A popular laptop sells for $199.99. Since sales are so
good, the store raises the price by 13%. What is the cost
of the laptop after the markup?

The value of y that satisfies the equation is 3.35 or - 5.35.

The value of y that satisfies the equation is calculated as follows;

The given equation;

√ (y + 3) + √ ( y - 2) = 5

Square both sides of the equations as follows;

[√ (y + 3) + √ ( y - 2) ]² = 5²

y + 3 + 2(y + 3)(y - 2) + y - 2 = 25

2y + 1   +   2(y² + y - 6) = 25

2y + 1 + 2y² + 2y - 12 = 25

Collect similar terms and simplify the equation;

2y²  +  4y - 36 = 0

divide through by 2;

y² + 2y - 18 = 0

Solve the quadratic equation using formula method as follows;

a = 1, b = 2, c = -18

y = 3.35 or - 5.35

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Answer:

a

Step-by-step explanation:

Answer:

A - The Moon reflects light from the Sun.

Step-by-step explanation:

As the moon moves around the sun in a one month cycle, different parts of it are exposed to the sun. When it is exposed to the light from the Sun it is reflected and people on Earth could see it at night, and sometimes during the day as well.

Answer: about 0.79

Step-by-step explanation:

First divide 8 by 9 --> (8/9) = about 0.8889

then square that value --> (0.8889)^2 = about 0.79.

PEMDAS is your friend!

Answer:

at 50 minutes both containers will be at 1000 ml having the same amount of water

Step-by-step explanation:

look at the image

No, it is not correct to conclude that the sample means cannot be treated as being from a normal distribution solely based on a small sample size of n = 15.

The Central Limit Theorem states that the distribution of sample means will approach a normal distribution, regardless of the shape of the population distribution, as the sample size increases. Therefore, even with a small sample size, the sample means can still be considered to follow a normal distribution under certain conditions.

The Central Limit Theorem assures that, as the sample size increases, the distribution of sample means becomes approximately normal, regardless of the shape of the population distribution. Although a sample size of n = 15 may be considered small, it is not sufficient to conclude that the sample means cannot be treated as following a normal distribution.

The applicability of the Central Limit Theorem depends on certain conditions, such as the independence of observations, a sufficiently large sample size, and the absence of extreme outliers. If these conditions are satisfied, the sample means can be treated as approximately normally distributed, even with a small sample size.

Therefore, it is not appropriate to conclude that the sample means cannot be treated as being from a normal distribution based solely on a small sample size of n = 15. Further analysis and consideration of the Central Limit Theorem should be conducted to determine the distributional properties of the sample means.

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Answer:

17, 15, and  30

Step-by-step explanation:

sorry if I'm wrong

The surds are √17, √15 and √30.

The square roots of numbers that cannot be divided into a whole or rational number are known as surds ().

It is not capable of being correctly expressed in a fraction. A surd, then, is the root of a whole integer with an irrational value.

Take the example of 2 1.414213. If we leave it as a surd 2, it will be more correct.

As, surds those roots that cannot have square root of a number.

So, from the given number √17, √15 and √30 which do not have square roots.

Hence, the surds are √17, √15 and √30.

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There are 7 degrees of freedom.

In performing the pooled-variance t test, the degrees of freedom can be calculated using the formula:
df = (n1 - 1) + (n2 - 1)

Substituting the given values:
df = (4 - 1) + (5 - 1)
df = 3 + 4
df = 7

Therefore, there are 7 degrees of  freedom.

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There are 7 degrees of freedom for the pooled-variance t-test.

To perform a pooled-variance t-test, we need to calculate the degrees of freedom. The formula for degrees of freedom in a pooled-variance t-test is:

\(\[\text{{df}} = n_1 + n_2 - 2\]\)

where \(\(n_1\)\) and \(\(n_2\)\) are the sample sizes of the two independent samples.

In this case, \(\(n_1 = 4\)\) and \(\(n_2 = 5\)\). Substituting these values into the formula, we get:

\(\[\text{{df}} = 4 + 5 - 2 = 7\]\)

In a pooled-variance t-test, we combine the sample variances from two independent samples to estimate the population variance. The degrees of freedom for this test are calculated using the formula \(df = n1 + n2 - 2\), where \(n_1\)and \(n_2\) are the sample sizes of the two independent samples.

