Harriet spins this 6 colour spinner and flips a coin.

What is the probability of getting grey and tails?

Answer:

Step-by-step explanation:

The question is incomplete. The complete question is

Coaching companies claim that their courses can raise the SAT scores of high school students. But students who retake the SAT without paying for coaching also usually raise their scores. A random sample of students who took the SAT twice found 427 who were coached and 2733 who were uncoached. Starting with their verbal scores on the first and second tries, we have these summary statistics:

Try 1 Try 2 Gain

n x s x s x s

Coached 427 500 92 529 97 29 59

Uncoached 2733 506 101 527 101 21 52

Use Table C to estimate a 90% confidence interval for the mean gain of all students who are coached.

at 90% confidence.

Now test the hypothesis that the score gain for coached students is greater than the score gain for uncoached students. Let μ1 be the score gain for all coached students. Let μ2 be the score gain for uncoached students.

(a) Give the alternative hypothesis:

μ1 - μ2.

(b) Give the t test statistic:

(c) Give the appropriate critical value for \alpha =5%:

Solution:

The formula for determining the confidence interval for the difference of two population means is expressed as

Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)

Where

x1 = sample mean score gain for all coached students

x2 = sample mean score gain for all uncoached students

s1 = sample standard deviation score gain of coached students

s2 = sample standard deviation score gain of uncoached students

For a 90% confidence interval, the z score is 1.645

From the information given,

x1 = 29

s1 = 59

n1 = 427

x2 = 21

s2 = 52

n2 = 2733

x1 - x2 = 29 - 21 = 8

z√(s1²/n1 + s2²/n2) = 1.645√(59²/427 + 52²/2733) = 4.97

90% Confidence interval = 8 ± 4.97

a) The population standard deviations are not known. it is a two-tailed test. The random variable is μ1 - μ2 = difference in the score gain for coached and uncoached students.

We would set up the hypothesis.

The null hypothesis is

H0 : μ1 = μ2 H0 : μ1 - μ2 = 0

The alternative hypothesis is

H1 : μ1 > μ2 H1 : μ1 - μ2 > 0

This is a right tailed test.

b) Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

t = (29 - 21)/√(59²/427 + 52²/2733)

t = 2.65

The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [59²/427 + 52²/2733]²/[(1/427 - 1)(59²/427)² + (1/2733 - 1)(52²/2733)²] = 9.14/0.1564

df = 58

c) from the t distribution table, the critical value is 1.67

In order to reject the null hypothesis, the test statistic must be smaller than - 1.67 or greater than 1.67

Since - 2.65 < - 1.67 and 2.65 < 1.67, we would reject the null hypothesis.

Therefore, at 5% significance level, we can conclude that the score gain for coached students is greater than the score gain for uncoached students.

Answer:

No, it is not less expensive to keep the old car as the price calculation is higher then the New Car

Purchasing new car is less expensive

Step-by-step explanation:

NEW CAR EXPENSES= $21,240

OLD CAR EXPENSES= $25,800

NB: Kindly check attached picture for calculations

Answer: they deleted my answer but here is how to do it If that helps some

Step-by-step explanation:

way to solve a linear system algebraically is to use the substitution method. The substitution method functions by substituting the one y-value with the other. We're going to explain this by using an example.

y=2x+4

3x+y=9

We can substitute y in the second equation with the first equation since y = y.

3x+y=9

3x+(2x+4)=9

5x+4=9

5x=5

x=1

This value of x can then be used to find y by substituting 1 with x e.g. in the first equation

y=2x+4

y=2⋅1+4

y=6

The solution of the linear system is (1, 6).

You can use the substitution method even if both equations of the linear system are in standard form. Just begin by solving one of the equations for one of its variables.

Answer:

Step-by-step explanation:

The height is 6 units.

The radius is 8 units.

The volume is 128 π cubic units.

Answer:

1. We can't see any boat on the river at this scale.

2. 0.025 inches. We won't be able to see it

Step-by-step explanation:

the beginning of the question states that; according to this map, the driving distance is 3 miles, we're most interested in the graphics at the bottom left, which indicates that 1 inches on the map corresponds to 2,000 ft in real life.

