Sara and Fiona have played 53 tennis matches.

Sara has won 29 times.

Fiona won the rest.

a) Estimate the probability that Sara wins.

b) Estimate the probability that Fiona wins.

To calculate the p-value, we have to follow the following steps:

To calculate the p-value, we need

p = sample proportion

p' = assumed population proportion in the null hypothesis

n = sample size

Example

Given, n =40, σ = 32.17 and X = 105.37. calculate p-value.

σₓ = σ/ √n

σₓ = 32.17 / √40

    = 5.0865

Now, by applying the test static formula, we get

t = (105.37 – 120) / 5.0865

t = -2.8762

Using the table, we find the value of P(t>-2.8762)

From the table, we get

P (t<-2.8762) = P(t>2.8762) = 0.003

If P(t>-2.8762) = 1- 0.003 = 0.997

P- value = 0.997 > 0.05

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Answer:

they would be 58 rn. and simp means someone who is willing to do anything for someone they like. they try to get with that person everyday and they like them alot.

Step-by-step explanation:

hope this helped

1. person would be 58

2. 16549 x 1348965= 8834371785

3. a simp is someone who would do anything for someone and they dont really expect anything back except for a relationship *sad*

Answer: the answer is $796.32

Step-by-step explanation:

Answer:

Step-by-step explanation:

y-y1=m(x-x1)

m=-5/8 ; x1=-14; y1=6

y-6=-5/8(x+14)

8(y-6)=-5(x+14)

8y-42=-5x-70

5x+8y-42+70=0

5x+8y+28=0

Slope intercept form is y=mx+c

8y = -5x-28

y=-5/8x +(-7/2)

The Odds in favour for ball landing on even is 10 to 9.

The Odds against for ball landing on even is 9 to 10.

The given number of slots is 38.

By using the empirical formula of probability we have,

P(E) = (number of times an event occurs) / (total number of trials)

There are 20 ways it can land on even slot

{0,00,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36}

The probability of ball landing on even slot= 20/38

The landing on even number = favorable cases to unfavorable cases

The probability of ball landing on even slot= 20/38 = 10/9

Therefore, Odds for ball landing on even is 10 to 9.Odds against ball landing on even is 9 to 10.

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To find the probability of making the first sale on the fifth call using the geometric distribution, we can use the formula:

P(make your first sale on the fifth call) = (1 - p)^(k-1) * p

where p is the probability of making a sale on any given call and k is the number of trials (calls) until the first success.

In this case, p = 0.17 and k = 5. Substituting these values into the formula, we get:

P(make your first sale on the fifth call) = (1 - 0.17)^(5-1) * 0.17

Calculating this expression, we find:

P(make your first sale on the fifth call) ≈ 0.472

So, the probability of making the first sale on the fifth call is approximately 0.472.

Since this probability is greater than 0.05 (the typical threshold for defining an event as unusual), we can say that it is not an unusual event.

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Answer:

I think it is no c

Step-by-step explanation:

The vertex is at (-6,-5)

The interval is from -10 to 5 (inclusive of both endpoints...

Absolute function is open up because 4 is positive

I will plug in both endpoints now:

f(-10)=4|-10+6|-5 f(5)=4|5+6|-5

f(-10)=4(4)-5 f(5)=4(11)-5

f(-10)=11 f(5)=39

So the highest reached by f(5) which is 39 so our range will go up to 39 (inclusive)

11 is not the lowest reached, -5 is because our vertex was included within the domain

So the range is [-5,39]

Answer: What you need help with

Step-by-step explanation:

Answer:

m=7

n=12

Step-by-step explanation:

i took the test

The smaller triangle is DEF which has sides

The larger triangle ABC has side lengths of

Note how the sequence 2,4,6 is exactly double that of 1,2,3. Therefore, the sides of triangle ABC are twice as large as the corresponding sides of triangle DEF.

