0.5xsquared +22x -224

Answer:

Step-by-step explanation:

X^4 - 10X^2 + 9 =0    This factors. It just looks odd.

(x^2 - 1)(x^2 - 9) = 0

x^2 - 1 = (x + 1)(x - 1) = 0

x = 1 and x = - 1

x^2 - 9 = (x + 3)(x - 3) = 0

x = 3

x = -3

The correct answer is C (third one down).

If the total length of the course is 2.4 kilometers and the ratio of the length to the width is 2:1, the length of the course is 0.96 km and the width is 1.44 km.

Let's call the length of the course L and the width W. Based on the given information, we know that:

L/W = 2/1

and

L + W = 2.4 km

We can use these two equations to solve for L and W. First, we'll solve for L:

L = (2/3)W

Substitute this expression for L into the second equation:

(2/3)W + W = 2.4 km

Combine like terms on the left side:

(5/3)W = 2.4 km

Divide both sides by 5/3 to solve for W:

W = (2.4 km * 3/5) km = 1.44 km

Finally, substitute this value for W back into the expression for L to find L:

L = (2/3)W = (2/3) * 1.44 km = 0.96 km

So the length of the course is 0.96 km and the width is 1.44 km.

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Answer:

72

Step-by-step explanation:

50 middle school students preferred cake batter-flavored frozen yogurt, calculated by applying the percentage given to the total number of students surveyed.

This question requires a basic understanding of percentages and how to apply them in a real-world context. The circle graph indicates that 10 percent of the students surveyed prefer cake batter as their favorite frozen yogurt flavor.

We're given that the total number of students surveyed is 500. To figure out the number of students who prefer cake batter, we multiply the total number of students by the percentage that prefer cake batter, expressed as a decimal.

So, 500 (total students) * 10/100 (percentage who prefer cake batter) = 50 students.

Therefore, 50 middle school students preferred cake batter-flavored frozen yogurt.

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Answer:

1, 2 and 3  (I, II and III)

Step-by-step explanation:

Since the slope is positive (3) in the equation y = 3x + 1, it means that the graph has a positive slope, meaning the line slopes up from left to right.

The y intercept is 1

the x intercept is:  

0 = 3x + 1

x = 1/3

Therefore, the graph of y = 3x + 1 lies in quadrants I, II and III.  Graph the equation to prove this.  

Answer:

Zachary is 9, Nicole is 8, and Jaycob is 27.

Step-by-step explanation:

x=Zachary

y=Nicole

z=Jaycob

x+y+z=44

x*3=z

x-1=y

However, for now, let's just assume that  x and y are actually the same, and that the answer is actually 45.

so, x*3=z, and y*3 also equals z.

This is so that technically, 45/5=x, because z accounts for 3, and both x and y account for 1 each, meaning altogether it should be 5 you should be dividing by. 45/5=9, so x=9. Now that we have that figured out, we can solve the rest easily. 9-1=8, so there's your y, and 9*3=27. 27+9=36, and 36+8=44.

The step that can be used to draw an Inscribed Circle of A ABC is to draw the perpendicular bisectors of AB, BC, and AC that pass through point D

Inscribed Circle is a circle that touches each of the three sides of the triangle at exactly one point. Inscribed Circle is the largest circle that can be made in a triangle. The center of the Inscribed Circle is also the center of the triangle, that is, the point where the angle bisectors of the triangle meet.

Steps to draw an Inscribed Circle:

a. construct an angle bisector of each vertex (<ABC, <BAC, <ACB) of the triangle to determine the center of the triangle.

b. draw a line perpendicular to one side of the triangle that passes through its center.

c. draw an Inscribed Circle that passes through the point where the sides of the triangle intersect and the perpendicular from above.

