= 3*x + 3*6

= 3x + 18

Answer:

Step-by-step explanation:

expand 3(x+6)

3(x + 6) =      

3 * x + 3 * 6

3x + 18

Answer:

1/5 is the right answer in my opinion but I'm not sure

The roots of the equation x² - 5x + k are z = (5/a - 3)/2 and z+3 = (5/a + 3)/2, and the value of k is 9/4.

The roots of an equation are the values of the variable that satisfy the equation and make it true. In the case of a quadratic equation of the form ax² + bx + c = 0, the roots are the values of x that satisfy the equation and make it equal to zero.

Given:  z and z+3 are the roots of the equation x² - 5x + k

The sum of the roots z and z+3 is:

z + (z + 3) = 2z + 3

And the product of the roots z and z+3 is:

z (z + 3) = z² + 3z

By Vieta's formulas, we know that the sum of the roots of a quadratic equation ax² + bx + c = 0 is -b/a and the product of the roots is c/a. Therefore, we can equate these expressions to the sum and product of the roots of the given equation:

2z + 3 = 5/a (since b = -5 and a = 1)

z² + 3z = k/a (since c = k and a = 1)

Solving for z in the first equation, we get:

2z = 5/a - 3

z = (5/a - 3)/2

Substituting this value of z into the second equation, we get:

[(5/a - 3)/2]² + 3[(5/a - 3)/2] = k/a

Simplifying and solving for k, we get:

k = a[(5/a - 3)/2]² + 3a[(5/a - 3)/2]

= (5a - 9a + 18)/4

= 9/4

Therefore, the roots of the equation x² - 5x + k are z = (5/a - 3)/2 and z+3 = (5/a + 3)/2, and the value of k is 9/4.

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If the value of C, the circumference is known, then the diameter is:

D = C/pi

For a circle whose radius is R, the formula for the circumference is:

C = 2*pi*R

Where pi = 3.14

Particularly, we know that the diameter of a circle is twice the radius, os:

D = 2*R

We can rewrite the circumference equation to get:

C = pi*(2*R) = pi*D

So, solving that equation for the diameter, we will get:

D = C/pi

That equation gives the diameter if we know the value of the circumference.

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Answer:

x^3 + 5x - 23

Step-by-step explanation:

(Q+R)(x) is the same as Q(x) + R(x).

you just add them like so:

(x^3 - 9x^2 - 14) + (9x^2 + 5x - 9)

= x^3 + 5x - 23

Answer:

  1/2

Step-by-step explanation:

You want to know the average rate of change of f(x) = 1/2x -7 on the interval [2, 10].

A linear function has the same rate of change everywhere. Its instantaneous rate of change, average rate of change, and slope are all the same constant.

The given function is written in slope-intercept form, so we can identify the slope as the coefficient of x: 1/2.

The average rate of change is 1/2.

__

Additional comment

If you feel the need to "show work", you can evaluate ...

  AROC = (f(10) -f(2))/(10 -2) = (-2 -(-6))/8 = 4/8 = 1/2

in this particular data set, there is only one value that appears most frequently, which is 5.

What are statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It provides a set of methods and tools for extracting meaningful insights and making decisions based on data.

In statistics, the mοde is the value that is repeatedly οccurring in a given set. We can alsο say that the value οr number in a data set, which has a high frequency οr appears mοre frequently, is called mοde οr mοdal value. It is οne οf the three measures οf central tendency, apart frοm mean and median. Fοr example, the mοde οf the set {3, 7, 8, 8, 9}, is 8.

Therefοre, fοr a finite number οf οbservatiοns, we can easily find the mοde. A set οf values may have οne mοde οr mοre than οne mοde οr nο mοde at all.

In the given data 5 has the maximum frequency so 5 is style mode of the given data

Mode=5

Therefore, in this particular data set, there is only one value that appears most frequently, which is 5.

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According to the question the height of the ladder is 34.641 feet, or approximately 19.98 feet.

Height is the measure of vertical distance, either how "tall" something or someone is, or the distance between the top and bottom of an object. It is measured in either centimeters, meters, or feet and inches, and can be used to describe the elevation of land or the altitude of an aircraft.

Let x be the height of the ladder.
For a 20-foot ladder at an angle of 45°, we have the following trigonometric equation:
tan(45°) = x/20
Solving for x we get:
x = 20tan(45°)
x = 20 × 1
x = 20
Therefore, the height of the ladder is 20 feet.
For a 20-foot ladder at an angle of 75°, we have the following trigonometric equation:
tan(75°) = x/20
Solving for x we get:
x = 20tan(75°)
x = 20 × 1.73205
x = 34.641
Therefore, the height of the ladder is 34.641 feet, or approximately 19.98 feet.

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The range of height can be determined by trigonometric ratios and the rage is 20ft to 74.6 ft(approximately).

