20. A pair of standard dice are rolled. What is
the probability that at least one die is a 5,
given that the sum of the numbers on the
dice is at least 8?

Answer: [tex]g(x)=(x+3)^2[/tex]

Step-by-step explanation:

When shifting a function left [tex]3[/tex] units, [tex]f(x) \to f(x+3)[/tex].

Therefore, [tex]g(x)=(x+3)^2[/tex].

Answer: To write the equation in slope-intercept form, we need to isolate the y term on one side of the equation. We can do this by adding 4 to both sides of the equation:

y - 4 + 4 = x - 3 + 4

Combining like terms on each side, we get:

y = x - 3

This is the slope-intercept form of the equation. The slope of the line is 1, and the y-intercept is -3. The slope-intercept form of the equation is y = 1x - 3.

Answer: y = x + 1

Step-by-step explanation:

Write y - 4 =(x-3) in slope-intercept form

This is in Point Slope Form.

y - 4 =(x-3)

We add 4 to both sides

==> y - 4 + 4 = x-3 + 4

==> y = x + 1

This is slope intercept form, since it resembles the equation, y = mx + b, but m equals zero.

Answer: 27

Step-by-step explanation:

You know that the whole shape equals 180. So you add 133+20=153 then subtract that from 180 and that should give you 27.

Hope that helps!

Answer: With a 95 percent confidence interval, you have a 5 percent chance of being wrong. With a 90 percent confidence interval, you have a 10 percent chance of being wrong. A 99 percent confidence interval would be wider than a 95 percent confidence interval (for example, plus or minus 4.5 percent instead of 3.5 percent)

Step-by-step explanation:

Answer:

[tex] \sqrt[3]{z} [/tex]

Step-by-step explanation:

The expression for the final price of a hat would be h(0.775)(0.08875) and the final price of buying four hats after the discount and sales tax would be $142.

Option (C) is correct.

What is a discount?

A discount is a reduction in the price of a product or service. It can be offered for a variety of reasons, such as to encourage customers to make a purchase or to clear inventory. Discounts can be expressed as a percentage off the original price, or as a fixed dollar amount.

Part A: The expression that would calculate the final price of a hat is h(0.775)(1.08875). This takes into account the 22.5% discount by multiplying the original price by 0.775, and then adds the 8.875% sales tax by multiplying the discounted price by 1.08875.

Part B: If the original price of a hat is $42, then the final price of buying four hats after the discount and sales tax would be $42 x 4 x 0.775 x 1.08875 = $142.

Hence, the expression for the final price of a hat would be h(0.775)(0.08875) and the final price of buying four hats after the discount and sales tax would be $142.

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Answer:

12.1 cm (nearest tenth)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Sine Rule} \\\\\\$\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c} $\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}[/tex]

From inspection of the given triangle:

Substitute the values into the sine rule to find the measure of angle C:

[tex]\implies \dfrac{\sin A}{a}=\dfrac{\sin C}{c}[/tex]

[tex]\implies \dfrac{\sin 81^{\circ}}{13.5}=\dfrac{\sin C}{8.2}[/tex]

[tex]\implies \sin C=\dfrac{8.2\sin 81^{\circ}}{13.5}[/tex]

[tex]\implies C=\sin ^{-1} \left(\dfrac{8.2\sin 81^{\circ}}{13.5}\right)[/tex]

[tex]\implies C=36.86482816..^{\circ}[/tex]

Interior angles of a triangle sum to 180°.

[tex]\implies A+B+C=180^{\circ}[/tex]

[tex]\implies 81^{\circ}+B+36.86482816...^{\circ}=180^{\circ}[/tex]

[tex]\implies B=62.13517184...^{\circ}[/tex]

Substitute the found value of angle B into the sine rule and solve for b:

[tex]\implies \dfrac{\sin A}{a}=\dfrac{\sin B}{b}[/tex]

[tex]\implies \dfrac{\sin 81^{\circ}}{13.5}=\dfrac{\sin 62.13517184...^{\circ}}{b}[/tex]

[tex]\implies b=\dfrac{13.5\sin 62.13517184...^{\circ}}{\sin 81^{\circ}}[/tex]

[tex]\implies b=12.08347925...[/tex]

Therefore, the measure of b is 12.1 cm (nearest tenth).

On solving the question, The possible combinations when choosing two letters randomly are: T-I, T-M, T-E, I-T, I-M, I-E, E-T, E-M, E-I, M-I, M-T, M-E.

When the order of selection is irrelevant, the mathematical operation of combining counts the number of possible configurations for a set of elements.

[tex]Letters are given as - T I M E[/tex]

Given that there is no alternative for the choice, we have the following number of possibilities:

[tex]= > n = 4^2\\[/tex]

here -

4 =the number of letters

2 =the number of selection

so, n= 16

The choices are then shown as follows:

TI, TM, TE

IT, IM, IE

MT, MI, ME

ET, EI, ET

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The line segment will be needed to create step 4 is 30. Hence option D is the correct option.

What is line segment?

Line segment is line whose distance fixed. There are two fixed end points. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction.

The number of line segment in step 1 is 2.

The number of line segment in step 2 is 6.

The number of line segment in step 3 is 14.

Now finding the pattern:

Step 2: 6 = 2 × 2 + 2

Step 3: 14 = 6 × 2 + 2

The number of line segment is equal to 2 more than 2 times the number of line segment of previous step.

According to this pattern,

step 4: 14 × 2 + 2 = 30

The number of line segment is 30.

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Answer: To determine which expression is equivalent to the one Shea wrote, we can first evaluate the expression 5(y + 2) + 4. The parentheses indicate that we should first perform the operation inside the parentheses, which is to add 2 to y. This results in 5(y + 2) = 5y + 10.

We can then add 4 to both sides of the equation to get 5y + 10 + 4 = 5y + 14. This expression is equivalent to the one Shea wrote, 5(y + 2) + 4.

Therefore, the expression that is equivalent to the one Shea wrote is 5y + 14.

15,386 ft² an area of helicopter pad covers .

What does a circle's area mean?

The area a circle occupies in a two-dimensional plane is known as the area of the circle. It can be simply calculated using the formula A = r2, (Pi r-squared), where r is the circle's radius.

                          Area is measured in square units, such as m2, cm2, etc. Where = 22/7 or 3.14, the area of a circle is equal to r2 or d2/4, in square units.

D = 140

r = 140/2 = 70

area of helicopter = πr²

                              = 3.14 ×70 × 70

                              = 15,386 ft²

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The average rate of change of the enrollment during this time period is increasing with 48 students/year.

What is rate of change?

In 2001, there were 940 students.

In 2009, there were 1324 students.

Represent year with y and students with x.

Average rate of change = (x₂ - x₁) / (y₂ - y₁)

= (1324 - 940) / (2009 - 2001)

= 384/ 8

= 48

Average rate of change = 48 students/year

Hence, the average rate of change of the enrollment during this time period is increasing with 48 students/year.

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1: 17/4 or 4.25

2: 375/35 or 10.63          

3: 146/15 or 9.73        

4: 22/3 or 7.3

5: 265/24 or 11.04

Step-by-step explanation:

The square root of 25 is 5. It is the positive solution of the equation x2 = 25. The number 25 is a perfect square.

Answer:

Yeah, √(25) is 5.

Step-by-step explanation:

Given problem,

→ √(25) = 5

Checking the equation,

→ √(25) = 5

→ 25 = (5)²

→ 25 = 25

→ LHS = RHS

Thus, equation is proved.

The vote received by the candidate if he receives 45 % of the votes and a total of 440 votes were cast is 198.

A percentage, often known as percent, is a division by 100. Percentage, which means "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of a whole in terms of 100 is what percentage calculation is.

Given:

The Total vote of the election = 440,

The vote received by one candidate = 45 % of total votes,

Solve the expression as given below,

The vote received by one candidate = 45 % of 440

The vote received by one candidate = 45 / 100 × 440

The vote received by one candidate = 0.45 × 440

The vote received by one candidate = 198

Therefore, the vote received by the candidate if he receives 45 % of the votes and a total of 440 votes were cast, is 198.

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The equation that represents circles that have a diameter of 12 units and a center that lies on the y-axis is x²+ (y-3)² = 36

The standard form for finding the equation of a circle is expressed as;

[tex](x-a)^{2} + (y-b)^{2} = b = r^{2}[/tex]

where;

(a, b) is the center of the circle

r is the radius of the circle

Given the following

diameter = 12 units

radius = 12/2 = 6 units

If the centre lies on the y-axis, the center will be at (0, 3).

Substituting into the formula, we will have[tex](x-0)^{2} + (y-3)^{2} = (6)^{2}[/tex]equivalent to x²+ (y-3)² = 36

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A line's equation can be written as y = mx + b, y = ax + b, or y = a + bx. As may be seen, the equation for the regression line is similar as true slope.

Understanding the distinction between negative, positive, zero, and undefinable slopes is crucial.

As a result, the rather perplexing term "no slope" is also frequently used in this context.

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The statement "In a normal distribution, the z-score for the mean is 0" is true. A z-score describes how many standard deviations a data item in a normal distribution lies above or below the mean. Since the mean of a normal distribution is defined as the value at which the distribution is centered, a data item with a value equal to the mean will have a z-score of 0.

Therefore, the correct answer is option A: "The statement is true because a z-score describes how many standard deviations a data item in a normal distribution lies above or below the mean." Option B, C, and D are all false because they do not accurately describe the relationship between z-scores and the mean in a normal distribution.

Answer: 2.5 inch

Step-by-step explanation:

The 90% C.I. is more precise in estimating a mean than the 95% C.I.

What does confidence interval mean?

Your estimate's mean plus and minus the range of that estimate's fluctuation is called a confidence interval.

                        If you repeat your test, you can expect your estimate to fall between these numbers with a reasonable degree of certainty. In statistics, confidence is another word for probability.

What does the term "confidence interval" mean?

A claim of 95% confidence in statistics essentially means that the researcher has observed one conceivable interval out of many possible ones, and that 19 out of 20 of those intervals contain the correct value of the parameter.

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54899.91 is the salary level that divides the teachers into one group that gets a raise and one that doesn't. Using the concept of probability -

Probability is a mathematical discipline that concerns with numerical figures of how probable an occurrence is to occur or how probably a statement is to be true. A number between 0 and 1 is the probability of an occurrence, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Given that,

the salary of teachers in a particular school district is normally distributed with a mean of 50000.

standard deviation of 2500

2.5% of the salaries would not get a raise

P (X > x) = 0.025

or, P {( X - 50000)/2500} ≤ {x - 50000/2500} = 0.975

or, P (Z ≤ ( x - 50000)/2500) = 0.975

or, Φ ((x - 50000)/2500) = 0.975

or, (x - 50000)/2500 = Φ⁻¹ (0.975)

or, (x - 50000)/2500) = 1.959964

or, x = 50000 + (1.959964 × 2500)

or, x = 54899.909961

or, x = 54899.91

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Note that:

Recall that we are given the following:

To determine the number of packages Rita started with, we must resolve:

(Number of saplings planted by Rita + Number of saplings left)/Number of saplings per package

that is:
x = (15 + 20)/5

x = 35/5

x = 7

Thus, when she started, she actually had 7 packages. By the time she was done, she had 4.

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Answer:

GE is congruent to GE

Step-by-step explanation:

This is true because both triangles use this same line, so it is referred to as the reflexive property.

Answer:

False, a transformation is the one that stretches or compresses the graph. A translation just shifts the graph up, down, left, or right.

Answer: False

Step-by-step explanation:

A translation is just moving the graph up, down, left, and right! It doesn't make a graph bigger or smaller, so this is a False

Answer:

d=12 and the remainder is -42

Step-by-step explanation:

a.

put x=1 into f(x)

6(1)³-7(1)²-11(1)+d=0

6-7-11+d=0

-12+d=0

d=12

b.

Put x=-2 into the polynomial

6(-2)³-7(-2)²-11(-2)+12

6(-8)-7(4)+22+12

-48-28+22+12

-42

6000 dollars at 5% compounded daily for 3 years will amount to $6,970.93.

Compound interest is the interest you earn on interest.  In other words, compound interest is the interest calculated on the principal and the interest accumulated over the previous period.

Compound interest formula can be use to find the amount of the money after 3 years.

Using the compound interest formula,

[tex]A = p(1 + \frac{r}{n} )^{nt}[/tex]

where

Therefore,

p = 6000 dollars

rate = 5% = 0.05

n = 365

t = 3

Hence,

[tex]A = 6000(1+\frac{0.05}{365} )^{(365)(3)}[/tex]

A = 6,000.00(1 + 0.00013698630136986)¹⁰⁹⁵

Therefore,

A = $6,970.93

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Answer:

10 should be the correct answer

Step-by-step explanation:

im sooooo sorry if its wrong :|

Answer:  y= 93

Step-by-step explanation:

10y + 21 = 951

10y = 930

y= 93