In the history of NBA, many champion teams have featured two star players. For example, 2000-2001 and 2001-2002 LA Lakers featured Shaquille O'Neal and Kobe Bryant, 2019-2020 LA Lakers featured LeBron James and Anthony Davis. Having one-two punches in a team can reduce the chance of inconsistent performance by compelementing each other.
Suppose that two star players in the same team, A and B, have the following stats in a season:
Player A's average points per game 25 with the standard deviation of 5.
Player B's average points per game 20 with the standard deviation of 4.
The correlation coefficient between their points per game is 0.2.
Find the standard deviation of the sum of the two player's points per game.
a. 3
b. 4
c. 5
d. 6
e. 7

Least to greatest slope, the segments are B, C, A.

What is the segment's slope ?

The slope of a line segment indicates how steep the line segment is. It is the ratio of rise (the change in vertical height between the endpoints) to run (the change in horizontal length between the endpoints).

The segment's slope provides information about how quickly the water level is rising. In relation to the angle the segment makes with the +x axis, the slope is defined as the rise to run ratio.

Greater slope can be found in segments that have more ascent for a given run. With respect to the +x axis, segments with a greater reference angle have a steeper slope.

Segment B has the least slope in this case, followed by segment C, and then segment A, which has the greatest slope.

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It is expected that 300 participants out of the 900 who participate in the survey would receive a coupon for sleigh rides.

To determine the number of participants expected to receive a coupon for sleigh rides, we need to divide the total number of participants (900) by the number of coupon options (3) since each option has an equal chance of being received.

The expected number of participants receiving a coupon for sleigh rides can be calculated as follows:

Total participants / Number of coupon options = Expected number of participants receiving a sleigh ride coupon

900 participants / 3 coupon options = 300 participants.

Therefore, it is expected that 300 participants out of the 900 who participate in the survey would receive a coupon for sleigh rides.

It's important to note that this calculation assumes an equal chance of receiving each type of coupon and does not consider any specific preferences or biases that participants may have.

The calculation is based on the assumption of a random distribution of coupons among the participants.

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To multiply a square root by a square root and a whole number, you can use the distributive property of multiplication

Given data ,

Let the numbers be represented by the expression A

Now , the value of A is

A = √2 × 3√5

First, you can simplify each square root:

√2 = 1.4142 (rounded to 4 decimal places)

3√5 = 5.1962 (rounded to 4 decimal places)

Next, you can multiply the two simplified square roots and the whole number:

√2 × 3√5 = 1.4142 × 5.1962 × 3

= 22.3607 × 3

= 67.0821

Hence , the expression is A = √2 × 3√5 = 67.0821

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Answer:

7x+39>=53 and 16x+ 15>31 x>=2 (no solutions exist)

Step-by-step explanation:

Answer:

14.5 =x

Step-by-step explanation:

Since this is a right triangle we can use trig functions

sin theta = opposite side/ hypotenuse

sin A = BC / AB

sin 65 = x /16

Multiply each side by 16

16 sin 65 =x

14.50092459 =x

14.5 =x

Answer:

C on edge

Step-by-step explanation:

Answer:

=48x2^+3097x+12

Step-by-step explanation:

3(4x+9)(4)x+2712x+277x+12

Distribute:

=48x2+108x+2712x+277x+12

Combine Like Terms:

=48x2+108x+2712x+277x+12

=(48x2)+(108x+2712x+277x)+(12)

=48x2+3097x+12

Answer:

Hello~

12x+3×9

12x + 27

Ary~

Answer:

B. 59.66

Step-by-step explanation:

In order to solve this youd have to multiply 745.75 by 8% in order to find it

First you'd need to turn 8% into a decimal

8%/100 = 0.08

0.08 x 745.75 =59.66

So the sales tax rate for this price is 59.66

Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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x >= -13/5

x >= - 2 ³/5

that's the final answer

Answer:

D. The other solution to function g is 9 + √2i

Step-by-step explanation:

The roots of a quadratic equation of the form ax² + bx + c = 0

are

\(x = -\dfrac{b}{2a} + \dfrac{\sqrt{b^2-4ac}}{2a}\\and\\x = -\dfrac{b}{2a} - \dfrac{\sqrt{b^2-4ac}}{2a}\\\)

