A recent article in a university newspaper claimed that the proportion of students who commute more than miles to school is no more than . Suppose that we suspect otherwise and carry out a hypothesis test. State the null hypothesis and the alternative hypothesis that we would use for this test.

Answer:

H0 : σ²=10²

H1 : σ²>10²

χ² = 45.796

Pvalue = 0.2442

Do not reject H0 because Pvalue is greater Than significance level

There is insufficient evidence to warrant rejection of the claim that the standard deviation of​ men's pulse rates is equal to 10 beats per minute.

Step-by-step explanation:

Given that :

Sample size, n = 41

Sample standard deviation, s = 10.7

Population standard deviation, σ = 10

Significance level, α = 0.10

The Hypothesis :

H0 : σ²=10²

H1 : σ²>10²

Using the χ² test for population variance :

The test statistic, χ² = (n-1)*s²/σ²

χ² = (41 - 1) * 10.7²/ 10²

χ² = (40 * 114.49) / 100

χ² = 4579.6 / 100

χ² = 45.796

The Pvalue ;

df = n - 1 ; 41 - 1 = 40

Pvalue(45.796, 40) = 0.2442

Since Pvalue > α ; WE fail to reject H0

Do not reject H0 because Pvalue is greater Than significance level

There is insufficient evidence to warrant rejection of the claim that the standard deviation of​ men's pulse rates is equal to 10 beats per minute.

Answer:

6.5%

Step-by-step explanation:

sales price x sales tax rate = sales tax

156.50 x sales tax rate = 10.17

sales tax rate = 10.17/156.50

sales tax rate = .065 or 6.5%

What we need to memorize when finding the slope is this formula:

[tex] \displaystyle \large{m = \frac{y_2 - y_1}{x_2 - x_1} }[/tex]

m here represents the slope. I hope this does not confuse you with line m.

The problem here is that we do not have any given points, but we have a way.

If we notice on the graph, the graph contains or passes through (2,-1) and (-2,1). We can use these points to find the slope. So let these be the following:

[tex] \displaystyle \large{(x_1,y_1) = (2 ,- 1)} \\ \displaystyle \large{(x_2,y_2) = ( - 2 ,1)} [/tex]

Then we substitute these points in the formula.

[tex] \displaystyle \large{m = \frac{ 1 - ( - 1)}{ - 2 - 2} }[/tex]

negative × negative = positive.

[tex] \displaystyle \large{m = \frac{ 1 + 1}{ - 2 - 2} } \\ \displaystyle \large{m = \frac{ 2}{ - 4} } \longrightarrow \boxed{m = - \frac{1}{2} }[/tex]

Since m represents the slope. Therefore, the slope of line m is -1/2

Answer:

4

Step-by-step explanation:

First, we can take two triangles -- one with 2 as a side and the big one. Literally every side of the triangle with the 2 in it is parallel to its corresponding side the big triangle. Therefore, we can say that the two triangles are similar.

In similar triangles, we can say that the ratios of corresponding sides are the same. Let's say that the bottom side of the big triangle is x, and the question mark is y. Therefore, the hypotenuse of the big triangle is 6+y. Furthermore, the ratio of corresponding sides ((6+y)/y and x/2) are equal, so

(6+y)/y = x/2

Since x is clearly made up of 3 and 2, we can say 3+2=x=5

(6+y)/y = 5/2

multiply both sides by y to remove a denominator

6+y = 5*y/2

multiply both sides by 2 to remove the other denominator

12+2y = 5*y

subtract both sides by 2y to isolate the y and its coefficient

12 = 3y

divide both sides by 3 to isolate the y

y=4

Answer:

The correct answer is the letter C.

