mina 15. a car gets $12$ miles per gallon uphill and $24$ miles per gallon downhill. if the car goes to the top of pike's peak and back ($48$ miles uphill followed by $48$ miles downhill), what is the car's gas mileage, in miles per gallon, for the entire trip?

Answer:

I could be wrong but I think its B

Step-by-step explanation:

Answer: 65

Step-by-step explanation: correct answer is 65 b

Answer:

6x-9

Step-by-step explanation:

you do

Answer: 6x-9

Step-by-step explanation:

We know that the word than is a switch word. Therefore, the nine will go after the minus sign. X is the variable (unknown number). Times is a multiplication word but you do not put a multiplication symbol when there is just a variable.

Hence, our answer is 6x - 9

Step-by-step explanation:

the construction of a right angle (2 lines at 90° interception angles).

The measure of angle ABP is 90° and the measure of angle APB is 48°.

In the given figure, the measure of arc AB is 108° and the measure of angle ACB is (x+3)°.

Tangent and radius of a circle meet at 90°. If we draw a radius that meets the circumference at the same point, the angle between the radius and the tangent will always be exactly 90°.

Question 6:

Here, The measure of arc AB = 2×The measure of angle ACB

108 = 2(x+3)

⇒ x+3=54

⇒ x =51°

Question 7:

Given that, ∠PAB=42° and line PB is tangent to circle A

Now, ∠ABP =90° (Angle formed by tangent and radius is 90°)

Here, ∠ABP+∠PAB+∠APB=180°

⇒ 90°+42°+∠APB=180°

⇒ 132°+∠APB=180°

⇒ ∠APB=180°-132°

⇒ ∠APB=48°

Therefore, the measure of angle ABP is 90° and the measure of angle APB is 48°.

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Answer: 4

Step-by-step explanation:

24 can be written as 24/1

24/1 times 1/6 = 24/6 = 4

Answer: 4

Step-by-step explanation:

24x1/6=4

The 90% confidence interval is given by (3.9911; 7.9911)

It is 90% confident that the true average speed of a vehicle on a highway is between 3.9911 and 7.9911 miles per hour.

1) Former concept

A confidence interval is "a range of values ​​that is likely to encompass the values ​​of a population with some degree of confidence. Often expressed as a percentage.

The error bar is the range of values ​​above and below the sample statistic in the confidence interval.

A probability distribution that is symmetric about the mean and indicates that data close to the mean are more common than data far from the mean.

X = 2, represents the sample mean of the sample

μ = population mean (variable of interest)

s = 1 represents the standard deviation of the sample

n = 11 represents the sample size

2 ) Confidence Interval:

Confidence Interval for mean is given below:

                  X ± t (α/2) s/√n

To compute the critical value, we first need to find the degrees of freedom given by

df = n -1

   = 11 -1 = 10

Confidence is 0.90 or 90%, so the value of and is α = 0.1 , and α/2 = 0.05 you can use Excel, a calculator, or a spreadsheet to find the critical values. The Excel command would be "=-T.INV(0.05,10)".

2 - 1.81 (1/√11) = 3.9911

2 + 1.81 (1/√11) = 7.9911

So in this case the 90% confidence interval is (3.9911 , 7.9911)

We are 90% confident that the true mean for the speeds of vehicles traveling on a highway is between 3.9911 and 7.9911 miles per hour.

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Answer: $108

Step-by-step explanation:
3% = 0.03
1800 x 0.03 x 2 = 108

The lengths of the edges of the considered rectangular box which will give the minimum surface area are all ∛34.

How to find the surface area and volume of a closed rectangular box?

Suppose the dimensions of the rectangular box be 'a', 'b' and 'c' units respectively. Then, we get:

Surface area of the box, S = 2(ab + bc + ca) unit²

Volume of the box, V = abc unit³

For the considered box, let the dimensions be 'a', 'b' and 'c' cm.

Then, as we're provided that the volume of the box is 34 cubic cm, we get:

abc = 34

c = 34/ab

Thus, the surface area of the considered figure would be given as:

S = 2(ab + bc + ca) unit²

S = 2(ab+ c(b+a))

= 2(ab+ (34/ab) (b+a))

=( 2a²b² + 68b + 68a)/ ab cm²

There is symmetry in the equation we obtained for surface area between 'a' and 'b'.

