A newsletter publisher believes that over 30% of their readers own a Rolls Royce. For marketing purposes, a potential advertiser wants to confirm this claim. After performing a test at the 0.05 level of significance, the advertiser failed to reject the null hypothesis.

The length of the arc of the circle is 3.67 meters

The arc of a circle is a part of the circumference that makes up the circle

From the question, we have the following parameters

Diameter, d = 14 meters

Central angle = π/6 radians

Start by calculating the radius of the circle using

Radius, r = Diameter/2

This is so because radius is half the diameter

So, we have

r = 14 meters/2

Evaluate the quotient of 14 meters and 2

r = 7 meters

The length of the arc of the circle is then calculated using

L = Radius * Central angle

Substitute known values in the above equation

L = 7 meters * π/6

Evaluate the product of 7 and π/6

L = 3.67 meters

Hence, the length of the arc of the circle is 3.67 meters

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Answer:

vertex : (-5/2, -53/4)

solutions: (-(5-sqrt53)/2, 0) (-(5+sqrt53)/2, 0)

Step-by-step explanation:

1.The vertex of the function is (-5/2, -53/4).

2.We have two solutions:

x = (-5 + √53) / 2 ≈ 0.73

x = (-5 - √53) / 2 ≈ -5.73

To find the vertex and solutions of the function y = x^2 + 5x - 7, we can use the formula for the vertex and the quadratic formula for finding solutions.

1. Vertex:

The vertex of a quadratic function in the form y = ax^2 + bx + c can be found using the formula:

x = -b / (2a)

y = f(x) = ax^2 + bx + c

Given: a = 1, b = 5, c = -7

x = -5 / (2 * 1) = -5 / 2

Now, substitute the value of x into the equation to find y:

y = (-5/2)^2 + 5 * (-5/2) - 7

y = 25/4 - 25/2 - 7

y = 25/4 - 50/4 - 7

y = (25 - 50 - 28) / 4

y = -53 / 4

So, the vertex of the function is (-5/2, -53/4).

2. Solutions (or roots or x-intercepts):

To find the solutions (x-intercepts) of the function, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

Given: a = 1, b = 5, c = -7

x = (-5 ± √(5^2 - 4 * 1 * -7)) / 2 * 1

x = (-5 ± √(25 + 28)) / 2

x = (-5 ± √53) / 2

Now, we have two solutions:

x = (-5 + √53) / 2 ≈ 0.73

x = (-5 - √53) / 2 ≈ -5.73

So, the solutions of the function are approximately x ≈ 0.73 and x ≈ -5.73.

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Using the Fundamental Counting Theorem, it is found that there are 124 three-digit multiples of 5 that have three different digits and at least one prime digit.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

Multiples of 5 finish at 0 or 5, hence the parameters to find the number of three-digit multiples of 5, with different digits are:

[tex]n_1 = 9, n_2 = 8, n_3 = 2[/tex]

And the number is:

N = 9 x 8 x 2 = 144.

With no prime digits, 2, 3, 5 and 7 cannot be used, hence the parameters are:

[tex]n_1 = 5, n_2 = 4, n_3 = 1[/tex]

Hence 20 of the numbers have no prime digits, and 144 - 20 = 124 have at least one prime digit.

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The 7th term of an Arithmetic Progression 50+45+40 is 20

The Arithmetic Progression is given as:

50+45+40

In the above Arithmetic Progression, we have

First term, a= 50

Common difference, d = 45 - 50 = -5

The nth term of the Arithmetic Progression is calculated as:

Tn = a + (n - 1)d

Substitute the known values in the above equation

Tn = 50 + (n - 1) * -5

Substitute 7 for n in the above equation

Tn = 50 + (7 - 1) * -5

Evaluate the product

Tn = 50 - 30

Evaluate the difference

T7 = 20

Hence, the 7th term of an Arithmetic Progression 50+45+40 is 20

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Answer:

30°

Step-by-step explanation:

[tex]\frac{195-(8x+17)}{2}=5x-10 \\ \\ 178-8x=10x-20 \\ \\ 198=18x \\ \\ x=11[/tex]

So, this means arc FH measures 105 degrees.

