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Answer:

The null hypothesis is [tex]H_0: \mu = 16.1[/tex].

The alternate hypothesis is [tex]H_1: \mu < 16.1[/tex]

Step-by-step explanation:

A manufacturer claims that the mean amount of juice in its bottles is 16.1 ounces.

This means that at the null hypothesis, we test if the mean amount of juice is of 16.1, as claimed, that is:

[tex]H_0: \mu = 16.1[/tex]

A consumer advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this.

This means that at the alternate hypothesis, we test if the mean amount of juice is less than the claimed mean of 16.1 ounces. So:

[tex]H_1: \mu < 16.1[/tex]

Answer:

[tex]y=-3x-8[/tex]

Step-by-step explanation:

Hi there!

What we need to know:

1) Determine the midpoint of the line segment

When two lines bisect each other, they intersect at the middle of each line, or the midpoint.

[tex](\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex]

Plug in the endpoints (5, -3) and (-7, -7)

[tex](\frac{5+(-7)}{2} ,\frac{-3+(-7)}{2} )\\(\frac{-2}{2} ,\frac{-10}{2} )\\(-1,-5)[/tex]

Therefore, the midpoint of the line segment is (-1,-5).

2) Determine the slope of the line segment

Recall that the slopes of perpendicular lines are negative reciprocals. Doing this will help us determine the slope of the perpendicular bisector.

Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] where the given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the endpoints (5, -3) and (-7, -7)

[tex]\frac{-7-(-3)}{-7-5}\\\frac{-7+3}{-7-5}\\\frac{-4}{-12}\\\frac{1}{3}[/tex]

Therefore, the slope of the line segment is [tex]\frac{1}{3}[/tex]. The negative reciprocal of [tex]\frac{1}{3}[/tex] is -3, so the slope of the perpendicular is -3. Plug this into [tex]y=mx+b[/tex]:

[tex]y=-3x+b[/tex]

3) Determine the y-intercept of the perpendicular bisector (b)

[tex]y=-3x+b[/tex]

Recall that the midpoint of the line segment is is (-1,-5), and that the perpendicular bisector passes through this point. Plug this point into [tex]y=-3x+b[/tex] and solve for b:

[tex]-5=-3(-1)+b\\-5=3+b[/tex]

Subtract 3 from both sides

[tex]-5-3=3+b-3\\-8=b[/tex]

Therefore, the y-intercept of the line is -8. Plug this back into [tex]y=-3x+b[/tex]:

[tex]y=-3x-8[/tex]

I hope this helps!

Answer:

B. 49

Step-by-step explanation:

f(7) = 7² = 49

_______

Answer:

0.24

Step-by-step explanation:

Convert [tex]\frac{6}{25}[/tex] into decimal

which will give 0.24

Answer:

0.279

0.613

-0.44

Step-by-step explanation:

The Zscore that seperates the middle 22% of the distribution ; could be obtained thus. The midpoint is the mean and the probability to either the right or left could be obtained.

To obtain the Zscore that seperates the middle 22% is equivalent to :

The probability to the left of the distribution :

P(x < (0.5 + 0.22/2) = p(x < 0.61)

Using the Z probability calculator :

P(x < 0.61) is equivalent to a Zscore of 0.279

α = 0.27

Z(1 - α) = Z(1 - 0.27) = Z0.73 = p(Z < 0.73) = 0.613

P(x < 0.33) = - 0.44 (Z probability calculator)

Answer:

C = 69.12 in.

A = 380.13 in.²

Step-by-step explanation:

Circumference of a circle is the length around the circle.

