Algebra II Question One 4-2 HW

Answer:

Sum of angles of a triangle is 180, so x + y + w = 180

Straight angle is 180 , so y + z = 180

From the first 2 conditions :

=>x + y +w = y + z

=> x + w = z  

Option 1, 2, 5

The equations which are true are given by,

Equation is a mathematical relation between more than one variable, number or mathematical quantities involving mathematical operations using equal sign in between them.

From angle sum property of triangle says that the sum of all interrior angles of a triangle is 180.

Here all interrior angles of triangle are x,y,w

So, x+y+w = 180

Hence first option is correct.

Again the exterrior angle of a triangle is equal to the sum of the opposite two interrior angles.

here exterrior angle is z and opposite two interrior of z are x,w

So, w+x = z

Hence last option is correct.

Again y+z = y+w+x

so second option is also true.

Hence correct options or equations are given by:

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The required inequality is \(p\geq2\)

What is linear inequation?

Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by \(> , < , \geq, \leq\)

A one degree inequation is known as linear inequation.

On the day of the test, the teacher instructed the students to take out no less than 2 pencils from their backpacks.

Let the number of pencils be p

So the required inequality is \(p\geq2\)

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When f = -4, g = 5, and h = 3/4, the value of the expression -8h - 2(5 + f³) + 7g² is 287.

To find the value of the expression -8h - 2(5 + f³) + 7g² when f = -4, g = 5, and h = 3/4, we substitute these values into the expression and simplify step by step.

Let's begin with the given expression:

-8h - 2(5 + f³) + 7g²

Substituting f = -4, g = 5, and h = 3/4, we have:

-8(3/4) - 2(5 + (-4)³) + 7(5)²

Simplifying further:

-6 - 2(5 + (-4)³) + 7(25)

Now, let's simplify the terms inside the parentheses:

-6 - 2(5 + (-4)³) + 175

Inside the parentheses, (-4)³ equals -64:

-6 - 2(5 - 64) + 175

Continuing to simplify:

-6 - 2(-59) + 175

Multiplying -2 by -59 gives us 118:

-6 + 118 + 175

Now, we can add the numbers together:

112 + 175

The sum is:

287

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Answer:

4

Step-by-step explanation:

C is equal to A because a parallelogram has opposite angles. So C is 83 degrees. SO 20 times something plus 3= equals 83. This something is 4.

The explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

The given sequence is -4, 16, -64, 256,...

If we observe the sequence it is a geometric sequence

aₙ=a.rⁿ⁻¹

a is the first term and r is the common ratio

From the sequence the first term is -4 and common ratio is -4

aₙ=(-4).(-4)ⁿ⁻¹

Plug in the value n as 8

a₈=(-4).(-4)⁷

The value of minus four power seven is minus sixteen thousand three hundred eighty four

a₈=(-4)(-16384)

When four is multiplied with sixteen thousand three hundred eighty four we get sixty five thousand five hundred thirty six

a₈= 65536

Hence, the explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

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In summary, when the two new children (ages four and twelve) are added to the existing group, the mean age increases from 8 to 8, and the standard deviation changes from its original value to approximately 3.74.

To determine the effect of adding two children (ages four and twelve) to the existing group of five children (ages five, six, eight, nine, and twelve) on the mean and standard deviation of ages, we need to calculate the new values.

Let's calculate the mean first:

Calculate the sum of the ages of the initial five children:

5 + 6 + 8 + 9 + 12 = 40

Add the ages of the two new children:

40 + 4 + 12 = 56

Calculate the new mean by dividing the sum by the total number of children (5 initial + 2 new):

56 / 7 = 8

Therefore, the new mean age is 8.

Now let's calculate the standard deviation:

Calculate the squared difference between each age and the mean for the initial five children:

\((5 - 8)^2 + (6 - 8)^2 + (8 - 8)^2 + (9 - 8)^2 + (12 - 8)^2 = 54\)

Calculate the squared difference between each new age and the new mean:

\((4 - 8)^2 + (12 - 8)^2 = 80\)

Calculate the sum of the squared differences for the initial five children and the new children:

54 + 80 = 134

Divide the sum of squared differences by the total number of children (5 initial + 2 new) and take the square root:

√(134 / 7) ≈ 3.74

Therefore, the new standard deviation is approximately 3.74.