Put another way, computing the ratios of the corresponding sides all lead to the same value, so we have BC/EF = 6/3 = 2, and we have  AB/DE = 4/2 = 2, and finally AC/DF = 2/1 = 2. These three equations all confirm ABC is twice as large as DEF.

By the SSS (side side side) similarity theorem, we can conclude the triangles are similar. They have the same shape, but different size.

Answer:

-3/4

Step-by-step explanation:

If you take two points, the rise is 3. Also, the change in y is 4. Since the line is going downwards from left to right, it has to be negative.  

The partial derivatives are:
f_x = 2x - 6λ
f_y = 2y - 9λ
f_λ = -(6x + 9y - 10)

To find the partial derivatives of f(x, y, λ) = x^2 + y^2 - λ(6x + 9y - 10), we'll differentiate with respect to each variable (x, y, and λ) while treating the others as constants:

1. Partial derivative with respect to x (f_x):
f_x = ∂f/∂x = 2x - λ(6)

2. Partial derivative with respect to y (f_y):
f_y = ∂f/∂y = 2y - λ(9)

3. Partial derivative with respect to λ (f_λ):
f_λ = ∂f/∂λ = -(6x + 9y - 10)

So, the partial derivatives are:
f_x = 2x - 6λ
f_y = 2y - 9λ
f_λ = -(6x + 9y - 10)

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By finding the average rate of change, we can see that:

a) The cost decreases.

b) The cost increases.

To check that, we need to find the average rate of change on the interval.

Remember that for function f(x) on an interval (a, b), the average rate of change is:

R = (f(b) - f(a))/(b - a)

Here the cost function is:

c(n) = 0.25*n² - 10n + 800

a) In the interval [10, 15] the average rate of change is given by:

R = (c(15) - c(10)/(15 - 10)

Where:

c(15) = 0.25*15^2 - 10*15 + 800 = 706.25

c(10) = 0.25*10^2 - 10*10 + 800 = 725

Then the average rate of change is:

R = (706.25 - 725)/(15 - 10) = -3.75

This means that between 10 and 15 light fixtures, the cost is decreasing.

b) Now we have the interval [20, 25], so let's do the same ting:

c(20) = 0.25*20^2 - 10*20 + 800 = 700

c(25) = 0.25*25^2  - 10*25 + 800 = 706.25

Here the average rate of change is:

R = (706.25 - 700)/(25 - 20) = 1.25

It is positive, which means that the cost is increasing.

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Answer:

A system of equations are two or more equations that has to be valid at the same time. It means that the variables of one equation can be substitute in the other equation.

For example we have y=5x−8 and we can substitute this value of y in the other equation

4x+3y=33

4x+3(5x−8)=33 we can solve now for x

4x+15x−24=33

19x=33+24

19x=57

x=5719=3.

y can be obtained from the first equation

y=5x−8

y=5⋅3−8=15−8=7

Then x=3 and y=7.

Step-by-step explanation:

Answer:

x = 3

y = 7

Step-by-step explanation:

y = 5x - 8  ---------------(I)

4x + 3y = 33 ------------(II)

Substitute y = 5x - 8 in equation (II)

4x + 3 (5x - 8) = 33  

4x + 3*5x - 8*3 = 33

4x + 15x - 24 = 33           {Combine like terms}

      19x  - 24 = 33            {Add 24 to both sides}

            19x = 33 + 24

           19x = 57           {Divide both sides by 19}

             x = 57/19

x = 3

Substitute x = 3 in equation (I)

y = 5*3 - 8

y = 15 - 8

y = 7

Answer:

D

Step-by-step explanation: 2 x square root of 2 is 2.8284.......

Answer:

y=5 x=-2

Step-by-step explanation:

the easiest answer would be a vertical or . horizontal line

Answer:

You can determine whether each element of the domain is paired with exactly one element of the range. For example, if given a graph, you could use the vertical line test; if a vertical line intersects the graph more than once, then the relation that the graph represents is not a function

Step-by-step explanation:

First find 28% of $19.50:

($19.50) / (100) × (28) = $5.46

Now minus the 285 from the original price:

($19.50) - ($5.46) = $14.04

The answer is $14.04

Hope it helped :)

Answer:

43

Step-by-step explanation:

2v+v-7+58=180(Angle Sum Property)

3v+51=180

3v=180-51=129

3v=129

v=129/3

=43

2,889 mi

Distance from South Atlantic Ocean to Gulf of Guinea

(a) There are 81 possible answer sequences for the four questions.

