Kenton compared gas mileage for three cars.


Car A—450 miles for 15 gallons
Car B—651 miles for 21 gallons
Car C—598 miles for 23 gallons

Which car has the best rate of miles per gallon?
Car A has the best rate at 30 miles per gallon.
Car B has the best rate at 31 miles per gallon.
Car C has the best rate at 26 miles per gallon.
All three cars had the same rate of miles per gallon.

a). 115.26 is the upper bound of a 98% band (b). 93.36 to 116.63 is the 98% confidence interval (c). We have 98% confidence that the collected sample data will include the true worth of the population parameter.

By multiplying the total number of numbers by amount of all the numbers, one can approximate the average. A mean can be established by the average of such probabilities in a survey of data. In other words, an average is also known as the arithmetic mean. The average is referred to as having a mean.

[tex]\begin{aligned}& \mu=105 \\& \sigma_x=\frac{\sigma}{\sqrt{n}}=\frac{15}{\sqrt{9}}=5\end{aligned}[/tex]

(a). The maximum 98% interval

[tex]=\mu+Z_{0.02} * S D=105+2.0537 * 5=115.2685[/tex]

(b). 98 percent confidence band

[tex]\begin{aligned}& \left(\mu-Z_{\frac{0.02}{2}} * S D, \mu+Z_{\frac{0.02}{2}} * S D\right) \\& (105-2.3263 * 5,105+2.3263 * 5)=(93.3685,116.6315)\end{aligned}[/tex]

(c). We have 98% confidence that the collected random sample would also include the true value of said population parameter.

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The complete question is-

Suppose you administer a certain aptitude test to a simple random sample of 9 students in your school, and that the average score is 105 . From past experience, scores on such a test among students like those at your school follow a Normal distribution. We want to determine the mean score [tex]$\mu$[/tex] of the population. Assume a standard deviation of [tex]$\sigma=15$[/tex] for the test.

(a). What is the upper critical value for a 98% confidence interval? (Show the key numbers in the sketch of the distribution.)

(b). Construct and interpret a 98% confidence interval for the mean score [tex]$\mu$[/tex]. Follow the Inference Toolbox.

(c). Explain the meaning of 98 % confident.

The area of the region inside the circle (x − 2)^2 + y^2 = 4 and outside the circle x^2 + y^2 = 4 is given by

Area = ∬R dA where R is the region we're trying to find the area of.

We can find the area of the region by subtracting the area of the smaller circle from the area of the larger circle.

The area of the larger circle is:

Area = ∬R dA = ∬((x − 2)^2 + y^2 <= 4) dA = π*4 = 4π

The area of the smaller circle is:

Area = ∬((x^2 + y^2) <= 4) dA = π*4 = 4π

Therefore, the area of the region inside the circle (x − 2)^2 + y^2 = 4 and outside the circle x^2 + y^2 = 4 is

Area = 4π - 4π = 0

The area of the region is 0 square units.

Answer:

I agree with kiddobreeze08

The union of two or more events is a single event that represents all the outcomes that belong to at least one of the original events.

16) It is often represented using the symbol "U" or "∪". For example, if event A is "rolling a 3 on a die" and event B is "rolling a 4 on a die", the union of A and B would be "rolling a 3 or a 4 on a die".

17)  The intersection of two or more events is a single event that represents all the outcomes that belong to all of the original events. It is often represented using the symbol "∩". For example, if event A is "rolling an even number on a die" and event B is "rolling a number greater than 3 on a die", the intersection of A and B would be "rolling a 4 on a die".

18)  The union of two or more events represents all the outcomes that belong to at least one of the original events, while the intersection of two or more events represents all the outcomes that belong to all of the original events. The union is a "larger" event that includes all outcomes from the original events, while the intersection is a "smaller" event that only includes outcomes that belong to all of the original events.

For example, if event A is "rolling an odd number on a die" and event B is "rolling a number less than 4 on a die", the union of A and B would be "rolling a 1,3, or a 2 on a die" while the intersection of A and B would be "rolling a 1 or a 3 on a die".

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The slope of the line parallel to BC is 18/7 * (x + 0) is 18/7 y. the orthocenter is where concurrency occurs.

Hana fastens tiny wood strips perpendicular to the opposing edge from each vertex. As a result, the orthocenter is where concurrency occurs.

Given: Hana fastens small wood strips perpendicular to the opposing edge from each vertex.

As a result, the orthocenter is where concurrency occurs.

Think of the ABC triangle with coordinates.

A(0, 0) B(0, 58), C(36, 44) (36, 44)

first determine the angles of the triangle's two sides.

Formula for slope: (y 2 - y 1)/(x 2 - x 1)

slope of the AB& A(0, 0) matrix side matrix, Slope of BC side B(0,58), B(0, 58) = (58 + 0)/(0 + 0) = 0 C(36,44) = (44 - 58)/(36 + 0) = - 14/36 = - 7/18

Use Equation of the altitude perpendicular to AB's point slope form after that.