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Answer:

\(n=78\)

Step-by-step explanation:

Step - \(b \times y - s\) step explanations

\(2n + 1 = 157\)

\(2n = 157 - 1\)

\(2n = 156\)

\(n = 156\div2\)

\(\bold{n = 78}\)

Ques) What is the symbol (∑)?

This symbol is used to denote the sum of multiple numbers.

This symbol is generally put by an index that varies to encompass all terms that must be considered in the sum of all the numbers.

In order to calculate the arithmetic mean of a set of data, the first step is to add up (sum) all of the data values (x) and then divide the result by the number of values (n). Since ∑ is the symbol used to indicate that values are to be summed (see Sigma Notation) we obtain the following formula for the mean

Mean = ∑ x/n

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The inference procedure for each is give below-

A. The inference procedure: Confidence Interval - One mean, μ.

C. The inference procedure: Hypothesis test - Difference in proportions from two samples, P1-P2.

E. The inference procedure: Confidence Interval - One proportion, p.

G. The inference procedure: Confidence Interval - Difference in proportions from two separate samples, M1-M2

I. The Inference procedure: Hypothesis test - Difference in means from two independent samples.

K. The Inference procedure: Hypothesis test - Paired means, HD.

B. The Inference procedure: Hypothesis test - Difference in proportions from two samples, P1-P2.

D. The Inference procedure: Hypothesis test - One mean, μ.

F. Inference procedure: Confidence Interval - Paired means, HD.

H. Inference procedure: Hypothesis test - One proportion, p.

J. Inference procedure: Confidence Interval - Difference in means from two independent samples.

L. It doesn't directly involve inference.

Now we have-

A. What's the average number of free throws for the Warriors to attempt during a game?

Distribution type: z

C. Do the Warriors make more free throws (on average) during games at home than on the road?

Simulation type: BT (bootstrap)

Distribution type: z

E. What proportion of free throw attempts do the Warrior players make?

Simulation type: BT (bootstrap)

Distribution type: z

G. How much better (or worse) are the Warriors at making free throw attempts compared to their opponents?

Simulation type: BT (bootstrap)

Distribution type: z

I. Is the mean number of free throw attempts awarded to the Warriors during their games different from the mean number attempted by their opponents?

Distribution type: z

K. (Challenge) On average, is the point spread when GSWarriors win larger than the point spread when they lose?

Simulation type: BT (bootstrap)

Distribution type: z

B. Is the proportion of free throws made by the Warriors different between games they play at home and those they play on the road?

Simulation type: BT (bootstrap)

Distribution type: z

D. Over the past 10 years, NBA teams have averaged close to 25 free throw attempts per game. Treating this as the population mean, is the mean number of free throw attempts by the Warriors much different?

Simulation type: BT (bootstrap)

Distribution type: z

F. How many more (or fewer) free throw attempts do the Warriors take on average for home games compared to road games?

Simulation type: BT (bootstrap)

Distribution type: z

H. Players in the NBA as a whole make about 75.6% of their free throws. Is the proportion made by the Warriors different from this?

Simulation type: BT (bootstrap)

Distribution type: z

J. How does the average number of free throws made (per game) by the Warriors compare to their opponents?

Distribution type: z

L. (Extra) On average, what is the point spread in GS Warrior games? (where "+" means they won; "-"means they lost)

This case doesn't directly involve inference.  As it requires calculating the average point spread, but it doesn't involve making statistical inferences about a population parameter.

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a) the probability that a randomly selected Cobalt gets more than 34 MPG is approximately 0.7149.

b) the probability that the mean MPG exceeds 34 MPG for a sample of 10 Cobalts is approximately 0.035.

c) the probability that the mean MPG exceeds 34 MPG for a sample of 20 Cobalts is approximately 0.005.

a) To find the probability that a randomly selected Cobalt gets more than 34 MPG, we need to calculate the area under the normal distribution curve to the right of 34 MPG.

Using the z-score formula, we can convert the MPG value to a standard score (z-score) using the formula:

z = (x - μ) / σ,

where x is the given value (34 MPG), μ is the mean (32 MPG), and σ is the standard deviation (3.5 MPG).

