Solve Using Substitution
-9x + 6y = 18
y = -6​

Answer:

(e - 7)(e + 5)

Step-by-step explanation:

If factored form is (e + a)(e + b), then a*b will equal the constant (last term, -35) and a+b will equal the second term’s coefficient (-2). Notice that -7*5 = -35 and -7+5 = -2. Thus, -7 and 5 will be values a and b:

(e - 7)(e + 5)

The critical value of t for constructing a 99% confidence interval with a sample size of 30 and a sample standard deviation of 0.05 is 2.7564.

A confidence interval is a range of values within which the population parameter is estimated to lie with a certain level of confidence. In this case, we are constructing a 99% confidence interval for the population mean. The critical value of t is used to determine the width of the confidence interval.

The formula for calculating the confidence interval for the population mean is:

Confidence interval = sample mean ± (critical value) * (standard deviation of the sample / square root of the sample size)

Given that the sample size is 30 (n = 30) and the standard deviation of the sample is 0.05 (S = 0.05), we need to find the critical value of t for a 99% confidence level. The critical value of t depends on the desired confidence level and the degrees of freedom, which is equal to n - 1 in this case (30 - 1 = 29). Looking up the critical value in a t-table or using statistical software, we find that the critical value of t for a 99% confidence level with 29 degrees of freedom is approximately 2.7564.

Therefore, the 99% confidence interval for the population mean would be calculated as follows: sample mean ± (2.7564) * (0.05 / √30). The final result would be a range of values within which we can be 99% confident that the true population mean lies.

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the minimum number of subjects needed for a research study regarding the proportion of respondents who reported a history of diabetes using the following criteria is 384.12, which can be rounded up to 385.

The minimum number of subjects needed for a research study regarding the proportion of respondents who reported a history of diabetes using the following criteria is as follows:

95% confidence, within 5 percentage points, and a previous estimate of 0.25.

The formula to calculate the sample size required for the study to determine the proportion is given by:

`n = Z²pq / E²`

Where n = sample size

Z = z-value (1.96 at 95% confidence interval)

E = margin of error

p = estimated proportion of the population

q = 1 - pp

q = estimated proportion of population without the condition (1 - 0.25 = 0.75)

Given,

Z = 1.96E = 0.05p = 0.25q = 0.75

Substituting these values in the above formula, we get;

`n = (1.96)²(0.25)(0.75) / (0.05)²``n = 384.16`

Therefore, the minimum number of subjects needed for a research study regarding the proportion of respondents who reported a history of diabetes using the following criteria is 384.12, which can be rounded up to 385.

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Answer: w=5

Step-by-step explanation:

Answer:

The answer is true.

The P-value is 0.0764 and the conclusion is that Since P > α , reject H0.

From the question above, test statistic of Z = −1.42.

The P-value for a left-tailed hypothesis test is the probability that the test statistic will be less than the observed value of the test statistic.

Since it is left-tailed, we find the area to the left of Z. Using the Z-table, we find the probability associated with the test statistic as follows:

P-value = P(Z < −1.42) = 0.0764 (rounded to four decimal places)

If the level of significance is α = 0.10.

Since P-value (0.0764) is greater than the level of significance α (0.10), we fail to reject H0.

Therefore, the correct answer is:

Since P > α, fail to reject H0.

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Answer:

3/8

Step-by-step explanation:

(3/4)/2=3/8

The equilibrium level of income (Y), interest rate (i), consumption (C), investments (I), and budget surplus can be calculated using the given equations and information. When G increases by 100, the new values for investments and budget surplus can be determined. The crowding out effect resulting from the increase in G can also be evaluated. Additionally, if the increase in G is accompanied by an increase in M/P by 100, the equilibrium level of Y and r, as well as the crowding out effect, can be determined and explained.

To calculate the equilibrium level of income (Y), we set the total income (Y) equal to total expenditures (C + I + G), solve the equation, and find the value of Y that satisfies it. Similarly, the equilibrium interest rate (i) can be determined by equating the demand for money (L) with the money supply (M/P). Consumption (C), investments (I), and budget surplus can be calculated using the respective equations provided.

When G increases by 100, we can recalculate the new values for investments and budget surplus by substituting the updated value of G into the equation. The crowding out effect can be assessed by comparing the initial and new values of investments.

If the increase in G is accompanied by an increase in M/P by 100, the equilibrium level of Y and r can be calculated by simultaneously solving the equations for total income (Y) and the interest rate (i). The crowding out effect in this case refers to the reduction in investments resulting from the increase in government spending (G) and its impact on the interest rate (r), which influences private sector investment decisions.

Overall, by analyzing the given equations and their relationships, we can determine the equilibrium levels of various economic variables, evaluate the effects of changes in government spending, and understand the concept of crowding out.

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Answer:

1: $53750

2: $15975

3: 40

4: 90

5: 51

6a: 20%

6b:204

Step-by-step explanation:

1: to calculate this mulitply 50000*1.075= 53750

2: same deal 15000*1.065=15975

3: We have a ratio of 3:2 and then 60:x because we multiplied the first ratio by 20 to get the 60 in the second we multiply the 2 by 20 as well and get x=40

4: This one is kind of tricky. we know that there are 4 dogs for every 3 cats. We also know that there are 210 animals. This means that 4x+3x=210 solve this and get x=30 you then multiply the ratio 4:3 by 30 and get 120:90

5: 1/5*255=51

5a: 1/5=.2=20%

5b: 255-51=204

Answer:

1. What is the total price of a $50,000 house plus 7.5% sales tax?

answer

total price =$50000+7.5% of 50000=$53750

2. What is the total price of a $15,000 car plus 6.5% sales tax?

total price =$15,000+6.5% of $15,000=$15975

3.The ratio of boys to girls in the assembly was 3 to 2. If 60 boys were in the assembly,

how many girls were there?

let ratio be 3x and 2x

we have

3x=60

x=60/3=20

no of girls =2x=2×20=40

4.The ratio of dogs to cats at the vet was 4 to 3. If 210 pets were in the vet, how many cats were there?

let ratio be 4x and 3x

we have

4x+3x=210

x=210/7=30

no of cats =3x=3×30=90

Answer:

D is the answer

Step-by-step explanation:

EDGE 2020

The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.

The population proportion who participated in voting is given as 63% of all registered voters.

This means that out of every 100 registered voters, 63 participated in voting.

In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.

Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .

Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.

It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.

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Answer:L

Step-by-step explanation:L is aligned with both J and N

Answer:

The ratio of girls to total students is 12:30, which can be simplified to 2:5.

Step-by-step explanation:

You can express the ratio in different ways by using the same numbers, for example, you could say that for every 2 girls, there are 5 total students, or that for every 5 total students, 2 of them are girls.

The total area under a normal distribution curve represents 100% of the data set. The normal distribution curve is a continuous probability distribution that is symmetric and bell-shaped.

It is often used to model real-world data. The area under the curve represents the probability of an event occurring within a certain range of values.

To understand this concept better, let's consider an example. Imagine we have a data set that follows a normal distribution, such as the heights of a group of people. The normal distribution curve is bell-shaped, with the mean height in the center and the majority of the data falling within a certain range.

The area under the curve represents the probability of observing a certain range of values. Since the total area under the curve accounts for all possible values in the data set, it corresponds to 100% of the data.

In this case, the correct answer is 100%. This means that the total area under a normal distribution curve represents the entirety of the data set.

To summarize, the total area under a normal distribution curve represents the entire data set, which is equivalent to 100% of the data set.

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The diver collected water samples at every 3 meters, starting from 5 meters below the water surface, up to a final depth of 35 meters.

We can find the number of samples collected by dividing the total depth range by the distance between each sample and then adding 1 to include the first sample.

The total depth range is:

35 m - 5 m = 30 m

The distance between each sample is 3 m, so the number of samples is:

(30 m) / (3 m/sample) + 1 = 10 + 1 = 11

Therefore, the diver collected a total of 11 water samples.

The absolute maximum and  minimum value of f(x) on the interval [-7, 16] is 2.358, -2.358 at x = 8 and x = -8

To find the absolute maximum and absolute minimum values of the function \(f(x) = x*e^{(-x^2/128)}\) on the interval [-7, 16], we need to look for the critical points and the endpoints of the interval.

First, let's find the critical points by taking the derivative of f(x) and setting it equal to zero:

\(f(x) = x*e^{(-x^2/128)}\)

\(f'(x) = e^{(-x^2/128)} - (x^2/64)*e^{(-x^2/128)}\)

Setting f'(x) equal to zero, we get:

\(e^{(-x^2/128)} - (x^2/64)e^{(-x^2/128)} = 0\)

\(e^{(-x^2/128)(1 - x^2/64) }= 0\)

So either\(e^{(-x^2/128)} = 0\) (which has no solutions), or\(1 - x^2/64 = 0\), which gives us x = ±8.