That means, they will be of same measure to minimize or maximize the surface area. It is because if one of them is bigger than other, it is possible to prove that other one, by same tricks, can be proved bigger than first one.

Thus, we have a = b for S to be maximum or minimum.

Thus, we get:

Smax or min = (2a⁴+136a) / a²

= (2a²+ 136) / a

= f(a)

Taking first derivative of f(a), we get:

f'(a) = 4a - 136 / a²

f''(a) = 4 + 272/a³

Putting second rate = 0, we get critical points as:

f'(a) = 0

4a = 136/ a²

a³ = 34

a = ∛34 = b

Thus, the only critical value found is corresponding to minima.

Thus, S is minimum when a = b = ∛34

The value of c is:

c = 34/ab

= 34/ [tex]\sqrt[3]{34^{2} }[/tex]

= (34)¹/³

c = ∛34

Thus, the lengths of the edges of the considered rectangular box which will give the minimum surface area are all ∛34.

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Answer: p-3[tex]\leq[/tex]29

Step-by-step explanation:

Rounded Answer:

0.005 or 0.0049

Answer: A total of 30 teachers

Step-by-step explanation:

20% = 6 (science) teachers

20x5= 100

6x5=30 teachers

Hope this helps you!

Answer:

30 teachers

20% is 2/10 of 100

20 x 5 = 100

6 x 5 = 30

Therefore, 30 teachers.

The population means may be the same

So, option D is correct.

In statistics, the probability that a population parameter will fall between a set of values a predefined percentage of the time is known as the confidence interval. Analysts typically use confidence intervals that cover 95% or 99% of the expected observations while assessing data. In frequentist statistics, an estimation range for an unknown parameter is referred to as a confidence interval. The most common confidence level for computing confidence intervals is 95%, however other levels, such 90% or 99%, are also occasionally employed. The conclusion is reached that the result is statistically significant if the confidence interval eliminates the value of zero effect.

If (μ₁- μ₂=0) is included in the confidence interval, that means this two means have the same difference that is zero.

Therefore, they may be nearly same,

So, The population means may be the same

Hence, option D is correct.

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Answer:

The slope is 3/8

Step-by-step explanation:

The slope of the line given by the equation 3x - 8y = -16 is 3/8.

To find the slope of the line given by the equation 3x - 8y = -16, we need to rearrange the equation into slope-intercept form, y = mx + b, where m represents the slope.

Starting with the given equation:

3x - 8y = -16

We can isolate y by subtracting 3x from both sides:

-8y = -3x - 16

Next, we divide both sides of the equation by -8 to solve for y:

y = (3/8)x + 2

Now, we can observe that the equation is in slope-intercept form, y = mx + b, with m = 3/8.

This means that for every increase of 1 in the x-coordinate, the y-coordinate increases by 3/8.

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The domain of the function y = 2 - √(-3x+2) is (-∞ , 2/3] and the range of the function is (-∞ , 2]  .

In the question ,

it is given that , the function is ⇒ y = 2- √(-3x+2) .

For Domain ,

we know that the square root function is defined only when the number inside the root is non negative .

that means ,

-3x [tex]+[/tex] 2 ≥ 0

Subtracting 2 from both the sides ,

we get ,

-3x ≥ -2

x ≤ 2/3

the Domain is (-∞ , 2/3] .

For range , we know that the root function value in always non negative .

√(-3x + 2) ≥ 0

Multiply by -1 on both sides

we get ,

-√(-3x + 2) ≤ 0

Adding 2 to both the sides

2 - √(-3x + 2) ≤ 2

y ≤ 2

the range is (-∞ , 2] .

Therefore , the domain is (-∞ , 2/3]   and the range is (-∞ , 2] .

How do we find the domain and range of the function y = 2- √(-3x+2) ?

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The standard equation of parabola that has focus (5, 0) and directrix x = -5 is y² = 20x.

Any point in a parabola has an identical distance from the fixed point, making it resemble a curve.

Given that,

The focus of the parabola is (5, 0).

And Directrix x = -5

Since the directrix is horizontal here, use the standard equation of parabola,

(y - k)² = 4 p (x  - h)

Vertex = (h, k)

= ((x coordinate of focus + directrix)/2 , 0)

= ((5 - 5)/2, 0)

= (0, 0)

p = distance from focus to the vertex = 5 - 0 = 5

The required equation of parabola,

(y - 0)² = 4 × 5(x - 0)

y² = 20x

The equation of parabola is  y² = 20x.