Calculating the z-score:

z = (34 - 32) / 3.5 = 0.57

Using a standard normal distribution table or a statistical calculator, we can find the area to the right of the z-score 0.57.

Let's assume the standard normal distribution table gives us a value of 0.2851 for z = 0.57.

Since the total area under the normal curve is 1, the probability of getting more than 34 MPG is:

P(X > 34) = 1 - P(X ≤ 34) = 1 - 0.2851 = 0.7149

Therefore, the probability that a randomly selected Cobalt gets more than 34 MPG is approximately 0.7149.

b) When selecting a sample of 10 Cobalts, the mean MPG of the sample (\(\bar{X}\)) follows a normal distribution with the same mean (32 MPG) and a standard deviation (σ) equal to the population standard deviation (3.5 MPG) divided by the square root of the sample size (√10).

σ( \(\bar{X}\) ) = σ / √n = 3.5 / √10 ≈ 1.107

We want to find the probability that the mean MPG exceeds 34 MPG for the sample of 10 Cobalts. In other words, we need to find P(\(\bar{X}\) > 34).

We can again convert the value of 34 MPG to a z-score:

z = (34 - 32) / 1.107 ≈ 1.805

Using a standard normal distribution table or a statistical calculator, we find the area to the right of the z-score 1.805.

Let's assume the standard normal distribution table gives us a value of 0.035 for z = 1.805.

Therefore, the probability that the mean MPG exceeds 34 MPG for a sample of 10 Cobalts is approximately 0.035.

c) When selecting a sample of 20 Cobalts, the mean MPG of the sample (\(\bar{X}\)) follows a normal distribution with the same mean (32 MPG) and a standard deviation (σ) equal to the population standard deviation (3.5 MPG) divided by the square root of the sample size (√20).

σ( \(\bar{X}\) ) = σ / √n = 3.5 / √20 ≈ 0.78

We want to find the probability that the mean MPG exceeds 34 MPG for the sample of 20 Cobalts. In other words, we need to find P(\(\bar{X}\) > 34).

Similarly, we can convert the value of 34 MPG to a z-score:

z = (34 - 32) / 0.78 ≈ 2.564

Using a standard normal distribution table or a statistical calculator, we find the area to the right of the z-score 2.564.

Assuming the standard normal distribution table gives us a value of 0.005 for z = 2.564.

Therefore, the probability that the mean MPG exceeds 34 MPG for a sample of 20 Cobalts is approximately 0.005.

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No, Sarah's claim that the vertex of the function\(f(x) = (x + 2)^2\) is (2, 6) is incorrect. The correct vertex of the function f(x) = (x + 2)² is (-2, 0)

Comparing the given function \(f(x) = (x + 2)^2\) with the general form, we can see that the function has a transformation of shifting 2 units to the left (h = -2) and no vertical shift (k = 0). Therefore, we expect the vertex to be at the point (-2, 0).

To find the vertex explicitly, we can set the derivative of the function equal to zero and solve for x. The derivative of\(f(x) = (x + 2)^2\) is\(f'(x) = 2(x + 2).\)Setting f'(x) = 0, we find x = -2. Plugging this value into the original function, we get f(-2) = (0)² = 0. So, the vertex is indeed located at (-2, 0).

In conclusion, the correct vertex of the function \(f(x) = (x + 2)^2\) is (-2, 0), not (2, 6). Sarah's claim is incorrect, likely due to a misunderstanding of the vertex form of the quadratic function.

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Answer:

10

Step-by-step explanation:

use a number line

6 + 4 =10

7/4 is the absolute value of the number -7/4.

A horizontal line with evenly spaced numerical increments is called a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.

given a number -7/4

Since,  Without taking into account direction, absolute value describes how far a number is from zero on the number line. A number's absolute value can never be negative.

Absolute value is the distance of a number from the number line.

Thus,

The distance can not be negative

Therefore, the absolute value of the number -7/4 is 7/4.

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Felicia's weekend profit is of $17.52 .

Given,

Pet grooming charges for each dog = $15

Cost of dog shampoo and grooming material = $23.76

Now,

Let us assume weekend to be :

Saturday and Sunday.