Since the circumference of a circle measures 360 degrees, arc EF measures 60 degrees.

By the inscribed angle theorem, angle EHF measures 30°.

The Smith family's and Stewart family's sprinkler was used 40 and 25 hours.

According to the statement

we have given that the Smith family's sprinkler was 25L per hour and

Stewart family's sprinkler was 30L per hour and The families used their sprinklers for a combined total of 65 hours, resulting in a total water output of 1750L.

And we have to find the How long was each sprinkler used.

So, For this purpose,

The given statements in the equation form become:

Let Smith family's sprinkler be x

Let Stewart family's sprinkler be y then

The equation become

x + y = 65 -(1)

25x + 30y = 1750 -(2)

Here we use the elimination method.

So, Multiply (1) by 25 and (2) by 1 then

25x + 25y = 1625

25x + 30y = 1750

Now eliminate x from the equations then

-5y = -125

y = 25

then x value becomes

x + y = 65

x + 25 = 65

x = 40.

So, The Smith family's and Stewart family's sprinkler was used 40 and 25 hours.

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The number of strings that can be formed by ordering the letters SCHOOL using some or all of the letters is 1440 strings

Permutation can be defined as number of ways in which things can arranged.

We were given to find how many strings that can be formed by ordering the letters SCHOOL using some or all of the letters.

First of all, How many distinct letters are in the word SCHOOL ?

The distinct letters are 5 in numbers.

What is the total number of letters in the word SCHOOL ?

The total number of letters is 6.

Then

6! + 5[tex]P_{5}[/tex]

That is, 6 factorial + 6 permutation 5

( 6 x 5 x 4 x 3 x 2 x 1 ) + 6!/( 6 - 5)!

720 + 720

1440 strings

Therefore, the number of strings that can be formed by ordering the letters SCHOOL using some or all of the letters is 1440 strings

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Answer:

-

-

+

+

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

We are looking at the change in y over the change is x.  The change is y is always 0 and 0 divided by anything will be zero.

Answer:

Length = 52 ft

Width = 40 ft

Step-by-step explanation:

Given information:

Scale

[tex]\implies \sf 3 \: in : 8 \: ft[/tex]

[tex]\implies \sf 1 \: in : \dfrac{8}{3} \: ft[/tex]

To find the length and width of the studio in feet, multiply the length and width in inches by 8/3:

[tex]\sf Length = 19.5 \times \dfrac{8}{3}=52\:ft[/tex]

[tex]\sf Width = 15 \times \dfrac{8}{3}=40\:ft[/tex]

Therefore, the length of the actual studio is 52 ft and the width of the actual studio is 40 ft.

Scale is 3in:8ft

So

Length

Width

Answer:

12km/h

Step-by-step explanation:

s=d/t

900m is 0.9km and 4min and 30sec is 0.075h

0.9/0.075=12 which gives us 12km/h

Answer:

Step-by-step explanation:

4 min 30 seconds = 270 seconds

900m = 270 seconds

100m = 30 seconds

1000m= 300 seconds (5min)

12,000m=3600seconds (60min)

Answer = 12km/h

need help I don't know the answer

Answer: B. (-1, -5)

Step-by-step explanation:

Given equations

2x + y = -7

x - y = 4

Concept

[tex]A^{-1}=\frac{1}{ad-bc}\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex]

[tex]A*A^{-1}=A^{-1}*A=I~(Which~is~basically~1)[/tex]

Convert into matrix

[tex]\left[\begin{array}{ccc}2&1\\1&-1\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right]=\left[\begin{array}{ccc}-7\\4\\\end{array}\right][/tex]

Calculate the inverse of the matrix

[tex]A=\left[\begin{array}{ccc}2&1\\1&-1\\\end{array}\right][/tex]

[tex]A^{-1}=\frac{1}{ad-bc}\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex]

[tex]A^{-1}=-\frac{1}{3} \left[\begin{array}{ccc}-1&-1\\-1&2\\\end{array}\right][/tex]

