Identify the slope and y-intercept of the line y=−2x−1.

Solution:

Note that:

Substitute the values given into the expression to find the surface area.

The surface area of the rectangular prism is 332 mm².

Length = 6 mm

Height = 7 mm

Width = 10 mm

\( \boxed{\rm Surface\:area\:of\:rectangle=2(LB)+2(BH)+2(HL)}\)

\( \sf \nrightarrow \: SA = 2 \times (6 \times 10) + 2 \times (7 \times 10) + 2 \times (6 \times 7)\)

\( \sf \nrightarrow \: SA = 2 \times 60 + 2 \times 70 + 2 \times 42\)

\( \sf \nrightarrow \: SA = 120 + 140 + 84\)

\( \tt \multimap \: SA = 344 \: {mm}^{2} \)

The correct answer is Part 1: The 99% confidence interval for the population proportion is approximately (0.4716, 0.5416).Part 2: With 99% confidence, the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.

Part 1:

To construct a 99% confidence interval for the population proportion, we can use the formula:

Confidence Interval = Sample Proportion ± Margin of Error

where the margin of error is determined by the level of confidence and the standard error.

First, let's calculate the sample proportion:

Sample Proportion = (Number of adults who say they have started paying bills online) / (Total number of adults surveyed)

Sample Proportion = 1436 / 2837 ≈ 0.5066 (rounded to four decimal places)

Next, we need to calculate the standard statistics error, which is the measure of the variability in the sample proportion:

Standard Error = sqrt((Sample Proportion * (1 - Sample Proportion)) / Sample Size)

Standard Error = sqrt((0.5066 * (1 - 0.5066)) / 2837) ≈ 0.0136 (rounded to four decimal places)

Now, we can calculate the margin of error:

Margin of Error = Critical Value * Standard Error

The critical value is based on the desired confidence level. For a 99% confidence level, the critical value is approximately 2.576 (obtained from a standard normal distribution table).

Margin of Error = 2.576 * 0.0136 ≈ 0.0350 (rounded to four decimal places)

Finally, we can construct the confidence interval:

Confidence Interval = Sample Proportion ± Margin of Error

Confidence Interval = 0.5066 ± 0.0350

Confidence Interval ≈ (0.4716, 0.5416) (rounded to four decimal places)

Part 2:

The correct interpretation is:

C. With 99% confidence, it can be said that the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.

This means that we are 99% confident that the true proportion of adults who have started paying bills online falls within the range of 0.4716 to 0.5416. The survey results suggest that approximately 47.16% to 54.16% of the population of adults have started paying bills online in the last year.

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The quadratic function for the path of the basketball as it is thrown indicates;

The path of the basketball will not make the shot

The height reached is about 5.24 meters

A quadratic function is a function of the form; f(x) = a·x² + b·x + c, where a ≠ 0, and a, b, c, are numbers.

The function for the path of the basketball is; b(x) = (-1/7)·x² + 1.36·x + 2

The function for the location of the basketball net is; n(x) = 3 and (8 < x < 8.5), where;

n(x) = The vertical height of the basketball

Plugging in the value of the n(x) = b(x), to check if equations have a common solution, we get;

b(x) = n(x) = 3 = (-1/7)·x² + 1.36·x + 2

(-1/7)·x² + 1.36·x + 2 - 3 = 0

(-1/7)·x² + 1.36·x - 1 = 0

(1/7)·x² - 1.36·x + 1 = 0

Solving the above equation, we get;

x = (119 - √(9786))/(25) ≈ 0.803, and x = (119 + √(9786))/(25) ≈ 8.717

Therefore, the x-coordinates of the height of the path of the basketball when the height is 3 meters are 0.803 and 8.717, neither of which are within the range (8 < x < 8.5), therefore, the baseketball will not go through the net and the path will not make the shot.

Bonus; The x-coordinates of the highest point of a quadratic function, f(x) = a·x² + b·x + c is; -b/(2·a)

Therefore, the x-value at the highest point of the equation, b(x) = (-1/7)·x² + 1.36·x + 2 is; x = -1.36/(2 × (-1/7)) = 1.36 × 7/2 = 9.52/2 = 4.76

The height of the highest point is; b(9.52) = (-1/7)·(4.76)² + 1.36·(4.76) + 2 ≈ 5.24 meters

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Answer:

I have completed the answers and attached them to the explanation.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The question asks for a subtraction expression:

length is always a positive number so bigger number first here.

OB = 4-(-1)              >only moves in x direction so subtract x's

AB = 4-(-2)             >only moves in y direction so subtract y's

Okay, here we have this;

Considering the provided information, we are going to calculate the requested simple interest rate, so we obtain the following:

So to solve it we will substitute in the following simple interest formula, then we have:

I=Prt

(1615-1000)=1000(r)(3)

615=3000(r)

r=615/3000

r=0.205

r=20.5%

Finally we obtain that the simple interest rate is 20.5% per year.

Answer:   \(w \le 3000\)

w is the weight of the truck in pounds.

Since w cannot be negative, we can write \(0 \le w \le 3000\) or we could tack on the statement "w must be positive"

The phrase "at most" means "that is the largest w can get". Think of it as the ceiling.

Answer:

Step-by-step explanation:

It’s $6.82 I believe

you got to add $2.10 three times and you get $6.30

then divide the 2.10 with the remaining 4 syringes and youll get $6.82

Hope this helped

\(x = - \frac{2(5 + 3y)}{5} \)

\(y = - \frac{5(2 + x)}{6} \)

\(x = \frac{2(y - 3)}{3} \)

\(y = \frac{3(2 + x)}{2} \)

Answer:

122 1/4

Step-by-step explanation:

Hope this helps! :)

(12x12) 12x \(\frac{2}{3\\}\) x12) / (3/2 x3/2)

PEMDAS = parathesis exponents multiplictation division add subtract.

12x12=24

3/2x3/2=9/4

12x2/3=8x12=96

so 24+96=120

9/4 can be like 4x2=8 so i remaing

120+2=122 1/4?

Answer:

50

Step-by-step explanation:

44% of 50 is 22.

Answer: is 50

Step-by-step explanation:

Just listen to the other awnswer

Answer:

n = 2

Step-by-step explanation:

1.2n - 1.5 = 0.45n

collect like terms

1.2n - 0.45n = 1.5

0.75n = 1.5

divide both side by 0.75

0.75n/0.75 = 1.5/0.75

n =2

The required value of trigonometric ratios is,

sin 45° = 1/\(\sqrt{2}\)

cos 30 = \(\sqrt{3}\)/2

tan 60 = 1/  √3

We know that,

Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.

Therefore,

sin 45° = 1/\(\sqrt{2}\)

cos 30 = \(\sqrt{3}\)/2

tan 60 = 1/  √3

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Tables are used to show the relationship between related quantities. From the given table, the value of f(10) is 14.8

See attachment for the table of \(A = f(d)\)

To solve for f(10), we simply locate the value of A when d = 10

From the table

A = 14.8 when d = 10

This means that:

\(A =f(10) = 14.8\)

Hence:

\(f(10) = 14.8\)

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Answer:

Mean = 59

Median = 56.5

Step-by-step explanation:

56 + 57 + 53 + 63 + 68 + 52 + 55 + 65 + 62 = 531

531 / 9 = 59

Mean = 59

52, 53, 55, 56, 57, 62, 63, 65, 68

Num between 56 and 57

56.5

Median = 56.5

Plz mark as brainliest if correct! Have a nice day!!!

-Lil G

Answer:

22.5%

Step-by-step explanation:

math

Answer:

5(3)+10=15+10

=25

Step-by-step explanation:

EXPLANATION

The line of reflection from WXY to W'X'Y' is the line y=-x as shown in the following graph:

To solve this problem, we need to use the basic trigonometric identities, which state that for any angle x:

sin^2(x) + cos^2(x) = 1

1 + tan^2(x) = sec^2(x)

1 + cot^2(x) = csc^2(x)

We can use these identities to simplify the expression (sin0 + cos0) = 2 + sec0 csc0/Sec0 CSC0. First, we note that sin0 + cos0 = 1, because sin^2(0) + cos^2(0) = 1. So, the left-hand side of the equation becomes 1 = 2 + sec0 csc0/Sec0 CSC0.

Next, we note that sec0 = 1/cos0 and csc0 = 1/sin0, so we can rewrite the right-hand side of the equation as 1 = 2 + 1/cos0 * 1/sin0 / Sec0 CSC0.

Then, we note that Sec0 = 1/cos0 and CSC0 = 1/sin0, so the right-hand side of the equation becomes 1 = 2 + 1/cos0 * 1/sin0 / 1/cos0 * 1/sin0. This simplifies to 1 = 2 + 1/cos0^2 * 1/sin0^2, which simplifies further to 1 = 2 + 1/cos0^2 / sin0^2.

Finally, we use the identity 1 + cot^2(0) = csc^2(0) to replace 1/sin0^2 with 1 + 1/cos0^2, which gives us 1 = 2 + 1/cos0^2 / (1 + 1/cos0^2). Solving for 1/cos0^2, we get 1/cos0^2 = -1. This means that cos0 = 0, which is not a valid value for the cosine function. Therefore, the original equation has no solution.

Answer:

540 feet

Step-by-step explanation:

\(\frac{36}{100} = \frac{x}{1500}\)  Cross multipy

100x = 54000

54000/100 = 540

x = 540

Answer:

D. Place the point of the compass on the midpoint of AB and mark

the points directly above and below the midpoint.

Step-by-step explanation:

Below are the simple steps to follow to draw a perpendicular bisector of line AB.

First step

Set the compass at the end of one line segment and move the compass so that it would be slightly longer than half of the line AB.

Second step

Set the compass at point A and make some arcs just above line AB.

Third step

Draw an arc from point B with the same compass width.

Fourth step

Carefully set a ruler at the intersection of the arcs and draw the line segment.

Answer:place the point of the compass on point a and draw an arc across ab.

Step-by-step explanation:

Answer:

A. Eva

Step-by-step explanation:

Given that

The entire school, 250 students, went to the soap box derby.2 vans went to soap box derby and each van held 6 students.

To find the total number of students from the Math Club who went to the soap box derby, we need to add the number of students in each van, the number of times equal to the number of vans.

i.e. by adding 6 (i.e. number of students in each van) 2 (number of vans )number of times, we can get the number of students from Math Club who went to the soap box derby.

Number of Math Club students who went to the soap box derby = 6 + 6 = 12

OR

Simply, multiply number of students in each van with the number of vans .

6 \(\times\) 2 = 12

Therefore, Eva is correct about the calculations.

Answer:

40 students in each bus.

Step-by-step explanation:

Subtract the 8 extra students from the total to get the total number of students who rode in buses. Then divide that total by 6.

248-8=240

240/6=40

40 students in each bus.

Answer: (x+6)(x-3)

Step-by-step explanation:

y=x^2+3x-18

(x+6)(x-3 )

Maria’s net pay is $2,025.82.

The net pay is the gross pay minus mandatory and voluntary deductions, like taxes, insurance, and other expenses.

The net pay represents the amount of money the income earner receives.

The net pay is also known as the take-home.

Monthly salary = $2,750

FICA withholding = 15%

Social security tax withholding = 7.2%

Medicate tax withholding = 1.37%

Health Insurance Premium = $76 per month

Total withholding = 23.57%

= $648.18 (2,750 x 23.57%)

Total deductions and withholding = $724.18 ($76 + $648.18)

Net pay = $2,025.82 ($2,750 - $724.18)

Thus, Maria's net pay after the withholdings and deductions is $2,025.82.

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The calculated value of k on the line is 9

From the question, we have the following parameters that can be used in our computation:

XZ is the perpendicular bisector of segment WY

This means that

WX = XY

substitute the known values in the above equation, so, we have the following representation

3k - 4 = 2k + 5

So, we have

3k - 2k = 4 + 5

Evaluate

k = 9

Hence, the value of k is 9

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Answer:

20°

Step-by-step explanation:

These angles add up to 90° so we have:

x + 2x + x + 10 = 90

4x + 10 = 90

4x = 80

x = 20°

Answer:

12

Step-by-step explanation:

10x - 20 + 6x + 8 = 180

Supplementary angles

Answer:

x = 12

Step-by-step explanation:

The two given angles create a straight line (Definition of Straight Line). This means that:

\((10x - 20) + (6x + 8) = 180\)

First, combine like terms. Like terms are terms that share the same amount of the same variables:

\((10x + 6x) + (8 - 20) = 180\\(16x) + (-12) = 180\\16x - 12 = 180\\\)

Next, isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operations and stands for:

Parenthesis

Exponents (& Roots)

Multiplications

Divisions

Additions

Subtractions

~

First, add 12 to both sides of the equation:

\(16x - 12 = 180\\16x - 12 (+12) = 180 (+12)\\16x = 180 + 12\\16x = 192\)

Next, divide 16 from both sides of the equation:

\(\frac{16x}{16} = \frac{192}{16} \\x = \frac{192}{16}\\ x = 12\)

12 is your answer.

~

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Answer:

6 without repetition

27 with repetition

Step-by-step explanation:

without repetition, you have 3 digits to choose from initially, then only 2, then only one, i.e.:

3×2×1 = 6

with repetition, you have 3 digits to choose from for every spot:

3×3×3 = 27