Step-by-step explanation:

We can use the following trigonometric identity:

[tex]cos(60)=\frac{6}{b}[/tex] (1)

[tex]cos(45)=\frac{c}{b}[/tex] (2)

Solving each equation by b and equaling we have:

[tex]\frac{6}{cos(60)}=\frac{c}{cos(45)}[/tex]

[tex]\frac{6}{cos(60)}=\frac{c}{cos(45)}[/tex]

Let's recall that:

[tex]cos(45)=\frac{1}{\sqrt{2}}[/tex]

[tex]cos(60)=\frac{1}{2}[/tex]

Then we have:

[tex]c=\frac{cos(45)*6}{cos(60)}[/tex]

[tex]c=\frac{2*6}{\sqrt{2}}[/tex]

[tex]c=\frac{12}{\sqrt{2}}[/tex]

[tex]c=6\sqrt{2}[/tex]

Using equation (1) we can find b.

[tex]cos(60)=\frac{6}{b}[/tex]  

[tex]b=12[/tex]      

Finally, we can find a using the next equation:

[tex]tan(60)=\frac{a}{6}[/tex]

[tex]a=6*tan(60)[/tex]

[tex]a=6\sqrt{3}[/tex]

Therefore, the correct answer is the letter C.

I hope it helps you!

Answer:

opposite angles

Step-by-step explanation:

They are formed in the intersection of lines AD and BD.

Answer:

opposite angles

Step-by-step explanation:

they are formed in the intersection of lines AD and BD. two figures are called similar if they have same shape however have different size.

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Answer:

  Tn = -4n² +40n +36

Step-by-step explanation:

A graphing calculator readily performs the quadratic regression, yielding the formula ...

  Tn = -4n² +40n +36

__

The first and second differences of the given sequence terms are ...

  28, 20, 12 and -8, -8

The coefficient of the squared term is half the second difference, so is -4. Then the sequence of squared terms is -4n²:

  -4, -16, -36, -64

Subtracting these values from the original sequence gives the linear sequence ...

  76, 116, 156, 196

which has first term 76 and common difference 40. The equation for the n-th term of this is ...

  an = 76 +40(n -1) = 36 +40n

Adding this linear sequence to the sequence of squared terms, we get ...

  Tn = -4n² +40n +36

Answer:

Im pretty sure its 1,000 miles (dont forget the unit)

Step-by-step explanation:

Determine if this problem is a inverse variation or direct variation problem! This means that:

equation would be:

1=40

25=x

cross multiply*

x=25*40

x=1,000 miles apart! (dont forget the unit)

If this doesnt work then try this equation!

1=40

25=x

Multiply 1*40 and 25 *x

40=25x......    

40/25= 1.6

x=1.6! (Extra step)

Cheers!

Answer: 100 Miles

Step-by-step explanation: took the miles and got it correct.

(Also it's 2.5 inches apart, not 25.)

Answer:

340 cars at $ 34 should be rented to produce the maximum income of $ 11,560.

Step-by-step explanation:

Given that a car rental agency rents 480 cars per day at a rate of $ 20 per day, and for each $ 1 increase in rate, 10 fewer cars are rented, to determine at what rate should the cars be rented to produce the maximum income and what is the maximum income, the following calculations must be performed:

480 x 20 = 9600

400 x 28 = 11200

350 x 33 = 11550

300 x 38 = 11400

310 x 37 = 11470

320 x 36 = 11520

330 x 35 = 11550

340 x 34 = 11560

Therefore, 340 cars at $ 34 should be rented to produce the maximum income of $ 11,560.

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Answer:

  $19.36

Step-by-step explanation:

Any average is the sum of numbers, divided by the number of them.

Here, the numbers are grouped, but the computation of the average works the same way.

The total value of donations received is ...

  $100×10 +$50×20 +$20×30 +$10×100 +$5×35

  = $1000 +1000 +600 +1000 +175 = $3775

The total number of donations received is ...

  10 +20 +30 +100 +35 = 195

Then the average (mean) donation is the total value divided by the total number ...