If 1 inches = 2000 ft,

x inches = 50 ft

we cross multiply to give

2000x ft = 50 ft-inches

x = 50/2000 = 0.025 inches

Answer:

Option D.

Step-by-step explanation:

The given graph represents the function f(x).

If graph of a function f(x) intersect x axis at x=c, then (x-c) is a factor of f(x).

From the given graph it is clear that the graph of f(x) intersect x axis at x=-6,-3,0. It means factors of given function are

[tex](x-(-6))=(x+6)[/tex]

[tex](x-(-3))=(x+3)[/tex]

[tex](x-0)=x[/tex]

It means (x+6), (x+3) and x are factors of given function.

Therefore, option D is correct.

Answer:

The answer is (x+6)

Step-by-step explanation:

Just took the test

Hope this helps

Answer:

B the mean increases by 6.8

Answer:

23 sides

Step-by-step explanation:

The sum S of the interior angles of an n sided polygon is given as

S = (n - 2)180°

Where S is the sum of the interior angles and n is the number of sides.

Given that the sum of the interior angles is 3780° then

3780° = (n - 2)180

Divide both sides of the equation by 180

21 = n - 2

n = 21 + 2

= 23

The polygon has 23 sides

Answer:

[tex]3\sqrt{5}[/tex]

Step-by-step explanation:

Use the distance formula:

[tex]\sqrt{(8-5)^2+(-4-2)^2}=\sqrt{9+36}=3\sqrt{5}[/tex]

Answer: [tex]\sqrt{45} =3\sqrt{5}[/tex]

Step-by-step explanation:

To find the distance between 2 points use this formula:

[tex]\sqrt{(x1-x2) ^{2} +(y1-y2)^{2} }[/tex]

rad[(2+4)^2+(5-8)^2)]

=rad[36+9]

=rad45

=3rad5

Answer:

the answer is 26

Step-by-step explanation:

The ratio of students who cheer to those who participate in a sport is 13/82.

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Total students participated in sports

= 35 + 27 + 43 + 33 + 26

= 164

and, students who cheered = 26

So, the ratio of students who cheer to those who participate in a sport

= 26 / 164

= 13 / 82

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Answer:

3 I think it's 3. sorry if I'm wrong

The correct answer is (3) they map lines to parallel lines

Transformation is the movement of a point from the initial location to a new location. Types of transformation is rotation, reflection, translation and dilation.

Translation is the movement of a point up, down, left or right in the coordinate plane.

Translation is a rigid transformation, that is, it preserves the size and shape of the figure. Reflection and rotation are also rigid transformation.

Translation maps lines to parallel lines whereas rotation does not since it changes the direction of the line.

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Answer:

x-intercept: 4    y-intercept: - 6

Step-by-step explanation:

To find the y-intercept, we must first solve for y.

Isolate variable y on the left side of the equation by subtracting 3x from both sides.

- 2y = - 3x + 12

Now divide both sides by - 2 to find y.

y = 3/2x - 6

The y-intercept is - 6.   (remember formula y = mx + b, where b is the y-intercept)

To find the x-intercept, we must solve for x.

Isolate variable x on the left side of the equation by adding 2y to both sides.

3x = 2y + 12

Now divide both sides by 3 to find x.

x = 2/3y + 4

The x-intercept is 4.    (remember formula x = my + b, where b is the x-intercept)

Answer:

4 and - 6

Step-by-step explanation:

3x-2y=12

Answer:0.007

Step-by-step explanation:

Answer:

  199

Step-by-step explanation:

All of the terms of the sum cancel except the last two.

The total is 199.

Answer:

Mass of other chemicals to be evaporated is 24 grams.

Step-by-step explanation:

The initial mass of the hand sanitizer = 400 grams, and has an alcohol content of 24%.

mass of its alcohol content = [tex]\frac{24}{100}[/tex] × 400

                                            = 96 grams

mass of non-alcoholic content = 400 - 96

                                                  = 304 grams

If the percentage of alcohol is increased to 30%, then;

mass of its alcohol content = [tex]\frac{30}{100}[/tex] × 400

                                             = 120 grams

The mass of other chemicals to be evaporated = 120 - 90

                                                 = 24 grams

Answer:

4x+1

Step-by-step explanation:

f(x)=x-4 and g(x)=3x+5,

(f+g) (x) = x-4 +3x+5

Combine like terms

           = 4x+1

Answer:

Step-by-step explanation:

Volume of a rectangular prism=length x width x height

450=43*12*x

x=0.87209cm

Answer:

The value of b is 19.