What is Trigonometric Ratios?

Trigonometric Ratios are  based on the value of the ratio of sides of a right-angled triangle where Hypotenuse is the longest side Perpendicular is opposite side to the angle and Base is the Adjacent side to the angle. The ratios of these three sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

Given that a ladder should not be set up at an angle less than 45 degrees or at an angle greater than 75 degrees.

The ladder is 20 foot.

here the trigonometric function tangent will be used.

By the formula, tan Ф = Perpendicular/ adjacent side [ where Ф is the acute angle]

Let, the height of the ladder is x foot.

Then by formula of trigonometric ratio,

tan 45° = x/20

⇒ x/20 =1 [ since tan 45° =1 ]

⇒ x= 20

Again,

tan 75° = x/ 20

⇒ x= 20× tan 75°

⇒ x= 74.6 [ since tan 75° = 3.732]

Hence, the range of height is 20 foot to 74.6 foot ( approx ).

The rough diagram is attached below.

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Answer:b

Step-by-step explanation:

just took the quiz

Step-by-step explanation:

If the area of the bean field is 440ft^2 and each bag of fertilizer covers 100 ft^2, then Farmer Bob will need:

440 ft^2 / 100 ft^2 per bag = 4.4 bags of fertilizer

Since Farmer Bob can't buy a fraction of a bag, he will need to round up to 5 bags of fertilizer.

The total cost of the fertilizer will be the number of bags multiplied by the cost per bag, which is $5.50. Therefore, the total cost of the fertilizer will be:

5 bags x $5.50 per bag = $27.50

A procession typically has one-fourth of the participants with red hair, one-sixth with brown hair, and the remaining participants with black hair. 7/12 of the population has black hair.

We are given that 1/4 of the people have red hair and 1/6 of them have brown hair.

Let's add these fractions together to find the fraction of people who have either red or brown hair:

[tex]\\\frac{1}{4} + \frac{1}{6}\\ =\frac{3+2}{12} \\ =\frac{5}{12}[/tex]

This means that 5/12 of the people have either red or brown hair.

Since the remaining people must have black hair, we can subtract this fraction from 1 to find the fraction of people who have black hair:

1 - 5/12

=12-5/12

= 7/12

Therefore, the fraction of people who have black hair is 7/12.

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Answer:

≈ 31,53 cm

Step-by-step explanation:

[tex]2\pi \times r = 198[/tex]

[tex]r = \frac{198}{2\pi} = \frac{198}{2 \times 3.14} = \frac{198}{6. 28} ≈ 31.53[/tex]

Answer:

LM = 5

Step-by-step explanation:

A secant is a straight line that intersects a circle at two points.

A segment is part of a line that connects two points.

The product of the measures of one secant segment and its external part is equal to the product of the measures of the other secant segment and its external part.

The given diagram shows two secant segments LN and PN that intersect at exterior point N.  Their external parts are MN and ON, respectively.

Therefore, according to the Intersecting Secants Theorem:

[tex]\implies \sf LN \cdot MN =PN \cdot ON[/tex]

Given values:

Substitute the values into the equation and solve for x:

[tex]\implies \sf LN \cdot MN =PN \cdot ON[/tex]

[tex]\implies (x+1)\cdot 3=(x-1)\cdot 4[/tex]

[tex]\implies 3x+3=4x-4[/tex]

[tex]\implies 4x-4=3x+3[/tex]

[tex]\implies 4x-4-3x=3x+3-3x[/tex]

[tex]\implies x-4=3[/tex]

[tex]\implies x-4+4=3+4[/tex]

[tex]\implies x=7[/tex]

To determine the length of LM, substitute the found value of x into the expression for the line segment:

[tex]\implies \overline{LM}=7-2=5[/tex]

Therefore, the length of LM is 5.

The inflection points are at x = -[tex]\sqrt{(1/3)}[/tex] and x = sqrt(1/3), and f is concave up on (-[tex]\sqrt{1/3}[/tex]), [tex]\sqrt{(1/3)}[/tex]), and concave down elsewhere.

(a) To find the intervals on which f is increasing or decreasing, we need to find the first derivative of f and determine its sign.

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

[tex]f'(x) = 4x^3 - 4x[/tex]

Setting f'(x) = 0, we get:

[tex]4x(x^2 - 1) = 0[/tex]

This equation has roots at x = 0, x = -1, and x = 1. We can use the first derivative test to determine the intervals of increasing and decreasing.

When x < -1, f'(x) is negative, so f is decreasing.

When -1 < x < 0, f'(x) is positive, so f is increasing.

When 0 < x < 1, f'(x) is negative, so f is decreasing.

When x > 1, f'(x) is positive, so f is increasing.

Therefore, f is decreasing on (-∞, -1) and (0, 1), and increasing on (-1, 0) and (1, ∞).

