Which of the following is an obtuse angle in this figure?
a protractor, with segment DEF along the bottom, EH point to the 55 degree on the left, EJ to 90 degrees, EK to the 30 degrees on the right
angle DEK
angle DEJ
angle DEH
angle FEK

Answer:

-25

Step-by-step explanation:

175÷-7=-25

-25×-7=175

Answer:

96.25%

Step-by-step explanation:

The empirical rule regarding mean and standard deviation is that

Therefore between mean and +2 standard deviation or between mean and -2 standard deviation you will find  approximately 95/2 = 47.5% of the values

Between mean and ± 3 standard deviations you will find approximately 97.5/2 = 48.75% of the values

Therefore between 2 standard deviations above and 3 standard deviations below you will find approximately 47.5 + 48.75 = 96.25% of values

It can be seen that sin20, given that cos0 = 40/41, is 720/1681.

Firstly, we can determine sin0 using the Pythagorean identity:

[tex]sin^20 + cos^20 = 1,[/tex] which gives [tex]sin0 = \sqrt(1 - cos^20) = 9/41.[/tex]

Next, using the double-angle identity

sin2θ = 2sinθcosθ, we find sin20

= 2sin0cos0 = 2 * (9/41) * (40/41)

= 720/1681.

Therefore, sin20, given that cos0 = 40/41, is 720/1681.

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Answer:

Top Right: 26

Bottom Right: 16

Top Left: 36

Bottom Left: 20

Center: 26

Step-by-step explanation:

TR: 5 + 3 + 12 + 6 = 26

BR: 2 + 2 + 4 + 5 + 3 = 16

TL: 14 + 10 + 8 + 3 + 1 = 36

BL: 6 + 6 + 2 + 2 + 2 + 2 = 20

Center: 2 + 2 + 8 + 8 + 6 = 26

The population mean is 4.25, population variance is 4.6875 and standard deviation is 2.166.

In order too find the population mean and variance, we can use the formula:

μ = ∑(x * P(x))

= 0*(3/16) + 4*(15/40) + 6*(7/16)

= 4.25

The population variance will be:

σ² = ∑[(x - μ)² * P(x)]

= (0 - 4.25)²*(3/16) + (4 - 4.25)²*(15/40) + (6 - 4.25)²*(7/16)

= 4.6875

The population standard deviation:

σ = √(σ²) = √(4.6875) = 2.166

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Answer:

  x = 9 inches

Step-by-step explanation:

You want the value of x in the similar triangles shown.

Corresponding sides are proportional. This means the ratio of the horizontal side of the triangle to the vertical side is the same for both.

  6/4 = (6+x)/10

  15 = 6 +x . . . . . . . . multiply by 10

  9 = x . . . . . . . . . subtract 6

The measure of x is 9 inches.

__

Additional comment

You could also write the proportion ...

  6/4 = x/(10 -4)

  x = 36/4 = 9 . . . . . . . multiply by 6

You can see this if you draw a horizontal line through the figure at the top of the side marked 4 in.

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Nina makes a profit of $39.25

To calculate Nina's profit, we need to determine the total revenue generated from selling the brownies and cookies and subtract the cost of ingredients.

The total revenue from selling the brownies can be calculated by multiplying the number of brownies sold (25) by the price per brownie ($1.25):

Revenue from brownies = 25 * $1.25 = $31.25

Similarly, the total revenue from selling the cookies can be calculated by multiplying the number of cookies sold (30) by the price per cookie ($0.60):

Revenue from cookies = 30 * $0.60 = $18.00

The total revenue from both brownies and cookies is the sum of the revenues from each:

Total revenue = Revenue from brownies + Revenue from cookies

= $31.25 + $18.00

= $49.25

Now, to calculate the profit, we subtract the cost of ingredients ($10) from the total revenue:

Profit = Total revenue - Cost of ingredients

= $49.25 - $10.00

= $39.25

Therefore, Nina makes a profit of $39.25.

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the equation for the position vector r(t) is:

r(t) = (x₀ + v₀xt + (1/2)at²)i + (y₀ + v₀yt + (1/2)at²)j + (z₀ + v₀zt + (1/2)at²)k.

To find the equation for the position vector r(t) of the particle at time t, we can utilize the kinematic equations of motion.

Given that the particle travels in a straight line from point

P₀(x₀, y₀, z₀) to point P₁(x₁, y₁, z₁),

with speed v₀ at point P₀ and constant acceleration a,

we need to determine the equation in terms of the position vector r(t).

Let's break down the problem into components:

   For the x-component:

   Using the equation of motion x = x₀ + v₀t + (1/2)at², we have:

   x = x₀ + v₀xt + (1/2)at².

   For the y-component:

   Similarly, using the equation of motion y = y₀ + v₀yt + (1/2)at², we have:

   y = y₀ + v₀yt + (1/2)at².

   For the z-component:

   Applying the equation of motion z = z₀ + v₀zt + (1/2)at², we have:

   z = z₀ + v₀zt + (1/2)at².

Therefore, the equation for the position vector r(t) is:

r(t) = (x₀ + v₀xt + (1/2)at²)i + (y₀ + v₀yt + (1/2)at²)j + (z₀ + v₀zt + (1/2)at²)k.

This equation represents the position vector of the particle at any given time t, considering its initial position, speed, and constant acceleration.

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The solution is -2x^2 - 20x - 53 is the standard form of the given vertex form.

Here, we have,

Vertex and standard form of an equation

Given the vertex form of a quadratic equation expressed as:

y = -2(x+5)^2 - 3

The standard form is in the form y = ax^2 + bx + c

Expand the given vertex form

y = -2(x+5)^2 - 3

y = -2(x^2+ 10x + 25) - 3

y = (-2x^2 - 20x - 50) - 3

y = -2x^2 - 20x - 53

Hence the standard form of the given expression is -2x^2 - 20x - 53

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complete question:

Convert the following from vertex to standard form

Answer:

x = 2  or  x = -6

Step-by-step explanation:

|2x + 4| = 8

2x + 4 = 8  or  2x + 4 = -8

2x = 4  or 2x = -12

x = 2  or  x = -6

The money that would be in the savings account after 21 years is shown by option C

Through the process of accruing interest, money in a savings account can increase. The bank or other financial institution may provide you with an interest rate when you make a deposit into a savings account. The bank will offer you interest as compensation for keeping your funds in the account as a proportion of the amount you have placed.

Given that;

f(t) = [tex]425(1.025)^t[/tex]

f(t) = [tex]425(1.025)^21[/tex]

= 713.8

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Answer:

36 in

Step-by-step explanation:

Volume of cone = (1/3) X vertical height X π r ²

432π = (1/3) π (r)²

r² = (432π) / (π/3)

= (1296 π) / π

= 1296.

r = √1296

= 36 in

Answer:

I didn't mean to click give answer, sorry

The number of cups that Mandy can fill from 4 quarts of juice comes out to be 32 cups.

Total juice = 4 quarts

Juice in one cup = 1/8 quarts

Number of total juice cups = 4 ÷ 1/8

Division of the whole number and the fraction is done as follows:

1. We take the reciprocal of the fraction after the sign of division.

2. We multiply the numerator by the numerator and get the final numerator. Similar is done with the denominator.

3. Simplify the resultant fraction

Thus,

= 4 * 8

= 32

Thus, Mandy can fill 32 cups with 4 quarts of juice.

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The complete question is:

Mandy has 4 quarts of juice for her party. How many party cups can Mandy fill if each one holds 1/8 quarts

After the first year, Carlotta will have the amount of $124.80 in the investment portion of her policy.

Calculated by taking 40% of her annual premium;

($780 x 0.40 = $312),

then adding the interest earned on that amount at a rate of 2.2% as;

($312 x 0.022 = $6.84).

Thus the total amount in the investment portion is; $312 + $6.84 = $318.84,

= $124.80.

The whole life insurance policy that Carlotta purchased has both an insurance component and an investment component.

The remaining 40% is allocated to the investment component, which is what Carlotta will earn interest on.

At a rate of 2.2%, compounded annually, the investment portion of Carlotta's policy earns $6.84 in interest after the first year. which is added to the $312 that was allocated to the investment portion, giving a total of $318.84.

We conclude that Carlotta has $124.80 in the investment portion of her policy after the first year.

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Answer: 3 US cups

Step-by-step explanation: 20 quarts equal 80 US cups. Then you divide 80 by 23 which equals to 3

The sale price of the $50 item after a 30% discount is $35.

A discount is a deduction from the general price of goods and services. If an item is sold at a price lower than the actual price.

Given, sale price = $50

discount = 30%

By basic calculation;

$50 × 30 = $15

         100

Eliminating discount from the price we have,

$50 - $15 = $35

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[tex]-a^3b - 8ab^2[/tex] is the simplification of the given expression.

To simplify the expression (3a^3b - 4ab^2 + 5ab) - (4a^3b + 4ab^2 + 5ab), we can perform the subtraction by distributing the negative sign to each term inside the second parentheses:

[tex](3a^3b - 4ab^2 + 5ab) - (4a^3b + 4ab^2 + 5ab)\\\\= 3a^3b - 4ab^2 + 5ab - 4a^3b - 4ab^2 - 5ab[/tex]

Now, let's combine like terms:

[tex](3a^3b - 4a^3b) + (-4ab^2 - 4ab^2) + (5ab - 5ab)\\\\= -a^3b - 8ab^2 + 0[/tex]

Simplifying further, we have:

[tex]-a^3b - 8ab^2[/tex]

Therefore, the simplified expression is[tex]-a^3b - 8ab^2[/tex].

