How much money do winners go home with from the television quiz show Jeopardy? To determine an answer, a random sample of winners was drawn and the amount of money each won was recorded and listed below. Estimate with 96% confidence the mean winning's for all the show's players.

Answer:

B. [tex]y = -\frac{3}{10}x + \frac{1}{2}[/tex]

Step-by-step explanation:

Well slope-intercept form is [tex]y = ax + b[/tex].

Let's start with the slope.

In this case, finding the slope is easy.

It should have a negative slope.

So we can cross out answer choices A. and C.

Also, we can cross out D. because it just makes no sense, -10/3, if you start from the y-intercept and go down 10 and across 3, yeah that's

not the slope.

So we can cross out D.

The only answer choice left is B.

We can tell the y-intercept is 1/2 because like come on so B is the correct answer.

B. [tex]y = -\frac{3}{10}x + \frac{1}{2}[/tex]

Looking at the graph, we can figure out our y-intercept or b simply by looking at the line to see where it intersects the y-axis.

So, we can see that the line intersects the y-axis at 1/2 or 0.5

That means, our y-intercept or b is 1/2 (0.5).

Now, to find out the slope of the line, we can pick two pairs of coordinates on the line and plug it into the slope equation to figure out the slope.

Let's use the two coordinate pairs: (-5, 2) and (0, 1/2).

Plug it in.

1/2 - 2 = - 1.5

0 - - 5 = 5

-1.5/5 = -0.3

Convert it into a fraction: -0.3 = -3/10

Thus, our slope intercept form for this line is: y = -3/10 + 1/2

Answer:

The value of x is 30.

We have to find the value of x in the given equation.  

Using distributive property  

We have,

[tex]1/2(x+6)=18\\a.(b+c)=a.b+a.c\\1/2(x+3)=18\\1/2x=15\\x=3[/tex]

other are also solve by this methode;)

The required solution of the expression [tex]1/2(x+6) = 18[/tex] is 30.

To solve the equation using the distributive property and properties of equality. One-half (x + 6) = 18 and value of x to be determined.

The equation is the well-organized link of the variables of two expressions that contain equal between them.

distributive properties are used to evaluate the math problem easily by distributing numbers to the numbers present in parenthesis. eg, if we apply the distributive property of multiplication to solve the expression
a( b + c ) = a.b + a.c

[tex]1/2(x+6) = 18[/tex]
Using distributive property a( b + c ) = a.b + a.c

[tex]1/2.x+1/2*6 = 18\\1/2x+3=18\\1/2x=18-3\\1/2x=15\\x=2*15\\x=30\\[/tex]

Thus, The required solution of the expression [tex]1/2(x+6) = 18[/tex] is 30.

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Answer:

$200 at 2%.

$2200 at 3.5%.

Step-by-step explanation:

Let the two amounts be x and y.

x earns 2% interest, and y earns 3.5% interest.

Since the total is $2400, then

x + y = 2400

Now we can solve for y and express the second amount in terms of x.

y = 2400 - y

The two amounts are x and 2400 - x.

In one interest period, the amount of interest earned is the amount of money in the account multiplied by the interest.

2% = 0.02; 3.5% = 0.035

The x amount earns 0.02x interest.

The y amount earns 0.035y interest.

The total interest earned is the sum of the interest amounts of the two accounts.

0.02x + 0.035y

We now replace y with 2400 - x, and we set the sum of the interest amounts equal to the total interest earned, $81.

0.02x + 0.035(2400 - x) = 81

The equation above is the linear equation.

Now we solve it. Distribute on the left side.

0.02x + 84 - 0.035x = 81

Combine like terms on the left side.

-0.015x + 84 = 81

Subtract 84 from both sides.

-0.015x = -3

Divide both side by -0.015.

x = 200

$200 was deposited in the account earning 2%.

y = 2400 - x

y = 2400 - 200

y = 2200

$2200 was deposited in the account earning 3.5%.

Answer:

no

Step-by-step explanation:

it was slower the way there and if he was going 40 it would have taken the same time to get there as it would have to go back

Answer:

Yes.

Step-by-step explanation:

Reiko's average speed was 80 miles per hour. That is more than 40 miles per hour. Even if it took him longer to drive from A to B, his speed would still be more than 40 miles per hour to have the average speed be 80 miles per hour.

Hope this helps!

Answer:

i) Estimate the value of the population proportion = 0.8

ii) 95% confidence interval for the population proportion

(0.7214 , 0.8784)

iii)    Lower bound = 0.7214

     upper bound = 0.8784

Step-by-step explanation:

Step(i):-

Given sample size 'n' = 100

Given data  he surveys 100 customers and finds that 80 paid at the pump

sample proportion

                     [tex]p = \frac{x}{n} = \frac{80}{100} = 0.8[/tex]

Step(ii):-

95% confidence interval for the population proportion is determined by

[tex](p^{-} - Z_{\alpha } \sqrt{\frac{p(1-p)}{n} } , p^{-} + Z_{\alpha } \sqrt{\frac{p(1-p)}{n} })[/tex]

Level of significance  

∝ =0.05

Z₀.₀₅ = 1.96

[tex](0.8 - 1.96 \sqrt{\frac{0.8 X 0.2)}{100} } , 0.8 + 1.96 \sqrt{\frac{0.8 X 0.2}{100} })[/tex]

On calculation , we get

(0.8 - 0.0784 , 0.8 + 0.0784)

(0.7214 , 0.8784)

Conclusion:-

95% confidence interval for the population proportion

(0.7214 , 0.8784)

Answer:

The hikers each receive 2 1/3 cups of trail mix.

1. Multiply 8 by 3 1/4 to get how much cups of trail mix they have in total which  will come out as 28.

2. Then divide the 28 cups by the 12 hikers, and you will get 2 1/3 as your answer.

Answer:

42

Step-by-step explanation:

You can get this right from the table. 42 females had a positive opinion about the campus.

Answer:

42

Step-by-step explanation:

Let's look at the intersection of the "positive opinion" column and "female" row, the number we see at the intersection is 42.

Answer:

Option (4)

Step-by-step explanation:

In the given picture,

Trapezoid PQRS has two points T and U as the midpoints of sides PS and RQ.

Segment TU joins the midpoints of the sides PS and RQ.

Mid-segment theorem states that "If a line joining midpoints of a trapezoid is parallel to the bases, length of this segment is half the sum of lengths of the bases."

Therefore, m(TU) = [tex]\frac{1}{2}(m\text{PQ}+m\text{SR})[/tex]

7x - 26 = [tex]\frac{1}{2}[(3x+23)+(9x-3)][/tex]

7x - 26 = 6x + 10

7x - 6x = 26 + 10

x = 36

m(TU) = 7x - 26

          = 7(36) - 26

          = 252 - 26

          = 226

Therefore, Option (4) will be the answer.

Answer:

The function is:

y = 150*x

where y is the number of calories consumed, and x is the number of pieces of candy consumed.

Now, the domain of a function is the possible values of x that you can input in the function.

For this particular case you can have:

x = 0 (no pieces candy)

x = 1 (one piece of candy)

x = 2 (two pieces of candy)

Notice that x can be only whole numbers because, in principle, you can't eat a fraction of a piece of candy.

So we only use x = whole numbers.

Then the domain of the function is equal to all the natural numbers plus the zero, or:

D = {x ∈ N ∪ {0}}

"x belongs to the union between the set of the natural numbers and the zero"

The amount of candies can only be positive values, hence the domain of the value exists on all natural numbers that are x≥0

The domain of a function is the input values of the function for which it exists.

Given the expression that relates the number of calories you consume after eating x pieces of candy as shown:

y = 150x

The amount of candies can only be positive values, hence the domain of the value exists on all natural numbers that are x≥0

The function is also discrete because the number of candies can be counted. Note that the domain of all discrete functions is countable.

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Answer:

Mark as BRAINLIEST plz

|x-323|<50: answer

Step-by-step explanation :

For water to be a liquid, the temperature must be within 50 Kelvin of 323 K.

So, the range of the temperature of water will lie between 50 kelvin more than 323 kelvin and 50 kelvin less than 323.

The equation that can be used to determine the maximum temperature at which water is a liquid can be given by :  x < 323 + 50

The equation that can be used to determine the minimum temperature at which water is a liquid can be given by : x > 323 - 50

So the resultant equation can be written as :

|x-323|<50

The solution of inequality equation is  | x - 323 | < 50

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the temperature of the water be = x Kelvin

Now , the equation will be

For water to be in the liquid state, the temperature must be within 50 kelvin (K) of 323 K

So , the value of the temperature of water will lie between 50 kelvin more than 323 kelvin and 50 kelvin less than 323

Substituting the values in the inequality equation , we get

For maximum temperature ,

x should be 50 more than 323 and

For minimum temperature ,

x should be 50 less than 323

So ,

The inequality relation is

x > 50 + 323   be equation (1)

x < 323 - 50   be equation (2)

So , the modulus function is expressed as

It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.

Therefore , the value is | x - 323 | < 50

Hence , The solution of inequality equation is  | x - 323 | < 50

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Answer:

Hey mate... I don't know the first three... But mayb I can help u in last one.

Step-by-step explanation:

The answer is : 2: 6: 18: 54: 162: 426

I can see the pattern by multiplying.. As from 3

2x3=6 :6x3=18 :18x3= 54 :54x3=162 :162x3=426

So I guess this is the ans

Hope it helped u!

Answer:

33/2

Step-by-step explanation:

6 * 11/4 = 66/4 = 33/2

Answer:

what expressions?

Step-by-step explanation:

Answer:

x = 1, y = 6

Step-by-step explanation:

y = 6x

2x + 3y = 20

Plug y as 6x in the second equation and solve for x.

2x + 3(6x) = 20

2x + 18x = 20

20x = 20

[tex]\frac{20x}{20}= \frac{20}{20}[/tex]

x = 1

Plug x as 1 in the first equation and solve for y.

y = 6(1)

y = 6

Answer:

y=6 , x=1

Step-by-step explanation:

y=6x

2x+3y=20

Substitute 6x into y because y=6x.

2x+3(6x)=20

2x+18x=20

20x=20

x=1

Then subsitiute 1 into the first equation in x value

y=6(1)

y=6

Answer:

The answer is B.

Step-by-step explanation:

Since x < 1 the circle at the point is open and the arrow points infinitely in the negative direction (which happens to be answer A here)

x is also greater than or equal to -1 so a closed circle at the point -1 will complete this graph.

Answer:

volume=3x³+15x²+12x

Step-by-step explanation:

v= l*w*h =(3x )(x+1) (x+4)

v=3x(x²+5x+4)

volume=3x³+15x²+12x

Answer:

Step 1-Construct the perpendicular bisector of one side of the triangle.

Step 2-Construct the angle bisector of another side of the triangle.

Explanation:

A circumscribed circle is the circle that passes through all three vertices of the triangle. The center of the circumscribed circle is the circumcenter of the triangle, the point where the perpendicular bisectors of the sides meet

Answer: 3 toys

Step-by-step explanation:

equation will be 60 - 5 x t = 45

solving it we get

5 x t = 60 - 45 = 15

=> t = 15/5 = 3

Answer:

C

Step-by-step explanation:

To get the approximate number of pages in the chapters, what we need to do is to substitute for the value of x in the line of best fit equation.

Thus, we have;

y = 15.261(8) + 8.83 = 122.088 + 8.83 = 130.918

This is approximately equal to 131

Answer: I hope it helps :)

Step-by-step explanation:

1.

[tex]Hypotenuse =x\\Opposite =y \\Adjacent =6\\\alpha = 6\\Let's\: find\: the \:hypotenuse\: first\\Using SOHCAHTOA\\Cos \alpha = \frac{adj}{hyp} \\Cos 60 = \frac{6}{x} \\\frac{1}{2} =\frac{6}{x} \\Cross\:Multiply\\x = 12\\Let's\: find\: y\\Hyp^2=opp^2+adj^2\\12^2=y^2+6^2\\144=y^2+36\\144-36=y^2\\108=y^2\\\sqrt{108} =\sqrt{y^2} \\y=6\sqrt{3}[/tex]

2.

[tex]Opposite =x\\Hypotenuse = 46\\Adjacent =y \\\alpha =60\\Using \: SOHCAHTOA\\Sin \alpha =\frac{opp}{adj} \\Sin 60=\frac{x}{46}\\\\\frac{\sqrt{3} }{2} =\frac{x}{46} \\2x=46\sqrt{3} \\x = \frac{46\sqrt{3} }{2} \\x =23\sqrt{3} \\\\Hyp^2=opp^2+adj^2\\46^2=(23\sqrt{3} )^2+y^2\\2116=1587+y^2\\2116-1587=y^2\\529=y^2\\\sqrt{529} =\sqrt{y^2} \\y = 23[/tex]

3.

[tex]Hypotenuse = u\\Opposite =6\sqrt{3} \\Adjacent = v\\\alpha =60\\Sin\: 60 = \frac{6\sqrt{3} }{u} \\\frac{\sqrt{3} }{2} =\frac{6\sqrt{3} }{u} \\12\sqrt{3} =u\sqrt{3} \\\\\frac{12\sqrt{3} }{\sqrt{3} } =\frac{u\sqrt{3} }{\sqrt{3} } \\u = 12\\Hyp^2=opp^2+adj^2\\12^2= (6\sqrt{3} )^2+v^2\\144=108+v^2\\144-108=v^2\\36 = v^2\\\sqrt{36} =\sqrt{v^2} \\\\v =6[/tex]

4.