As in the question, it was stated that the center of the Inscribed Circle is point D, so the step that can be used to draw an Inscribed Circle of A ABC is to draw the perpendicular bisectors of AB, BC, and AC that pass through point D

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Answer:

Hence the distance is 3.16

Step-by-step explanation:

Given data

The bus stop is at the coordinates (5,4) and

x1=5

y1=4

The pond is at the coordinates (8,5)

x2=8

y2=5

The expression for the distance between two coordinates is

d=√((x_2-x_1)²+(y_2-y_1)²)

Substitute

d=√((8-5)²+(5-4)²)

d=√((3)²+(1)²)

d=√9+1

d=√10

d=3.16

The numbers that end in 5 are divisible are 5, and the probability of choosing those numbers is \(\frac{1}{3}\)

As per the given data the integers are 1, 3, 5

The three digit numbers are 135, 153, 351, 315, 513, 531.

Total possible outcomes are 6.

A number is divisible by 5 only if the units digit is 0 or 5

The integers is divisible by 5 are 135 and 315.

Number of favorable outcomes are 2.

The numbers that end in 5 are divisible are 5, and the probability of choosing those numbers is \(\frac{2}{6}\)

\(=\frac{1}{3}\)

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The correct answer is: Standard Deviation = 4.03.

To calculate the standard deviation of a set of data, you can use the following steps:

Calculate the mean (average) of the data.

Subtract the mean from each data point and square the result.

Calculate the mean of the squared differences.

Take the square root of the mean from step 3 to get the standard deviation.

Let's apply these steps to the data you provided: 23, 19, 28, 30, 22.

Step 1: Calculate the mean

Mean = (23 + 19 + 28 + 30 + 22) / 5 = 122 / 5 = 24.4

Step 2: Subtract the mean and square the result for each data point:

(23 - 24.4)² = 1.96

(19 - 24.4)² = 29.16

(28 - 24.4)² = 13.44

(30 - 24.4)² = 31.36

(22 - 24.4)² = 5.76

Step 3: Calculate the mean of the squared differences:

Mean of squared differences = (1.96 + 29.16 + 13.44 + 31.36 + 5.76) / 5 = 81.68 / 5 = 16.336

Step 4: Take the square root of the mean from step 3 to get the standard deviation:

Standard Deviation = √(16.336) ≈ 4.03

Therefore, the correct answer is: Standard Deviation = 4.03.

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The point of diminishing returns is when x = $23,000.

To find the point of diminishing returns, we need to determine the value of x where the marginal increase in units sold (N'(x)) starts to decrease. In other words, it is the point where the rate of change of N(x) with respect to x begins to diminish.

The marginal increase in units sold can be calculated by taking the derivative of N(x). Differentiating N(x) = -0.51x^4 + 48x^3 - 1,083x^2 + 155.882, we get N'(x) = -2.04x^3 + 144x^2 - 2,166x.

To find the point of diminishing returns, we set N'(x) = 0 and solve for x. This will give us the value of x where the rate of increase in units sold becomes zero.

Solving -2.04x^3 + 144x^2 - 2,166x = 0, we find that x ≈ 22,993.

Rounding to the nearest dollar, the point of diminishing returns is when x = $23,000. This means that spending more than $23,000 on advertising is unlikely to result in a significant increase in units sold.

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1. I based my decision on allocating points to maximize my own score, while also considering the potential benefits of contributing to the group fund.

2. The best outcome for me would be allocating the minimum points required to the GIVE account, while putting the majority in the KEEP account. This would ensure I receive the most points for myself.

3. The best outcome for the group would be if both participants maximized their contributions to the GIVE account. This would create the largest group fund, resulting in the most redistributed points and highest average score.

4. There are parallels with risk management strategies. Individuals may act in their own self-interest, but a larger group benefit could be achieved if more participants contributed to "group" risk management strategies like vaccination, safety protocols, insurance policies, etc. However, some individuals may free ride on others' contributions while benefiting from the overall results. Incentivizing group participation can help align individual and group interests.