(b) To find the local maximum and minimum values of f, we need to look for critical points and evaluate the function at those points.

Critical points occur where f'(x) = 0 or is undefined. We have already found that f'(x) = 0 at x = 0, x = -1, and x = 1.

f(0) = 3, f(-1) = 6, f(1) = 2

Therefore, f has a local maximum at x = -1, with a value of 6, and local minimums at x = 0 and x = 1, with values of 3 and 2, respectively.

(c) To find the intervals of concavity and inflection points, we need to find the second derivative of f and determine its sign.

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

[tex]f'(x) = 4x^3 - 4x[/tex]

[tex]f''(x) = 12x^2 - 4[/tex]

Setting f''(x) = 0, we get:

[tex]12x^2 - 4 = 0[/tex]

[tex]x^2 = 1/3[/tex]

x = ±sqrt(1/3)

We can use the second derivative test to determine the intervals of concavity.

When x < -sqrt(1/3), f''(x) is negative, so f is concave down.

When -sqrt(1/3) < x < sqrt(1/3), f''(x) is positive, so f is concave up.

When x > sqrt(1/3), f''(x) is negative, so f is concave down.

Therefore, the inflection points are at x = -sqrt(1/3) and x = sqrt(1/3), and f is concave up on (-sqrt(1/3), sqrt(1/3)), and concave down elsewhere.

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Applying mathematical operations, "Four times the sum of 5 and some number is 20," the number is 0.

The mathematical operations include addition, subtraction, division, and multiplication.

Mathematical or algebraic operations use mathematical operands to manipulate values, variables, constants, and numbers to solve mathematical problems.

Zero is considered to be a neutral number since it is neither positive nor positive.

Zero is important as a number placeholder.

4 (5 + x) = 20

20 + 4x = 20

4x = 20 - 20

4x = 0

x = 0

Thus, in the mathematical operations of multiplying the sum of 5 and some number by 4, the applicable number is zero.

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If 25 tapered pins are machined from a steel rod 15 ft long, then total 15 tapered pins can be made from a steel rod 9 ft long.

The unitary method is a method where you find the value of one unit and then find the value of the number of units you want. The formula for the units method is to find the value of a single unit and then multiply the value of the single unit by the number of units to get the desired value. We have specify that 25 tapered pins can be made up from a steel rod 15 ft long. Let 'x' represent the number of pins that can be made from 9 ft long steel rod. Now, using the unitary method,

number of pins machined from a 15 ft long steel rod = 25

number of pins machined from a 1 ft long steel rod = 25/15

So, number of pins machined from a 9 feet long steel rod, x = (25/15)×9

=> x = 3×5 = 15

Hence, required tapered pins made from a steel rod 9 ft long is equals to the 15 pins.

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Answer: We can only determine the cost for each burger if we know the total cost of all the ground beef. Let's assume that the ground beef costs $C in total.

If Coach Miller is using all the ground beef to grill 17 burgers, then the cost of each burger is:

Cost per burger = Total cost of ground beef / Number of burgers

We know that the total cost of ground beef is $C, and we know that there are 17 burgers. Substituting these values into the formula gives:

Cost per burger = C / 17

Therefore, the cost for each burger is C/17. We cannot determine the numerical value of C or the cost per burger without additional information.

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

0.3*65

=19.5 pounds

[tex]\frac{2}{10} =0.2\\0.2*65=13[/tex]

Step-by-step explanation:

Don't worry we will take care of everything. It's easy. listen carefully

first of all write your questions carefully.

i think it should be like this-

y= -6x +43 ------ (i)

y= -8x -59---------(ii)

1. We have two unknowns x and y. and two equations .

2. CONCEPT:- there are several ways to solve it like.

ACCORDING TO SUBSTITUTION METHOD:-

Simply, write the equation in term of single variable(unknown). * [ which is already done for us]

second step, substitute the expression of obtained variable in any one equation.

example: substitute the value of y from equation (i) in (ii)

we will obtained equation -

=> y= -8x -59 [ put value of y from (i) ]

=> -6x +43 = -8x -59

(solve and find x)

=> -6x +8x = -59 - 43

=> 2x = -102

=> x = -51

Third step in substitute method is, now substitute this obtained value of x in any equation (i) or (ii) to get unknown y.

y will be = 349

* your questions was wrong so i have made it by myself. if this does not match your question sorry from my side. buti have shown you the concept to solve this type of questions. You will be able to solve this by your self now by applying concepts.