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11% of the students were left-handed, and 89% were right-handed. Among the left-handed students, 48.75% preferred to write with a pen, while among the right-handed students, 55.5% preferred to write with a pen.

To fill out the two-way relative frequency table, we need to determine the total number of students who prefer to write with a pen or a pencil and whether they are left-handed or right-handed. Based on the given data, we can fill in the table as follows:

        Right Hand (%)    Left Hand (%)   Total (%)

Pen           11                       64                   75

Pencil        0                         9                    9

Total (%)    11                       73                   84

So, percentage of left-handed students who prefer to write with a pen)

=  percentage of students who prefer to write with a pen x  percentage of left-handed students  

= 75% x 11%

= 8.25%

Therefore, the complete two-way relative frequency table is:

            Right Hand (%)      Left Hand (%)       Total (%)

Pen            8.25                       48.75                   75

Pencil           0                          6.75                       9

Total (%)      8.25                     55.5                     84

We can interpret this table to mean that of the 84 students surveyed, 75% preferred to write with a pen, while 9% preferred to write with a pencil.

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Answer:d i think if im not mistaken

Step-by-step explanation:

.

Step-by-step explanation:

To conduct a One-Sample t-test in SPSS to obtain the same output, follow these steps:

Open SPSS and click on "File" and then "Open" to import the dataset with the heights of students.

Click on "Analyze" from the top menu, then "Compare Means", and then "One-Sample T Test".

In the "One-Sample T Test" dialog box, select the variable that contains the heights of the students from the "Test Variable(s)" box and move it to the "Test Variable(s)" box.

In the "Test Value" box, enter 170 as the value to be tested against the mean.

In the "Options" tab, check the box next to "95% Confidence Interval".

Click "Continue" and then click "OK".

The SPSS output will appear in the output viewer, which will include the One-Sample Statistics table and the One-Sample Test table. Check if the output matches the values provided in the original question. If there are any discrepancies, review the data and the steps followed to ensure accuracy.

Edit:

To replicate the analysis in SPSS, you would need to create a dataset that includes the heights of the 50 students in the university. You would need to create one variable for the heights, and each student's height would be entered as a separate value in the variable. Here are the steps to create the dataset:

Open SPSS and select "Type in Data" from the menu.

In the "Variable View" tab, create a new variable called "Height" and set the "Type" to "Numeric".

In the "Data View" tab, enter each student's height in the "Height" column.

For example, the dataset might look like this:

Height

175

168

180

...

173

Once you have entered all of the heights, you can follow the steps I provided earlier to perform the one-sample t-test analysis on the dataset.

1. The correct exponential function for each graph is

a.  f(x) = 2ˣ is graph (III)     b. f(x) = 2⁻ˣ is graph (I)   c. f(x)= -2ˣ graph (II)  D. f(x) = -2⁻ˣ is graph (IV)

2. The evaluated exponential functions are;

a. f(1) = 1  b. f(-1) = 0.1  c. f(0) = 0.3

3. The exponential function for the graph  is f(x) = [tex]\frac{1}{2}^x[/tex]

4. The model for the rate population is N(t) = 320 × [tex]2^{t}[/tex] . After 8 years, the population will be 81,920.

5. The compounded interest after 2 years: 2628.17. After 3 years 2694.7. After 6 years 2904.57

6. The compounded interest after a) 3 years = 4221.81  b) 6 years = 5092.47  c) 9 years = 6142.69

7. At time t = 0, the mass is 13 kg. After 45 days, the mass is approximately 6.62 kg

1. For the exponential function,  

a. f(x) = 2ˣ has a coordinate (0,1).  f(1) = 2⁰ = 1 It matches (III)

b.  f(x) = 2⁻ˣ When x = -1, f(x) = 2,  x = 0, f(x) = 1, x = 1, f(x) = 0.5; x = 2, f(x) = 0.25. If you plot this coordinates, you will see the graph falls from left to right

c. f(x)= -2ˣ it should pass through  (0, -1),  x = -1, when f(x) = -0, x = 0, f(x) = -1, x = 1, f(x) = -2

d. f(x) = -2⁻ˣ will pass through the point (0, -1). When x = -1, f(x) = -2; x = 0, f(x) = -1; x = 1, f(x) = -0.5. The graph should rise from left to right.

