Select the correct answer.

Which function does this graph represent?

A downward open parabola rises from (negative 2 point 4, negative 4) to (negative 1, 2) and declines through (0 point 4, negative 4) on the x y coordinate plane.

A.
f(x) = 3(x + 1)2 + 2
B.
f(x) = -3(x + 1)2 + 2
C.
f(x) = -3(x + 1)2 − 2
D.
f(x) = 3(x − 1)2 + 2

Using the Laplace transform, the value o y' − 2y = (t − 4), y(0) = 0 is⇒y(t) = 0 e^-t + u(t -1)e^1-t

Laplace rework is an critical rework approach that is in particular useful in fixing linear normal equations. It unearths very huge applications in  regions of physics, electrical engineering, control optics, arithmetic and sign processing.

y' − 2y = (t − 4),

y(0) = 0

Taking the Laplace transformation of the differential equation

⇒sY(s) - y (0) + Y(s) = e-s

⇒(s + 1)Y(s) = (0+ e^-s)/s + 1

⇒y(t) = L^-1{0/s+1} + {e ^-s/s + 1}

⇒y(t) = 0 e^-t + u(t -1)e^1-t

The Laplace remodel method, the feature within the time area is transformed to a Laplace characteristic within the frequency domain. This Laplace feature will be inside the shape of an algebraic equation and it can be solved easily.

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The company is considering the purchase of a new machine for $75,660 (based on the available data), and the payback period is 24 years.

The payback period is the time the company requires to recoup its investment for the new machine.

The payback period can be computed by dividing the investment cash outflows by the annual net cash inflows.

Initial investment in new machine = $75,660

Annual depreciation expense = $4,600

Investment period = 10 years

Annual sales revenue = $20,000

Annual expenses = $16,800

Ne annual cash inflow = $3,200 ($20,000 - $16,800)

Payback period = 24 years ($75,660/$3,200)

Thus, since the payback period is 24 years, while the investment period is 10 years, it sounds unwise for the company to continue the investment.

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The purpose of statistical inference population based upon information obtained from the sample.

statistical inference uses sample data to make estimates of or draw conclusions about one or more characteristics of a population.

The purpose of statistical inference is to estimate this sample to sample variation or uncertainty. Understanding how much our results may differ if we did the study again, or how uncertain our findings are, allows us to take this uncertainty into account when drawing conclusions. It allows us to provide a plausible range of values for the true value of something in the population, such as the mean, or size of an effect, and it allows us to make statements about whether our study provides evidence to reject a hypothesis.

We have four ideas for using the statistical inference.

1. Estimating uncertainty.

2. Confidence intervals.

3. Hypothesis tests.

4. Connections with other material.

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The given question is not complete.

The purpose of statistical inference is to make estimates or draw conclusions about a population based upon information obtained from the sample.

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The value of tan(X) in fraction is 7.2/6.4 and in decimal is 1.13

The complete question is added as an attachment

From the question, the given parameters are as follows:

Hypotenuse = XZ

Hypotenuse XZ = 9.6

Leg ZY = 7.2

Leg YX = 6.4

The tangent of X is then calculated as:

tan(X) = ZY/YX

Substitute the known values in the above equation

tan(X) = 7.2/6.4

Evaluate the above quotient

tan(X) = 1.125

Approximate the above result

tan(X) = 1.13

Hence, the value of tan(X) in fraction is 7.2/6.4 and in decimal is 1.13

So, the complete parameters are:

Hypotenuse = XZ

Hypotenuse XZ = 9.6

Leg ZY = 7.2

Leg YX = 6.4

tan(X) = 7.2/6.4

tan(X) = 1.13

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Given that a is an acute angle in a right triangle, cos a = [tex]\frac{15}{17}[/tex]. The trigonometric ratio sin a = [tex]\frac{8}{17}[/tex] and tan a = [tex]\frac{8}{15}[/tex].

The trigonometric ratios are six different proportions of the three sides of right angled triangle, namely, hypotenuse, perpendicular and base. The trigonometric ratios are sine, cosine, tan, sec, cosec and cot.