  $3775/195 ≈ $19.35897 ≈ $19.36 . . . mean donation

Answer:

15.56

Step-by-step explanation:

Given the vectors ||u|| = 5√2 units, and ||v|| = 6√2 units.

||u + v|| ≈  5√2 +  6√2

||u + v|| ≈  (5+6)√2

Since √2≈ 1.4142

||u + v|| ≈   11(1.4142)

||u + v|| ≈  15.56

Hence the correct option is D

Answer: 11.05

Step-by-step explanation: got it right

Answer:

[tex]-32^\frac{3}{5} = -8[/tex]

Step-by-step explanation:

Given

[tex]-32^\frac{3}{5}[/tex]

Required

The equivalent expression

We have:

[tex]-32^\frac{3}{5}[/tex]

Rewrite as:

[tex]-32^\frac{3}{5} = (-32)^\frac{3}{5}[/tex]

Expand

[tex]-32^\frac{3}{5} = (-2^5)^\frac{3}{5}[/tex]

Remove bracket

[tex]-32^\frac{3}{5} = -2^\frac{5*3}{5}[/tex]

[tex]-32^\frac{3}{5} = -2^3[/tex]

[tex]-32^\frac{3}{5} = -8[/tex]

Answer:

24cm

Step-by-step explanation:

Question: Find the length of side OR.

Answer + explanation:

24cm

Since PQ = 24 cm, OR = 24 cm because they're paralleled and congruent!

Answer:

<O = 125

OR = 24

Step-by-step explanation:

consecutive angles are supplementary in a parallelogram

<R + <O = 180

55 + <O =180

<O = 180-55

< O = 125

opposite sides are congruent in a parallelogram

PQ = OR = 24

Answer:

true

Step-by-step explanation:

because some of x if x=3 then 3<6 is true

Answer:

-3; 1

Step-by-step explanation:

y-intercept is when x = 0

y = -4(0.3)^0 + 1

anything to the power of 0 is 1

y = -4(1) + 1

y = -4 + 1

y = -3

The asymptote of an exponential function is the vertical translation which in this case is 1

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Answer:

  a) quadrant III

  b) 4π/3, -2π/3

  c) (1/2, (√3)/2)

  d) ((√3)/2, -1/2

Step-by-step explanation:

a) The attachment shows the point P and the numbering of the quadrants (in Roman numerals). Point P lies in quadrant III.

__

b) Measured counterclockwise, the angle to point P is 240° or 4π/3 radians. Measured clockwise, the angle is -120° or -2π/3 radians. In the diagram, these are shown in green and purple, respectively.

__

c) Adding π/2 to the angle 4π/3 or -2π/3 brings it to 11π/6, or -π/6. This point is marked as P' (blue) on the diagram. The coordinate transformation for π/2 radians CCW rotation is ...

  (x, y) ⇒ (-y, x)

  P(-1/2, -√3/2) ⇒ P'(√3/2, -1/2)

In terms of trig functions, the coordinates of the rotated point are ...

  P'(cos(-π/6), sin(-π/6)) = P'(√3/2, -1/2)

__

d) Adding or subtracting π radians to/from the angle moves it directly opposite the origin. Both coordinates change sign. This point is P'' (red) on the diagram.

Answer:

20

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

count up from -5 to -1

so -5,-4,-3,-2,-1 and there are four numbers excluding-5

Answer:

y = 11/20

Step-by-step explanation:

-4/5 + y = -1/4

Add 4/5 to each side

-4/5  +4/5 + y = -1/4+4/5

y = -1/4 + 4/5

Get a common denominator

y = -1/4 *5/5   + 4/5 *4/4

y = -5/20 + 16/20

y = 11/20

Check

-4/5 +11/20 = -1/4

Get a common denominator

-4/5*4/4 + 11/20 = -1/4*5/5

-16/20 +11/20 = -5/20

-5/20 = - 5/20

Check

Step-by-step explanation:

[tex] - \frac{4}{5} + y = - \frac{1}{4} \\ y = \frac{ - 1}{4} + \frac{4}{5} \\ y = \frac{ - 5 + 16}{20} \\ y = \frac{11}{20} [/tex]

[tex]y = \frac{11}{20} [/tex]

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Answer:

  a. Definition of bisector.

Step-by-step explanation:

Line l is a line through the midpoint M. We can conclude it is a bisector, because, by definition, a bisector is a line through the midpoint.

The conclusion is justified by the definition of a bisector.