The vertex in opposition to AB is point C.

A line perpendicular to AB has a slope of zero.

y-y 1 = m(x-x 1) y-44 = 0(x-36) y = 44

Altitude Equation Perpendicular to BC

The vertex opposite BC is Point A. A line perpendicular to BC has a slope of 18/7.

y + 0 = 18/7 * (x + 0)

y = 18/7 * x

Change the value of y in the equation above. y = 18/7 * x 44 = 18/7 * x

x = 17.11 The slope of the line parallel to BC is 18/7 * (x + 0) = 18/7 y.

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The expression 5+4*2+6-2*2-1 has a value of 14 using order of operations

The order of operations are the rules that tell the sequence in which the multiple operations in an expression should be solved. A way to remember the order of the operations is PEMDAS, where each letter stands for a mathematical operation

Parenthesis            (  )

Exponent                a⁷

Multiplication          x

Division                   ÷

Addition                  +

Subtraction             -

Let's use PEMDAS:

Remember, multiplication comes before addition and subtraction, thus, we have:  

5+4×2+6-2×2-1 = 5 + (4×2) + 6 - (2×2) - 1

                        =  5 + 8 + 6 - 4 - 1

                        =  14

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Answer:

V÷ 2

Step-by-step explanation:

Get peevious number and divide by half.

Using Euclid's theorem for the right triangle AD  is ≈ 2.67

DB = 4 and DC = 6 , We need to find AD

Using Euclid's theorem for the right triangle

∴ DB² = AD * DC

∴ 4² = AD * 6

∴ 6 AD = 16

∴ AD = 16/6 = 8/3 ≈ 2.67

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The distance from the initial point to the corner pocket is 164 cm.

The angle between the path as the ball approaches the rail and the path after it strikes the rail is 45 degrees.

We know that the ball traveled 100cm before ricocheting off the rail and another 120cm into the corner pocket.

We can use the Pythagorean Theorem to find the distance from where the cue initially struck the ball to the corner pocket.

Let x be the distance from the initial point to the corner pocket.

x^2 = 100^2 + 120^2 - 2100120*cos(45^{\circ})

x = \sqrt{28000} = \sqrt{700*40} = \sqrt{28000} = 164.856

Rounded to the nearest centimeter, the distance from the initial point to the corner pocket is 164 cm.

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The number of ways for the four beasts to wear these hats so each beast is wearing a different hat, and no one is wearing a hat marked with the first letter of their name is given as follows:

8.

Winnie is wearing a hat that does not have any letter, while the letters on the other helmets are G, L and A, meaning that Winnie can wear four helmets.

For Grogg, Lizzie, and Alex, they can't wear the helmet with their own letters.

Hence the possible combinations, considering only them, are listed as follows:

As Winnie can wear any of the four helmets, and Grogg/Lizzie/Alex can also wear the red helmet, the number of outcomes is given as follows:

4 x 2 = 8.

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Answer:

34

Step-by-step explanation:

They gave us -3+5i.

The conjugate of -3+5i is

-3 - 5i

You use the same numbers -3 and 5i, but with a minus sign instead of a plus.

Then multiply them together.

(-3 + 5i)(-3 - 5i)

-3•-3 + 15i - 15i - 25i^2

= 9 - 25i^2

Remember i^2 is -1.

= 9 - 25(-1)

= 9 + 25

= 34

Shortcut version:

When you multiply a complex number and its conjugate, square both numbers and add them together.

3^2 + 5^2

= 9 + 25

= 34

Answer:

Grouping of like terms.

Step-by-step explanation:

(x² - 2x - 4) - (x² + 3x + 5)

= x² - 2x - 4 - x² + 3x + 5

Grouping of like terms

= x² - x² - 2x + 3x- 4 + 5

= x + 1.

For the given line segments 12cm ,7cm and 5cm , a triangle cannot be constructed as the sum of two sides is not greater than third side .

What is a Triangle ?

a Triangle is closed figure joined by three line segments .

The condition for the sides to form a triangle , is :

the sum of any two sides of triangle should be greater than the third side of the triangle :

the given side lengths are : 12cm ,7cm and 5cm ;

on adding the two sides of triangle ,

we get ;

⇒ 12+7 = 19 > 5 ; True

⇒ 12+5 = 17 > 5 ; True

⇒ 7+5 = 12 > 12 ; False

The third condition is not met .

Therefore , the line segments 12 , 7 and 5 do not form a triangle .