To understand why the formula is \(df = n1 + n2 - 2\), we need to consider the concept of degrees of freedom. Degrees of freedom represent the number of independent pieces of information available to estimate a parameter. In the case of a pooled-variance t-test, we subtract 2 from the total sample sizes because we use two sample means to estimate the population means, thereby reducing the degrees of freedom by 2.

In this specific case, the sample sizes are \(n1 = 4\) and \(n2 = 5\). Plugging these values into the formula gives us \(df = 4 + 5 - 2 = 7\). Hence, there are 7 degrees of freedom for the pooled-variance t-test.

Therefore, there are 7 degrees of freedom for the pooled-variance t-test.

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Answer:

The coordinates of the image triangle will be:

Please also check the attached figure.

The green triangle represents the image triangle.

Step-by-step explanation:

We know that when we reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate reveres its sign.

Thus,

The rule of reflection of the point P(x, y) across the x-axis is:

P(x, y) → P'(x, -y)

In the attached figure, let the coordinates of the triangle are:

Using the rule of reflection across the x-axis:

P(x, y) → P'(x, -y)

Thus, the coordinates of the image triangle will be:

A(-3, 1) → A'(-3, -1)

B(-3, 3) → B'(-3, -3)

C(-1, 3) → C'(-1, -3)

Therefore, the coordinates of the image triangle will be:

Please also check the attached figure.

The green triangle represents the image triangle.

Marx's analysis suggests that the organization of the production process determines ideas, beliefs, and consciousness. Class plays a crucial role in this relationship, as the dominant class shapes the prevailing ideology. Class consciousness refers to the awareness of one's social class and the recognition of shared interests with others in the same class.

1. Marx argues that the organization of the production process, particularly the relationship between the bourgeoisie (owners of the means of production) and the proletariat (the working class), influences ideas, beliefs, and consciousness. The dominant class, the bourgeoisie, controls the means of production and therefore holds power over the proletariat.

2. In this relationship, the dominant class promotes and disseminates its own ideology to maintain and justify its position of power. This ideology serves to reinforce the existing social order, perpetuating the interests of the dominant class while obscuring the exploitation of the proletariat.

3. Class consciousness, according to Marx, refers to the awareness among members of a particular social class about their common economic and social interests. It involves recognizing the shared experiences and struggles of individuals within the same class and understanding their collective potential for social change.

4. The dominant class actively works to suppress class consciousness among the proletariat by promoting false consciousness, which is the adoption of ideas and beliefs that are contrary to the proletariat's true interests. This false consciousness serves to maintain the status quo and prevent the emergence of a unified working-class movement.

5. Marx views ideology as a system of ideas and beliefs that reflect the interests and values of the dominant class. Ideology serves to justify and legitimize the existing social order by framing it as natural, fair, and inevitable. It operates through institutions such as the education system, media, and religion, which disseminate and reinforce the dominant ideology.

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Answer:

b 16.4 ft

Step-by-step explanation:

To solve this problem using a graphing calculator, we need to plug in the value of q (which is given as 7) into the equation y = 2 csc e, and then graph the resulting equation.

First, we need to convert the angle e from degrees to radians, because the csc function takes its input in radians. We can use the conversion formula:

radians = degrees x (π/180)

So for e = 2, we have:

e (in radians) = 2 x (π/180) = 0.0349 radians

Now we can plug this value into the equation y = 2 csc e:

y = 2 csc(0.0349) ≈ 103.8 feet

This tells us that the length of the rafters needed to make the roof is approximately 103.8 feet. However, the question asks us to round to the nearest tenth of a foot, so the answer is:

y ≈ 103.8 feet ≈ 103.8 rounded to the nearest tenth of a foot

Therefore, the length of the rafters needed to make the roof for q 7" is approximately 103.8 feet, rounded to the nearest tenth of a foot.

So the correct answer is (b) 16.4 feet.

Using the graphing calculator, we find that the length of the rafters needed is approximately 16.4 feet, Therefore, the correct answer is option B, 16.4 feet.