In any question,

cos a = [tex]\frac{base}{hypotenuse}[/tex] = [tex]\frac{15}{17}[/tex]

hypotenuse = side opposite of the right angle = 17

base  = side adjacent to the acute angled marked =  15

[tex]hypotenuse^{2} = perpendicular ^2+base^2\\\\perpendicular = \sqrt{hypotenuse^2-base^2}[/tex]

perpendicular = [tex]\sqrt{17^2- 15^2} = 8[/tex]

sin a = [tex]\frac{perpendicular}{hypotenuse} = \frac{8}{17}[/tex]

tan a = [tex]\frac{perpendicular}{base} = \frac{8}{15}[/tex]

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Answer:

See below

Step-by-step explanation:

Out of 25 games, they won 14

Fraction won = won / total = 14 / 25

Percent won = won /total * 100 % = 14/25 * 100 = .56 * 100 % = 56 %

To find the number of games lost

25-14 = 11

Fraction won = won / total = 11 / 25

Percent won = won /total * 100 % = 11/25 * 100 = .44 * 100 % = 44 %

To check your work, the percent total should be 100

56+44 = 100

The inverse maps (x,y) onto (y,x).

The general solution of the given differential equation be [tex]y(x)=c_1e^{4x}+c_2e^{-3x}+\frac{1}{7} xe^{4x}[/tex]

For given question,

We have been given a differential equation y'' − y' − 12y = e^(4x)

We need to solve the given differential equation by undetermined coefficients.

We can write given differential equation as [tex](D^2-D-12)y=e^{4x}[/tex] where [tex]D=\frac{d}{dx}[/tex]

First solve the corresponding homogeneous differential equation:

y'' - y' - 12y = 0

The characteristic equation is:

m² - m - 12 =0

Let's find the roots of above quadratic equation by factorization.

⇒ m² - m - 12 = 0

⇒ (m - 4)(m + 3) = 0

⇒ m - 4 = 0   OR  m + 3 = 0

⇒ m = 4   OR   m = -3

Hence the complementary solution is,

[tex]y_c=C_1e^{4x}+C_2e^{-3x}[/tex]

Let the general solution of a second order homogeneous differential equation be [tex]y(x)=C_1(x)e^{4x}+C_2(x)e^{-3x}[/tex]

The unknown functions C1(x) and C2(x) can be determined from the system of two equations:

[tex]C'_1e^{4x}+C'_2e^{-3x}=0~~~~~~~............(1)\\\\C'_1(4e^{4x})+C'_2(-3e^{-3x})=e^{4x}~~~~~~~...................(2)[/tex]

from (1),

[tex]C'_2e^{-3x}=-C'_1e^{4x}[/tex]

Substitute this value in equation (2)

[tex]4C'_1e^{4x}+3C'_1e^{4x}=e^{4x}[/tex]

[tex]\Rightarrow C'_1=\frac{1}{7}[/tex]  and  [tex]C'_2=-\frac{1}{7}e^{7x}[/tex]

[tex]\Rightarrow C_1=\frac{1}{7} x+c_3[/tex]     and     [tex]C_2=\frac{1}{49}e^{7x}+c_2[/tex]

Therefore, the general solution of the given differential equation be [tex]y(x)=c_1e^{4x}+c_2e^{-3x}+\frac{1}{7} xe^{4x}[/tex]

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The matrix exists as a set of numbers placed in rows and columns to create a rectangular array. The manager could achieve scalar multiplication on Matrix A, utilizing the scalar 1.15.

The matrix exists as a set of numbers placed in rows and columns to create a rectangular array. The numbers exist named the elements, or entries, of the matrix. Matrices contain wide applications in engineering, physics, economics, and statistics as well as in different branches of mathematics.

Increasing the price by 15% would mean we exist taking 100% of the value + another 15%

100 + 15 = 115%

115% = 115/100 = 1.15.

Multiplying every value in Matrix A by 1.15 will give the price raised by 15%.

Therefore, the correct answer is option c. by multiplying each entry of matrix a by 1.15.

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Answer:

C - by multiplying each entry by 1.15

Step-by-step explanation:

Edmentum.

The area of the triangle rounded to the nearest tenth is 33.3 squared inches.

Given the data in the diagram;

First we find the dimension of side b.

From the rule of cosines.

b = √[ a² + c² - 2acCosB ]

We substitute into the formula.

b = √[ 7² + 13² - ( 2 × 7 × 13 × cos( 133° ) ]

b = √[ 49 + 169 - ( 182 × cos( 133° ) ) ]

b = √[ 218 - 182×cos( 133° ) ]

b = √[ 342.1237 ]

b = 18.5

Next, we find angle C.

