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The time it take riders to pass over the hill and reach ground level is 111.19 seconds .

Given :

the roller coaster's height expressed by the equation below;

h = -0.067t^2 + 7t + 50

where

t is the time in seconds

The driver will hit the ground at the point where h = 0

Substitute

-0.067t^2 + 7t + 50 = 0

Multiply through  by -1

0.067t^2 - 7t +-50 = 0

Factorize :

On factorizing, the positive value of "t" is 111.19 seconds

Hence the time it take riders to pass over the hill and reach ground level is 111.19 seconds

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True, a data warehouse allows users to specify certain dimensions or characteristics.

In a data warehouse, dimensions represent the different aspects or characteristics by which data can be categorized or analyzed. These dimensions can include various attributes or variables that provide context and organize the data.

Users of a data warehouse can specify these dimensions based on their analytical needs and the nature of the data being stored.

For example, in a sales data warehouse, common dimensions may include product, customer, time, and location.

By specifying these dimensions, users can slice and dice the data based on different criteria and gain insights from various perspectives.

By defining dimensions, users can navigate through the data warehouse and perform multidimensional analysis using tools such as OLAP (Online Analytical Processing).

Dimensions provide a structure for organizing and querying data in a way that facilitates analysis and reporting.

In summary, a data warehouse allows users to specify dimensions or characteristics that help organize and analyze the data stored in the warehouse. These dimensions provide a framework for users to navigate and explore the data from different perspectives.

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Jamal would need approximately 7.9 gallons of gas to travel 296.25 miles.

We can use the concept of direct variation to solve this problem. Direct variation means that two quantities are related by a constant ratio. In this case, the number of miles driven is directly proportional to the number of gallons used.

To find the constant of proportionality, we can use the given data. From the table, we can see that when Jamal used 14 gallons, he drove 525 miles. So we can write:

14/525 = k

where k is the constant of proportionality.

Solving for k, we get:

k = 14/525

Now we can use this value of k to find how many gallons Jamal would need to travel 296.25 miles. Let x be the number of gallons he would need. Then we can write:

x/296.25 = k

Substituting the value of k, we get:

x/296.25 = 14/525

Solving for x, we get:

x = (296.25 × 14) / 525

x ≈ 7.9

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Answer:

\( log_{2}(9x) - log_{2}(3) = 3 \\ 3 = log_{2}(8) or log_{2}( {2}^{3} ) \\ log_{2}( \frac{9x}{3} ) = log_{2}(8) \\ \frac{9x}{3} = 8 \\ 9x = 8 \times 3 \\ 9x = 24 \\ x = \frac{24}{9} \\ x = \frac{8}{3} \\ x = 2 \times \frac{2}{3} \)

Answer:

\(\log _2\left(9x\right)-\log _2\left(3\right)=3 : x = \frac{8}{3}\)

Decimal:

\(x = 2.66666...\)

Step-by-step explanation:

\(\log _2\left(9x\right)-\log _2\left(3\right)=3\)

Add \(log _2\left(3)\) to both sides:

\(\log _2\left(9x\right)-\log _2\left(3\right)+\log _2\left(3\right)=3+\log _2\left(3\right)\)

Simplify:

\(\log _2\left(9x\right)=3+\log _2\left(3\right)\)

Use the logarithmic definition: If \(\log _a\left(b\right)=c\:\mathrm{then}\:b=a^c\)

\(\log _2\left(9x\right)=3+\log _2\left(3\right)\quad \Rightarrow \quad \:9x=2^{3+\log _2\left(3\right)}\)

\(9x=2^{3+\log _2\left(3\right)}\)

Expand \(2^{3+\log _2\left(3\right)} : 24\)

\(9x=24\)

Solve: \(9x=24 : x = \frac{8}{3}\)

\(x = \frac{8}{3}\)

Verify solutions: \(x = \frac{8}{3}\)  : True

The solution is:

\(x=\frac{8}{3}\)

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Answer:

1080 cm²

Step-by-step explanation:

Surface area pyramid shape = 2(15*12) = 360

Surface area cube = 5( 12 x 12) = 720

360 + 720 = 1080 cm²

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The required percentage of the 30 intermediate-level questions is 20%.

Given that,
Practice questions for a textbook are marked with difficulty levels of easy, Intermediate, and difficult. 30 of the 149 practice questions are rated as intermediate, approximately what percentage of the questions are intermediate level is to be determined.

the percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
the required percentage of the intermediate difficult question,
= 30 / 149 * 100
≈ 0.20 * 100
≈ 20%

Thus, the required percentage of the 30 intermediate level question is 20%.

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We need to first find the intersection between Q and R, which is the common elements between both groups. We have:

Now we need to determine the union between them:

The distance when the mass is 5kg is 15cm.

When two values vary directly, it means that both values move in the same direction. If one of the value increases, the other value increases and if one of the values decreases, the other value decreases.

The equation that is used to represent direct variation is:

d = km

Where:

The first step is to determine the value of k:

12 = 4k

k = 12 / 4

k = 3

d = 3 x 5 = 15cm

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Because results has been normally distributed and every group of 100 people would have different heights .

Answer:

  (c)  (15, -30)

Step-by-step explanation:

A proportional relationship has the equation ...

  y = kx

The value of the constant of proportionality is the ratio of y to x:

  k = y/x = 40/-20 = -2

__

The point that is on the line y = -2x is the point (15, -30).

Answer:

one temp that ice freezes or could exist would be 32°F and at -34°C

Step-by-step explanation:

Answer:

PC = 12 units

AP = 10 units

Step-by-step explanation:

In ΔACE

∵ P is the centroid of it

∴ P divides CF the ratio 2: 1 from C

∴ PC = 2 PF

∵ PF = 6 units

∴ PC = 2(6)

∴ PC = 12 units

∵ P divides AD at the ratio 2: 1 from A

→ That means AD = 2 + 1 = 3 parts, and AP = \(\frac{2}{3}\) AD

∴ AP = \(\frac{2}{3}\) AD

∵ AD = 15 units

∴ AP = AP = \(\frac{2}{3}\) (15)

∴ AP = 10 units

We will get that the angle theta is:

θ = β/2

Remember that the sum of the interior angles of any triangle must be equal to 180°.

Now, looking at the triangle in the left, we can see that the top angle is equal to:

180 - 2α

The right angle is equal to:

180 - 2β

And the left angle is α

Then we can write:

α + (180 - 2α) + (180 - 2β) = 180

-α - 2β = -180

α = 180 - 2β

Now we can go to the other triangle, where theta is, and write:

α + β + 2θ = 180

Replacing what we found above, we get:

180 - 2β + β + 2θ = 180

-β + 2θ = 0

θ = β/2

That is the best simplification we can get with the given diagram.

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For a continuous random variable, X, with probability density function, \(f(x) = \[ \begin{cases}C(4x −2x²)& 0 < x < 2 \\ 0 &otherwise \end{cases} \]\), the value of C is equals to \(C= \frac{ 3}{8}\).

A continuous random variable has an uncountably infinite number of possible values. The condition for valid pdf of a continuous random variable is \(\int_{- \infty }^{ \infty } f(x)dx = 1\). We have a continuous random variable, X, with probability density function (pdf), f(x), defined as \(f(x) = \[ \begin{cases}C(4x −2x²)& 0 < x < 2 \\ 0 &otherwise \end{cases} \]\) which is a pointwise function. Since f is a probability density function, we must have \(\int_{- \infty }^{ \infty } f(x)dx = 1\), implying that, so, \(\int_{-\infty }^{ 0 } f(x)dx + \int_{0 }^{ 2 }f(x)dx + \int_{2}^{\infty } f(x)dx = 1 \\ \)

Now, check the function carefully are plug the values of probability density function. So, \(\int_{- \infty }^{ 0 } 0dx + \int_{0 }^{ 2 } C(4x −2x²),dx + \int_{2}^{\infty }0 \ dx = 1 \\ \)

=> \( \int_{0 }^{ 2 } C(4x −2x²)dx = 1\)

Using the integration rules,

\(C(\int_{0 }^{ 2 }4 x dx − \int_{0 }^{ 2 } 2x²dx) = 1\)

\(4C[ \frac{x²}{2}]_{0 }^{ 2 } − C[\frac{2x³}{3}]_{0 }^{ 2 }= 1 \)

= >\(C[4 \frac{2²}{2}-0]−C[\frac{2× 2³}{3}-0] = 1\)

=> \(8C- \frac{16}{3}C = 1\)

=> \( \frac{ 8}{3}C= 1\)

=> \(C = \frac{ 3}{8}\)

Hence, required value is \(C = \frac{ 3}{8}\).

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Complete question:

Suppose that X is a continuous random variable whose probability density function is given by f (x) =C(4x −2x²), 0<x <2 0, (1) What is the value of C?

The scale factor used in the dilation is 1/2

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

The scale factor is calculated as

Scale factor  = A'/A

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

Scale factor  = (-1, 3)'/(-2, 6)

Evaluate

Scale factor  = 1/2

Hence, the scale factor is 1/2

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Answer:

13. Parallelogram

14. alternate interior angles (h & a)

same side interior angles (e+d & a)

Step-by-step explanation:

13. Parallelogram: Draw it out with the angles. It helps. It can't be a square, because the side lengths aren't the same (2 lines vs 1 line). It can't be a rectangle because rectangles have 90 degrees and not 152 and 28. It can't be a rhombus because the side lengths in a rhombus must be the same (a rhombus is a square that has been stretched).

14. Look at picture (there might be more than what I wrote in the answer)

Answer:

Step-by-step explanation:

definition of a square : Square has 4 congruent sides. 4 right angles (90°). Opposite sides are parallel. All angles are congruent.

first the shape seems a square, but looking at the information given shows the shape is quadrilateral because it has four sides, and it is not a square because the angles of the shapes are not equal to 90 degrees( even though it shows that) but the given information shows that the angles are 28,152,152, and C. The sum of the angles of any quadrilateral should equal 360,

152+152+28+28=304+56=360 degrees,

opposite angles are equal : angle D=Angle B=28 and angle A=angle C=152

AD=BC and DC=AB ( it seems the shape is a parallelogram).

second image : the two line are parallel then :

angle: g+h=e+d+h=180 degrees ( straight angles)

angle h=angle f

angle g= angle e+d

angle h+b=90 degrees

the sum of angles d+a+c=180 degrees ( the sum of angles of triangle=180).

sum of angles: d+h+90+d+a+c=360 degrees ( sum of angles of quadrilateral=360)

Answer:

Just count the number of zeros:

Step-by-step explanation:

There are 4 zeros, so the answer is 5 x 10^4.

Answer:

5 * 10^4

Step-by-step explanation:

In scientific notation, the amount an exponent has indicates how many zeroes are there.

Since we see four zeroes in the number 50,000

The only equation that would fit is of course 5 * 10^4

Answer:

$39

Step-by-step explanation:

Substitute 4 into the x variable in the equation. From there, multiply.

9.75 x 4 = y

y = 39

Extrapolation is the act of making predictions or estimations about values of the response variable that lie outside the range of the data used in regression analysis. In simpler terms, it is the process of extending a trend line beyond the range of data in order to predict future outcomes.

Extrapolation is considered a bad idea in regression analysis because it is based on the assumption that the linear trend observed in the data will continue indefinitely. However, this assumption may not always be true, and the further away the prediction is from the range of data, the less accurate the prediction is likely to be. In addition, when extrapolating, there is a greater risk of encountering outliers or extreme values that can skew the prediction. This is because the range of data used in the regression analysis may not fully represent the entire population, and therefore, extrapolation may not provide accurate predictions for the population as a whole.

Therefore, it is important to exercise caution when extrapolating and to be aware of the limitations and potential pitfalls associated with this technique. In general, it is recommended to only make predictions within the range of data used in the regression analysis, and to avoid making predictions too far outside this range.

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The converse of p→q, "If 77 is odd, then 77 is prime," is a false statement.

The proposition p→q, in English, is "If 77 is prime, then 77 is odd." The converse of p→q is q→p, which can be expressed as "If 77 is odd, then 77 is prime."

To determine whether this converse is true or false, let's first examine the truth values of the propositions p and q:

p: "77 is prime" - This statement is false, as 77 is not prime (it has factors 1, 7, 11, and 77).

q: "77 is odd" - This statement is true, as 77 is not divisible by 2.

Now, let's evaluate the truth value of the converse q→p:

q→p: "If 77 is odd, then 77 is prime" - Since the premise (q) is true and the conclusion (p) is false, the overall statement q→p is false. A conditional statement is only true when the premise being true leads to the conclusion being true. In this case, the fact that 77 is odd does not imply that it is prime.

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Answer:

y = 2x+4

Step-by-step explanation:

slope (m) = 2

point (-1,2)

so,

b = 2-2×(-1) = 4

y = mx+b

or, y = 2x+4

This value represents the present worth below which the probability is 0.5, indicating a negative present worth.

To estimate the probability that the present worth is negative using the NORM.INV function in Excel,

we need to calculate the present worth of the project and then determine the corresponding probability using the normal distribution.

The present worth of the project can be calculated by finding the sum of the present values of the annual receipts over the 10-year period, minus the initial investment. The present value of each annual receipt can be calculated by discounting it back to the present using the minimum attractive rate of return (MARR).

Using the given information, the present value of the initial investment is $10,000. The present value of each annual receipt is calculated by dividing the expected return of $1,800 by \((1+MARR)^t\),

where t is the year. We then sum up these present values for each year.

We can use the NORM.INV function in Excel to estimate the probability of a negative present worth. The function requires the probability value, mean, and standard deviation as inputs.

Since we have a mean and standard deviation for the present worth,

we can calculate the corresponding probability of a negative present worth using NORM.INV.

This value represents the present worth below which the probability is 0.5. By using the NORM.INV function,

we can estimate the probability that the present worth is negative based on the given data and assumptions.

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Answer:

B.  14 ft approx

Step-by-step explanation:

Given data

A teepee  has a conical shape

Diameter= 10ft

radius= 5 ft

Volume = 366ft³

Height = ????

The expression for the volume is

V= 1/3πr^2 h

substitute

366= 1/3*3.142*5^2*h

366= 1/3*78.55*h

366= 26.18h

h= 366/26.18

h=13.98 ft

h= 14 ft approx

Hence the Height is 14 ft approx

Answer:

14 ft

Step-by-step explanation:

a p e x!

Answer:

y = (1-2x)/(3x+6)

Step-by-step explanation:

To find the inverse of a function, we can swap the x and y variables in the original function and then solve for y. In this case, the original function is f(x) = (1-2x)/(3x+6). Swapping the x and y variables, we get:

y = (1-2x)/(3x+6)

To solve for y, we can first multiply both sides of the equation by (3x+6) to eliminate the fraction:

y(3x+6) = 1-2x

Expanding the left-hand side, we get:

3xy + 6y = 1-2x

Next, we can move all the terms containing y to the left-hand side of the equation and all the other terms to the right-hand side:

3xy + 6y = 1-2x

3xy + 6y - 1 + 2x = 0

Finally, we can divide both sides of the equation by 3 to solve for y:

y(3x+6) - (1-2x)/3 = 0

y = (1-2x)/(3x+6)

Thus, the inverse of the original function f(x) = (1-2x)/(3x+6) is y = (1-2x)/(3x+6).

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Answer:

h = - 103/8

Step-by-step explanation:

1) Re-order terms so constants are on the left

8h = = -2(8)²+4(8)-7

2) Evaluate the exponent

8h = -2·64+4(8)-7

3) Multiply the numbers

8h = -128+4(8)-7

4) Multiply the numbers

8h = -128+32-7

5) Add the numbers

8h = -103

6) Divide both sides of the equation by the same term

8h/8 = -103/8

7) Simplify

- Cancel terms that are in both the numerator and denominator

h = -103/8

Answer: 15 - 6i

Step-by-step explanation:

3(5-2i)

3×5+3×(−2i)

Do the multiplications.

15−6i

Answer:

3 = 14 and 4 = 8

Step-by-step explanation:

The reason as to why this is, is because of the line going down the middle. If you were to open one of the lengths as a door starting from the middle line it would fit perfectly with the top one.