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In the rectangle given, the values of x and m<VUT are;

i. x = 6

ii. m<VUT = 64^o

A rectangle is a plane figure which is a family of quadrilateral since it has four straight sides. It has some properties which are:

i. the diagonals are equal and divides it into two equal parts

ii. the opposite sides are equal in length

iii. the measure its internal angles are right angle

These properties can be used to determine the values required in the given question.

i. RT = SU = 5x + 16

But,

2RV = RT

2(3x + 5) = 5x + 16

6x + 10 = 5x + 16

collect like terms

6x - 5x = -10 + 16

x = 6

ii. m<RUV + m<VUT = 90^o

But,

m<RUV = m<VRU = 26^o

So that,

m<RUV + m<VUT = 90^o

26^o + m<VUT = 90^o

m<VUT = 90^o - 26^o

            = 64^o

m<VUT = 64^o

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Answer:

WXUV

Step-by-step explanation:

Well, you see, think of it as a reflection.

Answer: 150 miles

Step-by-step explanation: the car goes 30 miles every half hours, therefore, in five half hours it goes 150 miles.

Answer:

1/2

Step-by-step explanation:

i hope it helps you all

The probability is g / (b + g).

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are.

Let Gi be the event that the person in the ith position is a girl.

let the simple space S is all the ways to order (b + g) people, where b for boys and g for girls.

then, P(Gi) = [tex]\frac{|Gi|}{|s|}[/tex]

|s| = (b + g)! / b! g!

for the purpose of this problems, individuals of the same sex are indistinguishable.

since, if we put a girl in the ith position, the other (b + g - 1) positions can be filled in randomly.

|Gi| = (b + g - 1)! / (g - 1)! b!

then, P(Gi) = [tex]\frac{|Gi|}{|s|}[/tex]

P(Gi) = [ (b + g - 1)! / (g-1)! b! ] / [ (b + g)! / b! g! ]

P(Gi) = g / (b + g)

Therefore, the probability is g / (b + g).

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The Medicine Concentration drops 70 % each hour .

What is a graph ?

graph can be defined as a visual indicator in which we can represent the data.

Given,

A certain medicine is injected, its concentration in the bloodstream changes exponentially over time as shown in graph

Concentration of medicine when it was injected

=> at t = 0

Hence 100  mg/l  was concentration when medicine was injected

Nt  = No [tex]e^{-kt}[/tex]

N₀  - initial Quantity = 100 mg/l

at  t = 1  Concentration is 70 mg/l

=>  70 = 100   [tex]e^{-kt}[/tex]

=> k =  0.3567

Decay Constant = 0.3567

T = Half life period

50 = 100  [tex]e^{-kt}[/tex]

=> -0.693 = -kT

=>  1.943 hr

Hence , Medicine Concentration drops 70 % each hour .

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An Equation of the tangent line to the curve is 18y=x+81

Given equation

y²=x

This is an equation of a parabola. graph{y^² = x [-10, 10, -5, 5]}

For finding the tangent to the equation, we first differentiate it.

The goal here is to find the value of dy/dx which will give the slope of the tangent to the parabola.

So,

[tex]\frac{d}{dy}(y^2)=\frac{dx}{dy} \\\\2y=\frac{dx}{dy} \\\\\frac{1}{2y} =\frac{dx}{dy} \\\\[/tex]

Now, we want to evaluate the slope at the given point. So substituting y we get,

[tex]\frac{1}{18} =\frac{dx}{dy}[/tex]

This is the slope of the tangent.

It passes through (81,9) [as per in the question]

The general equation of a line is y=mx+c

m is the slope of the line.

For the line/tangent that we got

[tex]m=\frac{dy}{dx}[/tex]

[tex]y=\frac{x}{18} +C[/tex]

The point should satisfy the equation of the line/ tangent. So,

[tex]9=\frac{x}{18} +C[/tex]

So, c=9/2

Finally, substitute the value in our equation of the line/tangent:

[tex]y=\frac{x}{18} +\frac{9}{2}[/tex]

18y=x+81

Therefore, the equation of the tangent line to the curve at the given point, y =√ x, (81, 9) is 18y=x+81

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Using trigonometric ratio and the angle of depression, the altitude of the plane is 98m

The angle of depression is an angle formed by a horizontal line and a line of sight from a point above that line to an object below that line. It is used in trigonometry to calculate the distance between the observer and the object of interest.

Using trigonometric ratio, we can calculate the height or altitude which the plane is flying.

Data;

Using tangent of the angle;

tan θ = opposite / adjacent

tan 27 = x / 193

x = 193 * tan27

x = 98m

The altitude is 98m

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Answer: If 7 men can paint 42 square feet in a day, then we can say that each man paints 42/7 = 6 square feet per day.

If 20 men paint, then they would paint 20 * 6 = 120 square feet per day.

Step-by-step explanation:

On solving the provided question, we can say that here, in equation the greatest distance the ball is from the ground is -y = -4.9 + 9.8 +2 = 6.9

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

here,

the equation y=-4.9x^2+9.8x+2

where y = the distance the ball is from the ground in meters

x = the elapsed time in seconds

the greatest distance the ball is from the ground is -

[tex]y=-4.9x^2+9.8x+2[/tex]

x = 1

y = -4.9 + 9.8 +2 = 6.9

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B-The two distributions for number of cars in line are both skewed right.

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Answer:

123.2

Step-by-step explanation:

First find area of the square ABCD, then the triangle AMN.

Find CD:

sin30 = CD/20

CD = 20(sin30) = 10

CD = AD = 10

Find MD:

cos30 = MD/20

MD = 20(cos30) = 17.32

AM = MD - AD = 17.32 - 10 = 7.32

Area of ABCD = (10)(10) = 100

Find height of triangle AMN:  AN

cos30 = AN/7.32

AN = cos30(7.32) = 6.34

Area of triangle ANM = 1/2(7.32(6.34) = 23.2

Total Area of the shape = 100 + 23.2 = 123.2

The amount of money that John Xina wants would be = $47,899.8

Percentage is defined as the part of the value that can be expressed as per 100 of the whole given value. This can be represented with a symbol such as %.

The amount of money Uzi has = $69,420

The percentage of money John wants from uzi = 69%

The amount of money that is 69% of Uzi's money;

= 69/100×69,420

= 4789980/100

= $47,899.8.

Therefore, the amount of money that John wants from Uzi would be = $47,899.8.

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Answer:

see photo attached

Step-by-step explanation:

Answer: -4.2

Step-by-step explanation:

=1-6+0.8

=-4.2

The equation of a line is 3y+x+10 = 0 when it passes through the point (-5,5).

What is Equation of Straight line ?

Equation of Straight line as follows , y = mx+b

where m is slope of the line.

Given ,

The equation of line k is y+10=3(x+3).

Perpendicular to line k is line , which passes through the point (5,–5)

So, the given equation could be,

y = 3x+9-10

y = 3x-1

m = 3

So, the slope of the another line = -1/3

So, the equation could be ,

when it passes through the point (5,-5) is

y - (-5) = -1/3  ( x - 5 )

y+ 5 = -1/3  ( x-5)

3 (y+5) = -1 (x-5)

3y+15 = -x + 5

3y+x+15-5 = 0

3y+x+10 = 0

Hence, The equation of a line is 3y+x+10 = 0 when it passes through the point (-5,5).

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Answer: x=5

Step-by-step explanation:

[tex]\displaystyle(\frac{125}{27} )*(\frac{125}{27} )^x=(\frac{5}{3})^{18} \\\\(\frac{5^3}{3^3})*(\frac{5^3}{3^3})^x=(\frac{5}{3})^{18}\\\\(\frac{5}{3} )^3*((\frac{5}{3})^3)^x =(\frac{5}{3})^{18}\\\\(\frac{5}{3} )^3*(\frac{5}{3})^{3*x}= (\frac{5}{3} )^{18}\\\\(\frac{5}{3} )^3*(\frac{5}{3})^{3x}= (\frac{5}{3} )^{18}\\\\(\frac{5}{3})^{3x+3}= (\frac{5}{3} )^{18}\\\\Hence,\ \\\\3x+3=18\\\\3x+3-3=18-3\\\\3x=15\\\\[/tex]

Divide both parts of the equation by 3:

[tex]x=5[/tex]

The two possible sets of four numbers are (9,-27,81, -243) and (-18,-54,-162,-486).

A geometric progression is a special type of progression where the successive terms bear a constant ratio known as a common ratio. It is also commonly referred to as GP. The GP is generally represented in form a, ar, ar2.... where 'a' is the first term and 'r' is the common ratio of the progression. The common ratio can have both negative as well as positive values. To find the terms of a geometric series, we only need the first term and the constant ratio. Finite geometric progression contains a finite number of terms. It is the progression where the last term is defined. Infinite geometric progression contains an infinite number of terms. It is the progression where the last term is not defined.

Let the first term of the geometric progression be a and the common ratio be r.

The second term is less than the first by 36.

∴ a - ar = 36

⇒ a(1-r) = 36 --- (1)

The third term is greater than the fourth term by 324.

∴ ar² - ar³ = 324

⇒ ar²(1-r) = 324  --- (2)

Divide equation (2) by equation (1):

∴ r² = 9

⇒ r = ±3

Put r in the first equation:

⇒ a - ar = 36

⇒ a(1 - (±3) = 36

⇒ a = 36/4 or 36/-2

∴ a = 9 or -18

Similarly finding the other three terms:

ar = 9× -3 or -18×3  = -27 or -54

ar² = -27×-3 or -54×3 = -81 or -162

ar³ = -81×-3 or -162×3 = 243 or -486

Thus, the two possible sets of four numbers are (9,-27,81, -243) and (-18,-54,-162,-486).

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