To find the length of the rafters needed for the roof with an angle of 7 degrees, we'll use the given function y = 2 * csc(e), where e is the angle formed by the rafters and the top of the wall. Here's a step-by-step explanation:

1. Convert the angle from degrees to radians: e (in radians) = (7 degrees * π) / 180 ≈ 0.1222 radians.

2. Calculate the cosecant  (csc) of the angle e: csc(0.1222) ≈ 8.185.

3. Plug the value of csc(e) into the function: y = 2 * 8.185 ≈ 16.37.
Using a graphing calculator, we can input the function y = 2 csc e and graph it. Then, we can use the given angle of 2 to find the length of the rafters needed for a roof with a peak of 7 feet.

4. Round the length to the nearest tenth of a foot: 16.37 ≈ 16.4 feet.
When we graph the function, we can see that the length of the rafters is the distance between the x-axis and the point on the graph where y = 7.
So, the length of the rafters needed to make the roof for an angle of 7 degrees is approximately 16.4 feet (Option b).

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The equations that will represent the reflected function are:

(c)  \(f(x)=5(\frac{1}{5})^{-x}\) and;

(d) \(f(x)=5(5)^{x}\)

If two functions share the same domain and codomain and have values that are consistent across all domain elements, they are said to be equivalent.

Consider the function,

\(f(x)=5(\frac{1}{5})^{x}\)

Now,

Positive x-values and negative x-values are switched by a reflection over the y-axis, which also swaps the values of x and x.

So,

\(f(-x)=f(x)\)

The reflection of the function f(x) across the y axis will be:

\(f(x)=5(\frac{1}{5})^{-x}\)

Therefore, the equivalent function will be:

\(f(x)=5(\frac{1}{5})^{(-1)(x)}\)

\(f(x)=5 \times ((\frac{1}{5})^{-1})^{x} \\f(x)=5(5)^{x}\)

Therefore, the equations which represent the function are:

\(f(x)=5(\frac{1}{5})^{-x}\) and;

\(f(x)=5(5)^{x}\).

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The complete question is mentioned below:

The function \(f(x)=5(\frac{1}{5})^{x}\) is reflected over the y-axis. Which equations represent the reflected function? Select two options.

(a) \(f(x)=\frac{1}{5}(5)^{-x}\)

(b) \(f(x)=\frac{1}{5} \frac{1}{5} [\frac{1}{5} ]^{x}\)

(c)  \(f(x)=5(\frac{1}{5})^{-x}\)

(d) \(f(x)=5(5)^{x}\)

(e) \(f(x)=5(5)^{-x}\)

The 99 % confidence interval for u, given the lifetimes for the brand following a normal distribution, would be C. 48.39 to 51.61.

To construct a 99% confidence interval for the population mean (µ), we can use the formula for a confidence interval, which is:

Confidence Interval = Sample mean ± (Z-value * (Standard deviation / √(n)))

The Z-value for a 99% confidence level is approximately 2.58 according to the standard normal distribution table.

The confidence interval is therefore:

Confidence Interval = 50 ± (2.58 * (5 / √(64)))

Confidence Interval = 50 ± (2.58 * (5 / 8))

Confidence Interval = 50 ± 1.6125

Lower limit:

= 50 - 1.6125

= 48.39

Upper limit:

= 50 + 1.6125

= 51.61

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The components are Nx= Ncosθ  and Ny= -Nsinθ

We know that the vector quantities are those quantities that have magnitude as well as direction.

Each vector quantity can be divided into two parts a horizontal and vertical component, the vertical component is known as the sine component while the horizontal component is known as the cosine component.

A vector component is the product of its length and the component angle.