[tex]Hypotenuse = a\\Opposite =18 \\Adjacent = b\\\alpha =45\\Tan \alpha = opp/adj\\Tan \:45 =18/b\\1=\frac{18}{b}\\ b = 18\\\\Hyp^2=Opp^2+Adj^2\\a^2 = 18^2+18^2\\a^2=324+324\\a^2=648\\\sqrt{hyp^2} =\sqrt{648}\\ \\a =18\sqrt{2}[/tex]

5.

[tex]Hypotenuse = 13\sqrt{2}\\ Opposite =x\\Adjacent = y\\\alpha =45\\Sin\:\alpha = opp/hyp\\Sin 45=x/13\sqrt{2}\\ \\\frac{\sqrt{2} }{2} =\frac{x}{13\sqrt{2} } \\2x=26\\2x/2=26/2\\\\x = 13\\\\Hyp^2=opp^2+adj^2\\(13\sqrt{2})^2=13^2+y^2\\ 338=169+y^2\\338-169=y^2\\169=y^2\\\sqrt{169} =\sqrt{y^2} \\13 = y[/tex]

Answer: negative 2 minus radical 3

Step-by-step explanation:

We can use the tangent half-angle formula to find the exact value of tangent of 7π/12:

tan(θ/2) = ±√[(1-cosθ)/1+cosθ)]

Here, θ = 7π/6, and cos(7π/6) = -sqrt(3)/2.

Substituting these values, we get:

tan(7π/12) = ±√[(1-(-sqrt(3)/2))/(1+(-sqrt(3)/2))]

= ±√[(2+sqrt(3))/(2-sqrt(3))]

Multiplying the numerator and denominator by (2+sqrt(3)), we get:

= ±√[(2+sqrt(3))^2/(4-3)]

= ±√[(2+sqrt(3))^2]

= ±(2+sqrt(3))

Since 7π/12 lies in the second quadrant, and tangent is negative in the second quadrant, the exact value of tangent of 7π/12 is - (2+√3)

Answer:

Option A is the correct option

Step-by-step explanation:

[tex]5x = 35[/tex]

Divide both sides of the equation by 5

[tex] \frac{5x}{5} = \frac{35}{5} [/tex]

Calculate

[tex]x = 7[/tex]

Hope this helps...

Best regards!!

Answer:

Option A

Step-by-step explanation:

5x = 35

5x/5 = 35/5

x = 7

Answer:

The translation from quadrilateral EFGH to quadrilateral E'F'G'H' is [tex]T_{(2, -4)}[/tex], which is two units to the right (x direction) and 4 units down (negative y direction)

Step-by-step explanation:

The coordinates of quadrilateral EFGH are;

Point E has coordinates (-1, 1)

Point F has coordinates (0, 4)

Point G has coordinates (3, 1)

Point H has coordinates (3, 0)

The coordinates of the translation are;

Point E' has coordinates (0, -3)

Point F' has coordinates (1, 0)

Point G' has coordinates (4, -3)

Point H' has coordinates (4, -4)

The change in the y-coordinate values (y values) are;

From point E to point E', we have;

(-3 - 1) = -4 which is four units down

The change in the x-coordinate values (x values) are;

From point E to point E', we have;

(0 - (-1)) = 2 which is two units to the right

The total change in translation is [tex]T_{(2, -4)}[/tex].

Answer:

b=9.96≅10

Step-by-step explanation:

b^2=a^2+c^2−(2ac)cos(64)

b=√6²+11²-2(6*11)cos64

b=9.96≅10

Answer:  Annual Gross Income = $55,489.20

               Annual Net Income = $46,439.72

Step-by-step explanation:

Total hours worked per week = 3(10) + 5 + 11 = 46

Regular hours worked = 3(8) + 5 + 8 = 37

Overtime hours worked = 3(2) + 0 + 3 = 9

Weekly Tips at 20% of $60 for 46 hours:

0.2(60)(46) = $552.00

Annual tips = $552.00 x 52 weeks = $28,704.00

Weekly Regular pay at $10.20 per hour for 37 hours:

10.20(37) = $377.40

Annual regular pay = $377.40 x 52 weeks = $19,624.80

Weekly Overtime pay at time and a half for 9 hours:

10.20(1.5)(9) = $137.70

Annual overtime = $137.70 x 52 weeks = $7,160.40

Total Annual Gross Income = Tips + Regular Pay + Overtime

$28,704.00 + $19,624.80 + $7,160.40 = $55,489.20

****************************************************************************************

Deductions (per question 5):

a) Pension at 5% = $55,489.20(0.05) = $2,774.46

b) Employee Insurance at 2.4% = $55,489.20(0.024) = $1,331.74

c) Income Tax at 0% for $0-$11,000 = $11,000(0) = 0

   Income Tax at 8% for $11,000-$25,000 = $14,000(0.08) = $1,120.00

   Income Tax at 12% for $25,000-$50,000 = $25,000(0.12) = $3,000.00

   Income Tax at 15% for $50,000-$100,000 = $5,489.2(0.15) =$823.38

Total Income Tax = $4,943.28

Annual Net Income = Gross - Pension - Employee Insurance - Income Tax:

$55,489.20 - $2,774.46 - $1,331.74 - $4,943.28 = $46,439.72

Answer:

[tex] \boxed{\sf Length \ of \ leg \ y = 13} [/tex]

Step-by-step explanation:

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”.

[tex] \therefore \\ \sf \implies {84}^{2} + {y}^{2} = {85}^{2} \\ \\ \sf {84}^{2} = 7056 : \\ \sf \implies 7056 + {y}^{2} = {85}^{2} \\ \\ \sf {85}^{2} = 7225 : \\ \sf \implies 7056 + {y}^{2} = 7225 \\ \\ \sf Substract \: 7056 \: from \: both \: sides : \\ \sf \implies (7056 - 7056) + {y}^{2} = 7225 - 7056 \\ \\ \sf 7056 - 7056 = 0 : \\ \sf \implies {y}^{2} = 7225 - 7056 \\ \\ \sf 7225 - 7056 = 169 : \\ \sf \implies {y}^{2} = 169 \\ \\ \sf 169 = {13}^{2} : \\ \sf \implies {y}^{2} = {13}^{2} \\ \\ \sf \implies y = \sqrt{ {13}^{2} } \\ \\ \sf \implies y = {13}^{ \cancel{2} \times \frac{1}{ \cancel{2}} } \\ \\ \sf \implies y = 13 [/tex]

So,

Length of leg y of the right triangle = 13

Answer:

Step-by-step explanation:

inequality is a equation with |x|

a inequality equation is like this..

|x|>7

Answer:

a

Step-by-step explanation:

Answer:

[tex]4 \frac{1}{4} [/tex] hours

Step-by-step explanation:

Given,

Time spent in studies : [tex]1 \frac{3}{4} [/tex] hours

Time spent in playing cricket : [tex]2 \frac{1}{2} [/tex] hours

Now, let's find the time that he spent in all:

[tex]1 \frac{3}{4} + 2 \frac{1}{2} [/tex]

Add the whole number and fractional parts of the mixed numbers separately

[tex](1 + 2)( \frac{3}{4} + \frac{1}{2} )[/tex]

Add the numbers

[tex]3 +( \frac{3}{4} + \frac{1}{2} )[/tex]

Add the fractions

[tex]3 + ( \frac{3 + 1 \times 2}{4} )[/tex]

[tex]3 + ( \frac{3 + 2}{4} )[/tex]

[tex]3 + \frac{5}{4} [/tex]

Convert the improper fraction into mixed number

[tex] 3 + 1\frac{1}{4} [/tex]

Write the mixed number as a sum of the whole number and the fractional part

[tex]3 + 1 + \frac{1}{4} [/tex]

Add the numbers

[tex]4 + \frac{1}{4} [/tex]

Write the sum of whole number and the fraction as a mixed number

[tex]4 \frac{1}{4} [/tex] hours

Hope this helps..

Best regards!!

Answer:

4 1/4 hours.

Step-by-step explanation:

1 3/4 + 2 1/2

= 1 + 2 + 3/4 + 1/2

= 3 + 3/4 + 1/2   The LCM of 2 and 4 is 4 so 1/2 = 2/4. and so we have:

3 + 3/4 + 2/4

= 3 + 5/4

= 3 + 1 1/4

= 4 1/4 hours.

Answer:

(5,3)

Step-by-step explanation:

Well to solve the following,

y = 8 - x

y = x - 2

Graphically.

We need to graph both equations,

Look at the image below ↓

By looking at the graph we can tell the intercept point is at (5,3).

Thus,

the solution is (5,3).

Hope this helps :)