y=2x-8
13x + 2y = 18
solving systems by the elimination method

Answer:

d)

Step-by-step explanation:

50-18=324

32÷50=0,64

350×0,64=224

Based on the results of the hypothesis test, with a calculated t-value of -3.85 and a critical t-value of ±3.182 at the 5% significance level, the golfer can conclude that there is a significant difference in his score with the new clubs compared to his past average.

To determine if there is a significant difference in the golfer's score with the new clubs compared to his past average, we can conduct a hypothesis test.

Let's set up the null and alternative hypotheses:

Null Hypothesis (H₀): The golfer's score with the new clubs is the same as his past average score. µ = 84.

Alternative Hypothesis (H₁): There is a difference in the golfer's score with the new clubs compared to his past average score. µ ≠ 84.

We will use a two-tailed t-test since we have a small sample size (4 games) and the population standard deviation is unknown.

Next, we calculate the test statistic, which is the t-value. The formula for the t-value is:

t = (x⁻ - µ) / (s / √n)

where x⁻ is the sample mean, µ is the population mean, s is the sample standard deviation, and n is the sample size.

Plugging in the given values:

x⁻ = 79

µ = 84

s = 2.6

n = 4

t = (79 - 84) / (2.6 / √4)

t = -5 / 1.3

t ≈ -3.85

To determine if the golfer can conclude there is a difference in his score with the new clubs, we compare the calculated t-value to the critical t-value at the 5% significance level with (n-1) degrees of freedom. Since we have a small sample size of 4, the degrees of freedom is 3.

Looking up the critical t-value in a t-table or using statistical software, at a 5% significance level with 3 degrees of freedom, the critical t-value is approximately ±3.182.

Since the calculated t-value (-3.85) is greater in magnitude than the critical t-value (3.182), we reject the null hypothesis.

Therefore, the golfer can conclude that there is a significant difference in his score with the new clubs compared to his past average at the 5% significance level.

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We have sufficient evidence to conclude that there is a significant difference in the golfer's score with the new clubs compared to his past average score at the 5% significance level.

The null hypothesis (H₀) and the alternative hypothesis (H₁):

H₀: The golfer's score with the new clubs is not significantly different from his past average score (μ = 84).

H₁: The golfer's score with the new clubs is significantly different from his past average score (μ ≠ 84).

Now let us choose the significance level (α):

The significance level is given as 5%, which corresponds to α = 0.05.

Since we have the sample mean (X), the population mean (μ), and the sample standard deviation (s), we can use the t-test statistic.

The test statistic formula for comparing the sample mean to a known population mean is given by:

t = (X - μ) / (s / √n)

Where, X = 79, μ = 84, s = 2.6, and n = 4.

Plugging in these values, we can calculate the test statistic:

t = (79 - 84) / (2.6 / √4)

t = -5 / (2.6 / 2)

t = -3.846

Since the alternative hypothesis is two-sided (μ ≠ 84), we need to find the critical t-values for a two-tailed test with α = 0.05 and degrees of freedom (df) = n - 1 = 3.

Using a t-table , the critical t-values for a two-tailed test with α = 0.05 and df = 3 are ±3.182.

Compare the test statistic with the critical value(s):

Since the absolute value of the test statistic (3.846) is greater than the critical value (3.182), we reject the null hypothesis.

Based on the hypothesis test, we have sufficient evidence to conclude that there is a significant difference in the golfer's score with the new clubs compared to his past average score at the 5% significance level.

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Answer:

Using a standard normal distribution table, we can find that the percentage of homes that have a monthly utility bill of more than $83 is approximately 13.6%.

Step-by-step explanation:

If the distribution of the monthly utility bill for gas or electric energy can be considered mound-shaped and symmetric, we can use the standard normal distribution table to find the percentage of homes that have a monthly utility bill of more than $83.

To use the standard normal distribution table, we need to standardize the variable by subtracting the mean and dividing by the standard deviation:

(83 - 91) / 8 = -0.875

This means that a monthly utility bill of $83 is 0.875 standard deviations below the mean.

Using a standard normal distribution table, we can find that the percentage of homes that have a monthly utility bill of more than $83 is approximately 13.6%.

Step 1:

Write the graph of the parent function y = f(x)

Step 2

Given the graph of y=f(x)as shown, sketch y = f(-x).

Step 3

The function y = f(x) will reflect about the y-axis to form the function y = f(-x).

Final answer

y-axis

Answer:

3, 8, 13, 18

Step-by-step explanation:

Answer:

1. 225 km

2. 95 km

3. 412.5 km

Step-by-step explanation:

For this one, it is saying that for every 2 cm, that is 50 km. So if you look at 9 cm, you can divide that by 2 cm to get 4.5 cm, this is what you can multiply by 50 km to get 225. Or you can look at it this way, for every 1 cm, the actual distance is 25 km. Then you can multiply each value by 25 to get your answer. Whichever one works for you.

A cardioid is a mathematical curve that is commonly studied in geometry and calculus. It is defined by the equation r = 1 + cos(θ), where r is the radial distance from the origin and θ is the polar angle. The cardioid has a distinctive heart-shaped form, and it is a smooth curve that can have tangent lines at certain points.

Horizontal Tangent Line:

A horizontal tangent line is a tangent line that is parallel to the x-axis. To find the points on the cardioid at which there is a horizontal tangent line, we need to find the points where the derivative of the curve is equal to zero in the x direction. The derivative of r = 1 + cos(θ) with respect to θ is -sin(θ), and the derivative of r with respect to x is cos(θ). Setting these two derivatives equal to zero, we have:

-sin(θ) = 0

cos(θ) = 0

The first equation has a solution when θ = n * π, where n is an integer. The second equation has solutions when θ = (2n + 1) * π/2, where n is an integer. When θ = n * π, the cardioid is at its maximum value, and when θ = (2n + 1) * π/2, the cardioid is at its minimum value. These points correspond to horizontal tangent lines on the cardioid.

Vertical Tangent Line:

A vertical tangent line is a tangent line that is perpendicular to the x-axis. To find the points on the cardioid at which there is a vertical tangent line, we need to find the points where the derivative of the curve is equal to zero in the y direction. The derivative of r with respect to y is sin(θ), and setting this derivative equal to zero, we have:

sin(θ) = 0

This equation has solutions when θ = (2n) * π/2, where n is an integer. These points correspond to vertical tangent lines on the cardioid.

Singular Point:

A singular point is a point on the curve at which the curve is not smooth and its tangent line is undefined. To find the singular points on the cardioid, we need to find the points where the second derivative of the curve is equal to zero. The second derivative of r = 1 + cos(θ) with respect to θ is -cos(θ), and setting this derivative equal to zero, we have:

-cos(θ) = 0

This equation has solutions when θ = n * π, where n is an integer. These points correspond to singular points on the cardioid.

In conclusion, the points on the cardioid at which there is a horizontal tangent line are given by θ = n * π and θ = (2n + 1) * π/2. The points at which there is a vertical tangent line are given by θ = (2n) * π/2. The singular points are given by θ = n * π. These points can be used to study the properties and behavior of the cardioid in more detail.

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Answer:

The cost for the snow skis for 4.5 hours is $ 77.5.

Step-by-step explanation:

Since renting snow skis costs $ 15 per hour plus a $ 10 usage fee, to create a step function that models the cost of snow skis in terms of the number of hours the snow skis were rented and determine the cost for the snow skis if you were skiing for 4.5 hours the following calculation must be performed:

10 + (15X) = Cost per hour

10 + 15 x 4.5 = X

10 + 67.5 = X

77.5 = X

Therefore, the cost for the snow skis for 4.5 hours is $ 77.5.

Answer:

we need the diagram

Step-by-step explanation:

Answer:

the answer is 36

Step-by-step explanation:

The measures of central tendency of the first psychology exam in a semester are the average score, which was an 85.

The correlation coefficient and the range of scores from 95 to 65 are not measures of central tendency either.

The standard deviation is a measure of variability, not central tendency, that the measures of central tendency of the first psychology exam are the average and median scores. This states that the mode, correlation coefficient, range of scores, and standard deviation are not measures of central tendency.

Hence, the measures of central tendency for the first psychology exam in a semester are the average score (85) and the median score (80).

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The measures of central tendency for the psychology exam scores include the average, median, and mode.

The measures of central tendency of the first psychology exam in a semester include the average score, median score, and mode (most frequently occurring score).

The average score on the exam was 85, which represents the mean of all the scores.

The median score on the exam was 80, which represents the middle value when all the scores are arranged in order.

The most frequently occurring score was 82, which represents the mode of the scores.

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Answer:

x=25

Step-by-step explanation:

25 degree angle is the same as x

Answer:

See attached.  Line for x<5.

Step-by-step explanation:

Solve the equation for x.  Remember that the "<" and ">" signs are reversed when dividing or multiplying by a negative value.

Answer:

B

Step-by-step explanation:

B*H= Area of a Triangle

Substitute:

\(6.5*8\)

Answer:

52 in Squared (D)

d. Expected life in years of the depreciable asset. The acceptable way to express the useful life of a depreciable asset is in terms of the expected life in years.

The useful life refers to the period of time over which the asset is expected to contribute to the revenue-generating activities of a business.

While options a, b, and c may be relevant factors for certain specific assets (such as units produced, hours of productivity, or miles driven), they do not encompass the overall concept of useful life. Useful life is a broader measure that takes into account the anticipated duration of productive use, regardless of specific output or activity metrics.

Expressing the useful life in years provides a common standard for comparison and allows for consistency in depreciation calculations and financial reporting. It is a practical and widely accepted approach to estimating the lifespan of a depreciable asset.

It is worth noting that the estimated useful life in years may vary depending on the nature of the asset and industry practices. It is typically determined based on factors such as technological advancements, physical wear and tear, economic obsolescence, and the intended purpose of the asset.

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Martha's claim that the 25% of the learners are girls, is correct.

In this question,

There are 900 boys and 300 girls at Eqinisweni secondary school.

Martha claims that 25% of the learners are girls.

We need to verify her claim by means of calculations.

Based on the given conditions, we formulate:

300 / (900 + 300)

We simplify above expression.

= 300 / 1200

= 1/4               ..................(Cross out the common factor)

Now multiply a number 25 to both the numerator and the denominator:

= (1 × 25)/(4 × 25)

= 25/200

Now we rewrite a fraction with denominator equals 100 to a percentage: 25%

This means, Martha's claim that the 25% of the learners are girls, is correct.

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(x,y) has the meaning of an application from R to R in which to every element x, the application assign's the y element. (x,y) has the meaning of plane's point coordinates. The first x is the horizontal coordinate (abscissa) and second is the vertical coordinate (ordinate). Both are coordinates.

The True statements are It is less likely that your friend is late for more than 12 minutes than he is late for less than 2 minutes and  The standard deviation of the amount of time that your friend is late is at about 3.46 minutes. The correct answer is option a and c.

A. It is less likely that your friend is late for more than 12 minutes than he is late for less than 2 minutes.

This statement is true. Since the amount of time your friend is late follows a continuous uniform distribution between 1 and 13 minutes, the probability of him being late for more than 12 minutes is equal to the probability of him being late for less than 2 minutes. The probability is evenly distributed across the entire range of the uniform distribution.

B. The mean amount of time that your friend is late is 7 minutes.

This statement is false. The mean (or expected value) of a continuous uniform distribution is calculated by taking the average of the lower and upper limits of the distribution. In this case, the mean would be (1 + 13) / 2 = 7, so the statement is correct. However, it's important to note that the given information only states that the amount of time your friend is late follows a continuous uniform distribution; it does not provide direct evidence or calculations for the mean.

C. The standard deviation of the amount of time that your friend is late is at about 3.46 minutes.

This statement is true. For a continuous uniform distribution, the standard deviation can be calculated using the formula: standard deviation = (b - a) / sqrt(12), where 'a' is the lower limit and 'b' is the upper limit. In this case, the standard deviation would be (13 - 1) / sqrt(12) ≈ 3.46 minutes.

D. None of the above.

This statement is incorrect because statements A and C are true.

The correct answer is option a and c.

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Answer:

incomplete question friend

Answer:

pretty sure its 4b!

Step-by-step explanation:

Answer:

4b

Step-by-step explanation:

ANSWER

EXPLANATION

In linear functions we often have the slope-intercept form of the equation:

Which can also be written in a different order, for example:

m is the slope of the line. The slope of the graph of a function is the rate of change.

b is the y-intercept. This

The initial amount invested is  $2.88.

The formula that can be used to determine the initial amount invested is:

P = FV ÷ (1 + r)^n

Where:

8500 ÷ (1 + 0.00274)^2920

= 8500 ÷ (1.00274^2920) = $2.88

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Answer:

d. 16,092

Step-by-step explanation:

Staples: 1452 x 9 = 13,068

Office Depot: 504 x 6 = 3,024

13,068 + 3,024 = 16,092

Answer:

Equivalent

Step-by-step explanation:

The equation is equivalent because they are just written the other way around although if you were to rewrite them both they would both be 9x+7

Expressions 9x+7 and 7+9x are equivalent and the equation has infinitely many solutions.

An expression is combination of variables, numbers and operators.

The expressions 9x+7 and 7+9x are equivalent because they have the same terms, although the order of the terms is different.

Let us check their equivalence.

9x+7 = 7+9x (commutative property of addition)

9x = 9x (subtract 7 from both sides and subtract 9x from both sides)

Both expressions simplify to the same thing, which means they are equivalent.

In terms of an equation, if we set these two expressions equal to each other, we get:

9x+7 = 7+9x

Simplifying this equation gives:

9x - 9x = 7 - 7

0 = 0

This means that the equation has an infinite number of solutions, since any value of x will satisfy.

Hence, expressions 9x+7 and 7+9x are equivalent and the equation has infinitely many solutions.

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Answer:

A 9 12 and 13

Step-by-step explanation:

Answer:

I don't know, peace out.

Step-by-step explanation:

The expression has a quotient of 0.00274 with a remainder of 2002.

We have,

The expression:

19/6927

Applying the long division.

6927 ) 19000  ( 0.00274  

           13854

             51460

             48489

                29710

                27708

                  2002

We can continue the division as required.

Thus,

The expression has a quotient of 0.00274 with a remainder of 2002.

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Answer:

$51.60

Step-by-step explanation:

Step-by-step explanation:

(2x -5)(x+5)

FOIL method: multiply first, outer, inner, last pairs:

\(2x^2+10x-5x-25\\\\2x^2+5x-25\\\)

Answer:

= 2x² + 5x - 25

Step-by-step explanation:

(2x - 5)(x+5)

=2x*x + 2x*5 - 5*x - 5*5

=2x² + 10x  - 5x - 25

= 2x² + 5x - 25

inequalities by graphing. is x≥0,y≥0

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The number of combinations which are possible according to the specifications is; 119,700.

It follows from the task content that the 5ember teams to be formed must contain 3 girls and 2 boys.

On this note, it follows that the combinations possible are as follows

20C(3) × 15C2 = 1140 × 105 = 119,700.

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