Answer:

Step-by-step explanation:

Answer:

5805 words

Step-by-step explanation:

2 hours × 60 minutes/hour = 120 minutes

120 minutes + 15 minutes = 135 minutes

2 hours and 15 minutes = 135 minutes

135 minutes × 43 words/minute = 5805 words

The heights of the passenger as they move on the Colossus Ferris wheel described by the specified sine function are;

2. (a) 22 times

(b) 180 feet which is the highest point on the ride

3. (a) 15 feet

(b) The last passenger will not need to weight

A sine function is a mathematical function that describes a smooth repetitive oscillation. The sine function is a periodic function which repeats itself after certain interval. The sine function is the ratio of the opposite side to the hypotenuse side of a right triangle.

2. (a) The period of the sine function model, for the height, h = -82.5×cos(3·π·t) + 97.5 is 2·π/3. Therefore, the last passenger who boarded the ride makes a completer loop on the Ferris wheel every **2/3 minutes**. Since the duration of the ride is 15 minutes, the number of complete loops the passenger makes = 15/(2/3) = 22.5

(b) When the ride ends, the height of the last passenger can be found by evaluating the specified sine function at t = 15 minutes (the ride lasts for 15 minutes).

Therefore; h = -82.5 × cos(3 × π × 15) + 97.5 = 180.

3. (a) The time of operation of the ride when the power outage occurs is t = 6 minutes. The height of the last passenger at the time of the power outage is; h = -82.5 × cos(3 × π × 6) + 97.5 = 15

(b) The last passenger to board the ride will not need to weight in order to exit the ride. This is because the height of the last passenger at the moment of the power outage is 15 feet, which is the initial height of the passenger when they board the ride. Therefore, the last passenger will be at the same height as the ground, and can exit the ride without waiting.

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Answer:

54 , 90

Step-by-step explanation:

Let John = 10x
Let Anvil = 6x

10x = 36 + 6x

10 - 6x = 36

4x = 36

x=9

Anvil = 6*9 = 54
John = 10*9 = 90

Since the minimum upward velοcity cannοt be negative, the answer is (A) 7.5 feet per secοnd. If we had taken the absοlute value οf the velοcity, the answer wοuld be (B) 19.7 feet per secοnd.

Velοcity is a physical quantity that describes the rate οf change οf an οbject's pοsitiοn with respect tο time. It is a vectοr quantity that has bοth magnitude and directiοn, with the magnitude representing the speed οf the οbject and the directiοn indicating its mοtiοn. In οther wοrds, velοcity tells us hοw fast an οbject is mοving and in which directiοn.

Tο find the minimum upward velοcity needed tο reach the branch, we can use the cοnservatiοn οf energy principle. At the height οf 5.5 feet, the weight has pοtential energy, which will be cοnverted tο kinetic energy as it falls. When the weight reaches the branch at a height οf 15 feet, all οf its initial pοtential energy will be cοnverted tο kinetic energy. Therefοre, we can equate the pοtential energy at the initial height with the kinetic energy at the final height:

[tex]mgh = (1/2)mv^2[/tex]

There m is the mass οf the weight (which cancels οut), g is the acceleratiοn due tο gravity (32 ft/s²), h is the initial height (5.5 ft), and v is the velοcity at the final height (15 ft).

Substituting the values, we get:

(32 ft/s²) * (15 ft - 5.5 ft) = (1/2) * v²

v² = 2 * (32 ft/s²) * (15 ft - 5.5 ft) = 800 ft²/s²

Taking the square rοοt οf bοth sides gives:

v = √(800) = 28.28 ft/s

Hοwever, we need the minimum upward velοcity, sο we must subtract the initial dοwnward velοcity (due tο gravity) οf 32 ft/s:

minimum upward velοcity = v - g = 28.28 ft/s - 32 ft/s = -3.72 ft/s

Since the minimum upward velοcity cannοt be negative, the answer is (A) 7.5 feet per secοnd, which is the magnitude οf the upward velοcity.

Nοte: If we had taken the absοlute value οf the velοcity, the answer wοuld be (B) 19.7 feet per secοnd. Hοwever, the minimum upward velοcity is the cοrrect answer in this cοntext.

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The 95 percent confidence interval that the true mean lead level of crows in the region is between 4.4157 and 5.3843.

What is a confidence interval?

An estimated range for an unknown parameter is known as a confidence interval. The 95% confidence level is the most popular, however other levels, such as 90% or 99%, are occasionally used when computing confidence intervals.

Here, we have

Given:  the mean lead level of the 23 crows in the sample was 4.90 ppm and the standard deviation was 1.12 ppm.

= x ± t×s/√n

= 4.90 ± (2.074)×1.12/√23

= (4.4157, 5.3843)

Hence, the 95 percent confidence interval that the true mean lead level of crows in the region is between 4.4157 and 5.3843.

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The expression represent total number dime both have is 5d.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

Here Anna Has d dimes  and Brittany has 4 times as many dimes as Anna.

Then,

Number of dime Anna has = d Number of dime Brittany has = 4d

Now the total number of dimes both have is:

Total dimes = d+4d

= 5d

Hence the expression represent total number dime both have is 5d.

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