Generally, F sinθ is the vertical component and F cosθ is the horizontal component,

Now, from the diagram the horizontal component of vector 'r' is

Nx= Ncosθ

and, the vertical component will be

Ny= -Nsinθ

this is in the opposite direction

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Here, X represents the number of single-family homes with a porch, then the distribution of X can be approximated with a normal distribution, N(24,3.5). Mean (μ) is 24 Standard deviation (σ) is 3.5. And here the answer comes to be 0.1617

Using this approximation, we have to find the probability that 27 or 28 single-family homes will have a porch. Probability distribution is defined as the pattern of all possible values of random variables along with their respective probability values. To get the probability that 27 or 28 single-family homes will have a porch, we can use the formula for finding probability as follows:P(X = 27) + P(X = 28) = P(26.5 < X < 28.5)

We need to apply continuity correction because we need to convert the discrete probability distribution to a continuous probability distribution by adding and subtracting 0.5, respectively to make them continuous.Since the distribution of X can be approximated with a normal distribution, the given normal distribution can be written as follows;Normal distribution, N(24,3.5) Using the standard formula to find the z-score; Z = (X - μ)/σ, where X = 26.5, μ = 24, and standard deviation = 3.5. Substituting the given values in the above formula; Z = (26.5 - 24)/3.5 = 0.7142Z = (28.5 - 24)/3.5 = 1.2857. Using the standard normal distribution table, the probability for z-scores 0.71 and 1.28 is 0.2389 and 0.4006, respectively. Therefore, the required probability that 27 or 28 single-family homes will have a porch is:P(X = 27) + P(X = 28) = P(26.5 < X < 28.5) = P(0.7142 < Z < 1.2857)≈ 0.4006 - 0.2389 = 0.1617

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Answer:

45

Step-by-step explanation:

All angles of a triangle should add up to 180

35 + 80 + 45 = 180

To find out how many numbers counted by Alex were also counted by Matthew, we need to determine the common multiples of 6 and 4 between 6 and 2400.

First, let's find the number of terms counted by Alex. We can use the formula for the nth term of an arithmetic sequence: an = a1 + (n - 1)d, where an represents the nth term, a1 is the first term, and d is the common difference.

For Alex, a1 = 6 and the common difference is 6. We want to find the largest n such that an ≤ 2400.

2400 = 6 + (n - 1)6
2394 = 6n - 6
2400 = 6n
n = 400

So, Alex counted 400 terms.

Now let's find the number of terms counted by Matthew. Using the same formula, a1 = 4 and the common difference is 4. We want to find the largest n such that an ≤ 2400.

2400 = 4 + (n - 1)4
2396 = 4n - 4
2400 = 4n
n = 600

So, Matthew counted 600 terms.

To find the common multiples of 6 and 4, we need to find the least common multiple (LCM) of 6 and 4, which is 12.

The common multiples of 6 and 4 that are less than or equal to 2400 are: 12, 24, 36, ..., 2400.

To find the number of common terms, we need to find the number of terms in this sequence. We can use the formula for the nth term of an arithmetic sequence: an = a1 + (n - 1)d.

For this sequence, a1 = 12, the common difference is 12, and we want to find the largest n such that an ≤ 2400.

2400 = 12 + (n - 1)12
2388 = 12n - 12
2400 = 12n
n = 200

Therefore, there are 200 common terms counted by both Alex and Matthew.

In conclusion, out of the numbers counted by Alex and Matthew, there are 200 numbers that were counted by both of them.

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Answer:

82

Step-by-step explanation:

60 - 16/2 + 10(3)

60 - 16/2 + 30              multiplication

60 - 8 + 30                    division

 52 + 30                       addition or subtraction in order from left to right

 82

Answer:

7.4

Step-by-step explanation:

Answer:

7.4

Step-by-step explanation:

Because we have the adjacent length and we are trying to find the opposite of the angle we will use tan.

Tan = \(\frac{opposite}{adjacent}\)

Rearrange this to find opposite...

Opposite = Tan * Adjacent

Opposite = tan(42) * 8.2

Opposite = 7.4 (rounded to the nearest tenth)

The two-column proof that the perimeter of a midsegment triangle is half the perimeter of the triangle is shown below

Below is a two-column proof that the perimeter of a midsegment triangle is half the perimeter of the triangle:

Given: us, st, and tu are midsegments of pqr.

Prove: the perimeter of stu = 1/2(pq + qr + rp).

