#1) A scuba diver ascended at a rate of 8ft per second for one minute. What was the elevation over that period of time

#2) A gopher dug a burrow 6ft below ground. He came up 2ft to find food, then dug back down another 8ft. How many feet below ground is he?

Answer:

f(x) = (x - 3)^2 + 2

Step-by-step explanation:

The function with a graph that has a vertex 5 units horizontally to the right of the vertex of the graph of g(x) = (x + 2)^2 + 2 is f(x) = (x - 3)^2 + 2, which can be obtained by subtracting 5 from x + 2 to get x - 3 inside the parentheses of (x - 3)^2 and translating the vertex horizontally to (3, 2).

What the polynomial said when it sat down for dinner is "I've got a lot of roots" (sounds like "I've got a lot of fruits") as a polynomial equation can have multiple roots.

Polynomial equations are equations in which the variables and coefficients are combined using the mathematical operations of addition, subtraction, and multiplication, but not division by a variable.

The degree of a polynomial equation is determined by the highest power of the variable in the equation.

Polynomial equations can have one or more variables and are often used in mathematical modeling to represent real-world phenomena. The solutions to polynomial equations can be found by factoring, using the quadratic formula, or using numerical methods.

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The answer is (D) 5/10.

what is data?

Data refers to any set of observations, measurements, or facts that can be collected, analyzed, and interpreted to gain insights or knowledge about a particular subject or phenomenon. It can be in the form of numbers, text, images, audio, or any other type of information that can be recorded.

To create a line plot, we need to represent each value in the data set with a point on a number line and then connect the points with a line. Here is the line plot for the given data:

 4|              ●

 3|        ●     ●

 2|  ●     ●     ●

 1|  ●  ●  ●  ●  ●

  +-----------------

     1  2  3  4  5  6

Part A:

From the line plot, we can see that the greatest amount of rainfall in a month is 4 inches, and the least amount of rainfall is 1 inch. Therefore, the difference between the greatest and least amounts of rainfall in a month is:

4 - 1 = 3 inches

The answer is not given as one of the options provided.

Part B:

To determine the fraction of the 10 months that had more than 2 inches of rainfall, we count the number of months that had more than 2 inches and divide by the total number of months:

There are 6 months with more than 2 inches of rainfall: 1st, 2nd, 3rd, 7th, 8th, and 10th.

So, the fraction of the 10 months with more than 2 inches of rainfall is:

6/10 = 3/5

Therefore, the answer is (D) 5/10.

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Answer:

$701.20

Step-by-step explanation:

1.  If she earns $6 per hour and worked 79 hours, how much, in the form of pay, did she earn?

2.  If she sold $2292 in merchandise, she receives 10% of that as a bonus.  How much is this bonus?

3.  Add the results of (1) and (2) together.  The result will be her total earnings.

The area of the base of the prism is 6 cm².

To find the area of the base of the trapezoid-based right prism, we need to use the given information about the volume, height of the prism, larger base, and one slanted side of the trapezoid.
Step 1: We know the volume (V) of the prism is 30 cm³ and the height (h) of the prism is 5 cm.

We can use the formula for the volume of a prism:
V = Area of base × h
Step 2: Plug in the values:
30 cm³ = Area of base × 5 cm
Step 3: Solve for the Area of the base:
Area of base = 30 cm³ / 5 cm = 6 cm²

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Answer:

the answer is C

Step-by-step explanation:

Answer:

area: 100km

Explanation:

Answer:

Step-by-step explanation:

S(square) = Area, if it's true ===> 10km * 10 km = 100 km^2
Because u need just (10km)^2

Answer:

Add −40 and 18 to get −22.

−12−(−22)

The opposite of −22 is 22. (because of the two negatives it makes a positive)

−12+22

Add −12 and 22 to get 10.

Step-by-step explanation:

Considering the definition of an inequality, an inequality that represent the possible values for the number of hotdogs purchased and the number of drinks purchased is [tex]\bold{4.50h + 3d \leq 70}[/tex].

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

An inequality contains one or more unknown values, in addition to certain known data.

In this case, you know that:

Each hotdog costs $4.50 and each drink costs $3.

Mamadou has a total of $70 to spend on hotdogs and drinks.

Being:

the inequality that expresses the previous relationship is

[tex]\bold{4.50h + 3d \leq 70}[/tex]

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The inequality that represents the possible values for the number of hotdogs and drinks purchased is 4.50ℎ + 3d ≤ 70.