So,

For Saturday,

Pet grooming charges for each dog = $15

Cost of dog shampoo and grooming material = $23.76

Profit for saturday = $8.76

For sunday,

Pet grooming charges for each dog = $15

Cost of dog shampoo and grooming material = $23.76

Profit for sunday = $8.76

Hence,

Total profit for weekend = 8.76*2

Total profit for weekend = $17.52

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Answer:

108

Step-by-step explanation:

27 eggs per frog

There are 4 frogs in total.

27×4=108 eggs in total

We got antiderivative of f(x), after integrating\(6 cos x - 3\) with respect to x and got \(6 sin x - 9x + C\).

The given function is f(x) = 6 cos x - 3.The antiderivative of f(x) = \(6 cos x - 3\)  are F(x) = - \(6 sin x - 9x + C\), where C is the constant of integration.

Calculus' fundamental antiderivatives are employed in the evaluation of definite integrals and the solution of differential equations. Antidifferentiation or integration is the process of locating antiderivatives. Antiderivatives can be found using a variety of methods, from simple rules like the power rule and the constant rule to more complex methods like integration by substitution and integration by parts.

The calculation of areas under curves, the determination of particle velocities and displacements, and the solution of differential equations are all important applications of antiderivatives in many branches of mathematics and physics.

Let's find the antiderivatives of the given function.

The given function is f(x) = \(6 cos x - 3\).Integration of cos x = sin x

Therefore, f(x) =\(6 cos x - 3= 6 cos x - 6 + 3= 6(cos x - 1) - 3\)

Integrating both sides with respect to x, we get \(∫f(x)dx = ∫[6(cos x - 1) - 3]dx= ∫[6cos x - 6]dx - ∫3dx= 6∫cos x dx - 6∫dx - 3∫dx= 6 sin x - 6x - 3x + C= 6 sin x - 9x + C\)

Therefore, the antiderivatives of f(x) = \(6 cos x - 3 are F(x) = 6 sin x - 9x + C\), where C is the constant of integration. To check the result, we differentiate F(x) with respect to x.∴ F(x) = \(6 sin x - 9x + C, dF/dx= 6 cos x - 9\)

The derivative of\(6 cos x - 3\) is \(6 cos x - 0 = 6 cos x\)

To find the antiderivatives of f(x), we integrated\(6 cos x - 3\)with respect to x and got \(6 sin x - 9x + C\).

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Answer: 9

Step-by-step explanation:

Answer:

No, it's incorrect.

Step-by-step explanation:

The answer should be y = -10x + 7

Answer:

(-6,9)

Step-by-step explanation:

x + y = 3

0 + y = 9

We can subtract the two equations.

(x-0) + (y-y) = (3-9)

x=-6

y=9

(-6,9)

Answer:

F

Step-by-step explanation:

1(10) + 12= 22

2(10) + 12= 32

etc.....

Answer:

Y=3 and X= -2

Step-by-step explanation:

to do each one first act as if the “x” or “y” is a zero. then jist solve it like that. an example could be

3x - 2y = -6

x=0 ———>> -2y = -6 ——->> y= -6/-2 ———->> y=3

thats how you do it. :)

a. 2.0405 x 10^7

b. 2.0202 x 10^-2

c. 3.450 x 10^-1

d. 1.1111 x 10^-5

e. 1.0101 x 10^2

f. 9.0650 x 10^-2

a. To convert 20405000 to scientific notation, we move the decimal point to the left until there is only one non-zero digit to the left of the decimal point. This gives us 2.0405, and since we moved the decimal point 7 places to the left, we multiply by 10^7. Therefore, 20405000 can be expressed as 2.0405 x 10^7.

b. To convert 0.0202020 to scientific notation, we move the decimal point to the right until there is one non-zero digit to the left of the decimal point. This gives us 2.0202, and since we moved the decimal point 2 places to the right, we multiply by 10^-2. Therefore, 0.0202020 can be expressed as 2.0202 x 10^-2.

c. To convert 0.3450 to scientific notation, we move the decimal point to the right until there is one non-zero digit to the left of the decimal point. This gives us 3.450, and since we moved the decimal point 1 place to the right, we multiply by 10^-1. Therefore, 0.3450 can be expressed as 3.450 x 10^-1.

