simplify the expression

y−5=(x−3)2

sorry if im wrong i might be!

have a luvly day!

Answer:

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex:  

(

3

,

5

)

Focus:  

(

3

,

21

4

)

Axis of Symmetry:  

x

=

3

Directrix:  

y

=

19

4

x

y

1

9

2

6

3

5

4

6

5

9

A Type I error would occur if the test statistic is smaller than the critical value, leading to the rejection of the null hypothesis, but the option (a) actual population mean amount of liquid in a bottle is at least 12 ounces.

A Type I error is a mistake made when rejecting the null hypothesis when it is actually true. In other words, it is when we conclude that there is a difference between the sample and the population when there is no such difference.

In this case, a Type I error would occur if the test provides convincing evidence that the mean amount of liquid in a bottle is less than 12 ounces, but the actual mean is at least 12 ounces.

Mathematically, the null hypothesis is denoted as H0 => µ ≥ 12, where µ is the population mean amount of liquid in a bottle. The alternative hypothesis is denoted as H1 => µ < 12.

However, if the test statistic is larger than the critical value, we fail to reject the null hypothesis.

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Complete Question:

Machines at a bottling plant are set to fill bottles to 12 ounces. The quality control officer at the plant periodically tests the machines to be sure that the bottles are filled to an appropriate amount. The null hypothesis of the test is that the mean is at least 12 ounces. The alternative hypothesis is that the mean is less than 12 ounces. Which of the following describes a Type I error that could result from the test?

A. The test does not provide convincing evidence that the mean is less than 12 ounces, but the actual mean is at least 12 ounces.

B. The test does not provide convincing evidence that the mean is less than 12 ounces, but the actual mean is less than 12 ounces.

C. The test does not provide convincing evidence that the mean is less than 12 ounces, but the actual mean is 12 ounces.

D. The test provides convincing evidence that the mean is less than 12 ounces, but the actual mean is at least 12 ounces.

E. The test provides convincing evidence that the mean is less than 12 ounces, but the actual mean is 11 ounces.

Step-by-step explanation:

We have,

\(y=7x^2-3\)

It is required to find the value of the discriminant. It is given by :

\(D=b^2-4ac\)

Here, a = 7 b = 0 and c = -3

So,

\(D=(0)^2-4\times 7\times (-3)\\\\D=84\)

The discriminant is positive here, it means that it has two distinct real number solutions.

a) Marginal probability distributions for X and Y are: X 1 2 P(y) Y 0 0.30 0.10 1 0.40 0.20 P(x) 0.50 0.50 and b) Corr(X,Y) = -1.68 and c) Var(W) = -0.34

a) Marginal probability distributions for X and Y are: X 1 2 P(y) Y 0 0.30 0.10 1 0.40 0.20 P(x) 0.50 0.50

b) The covariance and correlation for X and Y are:

Cov(X,Y)= E(XY) - E(X)E(Y)

Cov(X,Y)= (1 * 0 + 2 * 0.3 + 1 * 0.1 + 2 * 0.2) - (1 * 0.5 + 2 * 0.5)(0 * 0.5 + 1 * 0.4 + 0 * 0.1 + 1 * 0.2)

Cov(X,Y)= (0 + 0.6 + 0.1 + 0.4) - (0.5 + 1) (0.4 + 0.2)

Cov(X,Y)= 0.12 - 0.9 * 0.6

Cov(X,Y)= 0.12 - 0.54

Cov(X,Y)= -0.42

Corr(X,Y)= Cov(X,Y)/σxσyσxσy

= √[∑(x-µx)²/n] × √[∑(y-µy)²/n]σxσy

= √[∑(x-µx)²/n] × √[∑(y-µy)²/n]σx

= √[∑(x-µx)²/n]

= √[(0.5 - 1.5)² + (0.5 - 0.5)² + (0.5 - 1.5)² + (0.5 - 1.5)²]/2σx

= 0.50σy

= √[∑(y-µy)²/n]

= √[(0 - 0.5)² + (1 - 0.5)²]/2σy

= 0.50

Corr(X,Y) = Cov(X,Y)/(0.50 * 0.50)