To write an inequality that represents the possible values for the number of hotdogs purchased, ℎ h, and the number of drinks purchased, �, we can use the following equation:

4.50ℎ + 3d ≤ 70

This inequality states that the sum of the cost of the hotdogs (4.50 multiplied by the number of hotdogs) and the cost of the drinks (3 multiplied by the number of drinks) should be less than or equal to 70, which is the total amount of money Mamadou has to spend.

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Answer:

So, the correct answer is (30.104, 32.896).

Step-by-step explanation:

To find the 95% confidence interval for the mean number of pounds of trash per person per week, we can use the following formula:

CI = X + Zα/2 * (σ/√n)

σ = population standard deviation = 7.8 pounds

n = sample size = 120

Plugging in the values, we get:

CI = 31.5 ± 1.96 \times(7.8/√120)

CI = 31.5 ± 1.96 \times 0.711

CI = 31.5 ± 1.39

Therefore, the 95% confidence interval for the mean number of pounds of trash per person per week is (30.11, 32.89).

So, the correct answer is (30.104, 32.896).

Answer:

To calculate the annual property tax on the Kreiner family house, we can use the formula:

annual property tax = assessed value x annual tax rate

where the annual tax rate is given as a percentage. We first need to convert the tax rate from a percentage to a decimal:

2.66% = 0.0266

Then, we can plug in the given values and calculate:

annual property tax = 457,000 x 0.0266

annual property tax = 12,157.80

Therefore, the annual property tax on the Kreiner family house is $12,157.80.

Hope This Helps!

The sample size necessary such that the margin of error of the estimate for a 90% confidence interval for the mean age of all residents is at most 3.4 years is 59.56.

What is a confidence interval?

An estimated range for an unknown parameter is known as a confidence interval. The 95% confidence level is the most popular, however other levels, such as 90% or 99%, are occasionally used when computing confidence intervals.

Here, we have

Given: A city official would like to estimate the mean age of all residents of Stuart. The standard deviation of the ages of all residents of Stuart is known to be 16 years.

σ = 16 ..Population SD

The margin of error, E = 3.4

c = 90% = 0.90 ...confidence level

a = 1 - c = 1 - 0.90 = 0.1

a/2 = 0.1/2 = 0.05

Using the Z table,

z = 1.64

Now, sample size (n) is given by,

= (za/E)²

= (1.64×16/3.4)²

=59.56

Hence, the sample size necessary such that the margin of error of the estimate for a 90% confidence interval for the mean age of all residents is at most 3.4 years is 59.56.

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the answers would be x = 1 and x = -2/3.

The graph of a simpler function, in this case, e-x, allows us to visualize how changes to the function, such as translations and reflections, impact the graph.

The graph of f(x) = e-x + 5 is a sequence of translations and reflections of the graph of a simpler function, namely the graph of f(x) = e-x. To understand this, let's first consider the graph of e-x. This is an exponential function that starts at 1 when x=0 and approaches zero as x goes to infinity. The graph is always decreasing and asymptotic to the x-axis.

Now, when we add 5 to e-x, we shift the entire graph upward by 5 units. This is a translation of the graph. Next, we take the negative of e-x, which reflects the graph across the x-axis. This gives us a decreasing function that starts at 6 (since e0 = 1) and approaches 5 as x goes to infinity.

So, the graph of f(x) = e-x + 5 is a translation of the graph of e-x by 5 units upward, followed by a reflection across the x-axis. This sequence of translations and reflections results in a decreasing function that starts at 6 and approaches 5.

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The true standard deviation of nicotine in menthol cigarettes is believed to be between 0.044 and 0.102 mg, with a 98% confidence level.

To find the number of degrees of freedom for the confidence interval estimate of sigma, we need to use the formula:

df = n - 1

where n is the sample size. In this case, n = 25, so:

df = 25 - 1 = 24

Next, we need to find the critical values x2/L and x2/R using a chi-square distribution table or calculator. For a 98% confidence interval and 24 degrees of freedom, the critical values are:

x2/L = 10.643

x2/R = 41.337

Finally, we can use the formula for the confidence interval estimate of sigma:              

s/√(x2/R) < σ < s/√(x2/L)

Plugging in the values we have, we get:

0.27/√(41.337) < σ < 0.27/√(10.643)

0.044 < σ < 0.102

Therefore, we can say with 98% confidence that the true standard deviation of nicotine in menthol cigarettes is between 0.044 and 0.102 mg.

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A. For any number of monthly calls "x" greater than 200, Plan 1 is more economical than Plan 2.

The answer to part a means that if a customer expects to make more than 200 local calls per month, it is more economical for them to choose Plan 1 over Plan 2. For example, if a customer makes 250 local calls per month, Plan 1 would cost $28 while Plan 2 would cost $20 ($12 + $0.08 x 250), so Plan 1 would be the better choice for them. However, if a customer expects to make fewer than 200 local calls per month, then Plan 2 would be more economical for them, as they would pay less than $28 per month.

The break-even point is the number of monthly calls for which the total cost of Plan 1 is equal to the total cost of Plan 2.

This occurs when the inequality $16 < $0.08x is satisfied, which simplifies to 200 < x.

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The correct value for the upper control limit (ucl) for the corresponding control chart for the informations contained in table is equals to the 706.232.

We have a chart table present in above figure and shows the sample informations for making a control chart. Now, control Limits are Calculated by:

For a Sample size, n = 10

Average = 705

Range, R = 4

Formula for calculating upper control limit, UCL= Average + mean factor(A) × range (R), here, x and R are known. The value of A is corresponding value of sample size in the table. The sample size here is 10. Therefore value of A is 0.308. So, UCL = 705 + 0.308(4)

= 706.232

Similarly, LCL = Average - mean factor(A) × range (R)

=> LCL = 705 - 0.308(4)

= 703.778

In case 3-sigma control chart, the Upper control limit is calculated as, Average +3σ

Lower control limit= Average - 3σ. Hence, required value is equals to 706.232 .

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Complete question:

The above figure completes the question.

Suppose you've been given the sample information in the following chart. what would be the correct value for the upper control limit (ucl) for the corresponding control chart? calculate your answer using values to three decimal places.

The value that measures the difference between a sample mean and the population mean on average is the standard error of the mean (SEM).

The value that measures the difference expected, on average, between a sample mean and the population mean is the standard error of the mean (SEM). The SEM is a measure of the variability of sample means around the true population mean, and it quantifies the precision of the sample mean as an estimate of the population mean. In general, the larger the sample size, the smaller the SEM, indicating that larger samples are more likely to provide a more accurate estimate of the population mean.

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Complete question:

when a random sample is selected from a population, the sample mean is not expected to be exactly equal to the population mean. what value measures the difference expected, on average, between a sample mean and the population mean? group of answer choices

A) the standard error

B) the expected value

C) the mean of the population

D) the standard deviation of the population

Answer: First, we need to find the coordinates of points P and Q. Since both P and Q lie on the line 3x + 4y + 15 = 0 and are equidistant from the origin, we can set up two equations:

3x + 4y + 15 = 0 (equation of the line)

x^2 + y^2 = 5^2 (equation of the circle with radius 5)

Solving these two equations simultaneously, we get:

x = -3, -12/5

y = -4, 3/5

Since P and Q lie on the same line, we can find the midpoint of PQ as:

(((-3) + (-12/5))/2, ((-4) + (3/5))/2) = (-33/10, -37/10)

Let O be the origin. Then the length of PO is the distance between O and P, which is:

sqrt((-3 - 0)^2 + (-4 - 0)^2) = 5

Similarly, the length of QO is also 5. Thus, we have a right triangle POQ with hypotenuse of length 5 and legs of length 5. Therefore, the area of triangle POQ is:

(1/2) * base * height

= (1/2) * 5 * 5

= 12.5 square units.

Step-by-step explanation:

The area of triangle POQ is approximately 17.32 square units.

We will apply  the formula for the distance between a point and a line to find their coordinates.

The formula for the distance between a point (x0, y0) and a line Ax + By + C = 0 is:

d = |Ax0 + By0 + C| / √t(A^2 + B^2)

Here we have, A = 3, B = 4, and C = 15.

5 = |3x0 + 4y0 + 15| / sqrt(3^2 + 4^2)

Solving for |3x0 + 4y0 + 15|, we get:

|3x0 + 4y0 + 15| = 5 * sqrt(3^2 + 4^2) = 25

This gives us two equations, solving these equations simultaneously, we get two points:

3x0 + 4y0 + 15 = 25

3x0 + 4y0 + 15 = -25

P = (-5, 0)

Q = (5, 0)

PO = √((-5 - 0)^2 + (0 - 0)^2) = 5

QO = √((5 - 0)^2 + (0 - 0)^2) = 5

PQ = √((5 - (-5))^2 + (0 - 0)^2) = 10

Using Heron's formula to find the area of triangle POQ:

s = (5 + 5 + 10) / 2 = 10

Area = √ (s(s-5)(s-5)(s-10)) = √(300)

=17.32

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Radical can also mean "basic" or "far-reaching," therefore it's possible that the cube root's radical shift involved erasing the cubic functions maths homework.

A function in mathematics is a relationship between a set of possible outputs (the range) and a set of inputs (the domain), with the property that each input is associated to exactly one outcome. A rule or procedure that transforms an input value into an output value is referred to as a function. Typically, the variable x represents the input value, while the object y or f represents the output value (x). A formula or equation that explains the relationship here between values of the input and output is frequently used to express functions.

given

The riddle's solution is: Since it desired a profound transformation!

Expressions using cubic functions can be made simpler by using the cube root, a kind of radical function.

Radical can also mean "basic" or "far-reaching," therefore it's possible that the cube root's radical shift involved erasing the cubic functions maths homework.

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Answer:

for Identify two-dimensional (2-D)Figures and their positions.

2D stands for 2-dimensional. 2-dimensional shapes are flat and only have two dimensions: length and width. They include squares, rectangles, circles, triangles

Step-by-step explanation:

The probability of getting all heads in three-coin tosses is 1/8 or 0.1251. This means that there is a 12.5% chance that all of Zack’s tulips will be pink.

We know that the formula for finding a probability for any outcome is:

Probability = Number of favorable outcomes ÷ Total number of outcomes.

We know that, when a coin is tossed one time then, there are two sample space: {H,T}.

This means that we can get either a head or a tail when a coin is tossed once. Now, since the coin has been tossed 3 times, hence:

The total number of possible outcomes = 2³ =8

This is due to the fact that there are a total of 2ⁿ possible outcomes when a coin is tossed n times.

The eight outcomes would be as follows:

{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

We are asked to find the probability of getting three heads, or tulips be pink. Therefore,

Probability = 1/8.

Therefore, there are 12.5% chances that all of the Zack's tulips would be pink.

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Complete question is:

Read the story. Zack planted an assortment of tulip bulbs in his garden. half of them were pink tulips. this morning, he noticed that 3 of the tulips had started to sprout. how likely is it that all of them will be pink? Zack simulates the situation by flipping a coin 3 times. Each time the coin lands on heads, it represents a pink tulip.

This table shows the results of 100 trials:

number of heads flipped   0   1   2   3

number of trials                  12 37 38 11

Based on zack's results, what is the probability that all of the tulips will be pink?

The average rate of change of the function is:

a) f(x) = 12x^3 + 12 over the interval [5,7] is 1032.

b) f(x) = 12x^3 + 12 over the interval [-4,4] is 507.

a) To find the average rate of change of the function f(x)=12x^3 + 12 over the interval [5,7], follow these steps:

. Evaluate the function at the endpoints of the interval: f(5) and f(7).
  f(5) = 12(5)^3 + 12 = 1532
  f(7) = 12(7)^3 + 12 = 3596

. Subtract the function values: f(7) - f(5) = 3596 - 1532 = 2064.
. Subtract the x-values: 7 - 5 = 2.
. Divide the difference in function values by the difference in x-values: 2064 ÷ 2 = 1032.
So, the average rate of change of the function f(x) = 12x^3 + 12 over the interval [5,7] is 1032.

b) To find the average rate of change of the function f(x) = 12x^3 + 12 over the interval [-4,4], follow these steps:
. Evaluate the function at the endpoints of the interval: f(-4) and f(4).
  f(-4) = 12(-4)^3 + 12 = -2028
  f(4) = 12(4)^3 + 12 = 2028
. Subtract the function values: f(4) - f(-4) = 2028 - (-2028) = 4056.
. Subtract the x-values: 4 - (-4) = 8.
. Divide the difference in function values by the difference in x-values: 4056 ÷ 8 = 507.
So, the average rate of change of the function f(x) = 12x^3 + 12 over the interval [-4,4] is 507.

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Enrique must read for at least 12 more minutes to complete his assignment of reading at least 40 pages.

Let's assume that Enrique needs to read for 'm' minutes to complete his assignment of reading at least 40 pages.

Since Enrique reads 2 pages every minute, the number of pages he will read in 'm' minutes will be 2m. Therefore, to satisfy the condition of reading at least 40 pages, we can write the following inequality:

2m + 16 ≥ 40

Simplifying the above inequality, we get:

2m ≥ 24

Dividing both sides by 2, we get:

m ≥ 12

Hence, Enrique must read for at least 12 more minutes to complete his assignment of reading at least 40 pages.

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With this information, we can now sketch the graphs of the functions f(x) and g(x) or analyze them further as needed.

Determine the behavior of each function as x increases:
  - f(x) decreases as x increases
  - g(x) increases as x increases.

To analyze the graphs of the given functions, let's first understand each function and their properties.
1. [tex]f(x) = (1/2)^x + 1[/tex]:

This is an exponential function with base (1/2) and a vertical shift of 1 unit up.

The graph of this function will have a horizontal asymptote at y = 1 and will decrease as x increases.

2. [tex]g(x) = log(x-1) + 1[/tex]:

This is a logarithmic function with a horizontal shift of 1 unit to the right and a vertical shift of 1 unit up.

The graph of this function will have a vertical asymptote at x = 1 and will increase as x increases.
Analysis:
1. Identify the type of each function:
  - f(x) is an exponential function
  - g(x) is a logarithmic function
2. Determine the transformations of each function:
  - f(x) has a vertical shift of 1 unit up
  - g(x) has a horizontal shift of 1 unit to the right and a vertical shift of 1 unit up

3. Identify the asymptotes for each function:
  - f(x) has a horizontal asymptote at y = 1
  - g(x) has a vertical asymptote at x = 1
4. Determine the behavior of each function as x increases:
  - f(x) decreases as x increases
  - g(x) increases as x increases.

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The probability of exactly 5 successes in 6 trials of a binomial experiment when we round to the nearest tenth of a percent is 29.2%.

The likelihood or chance of an event occurring is measured by probability. Usually, it is stated as a number between 0 and 1, where 0 denotes an event's impossibility and 1 denotes its certainty.

The probability of exactly k successes in n trials of a binomial experiment with probability of success p is given by the binomial probability formula:

P(k) = (n choose k) * [tex]p^k[/tex] * [tex](1-p)^(n-k)[/tex]

the number of ways there are to select k things from a group of n objects, where (n choose k) is the binomial coefficient.

In this problem, we are given that n = 6, p = 0.95, and we want to find the probability of exactly 5 successes.

P(5) = (6 choose 5) * 0.95⁵ * [tex](1-0.95)^(6-5)[/tex]

Simplifying the expression inside the parentheses:

P(5) = 6 * 0.95⁵ * 0.05¹

P(5) = 0.2915

Therefore, the probability of exactly 5 successes in 6 trials of a binomial experiment with probability of success 95% is approximately 0.2915, when we round to the nearest tenth of a percent. So we can write:

P = 29.2% (rounded to one decimal place).

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A cubic polynomial is the one with the highest degree of a variable as 3. The graph for the given cubic polynomial, y = x²- x³ is attached below:

A cubic polynomial is a type of polynomial in which the variable or degree has a maximum power of 3. The format is ax³ + bx² + cx + d. where 'x' is a variable and a,b,c,d are real numbers. Cubic polynomials are used in many areas of mathematics and science, including physics, engineering, and economics. A polynomial is an algebraic expression with variables and constants with integer exponents. A cubic polynomial is a polynomial with the largest exponent of any variable.

Based on the degree, polynomials are classified into four types: zero polynomials, linear polynomials, quadratic polynomials, and cubic polynomials.

The general way of representing a cubic polynomial is p(x) = ax³ + bx² + cx + d, a ≠ 0, where a, b, c are coefficients and d is a constant, all real numbers. Equations involving cubic polynomials are called cubic equations.

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The polynomial with the highest degree of a variable as three is called a cubic polynomial. The cubic polynomial presented in the graph, y = x²- x³ is attached below:

When the variable or degree of a polynomial has a maximum power of three, the polynomial is said to be cubic. The format is as follows: ax³ + bx² + cx + d, where x is a variable and a, b, c, and d are actual values. Physics, engineering, and economics are just a few of the fields in mathematics and science where cubic polynomials are employed. An algebraic expression having variables and constants with integer exponents is called a polynomial. A polynomial with the highest exponent of any variable is said to be cubic.

The four types of polynomials are zero polynomials, linear polynomials, quadratic polynomials, and cubic polynomials. These categories are based on the degree of the polynomial.

A cubic polynomial is typically represented as p(x) = ax³ + bx² + cx + d, a ≠0, where a, b, and c are coefficients and d is a constant, all of which are real values. Cubic equations are equations employing cubic polynomials.

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Therefore, the sales price is $151.25. So, the answer is (C) $151.25.

Sale price refers to the price of a product or service that has been reduced from its original or regular price. It is usually offered as a discount or promotion to attract customers and increase sales. The sale price can be expressed as a percentage or a dollar amount off the regular price. For example, a shirt with a regular price of $50 might be put on sale for 20% off, making the sale price $40.

To find the sales price, we need to apply the discount to the original price:

Discount amount = 45% of $275 = 0.45 x $275 = $123.75

[tex]Sales price = Original price - Discount amount[/tex]

[tex]Sales price = $275 - $123.75 = $151.25\[/tex]

Therefore, the sales price is $151.25. So, the answer is (C) $151.25.

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