Earthquake intensities are measured using a device called a seismograph, which is designed to be most sensitive to earthquakes with intensities between 4.0 and 9.0 on the Richter scale. Measurements of nine earthquakes are given as follows: 4.5 L 5.5 H 8.7 8.9 6.0 H 5.2 where L indicates that the earthquake had an intensity below 4.0 and an H indicates that the earthquake had an intensity above 9.0. The median earthquake intensity of the sample is a. 5.75 b. 6.00 c. 6.47 d. 8.70

The final image obtained after reflecting the triangle across the y-axis and translating it 5 units down is equivalent to reflecting the original triangle over the x-axis and then translating it 5 units down.

When we reflect the triangle across the y-axis, each point's x-coordinate is negated while the y-coordinate remains unchanged. This reflection essentially flips the triangle horizontally.

After reflecting the triangle, we then translate it 5 units down. This translation involves shifting each point of the triangle downward by 5 units along the y-axis.

Now let's consider the second transformation: reflecting the original triangle over the x-axis and then translating it 5 units down.

Reflecting the triangle over the x-axis means that each point's y-coordinate is negated while the x-coordinate remains unchanged. This reflection flips the triangle vertically.

After reflecting the triangle, we translate it 5 units down, which involves shifting each point of the triangle downward by 5 units along the y-axis.

By comparing the two sequences of transformations, we can see that they result in the same final image. First, we horizontally flip the triangle and then shift it downward, which is equivalent to first vertically flipping the triangle and then shifting it downward.

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Answer:

B. Translate 5 units down, and then reflect over the y-axis.

Step-by-step explanation:

\(\iint_{R} y^{2} d A=\int_{x=-2}^{3} \int_{y=-x-2}^{3 x+6} y^{2} d x d y d x\)

\(\text { (taking Strip as shown). }\)

\(=\int_{-2}^{3}\left(\frac{y^{3}}{3}\right)_{-x-2}^{3 x+6} d x\)

\(=\frac{1}{3} \int_{-2}^{3}(3 x+6)^{3}-(-x-2)^{3} d x\)

\(\begin{gathered}=\frac{1}{3}[4375]=\frac{4375}{3} \\=1458.33\end{gathered}\)

What is integral ?

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Answer:

16.6...

Step-by-step explanation:

A) V = π(6)²(21) is the correct equation to find the volume of the fulgurite in cubic inches. Therefore, the answer is A.

The equation that can be used to find V, the volume of the fulgurite in cubic inches is A) V = π(6)²(21). This is because the volume of a cylinder is given by the formula V = πr²h, where r is the radius of the base and h is the height of the cylinder. Since the diameter of the fulgurite is given as 6 inches, the radius (r) is half of that, which is 3 inches. And since the height is given as 21 inches, we can substitute these values into the formula to get V = π(3)²(21) which simplifies to V = π(9)(21) or V = π(6)²(21). Therefore, the correct answer is A) V = π(6)²(21)

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Complete question:

Fulgurites are pieces of glass in the shape of a cylinder produced when lightning strikes sand. A student found a fulgurite with a height of 21 inches and a diameter of 6 inches.

Which equation can be used to find V, the volume of the fulgurite in cubic inches?

A) V = π(6)²(21)

B) V = π(6)(21)

C) V = π(3)(21)

D) V = π(3)²(21)

If the interest rate is 7%, the present value of her promise today is $24,382.87.

The formula for the present value of an annuity is:PMT × (1 - 1/(1+r)n)/r

Where:PMT = periodic payment (the amount you'll receive each year)

R = interest rate (as a decimal)

n = number of payments (in this case, 20)

The payments are not equal, but each payment is 7% larger than the previous one.

So, we need to calculate the payment for year 1, and then calculate the payments for years 2 through 20 based on that.

The payment for year 1 is $2,000.

The payment for year 2 is 1.07 × $2,000 = $2,140.

The payment for year 3 is 1.07 × $2,140 = $2,299.80.

And so on.

We can simplify this by finding the total growth factor after 20 years:1.07^19 = 4.869

We multiply the payment for year 1 ($2,000) by this growth factor to get the payment for year 20:$2,000 × 4.869 = $9,738.71

Now we can use the formula for the present value of an annuity:

PMT × (1 - 1/(1+r)n)/r$2,000 × (1 - 1/(1+0.07)^20)/0.07 = $24,382.87 (rounded to the nearest cent)

Therefore, the present value of her promise today is $24,382.87.

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To determine the probability that a randomly selected guest is accepted by the host, we need more information about the scenario. For instance, we should know the total number of guests and the number of accepted guests. Let's say there are 'n' guests, and 'a' guests are accepted by the host.
Step 1: Identify the terms.
- n: Total number of guests
- a: Number of accepted guests
Step 2: Calculate the probability.
To find the probability, we'll divide the number of accepted guests (a) by the total number of guests (n). So, the probability is:
P(Accepted) = a / n
Step 3: Identify the type of probability.
In this case, the probability we've calculated is the "marginal probability," as it represents the likelihood of a single event occurring (a guest being accepted) without considering any other factors or events.

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ANSWER

y = 3.5x + 56

EXPLANATION

The slope of a line passing through points (x1, y1) and (x2, y2) is,

And the slope-intercept form of the equation of a line is,

Where m is the slope and b is the y-intercept.

In this problem, we have to use points (5, 73) and (7, 80) to find the equation of the line. First, we can find the slope,

For now, the equation is,

We have to find the y-intercept, by replacing x and y for the coordinates of one of the given points,

And solve for b,

The equation is,

The slope as a decimal is 3.5 and the y-intercept, rounded to the nearest whole number is 56, so the equation is y = 3.5x + 56

Answer:

<BAC = 80

Step-by-step explanation:

All triangle angles equal 180

<BAC = x

x + 50 + 50 = 180

x + 100 = 180

x = 180 - 100

x = 80

Answer:

$3.15

Step-by-step explanation:

Cost of 3 1/2 lb of turkey = $10.50

Cost of 1 lb of turkey = $ (10.50 ÷ 3 1/3) = $(10.50 ÷ 10/3) (∵ 3 1/3 = \(\frac{3*3+1}{3}\) = 10/3)
=> $ (10.50 x 3/10) = $(1.05 * 3) = $ 3.15

Hence the cost for 1 lb of turkey is $3.15.

Hope you understood!!

The solution of the given system of equations is x = -4, y = 5 and z = 2 is the answer.

The system of equations given below:x + 2y + 3z = 11;2x + 4y + 5z = 21;3x + 5y + 6z = 27.

Here, we will solve this system of equations using inverse of the matrix method as follows:

We can write the given system of equations in matrix form as AX = B where, A = [1 2 3; 2 4 5; 3 5 6], X = [x; y; z] and B = [11; 21; 27].

The inverse of matrix A is given by the formula: A-1 = (1/ det(A)) [d11 d12 d13; d21 d22 d23; d31 d32 d33]  where,

d11 = A22A33 – A23A32 = (4 × 6) – (5 × 5) = -1,

d12 = -(A21A33 – A23A31) = -[ (2 × 6) – (5 × 3)] = 3,

d13 = A21A32 – A22A31 = (2 × 5) – (4 × 3) = -2,

d21 = -(A12A33 – A13A32) = -[(2 × 6) – (5 × 3)] = 3,

d22 = A11A33 – A13A31 = (1 × 6) – (3 × 3) = 0,

d23 = -(A11A32 – A12A31) = -[(1 × 5) – (2 × 3)] = 1,

d31 = A12A23 – A13A22 = (2 × 5) – (3 × 4) = -2,

d32 = -(A11A23 – A13A21) = -[(1 × 5) – (3 × 3)] = 4,

d33 = A11A22 – A12A21 = (1 × 4) – (2 × 2) = 0.

We have A-1 = (-1/1) [0 3 -2; 3 0 1; -2 1 0] = [0 -3 2; -3 0 -1; 2 -1 0]

Now, X = A-1 B = [0 -3 2; -3 0 -1; 2 -1 0] [11; 21; 27] = [-4; 5; 2]

Therefore, the solution of the given system of equations is x = -4, y = 5 and z = 2.

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Answer:

5 < L < 18,5

5 < L < 18,52 < W < 5,5

Step-by-step explanation:

longeur = length = L

largeur = width = W

L = 3W +2

12 < 2L+2W < 48

———————————————

12 < 2*(3W+2)+2W < 48

12 < 6W+4 +2W < 48

12 < 8W+4 < 48

8 < 8W < 44

2 < W < 5,5

———————————————

12 < 2L+2W < 48

L = 3W +2

L - 2 = 3W

L/3 -2/3 = W

12 < 2L +2*(L/3 -2/3) < 48

12 < 2L + ⅔L -4/3 < 48

12 < 2⅔L -4/3 < 48

13⅓ < 2⅔L < 49⅓

5 < L < 18,5

hope it helps.

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Answer: 112

Step-by-step explanation:

By the exterior angle theorem, x=57+55 = 112

A checking account is used for daily basis transaction and a debt and is usually associated with it.Saving accounts is just used for saving money.It has a time limit then you can withdraw your money.It is not on daily basis.

A bank account that allow the user to withdraw the money ,pay bill,transfer money to other person or make a purchase anything by writing checks.Check accounts typically don't earn interest.By checking accounts we can easily deposit and withdraw money for daily transaction.

Saving accounts are intended for storing your money which you don't plan to use daily.saving accounts earns interest at your money.saving account is designed for the accumulation of money in a safe place for future use.saving accounts offer easy access to your money in any emergency.so keeping your money in a saving account means that your money is safe for your future use.

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None of the number lines represents the solution of the given inequality as the solution of the inequality is all real numbers less than -7/22 and it does not include the number -7/22.

The visual representation of numbers on a straight line is called a number line. On an endless line that extends on both sides, either horizontally or vertically, this line is used to compare numbers that are spaced at equal intervals.

A number line is an image of numbers plotted on a straight line, either horizontally or vertically. We can compare numbers and execute simple arithmetic operations on them easily by writing the numbers down on a number line. The starting point of a number line is often regarded as zero (0). The numbers to the left of zero are all negative whereas the numbers on the right of zero are all positive.

The given inequality is

1/7m < -1/22

Multiply both sides by 7

7 × 1/7 m< -1/22 × 7

m < -7/22

So, the solution to the inequality is all real numbers less than -7/22.

The graph (A) and (B) cannot be the solution to the inequality as they are going to the right.

Graph (C) also cannot be the solution, although it is going left, the point (-14./11) is closed and it does not belong to the solution of the inequality.

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Step-by-step explanation:

If angle 1 is 121 degrees, then angle 7 is 59 degrees. (same side exterior angles)

If angle 8 is 103 degrees, then angle 4 equals 103 degrees (corresponding angles) and angle 3 is 77 degrees. (to angle 4 supplementary angles)

If angle 5 is 116 degrees, then angle 3 is 64 degrees. (same side interior angles)

Answer:

11: $35

12. $106.8 (This one is the one I'm the most skeptical about)

13. $208.26

14. $109.42

15. $40.25

16. $43.32

Heya! This was a lot for one question, but I went through and attempted to solve them all. My answers could be well off, but I thought it would at least be worth a try. I hope this helps at least a little bit!

let $p$ and $q$ be the two distinct solutions to the equation$$\frac{4x-12}{x^2 2x-15}=x 2.$$if $p > q$. The value of $p - q$ is 4.

To find the value of $p - q$, we first need to solve the given equation and determine the values of $p$ and $q$.

The equation is:

$$\frac{4x-12}{x^2 - 2x - 15} = x^2.$$

Step 1: Factorize the denominator:

The denominator can be factored as $(x - 5)(x + 3)$.

Step 2: Simplify the equation:

$$\frac{4x-12}{(x - 5)(x + 3)} = x^2.$$

Step 3: Multiply both sides of the equation by $(x - 5)(x + 3)$ to eliminate the denominator:

$$(4x - 12) = x^2(x - 5)(x + 3).$$

Step 4: Expand and rearrange the equation:

$$4x - 12 = x^4 - 2x^3 - 15x^2 + 25x.$$

Step 5: Rearrange the equation and combine like terms:

$$x^4 - 2x^3 - 15x^2 + 21x - 12 = 0.$$

Step 6: Factorize the equation:

$$(x - 3)(x + 1)(x - 2)(x + 2) = 0.$$

From this, we get four possible solutions: $x = 3$, $x = -1$, $x = 2$, and $x = -2$.

However, we are interested in the two distinct solutions $p$ and $q$, where $p > q$. Therefore, the values of $p$ and $q$ are $p = 3$ and $q = -1$.

Finally, we can find the value of $p - q$:

$$p - q = 3 - (-1) = 3 + 1 = 4.$$

Hence, the value of $p - q$ is 4.

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Adjacent angles are two angles that lie in the same plane and have a common vertex and a common side but have no common interior points.

The terms adjacent, neighboring, contiguous, and juxtaposed all denote being close by. Although adjacent might indicate a touch or not, it is usually assumed that there is nothing of the same sort in between. a home with a garage close by. Adjoining clearly means coming together and touching at a certain location or line.

When two angles have a similar vertex and side, they are referred to as neighboring angles. The vertex of an angle is the point at which the rays that make up its sides come to a stop. When adjacent angles have the same vertex and side, they might be a complimentary angle or supplemental angle.

Thus, adjacent angles are two angles that lie in the same plane and have a common vertex and a common side but have no common interior points.

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a. Probability of completing the exam in one hour or less is 0.0228. b. Probability of completing the exam in more than 60 minutes but less than 75 minutes is 0.2857. c. About 10 students are expected to be unable to complete the exam in the allotted time.

a. To find the probability of completing the exam in one hour or less, we need to convert one hour (60 minutes) into a z-score using the formula:

z = (x - μ) / σ

where x is the value we want to convert, μ is the mean, and σ is the standard deviation. So, we have:

z = (60 - 80) / 10 = -2

Using a standard normal distribution table or a calculator, we find that the probability of a z-score being less than or equal to -2 is 0.0228 (to 4 decimals). Therefore, the probability of completing the exam in one hour or less is 0.0228.

b. To find the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes, we need to convert both values into z-scores:

z1 = (60 - 80) / 10 = -2

z2 = (75 - 80) / 10 = -0.5

Then, we can find the probability between these two z-scores using a standard normal distribution table or a calculator. The probability is:

P(-2 < z < -0.5) = P(z < -0.5) - P(z < -2)

= 0.3085 - 0.0228

= 0.2857 (to 4 decimals)

Therefore, the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes is 0.2857.

c. We know that the mean time to complete the exam is 80 minutes and the standard deviation is 10 minutes. To find the number of students who will be unable to complete the exam in the allotted time of 90 minutes, we need to find the number of students whose completion time is greater than 90 minutes.

We can convert 90 minutes into a z-score using the formula:

z = (x - μ) / σ = (90 - 80) / 10 = 1

Using a standard normal distribution table or a calculator, we find that the probability of a z-score being greater than 1 is 0.1587.

So, the proportion of students who will be unable to complete the exam in 90 minutes is 0.1587. To find the actual number of students, we can multiply this proportion by the total number of students:

0.1587 x 60 ≈ 9.52

Therefore, we can expect about 10 students to be unable to complete the exam in the allotted time.

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Answer:

-16 < -10

-10 > -16

Step-by-step explanation:

James = -16

Alexis = -10

-16 < -10

This means, James scored less than Alexis at the end of the card game

-10 > -16

This means Alexis scored more than James at the end of the card game

The inequality that compares the points Alexis and James scored could either be any of the following:

-16 < -10

-10 > -16

9514 1404 393

Answer:

  {-1, -3, -7}

Step-by-step explanation:

Dividing the given polynomial by (x+1) yields a quotient of x^2 +10x +21. That factors as (x+3)(x+7), so the three zeros are ...

  x ∈ {-1, -3, -7}

__

The factors of x^2 +10x +21 are found by looking for factors of 21 that have a sum of 10. Those factors are 3 and 7, so the complete factorization of f(x) is ...

  f(x) = (x +1)(x +3)(x +7)

The zeros are the values of x that make these factors be zero. In each case, that x-value is the opposite of the constant in the binomial term.

Answer:

1 1/2

Step-by-step explanation:

Answer:

#6:10

Step-by-step explanation:

Answer:

#9 is x=14

#7 is C 138

#6 is x=10

#5 is p=40

Answer:

\(10cm^2\)

Step-by-step explanation:

We are given that

Two parallel sides of trapezoid are

\(a=1\frac{1}{2}cm=\frac{3}{2}=1.5cm\)

\(b=3\frac{1}{2}=3+0.5=3.5 cm\)

Height of trapezoid, h=4 cm

We have to find the area of the trapezoid.

We know that

Area of trapezoid=\(\frac{1}{2}(a+b)h\)

Where a and b are two parallel sides

h=Height of trapezoid

Using the formula

Area of trapezoid=\(\frac{1}{2}(1.5+3.5)\times 2\)

Area of trapezoid=\(10cm^2\)

The possible error in the volume of the cube is cubic inches.

The edge of a cube with a length of inches and a possible error of % means that the actual length could be within % of the given length. Therefore, the minimum possible length of the edge is inches, and the maximum possible length is inches.

To calculate the possible error in cubic inches in the volume of the cube, we need to use the formula V = e^3, where V is the volume and e is the length of the edge.

Substituting the minimum and maximum values of the edge length, we get the minimum and maximum possible volumes of the cube:

V_min = ( inches)^3 = cubic inches
V_max = ( inches)^3 = cubic inches

The difference between the maximum and minimum volumes is the possible error in cubic inches:

V_error = V_max - V_min = ( inches)^3 - ( inches)^3 = cubic inches

Therefore, the possible error in the volume of the cube is cubic inches. This means that the actual volume of the cube could be within cubic inches of the given volume.    

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The machine discharge more than 7.0 oz or does the difference represent chance variation is 0.0274

What is meant by variation?

In math, variance refers any difference between the individuals in a species or groups of organisms of any species.

Here we have given that a coin-operated soft drink machine was designed to discharge, on average, 7 oz of beverage per cup. in a test of the machine, 10 cupful's of beverage were drawn from the machine and measured. the average and SD of the ten measurements were 7.1 oz and 0.12 oz, respectively. assume that the histogram of beverage discharge from this machine roughly follows a normal curve.

And we need to find machine discharge more than 7.0 oz or does the difference represent chance variation.

By using the Applet, to find the exact p-value we first need to find P(Z≥2.63) where Z is a t9​ random variable.

=> P(Z≥2.63)=0.0137

=> 2×P(Z≥2.63)=0.0274

=> P-value=0.0274

So, the p-value associated with the test is 0.0274

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The interest is %2 of 520 which, if you do the math, is 10.4 cents. You want to find out how much interest it is for 6 years so you have to multiply them.

10.4 x 6 = 62.4

The total interest for 6 years is $62.4

your welcome

Answer:

0,252

Step-by-step explanation:

De la pregunta,

1 minuto = 0.08

3,15 minutos = x

Cruz multiplicar

x = 3,15 × 0,08

x = 0,252

Por tanto, por su última llamada que duró 3,15 minutos, Laura estaría pagando 0,252