From rule of cosines.

cosC = [ b² + a² - c² ] / 2ba

cosC = [ 18.5² + 7² - 13² ] / [ 2 × 18.5 × 7 ]

cosC = [ 342.25 + 49 - 169 ] / [ 259 ]

cosC = [ 222.25 ] / [ 259 ]

cosC = [ 0.8581 ]

C = cos⁻¹[ 0.8581 ]

C = 30.9°

Now, we can find the area of the triangle.

Area = [ ab × sinC ] / 2

Area =  [ 7 × 18.5 × sin( 30.9 ) ] / 2

Area =  [ 129.5 × 0.51354 ] / 2

Area =  66.5 / 2

Area = 33.3 in²

The area of the triangle rounded to the nearest tenth is 33.3 squared inches.

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The value of the missing length in the image shown using the Pythagoras theorem is x = 65

An equation is an expression that shows the relationship between two or more variables and numbers.

Pythagoras theorem is used to show the relationship between the sides of a right angled triangle.

Let h represent the missing red line. Using Pythagoras:

x² = h² + 25²

h² = x² - 25²

Also:

r² = h² + 144²

r² = x² - 25² + 144²

And:

(144 + 25)² = r² + x²

(144 + 25)² = (x² - 25² + 144²) + x²

x = 65

The value of the missing length in the image shown using the Pythagoras theorem is x = 65

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Answer:

(x + 1)² + (y - 3)² = 16

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (- 1, 3 ) and r = 4 , then

(x - (- 1) )² + (y - 3)² = 4² , that is

(x + 1)² + (y - 3)² = 16

Answer:

(x+1)^2 + (y-3)^2 = 16

Step-by-step explanation:

The standard form of an equation of a circle with center (h,k) and radius r is (x-h)^2 + (y-k)^2 = r^2.  Plugging in those values, we get (x-(-1))^2 + (y-3)^2= 4^2  = (x+1)^2 + (y-3)^2 = 16.

Answer: Line D

Step-by-step explanation:

The points in the scatterplot are closest to line D.

Answer:

I don't understand the format of the questions and choices.  I simply made a few observation.

Step-by-step explanation:

The fraction - (2) can be described as the opposite of a positive number divided by a positive number.

-(2/1)?

A positive number divided by a positive number results in a Choose...     Negative Number

quotient, and its opposite is always Choose...    Opposite?  Still a negative number.

I don't understand the following:

The fraction can be described as a positive number divided by a negative number, which

-12

always results in a Choose...

quotient.

value, so Liam Choose...

The fractions have

Choose...

Y

correct.

The vertices of the quadrilateral after a dilation with scale factor 2.5 are A' = (0, 0), B' = (0,7.5), C' = (12.5, 7.5) and D' = (12.5, 0)

The coordinates of the quadrilateral ABCD are given as:

A(0,0), B(0,3), C(5,3), and D(5,0)

When dilated by a scale factor of 2.5, we have the following equation

A' = A * 2.5

So, we have:

A' = (0,0) * 2.5

A' = (0, 0)

B' = (0,3) * 2.5

B' = (0, 7.5)

C' = (5,3) * 2.5

C' = (12.5, 7.5)

D' = (5,0) * 2.5

D' = (12.5, 0)

Hence, the vertices of the quadrilateral after a dilation with scale factor 2.5 are A' = (0, 0), B' = (0,7.5), C' = (12.5, 7.5) and D' = (12.5, 0)

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Step-by-step explanation:

4 pictures correlate to 1/3 page.

how many 1/3 pages do we need to get 1 full page ?

3, as 3 × 1/3 = 3/3 = 1.

so, to keep the ratio, we need to multiply also the pictures by 3 and get

4×3 = 12 pictures per page

The conversion of 9.204 to a mixed number will be 9 51/250.

It should be noted that converting decimal to mixed numbers simply means changing them to whole numbers and fractions.

Therefore, 9.204 will be:

= 9 204/1000

= 9 51/250

The percentage equivalent of 3 7/8 will be:

= (3 × 100) + (7/8 × 100)

= 300 + 87.5

= 387.5%

Dividing 72 in the ratio 2:3:4 will be:

= 2/9 × 72 = 16

= 3/9 × 72 = 24

= 4/9 × 72 = 32

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Z = 1.555 should be used

If we seek an 88% confidence interval, that means we only want a 12% chance that our interval does not contain the true value.