(b) The probability of getting all four answers correct when guessing is approximately 0.01235 when rounded to five decimal places.

(c) The probability of answering at least one question correctly when guessing is approximately 0.51775 when rounded to five decimal places.

(a) Since there are three possible answers for each of the four questions, there are a total of 3^4 = 81 possible answer sequences for the four questions.

(b) If you are guessing on each question, the probability of getting one question correct is 1/3. Since there are four questions, the probability of getting all four correct is (1/3)^4 = 1/81, which is approximately 0.01235 when rounded to five decimal places.

(c) The probability of not getting any question correct is (2/3)^4, since there are two incorrect answers for each question and we are guessing on all four questions. Therefore, the probability of getting at least one question correct is 1 - (2/3)^4, which is approximately 0.51775 when rounded to five decimal places.

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The area of the parallelogram that has a width of 32.2 units and a height of 12.6 units will be 405.72 square units.

Let H be the height and W be the width of the parallelogram. Then the area of the parallelogram will be given as,

Area of the parallelogram = H × W square units

The width of the parallelogram is 32.2 units and the height of the parallelogram is 12.6 units. Then the area of the parallelogram is given as,

A = 32.2 x 12.6

A = 405.72 square units

The area of the parallelogram that has a width of 32.2 units and a height of 12.6 units will be 405.72 square units.

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Answer:

Step-by-step explanation:

2.5x-7x+1=-44

-4.5x=-45

X=10

Answer:

On the number line, mark the endpoint at 10 with a closed circle.  

Next, draw a ray to the right of 10. ➡️

➡️

Step-by-step explanation:

solve the inequality for x:

1,558 + 60x ≥ 2,158

60x ≥ 600

x ≥ 10

On the number line, mark the endpoint at 10 with a closed circle.  

Next, draw a ray to the right of 10. ➡️

An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.

here, we have,

solve the inequality for x:

1,558 + 60x ≥ 2,158

60x ≥ 600

x ≥ 10

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The coordinates of A'', B'' and C'' are (-1, 4), (-4, 3) and (-1, 2) respectively.

Transformation of geometrical figures or points is the manipulation of a given figure to some other way.

Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.

Given triangle has coordinates,

A(2, -2), B(5, -3) and C(2, -4).

First the triangle is translated by the rule (x, y) → (x - 1, y + 6)

A(2, -2) becomes A'(2 - 1, -2 + 6) = A'(1, 4).

B(5, -3) becomes B'(5 - 1, -3 + 6) = B'(4, 3)

C(2, -4) becomes C'(2 - 1, -4 + 6) = C'(1, 2)

Then the translated triangle is reflected across the Y axis.

When reflected a point (x, y) across the Y axis, y coordinate remains same and x coordinate flips.

A'(1, 4) becomes A''(-1, 4)

B'(4, 3) becomes B''(-4, 3)

C'(1, 2) becomes C''(-1, 2)

Hence the vertices of the triangle after undergoes translation and reflection becomes A''(-1, 4), B''(-4, 3) and C''(-1, 2).

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The desired values of a and b to conform the translation (x,y) -> (x+a, y-b) to the format of a reflection around line q preceded by a reflection across line p are a = 2x+2 and b = y.

Line q is a vertical line of equation x = -1, and the reflection of any point (x, y) across it provides its mirror image on the other side. Thus, reflecting a point (x, y) across line q results in the point (-x-2, y).

Additionally, line p is a horizontal line of equation y = b. When a point (x,y) is reflected across this line, its mirror image appears on the opposite side. Therefore, reflecting a point (x, y) across line p yields the point (x, 2b-y).