Next, we need to check the endpoints of the interval:

\(f(-7) = -7e^{(-49/128)} \approx -0.091\)

\(f(16) = 16e^{(-256/128)} \approx 0.090\)

Now we can compare the values of f(x) at the critical points and endpoints to find the absolute maximum and absolute minimum values:

f(-7) ≈ -0.091

\(f(8) = 8e^{(-64/128)} \approx 2.358\)

\(f(-8) = -8e^{(-64/128)} \approx -2.358\)

f(16) ≈ 0.090

So the absolute maximum value of f(x) on the interval [-7, 16] is approximately 2.358, and it occurs at x = 8.

The absolute minimum value of f(x) on the interval [-7, 16] is approximately -2.358, and it occurs at x = -8.

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Answer:

9 games.

Step-by-step explanation:

You need to find 75% of 12. 75% is equal to three fourths. 12 divided by 4 is 3, so one fourth of 12 is 3. 3 times 3 is 9, so three fourths (75%) of 12 is 9.

Answer:

190

Step-by-step explanation:

the weight is 191 lbs rounded is 190

Answer:

Step-by-step explanation:

The three points, the top and bottom of the building and the remote point form a right triangle where vertical and horizontal distances are the legs of this triangle.

Let the height be h.

Find its value using trigonometry:

Answer:

742.1 ft  (nearest tenth)

Step-by-step explanation:

Angle of Elevation

If a person stands at a point and looks up at an object, the angle between their horizontal line of sight and the object is called the angle of elevation.

To find the height of the building, model as a right triangle and solve using the tan trigonometric ratio.

Tan trigonometric ratio

\(\sf \tan(\theta)=\dfrac{O}{A}\)

where:

Given information:

Substitute the given values into the formula and solve for height:

\(\implies \sf \tan(8^{\circ})=\dfrac{height}{5280}\)

\(\implies \sf height=5280\tan(8^{\circ})\)

\(\implies \sf height=742.1\:ft\:\:(nearest\:tenth)\)

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Answer:

The value of K_eq for this system is approximately 1.19 × 10^(-9).

Step-by-step explanation:

To determine the value of the equilibrium constant (K_eq) for the given system, we need to use the concentrations of the reactants and products.

The balanced equation for the system is:

I2 ⇌ 2I

The expression for K_eq is defined as the ratio of the product concentrations raised to their stoichiometric coefficients divided by the reactant concentration raised to their stoichiometric coefficients. In this case, the expression is:

K_eq = [I]^2 / [I2]

Substituting the given concentrations:

K_eq = (3.2 × 10^(-2))^2 / (9.5 × 10^(-2))

K_eq = (3.2 × 10^(-2) × 3.2 × 10^(-2)) / (9.5 × 10^(-2))

K_eq = (10.24 × 10^(-4)) / (9.5 × 10^(-2))

K_eq = 1.078 × 10^(-5) / 9.5 × 10^(-2)

K_eq = 1.13368 × 10^(-7) / 9.5 × 10^(-2)

K_eq ≈ 1.19 × 10^(-9)

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The balance after 5 years is equal to $8,136.67.

In Mathematics and Financial accounting, compound interest can be calculated by using the following mathematical equation (formula):

\(A(t) = P(1 + \frac{r}{n})^{nt}\)

Where:

By substituting the given parameters into the formula for compound interest, we have the following;

\(A(5) = 6,500(1 + \frac{0.045}{12})^{12 \times 5}\\\\A(5) = 6,500(1.00375)^{60}\)

Future value, A(5) = $8,136.67

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Among the given expressions, the one that could be the possible leading term for the polynomial function graphed below is -18x¹⁴.

The leading term of a polynomial function is the term containing the highest power of the variable. Among the given expressions, the one that could be the possible leading term for the polynomial function graphed below is -18x¹⁴.

The degree of a polynomial function is the highest degree of any of its terms.

If a polynomial has only one term, then the degree of that term is the degree of the polynomial and is also called a monomial.

For example, consider the given function:Now, observe the degree of the function, which is 14, as the highest exponent of the function is 14.

Thus, the term containing the highest power of the variable x is -18x¹⁴.

Therefore, among the given expressions, the one that could be the possible leading term for the polynomial function graphed below is -18x¹⁴.

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In both the Vendor Compliance at Geoffrey Ryans (A) and Operational Execution at Arrows Electronics cases, there are common problems and challenges. These include issues related to vendor management.

One of the key problems faced by both companies is vendor compliance. This refers to the ability of vendors to meet the requirements and standards set by the company. Both cases highlight instances where vendors fail to meet compliance standards, leading to disruptions in the supply chain and operational inefficiencies. This problem affects the overall performance and profitability of the companies.