Assuming a two-sided test, that means we want a 6% chance attributed to each tail of the Z-distribution.

the zα/2 value of z0.06.

This z value at α/2=0.06 is the coordinate of the Z-curve that has 6% of the distribution's area to its right, and thus 94% of the area to its left. We find this z-value by reverse-lookup in a z-table.

The standard normal distribution, also called the z-distribution, is a special normal distribution where the mean is 0 and the standard deviation is 1.

Any normal distribution can be standardized by converting its values into z-scores. Z-scores tell you how many standard deviations from the mean each value lies.

The standard score (more commonly referred to as a z-score) is a very useful statistic because it

(a) allows us to calculate the probability of a score occurring within our normal distribution and

(b) enables us to compare two scores that are from different normal distributions.

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Lynn wants to wait because (D) she would likely have to pay more than $55 at the time of purchase for the convenience of using her credit card.

The answer to why Lynn wants to wait would be:

Therefore, Lynn wants to wait because (D) she would likely have to pay more than $55 at the time of purchase for the convenience of using her credit card.

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The complete question is shown below:

Lynn is at a store and wants to buy a new backpack that costs $55. she only has $35 with her, but she has the rest at home. Lynn also has a credit card that does not charge her any interest if she pays the balance in full by the end of the month. why might Lynn want to wait until she has $55 in cash at the store to purchase the backpack, instead of using her credit card?

a. Using a credit would cause the store to lose money because even if she pays back her bill in full, she will still need to pay the credit card company additional dollars for the convenience of borrowing money.

b. Using cash would cause the store to lose a large amount of money because credit card companies offer incentives to stores based on the number of people who use their cards.

c. She might forget to pay the credit card bill, which would make her purchase more expensive due to interest payments and late charges.

d. She would likely have to pay more than $55 at the time of purchase for the convenience of using her credit card.

Answer:

Option D

Step-by-step explanation:

Using the surd law :

[tex]\sqrt{ab} = \sqrt{a}\sqrt{b}[/tex]

We can find the largest square number that goes into 75 :

Let's write the multiples of 75 :

1 , 75

3 , 25

5 , 15

The only square number is 25

So using the law mentioned above we split √75 into :

√25√3

The square root of 25 is 5

Now we have our final answer of 5√3

Hope this helped and have a good day

The simplified form of expression √75 is 5√3.

Option D is the correct answer.

We have,

To simplify √75, we can factor it into its prime factors and then take the square root:

√75 = √(3 * 5 * 5)

= √(3 x 5²)

Take out the perfect square factor from under the square root:

= √3 x √5²

= √3 x 5

= 5√3

Thus,

The simplified form of expression √75 is 5√3 which is option D.

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The probability that out of 8 newly hired people is 3.2.

According to the statement

we have given that the some conditions and based on these conditions we have to find the probability that out of 8 newly hired people.

So, For this purpose,

we have given that the

new employee in a fast-food chain still being with the company at the end of the year is  0.5

Now, we See that is probability of remaining with the company.

There is only one is 0.5.

According to the probability law

P + Q = 1

and this become

Q = 1 - 0.60.

And the probability of one people hired is Q.

Then

Q = 0.4

And probability that out of 8 newly hired people is

8Q = 0.4 * 8

it become 3.2.

So, The probability that out of 8 newly hired people is 3.2.

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The following numbers are rounded up as follows:

8.6134

5.5218

Rounding up a number means to round a number to the smallest integer that is not less than it, or to some other greater value.

Thousandth, hundredth and tenth are used after the decimal point.

8.6134

5.5218

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Answer:

2√(133)

Step-by-step explanation:

Triangle 1 = 8, 12, ?

triangle 2 = 18, x, ?

we have to find value of x which is a hypotenuse

a² + b² = c²

8² + 12² = 64 + 144 = √208 = 14.4222051019

x = 14.4222051019² + 18²

= 208 + 324

= 532

x = √532 = 2√(133)

Answer:XDDXXDXD

DXDXXDXDDXDXDXDXXDDXDEDXXDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD

Step-by-XDDXDXDXstep explanation:

seria tu cacá XDXDXDXDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD

In step 2, the property of equality applied was addition property of equality.

In step 4, the property of equality applied was multiplication property of equality.