Step-by-step explanation:

With what the problem states, we have that:

[tex]\frac{4b + 19}{6b + 11} = 0.76[/tex]

Doing cross multiplication

[tex]4b + 19 = 0.76(6b + 11)[/tex]

[tex]4b + 19 = 4.56b + 8.36[/tex]

[tex]4.56b - 4n = 19 - 8.36[/tex]

[tex]0.56b = 10.64[/tex]

[tex]b = \frac{10.64}{0.56}[/tex]

[tex]b = 19[/tex]

The value of b is 19.

Answer:

y=2/5 - 1/5

explanation:

Answer:

A, of money in the account after 3 years subject to interest ... If you deposit P dollars at rate r, in decimal form, subject to compound interest paid

Step-by-step explanation:

Answer: A = 93.8 cm so if you round up it's about 100 cm

Step-by-step explanation:

Area means you have to multiply all measurements by each other in any order of course because it doesn't matter in this case.

                                    14 * 10 * 10     =     1400

Now you can/should divide the answer which is (1400) by how many measurements you have times the sides it has, sides - which is 5 , measurements - which is 3, so it would look like this:

                                     1400   /    15    =    93.8

Answer:

Dilation is done by the scale factor of Five-halves.

Step-by-step explanation:

Please refer to the image attached,

The graph clearly shows the triangles [tex]\triangle[/tex]ABC and [tex]\triangle[/tex]A'B'C'.

Let us calculate the sides of triangles first then we will be able to find scale factor of dilation.

Using the distance formula:

Distance between 2 points [tex]P (x_1,y_1) \text{ and } Q (x_2,y_2)[/tex] is given by formula:

PQ = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Side AB is along x-axis, side AB =

[tex]\sqrt{(2-0)^2+(2-2)^2}\\\Rightarrow \sqrt{4}\\\Rightarrow 2\ units[/tex]

Similarly side, BC = 2 units

Now, in [tex]\triangle[/tex]A'B'C', A'B' can be calculated by distance formula:

[tex]\sqrt{(1+4)^2+(-1- (-1))^2}\\\Rightarrow \sqrt{25}\\\Rightarrow 5\ units[/tex]

B'C' = 5 units

The ratio of sides:

AB : A'B' = 2:5

[tex]\Rightarrow \dfrac{AB}{A'B'} = \dfrac{2}{5}\\\Rightarrow A'B' = \dfrac{5}{2} AB[/tex]

So, scaling factor is [tex]\dfrac{5}{2}[/tex] or 2.5.

OR

Scaling factor is Five-halves.

Answer:

The answer is C on Edge.

Step-by-step explanation:

Answer:

[900, 1300]

Step-by-step explanation:

According to the empirical rule, 95% is within ±2 standard deviations.

1100 − 2(100) = 900

1100 + 2(100) = 1300

The answer is C. 65........

Answer:

25

Step-by-step explanation:

The angle of an arc is the same as the central angle. MarcCD is the same as the central angle COD which is given as 130o.

That means there are 50 degrees left for COA and DOA and because the chord and the diameter are equal, COA = DOA

That means that COA is 1/2 what is left over from 180 when 130 is subtracted from it.

1/2 * 50 = 25

The answer is A 25.

Answer:

[tex]\dfrac{dA}{dt}+ \dfrac{A}{100}=0[/tex]

A(0) = 70  (i.e the pounds of salt dissolved into the tank)

Step-by-step explanation:

Given that:

a large mixing tank initially holds 400 gallons of water  in which 70 pounds of salt have been dissolved.

The rate at which pure water is pumped into the tank is 4 gal/min

After stirring; the pure water is then pumped out at the same rate.

