Find the value of the expression 8a +b, if a=3 and b= 1

a) 23 b) 29 c) 30 d) 25

We can use the normal curve to measure the probability that our estimates are accurate because the errors roughly follow the normal curve.

We can use the following details to determine the likelihood that the estimates are accurate:

i. There is a 68% chance that the actual value of the average number of runs allowed per inning for a pitcher with given averages for strikeouts pitched and home runs per inning pitched will be within one standard deviation of the predicted value obtained from the estimated regression equation developed in part (c).

ii. There is a roughly 95% chance that the actual value of the average number of runs allowed per inning for a pitcher with a given average of strikeouts pitched and an average of home runs per inning pitched will fall within two standard deviations of the predicted value obtained from the estimated regression equation developed in part (c).

iii. There is a roughly 80% chance that the actual value of the average number of runs allowed per inning for a pitcher with a given average of strikeouts pitched and an average of home runs per inning pitched will fall within 1.28 standard deviations of the predicted value obtained from the estimated regression equation developed in part (c).

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Answer:

Down below :#

Step-by-step explanation:

The first one is False: reason \(\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}\)

\(b^9b^2=b^{9+2}\)

\(=b^{9+2}\)

And then its b^11

Second one is false

Third one is  True

Fourth false

Reason: \(\mathrm{Apply\:exponent\:rule:\:}\left(a^b\right)^c=a^{bc},\:\quad \mathrm{\:assuming\:}a\ge 0\)

\(=b^{6\cdot \:5}\)

fifth one is False

\(\mathrm{Apply\:exponent\:rule:\:}a^0=1,\:\quad \mathrm{\:assuming\:}a\ne \:0\)

That equals 1

:) hope this helps  

Answer: They played 25 games

Step-by-step explanation: If they had 15 wins and the total games they played is 60% then they lost 10 times and they played 25 games because if you divide 15 by 60 you get 0.25 so they played 25 games.

Step-by-step explanation:

let the numbers are:

a, b, and c

the equation would be:

a+b+c = 131

c = 4a

b = a+5

=>

a + a+5 +4a = 131

6a +5 = 131

6a = 131-5

6a = 126

a= 126/6

a = 21

b = a+5 = 21+5

b = 26

c = 4a = 4(21)

c = 84

Answer:

b = - 1.09

Step-by-step explanation:

- 2.9 + b ÷ 0.1 = - 39.9

- 2.9 + b ÷ 0.1 × 0.1 = - 39.9 × 0.1

- 2.9 + b = - 3.99

- 2.9 + 2.9 + b = - 3.99 + 2.9

b = - 1.09

Answer:

Exact form

b=-37/10

Decimal form

b=-3.7

Mixed Number form

b+-3 7/10

Step-by-step explanation:

-2.9+b/1/10+-39.9

-2.9+10b+-39.9

10b=-39.9+2.9

10b=-37

b=-37/10

Answer:

It is not valid because some angles that are not acute fit this definition

The interval of probability at the confidence interval is 95% is 0.3329 , 0.4043 and the margin of error is 0.0357.

The complete question is

A survey conducted by Conquest Communications Group randomly sampled 700 registered voters in the U.S. 258 of the 700 sampled voters correctly answered that fourth graders in the U.S. are above average for overall education compared to other countries.

Choose a number between 80 and 96. This is the level of confidence you will use for this section of problems. What is your number?

It is defined as the margin by which the values calculated will differ from the real values .

Let the chosen number is 95  %

95% Confidence Interval ,

\(\rm p = p \pm \dfrac{Z_{0.05}}{2} \sqrt \dfrac{p(1-p)}{n}}\\\\= \dfrac{258}{700} \pm 1.96 \sqrt \dfrac{\dfrac{258}{700}(1-\dfrac{258}{700})}{700}}\\\)

Therefore p at 95% Confidence Interval is given by 0.3329 , 0.4043

The margin of error is given by  0.4043-0.3329

= 0.0357

Therefore the interval of probability at the confidence interval is 95% is 0.3329 , 0.4043 and the margin of error is 0.0357.

