Find the slope of the line containing the pair of points f(1) = -6 and f(-7) = -6.

Answer:

Area: (3+√7) x (1+2√7) = 17+7√7 = 35.52

Perimeter: 2(3+√7) + 2(1+2√7) = 8+6√7 = 23.87

Haleema would have approximately £3947.46 in her account after 2 years and 11 months, considering the monthly compounding interest of 5%.

To calculate the amount of money in Haleema's account after 2 years and 11 months, we need to consider the monthly compounding interest on the account.

The interest rate is given as 5% per year, which means the monthly interest rate is (5%/12) = 0.4167%.

Let's calculate the final amount using the compound interest formula: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, P = £3700, r = 0.004167, n = 12 (monthly compounding), and t = 2.917 (2 years and 11 months).

Plugging these values into the formula, we get:

A = £3700(1 + 0.004167/12)^(12*2.917)

A ≈ £3947.46

The amount of money in Haleema's account after 2 years and 11 months would be approximately £3947.46.

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There is no change in its slope as initial and final slope is 1.

What is slope?

In arithmetic, the slope or gradient of a line may be a variety that describes each the direction and therefore the abruptness of the line.

Main body:

formula for slope with two points form is =

y -y₁ =( y₂-y₁ /x₂-x₁ )(x - x₁)

according to question ,

points are (0,0) and (3,3)

y - 0 = (3-0/3-0)(x -0)

y = 3/3 *x

y = x

hence slope of line is 1.

Now points are (0,0) and (-3,-3).

y - 0 = (-3-0/-3-0)(x -0)

y =- 3/-3 *x

y = x

hence slope of line is 1.

So there is no change in its slope.

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The based on this example, we can see that the converse of the Pythagorean theorem does not hold for this particular triangle.

To prove the converse of the Pythagorean theorem, we need to show that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

In the given triangle AABC, with vertices at A(1,6), B(1,1), and C(5,1), we can calculate the lengths of the sides using the distance formula or Pythagorean theorem.

AB = sqrt((1-1)^2 + (6-1)^2) = sqrt(25) = 5

BC = sqrt((5-1)^2 + (1-1)^2) = sqrt(16) = 4

AC = sqrt((5-1)^2 + (6-1)^2) = sqrt(40) = 2sqrt(10)

Now, let's check if AB^2 + BC^2 = AC^2:

AB^2 + BC^2 = 5^2 + 4^2 = 25 + 16 = 41

AC^2 = (2sqrt(10))^2 = 4(10) = 40

Since AB^2 + BC^2 is not equal to AC^2, the given triangle AABC does not satisfy the condition for the converse of the Pythagorean theorem.

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An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The value of the equation s - 5(r) at r = -7 and s = 7 is 42.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x = 3 is an equation.

we have,

s - 5(r)  ______(1)

r = -7 and s = 7

Substituting r = -7 and s = 7 in (1) we get,

= s - 5(r)

= 7 - 5 x (-7)

= 7 + 35

= 42

Thus,

The value of the equation s - 5(r) at r = -7 and s = 7 is 42.

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Answer: the answer is not in the multiple choice.

area = 60 in^2

Step-by-step explanation:

The total income and expenditure of Agri-small business limited in September is R 299596 and expenditure is R 193236.

We have to find the total income and expenditure in September.

The equation for insurance is mathematically given as :

Insurance = 42% of the balance

Insurance=0.42*0.64A

Insurance=0.2688A.

Total expenditure after all other expenditures = 0.64A-0.2688A

Total expenditures after all other expenditures = 0.3712A.

Total expenditures after all other expenditures is as 111210 (106360 +4850)

Equating both the equation and value:

111210 = 3712 A

A = 299596

Thus The total income is 299596.

Therefore the calculation of expense is given as:

Expense=0.25A+0.11A+0.2688A+4850

Expense=0.6288A+4850

=0.6288*299596+4850

=193236

The expense is 193236.

Hence, the total income and expenditure in September are "Income is R 299596 and expenditure is R 193236.

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Answer:

b

Step-by-step explanation:

Answer:

A≈78.54

Step-by-step explanation:

Answer:

78.5

Step-by-step explanation:

because i said so

The estimated regression equation developed in part (a) was found to be an effective predictor of overall customer satisfaction, as indicated by the significant F and t test results.

The estimated regression equation developed in part (a) to predict overall customer satisfaction is given by:

Overall Satisfaction = 0.3151*Trade Price + 0.3132*Speed of Execution + 1.5026

The coefficient of determination (R2) is a measure of how well the equation fits the data and is calculated as the proportion of the variation in overall satisfaction that is explained by the model. In this case, the R2 = 0.39, which means that 39% of the variation in overall satisfaction can be explained by the trade price and speed of execution variables.

