fy(y)=0.2e^(-0.2y),y>=0
What is the probability that the buyer waits more than 10 minutes?

The test statistic value for the given sample data with population mean difference is equal to optic C. 3.156.

As given in the question,

Given population mean difference μd = 0

sample size 'n' = 9

Sample data is:

x                y                [tex]d_{i}[/tex] ( x - y)                   [tex]( d_{i} - \bar{d} )^{2}[/tex]

168           162             6                                15.21

180           178              2                                62.41

157            145             12                               4.41

132            125             7                                  8.41

202           171              31                               445.21

124            126              -2                              141.61

190            180              10                              0.01

210            195              15                               26.01

171              163             8                                3.61

                                    ∑[tex]d_{i}[/tex] = 89                 ∑ [tex]( d_{i} - \bar{d} )^{2}[/tex] = 706.89

[tex]\bar{d}[/tex] = ( 1/ n ) ∑[tex]d_{i}[/tex]

  = (1/9) (89)

  = 9.889

  = 9.9

Standard deviation of the mean difference '[tex]S_{d}[/tex]'

= √[1 / (n - 1)]( ∑ [tex]( d_{i} - \bar{d} )^{2}[/tex] )

= √706.89/ 8

=√88.361

= 9.4

test statistic

t = ( [tex]\bar{d}[/tex] - μd)/ ( [tex]s_{d} /\sqrt{n}[/tex] )

 = ( 9.9 - 0) / ( 9.4 / √9)

 = 9.9/ 3.133

 = 3.156

Therefore, the test statistic value for the given sample data is equal to option C. 3.156

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The radius of the sphere with the given point and the center is √238.

Here we have to find the radius of the sphere.

Given data:

The point on the surface of a sphere is (-4, -6, 10) and the point on the center is (2, 3, -1).

The formula for the radius:

r² = (x2 - x1)² + (y2 - y1)² + (z2 - z1)²

where (x1, y1, z1) = point on the center

(x2, y2, z2) = point on the sphere

Now putting the values we have

r² = (-4-2)² + ( -6-3)² + ( 10 +1)²

  =( -6)² +(- 9)²  + (11)²

  = 36 + 81 + 121

  = 238

r = √238.

Therefore the radius is √ 238.

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The solution set is for the given inequality is (-∞, -2.25]

Here we want to solve the following inequality:

-11 - 8k ≥ 23 - (7 - 4k)

To solve this, we need to isolate the variable k in one side of the equation.

First we can expand the right side so we get:

-11 - 8k ≥ 23 - (7 - 4k)

-11 - 8k ≥ 23 - 7 + 4k

Group like terms:

-11 - 23 + 7  ≥ 4k + 8k

-34 + 7 ≥  12k

-27 ≥  12k

-27/12 ≥  k

-2.25 ≥  k

Then the solution is the set of all values smaller than or equal to -2.25, then the solution set is (-∞, -2.25]

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all because all of the equianlangular triangles are equal

Answer:

$3.78

Step-by-step explanation:

To find the new price of the speaker after the sale, you can use the following formula:

New price = (1 + discount percentage) * (original price - discount amount)

In this case, the discount percentage is 40%, or 0.4, and the discount amount is 40% of the original price, or 0.4 * $4.50 = $1.80. Plugging these values into the formula, we get:

New price = (1 + 0.4) * ($4.50 - $1.80)

= 1.4 * $2.70

= $3.78

So the new price of the speaker after the sale and the subsequent price increase is $3.78.

Answer:

4 yellow tulips and 8 white lilies.

Step-by-step explanation:

Ratio is 1:2:3 for yellow tulips, white lilies and the total.

Set up a proportion

[tex]\frac{yellow}{total}[/tex] = [tex]\frac{yellow}{total}[/tex]  Three of these numbers you know, Solve for the unknown

[tex]\frac{1}{3}[/tex] = [tex]\frac{x}{12}[/tex]  Cross multiply and solve for x

3x = 12  Divide both sides by 3

x = 4  This is the number of yellow tulips

Set up another proportion:

[tex]\frac{white lilies}{total}[/tex] = [tex]\frac{white lilies}{todal}[/tex]

[tex]\frac{2}{3}[/tex] = [tex]\frac{x}{12}[/tex]  I can see that 3 x 4 = 12 so I will multiply the top number to 2 by 4 to get 8.