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ANSWER

f(-4) = -21

EXPLANATION

We have that:

f(x) = 6x + 3

We want to find f(-4)

To do this, we replace x with -4:

f(-4) = 6(-4) + 3

f(-4) = -24 + 3

f(-4) = -21

That is the answer.

Step-by-step explanation:

We can use trigonometry to solve this problem. Let's draw a diagram:

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A - observer (1.5 m above ground)

B - base of the clock tower

C - top of the clock tower

D - intersection of AB and the horizontal ground

E - point on the ground directly below C

C

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B

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A

```

We want to find the height of the clock tower, which is CE. We have the angle of elevation ACD, which is 19 degrees, and the distance AB, which is 100 m. We can use tangent to find CE:

tan(ACD) = CE / AB

tan(19) = CE / 100

CE = 100 * tan(19)

CE ≈ 34.5 m (rounded to 1 decimal place)

Therefore, the height of the clock tower is approximately 34.5 m.

Answer:

The first one

Step-by-step explanation:

Answer:

y=1/2x is a answer I think maybe

(a) The mean of Z in case (a) is -60 and the variance is 400.

(b) The mean of Z in case (b) is 280 and the variance is 3600.

(c) The mean of Z in case (c) is 60 and the variance is 65.

(d) The mean of Z in case (d) is -20 and the variance is 65.

(e) The mean of Z in case (e) is 80 and the variance is 505.

To find the mean and variance of the random variable Z for each case, we can use the properties of means and variances.

(a) Z = 40 - 5X

Mean of Z:

E(Z) = E(40 - 5X) = 40 - 5E(X) = 40 - 5 * 20 = 40 - 100 = -60

Variance of Z:

Var(Z) = Var(40 - 5X) = Var(-5X) = (-5)² * Var(X) = 25 * Var(X) = 25 * (4)² = 25 * 16 = 400

Therefore, the mean of Z in case (a) is -60 and the variance is 400.

(b) Z = 15X - 20

Mean of Z:

E(Z) = E(15X - 20) = 15E(X) - 20 = 15 * 20 - 20 = 300 - 20 = 280

Variance of Z:

Var(Z) = Var(15X - 20) = Var(15X) = (15)² * Var(X) = 225 * Var(X) = 225 * (4)² = 225 * 16 = 3600

Therefore, the mean of Z in case (b) is 280 and the variance is 3600.

(c) Z = X + Y

Mean of Z:

E(Z) = E(X + Y) = E(X) + E(Y) = 20 + 40 = 60

Variance of Z:

Var(Z) = Var(X + Y) = Var(X) + Var(Y) = (4)² + (7)² = 16 + 49 = 65

Therefore, the mean of Z in case (c) is 60 and the variance is 65.

(d) Z = X - Y

Mean of Z:

E(Z) = E(X - Y) = E(X) - E(Y) = 20 - 40 = -20

Variance of Z:

Var(Z) = Var(X - Y) = Var(X) + Var(Y) = (4)² + (7)² = 16 + 49 = 65

Therefore, the mean of Z in case (d) is -20 and the variance is 65.

(e) Z = -2X + 3Y

Mean of Z:

E(Z) = E(-2X + 3Y) = -2E(X) + 3E(Y) = -2 * 20 + 3 * 40 = -40 + 120 = 80

Variance of Z:

Var(Z) = Var(-2X + 3Y) = (-2)² * Var(X) + (3)² * Var(Y) = 4 * 16 + 9 * 49 = 64 + 441 = 505

Therefore, the mean of Z in case (e) is 80 and the variance is 505.

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Y in represents the following in this linear regression Y = α₀+α₁X+α₂X₂+ε: C. dependent variable.

In Mathematics and Geometry, a regression line is a statistical line that best describes the behavior of a data set. This ultimately implies that, a regression line simply refers to a line which best fits a set of data.

In Mathematics and Geometry, the general functional form of a linear regression can be modeled by this mathematical equation;

Y = α₀+α₁X+α₂X₂+ε

Where:

In conclusion, Y represent the dependent variable or response variable in a linear regression.

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Answer: 45ft

Step-by-step explanation:

You do 8 x 5 first which you get 40 then you do 10 x 5 which you get 50 you add 40 and 50 you get 90 and since it’s made out of triangles you do bh1/2 so you do 90 x 1/2 or 90 / 2 and you get 45ft

Answer:

Step-by-step explanation:

The Barnes family has a coupon for 10% off their dinner. If their bill comes to $82.50 and they wish to tip 15%, what will they pay in total? 0 $85.39 O $74.25 O $63.11 O $90.75​

Answer:$85.39

Step-by-step explanation:

Answer:

999,960

Step-by-step explanation:

let x be a multiple of 120

120x ≤ 999,999

999,999 / 120 = 8333.325

8333 ≤ x ≤ 8334

8333(120) = 999,960

8334(1200) = 1,000,080  this is a 7-digit number

Therefore, the largest 6-digit number that is exactly divisible by 120 is 999,960

a) The distance of the stone above ground level at time t is given by the equation h(t) = \(-4.9t^2\) + 400.

b) it takes 9.04 seconds for the stone to reach the ground

c) The velocity of the stone when it strikes the ground is approximately -88.5 m/s

d)  If the stone is thrown downward with a speed of 8 m/s it takes 8.54 seconds.

In the given problem, a stone is dropped from a tower 400 meters above the ground with acceleration due to gravity (g) equal to 9.8 \(m/s^2\). The distance of the stone above ground level at time t is given by h(t) = \(-4.9t^2\) + 400. It takes approximately 9.04 seconds for the stone to reach the ground, and it strikes the ground with a velocity of approximately -88.5 m/s. If the stone is thrown downward with an initial speed of 8 m/s, it takes approximately 8.54 seconds to reach the ground

(a) The term \(-4.9t^2\) represents the effect of gravity on the stone's vertical position, and 400 represents the initial height of the stone. This equation takes into account the downward acceleration due to gravity and the initial height.

(b) To find the time it takes for the stone to reach the ground, we set h(t) = 0 and solve for t. By substituting h(t) = 0 into the equation \(-4.9t^2\) + 400 = 0, we can solve for t and find that t ≈ 9.04 seconds.

(c) The velocity of the stone when it strikes the ground can be determined by finding the derivative of h(t) with respect to t, which gives us v(t) = -9.8t. Substituting t = 9.04 seconds into this equation, we find that the velocity of the stone when it strikes the ground is approximately -88.5 m/s. The negative sign indicates that the velocity is directed downward.

(d) If the stone is thrown downward with an initial speed of 8 m/s, we can use the equation h(t) = \(-4.9t^2\) + 8t + 400, where the term 8t represents the initial velocity of the stone. By setting h(t) = 0 and solving for t, we find that t ≈ 8.54 seconds, which is the time it takes for the stone to reach the ground when thrown downward with an initial speed of 8 m/s.

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Answer:

Step-by-step explanation:

y = -(x - 6)² + 2

At x-intercept y = 0

0 =  -(x - 6)² + 2

(x - 6)² = 2

Take square root both sides

x - 6 = ± √2

x = 6 ± √2

The function f(x) = {2 - x if x ≤ 1, x if x > 1} is one-to-one but not onto.

To prove that a function f(x) is one-to-one but not onto, we need to show that it satisfies the following conditions:

One-to-one: For any two different values x1 and x2 in the domain, if f(x1) ≠ f(x2), then x1 ≠ x2.

Not onto: There exists at least one value y in the codomain that is not the image of any value x in the domain.

Let's analyze the function f(x) = {2 - x if x ≤ 1, x if x > 1}.

One-to-one:

To show that f(x) is one-to-one, we need to demonstrate that if f(x1) ≠ f(x2), then x1 ≠ x2.

Consider two different values x1 and x2 in the domain such that f(x1) ≠ f(x2).

If both x1 and x2 are less than or equal to 1, then f(x1) = 2 - x1 and f(x2) = 2 - x2. Since x1 and x2 are different, f(x1) and f(x2) will also be different. Therefore, x1 ≠ x2.

If both x1 and x2 are greater than 1, then f(x1) = x1 and f(x2) = x2. Since x1 and x2 are different, f(x1) and f(x2) will also be different. Therefore, x1 ≠ x2.

If one value is less than or equal to 1 and the other is greater than 1, then f(x1) = 2 - x1 and f(x2) = x2. In this case, f(x1) and f(x2) will always be different because 2 - x1 will never be equal to x2. Therefore, x1 ≠ x2.

In all cases, we have shown that if f(x1) ≠ f(x2), then x1 ≠ x2. Hence, f(x) is one-to-one.

Not onto:

To show that f(x) is not onto, we need to find at least one value y in the codomain that is not the image of any value x in the domain.

The codomain of f(x) is the set of all real numbers. Let's consider the value y = 3. No matter what value of x we choose from the domain, the function f(x) will never be equal to 3. Therefore, there is no x in the domain such that f(x) = 3.

Since we have found a value y (3) in the codomain that is not the image of any value x in the domain, we can conclude that f(x) is not onto.

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1458x^3 - 2

2 (729x^3 - 1)

solution : 2 (9x - 1) x (81x^2 + 9x + 1)

Answer: (read the explanation)

Step-by-step explanation:

To graph the solution set to the given system of inequalities, we can begin by graphing the two inequalities separately. For the first inequality, y > x^2 – 2, we can graph the function y = x^2 – 2 on the coordinate plane and shade the region above the graph. This will represent the values of x and y that satisfy the inequality.

For the second inequality, y ≥ –x^2 + 5, we can graph the function y = –x^2 + 5 on the coordinate plane and shade the region below the graph. This will represent the values of x and y that satisfy the inequality.

Next, we can combine the two graphs by intersecting the shaded regions. The resulting graph will show the solution set to the system of inequalities. The solution set can be identified as the points on the coordinate plane that are contained within the shaded region on the combined graph.

Overall, to modify the graphs of f(x) and g(x) to graph the solution set to the given system of inequalities, we can graph the functions y = x^2 – 2 and y = –x^2 + 5 on the coordinate plane and shade the regions that satisfy the inequalities. The solution set can then be identified as the points within the shaded region on the resulting combined graph.

A second linearly independent solution of y₂ is \(-\frac{1}{6x^3}\)

The general Equation is y" + P(x)y' + q(x)y = 0 ...............(i)

where P(x), Q(x) are continues in the internal I ≤ R.

If y₁(x) is a solution of equation 1 in I then y₁(x) ≠ 0.

Then y₂(x) = y₁(x)\(\int{\frac{e^{-\intP(x)dx}}{(y_{1}x)^2}}dx\) is another solution.

The differential equation is x²y" + xy' – 9y = 0 where x > 0.

As y₁(x) = x³ is one solution of differential equation.

Divide throughout by (x²) to given differential equation.

1/x² (x²y" + xy' – 9y = 0)

y" + (y'/x) – (9/x²)y = 0 ................(ii)

By comparing equation (i) & (ii) we get:

p(x)=1/x , q(x)= –are continuous for x>0

So, another solution,

y₂(x) = y₁(x)\(\int{\frac{e^{-\intP(x)dx}}{(y_{1}x)^2}}dx\)

Now putting the values of P(x) And Q(x)

y₂(x) = \(x^3\int\limits {\frac{e^{\int(1/x)dx} }{(x^3)^2}} \, dx\)

y₂(x) = \(x^3\int\limits {\frac{\frac{1}{x} }{x^6} }} \, dx\)

y₂(x) = \(x^3\int\limits {\frac{1}{x^7} }} \, dx\)

y₂(x) = \(x^3\int\limits {x^-7} } \, dx\)

y₂(x) = \(x^3\left[\frac{x^{-7+1}}{-7+1}\right]\)

y₂(x) = \(-\frac{1}{6}(x^3\times x^{-6})\)

y₂(x) = \(-\frac{1}{6x^3}\)

So, the answer of this question is \(-\frac{1}{6x^3}\).

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Answer:

The answer would be 4,450

Step-by-step explanation:

:)

Answer:

Assume we want to find the solution to this system of equations.

The solution is (2,-2)

Step-by-step explanation:

We can find the solution either mathematically or by graphing.  I'll do both.

Math:

Rearrange:

-2x-6y=8

-6y=8 +2x

y = -(1/3)x -(4/3)

---

Now use this expression of y in the second equation:

-6x-6y=0

-6x-6(-(1/3)x -(4/3)) =0

-6x + 2x +8 =0

-4x = - 8

x = 2

---

Use x = 2 in the first equation to find y:

y = -(1/3)x -(4/3)

y = -(1/3)*(2) -(4/3)

y = -(2/3) -(4/3)

y = -(6/3) or -2

The solution is (2,-2)

===============

Graphing:

See attached graph.

Answer:

Step-by-step explanation:

-2x - 6y = 8

6x + 6y = 0

4x = 8

x = 2

-4 - 6y = 8

-6y = 12

y = -2

(2, -2)

The  the coordinate of point B is (6, -8)

The formula for calculating the midpoint of AB is expressed as;

M(x, y) = {(x1+x2)/2, (y1+y2)/2}

Given the following coordinate points

M(7, -7)

A(8, -6)

Required

Coordinate of S

Substitute

8+x2/2= 7

8+x2 = 14

x2 = 6

Similarly;

-6+y2/2 = -7

-6+y2 = -14

y2 = -8

Hence the coordinate of point B is (6, -8)

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The wrong value in Sally's list is 36. Sally did not have $36 left after she found $16 and put it in her pocket. She actually had $48 left.

Let x be the amount of money Sally started with.

She spent $12 on a hat, leaving her with x - 12 dollars.

She then spent one-third of her remaining money on some music. This means she spent

(1/3)(x - 12) dollars.

After that, she found $16 on the ground and put it in her pocket.

Sally now has (1/3)(x - 12) + 16 dollars.

Finally, Sally spent half of her remaining money on a new dress, leaving her with just $18.

Therefore, (1/2)[(1/3)(x - 12) + 16] = 18.

Now we can solve for x and determine how much money Sally started with.

(1/6)(x - 12) + 8 = 18

(1/6)(x - 12) = 10

x - 12 = 60

x = 72

So Sally started with $72. After each transaction, Sally had the following amounts of money: $72, $60, $20, $48, $18.

To check whether Sally's list is correct, we can work backward.

Starting with $18, we can reverse the process by adding $18 to the amount Sally had after each transaction.

After spending half of her remaining money on a new dress, Sally had (2)(18) = 36 dollars.

However, Sally actually had $48 left after she found $16 and put it in her pocket.

Therefore, the wrong value in Sally's list is 36.

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Answer:

b. interaction effect

Step-by-step explanation:

In a regression model, the interaction effect is present when a predictor variable changes the effect of another predictor variable on the outcome.

In a regression model, the interaction effect exists when one predictor variable impacts the outcome of another predictor variable differently than when examined individually. It refers to the interaction between two or more predictor variables and their influencers on an outcome or response variable. For example, in a regression model, studying and having a quiet place may individually contribute to a better score on a test, but perhaps studying in a quiet place provides a significantly better effect than the sum of those two effects separately. This would be considered an interaction effect.

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