2. If the exponential function is f(x) = 3ˣ⁻¹ then we evaluate

f(1) = 3¹⁻¹ = 3⁰ = 1

f(-1) = 3⁻¹⁻¹ = 3⁻² = 1/3² or 0.1

f(0) = 3⁰⁻¹ = 3⁻¹ = 1/3 or 0.3

3. For the graph whos exponential function should be in the form f(x) = aˣ, we can find the actual function by looking at the coordinated (-3, 8)

a⁻³ = 8

a = [tex]8^1/-3[/tex]

a = 1/2

f(x) = (1/2)ˣ

4. The mouse population can be modeled as

N(t) = N₀ × (1 + [tex]r)^{t}[/tex] ⇒ N(t) = 320 × [tex]2^{t}[/tex]

After 8 years ⇒ N(8) = 320 × 2⁸

N(8) = 320 × 256

N(8) = 81920

5. We use the formula A = P(1 + [tex]r/n)^{nt}[/tex]

$2500 invested at an annual interest rate of 2.5% compounded daily,

After 2 years (t = 2):                          After 3 years

A = 2500(1 + 0.025/365)⁽³⁶⁵ˣ²⁾         A = A = 2500(1 + 0.025/365)⁽³⁶⁵ˣ³⁾

A = 2628.17                                       A = 2694.7

After 6 years

A = 2500(1 + 0.025/365)⁽³⁶⁵ˣ⁶⁾

A = 2904.57

6. For a  continuous compounded interest, we use the formula;

A = P × [tex]e^{rt}[/tex]

the principal is $3500, the interest rate is 6.25%, or 0.0625 as a decimal.

a) After 3 years:                 After 6 years:             After 9 years

A = 3500 × [tex]e^{0.0625 * 3}[/tex]          A = 3500 × [tex]e^{0.0625 * 6}[/tex]     A = 3500× [tex]e^{0.0625 * 9}[/tex]

A = 4221.81                       A = 5092.47                A = 6142.69

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The simplified expression for this problem is given as follows:

2q/3 - 7/12.

Like terms are terms that share these two features listed as follows:

If terms are like terms, then they can be either added or subtracted.

The expression for this problem is given as follows:

11/12 - q/6 + 5q/6 - 1/3.

Hence the like terms for this problem are given as follows:

Hence the simplified expression is given as follows:

2q/3 - 7/12.

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The amount of binding needed to bind the edge of a circular rug that is 9 m in diameter, which is given by its circumference, is 28.26 m.

The circumference refers to the distance around a circle.

The circumference can be determined using the circumference formulas: 2πr or π × d.

Formula with radius:

C = 2πr

C = circumference

π = the constant pi

r = radius of the circle

However, since the diameter of the circular rug is given, we can find the circumference as:

Formula with diameter:

π × d

Where π = 22/7 or 3.14 and d = 9 m.

3.14 x 9

= 28.26 m

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Answer:

-----------------------

Find the length of two adjacent sides, AB and AD, then multiply them together to get the area.

Use distance formula:

The area is:

Step-by-step explanation:

The Boolean expression ∼(p ∨ q) ∨ (∼p ∧ q) is equivalent to ∼p.

The volume of the rectangular prism is 262 and one-half feet cubed.

The volume of a rectangular prism can be calculated by multiplying its length, width, and height. In this case, the length is 6 and one-fourth feet, the width is 14 feet, and the height is 3 feet.

To simplify the calculation, we can convert the length to a mixed number: 6 and one-fourth can be expressed as 6.25 feet.

Now, we can plug these values into the volume formula: V = l x w x h.

V = 6.25 feet x 14 feet x 3 feet = 262.5 feet cubed

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The equation of the line that passes through points (5, 8) and
(-2.2, -6.4) is y = 2x - 2.

Option D is the correct answer.

We have,

We can use the point-slope form of the equation of a line, which is:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope of the line.

Slope.

m = (y2 - y1) / (x2 - x1)

= (-6.4 - 8) / (-2.2 - 5)

= (-14.4) / (-7.2)

= 2

Next, we can use one of the two given points and the slope to write the equation of the line in the point-slope form:

y - 8 = 2(x - 5)

Expanding the right side and simplifying.

y - 8 = 2x - 10

y = 2x - 2

Therefore,

The equation of the line that passes through points (5, 8) and
(-2.2, -6.4) is y = 2x - 2.

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The radius is approximately 112.8ft, and the minimum speed is approximately 22.9mph.

To find the radius of the yaw mark, use the formula R = [tex](C^2 / 8M) + (M / 2),[/tex] where R is the radius, C is the chord length (56ft), and M is the middle ordinate (7ft).

Plugging in the values, we get R ≈ 112.8ft.

To find the minimum speed, use the formula V = √(15 * D * f), where V is the speed in mph, D is the distance traveled in feet (half the chord length), and f is the drag factor.

Using D = 28ft and f = 0.95, we find V ≈ 22.9mph.

Therefore, the radius is approximately 112.8ft, and the minimum speed is approximately 22.9mph.

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