Another challenge faced by both companies is operational execution. This encompasses various aspects of operations, including inventory management, order fulfillment, and delivery. In both cases, there are instances where operational execution falls short, leading to delays, errors, and customer dissatisfaction. This challenge requires the companies to streamline their processes, improve communication and coordination, and enhance overall operational efficiency.

Overall, the problems and challenges in both cases revolve around effective vendor management, supply chain optimization, and operational excellence. Addressing these issues is crucial for both companies to improve their performance, meet customer demands, and maintain a competitive edge in the market.

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An ellipse is a closed curve on a plane, that resembles an elongated circle. The formula for an ellipse is: (x-h)^2/a^2 + (y-k)^2/b^2 = 1

In this formula, if a = b, the ellipse is a circle. If a > b, the ellipse is elongated along the x-axis, and if b > a, the ellipse is elongated along the y-axis.

where (h, k) represents the center of the ellipse, and "a" and "b" represent the horizontal and vertical distances from the center to the edge of the ellipse, respectively.

To graph an ellipse, you can plot the center of the ellipse at the point (h, k), and draw the horizontal axis with length 2a and vertical axis with length 2b. You can then sketch the curve that passes through all points (x,y) that satisfy the equation.

It's also possible to rewrite the equation of an ellipse in terms of its standard form:

(x-h)^2/b^2 + (y-k)^2/a^2 = 1

where "a" and "b" are the same as before, but this time "a" represents the semi-major axis (the longest distance from the center to the edge of the ellipse) and "b" represents the semi-minor axis (the shortest distance from the center to the edge of the ellipse). The axes are interchanged because the larger denominator is associated with the longer axis.

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Answer:

0.65

Step-by-step explanation:

To reduce a quantity by 35%, multiply it by 100% - 35% = 65% = 0.65

Think of it like this:  if 35% of a quantity is gone, 65% remains.

This applies to all sorts of situations.  One example is discount or sale prices.

A $250 item goes on sale at a 35% discount.  The sale price is 0.65 x 250 = 162.5  ($162.50).  If you DON'T pay 35% of something, you DO pay 65%.

f = 46 cm

What is Convex Mirror?

A convex mirror, diverging mirror, or fisheye mirror is a curved mirror in which the reflecting surface bulges toward the light source. Convex mirrors reflect light outwards, so they are not used to focus light.... The image is smaller than the object, but gets larger as the object gets closer to the mirror.

To find the radius of curvature of a convex mirror, we can use the mirror formula:

1/f = 1/v - 1/u

where f is the focal length of the mirror, v is the image distance, and u is the object distance.

In this case, the image distance (v) is given as 46 cm, and since the object is very far away, we can consider the object distance (u) to be close to infinity. Therefore, we can approximate 1/u as 0.

After plugging in the values, we have:

1/f = 1/46 - 0,

1/f = 1/46,

f = 46 cm.

The radius of curvature of the convex mirror is therefore 46 cm.

To draw a ray diagram showing this situation, I'll describe the steps:

Draw a horizontal line representing the major axis of the mirror.

Mark a point on the major axis slightly above the line that will represent the top of the mirror.

Draw a line from the object (car) above the mirror parallel to the principal axis and extend it until it intersects the principal axis after reflection. This ray represents the incident ray.

Draw a line from the object through the center of curvature located at a distance equal to the radius of curvature (46 cm) from the top of the mirror. This ray passes through the center of curvature and is reflected back along itself.

Draw a line from the subject towards the top of the mirror and extend it after the reflection. After reflection, this ray passes through the focus (which is half the radius of curvature from the vertex).

The intersection of the elongated reflected rays gives the location of the image. In this case, the image will be virtual, upright and located behind the mirror.

Be sure to label the incident ray, reflected rays, image, object distance (u), and image distance (v) on the diagram.

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Answer:

3/8

Step-by-step explanation:

slope = rise/run = 3/8

The pH of 0.050 aqueous ammonium chloride falls within 0 to 2. Option A

pH scale is a scale that is used to measure how acidic or basic an aqueous solution is. The scale ranges from 0 to 14 and from 0 to 6 shows the acidic property and 8 to 14 shows the basic property of a solution.

Ammonium Chloride is a systemic and urinary acidifying salt. Therefore when in aqueous form it will be acidic solution.

pH = - log\((H^+\))

pH = - log(0.05)

pH = 1.3

This is the pH range of the solution as shown.

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Recall the following information:

1) In a plane, two lines that are parallel exist on the same axis.

2) Hence, any line which is perpendicular to one of two parallel lines is also perpendicular to the other.

3) This concept is evident in the model of ladders, where each of the vertical lines is perpendicular to the parallel step lines(horizontal lines).

With this information, it can be said that if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.

T