To determine the overall significance of the relationship, the F test was used. The F statistic was calculated to be 17.874, which was significant at the 0.05 level (p-value = 0.000), indicating that the model was an effective predictor of overall customer satisfaction.

The t tests were then used to determine the significance of each independent variable. The t statistic for Trade Price was 2.639 (p-value = 0.009), indicating that the variable was significant at the 0.05 level, while the t statistic for Speed of Execution was 2.565 (p-value = 0.012), indicating that the

The estimated regression equation developed in part (a) was found to be an effective predictor of overall customer satisfaction, as indicated by the significant F and t test results.

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Answer:

y = 5^(x+1)

Step-by-step explanation:

y = 5^(x+1)

x = 1 for the initial step

Answer:

477.3

Step-by-step explanation:

3.14x 4² x 9.5

477.28

to the nearest tenth= 477.3

A director of a company, like Luke, is normally immune from liability under the professional conduct rule for decisions made in good faith and the corporation's best interests.

This implies that even if Luke makes a bad business decision, he won't be held accountable for the corporation's losses or damages as long as he operated honestly and without breaking any obligations committed to the company.

Nevertheless, if it can be demonstrated that Luke acted dishonestly, selfishly, or in violation of his obligations to the company, he may be held accountable for any damages or losses the company incurs as a result of his conduct.

Furthermore, Luke might be held accountable for any personal gain he makes as a result of his work as a director.

In conclusion, the rule of business judgment protects directors like Luke from accountability for bad decisions as long as they are made in good faith & without breaking any obligations to the corporation. However, he could be held accountable if he behaves dishonestly, has a self-serving motivation, or reaps advantages from his directorship.

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The quartile deviation is 13.355 and the quartile coefficient of dispersion is 0.890 for the given frequency distribution.

We have,

To calculate the quartile deviation and coefficient, we need to first find the first and third quartiles.

Step 1: Calculate the cumulative frequency distribution:

Marks above   No. of students'  Cumulative frequency

0                           150              150

10                              142                      292

20                           130              422

30                          120                      542

40                            72                       614

50                           20                       634

60                            12                       646

70                            4                       650

Step 2: Find the median (second quartile) by interpolating between the values with cumulative frequencies just above and below n/2, where n is the total number of observations:

n = 650

n/2 = 325

The cumulative frequency just above 325 is 422, which corresponds to a mark above of 20.

The cumulative frequency just below 325 is 292, which corresponds to a mark above of 10. So the median mark above is:

Median = 10 + ((325 - 292) / 142) * 10 = 13.10

Step 3: Find the first quartile (Q1) by interpolating between the values with cumulative frequencies just above and below n/4:

n/4 = 162.5

The cumulative frequency just above 162.5 is 292, which corresponds to a mark above of 10. The cumulative frequency just below 162.5 is 150, which corresponds to a mark above of 0.

So the first quartile mark above is:

Q1 = 0 + ((162.5 - 150) / 150) * 10 = 1.67

Step 4: Find the third quartile (Q3) by interpolating between the values with cumulative frequencies just above and below 3n/4:

3n/4 = 487.5

The cumulative frequency just above 487.5 is 542, which corresponds to a mark above of 30.

The cumulative frequency just below 487.5 is 422, which corresponds to a mark above of 20.

So the third quartile mark above is:

Q3 = 20 + ((487.5 - 422) / 120) * 10 = 29.38

Step 5: Calculate the quartile deviation:

Quartile deviation = (Q3 - Q1) / 2

Quartile deviation = (29.38 - 1.67) / 2 = 13.355

Step 6: Calculate the quartile coefficient of dispersion:

Quartile coefficient of dispersion = (Q3 - Q1) / (Q3 + Q1)

Quartile coefficient of dispersion = (29.38 - 1.67) / (29.38 + 1.67) = 0.890

Therefore,

The quartile deviation is 13.355 and the quartile coefficient of dispersion is 0.890 for the given frequency distribution.

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Answer:

88

Step-by-step explanation:

Answer:

88

Step-by-step explanation:

For the first question, how do you know that

Then, then angles

satisfy the definition of alternate interior angles

The same goes for angles

Therefore, for the first question, the correct answer is Alternate interior angles are congruent.

For the second question, you know that

And this satisfies the triangle congruence theorem ASA (Angle-side-Angle).

Therefore, for the second question, the correct answer is ASA Triangle Congruence Theorem.

For the third question, since you already know that the triangles ABD and CDB are congruent, then the respective segments that make up the triangles will also be congruent.

Therefore, for the third question, the correct answer is Corresponding parts of congruent triangles are congruent.

Answer:

Explained below.

Step-by-step explanation:

A statistical hypothesis test is being performed to determine whether there was a significant difference in the type of primary residence (home vs. student housing) for abused versus non abused college aged women.