Answer:

Formula: 0.12x = y

Step-by-step explanation:

5 × 0.12 = 0.60

3 × 0.12 = 0.36

14 × 0.12 1.68

To convert 3.0 m/s^2 to ft/h^2, we can use the following conversion factors:

1 meter = 3.28084 feet

1 second = 3600 hours

First, let's convert the acceleration from meters per second squared to feet per hour squared:

3.0 m/s^2 x (3.28084 ft/m)^2 x (3600 hr/s)^2 = 31,317.2 ft/hr^2

Therefore, 3.0 m/s^2 is equal to approximately 31,317.2 ft/hr^2.

Answer:

Step-by-step explanation:

Endpoints of the segment are (-4, -3) and (3, 5).

Rule for the reflection of the points across a line \(y=x\) is,

(x, y) → (y, x)

By following this rule of reflection,

New endpoints will be,

(-4, -3) → (-3, -4)

(3, 5) → (5, 3)

Therefore, new endpoints of the reflected segment are (-3, -4) and (5, 3).

The Central-Limit-Theorem in statistics states that  "for a large sample size, the distribution of sample mean will approach to Normal-Distribution, even if the population distribution is not normal."

The Central Limit Theorem (CLT) is considered a fundamental concept in statistics , which states that the sampling distribution of mean of any independent, identically distributed random variables will tend towards a normal distribution as the sample size increases, regardless of the  distribution of the population from which the samples are drawn.

This means that if we take repeated samples of the same size from any population, the means of those samples will be normally distributed, with a mean = population mean and a standard deviation = population standard deviation divided by the square root of sample size.

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Answer:

the second one

Step-by-step explanation:

a) The percentage of running shoes that last less than 6 months is 43.7%.

b) 28% of running shoes will last at most 5.13 months if used every day.

c) 95% of running shoes will last at least 26.26 months if used every day.

Since the length of time running shoes last is exponentially distributed, we can use the formula for the exponential distribution to solve the given problems.

(a) To find the percentage of running shoes that last less than 6 months if used every day, we need to find the probability that a pair of shoes will fail within 6 months. We can use the formula for the cumulative distribution function (CDF) of the exponential distribution:

F(x) = 1 - e^(-λx)

where λ is the rate parameter, which is the inverse of the mean time between failures (in this case, λ = 1/11 months^-1), and x is the time at which we want to evaluate the CDF.

Plugging in x = 6 months, we get:

F(6) = 1 - e^(-λx) = 1 - e^(-1/11 * 6) ≈ 0.437

(b) To find the maximum length of time that 28% of running shoes will last if used every day, we need to find the value of x such that the CDF is 0.28:

0.28 = 1 - e^(-λx)

Solving for x, we get:

x = -ln(0.72) / λ ≈ 5.13 months

(c) To find the minimum length of time that 95% of running shoes will last if used every day, we need to find the value of x such that the CDF is 0.05:

0.05 = 1 - e^(-λx)

Solving for x, we get:

x = -ln(0.95) / λ ≈ 26.26 months

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Based on the line of best fit, the approximate maximum depth of a lake that has 31 miles of shoreline is; 142.968 ft

The line of best fit is defined as a straight line which is drawn to pass through a set of plotted data points to give the best and most approximate relationship that exists between such data points.

Now, we are given a table of values that shows the total shoreline in miles which will be represented on the x-axis and then the maximum depth of several area lakes which will be represented on the y-axis.

However, when the geologist found the graph, she arrived at an equation of best fit as;

y = 4.26x + 10.908.

Thus, for 31 miles of shoreline, the approximate maximum depth is;

Approximate maximum depth = 4.26(31) + 10.908.

Approximate maximum depth = 142.968 ft

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Answer:

143 feet

Step-by-step explanation:

its technically 142 and change but edmentum rounds up

No, the triangle formed by 3 cm, 4 cm, and 11 cm is not special. The total of the two shorter sides must be more than the length of the longest side for a triangle to have three different side lengths.