Circumference, C = 2πr

where,

Radius (r) = 11 in. (Given)

To find the circumference, substitute r = 11 into the circumference formula

C = 2*π*11

Input this into your calculator, you would get:

C = 69.1150384

C = 69.12 in. (Approximated to nearest hundredth)

Area = πr²

Plug in the value of r

A = π*11²

A = 380.132711

A = 380.13 in.² (to nearest hundredth)

Answer:

Mean = 31.22

Midrange = 28.50

Geometric mean = 28.74

Trimmed mean = 31.56

Step-by-step explanation:

Given the data :

39 41 25 17 48 29 31 17 24 36 17 24 40 38 42 11 43 47 27 25 17 23 43 20 32 48 26 26 9 46 44 44

Ordered data :

9, 11, 17, 17, 17, 17, 20, 23, 24, 24, 25, 25, 26, 26, 27, 29, 31, 32, 36, 38, 39, 40, 41, 42, 43, 43, 44, 44, 46, 47, 48, 48

The mean, xbar :

Xbar = Σx / n = 999 / 32 = 31.22

The midrange : (maximum - minimum) / 2

Midrange = (48 + 9) / 2 = 57 / 2 = 28.5

Geometric mean :

(x1*x2*.. xn)^1/n

Geometric mean = (x1*x2*.. xn)^1/32 = 28.74

24% trimmed mean :

24% of 32 = 0.24 * 32 = 7.68 ; this mean cutting off 8 values from the top and bottom and calculating the mean of the remaining values.

Data left :

24, 24, 25, 25, 26, 26, 27, 29, 31, 32, 36, 38, 39, 40, 41, 42

Σx / n = 505 / 16 = 31.5625

Trimmed mean = 31.56

Answer:

D 41

Step-by-step explanation:

remember, the sum of all angles in a triangle is always 180 degrees.

so, we have already 35 for one angle, that leaves 145 for the other two.

x + 2 + 2x + 20 = 145

3x + 22 = 145

3x = 123

x = 41

Answer:

yes 8x is a coefficient

Step-by-step explanation:

because I know but if I'm wrong than sry

Answer:

z₁(s)  = - 1.53

Step-by-step explanation:

a)  Value of  z   or   z₁(s)   area to the right is .9370

 1  -  0.9370  =  0.063

Then if area to the left is   0.063     z₁(s)  = - 1.53

Answer:

C)Systematic Random Sample

Step-by-step explanation:

Samples may be classified as:

Convenient: Sample drawn from a conveniently available pool.

Random: Basically, put all the options into a hat and drawn some of them.

Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.

Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.

Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.

In this case:

Every kth element(in this exercise 10th) is systematic sample. So the answer is given by option c.

Answer:

1/3

Step-by-step explanation:

Probability is the ratio of the number of possible outcome to the number of total outcome. On a fair die, the number are 1 to 6 while 1 and 2 are the only numbers less than 3.

Hence the odds of getting  a number is the ratio of 6 to 6 while the odds of getting a number lower than 3 will be

= 2/6

= 1/3 (in the lowest term)

This is because the odd of getting 1 is 1/6 and the odd of hetting 2 is 1/6 9 recall that both numbers appear once on a die). Hence the odd of getting 1 or 2 will be

= 1/6 + 1/6

= 2/6

=1/3

Answer:

No solution

Step-by-step explanation:

see the steps below:)

9514 1404 393

Answer:

  60 cm²

Step-by-step explanation:

The lateral surface area is the area of the four blue triangles. Each one has an area of ...

  A = 1/2bh

  A = 1/2(6 cm)(5 cm) = 15 cm²

The lateral surface area is 4 times the area of one triangle, so is ...

  LA = 4(15 cm²) = 60 cm²

9514 1404 393

Answer:

  3.  (x, y) = (-1, -2)

  4.  (x, y) = (-8, 6)

Step-by-step explanation:

The equations are graphed in the attachments.

3. The equations of problem 3 are easily graphed using the slope and intercept. The second equation is ...

  y = 2x

when solved for y.

__

4. The equations of problem 4 may be more easily graphed using the x- and y-intercepts. These are found by dividing the constant by the coefficients of x and y, respectively. Once the intercepts are plotted, a line can be drawn through them to make the graph of the equation.