Corr(X,Y) = (-0.42)/0.25

Corr(X,Y) = -1.68

c) The mean and variance for the linear function W = X + Y are:

Hw = E(W)

Hw = E(X + Y)

Hw = E(X) + E(Y)

Hw = 1.5 + 0.5

Hw = 2

Var(W) = Var(X + Y)

Var(W) = Var(X) + Var(Y) + 2Cov(X,Y)

Var(W) = 0.25 + 0.25 - 2(0.42)

Var(W) = 0.50 - 0.84

Var(W) = -0.34

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Answer:

I got 14

Step-by-step explanation:

(Pemdas) -9 - -9 = 0

0+14=14

14

A.  To ensure that the probability is at least 0.95 that the relative frequency estimate differs from 0.20 by less than 0.02, at least 7976 voters should be polled.

b. We find the z-score corresponding to a cumulative probability of 0.95 to be approximately 1.96.

n > 2401

a) Using the Chebyshev inequality, we can determine the minimum number of voters that should be polled to ensure that the probability is at least 0.95 that the relative frequency estimate differs from 0.20 by less than 0.02.

The Chebyshev inequality states that for any random variable X with mean μ and standard deviation σ, the probability of X deviating from the mean by k standard deviations is at least 1 - 1/k^2.

In this case, we want the relative frequency estimate to deviate from 0.20 by less than 0.02, which means we want the difference to be within 0.02 standard deviations of the mean. Since the relative frequency estimate is a sample proportion, its standard deviation can be approximated by sqrt(p(1-p)/n), where p is the true proportion (0.20) and n is the sample size.

We can set up the inequality as follows:

1 - 1/k^2 ≥ 0.95

Solving for k:

1/k^2 ≤ 0.05

k^2 ≥ 1/0.05

k^2 ≥ 20

Taking the square root of both sides:

k ≥ sqrt(20)

k ≥ 4.47

To ensure that the difference between the relative frequency estimate and 0.20 is within 0.02, we need k standard deviations to be less than 0.02. So, we have:

k * sqrt(p(1-p)/n) < 0.02

4.47 * sqrt(0.20(1-0.20)/n) < 0.02

Simplifying:

sqrt(0.20(1-0.20)/n) < 0.02/4.47

sqrt(0.16/n) < 0.00448

0.4/sqrt(n) < 0.00448

sqrt(n) > 0.4/0.00448

sqrt(n) > 89.29

n > 89.29^2

n > 7975.84

Therefore, to ensure that the probability is at least 0.95 that the relative frequency estimate differs from 0.20 by less than 0.02, at least 7976 voters should be polled.

b) Using the central limit theorem, we can determine the minimum number of voters that should be polled to ensure that the probability is at least 0.95 that the sample mean differs from 0.20 by less than 0.02.

According to the central limit theorem, the sample mean follows a normal distribution with mean μ and standard deviation σ/sqrt(n), where σ is the population standard deviation (unknown in this case), and n is the sample size.

To ensure that the difference between the sample mean and 0.20 is within 0.02, we can set up the following inequality:

z * (σ/sqrt(n)) < 0.02

Since the population standard deviation σ is unknown, we can use a conservative estimate by assuming the worst-case scenario, which is p(1-p) = 0.25. Therefore, σ = sqrt(0.25) = 0.5.

Using the standard normal distribution table, we find the z-score corresponding to a cumulative probability of 0.95 to be approximately 1.96.

1.96 * (0.5/sqrt(n)) < 0.02

0.98/sqrt(n) < 0.02

sqrt(n) > 0.98/0.02

sqrt(n) > 49

n > 49^2

n > 2401

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7)

8)
Therefore, the composition of g and h is not possible.

9)

The inverse relation is: {(-4,-5), (2,1), (4,3), (8,7)}

10) the inverse of g(x) is h(x) = x - 3. We can also write it as g⁻¹(x) = x - 3. See the graph attached.

7)
To find f°g, we need to perform the composition of functions by applying g first, and then applying f to the result.