The scores of both test Solomon took are 14 for the first test and 4 for the second test.

let a represent the first score and b represent the second score.

since the average score is 18, you get (a + b) / 2 = 18

multiply both sides of this equation by 2 to get a + b = 36

the product of her scores is 56 means that a × b = 56.

you have 2 equations that need to be solved simultaneously.

they are a + b = 36 and a × b = 56

solve for a in the second equation to get a = 56 / b.

replace a with 56/ b in the first equation to get 56/ b + b = 18

multiply both sides of this equation by b to get 56 + b^2 = 18b

subtract 14b from both sides of this equation and arrange the terms in descending order of degree to get b^2 - 18b + 56 = 0

Factorise the quadratic equation to get the following:

(b-4 ) ( b - 14) = 0

Solve for b to get b = 4 and b = 14

Therefore, the product of the of the two scores:

= 14×4 = 56. This means that he scored 14 in first test and 4 in the second test.

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The forecast of soccer ball demand for the month of April is 123.

What is regression?

Regression analysis is a group of statistical procedures used in statistical modelling to determine the relationships between a dependent variable and one or more independent variables.

The main focus of regression to the mean is how data balances. In essence, it says that if a variable is extreme when measured for the first time, it will be more typical the next time.

The regression equation is Y = 98 + 2.2x, where x = 4 for April.

So the unadjusted forecast for April,

= 98 + 2.2x = 98 + (2.2 × 4) = 98 + 8.8 = 106.8

Seasonal index for April = 1.15

Adjusted forecast for April = Unadjusted forecast × seasonal index = 106.8 × 1.15 = 122.82 or rounded to 123

So the answer is 123.

Hence, the forecast of soccer ball demand for the month of April is 123.

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Complete question:

Complete question is attached below.

Answer: the answer is 8

Answer:8  or 18

Step-by-step explanation: 5+13 is 18 and -5+13 is 8

Answer:

p=31

Step-by-step explanation:

sum of all three angles of any triangle equal 180 degrees

2p+(p+46)+(p+10)=180

4p+56=180

    -56.  -56

4p=124

/4.   /4

p=31

hopes this helps please mark brainliest

The amount of piles of fake vomit that the manufacturing line can produce at medium speed is of:

2 piles.

A proportion is a fraction of a total amount, and this fraction is used along with the basic arithmetic operations, especially multiplication and division, to find the equivalent measures in the context of a problem.

The amount that can be produced at high speed is of:

4 piles of vomit.

(as stated in the text).

At medium speed, the amount is 50% of the amount of 4 piles of vomit produced at high speed, hence 4 is multiplied by 0.5 to give the amount, as follows:

0.5 x 4 = 2 piles of vomit.

(as the decimal equivalent of the percentage of 50% is of 0.5).

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At a significance level of 0.10, there is enough evidence to conclude that the treatment is dependent to the side effect of Nausea

The observed values are given as;

Result          Drug           Placebo          Total

Nausea          36                 13                 49

No Nausea     254              262              516    

Total              290               275              565      

The expected values are as follows;

EXPECTED    

                              DRUG                    PLACEBO

NAUSEA    (290 * 49/565) = 25.150442         (275*49/565) = 23.849558

NO NAUSEA (290*516/565) = 264.849558   (275*516/565) = 251.150442

Test statistic = ∑((observed - (expected)²)/expected    =  ∑(O - E²)/E

This gives the test statistic as;

                           DRUG            PLACEBO

NAUSEA         4.680351           4.935643

NO NAUSEA     0.444452        0.468695

∑(O - E²)/E = 10.52914

From a chi square calculator, our critical Value = 2.71

The conditions are;

If (calculated value > crit Value), then we reject Null hypothesis and accept the Alternative hypothesis

If (calculated value < critical value) we accept Null hypothesis and reject Alternative hypothesis

We are given;

Null Hypothesis; The two variables are independent

Alternative Hypothesis; The two variables are dependent

Since (10.52914 > 2.71) we reject Null Hypothesis and Accept Alt Hypothesis

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To find the value of F1, we can start by writing out the given equations in a more standard form.

First, we can rewrite the equation "F1 + F2 = 100" as "F1 = 100 - F2".

Then, we can rewrite the equation "F1 - F2 = 20" as "F1 = 20 + F2".

If we set these two equations equal to each other, we get "100 - F2 = 20 + F2".

If we simplify this equation, we get "80 = 2 * F2".

If we divide both sides of the equation by 2, we get "40 = F2".

Substituting this value back into either of the original equations, we can find that "F1 = 100 - F2" or "F1 = 100 - 40" which gives us "F1 = 60".

Therefore, the value of F1 is 60.

Yes, it's true that the interpretations that participants make of events can be best studied through qualitative research techniques like participant observation or in-depth interviews.

Going into the field without telling every subject of the field research who you are is always unethical. The following are a number of the methodologies normally utilized in qualitative research: Ethnography commonly entails researchers immediately gazing members of their herbal environments over time. A key characteristic of ethnography is the truth that herbal settings, unadapted for the researchers' interests, are used.