Presently, we seek to ascertain whether these two reflections are equivalent to shifting a point (x,y) to another point (x+a, y-b). Consequently, let us experiment with an arbitrary point (x,y): when we reflect it across line q, then over line p, then shift it by (a,-b), we should end up at (x+a, y-b).

Applying this pathway to our chosen point (x,y) gives the resultant point of (-x-2, y); followed by (-x-2, 2b-y); and finally (-x-2+a, 2b-y-b). Hence, for the transformation (x,y) -> (x+a, y-b) to be equivalent to one reflection about line q trailed by a reflection about line p, the following equations must resolve simultaneously:

-x-2+a = x+a

2b-y-b = y-b

By solving these equations, it is revealed that the desired values of a and b to conform the translation (x,y) -> (x+a, y-b) to the format of a reflection around line q preceded by a reflection across line p are a = 2x+2 and b = y.

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The integral, ∫ [ (9ˣ - eˣ )/3ˣ ] dx evaluate value is 3ˣ/ ln(3) - eˣ/3ˣ(1 - ln 3). So, the correct answer is option (c).

Integration is defined as the process of finding the area of the region under the curve. This is done by drawing as many small rectangles covering up the area and summing up all their areas. If d/dx(F(x) = f(x), then ∫ f(x) dx = F(x) + C, where C is integration constant and indefinite integrals. We have an integral, say , I = ∫ [ (9ˣ - eˣ )/3ˣ ] dx

and we have to determine its value.

I = ∫ [ (9ˣ - eˣ )/3ˣ ] dx

=> I = ∫ [ (9ˣ/3ˣ - eˣ/3ˣ ] dx

=> I = ∫ [ (3²ˣ/3ˣ - eˣ/3ˣ ] dx

=> I = ∫ [ (3²ˣ/3ˣ - eˣ/3ˣ ] dx

=> I = ∫ [ (3ˣ - eˣ/3ˣ ] dx

=> I = ∫ 3ˣ dx - ∫ eˣ3⁻ˣ dx

=> I = 3ˣ/ ln(3) - eˣ/3ˣ(1 - ln 3) + C

( since, ∫aˣ dx = aˣ/ln a)

where C --> integration constant

So, the required value is 3ˣ/ln(3)-eˣ/3ˣ(1 - ln 3).

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Complete question:

Find integral ∫ [ (9ˣ - eˣ )/3ˣ ] dx .

a) 3ˣ - eˣ/(1 - ln 3) + C

b) 9ˣ/2ln3 - eˣ/(3ˣ ln 3) + C

c) 3ˣ/ln3 - eˣ/3ˣ(1 - ln 3) + C

d) 3ˣ/ln3 - eˣ/3ˣ + C

A sampling technique that is based on the cumulative effect of information that every additional item in the sample adds as it is inspected is called: sequential sampling.

What is sequential sampling?

Sequential sampling is a non-probability sampling strategy where the researcher selects one or more populations within a time frame, conducts his research, evaluates the findings, and then selects further populations as necessary.

An auditor develops a set of three groups of sampling units, where each successive group contains the same number of units to be sampled. The sampling plan is to continue to the next group of sampling units if the preceding group contains at least one deviation

Simple random sampling, systematic sampling, stratified sampling, and cluster sampling are examples of probability sampling techniques.

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Answer:

csc θ * sin θ

Simplified using trig identities:  

csc (x) = 1/sin(x)  

so, csc (0) = 1/sin(0)  

1/sin(0) * sin (0), the result will be sin(0) / sin (0) which is equal to 1.  

Therefore, the answer is 1.

Step-by-step explanation:

Expression in sin θ and cos θ below

4cos ec^2  2θ as 2 /    2 (4 sin θ cos θ )^2

or

cos ec^2 θ as 1 / sin ^2  θ

. Accept terms like

cos ec^2 θ = 1  +cot^2 θ =1 +  cot^2 θ /sin^2 θ