Which variable is most important to the following problem?

Ralph and Patrick play on a basketball team.
Ralph played the whole first quarter and the first 4 minutes of the second quarter.
Patrick played the rest of the second quarter and all of the third quarter.
Ralph played the whole
fourth quarter.
Each quarter is 10 minutes long.
How long did Patrick play
during the second quarter?


A. the number of times Patrick was substituted into the game

B. the number of minutes Patrick played in the second quarter

C. the length of a quarter

D. the number of players on the team

Answer:

2700

Step-by-step explanation:

108*25=2700

100*25=2500

            +

    8*25=200

-------------------------------

               2700

Answer:

The probability that x equals 19.62 is 0

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

In the normal probability distribution, the probability of an exact value, that is, P(X = x) is 0. Thus, the probability that x equals 19.62 is 0

Answer:

f(x) = 3 cos  (2Pi / period value ; x  )+ 2

or see answer using 2 as the period see answer in bold below.

Step-by-step explanation:

cosine function amplitude of 3 is  A = 3

The period is used to find B

You need to show period value as the denominator and work out from there with 2PI as a function numerator to show as 2pi / period can be a data angle

C is the adding value.

Acos (Bx) + C

A = 3

Bx =  2 pi / period

C = + 2

However f 2 is also the period found

then we just plug in 2 to above formula

f(x) = 3 cos  (2Pi / 2 ; x  )+ 2

f(x) = 3cos (x pi) + 2

9514 1404 393

Answer:

  20

Step-by-step explanation:

As with any evaluation problem, take it step by step according to the order of operations.

The first thing you need to do here is compute a#b.

The given definition can be simplified a bit for evaluation purposes:

  a#b = a²b -ab² = ab(a -b)

Then for a=3 and b=-2, you have ...

  (3)#(-2) = (3)(-2)(3 -(-2)) = -6(5) = -30

Now, you are in a position to evaluate the expression you're asked for.

  [tex]\dfrac{(a\#b)^2}{15-(a\#b)}=\dfrac{(-30)^2}{15-(-30)}=\dfrac{900}{45}=\boxed{20}[/tex]

Answer:

third and last one

Step-by-step explanation:

im pretty sure those are the answers i used a graphing calculator.

9514 1404 393

Answer:

  C and E

Step-by-step explanation:

The rules of exponents apply:

  (a^b)(a^c) = a^(b+c)

__

  [tex]200(10^x)=20\cdot10^1\cdot10^x=\boxed{20(10^{x+1})}\\\\=2\cdot10^2\cdot10^x=\boxed{2(10^{x+2})}[/tex]

These match the 3rd (C) and last (E) choices.

Answer:

If both cars maintain their average speeds, it will take 12 hours for Mary to catch up with Susan.

Step-by-step explanation:

Since Susan drives north on the 405 Freeway at 50 miles per hour, and two hours after Susan passes under Westminster Blvd, Maria enters the 405 Freeway at Westminster Blvd and heads north at 60 miles per hour, if both cars maintain their average speeds, to determine how long will it take Mary to catch up with Susan the following calculation must be performed:

Hour 1 = 50

Hour 2 = 100

Hour 3 = 150 - 60

Hour 4 = 200 - 120

Hour 5 = 250 - 180

Hour 6 = 300 - 240

Hour 7 = 350 - 300

Hour 8 = 400 - 360

Hour 9 = 450 - 420

Hour 10 = 500 - 480

Hour 11 = 550 - 540

Hour 12 = 600 - 600

Therefore, if both cars maintain their average speeds, it will take 12 hours for Mary to catch up with Susan.

Answer:

x = 19

Step-by-step explanation:

Since the angles are vertical, that means these angles are equal to each other:

7x + 34 = 10x - 23

7x - 10x = -23 - 34

-3x = -57

x = 19

Answer:

Step-by-step explanation:

7x+34=10x-23 (being vertically opposite angles)

34+23=10x-7x

57=3x

57/3=x

19=x

Answer:

-11

Step-by-step explanation:

(8+3)(-1)   Add 8 + 3

(11)(-1)       Multiply

-11           Final Answer

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\large\textsf{(8 + 3)(-1)}\\\\\large\textsf{(8 + 3) = \bf 11}\\\\\large\textsf{11(-1)}\\\\\large\textsf{= \bf -11}\\\\\boxed{\boxed{\large\textsf{\large\textsf{Answer: \huge \bf -11}}}}\huge\checkmark\\\\\\\\\\\large\text{Good luck on your assignment and enjoy your day!}\\\\\\\\\\\\\\\\\\\\\\\frak{Amphitrite1040:)}[/tex]

Answer:

Step-by-step explanation:

Im not sure but i think

452.16/3.14.= 3.14r^2/3.14

144(square root sign) = squarw root sign r^2)

12=r

Answer:

x = 79

Step-by-step explanation:

All triangles have a sum of 180°. Knowing this, we can solve for the unknown angle.