A famous and useful categorization separate qualitative strategies into 5 groups: ethnography, narrative, phenomenological, grounded theory, and case study. John Creswell outlines those 5 strategies in Qualitative Inquiry and Research Design. As maximum qualitative information is amassed via interactions with members via the usage of interviews, surveys, questionnaires, or awareness groups, a researcher have to discover members who're inclined to talk approximately their experiences.

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Correct Question:

Qualitative research methods, such as participant observation or intensive interviews, are particularly strong in studying the meanings that participants attach to events. state true or false.

The distance between the line segment from P to RQ is 2.83 units

Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x₂ – x₁)² + (y₂ – y₁)²).  This formula is used to find the distance between any two points on a coordinate plane or x-y plane.

In this case, we need to find the coordinate of P and RQ

From P to the line RQ, we will meet the midpoint of the line RQ which has a coordinate of (3, 3)

Let's use the formula of distance of a line segment and solve this

d = √((x₂ - x₁)² + (y₂ + y₁)²)

d = √(3 - 1)² + (3 - 1)²

d = √(2)² + (2)²

d = √8

d = 2√2

d = 2.83 units

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The area on the graph that is not shaded is the region of feasibility. The shape is a triangle and the vertices of the feasible region are: (5,1.5), (.75,.75), (1.5,.5)

The system of inequalities below, We need to determine the shape of the feasible region and find the vertices of the feasible region

x+y<=2

3x+y>=3

x+3y>=3

x>=0

y>=0

Now, we would graph with the following inequalities

x+y>=2

3x+y<=3

x+3y<=3

x<=0

y<=0

Therefore, the area on the graph that is not shaded is the region of feasibility and the shape is a triangle, the vertices of the feasible region are: (5,1.5) (0.75, 0.75), (1.5,.5).

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The values of x in the triangles are (a) 15 and (b) 4

From the question, we have the following parameters that can be used in our computation:

Triangle 1 and Triangle 2

Solving triangle 1

In this triangle, we can see that the side lengths of the triangles are congruent

This means that the triangles is an equilateral triangle

The individual angles in an equilateral triangle are 60 degrees

So, we have the following representation

4x = 60

Divide both sides of the equation by 4

x = 15

So, the value of x is 15

Solving triangle 2

In this triangle, we can see that the length KM of the triangle divides the length JL into congruent parts

This means that the JM and LM are congruent

So, we have the following representation

x + 1 = 5

Subtract from both sides of the equation by 1

x = 4

So, the value of x is 4

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The base angle is calculated to be 45 degrees if the vertex angle of the isosceles triangle is 90 degrees

An isosceles triangle in mathematics is used to describe a triangle with two equal sides and two equal angles.

As the vertex angle is given to be 90 degrees, therefore the other two angles of the triangle will be equal. Considering x to be the base angle;

x + x + 90° = 180°

2x + 90° = 180°

Rearranging;

2x = 180° - 90°

2x =  90°

Solving for x;

x = 90° ÷ 2

x = 45°

Therefore, 45° is calculated to be the base angle of the isosceles triangle.

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The length of the unknown side is 6 units

From the question, we have the following parameters that can be used in our computation:

Triangles ABC and QRS

This triangles are similar triangles

This means that

AB : AC= QR : QS

Substitute the known values in the above equation, so, we have the following representation

5 : 3 = 10 : QS

Multiply the first ratio by 2

So, we have

10 : 6 = 10 : QS

By comparison, we have

QS = 6

Hence, the length is 6 units

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The ways you can draw all of the marbles from the bag is 33! ways

From the question, we have the following parameters that can be used in our computation:

Total number of marbles, n = 33

Total numbers of marbles picked at a time, r = 1

From the question, the marbles are selected without replacement

This means that the number of ways the marbles can be drawn from the bag is calculated using the following factorial formula

Total = n!

Where

n = 33

Substitute the known values in the above equation

Total = 33!

Apply the factorial formula

n! = n * (n - 1) * (n - 2) * .... * 1

So, we have

Total = 33 * 32 * 31 * 30 * .... * 1

Evaluate

Total = 8.6833176e+36

Hence, the number of ways is 33!

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$9483.774 money should be deposited in the account.

Let the amount to be invested be P=$x so that the amount accumulated is A = $12000. We have t=3 years. The rate of interest is r=0.04 per year.     n  = 2 as interest will be compounded twice a year.

Interest, in its most simple form, is calculated as a percent of the principal.

Interest is the amount of money a lender or financial institution receives for lending out money. Interest can also refer to the amount of ownership a stockholder has in a company, usually expressed as a percentage.