The addition property of equality states that, to move a negative number over to the other side of an equation, add the number to both sides of the equation. For example, given the equation: a - c = b, to move c over to the other side of the equation, add c to both sides of the equation. we will have:

a - c + c = b + c

a = b + c.

According to the multiplication property of equality, if we have, a/c = b, to isolate a, we would multiply both sides of the equation by c. Thus:

a/c × c = b × c

a = bc

In the table given, in step 2, 6 was added to both sides of the equation. This means the property of equality that was applied was: addition property of equality.

In step 4, both sides of the equation was multiplied by -2. Thus, the property of equality that was applied was: multiplication property of equality.

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Answer: step 2 - addition property

              step 4 - multiplication property

Step-by-step explanation:

There are 66 ways Kim can put the 10 identical lamps on the 3 identical tables

The given parameters are:

The combination involving identical objects is calculated using:

(n + r - 1)C(r - 1)

So, we have:

n + r - 1 = 10 + 3 - 1

Evaluate the sum

n + r - 1 = 13 - 1

Evaluate the difference

n + r - 1 = 12

Also, we have:

r - 1 = 3 - 1

Evaluate the difference

r - 1 = 2

So, we have:

(n + r - 1)C(r - 1) = 12C2

Apply the following combination formula:

nCr = n!/((n - r)!r!)

So, we have:

12C2 = 12!/((12 - 2)! * 2!)

Evaluate the difference

12C2 = 12!/(10! * 2!)

Expand the numerator

12C2 = 12 * 11 * 10!/(10! * 2!)

Evaluate the quotient

12C2 = 12 * 11/2!

Expand the denominator

12C2 = 12 * 11/2 * 1

Evaluate the product

12C2 = 132/2

Evaluate the quotient

12C2 = 66

Hence, there are 66 ways Kim can put the 10 identical lamps on the 3 identical tables

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The expression [tex]$-500 \times 18+15000=-9000+15000=6000[/tex] which best fit exists in the Linear model.

Given: Monthly Rate = $20

Number of customers = 5000

If there exists a decrease of $1 in the monthly rate, the number of customers increases by 500.

Let us decrease the monthly rate by $1.

Monthly Rate = $20 - $1 = $19

Number of customers = 5000 + 500 = 5500

Let us decrease the monthly rate by $1 more.

Monthly Rate = $19 - $1 = $18

Number of customers = 5500 + 500 = 6000

Linear change in the number of customers whenever there exists a decrease in the monthly rate.

We have 2 pairs of values here,

x = 20, y = 5000

x = 19, y = 5500

The equation in slope-intercept form: y = mx + c

The slope of a function: [tex]$&m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\[/tex]

[tex]$&m=\frac{5500-5000}{19-20} \\[/tex]

[tex]$&\Rightarrow-500[/tex]

So, the equation is y = -500x + c

Putting x = 20, y = 5000:

[tex]$&5000=-500 \times 20+c \\[/tex]

[tex]$&\Rightarrow c=5000+10000=15000 \\[/tex]

[tex]$&\Rightarrow \mathbf{y}=-500 \mathbf{x}+15000[/tex]

Whether (18,6000) satisfies it.

Putting x = 18

[tex]$-500 \times 18+15000=-9000+15000=6000[/tex]

Therefore, the expression [tex]$-500 \times 18+15000=-9000+15000=6000[/tex] which best fits exist Linear model.

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Answer:

2

-2

Step-by-step explanation:

Use the second equation for x = -4.

f(-4) = 2

Use the third equation for x = 3.

f(x) = -x + 1 = -3 + 1 = -2

Answer:

D. 70,244 and 70,632

Step-by-step explanation:

Got it right on PLATO/EDMENTUM

70,244 and 70,632 is the approximate 90% confidence interval for this situation.

A confidence interval, in statistics, refers to the probability that a population parameter will fall between a set of values for a certain proportion of times.

Confidence intervals measure the degree of uncertainty or certainty in a sampling method. They can take any number of probability limits, with the most common being a 95% or 99% confidence level. Confidence intervals are conducted using statistical methods.

Statisticians use confidence intervals to measure uncertainty in a sample variable. For example, a researcher selects different samples randomly from the same population and computes a confidence interval for each sample to see how it may represent the true value of the population variable. The resulting datasets are all different; some intervals include the true population parameter and others do not.

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