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The area that park will need to cover 67.95 square feet of the ramp.

The trigonometric ratios are defined for a right angled triangle.

The example of these ratios are sin, cos, tan, cosec, sec and cot.

The trigonometric ratios are useful in determining the heights and distances of the large objects.

Suppose the length of the wood be x.

The length of wood forms the right triangle as shown in the figure.

Apply trigonometric ratio to the triangle to get,

Cos (28°) = 12/x

⇒ x = 12/Cos (28°) = 13.59

Now, the area of the wood is given as,

Length × width

⇒ 13.59 × 5 = 67.95

Hence, the area of wood required is 67.95 square feet.

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This is a fraction, so it can also be written as a decimal by dividing the numerator by the denominator: 1/62 = 0.0161.

What is conditional probability?

Conditional probability is a measure of the probability of an event occurring given that another event has already occurred. It is written as P(A|B), where A and B are events and P(A|B) represents the probability of event A occurring given that event B has already occurred.

To find the probability that one of each color is drawn from the bag, you can use the following steps:

Calculate the total number of possible combinations of three balls that can be drawn from the bag without replacement. This is equal to the number of ways to choose 3 balls from a total of 16 balls, which is calculated using the combination formula:

Total number of combinations = 16 choose 3

= (16 * 15 * 14) / (3 * 2 * 1)

= 560

Calculate the number of combinations that include one ball of each color. There are 3 ways to choose the red ball, 3 ways to choose the black ball (since one of each color has already been chosen), and 1 way to choose the white ball (since there is only 1 white ball left). Therefore, the total number of combinations that include one ball of each color is:

Combinations with one ball of each color = 3 * 3 * 1

= 9

Calculate the probability by dividing the number of combinations with one ball of each color by the total number of combinations:

Probability = 9 combinations / 560 combinations

= 9/560

= 1/62

Therefore, the probability that one of each color is drawn from the bag is 1/62. This is a fraction, so it can also be written as a decimal by dividing the numerator by the denominator: 1/62 = 0.0161.

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Answer: The answer is A) True.

Step-by-step explanation: It is possible, although the only thing that wouldn't be possible is an equilateral triangle, since there is one side length that is different.

I hope this helps!!

The amount of butter that is used this month will be 320 kilograms.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

A pastry shop utilized 25% less spread for the current month than a month ago. The pastry shop utilized 240 kilograms of spread for the current month.

Let 'x' be the amount of butter used in the last month. Then the equation is given as,

(1 - 0.25) x = 240

Simplify the equation, then we have

(1 - 0.25) x = 240

0.75x = 240

x = 240 / 0.75

x = 320 kilograms

The amount of butter that is used this month will be 320 kilograms.

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There is no single formula for a figure. Different figures may have different equations or formulas, depending on the type of figure and the desired result as triangle.

The formula of a figure depends on the type of figure in question. For example, a circle has a circumference formula of C = 2πr, while a square has an area formula of A = s^2, where s is the length of a side. The formula for a triangle is A = (1/2)bh, where b is the base and h is the height. The formula for a sphere is V = (4/3)πr^3, where r is the radius. Different figures may also have different formulas for calculating their perimeter, area, or volume.

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Therefore solution to the given problem is the p-value is 0.08 .

It is common practice to evaluate statistical hypotheses using test statistics. A popular way to describe a hypothesis test is with a test statistic, which is a count of a data set that can be used to perform the test and reduces the data to a single number.

Here,

test statistics Z

=> Z =  [tex]\frac{p-p'}{\sqrt{p'(1-p')/n} }[/tex]

Null hypothesis H0 : p= 0.15

And

Alternate hypothesis Ha: p>0.15

Z = (0.2 -0.15) / √0.15 *0.85/100

Z=1.40

Thus

p- value= P(Z>1.40)=1-Ф(1.4)=1-0.92 =0.08

Therefore , the p- value is 0.08 , thus half of population is supporting

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The remaining root of f(x) will be 3 - [tex]\sqrt{11}[/tex]

To answer this question we have to find the conjugate of 3+[tex]\sqrt{11}[/tex],

For example, the conjugate of p+q will be p-q or vice versa.

Let us consider x= 2+[tex]\sqrt{11}[/tex]

To simplify the equation let us subtract 3 on both sides of the equation

x - 3 = 3+[tex]\sqrt{11}[/tex] - 3

x - 3 = [tex]\sqrt{11}[/tex]

Square both,

[tex](x - 3)^{2}[/tex] = 11

[tex](x - 3)^{2}[/tex] - 11 =0

Now we will use the principle of Square difference to factorize both sides-

[tex](d^{2} - e^{2}) = (d - e)(d + e)[/tex]

(x - 3) - 11 × (x - 3) + 11 = 0

on solving the equation we get,

(x - 3) - 1 = 0  let us consider this first equation

or (x - 3) + 11 = 0 let us consider this second equation

Add [tex]\sqrt{11}[/tex] on both sides of the first equation,

[tex]x - 3 = \sqrt{11}[/tex]

Subtract [tex]\sqrt{11}[/tex] on both sides of the second equation,

[tex]x - 3 = -\sqrt{11}[/tex]

Now by adding 3 on both sides of the first and second equation,

[tex]x = 3 + \sqrt{11}[/tex] or [tex]x = 3 - \sqrt{11}[/tex]

Therefore, the remaining root of f(x) will be = [tex]3 - \sqrt{11}[/tex]

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Complete Question - If a polynomial function f(x), with rational coefficients, has roots 0, 4, and 3 + [tex]\sqrt{11}[/tex], what must also be a root of f(x)?.

The contrapositive of the given conditional statement will  be If I did not buy a car, then I did not win the lottery.

When two statement P and Q are written in the formate of if P then Q,  it means Q must be true whenever P is true, these types of statements that follow some conditions are called conditional statement.

Given that, a conditional statement, "If I won the lottery, then I would buy a car."

Here the P part is If I won the lottery and Q part is I would buy a car.

The rule for statement being contrapositive, for two statement P and Q is,

If not-Q then not-P

Therefore, the contrapositive will be, If I did not buy a car, then I did not win the lottery.

Hence, The asked statement is If I did not buy a car, then I did not win the lottery.

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The percentage of the guests ordered food is 40%

"Information available from the question"

In the question:

There were 425 guests at a hotel. 170 guests ordered food.

To find the what percentage of the guests ordered food?

Now, According to the question:

Total guests in hotel is 425

and, 170 guests ordered food

=> Divide 170 by 425

= 170/ 425 = 0.4

The percentage of the guests ordered food:

=> 0.4 x 100 = 40%

Hence, The percentage of the guests ordered food is 40%

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Answer:

Step-by-step explanation:

1.25, The store has a meter. P is equal to 0.8 times L where P is the price and dollars, and L is the length in meters. The nylon rope cost per meter is the first equation. It comes out to be 80 cents, because our price is equivalent to 0.8 times one Meet her. 80 cents per meter is how much this is. We need to figure out how long of a rope we got. If we have that, the dollar is equal to 0.8 times out. One side that is divided by.8 is equal to the other side. 1.25 m of rope was bought for this question.

To find the the measures of missing angles, it's important to know the total sum in the angles and then subtract by the angles given.

Let's take for instance, a triangle has a total angle of 180°. It should be noted that a triangle has three sides and angles.

Let's say that two of the angles are 50° and 70°, therefore, the value of the third angle be be represented thus:

(50 + 70 + x) = 180

120 + x = 180

Collect like term

x = 180 - 120

x = 60°

The third angle is 60°

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The given equation can be solved for the value of x and y

i.e. x = (3y - 7)/4 & y = (4x + 7)/3.

What is the linear equation?

An algebraic equation of the form y=mx+b is referred to as a linear equation. m is the slope, and b is the y-intercept, and all that is involved is a constant and a first-order (linear) term. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

We have,

The equation 4x=3y-7

So, here we can solve this equation for the x as well as y equals,

Firstly we will solve for x:

4x = 3y - 7

dividing the whole equation by 4 we get,

4x/4 = (3y - 7)/4

x = (3y - 7)/4

Similarly, we will solve for y:

4x = 3y - 7

3y = 4x + 7

dividing the whole equation by 3 we get,

3y/3 = (4x + 7)/3

y = (4x + 7)/3

Hence, the given equation can be solved for the value of x and y

i.e. x = (3y - 7)/4 & y = (4x + 7)/3

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Different types of quadrilateral with four sides and four angle but have different properties make the quadrilateral unique.

Explanation:

Points which makes the quadrilateral unique are as follow:

Therefore, properties of the quadrilateral make them unique.

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