three people are asked to throw a fair die. what is the probability that all ofthem get the same number? [10 pts]

[tex] \angle 1=\angle 2=62.5^{\circ}[/tex] (isosceles triangle)

[tex]\angle 3=55^{\circ}[/tex] (vertical angles)

[tex]\angle 4=75^{\circ}[/tex] (linear pair)

[tex]\angle 5=50^{\circ}[/tex] (exterior angle theorem)

Answer:

120º

Step-by-step explanation:

This might be the correct answer if I'm not mistaken:

Extending the right side of the bottom triangle leads to m<1 and 120 vertical angles.

You use the Vertical Angles Theorem, and figure that 120 is congruent to m<1. Thus, i think 120 degrees is the answer.

The measure of each angle 2x°, 3x°, 4x°, and x° will be 72°, 108°, 144°, and 36°, respectively.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

The angle 2x and angle 3x is the supplementary angles. Then the value of 'x' is given as,

2x + 3x = 180

5x = 180

x = 36

Then the value of each angle is given as,

2x = 2 × 36 = 72°

3x = 3 × 36 = 108°

4x = 4 × 36 = 144°

 x = 1 × 36 = 36°

The measure of each angle 2x°, 3x°, 4x°, and x° will be 72°, 108°, 144°, and 36°, respectively.

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Answer:

[tex]8-9i[/tex]

Step-by-step explanation:

[tex]p-q=5-2i-(-3+7i) \\ \\ =5-2i+3-7i \\ \\ =8-9i[/tex]

Answer:

Step-by-step explanation:

....shhhhhhhhhhhhhhhhhhhhhhh

The question "Are you a faster runner than your best friend​" is a non statistical question.

A statistical question is a question that can be answered by collecting and analyzing data. The question is usually framed in a way that allows for the collection of data and the use of statistical methods to analyze the data and make inferences about a larger population. Examples of statistical questions include:

The question "Are you a faster runner than your best friend?" is a non-statistical question. It is asking for a comparison between two individuals rather than a statistical analysis of a dataset.

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Answer:

length = 10 in.

width = 8 in.

Step-by-step explanation:

volume of cuboid = length(l) * width(w) * height(h)

l = w + 2

(w + 2) * w * 6 = 480

(w + 2) * w = 480/6 = 80 in²

w² + 2w =  80

w² + 2w - 80 =  0

solve for w (AC method):

w² + 10w - 8w - 80 = 0

w(w + 10) - 8 (w + 10) = 0

(w-8)(w+10) = 0

w = 8 or w = -10

As length cannot be negative, w = 8 in.

substitute w with 8:

l = 8 + 2 = 10 in.

10 * 8 * 6 = 480 in³

Answer:

If you accept a job with a salary of $37,300 and receive a 6% raise after 6 months, your new salary will be $37,300 x 6/100 = $2,238. This is the amount of your raise. To determine your new salary, we can add the raise to your original salary, which gives us:

New salary = $37,300 + $2,238 = $39,538

Therefore, your new salary after receiving a 6% raise will be $39,538.

Step-by-step explanation:

Answer:

y = -x + 11

Step-by-step explanation:

y = mx + b

m is the slope and b is the y-intercept so m = -1

y = -x + b

Now substitute x = 8 and y = 3:

3 = -8 + b

b = 11

Thus the final equation is y = -x + 11.

QR≅SR (given)

PQ ≅ PS (given)

PR = PR (common to both triangles)

∠QPR ≅ ∠SPR (SSS rule)

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

SSS rule (side-side-side)

The three sides of one triangle are congruent to the corresponding sides of the other triangle, the two triangles are congruent.

From the given figure.

QR≅SR (given)

PQ ≅ PS (given)

PR = PR (common to both triangles)

∠QPR ≅ ∠SPR (SSS rule)

Thus,

∠QPR is congruent to ∠SPR by SSS rule.

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Answer:

3. y int= 6

4. m=6

5. y=-2x-8

Step-by-step explanation:

3.  since the y intercept is when x=0 the table shows the y=6.

4.  to find m we use          change in y/change in x

the change in y is 6 because 6-0=6

change is x is 1 because 0--1=1

6/1=6

5.  y=mx+c

c is y intercept thus c= -8

m is function rate/ gradient of the line = -2

this is because:

change in y= -8--2=-6

change in x= 0--3=3

-6/3= -2

thus y=-2x-8

Answer: The function would have a minimum value because the least you will ever have is 0$. It cannot go below 0, so that is the minimum. However, depending on how much time has passed, the maximum amount of money you have can change. It can always go up more, so there is no set maximum.

Step-by-step explanation:

The simplified value of the given fractions is -11/12

What does division of fractions mean?

A fraction is divided into additional equal pieces when it is divided into fractions. For instance, if you had three-fourths of a pizza remaining and divided each slice into two pieces, you would have received six slices, which would be equivalent to six-eighths of the entire pizza.

Top expression = 5/8 + 3/4

                          = (5 + 6)/ 8 = 11/8  ( 8 is the lcm of 4 and 8 )

Bottom expression = -2/3 - 5/6

                                = (-4 - 5)/ 6

                                = -9/6 = -3/2

Top expression/ Bottom expression = (11/8)/ (-3/2  )

                                                            = - (11/8) * (2/3)

                                                            = -11/12

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3.

The value of x is 20°

The value of y is 30.

4.

The value of x is 30°

The value of y is 4.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

3.

An equilateral triangle.

Where all three angles and all three sides are equal and the angle is 60°.

Now,

16 + y = 46

y = 46 - 16

y = 30

And,

180 - 80° = 100°

The sum of the angles must be 180°.

x + 100 + 60 = 180

x = 180 - 160

x = 20°

4.

We have an equilateral triangle and an isosceles triangle.

All the angles in the equilateral triangle are 60°.

The two angles opposite to the equal sides of the isosceles triangle are equal.

So,

5y = 20

y = 4

And,

In the isosceles triangle.

The straight angle.

60 + angle = 180

angle = 180 - 60

angle = 120.

Now,

The sum of the angles of the isosceles triangle = 180.

2x + 120 = 180

2x = 60

x = 30°

Thus,

3.

The value of x and y is 20° and 30.

4.

The value of x and y is 30° and 4.

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Answer:

To find the percent of a number, we need to divide the number by the total and then multiply by 100%. In this case, we want to find the percent of 10 out of 25, so we need to divide 10 by 25 and then multiply by 100%. This gives us 10/25 * 100% = 40%. Therefore, 10 out of 25 is equal to 40%.

Step-by-step explanation:

The rate of change in elevation of the second scuba diver in feet per minute is; 12.5 ft/minute

We are given that;

The elevation of a certain scuba diver changes by 15⁵/₈ ft every minute.

Now, this rate of change was 1¹/₄ times the rate of change for a second scuba diver.

Thus, if the rate of change of elevation for the second scuba diver is x, then it means that;

15⁵/₈ = 1¹/₄x

Converting the fractions to improper fractions gives us;

125/8 = 5x/4

Thus making x the subject gives us;

x = (125 * 4)/(5 * 8)

x = 12.5 ft/minute

This represents the rate of change in elevation of the second diver.

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Answer:

In the third quadrant, the sine of an angle is negative, so the angle itself must be between 180 and 270 degrees. This means that the cosine of the angle, and therefore the cosine of half the angle, is also negative.

To find the exact value of the cosine of half the angle, we can use the double angle formula for cosine, which states that cos(2A) = 1 - 2sin^2(A). Since the sine of half the angle is sin(B/2) = sqrt((1 - cos(B))/2), we can plug this into the double angle formula to get:

cos(B/2) = sqrt(1 - cos(B))/sqrt(2) = sqrt((1 - (-1/3))/2) = sqrt(4/6)/sqrt(2) = sqrt(2/3)/sqrt(2) = sqrt(1/3)

Therefore, the value of cos(B/2) is sqrt(1/3), which is positive because B/2 is between 0 and 90 degrees. The exact value of the cosine of half the angle B in the third quadrant is sqrt(1/3).

The height and length of the base of A triangular banner which has an area of 351 cm² is l = 13, and h = 11 / 4 respectively.

One of the fundamental shapes in geometry is represented by the symbol Δ and consists of three connected vertices.

Given data:

A triangular banner has an area of, A =  351 cm²

The length of the base is two centimeters longer than four times the height

Write the equation as shown below,

l = 4h + 2

Here, l = base length, and h = height

Calculate the area,

A = 1 / 2 l × h

351 = 1/2 (4h + 2)h   Substitute the value of l

351 = (2h + 1)h

2h² + h = 351

Solve the quadratic equation to get the value of l,

l = 13 so 4h + 2 = 13

so 4h + 2 = 13

4h = 13 -2

h = 11 / 4

Therefore, the height and length of the base of A triangular banner has an area of 351 cm² is l = 13, and h = 11 / 4

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If they were to use the hypothesis testing procedure for this research question, the appropriate test statistic to use is; Z-test

A test statistic is defined as a random variable that is calculated from sample data and thus used in a hypothesis test. You can use test statistics to determine whether to reject the null hypothesis.

Now, there are many different types of tests in statistics such as t-test, Z-test, chi-square test, anova test , binomial test, one sample median test e.t.c.

Now, in this case, a z-test is required because a z-test is used in hypothesis testing to evaluate whether a finding or association is statistically significant or not.

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Length of bike route A is 12(65)=780 and length of bike route B is 65.

Two or more expressions with an Equal sign is called as Equation.

Given that the Bike route A is 12 times as long as bike route B.

Let x be the length of the bike route B.

12x be the  length of the bike route B.

The total length of the bike trails is 845 miles

12x+x=845

13x=845

Divide both sides by 13

x=65

Length of bike route A is 12(65)=780 and length of bike route B is 65.

Hence, Length of bike route A is 12(65)=780 and length of bike route B is 65.

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Answer:

A  -0.16

Step-by-step explanation:

I got it right on edge

Answer: 6

Step-by-step explanation:

14-8=6

x=6

The length of side X in the simplest radical form exists 22/√3.

Trigonometry is the study of angles and the angular connections between figures in two and three dimensions. The trigonometric functions that make up trigonometry are cosecant, cosine, cotangent, secant, sine, and tangent. These are also known as the circle functions.

Trigonometric Identities are equality statements involving trigonometry functions that hold true for all values of the input variables in the equation. The side length and angle of a triangle are both subject to a variety of distinctive trigonometric identities.

The triangle is right angled, therefore we can apply trigonometry :

To obtain the value of X which is the hypotenuse :

Using trigonometric identities,

Cosθ = adjacent / hypotenuse

Substitute the values in the above equation, we get

Cos 30 = 11 / X

√3/2 = 11 / X

simplifying the above equation, we get

√3 / 2 × X = 11

X = 11 ÷ √3 / 2

X = 11 × 2 / √3

X = 22/√3

Therefore, the length of side X in the simplest radical form is 22/√3.

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Answer:

3 terms

Step-by-step explanation:

There are 3 terms: 7y, 4z, and 9. To explain simply, terms are a letter, number, or a group of letters and numbers that are multiplied, but not added or subtracted.

The equation of the line shown is; y= -1/2x+2. Also the graph of line with equation y=1/3x-5 is attached.

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) and has a gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Where x₁ - x coordinate, y₁ - y coordinate

m - slope

Then Slope line with equation y=1/3x-5

m = 1/3

Now Write the equation for the line shown as;

y= -1/2x+2

Slope = -1/2

Hence, the equation of the line would be;

y= -1/2x+2.

Thus the graph of line with equation y=1/3x-5 is attached below.

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Answer:

13n+8

Step-by-step explanation:

8 more = 8+

product of 13 and n= 13n

8more then 13n

Answer:

Step-by-step explanation:

Eight more than the product of 13 and a number = 13n+8

13n+8=0

13n=-8

n=-8/13

9. The dilation of the larger solid figure on the coordinate grid to obtain the dashed figure can be represented by the expression in option C

C. (x, y), (-5/8·x, 5/8·y)

A dilation transformation is one in which the dimensions of the sides of the pre-image are increased (enlarged) or decreased to get the image.

9. The dilation of a function, f(x), by a factor k are; f(k·x), and k·f(x), where;

f(k·x) is an horizontal dilation, and k·f(x) is a vertical dilation

The ordered pair (x, y) which can be expressed as (x, f(x)), where, y = f(x), following a dilation by a factor of k is therefore;

[tex](x, \, y) \overset{D_k}\rightarrow (k\cdot x, \ k\cdot f(x)) = (k\cdot x, \ k\cdot y)[/tex]

The representation of a dilation of a point (x, y), by a factor of k is therefore, obtained by multiplying both the x and y-values by the factor k, as follows;

(x, y)   [tex]\overset{D_x} \rightarrow[/tex]   (k·x, k·y)

Similarly, the representation of the reflection of the point (x, y) across the y-axis is the point (-x, y)

The point (-5.8·x, 5/8·y),m is therefore obtained from the dilation of the point (x, y), by a factor of 5/8, followed by a reflection across the y-axis.

The option that represents the dilation is therefore, option C

C. (x, y), (-5/8·x, 5/8·y)

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The linear equation can be written as:

y = -5*(x + 3) - 4

And its graph can be seen at the end of the answer.

Here we want to graph a line with a slope of -5 that contains the point (-3, -4).

Particularly, for a line with a slope a and a known point (h, k) can be written in the point-slope form as:

y = a*(x - h) + k

So our line can be written as:

y = -5*(x + 3) - 4

Now let's graph it. To graph the line we need to know two points on the line. We already know one that is (-3, -4)

Let's find another, if we evaluate the line in x = 0 we will get:

y = -5*(0 + 3) - 4

y = -5*3 - 4

y = -15 + 4

y = -19

Then the linear equation also contains the point (0, -19), now just let's graph the two known points and connect them with a line. The graph of the g can be seen below.

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Answer: pay 40,000 up front i believe sorry if its wrong

Step-by-step explanation:

A) The population P after t hours as a function of t p(t) = 820 [tex]e^{0.3465t}[/tex]  k = 0.3465 , B)The population after 8 hours of

bacteria is p(8) = 13120 , C) The population to reach 2450, time will be t= 3.15 hour

A linear relationship between two amounts or variables is shown by proportionality. Both quantities increase in size when one doubles, and both decrease in size when one drops to a tenth of its original amount.

It is given that  

dp/dt ∝ p

dp/dt = kp

dp/p = kdt

log p = kt +c

p(t) = c[tex]e^{kt}[/tex]

when t = 0 then p = 820

therefore c = 820

p(t) = c[tex]e^{kt}[/tex]

when t = 2hours then p = 1640

1640 = 820[tex]e^{2k}[/tex]

2k = ln2

k = ln2/2

k = 0.3465

p(t) = 820[tex]e^{0.3465t}[/tex]  bacteria

B)

when t = 8hours

p(8) = 820[tex]e^{0.3465* 8}[/tex]

p(8)= 820*16

p(8) = 13120 bacteria

c)

when p = 2450 then t = ?

2450 = 820[tex]e^{0.3465t}[/tex]

2450/820 = [tex]e^{0.3465t}[/tex]

t =1.0945/0.3465

t= 3.15hours

Thus

A) The population P after t hours as a function of t p(t) = 820 [tex]e^{0.3465t}[/tex]  k = 0.3465 , B)The population after 8 hours of

bacteria is p(8) = 13120 , C) The population to reach 2450, time will be t= 3.15 hour

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