The hypothesis can be defined as:

H₀: There is no difference in the type of primary residence or abused versus non abused college aged women.

Hₐ: There is a significant difference in the type of primary residence or abused versus non abused college aged women.

The significance level of the test is:

α = 0.05

The computed p-value is:

p-value = 0.35

p-value = 0.35 > α = 0.05

The null hypothesis will not be rejected.

The p-value is inversely related to the sample size of the test.

That is, larger the sample size smaller is the p-value and smaller the sample size larger is the p-value.

A p-value of 0.35 is very large and unusual. This can happen because of the inadequate sample size selected.

As the p-value indicates an unusual result, it can be said that an error has been made while concluding that the null hypothesis is true, when in fact it is not.

This type of error is known as the type II error.

The correct decision should be:

There is a statistically significant difference in the type of primary residence for abused vs. non-abused college aged women.

Answer:

The total cost per month is $190.76 to the nearest cent.

Step-by-step explanation:

From the given table, the monthly service plan costing $52.00 is:

The base calling plan includes two lines.

Therefore, for 4 lines, we will need to pay for 2 additional lines per month:

⇒ $21.99 × 2 = $43.98 per month

If 3,487 minutes are used per month, then the overage of minutes is:

⇒ 3487 - 2000 = 1487 minutes per month

As the overage rate is $0.06 per minute, then the cost of the additional minutes is:

⇒ 1487 × $0.06 = $89.22 per month

Therefore, the total cost per month before tax is:

⇒ $52.00 + $43.98 + $89.22 = $185.20

To apply the federal tax of 3%, multiply the total cost by 1.03:

⇒ $185.20 × 1.03 = $190.756 = $190.76 (nearest cent)

Therefore, the total cost per month is $190.76 to the nearest cent.

The formula of the function, where x is entered in radians is   y = -3sin(πx/5) -6

The key components: amplitude, period, phase shift, and vertical shift.

Amplitude is the distance between the midline and max/min points. Midline at (0, -6), so distance to min point (2.5, -9) is 3. Amplitude: 3.

Vertical shift: Displacement along y-axis. Midline at y = -6, vertical shift is -6. Period: distance between max/min points. Graph intersects midline at (0, -6) and minimum point at (2.5, -9).  Period is 5 (2 * 2.5). Freq: Reciprocal of period, 1/5.

Phase shift: Horizontal shift of graph. Graph intersects midline at x=0, no phase shift.

Hence:

The general form of the sinusoidal function is y = A sin (B(x-C)) + D

So, Substituting the known values into the general formula:

y = 3 x  sin((1/5)x - 0) - 6

Hence: Simplifying it will be:

y = 3 x sin(πx/5) - 6

Then, the formula of the function, where x is entered in radians, is: y = -3sin(πx/5) - 6

Based on the image attached, the first given point is one that informs one that the function is a sine (not a cosine) function, and that it is one that has its offset as -6.

Also, the second given point is one that informs you of the first peak is at x=2.5, hence the argument of the sine function is π/2 if x=2.5: (πx/5).

Based on the fact that the peak is 3 units smaller than the midline, the amplitude is said to be -3.

Therefore the  formula for the function is  seen as:  y = -3·sin(πx/5) -6

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Answer:

Answer is Option 2

Step-by-step explanation:

Triangles equal to 180 degrees in total. So it is 55+54+x+74=180

The simplified version that I just wrote is Option 2

A total of 7 Cyclists traveled more than 45 miles. 4 cyclists traveled 50 miles or more, and 3 cyclists traveled more than 54 1/4 miles.

A line plot is drawn with the cyclists' names plotted on the x-axis and their corresponding distances covered plotted on the y-axis.

The dots are then joined to form a line, revealing the relationship between the cyclist's names and their corresponding distance traveled. The cyclist names and their corresponding distances are given in the table below.

Name Distance (in miles) Gina 40 1/2 Rey 50 Faye 35 3/4 Mark 60 John 45 1/2 James 40 1/2 Albert 40 1/4 William 54 1/4 Nathan 40 Kate 40 1/4 Mary 60 Risa 40 Abi 35 3/4 Joan 50 1/2 1. The number of cyclists is 14. 2. The longest distance covered by a cyclist is 60 miles.

Mary and Mark both covered this distance.3. A total of 7 cyclists traveled less than 50 miles. 4. The most common distance traveled by cyclists is 40 1/2 miles. Gina, James, and Albert covered this distance. 5. 2 more cyclists traveled 45 miles than 55 1/4 miles. Only William traveled 55 1/4 miles, while John and James both traveled 45 1/2 miles.6.

A total of 7 cyclists traveled more than 45 miles. 4 cyclists traveled 50 miles or more, and 3 cyclists traveled more than 54 1/4 miles.

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Answer:

2

Step-by-step explanation:

2 to the second power is 4 and 3 to the second power is 9 if you add 4 and 9 you will get 14. hope i could help:)!

Answer:

C 136

Step-by-step explanation:

2×68= 136

...........

....

The objective function of a linear programming problem is a linear function.

A valid objective function is (b) Min 4x+3y+(2/3)z

The form of the objective function of a linear programming problem is:

\(\mathbf{ax + by + cz +.....}\)

The above function means that:

The above highlights mean that:

Hence, the valid objective function is (b) Min 4x+3y+(2/3)z

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Using proportions, it is found that due to the smaller division of the exchange rate by the cost, the souvenir would be less expensive in Egypt.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The souvenir would be less expensive in the country in which the division of the exchange rate by the cost is smaller.

In Britain, the cost is of 17, with an exchange rate of 0.83, hence the cost in US dollars is:

c = 17/0.83 = $20.48.

In Egypt, the cost is of 288, with an exchange rate of 18, hence the cost in US dollars is:

c = 288/18 = $16.

16 < 20.48, hence the souvenir would be less expensive in Egypt.

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Answer:

D. The zeros are the hot dog prices that give $0.00 profit (no profit).

Step-by-step explanation:

Given the function  y=-2(x-3)² + 4

The zeros of the function are the points at which the graph of the function crosses the x axis if plotted. y is the daily profit (in hundreds of dollars) and x is the price of the hot dog. To find the zeros, we substitute x = 0 and solve.

Therefore:  y=2(x-3)² + 4

0 = 2(x-3)² + 4

-2(x² - 6x + 9) + 4 = 0

-2x² + 12x - 18 + 4 = 0

2x² - 12x + 18 - 4 = 0

2x² - 12x + 14 = 0

2(x² - 6x + 7) = 0

x² - 6x + 7 = 0

Solving the quadratic equation gives:

x = 3 + √2 and x = 3 - √2

This means that the graph crosses x at 3 + √2 and 3 - √2.

The zeros of the function are 3 + √2 and 3 - √2. The zeros of the function is the point where y = 0, that is the point that the hot dog prices that give $0.00 profit (no profit).

The surface area of the vase is 168.4 square inches.

What is a cylinder?

A cylinder is a three-dimensional geometric shape that has two congruent circular bases connected by a curved surface.

The surface area of the cylindrical vase can be found using the formula SA = B + Ph, where B is the area of the base, P is the perimeter of the base, and h is the height of the vase. Since the vase has a circular base, the area of the base can be found using the formula for the area of a circle: B = πr², where r is the radius of the base.

The diameter of the vase is 4.3 inches, so the radius is half of that, or 2.15 inches. The area of the base is therefore:

B = πr² = 3.14 * (2.15)² ≈ 14.46 square inches.

The perimeter of the base is the circumference of the circle, which can be found using the formula C = 2πr:

P = 2πr = 2 * 3.14 * 2.15 ≈ 13.53 inches.

Now we can use the formula SA = B + Ph to find the surface area of the vase:

SA = B + Ph = 14.46 + 13.53 * 11 ≈ 168.39 square inches.

Rounding to the nearest tenth of a square inch, the surface area of the vase is approximately 168.4 square inches.

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Option (B) is correct. Thus, percentage of students with scores between 70 and 130 is 95% .

The term "standard deviation" refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed. The average degree of variability in your data set is represented by the standard deviation.

It reveals the average deviation of each score from the mean. Think about the following data: 2, 1, 3, 2, 4. The average and the total square of the observations' departures from the mean will be 2.4 and 5.2, respectively. This means that √(5.2/5) = 1.01 will be the standard deviation.

Here:

μ = 100, σ = 15

Thus we have

30 μ - kσ = 70

= 100 – k(15) = 70

= k= 30/15 = 2

Also we have, μ + Ασ: = 130

100+ k(15) = 130

k = 30/15 = 2

Now, the percentage of students with scores between 70 and 130 is same as the percentage of students between μ - 2σ, μ+ 2σ  and by empirical rule the area between μ (+-) 2σ  is 95%. Thus, percentage of students with scores between 70 and 130 is 95%

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3. The factored polynomial is p(x) = (x - 1)(x - 5)

4. The factored polynomial is p(x) = (x + 3)²

A polynomial is a mathematical expression in which the power of the unknown is greater than or equal to 2.

3. To factorize the polynomial using the graph, we see that the polynomial cuts the x - axis at x = 1 and x = 5.

This implies that its factors are (x - 1) and (x - 5)

So, the factored polynomial is p(x) = (x - 1)(x - 5)

4. To factorize the polynomial using the graph, we see that the polynomial touches the x - axis at only one point x = -3. So,it has repeated roots

This implies that its factors are (x - (-3)) = (x + 3) twice

So, the factored polynomial is p(x) = (x + 3)²

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