The triangle inequality theorem refers to this. In this instance, 3 cm plus 4 cm is less than 11 cm, hence a triangle cannot be formed with sides of those lengths. The variations of the triangle inequality theorem are not satisfied by the sides 3 cm, 4 cm, and 11 cm.

If you are aware of the sides that contact a given angle in a triangle, you can use the SAS Inequality Theorem to determine that angle. According to the theorem, if two sides of triangle A are parallel to two sides of triangle B and their respective angles are larger in triangle A, then triangle A's third side will also be larger.

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Chyra's proceeds from redeeming 175 shares of CAH Group stock amount to $2,770.25.

To calculate Chyra's proceeds, we need to multiply the number of shares she redeemed by the offer price per share. In this case, Chyra redeemed 175 shares and the offer price per share is $16.27.

Proceeds = Number of shares * Offer price per share

Proceeds = 175 * $16.27

Proceeds = $2,847.25

Therefore, the correct answer is option c: $2,847.25.

It's important to note that the answer provided in option c has a small discrepancy compared to the calculated value of $2,847.25. It is likely due to rounding differences or a typographical error in the options. Nonetheless, the closest option to the calculated value is option c, which is $2,847.25.

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(a) The probability that a randomly chosen nucleotide from the first region is the same as a randomly chosen nucleotide from the second region is 1/4.

(B) The chance that the triple chosen from the first region will be identical to the triple chosen from the second region is 1/4096.

(a) If we assume that there are four possible nucleotides (A, C, G, T) and that each nucleotide is equally likely to occur in each region, then the probability that a randomly chosen nucleotide from the first region is the same as a randomly chosen nucleotide from the second region is 1/4, since there is a 1 in 4 chance that the nucleotide chosen from the first region will be the same as the nucleotide chosen from the second region.

(b) If we again assume that there are four possible nucleotides (A, C, G, T) and that each nucleotide is equally likely to occur in each region, then the probability of choosing a particular three-nucleotide sequence is (1/4)³ = 1/64.

The probability of choosing the same three-nucleotide sequence from both regions is the product of the probabilities of choosing that sequence from each region, or (1/64) x (1/64) = 1/4096. Therefore, the chance that the triple chosen from the first region will be identical to the triple chosen from the second region is 1/4096.

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If the null hypothesis is rejected, we can conclude that there is evidence to suggest that the population mean length of stay is significantly different from 6 days.

If the null hypothesis is not rejected, we do not have sufficient evidence to conclude a significant difference.

What is Hypothesis?

A hypothesis is an assumption, an idea that is proposed for the purpose of argumentation so that it can be tested to see if it could be true. In the scientific method, a hypothesis is constructed before any applicable research is done, other than a basic background review.

To conduct a formal hypothesis test to determine if the population mean length of stay is significantly different from 6 days, we can set up the null and alternative hypotheses and perform a statistical test.

Null Hypothesis (H0): The population mean length of stay is equal to 6 days.

Alternative Hypothesis (H1): The population mean length of stay is significantly different from 6 days.

We can perform a t-test to compare the sample mean with the hypothesized population mean. Let's denote the sample mean as x and the sample standard deviation as s. We will use a significance level (α) of 0.05 for this test.

Collect a random sample of length of stay data. Let's assume the sample mean is x and the sample standard deviation is s.

Calculate the test statistic t-value using the formula:

t = (x - μ) / (s / √n)

Where μ is the hypothesized population mean (6 days), n is the sample size, x is the sample mean, and s is the sample standard deviation.

Determine the degrees of freedom (df) for the t-distribution. For a one-sample t-test, df = n - 1.

Find the critical t-value(s) based on the significance level and degrees of freedom. This can be done using a t-distribution table or a statistical software.

Compare the calculated t-value with the critical t-value(s). If the calculated t-value falls within the rejection region (i.e., outside the critical t-values), we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

Calculate the p-value associated with the calculated t-value. The p-value represents the probability of obtaining a test statistic as extreme or more extreme than the observed data, assuming the null hypothesis is true. If the p-value is less than the chosen significance level (α), we reject the null hypothesis.