If one of the roots is 9 - √2i then
\(-\dfrac{b}{2a} = 9\)

and

\(\dfrac{\sqrt{b^2-4ac}}{2a} = 2i\)

So if one root is 9 - √2i then the other root must be 9 -+ 2i

This is answer choice D

Answer:

$60

Step-by-step explanation:

1 slice = $1.50

1 cake = 8 slices = 8 × $1.50 = $12

5 cakes = 5 × $12 = $60

Answer: $60

ANSWER

9.5

EXPLANATION

To find the distance between home and work, we have to use the formula:

We have that home is at point (3, -3) and work is at point (0, 6).

Therefore:

(x1, y1) = (3, -3)

(x2, y2) = (0, 6)

Therefore, we have that:

The answer is 9.5

The values in the missing observation are:

X1    X2

76 22  

82 25

91 32

101    41

88 28

An expression contains terms with addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

x1 x2

76 22  

82 __

91 32

__    41

88 28

The difference between each row are:

76 - 22 = 54

82 - 25 = 57

91 - 32 = 59

101 - 41 = 60

88 - 28 = 60

We see that,

57 - 54 = 3

59 - 57 = 2

60 - 59 = 1

60 - 60 = 0

So,

The difference between the numbers is consecutive as 3, 2, 1, 0.

Thus,

The missing values of X1 and X2 are 101 and 25.

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In order to calculate the time it will take for Andrew to settle the loan, we can use the formula for compound interest. So, it will take Andrew approximately 5.22 years to settle the loan.

The formula is given as A = P(1 + r/n)^(nt), Where: A = the final amount, P = the principal (initial amount borrowed), R = the annual interest rate, N = the number of times the interest is compounded in a year, T = the time in years.

We know that Andrew borrowed R200 000 from a bank at an annual interest rate of 5.25% compounded quarterly and that he will make repayments of R6 000 at the end of every 3 months.

Since the first repayment will be made 3 months from now, we can consider that the initial loan repayment is made at time t = 0. This means that we need to calculate the value of t when the total amount repaid is equal to the initial amount borrowed.

Using the formula for compound interest: A = P(1 + r/n)^(nt), We can calculate the quarterly interest rate:r = (5.25/100)/4 = 0.013125We also know that the quarterly repayment amount is R6 000, so the amount borrowed minus the first repayment is the present value of the loan: P = R200 000 - R6 000 = R194 000

We can now substitute these values into the formula and solve for t: R194 000(1 + 0.013125/4)^(4t) = R200 000(1 + 0.013125/4)^(4t-1) + R6 000(1 + 0.013125/4)^(4t-2) + R6 000(1 + 0.013125/4)^(4t-3) + R6 000(1 + 0.013125/4)^(4t)

Rearranging the terms gives us: R194 000(1 + 0.013125/4)^(4t) - R6 000(1 + 0.013125/4)^(4t-1) - R6 000(1 + 0.013125/4)^(4t-2) - R6 000(1 + 0.013125/4)^(4t-3) - R200 000(1 + 0.013125/4)^(4t) = 0

Using trial and error, we can solve this equation to find that t = 5.22 years (rounded to 2 decimal places). Therefore, it will take Andrew approximately 5.22 years to settle the loan.

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Answer:

Ratio of number of boys to girls= 2:3

Ratio of number of boys to girls to total number of children= 2:3:5

Step-by-step explanation:

42 boys and 63 girls took part in an art competition

The ratio of the number of boys to the number of girls can be calculated as follows

= 42/63

= 2:3

The ratio of the number of boys to girls to total number of children can be calculated as follows

= 42/63/105

= 2:3:5

The probability that the mean of the sample would differ from the population mean by less than 2.8 points if 63 exams are sampled is 0.9592 or approximately 95.92%.

It is necessary to determine the region under the normal distribution curve between -2.8/0.5916 and 2.8/0.5916 standard deviations from the mean in order to determine the likelihood that the sample mean deviates from the population mean by less than 2.8 points. We can use a standard normal distribution table or a calculator to find this probability.

Mean of the distribution of sample means = 103

Variance of the distribution of sample means = 169/63 = 2.68

Using the z-score method, we can determine the likelihood that the sample mean deviates from the population mean by no more than 2.8 points.:

z = (x - μ) / (σ / √(n))

where n is the sample size, x is the sample mean, is the population mean, is the population standard deviation (square root of the variance), and is the population mean.

Plugging in the values, we get:

z = (x - 103) / (√(169/63))

z = (x - 103) / 0.5916

We calculate the chance to be roughly 0.9592 using a conventional normal distribution table.

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First, we will make a list of the bacteria growth during each hour.

Start: 15

1st hour: 30

2nd hour: 60

3rd hour: 120

4th hour: 240

5th hour: 480

6th hour: 960

7th hour: 1920

8th hour: 3840

9th hour: 7680

10th hour: 15360

11th hour: 30720

12th hour: 61440

As you can see, the number of bacteria present is doubled at the end of each hour, as the question states.

However the question refers to the number of bacteria that grow in the twelfth hour and not the total number of bacteria in the twelfth hour.

So the answer will be the subtraction between the bacteria in the twelfth hour minus the bacteria in the eleventh hour.

In conclusion, the answer is 30720

Answer:

y = 3x + 19

Step-by-step explanation:

Apply point-slope form. Our point (y1, y2) is (-4, 7) and our slope (m) is 3. The slope of y = 3x - 5 is 3 because it is "m" in y = mx + b. Parallel lines have the same slope.

y - y1 = m(x-x1)

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

y - 7 = 3(x+4)

y - 7 = 3x + 12

y = 3x + 19

The volume of the right prism include the following: 8,640 in³.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

Next, we would determine the area of the triangle at the base of the right prism as follows:

Base area = 1/2 × ( 36 × 12)

Base area = 1/2 × 432

Base area = 216 in².

Now, we can calculate the the volume of this right prism:

Volume = base area × height

Volume = 216 × 40

Volume = 8,640 in³.

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When a coin will be flipped three times, and the number of heads recorded. The reason that, this is a binomial experiment is "there are a set number of trials, n. The coin would be flipped three times, a fixed number of times."

A binomial experiment is one that has a fixed number of independent trials only with two outcomes. For instance, the outcome could be a yes or no response. When you toss a coin, you might wonder, "Will I get heads?" The response is either yes or even no.

That is the basic idea, but in order to label an experiment a binomial experiment, the following rules must be followed.

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the flux of the curl of F(x, y, z) across the upper hemisphere of x² + y² +² = 1, oriented upwards is 3π/2.

The given vector field is F(x, y, z) = (zz - y³ cos(z), x³e², ze⁺²⁺²⁺³).

The curl of F(x, y, z) is given as :

curl(F) = (∂Q/∂y - ∂P/∂z)i + (∂P/∂z - ∂R/∂x)j + (∂R/∂x - ∂Q/∂y)k= (3x² + 3z)k.

Here, P = zz - y³ cos(z), Q = x³e², and R = ze⁺²⁺²⁺³.

So, the curl(F) has only a z-component. Now, apply Stokes' Theorem. So,

∫C(F . dr) = ∬S(curl(F) . n) dS.

For the given surface x² + y² + z² = 1, consider the upper hemisphere, say S. Then, the projection of S on the xy-plane is the unit circle x² + y² = 1. Therefore,  apply Stokes' Theorem to S by the plane curve C, which is the counter-clockwise oriented unit circle in the xy-plane. So, the parameterization for C is given by :

r(t) = cos(t)i + sin(t)j, where 0 ≤ t ≤ 2π.

So, the tangent vector and normal vector to C are given as :

r'(t) = -sin(t)i + cos(t)j, and n = k.

The curl of F(x, y, z) = (3x² + 3z)k.

Therefore, the flux of the curl of F across S is given by :

∫C(F . dr) = ∬S(curl(F) . n) dS= ∬S (3x² + 3z) dS.= ∬S (3x² + 3√(1 - x² - y²)) dS.

Now, convert this to a double integral in polar coordinates. Since the surface S is the upper hemisphere of the sphere,  z = √(1 - x² - y²) and -√(1 - x² - y²) ≤ z ≤ 0.

Then, the limits of integration for x and y are -1 ≤ x ≤ 1 and -√(1 - x²) ≤ y ≤ √(1 - x²).

Therefore, we have :∫C(F . dr) = ∫[0, 2π] ∫[0, 1] (3r⁴ cos²θ + 3r³√(1 - r²)) dr dθ= 3π/2.

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Answer:

\(\displaystyle d = 5\sqrt{2}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Coordinate Planes

Algebra II

Distance Formula: \(\displaystyle d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

Step-by-step explanation:

Step 1: Define

Identify.

Point (2, 2)

Point (7, 7)

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d.

Answer:

2 (2x+5) +4 (x+2) = 66       x = 6

Step-by-step explanation:

EXPLANATION.

When the mean and median are of the same value, the data are said to be symmetric or to form a symmetric set.

therefore the answer is: the option B.

Answer:

s = 10

Step-by-step explanation:

Given s is inversely proportional to t , then the equation relating them is

s = \(\frac{k}{t}\) ← k is the constant of proportion

To find k use the condition when s = 0.6, t = 5

0.6 = \(\frac{k}{5}\) ( multiply both sides by 5 )

3 = k

s = \(\frac{3}{t}\) ← equation of proportion

When t = 0.3, then

s = \(\frac{3}{0.3}\) = 10

Answer:

(5,-6)

Step-by-step explanation:

ONE WAY:

If \(f(x)=x^2-6x+3\), then \(f(x-2)=(x-2)^2-6(x-2)+3\).

Let's simplify that.

Distribute with \(-6(x-2)\):

\(f(x-2)=(x-2)^2-6x+12+3\)

Combine the end like terms \(12+3\):

\(f(x-2)=(x-2)^2-6x+15\)

Use \((x-b)^2=x^2-2bx+b^2\) identity for \((x-2)^2\):

\(f(x-2)=x^2-4x+4-6x+15\)

Combine like terms \(-4x-6x\) and \(4+15\):

\(f(x-2)=x^2-10x+19\)

We are given \(g(x)=f(x-2)\).

So we have that \(g(x)=x^2-10x+19\).

The vertex happens at \(x=\frac{-b}{2a}\).

Compare \(x^2-10x+19\) to \(ax^2+bx+c\) to determine \(a,b,\text{ and } c\).

\(a=1\)

\(b=-10\)

\(c=19\)

Let's plug it in.

\(\frac{-b}{2a}\)

\(\frac{-(-10)}{2(1)}\)

\(\frac{10}{2}\)

\(5\)

So the \(x-\) coordinate is 5.

Let's find the corresponding \(y-\) coordinate by evaluating our expression named \(g\) at \(x=5\):

\(5^2-10(5)+19\)

\(25-50+19\)

\(-25+19\)

\(-6\)

So the ordered pair of the vertex is (5,-6).

ANOTHER WAY:

The vertex form of a quadratic is \(a(x-h)^2+k\) where the vertex is \((h,k)\).

Let's put \(f\) into this form.

We are given \(f(x)=x^2-6x+3\).

We will need to complete the square.

I like to use the identity \(x^2+kx+(\frac{k}{2})^2=(x+\frac{k}{2})^2\).

So If you add something in, you will have to take it out (and vice versa).

\(x^2-6x+3\)

\(x^2-6x+(\frac{6}{2})^2+3-(\frac{6}{2})^2\)

\((x+\frac{-6}{2})^2+3-3^2\)

\((x+-3)^2+3-9\)

\((x-3)^2+-6\)

So we have in vertex form \(f\) is:

\(f(x)=(x-3)^2+-6\).

The vertex is (3,-6).

So if we are dealing with the function \(g(x)=f(x-2)\).

This means we are going to move the vertex of \(f\) right 2 units to figure out the vertex of \(g\) which puts us at (3+2,-6)=(5,-6).

The \(y-\) coordinate was not effected here because we were only moving horizontally not up/down.

The correct first step for solving the equation 3(x+8) = 42 is (3×x)+(3×8) = 42.

For the given equation;

3(x+8) = 42

The first step will be to open the parenthesis, and multiply each term with 3.

(3×x)+(3×8) = 42.

Thus, the first step to solve the linear equation is  (3×x)+(3×8) = 42.

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