Answer:

78 slices

Step-by-step explanation:

195/2.5=78

Answer:

78

Step-by-step explanation:

195/2.5=78

he will need to sell 78 pizzas in order to get $195

Answer:

d=2

Step-by-step explanation:

8(d+2)-36=2+6(1-d)

Expand the equation

8d+16-36=2+6-6d

Put like terms together

8d+6d = 2+6-16+36

14d= 28

Divide 14 on both sides to get the value of d

[tex] \frac{14d}{14} = \frac{28}{14} [/tex]

d=2

Answer:

96

Step-by-step explanation:

Answer:

114

Step-by-step explanation:

angle one is vertical opposite angle and also angle on a straight line

Answer:

1) 1/3   2a)2/5  2b)1/2  2c)9/20

Step-by-step explanation:

1) A fair die has 6 sides (1,2,3,4,5,6) so there are 2 sides that are greater than 4. Probability is chance of occurance/total chances so 2/6 which simplifies to 1/3

2) The set is (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19, 20) The prime numbers in that set are (2,3,5,7,11,13,17,19)

a)So the probability that a prime number is picked is 8/20 which simplifies to 2/5

b) The odd numbers are (1,3,5,7,9,11,13,15,17,19) so probability of odd is 10/20 which simplifies to 1/2

c) The single digit numbers are (1,2,3,4,5,6,7,8,9) so the probability is 9/20

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Work Shown:

Use the tangent ratio

tan(angle) = opposite/adjacent

tan(B) = AC/AB

tan(61) = AC/1

tan(61) = AC

AC = tan(61)

AC = 1.80404775527142

AC = 1.8

The river is about 1.8 miles wide between points A and C.

Make sure your calculator is in degree mode. One way to check is to type in tan(45) and you should get 1.

Answer:

[tex]Pr(Odd\ or\ <4) = \frac{2}{3}[/tex]

Step-by-step explanation:

Given

[tex]S = \{1,2,3,4,5,6\}[/tex] --- roll of a die

[tex]n(S) = 6[/tex] ---- the sample size

[tex]Odd = \{1,3,5\}[/tex]

[tex]<4 = \{1,2,3\}[/tex]

Required

[tex]Pr(Odd\ or\ <4)[/tex]

First, list out the event of odd or <4

[tex]Odd\ or\ <4 = \{1,2,3,5\}[/tex]

So, the probability is:

[tex]Pr(Odd\ or\ <4) = \frac{n(Odd\ or\ <4)}{n(S)}[/tex]

[tex]Pr(Odd\ or\ <4) = \frac{4}{6}[/tex]

Simplify

[tex]Pr(Odd\ or\ <4) = \frac{2}{3}[/tex]

Answer:

Step-by-step explanation:

cosine W=9/41

Answer:

cos W = [tex]\frac{9}{41}[/tex]

Step-by-step explanation:

cos W = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{WY}{XW}[/tex] = [tex]\frac{9}{41}[/tex]

Answer:

Hello! answer: 585

Step-by-step explanation:

This polygon can be split into 6 triangles so all you have to do is find the area of 1 then multiply by 6 to get the whole things area so...

15 × 13 = 195 195 ÷ 2 = 97.5 97.5 × 6 = 585 therefore the area is 585 hope that helps you!

Answer:

A non-equilateral rhombus.

Step-by-step explanation:

We can solve this graphically.

We start with square:

ABCD

with:

A = (11, - 7)

B = (9, - 4)

C = (11, - 1)

D = (13, - 4)

Only with the vertices, we can see that ABCD is equilateral, as the length of each side is:

AB = √( (11 - 9)^2 + (-7 -(-4))^2) = √( (2)^2 + (3)^2) = √(4 + 9) = √13

BC =  √( (11 - 9)^2 + (-1 -(-4))^2) = √13

CD =  √( (11 - 13)^2 + (-1 -(-4))^2)  = √13

DA =  √( (11 - 13)^2 + (-7 -(-4))^2) = √13

And we change C by C' = (11, 1)

In the image you can see the 5 points and the figure that they make:

The figure ABCD is a rhombus, and ABC'D is also a rhombus, the only difference between the figures is that ABCD is equilateral while ABC'D is not equilateral.

Answer:

2+4+5 = 11. since there are 5 green marbles the answer is 5/11