In the figure below, triangle O P N is a reflected image of triangle M P N. Anne states that reflections preserve side lengths, so stack P N with bar on top approximately equal to stack P N with bar on top comma space stack P M with bar on top approximately equal to stack P O with bar on top comma and stack M N with bar on top approximately equal to stack O N with bar on top comma therefore the triangles are congruent. Tim states that reflections preserve angle measures, so angle M P N approximately equal to angle O N P comma space angle M N P approximately equal to angle O P N comma and angle P M N approximately equal to angle P O N comma therefore the triangles are congruent.

The angles of a triangle with side lengths 5 , 12 and 13 are 90°, 22.63°, 67.38°.

In trigonometry, the law of cosines, also known as the law of cosines or cosine formula, basically relates the length of a triangle to one cosine of its angle. It states that if we know the lengths of two sides of a triangle and the angle between them, we can determine the length of the third side. c² = a²+ b² – 2ab cosγ

where a, b, c are the sides of the triangle and γ is the angle between a and b, see image above.

To find the length of a side of a triangle, take △ABC according to the cosine formula, which can be written as follows.

We have , a = 5 , b = 12 , c= 13

cos α =( 12² + 13² - 5² )/2×12×13= 288/312

=> α = cos⁻¹(0.923 ) = 22.63°

cos β = (5² + 13² - 12² )/2×13×5 = 50/130

=> β = cos⁻¹(5/13) = 67.38°

cos γ = (12² + 5² - 13² )/2×12×5= 0

=> γ = cos⁻¹(0) = 90°

Hence, the required angles are 90°, 22.63°, 67.38°.

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The distance between the points G(-9, 6) and Q(-2, 1) in the coordinate plane is approximately 8.6.

To calculate the distance between two points in a coordinate plane, we can use the distance formula. The distance formula is derived from the Pythagorean theorem and can be stated as follows:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, the given points are G(-9, 6) and Q(-2, 1).
Step 1: Identify the coordinates of the two points.
G has coordinates (-9, 6) and Q has coordinates (-2, 1).
Step 2: Substitute the coordinates into the distance formula.
Using the distance formula, we can plug in the values as follows:
Distance = sqrt((-2 - (-9))^2 + (1 - 6)^2)
Simplifying the formula:
Distance = sqrt((7)^2 + (-5)^2)
Distance = sqrt(49 + 25)
Distance = sqrt(74)
Step 3: Calculate the square root.
Taking the square root of 74, we get:
Distance ≈ 8.6
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See attachment for math work and answer.

a) Straight Line: The Excel function used for the straight-line method is "SLN." b) Double Declining Balance: The Excel function used for the double declining balance method is "DDB." c) Sum of Years Digits: The Excel function used for the sum of years digits method is a combination of "SYD" and other mathematical functions. d) Variable Declining Balance: The Excel function used for the variable declining balance method may vary depending on the specific calculation required.

a) Straight Line: The straight-line method calculates depreciation by dividing the asset's cost by its useful life. In Excel, the "SLN" function is used, which takes three arguments: cost, salvage value, and useful life. The formula is "=SLN(cost, salvage, life)."

b) Double Declining Balance: The double declining balance method applies a constant depreciation rate to the asset's book value. In Excel, the "DDB" function is used, which takes five arguments: cost, salvage value, useful life, period, and factor. The formula is "=DDB(cost, salvage, life, period, [factor])."

c) Sum of Years Digits: The sum of years digits method calculates depreciation by assigning weights to each year based on the asset's useful life. In Excel, the "SYD" function is used, which takes four arguments: cost, salvage value, useful life, and period. The formula is "=SYD(cost, salvage, life, period)."

d) Variable Declining Balance: The variable declining balance method calculates depreciation using a varying depreciation rate based on the asset's expected usage or production levels. The Excel function to be used may depend on the specific calculation or formula required for the variable declining balance method.

Conclusion:

Excel provides specific functions to facilitate the calculations for different depreciation methods. The "SLN" function is used for straight-line depreciation, "DDB" function for double declining balance, and "SYD" function for sum of years digits method. These functions simplify the calculations by taking relevant arguments and producing accurate results. However, for the variable declining balance method, the specific Excel function may vary depending on the formula or calculation required. By utilizing the appropriate Excel functions, depreciation calculations can be performed efficiently and accurately within the chosen depreciation method.

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The expression that best represents the area of the shaded region is B. x² - 7x + 33.

The correct answer is x² - 7x + 33.

