How many pennies could you have if:
When you break the pennies into groups of 2, you have 1 penny left over AND when you break the pennies into groups of 3, you have 1 penny left over?

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2-19-21

To find the probability P(X ≤ \(X_{max\)), we need to find the cumulative probability corresponding to the calculated z-score using a standard normal distribution table or a calculator.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.

To find the probability that a randomly selected examinee will complete the exam on time, we need to calculate the z-score and then use the standard normal distribution.

Given:

Mean time per question (μ) = minutes

Standard deviation (σ) = minutes

Time allowed for the exam (X) = minutes

We want to find P(X ≤ \(X_{max\)), where \(X_{max\) is the maximum time allowed for the exam. Let's assume the maximum time allowed is \(T_{max\).

To calculate the z-score, we use the formula:

z = (X - μ) / σ

z = (\(T_{max\) - μ) / σ

The z-score tells us how many standard deviations an observation is from the mean.

To find the probability P(X ≤ \(X_{max\)), we can use a standard normal distribution table or a calculator to find the cumulative probability associated with the calculated z-score.

Now, let's calculate the z-score using the given values:

z = (\(T_{max\) - μ) / σ

z = (\(T_{max\) - minutes) / minutes

To find the probability P(X ≤ \(X_{max\)), we need to find the cumulative probability corresponding to the calculated z-score using a standard normal distribution table or a calculator.

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The required statement that is NOT true is option B: P(greater than 8) = 20%.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

here,
The number tile set is {3, 4, 1, 6, 8}.

A. P(greater than 8) = 0%: This statement is true because the largest number in the set is 8, so it's not possible to draw a number greater than 8 from this set.

B. P(greater than 8) = 20%: This statement is not true because as explained above, it's not possible to draw a number greater than 8 from this set, so the probability is 0%.

C. P(less than 9) = 100%: This statement is true because all the numbers in the set are less than 9, so it's guaranteed that any number drawn from this set will be less than 9.

D. P(less than 1) = 0%: This statement is true because none of the numbers in the set are less than 1, so it's not possible to draw a number less than 1 from this set.

Therefore, the statement that is NOT true is option B: P(greater than 8) = 20%.

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The  vertices of the rotation of 180⁰  are P'(2, 2), Q'(-1, 2), R'(-2, 4) and S'(3, 4)

The angle of rotation is a measurement of the amount, of namely angle, that a figure is rotated about a fixed point, often the center of a circle

When we rotate a figure of 180 degrees about the origin either in the clockwise or counterclockwise direction, each point of the given figure has to be changed from (x, y) to (-x, -y) and graph the rotated figure.

Before Rotation                                 After Rotation

(x, y)                                                          (-x, -y)                            

Let P(-2, -2), Q(1, -2), R(2, -4) and S(-3, -4) be the vertices of a four sided closed figure. If this figure is rotated 180° about the origin, find the vertices of the rotated figure and graph.

Here, the given is rotated 180° about the origin. So, the rule that we have to apply here is

(x, y) ----> (-x, -y)

Based on the rule, we have to find the vertices of the rotated figure.

Also, (x, y) ----> (-x, -y)

P(-2, -2) ----> P'(2, 2)

Q(1, -2) ----> Q'(-1, 2)

R(2, -4) ----> R'(-2, 4)

S(-3, -4) ----> S'(3, 4)

There, the vertices of the rotated figure are

P'(2, 2), Q'(-1, 2), R'(-2, 4) and S'(3, 4)

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Complete question:

Let P(-2, -2), Q(1, -2), R(2, -4) and S(-3, -4) be the vertices of a four sided closed figure. If this figure is rotated 180° about the origin, find the vertices of the rotated figure and graph.

Answer:

-1/5

Step-by-step explanation:

\(\frac{2}{3}+\frac{-13}{15} \\=\frac{10}{15} +\frac{-13}{15}\\ =\frac{-3}{15} \\=\frac{-1}{5}\)

Answer:

-2

Step-by-step explanation:

\(\frac{-7-5}{3-(-3)}= \frac{-7+-5}{3+3} =\frac{-12}{6} =-2\)

Answer:

12/-6 or -2

Step-by-step explanation:

-3-3= -6 (run)

5-(-7)= 12(rise)          

        12/-6 rise over run

Step-by-step explanation:

Let Matthew be x years old now. April is thus x-6 years old now.

Next year, Matthew will be x+1 years old and April will be x-5 years old.

x+1 = 2(x-5)

x+1 = 2x - 10

x=11

Thus Matthew is 11 while April is 5.

Answer:

-4y-7

Step-by-step explanation:

you combine -4 and -3 to get -7

Answer:B

Step-by-step explanation:

4 miles = 30 minutes

8 miles = 1 hour

24 miles = 3 hours

c) The solutions to the equation (3 / x²) - 12 = 0 are

x = 1/6 and

x = -1/6.

d) The solutions to the equation (5 / (x+5)) - (4 / (x² + 2x)) = (6 / (x² + 7x + 10)) are x = 40 and

x = -1.

c) To solve the rational equation (3 / x²) - 12 = 0:

Step 1: Add 12 to both sides of the equation:

(3 / x²) = 12

Step 2: Take the reciprocal of both sides:

x² / 3 = 1 / 12

Step 3: Multiply both sides by 3:

x² = 1 / (12 * 3)

x² = 1 / 36

Step 4: Take the square root of both sides:

x = ± √(1 / 36)

x = ± (1 / 6)

Therefore, the solutions to the equation (3 / x²) - 12 = 0 are x = 1/6 and

x = -1/6.

d) To solve the rational equation (5 / (x+5)) - (4 / (x² + 2x)) = (6 / (x² + 7x + 10)):

Step 1: Simplify the denominators:

(5 / (x+5)) - (4 / x(x + 2)) = (6 / (x + 2)(x + 5))

Step 2: Find a common denominator, which is (x + 2)(x + 5)(x):

(5(x)(x + 2) - 4(x + 2)(x + 5)) / (x(x + 2)(x + 5)) = (6 / (x + 2)(x + 5))

Step 3: Simplify the numerator:

(5x² + 10x - 4x² - 36x - 40) / (x(x + 2)(x + 5)) = (6 / (x + 2)(x + 5))

Simplifying further:

(x² - 26x - 40) / (x(x + 2)(x + 5)) = (6 / (x + 2)(x + 5))

Step 4: Multiply both sides by (x + 2)(x + 5) to eliminate the denominators:

(x² - 26x - 40) = 6x

Step 5: Rearrange the equation to bring all terms to one side:

x² - 26x - 6x - 40 = 0

x² - 32x - 40 = 0

Step 6: Factorize the quadratic equation or use the quadratic formula to solve for x:

(x - 40)(x + 1) = 0

Setting each factor equal to zero:

x - 40 = 0 or

x + 1 = 0

Solving for x:

x = 40 or

x = -1

Therefore, the solutions to the equation (5 / (x+5)) - (4 / (x² + 2x)) = (6 / (x² + 7x + 10)) are x = 40 and x

= -1.

c) The solutions to the equation (3 / x²) - 12 = 0 are

x = 1/6 and

x = -1/6.

d) The solutions to the equation (5 / (x+5)) - (4 / (x² + 2x)) = (6 / (x² + 7x + 10)) are x = 40 and

x = -1.

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The convergence radius (R) of a power series is the distance from the origin within which the series converges.

It is calculated as the reciprocal of the absolute value of the largest coefficient of the terms in the series. Mathematically, the formula for the convergence radius is expressed as

R = 1/|a_n|

where a_n is the largest coefficient of the terms in the series.

For example, consider a power series a_0 + a_1x + a_2x^2 + ... + a_nx^n. The convergence radius is calculated by taking the absolute value of the largest coefficient a_n and then taking the reciprocal of it. Hence, the convergence radius (R) can be calculated as

R = 1/|a_n|

This means that if the absolute value of the largest coefficient is greater than 1, the series will not converge. If it is equal to 1, the series will converge at the origin, and if it is less than 1, the series will converge within the radius.

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a. Proportions in both the left-hand and right-hand tails tend to be relatively small.

The correct answer is: a. Proportions in both the left-hand and right-hand tails tend to be relatively small. This is because a normal distribution is symmetric and bell-shaped, with the majority of the data concentrated around the mean. As a result, the tails of the distribution have fewer data points and smaller proportions compared to the center. This is because a normal distribution is symmetric and bell-shaped, with the majority of the data concentrated around the mean.

So, a. Proportions in both the left-hand and right-hand tails tend to be relatively small.

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The ratio of the weight of a semi-truck trailer tire compared to the weight of a mobile home will be 51: 52.

The utilization of two or more additional numbers that compares is known as the ratio.

The weight of the semi-truck trailer tire is 102 pounds.

The weight of the mobile home is 104 pounds.

The ratio of the weight of a semi-truck trailer tire to a mobile home is given as.

Ratio = 102 / 104

Ratio = 51 / 52

Ratio = 51: 52

The ratio of the weight of a semi-truck trailer tire to a mobile home will be 51: 52.

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Answer:

The anwser is 10

Step-by-step explanation:

Its not very hard just hold up 8 fingers then add 2 more

im and very sorry if i didn't understand the question its my first time using this app

3.

3+-2-15.25

1−15.25

-14.25

4. 3*8=24

Multiplying a positive and negative makes a negative, so -3*8=-24.

5. Two negatives make a positive, so -12*-8=96

So, Bob is 12 years old and his father is 36 years old solved by using the substitution method.

To determine the ages of Bob and his father, let's use the given information and set up two equations.

Let Bob's age be represented as B and his father's age as F. The terms provided are:

1. Bob's father is three times as old as he is: F = 3B
2. Four years ago, Bob's father was four times as old as he is: F - 4 = 4(B - 4)

Now, we can solve these equations simultaneously. Substituting the first equation into the second equation, we get:

3B - 4 = 4(B - 4)

Simplify the equation:

3B - 4 = 4B - 16

Add 4 to both sides:

3B = 4B - 12

Subtract 4B from both sides:

-B = -12

Finally, divide by -1:

B = 12

Now that we know Bob's age, we can find his father's age using the first equation:

F = 3B
F = 3(12)
F = 36

So, Bob is 12 years old and his father is 36 years old.

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Answer:

0.31x + 2.4 + 3.4p

Step-by-step explanation:

combine like terms

a)  lim (8 - 7)/(1 - sin 0) = 1/0, which is undefined. b) we have lim [(1/x) * tan (7x/2) + (7/2) * ln x * sec² (7x/2)]. c) we find lim [3cos 0] = 3.

To find the limits and apply L'Hôpital's Rule where appropriate, we will analyze each given limit and determine if the conditions for applying L'Hôpital's Rule are met. Then, we will proceed with the steps to evaluate each limit.

a) lim (8 - 7)/(1 - sin x)

We can directly evaluate this limit as it is a simple algebraic expression. Substituting x = 0, we get lim (8 - 7)/(1 - sin 0) = 1/0, which is undefined.

b) lim (ln x * tan (7x/2))/(x - 1)

To apply L'Hôpital's Rule, we check if the limit is of the form 0/0 or ∞/∞. Differentiating the numerator and denominator, we get lim [(1/x) * tan (7x/2) + ln x * (7/2) * sec² (7x/2)]/(1). Simplifying, we have lim [(1/x) * tan (7x/2) + (7/2) * ln x * sec² (7x/2)].

c) lim (1 + sin 3x)/x

Again, to apply L'Hôpital's Rule, we check if the limit is of the form 0/0 or ∞/∞. Differentiating the numerator and denominator, we get lim [3cos 3x]/1. Evaluating this limit as x approaches 0, we find lim [3cos 0] = 3.

Note: The limit in part (a) is undefined, while the limits in parts (b) and (c) evaluate to specific values without requiring the application of L'Hôpital's Rule.

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13 and 13√2 is the value of x and y in the given diagram

The given diagram is a right triangle, we need to determine the value of x and y.

Using the trigonometry identity

tan45 = opposite/adjacent
tan45 = x/13

x = 13tan45
x = 13(1)
x = 13

For the value of y

sin45 = x/y

sin45 = 13/y
y = 13/sin45

y = 13√2
Hence the exact value of x and y from the figure is 13 and 13√2 respectively.

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Answer:

(0,7)

Step-by-step explanation:

The HRT (Hydraulic Retention Time) of an aeration tank with a volume of 425,000 gallons (1,609,000 liters) and an influent rate of 850,000 gallons (3,218,000 liters) is 0.5 hours.

To calculate the HRT, follow these steps:

1. Identify the tank volume: 425,000 gallons (1,609,000 liters).

2. Identify the influent rate: 850,000 gallons (3,218,000 liters) per day.

3. Convert the influent rate to an hourly rate by dividing by 24 hours: (850,000 gallons / 24) = 35,416.67 gallons per hour (145,750 liters per hour).

4. Calculate the HRT by dividing the tank volume by the hourly influent rate: (425,000 gallons / 35,416.67 gallons per hour) = 0.5 hours (1,609,000 liters / 145,750 liters per hour = 0.5 hours).

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Answer:

victor solved the equation correctly because you have to isolate the x and in order to do that you have to divide both sides by 5

Answer:

(r+s)÷3

Step-by-step explanation:

the sum of r and s - r+s

the quotient- ÷

by 3

Answer with step-by-step explanation:

f(x)=3x^2+17x+10

For a polynomial of the form ax^2+bx+c, rewrite the middle term as a sum of two terms whose product is a · c = 3 · 10 = 30 and whose sum is b=17.

f(x)=3x^2+2x+15x+10

Factor out the greatest common factor from each group.

f(x)=x(3x+2)+5(3x+2)

Factor the polynomial by factoring out the gcf, 3x+2

f(x)=(3x+2)(x+5)

Answer:

Step-by-step explanation:"To solve this equation, you can start by distributing the 0.20 and 0.30 terms. Then, you can simplify the equation by combining like terms. After that, you can isolate the variable Z on one side of the equation by adding or subtracting terms from both sides. Finally, you can solve for Z. The solution is Z = 1000. Does that help?"

a² + b² = c² is true for the first triangle but false for the second triangle.

In Mathematics and Geometry, Pythagorean's theorem is modeled or represented by the following mathematical equation (formula):

a² + b² = c²

Where:

a, b, and c represents the length of sides or side lengths of any right-angled triangle.

By substituting the given parameters into the formula for Pythagorean's theorem, we have the following;

a² + b² = c²

4² + 2² = c²

c² = 16 + 4

c = √20 or 2√5 units.

a² + b² = c²

5² + 2² = (√45)²

45 = 25 + 9

45 = 34 (False).

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First, we need to convert the mean from hours to minutes, which is 10 * 60 = 600 minutes.

The exponential distribution is given by the formula:

$P(X > x) = e^{-\lambda x}$

where $\lambda$ is the rate parameter, which is equal to 1/mean for an exponential distribution.

Thus, for this problem, we have:

$\lambda = 1/600$

We want to find the probability that the next customer will take more than 5 minutes, or in other words, $P(X > 5)$.

$P(X > 5) = e^{-\lambda \cdot 5} = e^{-(1/600) \cdot 5} \approx 0.991$

Therefore, the probability that the next customer will take more than 5 minutes is approximately 0.991.

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