56 + 23 + ? = 180

79 + ? = 180

? = 101

The variable x is known as an exterior angle. That and the angle we just solved for are supplementary meaning they add up to 180°.

101 + x = 180

x = 79

Answer:

79 degrees

Step-by-step explanation:

56 + 23 = 79

Answer:

4-2 = 2

2x5+9 = 19

2^19 = 2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2 = 524288

Answer:

29

Step-by-step explanation:

Use PEMDAS

P- Parenthesis

E- Exponents

M- Multiply

D- Divide

A- Add

S- Subtract

(4-2)^2×5+9 first you do parenthesis which is (4-2)=2

(2)^2×5+9 next the exponents (2)^2=4

4×5+9 now the multiplication, 4×5=20

20+9 And now finish it off with the addition

So the answer ends up being 29.

Answer and explanation:

Multicollinearity happens when multiple independent variables are correlated and therefore it is hard to determine which independent variable has the most impact or is most significantly affecting the dependent variable. This could be a source of confusion as the coefficients become less reliable.

Extreme multicollinearity occurs when there is exaggerated standard errors or increased variance of coefficient estimates.

Answer:

Set builder notation: {a | a ≥ -21}

Interval notation: [-21, ∞)

Step-by-step explanation:

A set represents a collection of things, objects, or numbers. A set builder notation is in the form y = {x | x is an odd number between 8 and 10}, which means y contains all the odd numbers between 8 and 10.

Interval notation is a way to define a set of numbers between a lower limit and an upper limit using end-point values. for example (8, 20) means numbers between 8 and 20.

Given -3a-15≤-2a+6; solving :

-3a - 15 ≤ -2a + 6

-3a + 2a ≤ 6 + 15

-a ≤ 21

dividing through by -1:

a ≥ -21

The solution is:

Set builder notation: {a | a ≥ -21}

Interval notation: [-21, ∞)

Let's divide the shaded region into two areas:

area 1: x = 0 ---> x = 2

ares 2: x = 2 ---> x = 4

In area 1, we need to find the area under g(x) = x and in area 2, we need to find the area between g(x) = x and f(x) = (x - 2)^2. Now let's set up the integrals needed to find the areas.

Area 1:

[tex]A\frac{}{1} = ∫g(x)dx = ∫xdx = \frac{1}{2} {x}^{2} | \frac{2}{0} = 2[/tex]

Area 2:

[tex]A\frac{}{2} = ∫(g(x) - f(x))dx[/tex]

[tex]= ∫(x - {(x - 2)}^{2} )dx[/tex]

[tex] = ∫( - {x}^{2} + 5x - 4)dx[/tex]

[tex]= ( - \frac{1}{3}{x}^{3} + \frac{5}{2} {x}^{2} - 4x) | \frac{4}{2}[/tex]

[tex] = 2.67 - ( - 0.67) = 3.34[/tex]

Therefore, the area of the shaded portion of the graph is

A = A1 + A2 = 5.34

9514 1404 393

Answer:

  A. (1, - 3/2)

Step-by-step explanation:

The coordinate of the midpoint is the average of the endpoint coordinates.

  M = (A +B)/2

  M = ((1, 2) +(1, -5))/2 = (1+1, 2-5)/2 = (2, -3)/2

  M = (1, -3/2) . . . . . matches choice A

Answer:

A. (1, - 3/2)

Step-by-step explanation:

Answer:

$3089.4

Step-by-step explanation:

A circle is a locus of a point such that its distance from a point known as the center is always constant.

The area of a circle is given by the formula:

Area = πr²; where r is the radius of the circle.

From the image attached, we can see that the garden is circular with a radius of 5.5 yard. Hence:

Amount of mulch needed to cover garden = area of garden = πr² = π(5.5)²  = 95 yd²

Since mulch cost $32.52 per square yard, hence:

Cost of mulch needed = $32.52 per yd² * 95 yd² = $3089.4

Answer:

The null hypothesis is [tex]H_0: p = 0.51[/tex].

The alternate hypothesis is [tex]H_1: p \neq 0.51[/tex].

The p-value of the test is 0.0164 > 0.01, which means that there is not sufficient evidence at the 0.01 level to refute the chief's claim.

Step-by-step explanation:

A local police chief claims that about 51% of all drug related arrests are ever prosecuted

At the null hypothesis, we test if the proportion is of 51%, that is:

[tex]H_0: p = 0.51[/tex]

At the alternate hypothesis, we test if the proportion is different from 51%, that is:

[tex]H_1: p \neq 0.51[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.51 is tested at the null hypothesis:

This means that [tex]\mu = 0.51, \sigma = \sqrt{0.51*0.49}[/tex]

A sample of 900 arrests shows that 47% of the arrests were prosecuted.

This means that [tex]n = 900, X = 0.47[/tex]

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.47 - 0.51}{\frac{\sqrt{0.51*0.49}}{\sqrt{900}}}[/tex]

[tex]z = -2.4[/tex]

P-value of the test:

Probability that the sample proportion differs from 0.51 by at least 0.04, which is P(|z|>2.4), which is 2 multiplied by the p-value of Z = -2.4.

Looking at the z-table, the Z = -2.4 has a p-value of 0.0082.

2*0.0082 = 0.0164.

The p-value of the test is 0.0164 > 0.01, which means that there is not sufficient evidence at the 0.01 level to refute the chief's claim.

Answer: $3648

Step-by-step explanation:

Firstly, we have to calculate the interest which will be:

= Principal × Rate × Time

= $1600 × 8% × 16

= $1600 × 0.08 × 16

= $2048

Therefore, the amount in the account after 16 years will be:

= Principal + Interest.

= $1600 + $2048

= $3648

Answer:

1/9 = 0.1111 = 11.11% probability that the first die is a 6 given that the minimum of the two numbers is a 2.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Minimum of the two numbers is 2.

Event B: First die in a 6.

Fair dice:

Each throw has 6 equally likely outcomes. Thus, in total, there are [tex]6^2 = 36[/tex] possible outcomes.

Minimum of the two numbers is a 2.

(2,2), (2,3), (3,2), (2,4), (4,2), (2,5), (5,2), (2,6), (6,2).

9 total outcomes in which the minumum of the two numbers is a two, which means that:

[tex]P(A) = \frac{9}{36}[/tex]

Minimum of the two numbers is a 2, and the first die is a 6.

Only one possible outcome, (6,2). So

[tex]P(A \cap B) = \frac{1}{36}[/tex]

Probability that the first die is a 6 given that the minimum of the two numbers is a 2.

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{\frac{1}{36}}{\frac{9}{36}} = \frac{1}{9} 0.1111[/tex]

1/9 = 0.1111 = 11.11% probability that the first die is a 6 given that the minimum of the two numbers is a 2.

Answer:

t < 3 is the answer

Step-by-step explanation:

source: https://www.tiger-algebra.com/drill/4_5t%3C19/

^ (it has an explanation too)

Answer:

0.1

Step-by-step explanation:

For a density curve, total area = 1

Probability lies in between 0 and 1

The Area of rectangle :

Area = Length * width

Length = 0 - 10 = 10

Area = 1

Hence,

Area = Length * width

1 = 10 * w

1 = 10w

w = 1 /10

w = 0.1

Answer:

- 4

Step-by-step explanation:

h(x) = sin x

f(x) = | 3x - 4 |

g(x) = 2x² - 6

h( [tex]\frac{\pi }{2}[/tex] ) = sin ( [tex]\frac{\pi }{2}[/tex] ) = 1

f ( 1 ) = | 3 × 1 - 4 | = 1

g ( 1 ) = 2( 1² ) - 6 = - 4

g ( f ( h ( [tex]\frac{\pi }{2}[/tex] ) ) ) = - 4

Answer: [tex]y=-\frac{1}{3}x[/tex]

Step-by-step explanation:

From the origin we can see to get to the point plotted we have to go down 1 and right three giving us the slope [tex]\frac{-1}{3}[/tex]

These are in the form of y=mx+b

b is the y-intercept and m is the slope

since the y-intercept is 0 b is 0 and isn't need leaving us with y=mx

We can put our slope into the equation giving us the answer in C

The required equation of the line is that passing through the point (3, -1) is y = -x/3.

Given that,
To determine the equation of the line that passes through the origin and a point (3, -1).

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
Since the line passes from the origin and a point (3, -1)
So, the slope of the line is given by,
m = (y₂ - y₁) /  (x₂ - x₁)

Substitute the respective values in the above equation,
m = -1 + 0 / 3 - 0
m = -1/3,
Now the point-slope form of the equation of a line is,

y - y₁ = m (x - x₁)
Substitute the respective values in the above equation,
y + 1 = -1/3 (x - 3)
y = -x/3

Thus, the required equation of the line is that passing through the point (3, -1) is y = -x/3.

Learn more about slopes here:

https://brainly.com/question/3605446

#SPJ2

Answer:

36123.5994797

Answer:

111degrees

Step-by-step explanation:

ArcAC + arcBC = 180

Given theat arcBC = 69degrees

arcAC + 69 = 180

arcAC = 180 - 69

arcAC = 111

Hence the length of minpr arc AC is 111degrees