The objective is to determine the differential equation  for the amount of salt A(t) in the tank at time t > 0. What is A(0)

Taking the differential of:

[tex]\dfrac{dA}{dt}=R_{in}-R_{out}[/tex]     ---- (1)

where ;

[tex]R_{in[/tex] = 0

[tex]R_{out} =\dfrac{A(t)}{400}*4[/tex]

[tex]R_{out} =\dfrac{A}{100}[/tex]

replacing them into (1) ; we have:

[tex]\dfrac{dA}{dt}=0 - \dfrac{A}{100}[/tex]

[tex]\dfrac{dA}{dt}=- \dfrac{A}{100}[/tex]

[tex]\dfrac{dA}{dt}+ \dfrac{A}{100}=0[/tex]

A(0) = 70 (i.e the pounds of salt dissolved into the tank)

The differential equation for the amount of salt A(t) in the tank at time t > 0 is [tex]\frac{dA}{dt} + \frac{A}{100} = 0[/tex]

A (0)= 70

Given that,

[tex]dA\div dt=R_{in}-R_{out}[/tex]

Rin=0

[tex]R_{out}=A(t)\div 400 \times (4)\\\\ =A\div 100[/tex]

so,

[tex]dA\div dt=R_{in}-R_{out}\\\\dA\div dt=0- A\div 100[/tex]

So,

[tex]dA\div dt +A\div 100=0[/tex]

A(0)=70

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Answer:  The change represents  growth with 89% of growth rate.

Step-by-step explanation:

The exponential function is given by :-

[tex]f(x)= Ab^x[/tex]... (i)

Where , A = initial value , b= multiplicative factor and  x= time period

The given function : [tex]y = 940(1.89)^x[/tex].

By comparing this to (i) , we get

b= 1.89 > 1 , thus it represent the growth.

Also,

[tex]b= 1+r\Rightarrow\ 1.89 = 1+r\\\\\Rightarrow\ r=1.89-1=0.89[/tex]

i.e. Percentage rate of growth = 0.89 x 100 = 89%.

Answer:

16/75, D

Step-by-step explanation:

6/5*1/3. We can cross simplify to make it 2/5*1/1. That is 2/5. Then, 2/5*8/15 is 16/75 which is answer choice D.

Answer:

[tex]x^{12} =400[/tex]

[tex]w^{-10} =\frac{1}{20}[/tex]

Step-by-step explanation:

[tex]x^{6} =20[/tex]

[tex]x^{12} =(x^{6} )^{2} =20^{2} =400[/tex]

[tex]w^{10} =20[/tex]

[tex]w^{-10} =\frac{1}{w^{10} } =\frac{1}{20}[/tex]

[tex]x^{12} *w^{-10} =400*\frac{1}{20} =20[/tex]

Answer:

There is enough evidence to support the claim that  the proportion of women working the graveyard shift is less than the proportion of men working the graveyard shift (z=-2.44).

Critical value (α=0.01) zc=-2.33.

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the proportion of women (subindex 1) working the graveyard shift is less than the proportion of men (subindex 2) working the graveyard shift.  

Then, the null and alternative hypothesis are:

[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0[/tex]

The significance level is 0.05.

The sample 1, of size n1=343 has a proportion of p1=0.0437.

[tex]p_1=X_1/n_1=15/343=0.0437[/tex]

The sample 2, of size n2=294 has a proportion of p2=0.0918.

[tex]p_2=X_2/n_2=27/294=0.0918[/tex]

The difference between proportions is (p1-p2)=-0.0481.

[tex]p_d=p_1-p_2=0.0437-0.0918=-0.0481[/tex]

The pooled proportion, needed to calculate the standard error, is:

[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{15+27}{343+294}=\dfrac{42}{637}=0.0659[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.0659*0.9341}{343}+\dfrac{0.0659*0.9341}{294}}\\\\\\s_{p1-p2}=\sqrt{0.0002+0.0002}=\sqrt{0.0004}=0.0197[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.0481-0}{0.0197}=\dfrac{-0.0481}{0.0197}=-2.44[/tex]

For a significance level of 0.01 and a left-tailed test, the critical value of z is zc=-2.326.

If the test statistic is smaller than the critical value, the null hypothesis is rejected.

The test statistic z=-2.44 is smaller than the critical value zc=-2.326, so the null hypothesis is rejected.

There is enough evidence to support the claim that  the proportion of women working the graveyard shift is less than the proportion of men working the graveyard shift.