Now,

                         [tex]x (1 + \frac{0.04}{2} )^{2 * 3}[/tex] [tex]= 12000[/tex]

                                 [tex]x(1.04)^{6}[/tex] [tex]= 12000[/tex]

                                           [tex]x = \frac{12000}{(1.04)^{6} }[/tex]

                                              ≈ 9483.774

                   ∴ Amount invested  ≈  $9483.774.

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In image.

In the Image is the anser and explanation.

If (x + 8) is a factor of f(x), then the true statement is f(-8) = 0 .

In the question ,

it is given that , x [tex]+[/tex] 8 is factor of f(x) ,

we have to select the correct option about f(x) from the given options .

When solving the polynomials, a factor of the polynomial gives the solution of  the polynomial.

that means , x + 8 = 0

So , x = -8 ,

So , it means that when x = -8 , then the value of the function f(-8) will be zero ,

which means that x = -8 will be a root of the given function f(x) .

Therefore , the true statement is f(-8) = 0 .

The given question is incomplete , the complete question is

If (x + 8) is a factor of f(x), which of the following must be true ?

(a) Both x = –8 and x = 8 are roots of f(x).

(b) Neither x = –8 nor x = 8 is a root of f(x).

(c) f(–8) = 0

(d) f(8) = 0

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To get 80% percentage you need to attempt 20 question

In mathematics, a percentage (from Latin: per centum, "by a hundred") is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%",although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number (pure number); it has no unit of measurement.

For example, 45% (read as "forty-five per cent") is equal to the fraction

45/100, the ratio 45:55 (or 45:100 when comparing to the total rather than the other portion), or 0.45. Percentages are often used to express a proportionate part of a total.

now we need to find  80% of a 25 question test

80% of 25 can be written as 80% × 25

= 80/100 × 25

= 20

To get 80% you need to attempt 20 question

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On solving the provided question we got to know that, the median value won't change if the greatest sample Observation is decreased to 1.3735.

One of three ways to gauge central tendency is the median. The center position of a record is specified when describing it. A measure of central tendency is what this is. The mean, median, and mode are the three most frequently used indicators of central tendency.

The sum of all the values is divided by the total number of values, giving the mean value.

[tex]0.736 + 0.863 + 0.865 + 0.913 + 0.915 + 0.937 + 0.983 + 1.001 + 1.011 + 1.064 + 1.109 + 1.132 + 1.140 + 1.153 + 1.253 + 1.397 = 16.472\\16.472 /16 = 1.0295\\1.0295 is the mean value[/tex]

The number near the middle of the point is the median value. At the halfway point, there are two values.

[tex](1.001 + 1.011) / 2 = 1.006\\ 1.006 is the median value.[/tex]

As a result, the median value, which depicts the middle value of the numbers in the result, is less than the mean value, which depicts the real middle value of the numbers if they were equally distributed.

Their difference is that 1.0295 - 1.006 = 0.0235

1.397 observations make up the biggest sample. It may be made smaller by taking the number and removing the difference between the mean and median.

Consequently, there is a 0.0235-point difference between the mean and median.

Therefore;

[tex]1.397 - 0.0235 = 1.3735[/tex]

The median value won't change if the greatest sample Observation is decreased to 1.3735.

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Answer:

First blank: 90°  Second blank: 12

Step-by-step explanation:

The two shapes have a ratio of 4:1, and have the same angles.

This means that if m∠B = 90°, then m∠D = 90°.

Because the shape ratio is 4:1 (16:4 simplified) we can use this to find out 48:?    48/4 = 12

A local minimum or a local maximum are both examples of local extremums.

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To make the similar cake for 8 persons , the number of cups of both flour and milk will be needed is [tex]4\frac{2}{3}[/tex] cups .

In the question ,

it is given that ,

number of cups of milk needed  to make the cake is = 1 cup

number of cups of flour needed  to make the cake is = [tex]2\frac{1}{2}[/tex] = 5/2 cups .

So , the total is = cups of milk + flour

= 1 + 5/2 = 7/2

So , for 6 persons , 7/2 cups of milk and flour is needed .

for 1 person 7/12 cups of milk and flour is needed .

and for 8 persons = 8×7/12 cups of milk and flour is needed .  

= 14/3

= [tex]4\frac{2}{3}[/tex] cups .

Therefore , the number of cups of milk and flour needed is  [tex]4\frac{2}{3}[/tex] cups .

The given question is incomplete , the complete question is

A recipe calls for 1 cup of milk for every [tex]2\frac{1}{2}[/tex] cups of flour to make a cake that would feed 6 persons. How many cups of both flour and milk will be needed to make a similar cake for 8 persons ?

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