Ms. King needs to frame the fish puzzle and plans on using the measurements shown

The area of the shaded region is the difference between the area of the entire rectangle and the area of the fish puzzle. The area of the entire rectangle is 15x + 20, and the area of the fish puzzle is 7x + 10.

Therefore, the area of the shaded region is:

(x + 4)(x + 10) - (3x - 1)(7)

= x² +14x + 40 - 21x - 7

= x² - 7x + 33

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Answer:

the answer is 3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

3 ÷ 3 = 1

6 ÷ 3 = 2

9 ÷ 3 = 3

12 ÷ 3 = 4

Hope it helps and have a great day! =D

~sunshine~

Answer:

34 jerseys

8 Social Media ads

$2,400 Spent on Radio ads

$360 per TV ad

Step-by-step explanation:

2856/84 = 34 jerseys

2000/250 = 8

200*12 = 2400

1800/5 = 360

If you know how many you have and how much they cost multiply

If you know how much was spent and how much they cost divide

If you know how much was spent and how many you have divide

The only two options with equations that are true for x = –2 and x = 2 are;

Option A: x² - 4 = 0

Option D: 4x² = 16

The domain of a function is the set of all input values  for which the function is possible.

Now, we are given the domain values as  x = –2 and x = 2.

a) x² - 4

f(-2) = (-2)² - 4

= 0

f(2) = (2)² - 2

= 0

b) x² = -4

f(-2) = (-2)²

= 4

f(2) = (2)²

= 4

c) 3x² + 12

f(-2) = 3(-2)²  + 12

= 24

f(-2) = 3(2)²  + 12

= 24

d) 4x²

f(-2) = 4(-2)²

= 16

f(2) = 4(2)²

= 16

e) 2(x - 2)²

f(-2) = 2(-2 - 2)²

= 32

f(2) = 2(2 - 2)²

= 0

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Answer:

15

Step-by-step explanation:

10.5 x (20/14)=14.99999999999...=15

The ratio of used books to all books is 7 : 13 and  the ratio of new books to used books is 6 : 7

If there are 13 books on a shelf. 6 of these books are new.

(a) The ratio of used books to all books

Number of all books = 13

Number of used books = total no. of books - no. of new books

                                       =  13 - 6

                                       = 7

So, ratio of used books to all books

= no. of all books : no. of total books

= 7 : 13

Thus, the ratio of used books to all books = 7 : 13

(b) The ratio of new books to used books

Number of new books = 6

Number of used books = 7

So, the ratio of new books to used books

= no. of new books : no. of used books

= 6 : 7

Thus, the ratio of new books to used books = 6 : 7

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Answer:

57c - 88d

Step-by-step explanation:

Answer:

-3 and 23,20,17

Step-by-step explanation:

35-3=32,32-3=29

The standard error of the sample mean is approximately 8.9 pounds.

What is standard error of the sample mean?

Simple division of the standard deviation by the square root of the sample size yields the SEM. By evaluating the sample-to-sample variability of the sample means, standard error determines the accuracy of a sample mean.

To find the standard error of the sample mean, we need to first find the sample mean weight of the students. To do this, we add up the weights of all the students and divide by the number of students:

(128 + 193 + 166 + 147 + 202 + 183 + 181 + 158) / 8 = 171.5

Next, we need to find the variance of the sample. The variance is a measure of the spread of the data around the mean, and is calculated as follows:

       \(variance = ((weight - mean)^2) / (n-1)\)

where weight is the weight of each student, mean is the sample mean weight, and n is the number of students.

Plugging in the values from our data, we get:

variance = (128 - 171.5)^2 + (193 - 171.5)^2 + (166 - 171.5)^2 + (147 - 171.5)^2 + (202 - 171.5)^2 + (183 - 171.5)^2 + (181 - 171.5)^2 + (158 - 171.5)^2 / 7

= 1096.5

Finally, we can find the standard error of the sample mean by taking the square root of the variance and dividing by the square root of the number of students:

                \(standard\ error = \sqrt{(variance / n)} \\\\= \sqrt{1096.5 / 8 )\\\\=8.9\)

So, The standard error of the sample mean is approximately 8.9 pounds.

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Answer:

545

Step-by-step explanation:

Answer:

96sq ft. u just multiple the length by the height then square it

Answer:

9.1 units

Step-by-step explanation:

formula of a distance of two points:

\(\sqrt{(x1-x2)^2+(y1-y2)^2}\) where x and y indicate the coordinates of the points

\(\sqrt{(4+5)^2 + (-1)^2} = \sqrt{81 + 1} = \sqrt{82} = 9.1 units\)

The calculated chi-squared value is [calculated value]. Since the calculated chi-squared value is [greater than/less than/equal to] the tabled chi-squared value of 9.488, we can [reject/fail to reject] the null hypothesis.

To determine whether the number of customers varies by day of the week, we can conduct a chi-squared test. The null hypothesis states that the number of customers coming into the shop is equal for each weekday, while the alternate hypothesis suggests that the number of customers differs by day. To perform the test, we need to calculate the chi-squared value.

First, we calculate the expected frequency for each day by taking the average of the total number of customers over the entire week. For this given week, the expected frequency would be the sum of all the customers (50 + 60 + 40 + 47 + 53) divided by 5, resulting in 50 customers per day. Next, we calculate the chi-squared value by summing up the squared differences between the observed and expected frequencies, divided by the expected frequency for each day. Once we have the calculated chi-squared value, we compare it with the tabled chi-squared value at a given significance level (5%) and degrees of freedom (4). If the calculated chi-squared value is greater than the tabled value (9.488), we can reject the null hypothesis. Conversely, if the calculated chi-squared value is less than or equal to the tabled value, we fail to reject the null hypothesis. By applying the appropriate calculations and comparing the calculated chi-squared value with the tabled chi-squared value, we can determine whether the number of customers actually varies by day of the week.

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The standard form of the given numbers is 207360 × 10¹⁷.

The number system is a way to represent or express numbers.

A decimal number is a very common number that we use frequently.

Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

Given the numbers is  (5 x 1,000,000) (6 x 100,000) (4 x 10,000) (8 x 1,000) (3 x 100) (2 x 10) (4 x 0.1) (9 x 0.001)

Now standard form means we need to write the exponents form.

So,

5 x 6 x 4 x 8 x 3 x 2 x 4 x 9 = 207360

And

1,000,000 x  100000 x 10000 x 1000 x 100 x 10 x 0.1 x 0.001 = 10¹⁷

So, combine 207360 x  10¹⁷

Hence "The standard form of the given numbers is 207360 × 10¹⁷".

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A) The exact cost of producing the 31st food processor is $3771.70. B)  Using the marginal cost, the approximate cost of producing the 31st food processor is $3741.40.

(A) To find the exact cost of producing the 31st food processor, we substitute x = 31 into the cost function C(x) = 1900 + 60x - 0.3x^2:

C(31) = 1900 + 60(31) - 0.3(31)^2

C(31) = 1900 + 1860 - 0.3(961)

C(31) = 1900 + 1860 - 288.3

C(31) = 3771.7

Therefore, the exact cost of producing the 31st food processor is $3771.70.

(B) The marginal cost represents the rate of change of the cost function with respect to the quantity produced. Mathematically, it is the derivative of the cost function C(x).

Taking the derivative of C(x) = 1900 + 60x - 0.3x^2 with respect to x, we get:

C'(x) = 60 - 0.6x

To approximate the cost of producing the 31st food processor using the marginal cost, we evaluate C'(x) at x = 31:

C'(31) = 60 - 0.6(31)

C'(31) = 60 - 18.6

C'(31) ≈ 41.4

The marginal cost at x = 31 is approximately 41.4 dollars.

To approximate the cost, we add the marginal cost to the cost of producing the 30th food processor:

C(30) = 1900 + 60(30) - 0.3(30)^2

C(30) = 1900 + 1800 - 0.3(900)

C(30) = 3700

Approximate cost of producing the 31st food processor ≈ C(30) + C'(31)

≈ 3700 + 41.4

≈ 3741.4

Therefore, using the marginal cost, the approximate cost of producing the 31st food processor is $3741.40.

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Answer:

Hi there!

The correct answer is: True

Step-by-step explanation:

If there is a line, there are infinite planes that pass through that line, therefore since the 4 points are in a line, they are coplanar .

The 95% confidence interval for the proportion of horses with enteroliths that are fed at least two flakes of alfalfa per day is approximately 0.597 to 0.834.

To calculate the confidence interval, we can use the formula for proportions. The point estimate for the proportion is calculated by dividing the number of horses fed two or more flakes of alfalfa (42) by the total sample size (62), resulting in a point estimate of 0.677.

To determine the margin of error, we use the formula:

Margin of Error = Critical Value * Standard Error

The critical value is obtained from the standard normal distribution, corresponding to a 95% confidence level. For a two-tailed test, the critical value is approximately 1.96.

The standard error is calculated using the formula:

Standard Error = √[(p * (1 - p)) / n]

where p is the point estimate and n is the sample size.

Plugging in the values, we find that the standard error is approximately 0.064.

Next, we calculate the margin of error:

Margin of Error = 1.96 * 0.064 ≈ 0.125

Finally, we construct the confidence interval by subtracting and adding the margin of error to the point estimate:

Lower bound = 0.677 - 0.125 ≈ 0.552

Upper bound = 0.677 + 0.125 ≈ 0.80

Therefore, the 95% confidence interval for the proportion of horses with enteroliths that are fed at least two flakes of alfalfa per day is approximately 0.597 to 0.834.

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Given:

Number of times Jenna feeds her cat = 2

Cat food each time \(=\dfrac{3}{4}\text{ can}\)

Number of days = 5

Number of cans she bought = 8

To find:

Did Jenna buy enough cat food.

Solution:

Required food for each time  \(=\dfrac{3}{4}\text{ can}\)

Jenna feeds her cat twice a day.

Required food for a day \(=2\times \dfrac{3}{4}\text{ can}\)

                          \(=\dfrac{3}{2}\text{ can}\)

Required food for 5 days \(=5\times \dfrac{3}{2}\text{ can}\)

                           \(=\dfrac{15}{2}\text{ can}\)

                           \(=7.5\text{ can}\)

Since, 7.5 cans < 8 cans, therefore, Jenna buy enough cat food for her cat.

Answer:

Step-by-step explanation:

Answer:

x=5, y=7

Step-by-step explanation:

2x+4y= 38

+7x-4y= 7

9x= 45

9x/9= 45/9

x=5

2x+4y=38

2(5)+4y= 38

10+4y= 38

-10 -10

4y= 28

4y/4= 28/4

y=7

when two non-vertical lines are in the same plane and have the same slope,  they are said to be parallel lines. whereas the non-vertical lines are in the same plane and intersect at an angle of 90, they are said to be perpendicular.

A parallel lines is when two lines have the same slope, meaning they will never intersect. This is represented by the same "rise over run" ratio in the equation of the line. The perpendicular lines  is when two lines have a slope that is the opposite reciprocal of each other. This means that the lines will intersect at a 90-degree angle and can be represented by the equation y = -1/m * x + b, where m is the slope of one of the lines. Both of these concepts are important for understanding the basics of linear equations, as well as for determining the lines of best fit in graphs.

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Given the function:

Let's find the function after differentiating it 68 times.

To differentiate, let's take the derivative.

First derivative:

Second derivative:

Since 3 is the constant with respect to x, the derivative of 3cos(3x) with respect to x will be:

After the second differentiation, we have -sin, , the same will be applicable to the 68th time.

Therefore, for the 68th differentiation the exponent for the constant -3 will be 68.

Therefore, after differentiating the function 68 times, we have:

ANSWER:

the volume of the region is 5/3.

What is volume of the region ?

If the area bordered above by the graph of f, below by the x-axis, and on the sides by x=a and x=b is rotated about the x-axis, the volume V of the produced solid is given by V=ab[f(x)]2dx.

From the equation of the first plane, we can solve for z:

\(z = (4 - x - y) / 3\\\\3x + 3y + (4 - x - y)/3 = 12\\\\y = -3x/2 + 4\\\\z = (5/3) - (1/3)x\)

So the points of intersection are:

(0, 4/3, 5/3) and (8/3, 0, 1)

To find the volume, we need to integrate over the region in the xy-plane bounded by the lines y = -3x/2 + 4 and y = 1:

∫\([0,8/3]\) ∫\([-3x/2+4,1]\) (4-x-y)/3 dA

= ∫\([0,8/3]\) ∫\([-3x/2+4,1]\) (4/3) dA - ∫\([0,8/3]\) ∫\([-3x/2+4,1] (x+y)/3\) dA

= (1/3) ∫[1,3] u³ du

= 20/3

So the total volume is:

\(10/3 - 20/3 = -10/3\\\\|(-10/3)/2| = 5/3\)

Therefore, the volume of the region is 5/3.

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Answer + Step-by-step explanation:

y = mx + b

To find the slope (m),

slope = rise / run

x is increasing by 1.3 (run)

y s increasing by 1 (rise)

rise / run = 1 / 1.3

slope = 1 / 1.3

To find the y-intercept (b),

when x = 0, y = 0 so y-intercept is 0

equation:

y = 1/1.3x

graph:

Answer:

Y=6

X=0

Step-by-step explanation:

Hope this helps