Solve by multiplying the inverse of the matrix

[tex]A*A^{-1}=A^{-1}*A=I[/tex]

[tex]-\frac{1}{3} \left[\begin{array}{ccc}-1&-1\\-1&2\\\end{array}\right]\left[\begin{array}{ccc}2&1\\1&-1\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right]=-\frac{1}{3} \left[\begin{array}{ccc}-1&-1\\-1&2\\\end{array}\right]\left[\begin{array}{ccc}-7\\4\\\end{array}\right][/tex]

[tex]1*\left[\begin{array}{ccc}x\\y\\\end{array}\right]=-\frac{1}{3}\left[\begin{array}{ccc}3\\15\\\end{array}\right][/tex]

Simplify by multiplication

[tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right]=\left[\begin{array}{ccc}-1\\-5\\\end{array}\right][/tex]

Therefore, the answer is [tex]\Large\boxed{(-1,~-5)}[/tex]

Hope this helps!! :)

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The volume of the grain storage building is 3770. 4 m³

From the given question, it can be deduced that the grain storage is a combination of a cylinder and a cone

The volume of the grain storage = volume of the cone + the volume of the cone

The formula for finding the volume of a cylinder is given as;

Volume of cylinder = πr²h

But we know that radius is the diameter divided by 2

radius = 20/2

radius = 10 meters

height = 10 meters

Substitute the values in the formula

Volume of cylinder = 3. 142 × 10 × 10 × 10

Volume = 3. 142 × 1000

Volume = 3142 m³

The formula for finding the volume of a cone is given as;

Volume of cone = [tex]\pi r^2\frac{h}{3}[/tex]

If the cone has the same diameter, then the radius is 10 meters and the height is 6 meters

Substitute the values into the formula

Volume of the cone = 3. 142 × 10 × 10 × 6/ 3

Volume = 3. 142 × 100 × 2

Volume = 628. 4 m³

The volume of the grain storage building = 3142 + 628. 4

The volume of the grain storage building = 3770. 4 m³

Thus, the volume of the grain storage building is 3770. 4 m³

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Answer:

3770. 4 m³

Step-by-step explanation:

i took the test

The probability that the person is a man or heavy smoker is 621 / 1124.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0. The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.

The probability that the respondent is a man or heavy smoker can be determined by adding the probability that the respondent is a man and the probability that the respondent is a heavy smoker together.

The probability that the person is a man or heavy smoker = (number of men / total number of respondents) + (number of heavy smokers / total number of respondents)

(531 / 1124) + (90 / 1124) = 621 / 1124

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This shows that 76 cookies will be made with the total pounds of cookies

Fractions are written as a ratio of two integers. Given the following parameters

Total pounds of cookies made = 4 3/4 pounds

Total pounds of cookies made = 19/4 pounds

If he uses 1/16 pound of dough for each cookie, the total amount of cookies made is given;

Number of cookies = 19/4 ÷ 1/16

Number of cookies = 19/4 * 16/1

Number of cookies = 19 * 4

Number of cookies = 76

This shows that 76 cookies will be made with the total pounds of cookies

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The false statement is given by:

c. If b×b=c, then c is even integer.

Hence, since b is odd, b x b = c is odd, hence statement c is false.

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Since the cost of the renovation or overhauling of the existing line would be recovered in Year 4 and the NPV of the new production line is $-360,000, Crane Manufacturing should renovate.

Renovation restores an old asset to a better state.  Replacement rids the old in preference for a new asset.

When the two investment options are weighed, a better choice can be arrived at.

Year 1 = $93,324 ($280,000 x 33.33%)

Year 2 = $124,460 ($280,000 x 44.45%)

Year 3 = $41,468 ($280,000 x 14.81%)

Year 4 = $20,748  ($280,000 x 7.41%)

Total cost = $280,000

NPV of new production line = $-360,000

Thus, based on the cost recovery of the old production line and the negative NPV of the new production line, Crane Manufacturing should renovate.

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Should Crane replace or renovate the existing line?

Answer: [tex]a_n=12(-\frac{1}{2})^{n-1}[/tex]

Step-by-step explanation:

Let's first find the common ratio this sequence. To get to the next term, we divide by 2 and we alternate signs. Hence, the common ratio is [tex]-\frac{1}{2}[/tex].

We can now use the formula [tex]a_n=a_1(r)^{n-1}[/tex] to get the formula, where [tex]a_1[/tex] is the first term and r is the common ratio.

[tex]a_n=a_1(r)^{n-1}\\a_n=12(-\frac{1}{2})^{n-1}[/tex]

One second later, the distance between the two stones will change in a speed of 6.86 m/s

Distance can be defined as the length of change of position. When an object change from one position to another, the length between the points or position is known as distance.

If a dropped stone has a distance d = 4.9t²

Let us assumed that the time taken = 3 seconds

The distance d = 4.9 × 3² = 44.1 m

If another stone is dropped one second later, then the time t = 4 s

The distance = 4.9 × 4² = 78.4 m

One second later, the time = 5 seconds

The speed of change in distance = ( 78.4 - 44.1 )/ 5

The speed of change in distance = 34.3 / 5

The speed of change in distance = 6.86 m/s

Therefore, one second later, the distance between the two stones will change in 6.86 m/s

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The company's inventory turnover ratio, based on the financial data, equals 10 times.

The inventory turnover ratio measures the number of times the company sells and replaces its inventory over a given period.

The formula for calculating the Inventory Turnover Ratio is the Cost of Goods Sold divided by the Average Inventory.

The Average Inventory is the mean of the beginning and ending inventories.

Sales revenue = $60,000

Cost of goods sold = $20,000

Beginning inventory = $1,600

Ending inventory = $2,400

Average inventory = $2,000 ($1,600 + $2,400)/2

Inventory turnover ratio = 10x ($20,000/$2,000)

Thus, the company sells and replaces its inventory over a period of 10 times.

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The option that is a proportion is: B. 4/6 = 2/3.

A proportion can be defined as an equation whereby two ratios are set equal to each other, in such a way that the ratio on one side equals the ratio on the other side of the equation when simplified.

First Option is not a proportion because:

5/7 ≠ 10/12 (10/12 can be simplified further as 5/6, which is not equal to 5/7).

Second option is a proportion because:

4/6 = 2/3

8/12 = 2/3

Thus, 4/6 = 8/12.

Third Option is not a proportion because:

14/21 = 2/3

9/12 = 3/4

Therefore, 14/21 ≠ 9/12.

Fourth Option is not a proportion because:

9/15 = 3/5

12/18 = 2/3

Therefore, 9/15 ≠ 12/18.

In conclusion, the option that is a proportion is: B. 4/6 = 2/3.

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The number of license plates is 11232000

The given parameters are:

Characters = 6 i.e. 3 letters and 3 digits

Letters = 3 different letters

Digits = 3 different digits

There are 10 different digits and 26 different letters.

Since each character is different from the other, then we have:

Digits = 10, 9 and 8

Characters = 26, 25 and 24

The number of license plates is then calculated as:

n = 10 * 9 * 8 * 26 * 25 * 24

Evaluate the product

n = 11232000

Hence, the number of license plates is 11232000

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Answer:

[tex]x^{2}+\frac{1}{2} x + \frac{33}{16}= 2 + (x + \frac{1}{4})^2[/tex]

Step-by-step explanation:

[tex]x^{2}+\frac{1}{2} x=x^{2}+2 \times \frac{1}{4} \times x +(\frac{1}{4})^2 - (\frac{1}{4})^2[/tex]

[tex]=[x^{2}+2 \times \frac{1}{4} \times x +(\frac{1}{4})^2] - (\frac{1}{16})[/tex]

[tex]=[x + \frac{1}{4}]^2 - (\frac{1}{16})[/tex]

____________________

then

[tex]x^{2}+\frac{1}{2} x = [x + \frac{1}{4}]^2 - (\frac{1}{16}) -2 + 2[/tex]

then

[tex]x^{2}+\frac{1}{2} x = [(x + \frac{1}{4})^2 - (\frac{1}{16}) -2] + 2[/tex]

then

[tex]x^{2}+\frac{1}{2} x = [(x + \frac{1}{4})^2 - (\frac{33}{16}) ] + 2[/tex]

then

[tex]x^{2}+\frac{1}{2} x = (x + \frac{1}{4})^2 - \frac{33}{16} + 2[/tex]

then

[tex]x^{2}+\frac{1}{2} x + \frac{33}{16}= (x + \frac{1}{4})^2 + 2[/tex]

then

[tex]x^{2}+\frac{1}{2} x + \frac{33}{16}= 2 + (x + \frac{1}{4})^2[/tex]

The rat population is 2004 and 2012 are 24. 8 millions and 31. 6 millions respectively.

Given the function of the population to be;

n (t) = 24 e^0. 015t

Where;

In 2004, t = 1

Substitute into the formula;

n(1) = 24 e^0. 015t

n(1) = 24 e^(0.015 × 1)

n(1) = 24 e^0. 015

n(1) = 24. 8 millions

In year 2012, t = 8

n(8) = 24 e^(0. 015 × 8)

n(8) = 24e^0. 12

n(8) = 31. 6 millions

Thus, the rat population is 2004 and 2012 are 24. 8 millions and 31. 6 millions respectively.

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Answer:

x = -7

x = 5

Step-by-step explanation:

The standard form of quadratic equations is

Ax^2 + Bx + C = 0

The factors need to multiply together to be C and add together to be B.

The two numbers that will multiply together to be -35 and add together to be 2 are -5 & 7.

The factor pairs are (x+7)(x-5). Zero product property means we set each of those factor pairs = 0 and solve.

x + 7 = 0

-7 -7 Subtract 7 from each side to solve

x = -7

x - 5 = 0

+5 +5 Add 5 to each side to solve

x = 5

To solve the equation, factor x²+2x−35 use the formula x² +(a + b) x + ab = (x + a)(x + b). To find a and b, set up a system to be solved.

a + b = 2

ab = −35

Since ab is negative, a and b have opposite signs. Since a+b is positive, the positive number has a greater absolute value than the negative. Show all pairs of integers whose product is −35.

Calculate the sum of each pair.

The solution is the pair that gives sum 2.

Rewrite the factored expression (x + a)(x + b) with the values obtained.

To find solutions to equations, solve x−5=0 and x+7=0.

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Answer:

233.35488 km (Rounded to 233 km)

Step-by-step explanation:

If you convert miles to kilometers then you would use this conversion factor:

1 mile = 1.609344 km (or 1.61 km)

so in this case,

145 mile = 1.609344 km x 145

145 mile = 233.35488 km

I could also round it to 233 km.

Since your on a trip... i hope u enjoy ur journey to Las Vegas!

The solution to the following equations is given below;

y - 6 = 12

y = 12 + 6

y = 18

-5 + k = 1

k = 1 + 5

k = 6

-2g = -14

g = -14/-2

g = 7

y - 4 = 12

y = 12 + 4

y = 16

12 + u = -12

u = -12 - 12

u = -24

f - 7 = 10

f = 10 + 7

f = 17

8t = 42

t = 42/8

t = 5.25

-9 + z = 18

z = 18 + 9

z = 27

7 + w = 14

w = 14 - 7

w = 7

13 - 5 = 12

8 ≠ 12

D - 2 = -10

D = -10 + 2

D = -8

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The formula for the nth term of the arithmetic sequence is [-3]n+10

What is the nth term of an arithmetic sequence?

⇒ The general form of the nth term of an arithmetic sequence is

an = a1 + (n - 1)d

Where,

a1 - first term

n - number of terms in the sequence

d - the common difference

Calculation:

It is given that the given sequence is an arithmetic sequence.

First term a1 = 7

Second term a2 = 4

Common difference d = 4-7

⇒ d=3

From the general formula,

an = a1 + (n - 1)d

On substituting,

an = 7+ (n-1)(-3)

an = 7-3n+3

an = -3n+10

⇒ Thus the general formula for the nth term of the arithmetic sequence  is -3n+10

an= [-3]n+10

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