Let's first apply g to the points in f:

g(-4,-5) = (6*(-4)+1,1*(-5)+0) = (-23,-5)

g(0,3) = (60+1,13+0) = (1,3)

g(1,6) = (61+1,16+0) = (7,6)

Now, we apply f to the result:

f(-23,-5) = (-5,-2)

f(1,3) = (3,-3)

f(7,6) is not defined since (7,6) is not in the domain of f.

Therefore, f°g is a function that maps (-4,-5) to (-5,-2) and (0,3) to (3,-3).

To find g°f, we need to apply f first, and then apply g to the result.

Let's apply f to the points in g:

f(6,1) is not defined since (6,1) is not in the domain of f.

f(-5,0) is not defined since (-5,0) is not in the domain of f.

f(3,-4) is not defined since (3,-4) is not in the domain of f.

Therefore, g°f is not defined.


8)

To find °gh, we need to perform the composition of functions by applying h first, and then applying g to the result.

h°g = h(g(x)) = h(x+6) = 3(x+6)² = 3(x²+12x+36) = 3x²+36x+108

Therefore, °gh = 3x²+36x+108.

To find h°g, we need to apply g first, and then apply h to the result.

g°h is not defined since g(x) = x+6 outputs a single value for each input, and h(x) = 3x² requires multiple inputs to produce a single output. Therefore, the composition of g and h is not possible.

Note that the order in which we perform the composition of functions matters, and it is not always possible to perform the composition in both directions.

9)
To find the inverse of this relation, we need to switch the positions of the x and y values in each ordered pair.

The inverse relation is: {(-4,-5), (2,1), (4,3), (8,7)}

Note that the inverse relation is also a function since each x value has only one corresponding y value.

10)

To find the inverse of g(x) = 3 + x, we start by replacing g(x) with y:

y = 3 + x

Next, we solve for x in terms of y:

y = 3 + x

y - 3 = x

Now we swap the positions of x and y:

x = y - 3

So the inverse of g(x) is h(x) = x - 3. We can also write it as g⁻¹(x) = x - 3.

Note that the domain and range of g(x) and its inverse have swapped. The domain of g(x) is all real numbers, while the range is all real numbers greater than or equal to 3. The domain of g⁻¹(x) is all real numbers greater than or equal to 3, while the range is all real numbers.

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The length of the side of the given square is 12.3 inches approx.

Due to the fact that this particular group of numbers makes up a square, they are known as square numbers (or squared numbers).

Finding the area of a square is easy because they all have equal sides. Just "square" (multiply by itself) one of their sides!

So, we have:

The area of the square is 151 in².

Area formula: s²

Now, calculate the length of the side as follows:

A = s²

151 = s²

s = √151

s = 12.3 approx

Therefore, the length of the side of the given square is 12.3 inches approx.

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Answer:

100

Step-by-step explanation:

because 1 x 100 = 100

If 1200 square centimeters of material is available to make a box with a square base and an open top,

The largest possible volume of the box is V = 4000cm^3.

We have 1200 cm^2 worth of material. This represents the surface area of a box with a square base and an open top.

the dimensions of the box.

Square base implies the length and width are the same.

Let x = length/width.

The box has a height as well.

Let h = height

the surface area ; S.

S = (area of base) + (area of 4 walls)

The area of the base is x^2

The area of one of the walls is length times height, or xh. Since there are 4 of them, it would be 4 times xh, or 4xh.

S = x^2 + 4xh

And we know that S = 1200cm^2, so

x^2 + 4xh = 1200

Let's solve for h.

4xh = 1200 - x^2

h = (1200 - x^2) / (4x)

we require the volume formula.

V = (length) x (width) x (height)

And we know all of these.

V = (x)(x)(h)

V = (x^2) h

putting h = (1200 - x^2) / (4x) in the formula

V = (x^2) ( 1200 - x^2)/(4x)

We get a cancellation,

V = x(1200 - x^2)/4

V = (1/4)x (1200 - x^2)

This will be our volume function, V(x).

V(x) = (1/4)(x)(1200 - x^2)

To maximize V(x), we must first take the derivative and then make it 0. Using the product rule (and ignoring the constant 1/4), we have

V'(x) = (1/4) [ (1200 - x^2) + (x)(-2x) ]

Simplify,

V'(x) = (1/4) [ 1200 - x^2 - 2x^2 ]

V'(x) = (1/4) [ 1200 - 3x^2 ]

V'(x) = (1/4) [ 3(400 - x^2) ]

V'(x) = (3/4) [ 400 - x^2 ]

To maximize, make V'(x) = 0, and solve for x.

0 = (3/4) [ 400 - x^2 ]

0 = 400 - x^2

x^2 = 400

x = +/- 20

Therefore,

x = { 20, -20 }

However, since x represents a dimension, it can never be negative, and we must discard the negative solution. That means

x = 20.

This tells us that the maximum volume occurs when x = 20. However, the question is asking WHAT the largest volume of the box is. Solving this is as simple as plugging x = 20 into our volume function, V(x).

V(x) = (1/4)(x)(1200 - x^2)

Therefore,

V(20) = (1/4) (20) (1200 - 20^2)

V(20) = (1/4) (20) (1200 - 400)

V(20) = (1/4) (20) (800)

V(20) = (20/4)(800)

V(20) = 5(800)

V = 4000cm^3

Hence the answer is, the largest possible volume of the box is V = 4000cm^3.

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The chi-square test of independence is typically used to analyze the relationship between two variables when both variables are nominal, the two variables have been measured on different individuals and the observations on each variable are within-subjects in nature. The answer is  D. all of the above

The chi-square test of independence is a statistical test that is used to determine if there is a significant association between two categorical variables. It is commonly used when both variables are nominal, meaning they consist of categories or groups rather than numerical values.

When conducting the chi-square test of independence, the data is typically collected by measuring the two variables on different individuals or units.

For example, researchers may collect data on the gender (nominal variable) and political affiliation (nominal variable) of different individuals and analyze whether there is a relationship between the two variables.

The test examines the observed frequencies of the different categories in a contingency table and compares them to the expected frequencies under the assumption of independence. If the observed and expected frequencies significantly differ, it suggests that there is an association between the two variables.

Therefore, the chi-square test of independence is applicable when both variables are nominal and the data is collected on different individuals. This allows researchers to investigate the relationship between the variables and determine if they are associated or independent.

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The experimental probability of landing on white is 10%.

To find the experimental probability, we divide the number of times white was landed on by the total number of spins and then express it as a percentage. In this case, white was landed on 15 times out of 150 spins.

So, the experimental probability of landing on white is 15/150 = 0.1, which is equivalent to 10% when expressed as a percentage.

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The stationary shop had 90 pens with them initially.

Let,

The number of pens initially at the stationary shop=x

The number of pens and the number of notepads are said to be equal. Therefore, The number of notepads initially at the stationary shop=x

After selling,

The number of pens = x-1250

The number of notepads = x-380

The number of pens was four times the number of the number of notepads. Modelling the linear equation for the situation:

x-1250=4(x-380)

x-1250=4x-1520

x=4x-270

-3x=-270

x=90

The stationary shop had 90 pens initially.

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Answer:

x − 9 x ^2 − 8

Step-by-step explanation:

Answer:

1.50 liter/hr

Step-by-step explanation:

using;

\( \frac{6 - 3}{4 - 2} \)

=3/2= 1.50 liter/hr

Answer:

All I know is that is between C and D

maybe...

Step-by-step explanation:

Answer:

The relationship between these two sequences is it always doubles.  When we look at each sequence, 1, 2, 3, 4, 5, each number is multiplied by 2 to create the other sequence.

1 x 2 = 2.

2 x 2 = 4.

3 x 2 = 6.

4 x 2 = 8.

5 x 2 = 10.

When we arrange these numbers, 2, 4, 6, 8, 10, this is the exact sequence as before.  Therefore, this is the relationship.

Answer: 2, 4, 6, 8, 10,                           <                                |

                                                                                               |

Step-by-step explanation:                                                    |                                if you just  arange the numbers to 1 x 2 = 2                         |

                                                          2 x 2 = 4                       |

                                                          2 x 3 = 6                       |

  and then so on and so on you would get this answerer. |

The values of a and b are 4 and -3

To solve for a, we make use of the function f(x).

x    f(x)

2     4

0     5

2     a

3     7

Remove the x values 0 and 3

x    f(x)

2     4

2     a

The above table implies that:

f(2) = 4 and f(2) = a

Substitute 4 for f(2) in f(2) = a

4 = a

Rewrite as:

a = 4

To solve for b, we make use of the function g(x).

x    g(x)

2     b

0     0

2     -3

3     -4

Remove the x values 0 and 3

x    g(x)

2     b

2     -3

The above table implies that:

f(2) = b and f(2) = -3

Substitute -3 for f(2) in f(2) = b

-3 = b

Rewrite as:

b = -3

Hence, the values of a and b are 4 and -3

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Complete question

Use the Symmetry of a Function to Find Coordinates

f is an even function             g is an odd function

x    f(x)                                        x             g(x)

2     4                                          2              b

0     5                                          0              0

2     a                                          2              -3

3     7                                          3              -4

Find a and b

Answer:

4, 3

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

I think I am not sure soo maibe u might want to double check and just saing I am a 7th grader

Answer:

Answer:

Step-by-step explanation:

Amount of tax on $8500:

Amount of income over $8500:

Amount of tax on $6500:

Total tax is:

Step-by-step explanation:

1/2 is equal to 0.5 and 5/4 is equal to 1.25

0.5_1.25

Which is greater?

1.25 by a long shot

Then we convert back to fractions.

The answer is 1/2<5/4

Hope it helps!

Answer:

1/2 is 50% and 5/4 = 125%

Step-by-step explanation:

Answer: Divide each side by '10'. x2 = 9 Simplifying x2 = 9 Take the square root of each side: x = {-3, 3

Step-by-step explanation:

The area of the semicircle with the given diameter is 189.97 mm^2

The given parameters are

Diameter, d = 22 mm

The area of the semicircle is calculated as

A = 1/2 * pi * (d/2)^2

So, we have

A = 1/2 * 3.14 * (22/2)^2

Evaluate the expression

A = 189.97 mm^2

Hence, the area of the semicircle with the given diameter is 189.97 mm^2

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Answer:

The probability of drawing a red marble then a yellow marble out of the bag is probably 0.48(Decimal) or 12/25(Fraction).

Answer:

Its 12

Step-by-step explanation:

1.   Following PEMDAS, we first solve the equation inside the parentheses.

       -4(-2) = 8

       -12 ÷ 3 = -4

       -20 + 4 = -16

2.    Now, we have the following expression:

       8 + (-4) + (-16)

 3.  Again, following PEMDAS, we solve the equation inside the parentheses first.

       8 + (-4) + (-16) = 8 - 4 - 16

  4. Finally, we solve the equation from left to right.

       8 - 4 - 16 = 8 - (4 + 16)

       8 - (20) = -12

Therefore, the value of the expression is -12.

The statement "P implies Q" is false under the following conditions: a) P is true and Q is false, and d) P is false and Q is true.

The statement "P implies Q" can be expressed as "if P, then Q." It is a conditional statement where P is the antecedent (the condition) and Q is the consequent (the result).

To determine when the statement is false, we need to identify cases where P is true but Q is false, or when P is false but Q is true.

Option a) states that both P and Q are true. In this case, the statement "P implies Q" holds true because if P is true, then Q is true.

Option b) states that both P and Q are false. In this case, the statement "P implies Q" is considered true because the antecedent (P) is false.

Option c) states that P is true and Q is false. Under this condition, the statement "P implies Q" is false because when P is true, but Q is false, the implication does not hold.

Option d) states that P is false and Q is true. In this case, the statement "P implies Q" is true because the antecedent (P) is false.

Therefore, the conditions under which the statement "P implies Q" is false are a) P is true and Q is false, and d) P is false and Q is true.

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