Answer:draw a triangle

Step-by-step explanation:

Answer:

A. Q1 = 4.6; Q2 = 5.5; Q3 = 5.95

Step-by-step explanation:

{4.3, 4.5, 4.7, 5, 5.5, 5.7, 5.9, 6, 6.1}

First find the median or the 2nd quartile

There are 9 data points so the middle is the 5th

4.3, 4.5, 4.7, 5,     5.5,     5.7, 5.9, 6, 6.1}

Q2 = 5.5

Now looking at the data on the left, we need to find the middle, which is Q1 or the first quartile

4.3, 4.5     , 4.7, 5,

It is between 4.5 and 4.7 so we average

(4.5+4.7)/2 = 9.2/2 = 4.6

Q1 is 4.6

We do the same for the data on the right, which is the third quartile or Q3

5.7, 5.9,  6, 6.1

(5.9+6)/2 = 11.9/2 = 5.95

Q3 = 5.95

Answer: IT'S A !!

Step-by-step explanation:

Step-by-step explanation:

The answer is mentioned above.

Answer:

search up the formula

Step-by-step explanation:

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Answer:

  d) 10.38%

Step-by-step explanation:

The multiplier for four quarters of quarterly compounding is ...

  (1 +10%/4)^4 = 1.025^4 = 1.103812890625

This is about 1 + 10.38%.

The effective rate of interest is about 10.38% per annum.

Answer:

So, remember that:

cos(x) > 0   for  -pi/2 < x < pi/2

cos(x) < 0 for  pi/2 < x < (3/2)*pi

and

sin(x) > 0 for 0 < x < pi

sin(x) < 0 for -pi < x <0  or  pi < x < 2pi

Also, we have the periodicty of the sine and cocine equations, such that:

sin(x) = sin(x + 2pi)

cos(x) = cos(x + 2pi)

Now let's solve the problem:

[tex]sin(\frac{13*\pi}{36} )[/tex]

here we have:

x = (13/36)π

This is larger than zero and smaller than π:

0 < (13/36)π < π

then:

[tex]sin(\frac{13*\pi}{36} )[/tex]

Is positive.

The next one is:

[tex]cos(\frac{7*\pi}{12} )[/tex]

Here we have x = (7/12)*pi

notice that:

7/12 > 1/2

Then:

(7/12)*π > (1/2)*π

Then:

[tex]cos(\frac{7*\pi}{12} )[/tex]

is negative.

next one:

[tex]sin(\frac{47*\pi}{36} )[/tex]

here:

x = (47/36)*π

here we have (47/36) > 1

then:

(47/36)*π > π

then:

[tex]sin(\frac{47*\pi}{36} )[/tex]

is negative.

the next one is:

[tex]cos(\frac{17*\pi}{10} )[/tex]

Here we have x = (17/10)*π

if we subtract 2*π (because of the periodicity) we get:

(17/10)*π - 2*π

(17/10)*π - (20/10)*π

(-3/10)*π

this is in the range where the cosine function is positive, thus:

[tex]cos(\frac{17*\pi}{10} )[/tex]

is positive.

the next one is:

[tex]tan(\frac{41*\pi}{36} ) = \frac{sin(\frac{41*\pi}{36} )}{cos(\frac{41*\pi}{36} )}[/tex]

here we have:

x = (41/36)*π

Notice that both functions, sine and cosine are negatives for that value, then we have the quotient of two negative values, so:

[tex]tan(\frac{41*\pi}{36} ) = \frac{sin(\frac{41*\pi}{36} )}{cos(\frac{41*\pi}{36} )}[/tex]

is positive.

The final one is:

[tex]tan(\frac{5*\pi}{9} ) = \frac{sin(\frac{5*\pi}{9} )}{cos(\frac{5*\pi}{9} )}[/tex]

Here:

x = (5/9)*π

The sin function is positive with this x value, while the cosine function is negative, thus:

[tex]tan(\frac{5*\pi}{9} ) = \frac{sin(\frac{5*\pi}{9} )}{cos(\frac{5*\pi}{9} )}[/tex]

Is negative.

Answer:

C

Step-by-step explanation:

The equation that described the graph is x<-5

Answer:

No, because the ratio of pay to hours is not the same for each pair of value.