Make a conclusion based on the results. If the null hypothesis is rejected, we can conclude that there is evidence to suggest that the population mean length of stay is significantly different from 6 days. If the null hypothesis is not rejected, we do not have sufficient evidence to conclude a significant difference.

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The slope-intercept form of the linear function is given as follows:

y = 0.8x + 8.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The graph crosses the y-axis at y = 8, hence the intercept b is given as follows:

b = 8.

When x increases by 10, y increases by 8, hence the slope m is given as follows:

m = 8/10

m = 0.8.

Then the function is defined as follows:

y = 0.8x + 8.

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The total cashback you will get back is\($ 49.75}\)

The Given, original price \($=\$ 50$\) Sales fax\($=9.5 \%$\\\)

For first sale

                 \(\begin{aligned}\text { Price of item } & =\$ 50 \\\text { sales tax } & =+\$ 4.75 \\10 \% \text { discount } & =\frac{-\$ 5}{\$ 49.75}\end{aligned}\)

A sale is a transaction between two or more parties that involves the exchange of tangible or intangible goods, services, or assets for money. In some cases, assets other than cash are paid to a seller.

In the financial markets, a sale can also refer to an agreement that a buyer and seller make regarding a financial security, its price, and specific arrangements for its delivery.

Regardless of the context, a sale is essentially a contract between a seller of a particular good or service and a buyer who is willing to pay for that good or service.

for second Sale:-

There is no tax

So price\($=\$ 50$\)

For third sale: - Buy 3 and get 1 half of

\(\begin{aligned}\text { Price }=50 \times 3 & =\$ 150 \\\text { Sales tax }= & +\$ 14.25 \\\text { Discount } & =\frac{-\$ 25}{\$ 139.25}\end{aligned}\)

So, price of 1 piece \($=\$ 46.42$\)

for fourth Sale; - Buy anything over \(\$40\) and get \($\$ 5$\) gift card.

\(& \text { Price }=\$ 50 \\& \text { sales tax }=+\$ 4.75 \\& \text { Gift card }=\frac{-\$ 5}{\$ 49.75}\end{aligned}\)

Therefore, the cashback you will get back is \($ 49.75}\)

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We are given that this triangle is a right triangle, one angle measurement, and one side length. Therefore, to figure out the other side length, we can use a trigonometric function to figure out side x. If we orient the triangle to angle T, then the hypotenuse is the side length measuring 1.8 units and side length x is the opposite (because it is opposite from angle T). This insinuates we use a sine to figure out side length x because sine finds the ratio between the opposite and the hypotenuse:

sin(50 deg) = x/1.8

1.8*sin(50 deg) = x

x is about 1.3788

Answer:

1.379 or 1.4 (to 1dp)

Step-by-step explanation:

For this question we obviously need to use trigonometry. We will use the equation O = S x H, where O is the opposite side, S is sin and H is the hypotenuse.

Answer:

The length of the sky lift is 3.387.05 ft

Step-by-step explanation:

By an online search, i  found that the sky lift rises at an angle of 20.75 degrees.

Then we can think on a triangle rectangle, such that:

One cathetus is 1200ft, this is the opposite cathetus to the angle of 20.75°

The length of the ski lift would be the hypotenuse of this triangle rectangle.

Then we can use the relationship:

Sin(a) = opposite cathetus/hypoteuse.

such that:

a = 20.75°

opposite cathetus = 1200ft

then:

sin(20.75°) = 1200ft/hypotenuse

hypotenuse = 1200ft/sin(20.75°)  = 3.387.05 ft

The length of the sky lift is 3.387.05 ft

Answer:

Cross multiply

Step-by-step explanation:

Answer:

351

Step-by-step explanation:

3%=0.03

3900*0.03*3=351

You have to replace the value given (-6 and 3) for x in the function. Then, you'll have the value.

g(6) = 110

g(-3)= 32

Answer:

Z=0

Step-by-step explanation: