Which type of data (categorical, discrete numerical, continuous numerical) is each of the following variables? (a) Age of a randomly chosen tennis player in the Wimbledon tennis tournament. O Discrete numerical O Continuous numerical O Categorical Which measurement level (nominal, ordinal, interval, ratio) is each of the following variables? (a) A customer's ranking of five new hybrid vehicles (1) Noise level 100 meters from the Dan Ryan Expressway strandomly the moment. (c) Number of occupants in a randomly chosen commuter vehicle on the San Diego Freeway Od to select Od to set Od to select

Answer: The length would be 10 in, and the width would be 5 in.

Step-by-step explanation:

10 is two times greater than 5, and 10 + 10 + 5 + 5 = 30. Therefore, the length of the rectangle would be 10 inches and the width of the rectangle would be 5 inches.

I hope this helps!

Using combinations, we concluded that  the probability that fewer than 2 of the next 5 vehicles are from out of state is 0.907.

A checkpoint sees 75% of its traffic coming from within the state.

Therefore, there is a 0.75 percent chance that the car comes from the state.

1-0.75=0.25 represents the likelihood that the car is from outside the state.

Let x now act as the random variable. Consequently, n=9 and X=4

It is necessary to determine the likelihood that less than 2 of the following 5 automobiles are from another state.

We are to calculate the probability of x<2

p=0.25

q=0.75.

Using the formula,

P(x≤2) = ∑ ⁿCₓ pˣ q⁽ⁿ⁻ˣ⁾

P(x≤2) = ∑ ⁵C₂ p² q³ + ⁵C₁ p¹ q⁴ +  ⁵C₀ p⁰ q⁵

P(x≤2) = ∑ \(\frac{5!}{2! 3!}\) (0.25)² (0.75)³ + \(\frac{5!}{1! 4!}\) (0.25)¹ (0.75)⁴ + \(\frac{5!}{0! 5!}\) (0.75)⁵

P(x≤2) = 10 × 0.065 × 0.421875 + 5 × 0.25 × 0.3164 + 0.2373

P(x≤2) = 0.2742 + 0.3955 + 0.2373

P(x≤2) = 0.907

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The extremas of the function f(x) = x³ - 7x² + 10x are given as follows:

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Answer:

-36m^3-21n^3+85mn^2+36m^2n

Step-by-step explanation:

That's what the calculator says:).

Answer:

Yes

Step-by-step explanation:

To know if a table is a function or not, we have to see if 1 input only has 1 output.

Looking at the table each input only has 1 output, so it is a function.

\(205\)

hope it helps

Answer:  

x    y-values

1    175

2   175

3   225

4    275

The domain is 1,2,3,4  it would be from 1 to 4 if the electrician bills for partial hours, or greater than 4, but this is not in the chart.

The range is 175,225,275.  Again there could be other values in between or greater than 275, but it is not in the chart.

Step-by-step explanation:  It is a function because for each x-value there is only one y-value, even if the y-value is the same for two of the x-valus

a. To find the best estimate for the percentage of people who were affected, we need to divide the affected people by the total population and multiply by 100%. Let's see:

The best estimate for the percentage of people who were affected is about 0.1%

b. To complete the statement, apply the proportion:

Solve for x:

Approximately 86 out of every 100,000 people in the United States were affected by the 1994 salmonella outbreak.

Answer:

8 pigs are there according to the questions because in question there is told that there are pigs as well as ducks

Answer:

Step-by-step explanation:

The vertex is given (-1, 4).

The axis of symmetry is a vertical line and passes through vertex.

Since the x- coordinate of vertex is  - 1, the line of symmetry is x = - 1.

Answer:

x=-1

Step-by-step explanation:

Parabola is symmetric on both sides of the vertex

The axis of symmetry is the x coordinate of vertex

Here the vertex is (-1,4)

So axis of symmetry is x=-1

Answer:

45/60 or 3/4

Step-by-step explanation:

You have to convert any mixed number into a fraction

1 4/5 = 9/5

5/12 = 5/12

Then you multiply across

9 x 5 = 45

5 x 12 =60

Then you would simplify the answer

Answer:

Step-by-step explanation:

The formula for determining distance is expressed as

Distance = speed × time

From the information given,

Speed of boat = 10 miles per hour

It means that the distance that the boat covered after t hours is 10 × t = 10t miles

Since the boat is 100 miles away from the marina and it is sailing directly towards it, then the equation for the distance of the boat from the marina after t hours is

Distance = 100 - 10t

Answer:

12.7

Step-by-step explanation:

Remember this rule when rounding 5 and below let it go (ex. 12.32 = 12.3) 6 and above give it a shove (ex. 12.47 = 12.5).

The area of the Region bounded by y = √x, y = 2-x², and y = -√2x is $\frac{32}{15}$.

To find the area of the region bounded by y = √x, y = 2-x², and y = -√2x, we need to graph the equations and determine the points of intersection. Then we can integrate to find the area.

Firstly, we'll graph the equations and find the points of intersection:

y = √xy = 2-x²y = -√2xGraph of y = √x, y = 2-x², and y = -√2xWe need to solve for the points of intersection, so we'll set the equations equal to each other and solve for x:√x = 2-x²√x + x² - 2 = 0Let's substitute u = x² + 1:√x + u - 3 = 0√x = 3 - u

(Note: Since we squared both sides, we have to check if the solution is valid.)u = -2x²u + x² + 1 = 0 (substituting back in for u

)Factoring gives us:u = (1, -2)We can then solve for x and y:x = ±1, y = 1y = 2 - 1 = 1, x = 0y = -√2x = -√2, x = 2y = 0, x = 0Graph of y = √x, y = 2-x², and y = -√2x with points of intersection to find the area, we need to integrate.

The area is bounded by the x-values -1 to 2, so we'll integrate with respect to x:$$\int_{-1}^0 (2 - x^2) - \sqrt{x} \ dx + \int_0^1 \sqrt{x} - \sqrt{2x} \ dx$$

We can then simplify and integrate:$$\left[\frac{2x^3}{3} - \frac{2x^{5/2}}{5/2} + \frac{4}{3}x^{3/2}\right]_{-1}^0 + \left[\frac{2x^{3/2}}{3} - \frac{4x^{3/2}}{3}\right]_0^1$$$$= \frac{4}{3} + \frac{4}{3} - \frac{4}{15} + \frac{4}{3} - \frac{4}{3}$$$$= \frac{32}{15}$$

Therefore, the area of the region bounded by y = √x, y = 2-x², and y = -√2x is $\frac{32}{15}$.

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Option (O log 7) refers to the base-10 logarithm of 7, represented as log10(7), which is not the same as ln (7). Optional (O log, 10) and (O log, e) mathematical expressions are not acceptable.

In mathematics, the logarithm is the reciprocal of a power. As a result, the exponent by which b must be raised to achieve a number x matches its logarithm in base b. For example, because 1000 = 103, the base-10 logarithm is 3, or log10 = 3. For example, the base 10 logarithm of 10 is 2, but the square of 10 is 100. Log 100 = 2. A logarithm (or log) is the mathematical word used to answer questions such as how many times a base of 10 must be multiplied by itself to get 1,000. The answer is 3 (1,000 = 10 10 10).

When you compute (In), you are calculating the natural logarithm of 7, which is indicated as ln(7) or loge (7).

As a result, the expression you'd be looking up the value of is: ln(7) or loge (7).

Option (O log 7) refers to the base-10 logarithm of 7, represented as log10(7), which is not the same as ln (7). Optional (O log, 10) and (O log, e) mathematical expressions are not acceptable.

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The binomials (x - 3) and (x - 10) are factors of the trinomial x² - 13x + 30.

To determine which binomial is a factor of the trinomial x² - 13x + 30, we need to factorize the trinomial completely.

In this case, we need to find two binomials in the form (x - a)(x - b) that satisfy the equation:

(x - a)(x - b) = x² - 13x + 30

So, (x - 3)(x - 10) = x² - 13x + 30.

Therefore, the binomials (x - 3) and (x - 10) are factors of the trinomial x² - 13x + 30.

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The solution when multiplied 6 times 3 and then dividing by 2 is 9.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

Given that,

Multiply six times three then divide by two.

First we have to multiply 6 times 3.

6 × 3 = 18

Then we divide the answer by 2.

18 ÷ 2 = 9

Hence the solution is 9.

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Answer:

2(x+2)(3x-2)

Step-by-step explanation:

Hope I helped you

The solution to the linear system is c = -6 and d = 3.

To solve the linear system using the elimination strategy, we can eliminate one variable by adding or subtracting the equations. Let's solve the first linear system:

(1) 12c + 28d = 12

(2) -20c + 16d = 168

To eliminate one variable, we can multiply equation (1) by 5 and equation (2) by 3, which will result in opposite coefficients for 'c'. This will allow us to eliminate 'c' when adding the equations together:

(1) 60c + 140d = 60

(2) -60c + 48d = 504

Now, we can add the equations:

(60c + 140d) + (-60c + 48d) = 60 + 504

188d = 564

d = 564/188

d = 3

Substituting the value of 'd' back into equation (1):

12c + 28(3) = 12

12c + 84 = 12

12c = 12 - 84

12c = -72

c = -72/12

c = -6

The solution to the linear system is c = -6 and d = 3.

Now let's analyze the second linear system:

(1) 7x - 3y = 43

(2) 7x - 3y = 13

By comparing the two equations, we can see that they have the same coefficients for both 'x' and 'y', and the constant terms on the right side are different. This means the lines represented by the equations are parallel and will never intersect.

The linear system has no solution.

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The sample space is (a) watermelon, watermelon, lemon-lime, lemon-lime, lemon-lime, grape gumballs, grape gumballs, grape gumballs, grape gumballs, grape gumballs

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

2 watermelon, 3 lemon-lime, and 5 grape gumballs

Rewrite the items according to their frequencies

So, we have the following representation

watermelon, watermelon, lemon-lime, lemon-lime, lemon-lime, grape gumballs, grape gumballs, grape gumballs, grape gumballs, grape gumballs

The above represents the sample space

Hence, the sample space is (a)

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Answer:

D. A pair of intersecting lines

Step-by-step explanation:

A conic section is a fancy name for a curve that you get when you slice a double cone with a plane. Imagine you have two ice cream cones stuck together at the tips, and you cut them with a knife. Depending on how you cut them, you can get different shapes. These shapes are called conic sections, and they include circles, ellipses, parabolas and hyperbolas. If you cut them right at the tip, you get a point. If you cut them slightly above the tip, you get a line. If you cut them at an angle, you get two lines that cross each other. That's what happened in your question. The plane cut the cone at an angle, so the curve is two intersecting lines. That means the correct answer is D. A pair of intersecting lines.

I hope this helps you ace your math question.

Answer:

7.77, 7.773, 7 9/11, 157/20

Step-by-step explanation:

First, convert any fractions to decimals to make it a bit easier to order.

7.773, 157/20, 7.77, 7 9/11

Now we have:

7.773, 7.85, 7.77, 7.82

Order from least to greatest:

7.77, 7.773, 7.82, 7.85

Rewrite using the original numbers in the question:

7.77, 7.773, 7 9/11, 157/20

Hope this helps!

if the square has the same perimeter as the rectangle then the value of y is 92.

The perimeter of a square is equal to the sum of all four sides, so a square with a side of 7 cm has a perimeter of 4 * 7 cm = 28 cm.

The perimeter of the rectangle is equal to twice the sum of the length and width. So for a rectangle of length y/8-3cm and width 4cm, the perimeter is 2 * (y/8-3+4) cm = (y/4-3+8) cm = y/4 . +5 cm.

Since squares and rectangles have the same perimeter, the two perimeter formulas can be equal.

28cm = y/4+5cm

You can solve for y by isolating it on one side of the equation.

years/4+5 = 28

y/4 = 23

y=92

So the value of y is 92.

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The mass per cup for the objects will be 320g and 272g respectively.

Mass simply means the weight that an object contains.

The mass of a teapot and 4 cups is 1,280 grams. The mass per cup will be:

= Mass / Number of cups

= 1280 / 4

= 320g

The mass of the same teapot and 10 cups is 2,720 grams. The mass per cup will be:

= 2720 / 10

= 272g

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The balance for each value of n is calculated by using the formula A = P(1 + r/n) ^nt. The rounded balance values are shown in the last column of the table above.

To complete the table and find the balance A if $3100 is invested at an annual percentage rate of 4% for 10 years and compounded n times a year.

The formula for calculating compound interest is as follows:

A = P(1 + r/n) ^nt,

where P represents the principal investment amount, r is the interest rate, n is the number of times the interest is compounded, t represents the time in years, and A represents the total amount, which includes the principal amount and the interest earned.

The table is given below:
\(\begin{array}{|c|c|c|} \hline \text{n} &

\text{A = P(1 + r/n) }^{nt} &

\text{Balance (rounded to nearest cent)} \\ \hline \text{1} &

\text{3100(1 + 0.04/1)}^{1*10} &

\text{\$4788.03} \\ \hline \text{2} &

\text{3100(1 + 0.04/2)}^{2*10} &

\text{\$4798.76} \\ \hline \text{4} &

\text{3100(1 + 0.04/4)}^{4*10} &

\text{\$4817.46} \\ \hline \text{12} &

\text{3100(1 + 0.04/12)}^{12*10} &

\text{\$4861.94} \\ \hline \end{array}\)

The balance is obtained by substituting the values of P, r, n, and t into the compound interest formula.

In this case, the investment is $3100, the annual interest rate is 4%, the investment is for 10 years, and n is the number of times the interest is compounded.

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To find the height of the shuttle, we can use trigonometry and the concept of similar triangles. The height of the shuttle is approximately 468.675 meters.

Let's assume that the height of the shuttle is represented by 'h' meters. From the information given, we know that the distance between the camera and the launch pad is 750 meters, and the angle of elevation from the camera to the shuttle is 32 degrees.

Using trigonometry, we can set up the following equation:

tan(32°) = h / 750

To find the value of h, we can rearrange the equation:

h = tan(32°) * 750

Using a calculator, we can find the value of tan(32°) ≈ 0.6249.

Now we can calculate the height of the shuttle:

h ≈ 0.6249 * 750

h ≈ 468.675 meters

Therefore, the height of the shuttle is approximately 468.675 meters.

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Answer:

a.H0 : u1= u2 against Ha : u1≠ u2 This is a two sided test

b) There isn't enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.

c) the p- value is 0.0359*2= 0.0718. It is greater than the value of ∝ so there isn't enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.

d) There is enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.

e) There isn't enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.

Step-by-step explanation:

Formulate the null and alternative hypotheses as

a) H0 : u1= u2 against Ha : u1≠ u2 This is a two sided test

Here ∝= 0.005

For alpha by 2 for a two tailed test Z∝/2 = ± 1.96

Standard deviation = s= 3.5 pounds

n= 49

The test statistic used here is

Z = x- x`/ s/√n

Z= 69.1- 70 / 3.5 / √49

Z= -1.80

Since the calculated value of Z= -1.80 falls in the critical region we reject the null hypothesis.

b) There isn't enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.

c) the p- value is 0.0359*2= 0.0718. It is greater than the value of ∝ so there isn't enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.

d) If standard deviation is 1.75 pounds

The test statistic used here is

Z = x- x`/ s/√n

Z= 69.1- 70 / 1.75 / √49

Z= -3.6

This value does not fall in the critical region.

d) There is enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.

e) If the sample mean is 69 pounds

Z = x- x`/ s/√n

Z= 69.1- 69 / 3.5 / √49

Z= 0.2

This value falls in the critical region

e) There isn't enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.

Hello there. To solve this question using the Law of Detachment, first we need to remember what does this law refers to:

Say we have two propositions p and q.

If p implies q and p is true, q is also true.

For the transitivity property, we'll have:

If p = q and q = r, then p = r.

We want to show that the angles 30º and 60º are complementary using that law.

Remember that two angles are complementary when their sum is equal to a right angle, i. e. 90º.

Most likely, to get to this conclusion, we may need to show that the sum of those terms in different orders, I mean, 30º + 60º = 90º = 60º + 30º won't change the value.

Thus, we'll get two properties in which we'll get to the same conclusion as the first thing marked down in bold.

Let's assume p is equal to the sum of angle 1 and angle 2.

r is the sum of angle 2 and angle 1 (just changed the order)

You can see that p = q, since 30º + 60º = 90º

and q, being the right angle, will also be equal to r, since 90º = 60º + 30º

Thus, p = r, which leads us to the conclusion.

p implies q, p is true and q is also true.

The angles are complementary.