Statement                                                                   Reason                                                                                    

us, st, and tu are midsegments of pqr                       Given  

us, st, and tu are line segments that connect           Definition of                                                                      

themidpoints of pq, qr, and rp, respectively.            midsegment

The midpoint of a line segment is the point that      Definition of

divides the line segment into two congruent            midpoint

(equal) parts

Therefore, us, st, and tu are each half the               Property of

length of pq, qr, and rp, respectively.                       midpoint

The perimeter of stu = us + st + tu                             Definition of perimeter

The perimeter of stu=(1/2)(pq) + (1/2)(qr) + (1/2)(rp)    Substitution

The perimeter of stu = 1/2(pq + qr + rp)                     Simplification

Thus, the perimeter of stu = 1/2(pq + qr + rp)             Conclusion

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Answer:

Step-by-step explanation:

two circles: 2(πr²)

1 rectangle:Lw

3.14(7)(7)

3.14(49)

2(153.86)=307.72

307.72(14)

4308.08

Answer:

3 OR 8  hope this helps!

Step-by-step explanation:

We need four D flip-flops to design a counter to count in the sequence 12, 20, 1, 0, and then repeat.

To count in the sequence 12, 20, 1, 0 and then repeat, we need a counter that has at least four states: 12, 20, 1, and 0. Each state corresponds to a unique output value, and the counter changes state after each clock pulse.

To implement the counter, we can use four D flip-flops, one for each state. The flip-flops will store the current state of the counter and change state on the rising edge of the clock signal. The outputs of the flip-flops will be combined to produce the counter's output.

Therefore, we need four D flip-flops to design a counter to count in the sequence 12, 20, 1, 0, and then repeat.

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Answer:

5.5

Step-by-step explanation:

We use right triangle XVW.

For <W, VX is the opposite leg.

WX is the hypotenuse.

The trig ratio that relates the opposite leg to the hypotenuse is the sine.

\( \sin W = \dfrac{opp}{hyp} \)

\( \sin W = \dfrac{VX}{WX} \)

\( \sin 43^\circ = \dfrac{VX}{8~mi} \)

\( VX = 8~mi \times \sin 43^\circ \)

\( VX = 5.5~mi \)

Answer:

ypotheses:

H0: μ = 2000

H1: μ < 2000

Claim: The average number of acres in the State Park is less than 2000.

Critical Value (s): -1.645 (z-score)

Acceptance Region: z < -1.645

Rejection Region: z ≥ -1.645

Test Value: z = -3.537

Conclusion: Since -3.537 is less than -1.645, we reject the null hypothesis and accept the alternate view. There is enough evidence to support the claim that the average number of acres in the State Park is less than 2000.

Step-by-step explanation:

Answer:

Step-by-step explanation:

he would have to pay 60 dollars but I don't really understand your question

Answer:

$20/3  or $6.67

Step-by-step explanation:

the question is incomplete the full question is Jon buys 3 shirts for 20 find his rate and the answer is above

Answer:

Multiply the first equation by 5 and the second equation by 2. Then add.

Multiply the first equation by 2 and the second equation by 5, then subtract.

Step-by-step explanation:

Given

\(- 2x + 5y = -15\)

\(5x + 2y = -6\)

Required

Steps to solve using elimination method

From the list of given options, option 2 and 3 are correct

This is shown below

Option 2

Multiply the first equation by 5

\(5(- 2x + 5y = -15)\)

\(-10x + 25y = -75\)

Multiply the second equation by 2.

\(2(5x + 2y = -6)\)

\(10x + 4y = -12\)

Add

\((-10x + 25y = -75) + (10x + 4y = -12)\)

\(-10x + 10x + 25y +4y = -75 - 12\)

\(29y = -87\)

Notice that x has been eliminated

Option 3

Multiply the first equation by 2

\(2(- 2x + 5y = -15)\)

\(-4x + 10y = -30\)

Multiply the second equation by 5

\(5(5x + 2y = -6)\)

\(25x + 10y = -30\)

Subtract.

\((-4x + 10y = -30) - (25x + 10y = -30)\)

\(-4x + 25x + 10y - 10y= -30 +30\)

\(21x = 0\)

Notice that y has been eliminated

Answer:

How many solutions does the system have?

✔ exactly one

The solution to the system is

(

⇒ 0,

⇒ -3).

Step-by-step explanation:

the next two parts

Answer:

circumference = 219.91 cm

65,973 cm

Step-by-step explanation:

circumference = 35 x 2 x π = 219.91 cm

219.91 x 5 x 60 = 65,973 cm