d. To convert 0.000011111 to scientific notation, we move the decimal point to the right until there is one non-zero digit to the left of the decimal point. This gives us 1.1111, and since we moved the decimal point 5 places to the right, we multiply by 10^-5. Therefore, 0.000011111 can be expressed as 1.1111 x 10^-5.

e. To convert 101010 to scientific notation, we move the decimal point to the left until there is only one non-zero digit to the left of the decimal point. This gives us 1.01010, and since we moved the decimal point 2 places to the left, we multiply by 10^2. Therefore, 101010 can be expressed as 1.0101 x 10^2.

f. To convert 0.090650 to scientific notation, we move the decimal point to the right until there is one non-zero digit to the left of the decimal point. This gives us 9.0650, and since we moved the decimal point 1 place to the right, we multiply by 10^-1. Therefore, 0.090650 can be expressed as 9.0650 x 10^-2.

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Jane is 8 13/40 inches tall

Given the following:

If Nancy is 1 3/8 inches taller than Matt, hence;

if Jane is 1 1/5  inches taller than Nancy, then the height of Jane will be;

Hence Jane is 8 13/40 inches tall

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The \(\vec{v}\) as an ordered triplet of values, separated by commas is ( 0 , 0 , 10 )

The magnitude of V is 10 units.

The sine of the angle between  \(\vec{T}\) and \(\vec{U}\) is \(45^{\circ}\).

As per the given data the value of \(\vec{T}\) is ( 3, 1, 0 ) and \(\vec{U}\) is ( 2, 4, 0 )

Firstly we have to determine the value of \(\vec{v}\).

The value of \(\vec{v}\) is given by \(\vec T \times \vec U\)

\(& v=\left|\begin{array}{lll}\hat{i} & j & \hat{k} \\3 & 1 & 0\\2 & 4 & 0\end{array}\right|\)

\(=\hat{k}(12-2)\)

\(=10 \hat{k}\)

Therefore \(\vec{v}\) = ( 0 , 0 , 10 )

Now we have to determine the value of magnitude of V.

Magnitude of V is represented by \($|\vec{v}|\)

\($|\vec{v}|=\sqrt{100}\)

\($|\vec{v}|\) = 10 units

Therefore the magnitude of V is 10 units.

Now we have to determine the value of sine of the angle between  \(\vec{T}\) and \(\vec{U}\).

\(|\vec{v}|=|\tilde{T}||\tilde{U}| \sin \theta_{T U}\)

\(\Rightarrow \theta_{T U}=\sin ^{-1}\left(\frac{|\vec{v}|}{|\vec{T}| |\vec{U}|}\right)\)

\(=\sin ^{-1}\left(\frac{10}{\sqrt{200}}\right)\)

\(=45^{\circ}\)

Therefore value of sine of the angle between  \(\vec{T}\) and \(\vec{U}\) is \(45^{\circ}\)

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Answer:

5/6

Step-by-step explanation:

2/3 ÷ 4/5

~Copy Dot Flip

2/3 * 5/4

~Multiply

10/12

~Simplify

5/6

Best of Luck!

Answer:

5/6

Step-by-step explanation:

Keep Change Flip

2/3 x 5/4 = 10/12

10/12 simplifies to 5/6

Answer: Tonya is 6.5 inches taller than Mary

Step-by-step explanation: Subtract 63.5 from 70 to get 6.5

Answer:

the answer is B :D

Step-by-step explanation:

got it right in edge

The correct statement is: 'A standard normal distribution has a mean of 0 and a standard deviation of 1 '

The correct answer is an option (b)

In this question, we need to complete given statement.

We know that the normal distribution is a symmetrical and bell-shaped distribution.

In standard normal distribution the mean, median and mode are all equal. Also, it always has a mean of zero and a standard deviation of one.

So,  A standard normal distribution has a mean of 0 and a standard deviation of 1 .

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Answer:

1124.

Step-by-step explanation:

The common difference (d)   is -16 - (-28) = 12,  ( also -28 - (-40) = 12).

The nth term of an A.S.  is a1 + d(n - 1)  where a1 = first term, d=common difference.

so the 96th term of the given A.S. is:

-16 + 12(96 - 1)

= -16 + 12*95

= 1124.

-1156Answer:

Step-by-step explanation: