As as you approach zero from the left on a number line the integers ____ , but the absolute values of those integers ___?

Answer:

plugging in those values you get 40+(81/9)=40+9=49.

Answer:

1. 5,25,125,625,3125, 15625,78125

Rule: We multiply each term of the sequence by 5.

2.12, 24, 48, 96, 192, 384, 768

Rule: We multiply each term of the sequence by 2.

3. 85, 80, 75, 70, 65, 60, 55

Rule:subtract 5 from each term of the sequence

4.3;5,7,9,11,13,15

Rule: Add 2 to every term in the sequence

5.12, 13,15,16,18,19,21,22

Rule: We first add 1 to the previoys term then add 2 to the new term of the sequence and so on.

The domain of the set of points {(0,1),(5,2),(2,-3),(-3,-3),(-5,3)} is {0, 5, 2, -3, -5}, and the range is {-3, 1, 2, 3}.

Given the relations in the question:

(0,1), (5,2), (2,-3), (-3,-3), (-5,3)

To determine the domain and range of a set of points, we need to look at the x-coordinates of the points to determine the domain, and the y-coordinates of the points to determine the range.

{(0,1),(5,2),(2,-3),(-3,-3),(-5,3)}

The x-coordinates of these points are: 0, 5, 2, -3, and -5.

Therefore, the domain of this set of points is:

Domain = {0, 5, 2, -3, -5}

The y-coordinates of these points are: 1, 2, -3, and 3.

Therefore, the range of this set of points is:

Range = {-3, 1, 2, 3}

Therefore, the domain is {0, 5, 2, -3, -5}, and the range is {-3, 1, 2, 3}.

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Answer: 5 divided by 465 is 0.010752688172

          465 divided by 5 is 93

Step-by-step explanation:

The only value of x where f'(x) = 0 is x = 0.

Let's find all values of x where the derivative of f(x) = [tex]arcsin(e^(2x) – 2x)[/tex] is equal to 0.

Step 1: Find the derivative f'(x) using the chain rule.

For this, we'll need to differentiate [tex]arcsin(u)[/tex] with respect to u, which is [tex](1/√(1-u^2))[/tex], and then multiply by the derivative of u [tex](e^(2x) – 2x)[/tex]with respect to x. So, f'(x) = [tex](1/√(1-(e^(2x) – 2x)^2)) * d(e^(2x) – 2x)/dx[/tex]

Step 2: Find the derivative of e^(2x) – 2x with respect to x. Using the chain rule and the derivative of [tex]e^u: d(e^(2x) – 2x)/dx = 2e^(2x) – 2[/tex]

Step 3: Combine the derivatives. f'(x) =[tex](1/√(1-(e^(2x) – 2x)^2)) * (2e^(2x) – 2)[/tex]

Step 4: Set f'(x) equal to 0 and solve for x. [tex](1/√(1-(e^(2x) – 2x)^2)) * (2e^(2x) – 2) = 0[/tex]

Since the first part of the product [tex](1/√(1-(e^(2x) – 2x)^2))[/tex] is never 0, we can focus on the second part: [tex]2e^(2x) – 2 = 0[/tex]

Step 5: Solve for x. [tex]2e^(2x) = 2 e^(2x) = 1[/tex]

The only way this is true is when 2x = 0, since [tex]e^0 = 1: 2x = 0 x = 0[/tex]

So, the only value of x where f'(x) = 0 is x = 0.

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Percentage of gumballs that are within standard deviations of the mean is 68% and have a diameter between 2.20 cm and 2.22 cm.

To find the percentage of gumballs that are within one standard deviation of the mean, we need to use the empirical rule, also known as the 68-95-99.7 rule. According to this rule, for a normal distribution:

Here we want to find the percentage of gumballs that are within one standard deviation of the mean. So we can use the first part of the empirical rule and say that approximately 68% of the gumballs have a diameter between:

Mean - Standard deviation = 2.21 - 0.01 = 2.20 cm and Mean + Standard deviation = 2.21 + 0.01 = 2.22 cm

Therefore, approximately 68% of the gumballs have a diameter between 2.20 cm and 2.22 cm.

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The shooter was located approximately 36.15 feet off the ground.

We can use trigonometry to solve for the height of the shooter.

First, we need to find the horizontal distance from the shooter to the man on the park bench. We can use the angle of 26° and the distance of 92 feet to calculate this distance:

horizontal distance = 92 feet * cos(26°)

horizontal distance = 82.33 feet

Next, we can use the height of 3.7 feet and the horizontal distance of 82.33 feet to find the height of the shooter:

tan(26°) = height difference / horizontal distance

height difference = horizontal distance * tan(26°)

height difference = 82.33 feet * tan(26°)

height difference = 36.15 feet

Therefore, the shooter was located approximately 36.15 feet off the ground.

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To find dy/dx for y = 1/3x³ + 7x, we need to take the derivative with respect to x using the power rule and the sum rule, which gives dy/dx = x² + 7.

The given equation is y = 1/3x³ + 7x. To find dy/dx, we need to take the derivative of y with respect to x. We can do this by using the power rule and the sum rule of differentiation.

Using the power rule, the derivative of x³ is 3x². Using the sum rule, the derivative of 7x is 7. Therefore, the derivative of y with respect to x is:

dy/dx = d/dx (1/3x³ + 7x)

= d/dx (1/3x³) + d/dx (7x)

= (1/3) d/dx (x³) + 7 d/dx (x)

= (1/3) (3x²) + 7

= x² + 7

Hence, we have found that the derivative of y with respect to x is x² + 7.

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The relative frequency for selecting a teen out of all the people who like chocolate is calculated by dividing the number of teens who like chocolate (N) by the total number of people who like chocolate (T).

To find the relative frequency for selecting a teen out of all the people who like chocolate, you need to follow these steps:

Step 1: Determine the total number of people who like chocolate (let's call this T).
Step 2: Determine the number of teens who like chocolate (let's call this N).
Step 3: Calculate the relative frequency by dividing the number of teens who like chocolate (N) by the total number of people who like chocolate (T).

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Megha's total movement involves biking 20km north, 30km east, 20km south, and 30km west, resulting in a displacement of zero as she ends up back at her starting point.

Given that,

Megha bikes 20km north.

Megha then bikes 30km east.

After that, Megha bikes 20km south.

Lastly, Megha bikes 30km west.

Megha stops after completing the above movements.

Megha's displacement can be calculated by finding the straight-line distance between her starting point and ending point.

In this case,

She initially bikes 20km north, then 30km east, followed by 20km south, and finally 30km west.

Let's break it down:

The north and south distances cancel each other out, as she ends up back at her starting point vertically.

The east and west distances also cancel each other out, as she ends up back at her starting point horizontally.

Hence,

Megha's displacement is zero. She has returned to her original position.

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Using quadratic formula, the value of x in the quadratic equation are 1.47 and -0.85

To find the value of x, we can either use quadratic formula or factorization method.

8x² - 2 - 5x = 8

Let's rewrite the equation properly

8x² - 5x - 2 - 8 = 0

8x² - 5x - 10 = 0

a = 8, b = -5, c = -10

Using quadratic formula;

-b ±[√b² - 4ac / 2a]

-(-5) ±[√(-5)² - 4(8)(-10) / 2(8)]

x = 5+ √345 / 16 or x = 5 - √345 / 16

x = 1.47 or x = -0.85

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Answer:

I believe the distance between these points is (2, 7), because the difference between -5 and -7 is 2, and the for -9 and -2, it's 7.  Hope I helped.

Rectangles are relatable to factors because of their areas and perimeter equations

From the question, we have the following parameters that can be used in our computation:

Explaining why rectangles are relatable to factors

Rectangles are relatable to factors because of the following reasons

Perimeter = 2 * (Length + width)

Area = Length * width

This means that in calculating the areas and the perimeters of a rectangles, we make use of arithmetic expressions

These arithmetic expressions, when expanded form terms and factors of  expression

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The average price of milk in 2018 was 6.45 dollars per gallon.

The average price of milk in 2021 was 189.95 dollars per gallon.

The given function is: Price = 3.55 + 2.90(1 + x)³

In order to find the average price of milk in 2018, we need to set x = 0:

Price in 2018 = 3.55 + 2.90(1 + 0)³ = 3.55 + 2.90(1) = 6.45 dollars per gallon

Price in 2021 = 3.55 + 2.90(1 + 3)³ = 3.55 + 2.90(64) = 189.95 dollars per gallon

Hence, the average price of milk in 2021 was 189.95 dollars per gallon.

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The critical points of f(x) are x = 0 and x = e^(-1/2) / 3, and x = e^(-1/2) / 3 corresponds to a local minimum of f(x). Cmin = e^(-1/2) / 3 and Cmax = 0.

Taking the derivative of f(x) with respect to x using the product rule and the chain rule, we get:

f'(x) = 14x ln(3x) + 7x

Setting f'(x) equal to zero and solving for x, we get:

14x ln(3x) + 7x = 0

Factor out x:

7x(2ln(3x) + 1) = 0

So either x = 0 or 2ln(3x) + 1 = 0.

If x = 0, then f'(x) = 0 and x is a critical point.

If 2ln(3x) + 1 = 0, then ln(3x) = -1/2 and 3x = e^(-1/2). Solving for x, we get:

x = e^(-1/2) / 3

So e^(-1/2) / 3 is also a critical point.

Now we need to apply the second derivative test to determine whether these critical points correspond to a local minimum or maximum.

Taking the second derivative of f(x), we get:

f''(x) = 14 ln(3x) + 21

For x = 0, we have:

f''(0) = 14 ln(0) + 21

The natural logarithm of zero is undefined, so the second derivative does not exist at x = 0. Therefore, we cannot apply the second derivative test at x = 0.

For x = e^(-1/2) / 3, we have:

f''(e^(-1/2) / 3) = 14 ln(1/e^(1/2)) + 21

= -14/2 + 21

= 7/2

Since the second derivative is positive at this point, we can conclude that x = e^(-1/2) / 3 is a local minimum of f(x).

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The location where the fourth child will stop running in the relay race is 4/5 of the way.

To determine the location where the fourth child will stop running in the relay race, we need to find out the total distance covered by the first four children.

Since each child runs 1/5 of a mile, we can find the total distance for the first four children by multiplying their individual distances.

Total distance = (Number of children) * (Distance run by each child)
Total distance = 4 * (1/5)

Now, let's multiply:
Total distance = 4/5

So, the fourth child will stop running at a location 4/5 of a mile from the starting point. To plot this point on a number line, locate the point between 0 and 1 that is 4/5 of the way. This point represents the location where the fourth child will stop running in the relay race.

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The volume of the different shapes have been calculated in the space below

Volume of rectangular prism = lwh

where we define the variables as :

l = length

w = width

h = height

then when we multiply, we will have

= 4 x 10 x 6

= 240

Volume of triangular pyramid = 1 / 3 b x h

where b = base

h = height

1 / 3 x 1.5 x 2

= 1

Volume of rectangular pyramid = lwh / 3

= 7.5 x 4.5 x 5 / 3

= 56.25

= 1/2 x b x h x l

= 1/2 x 3 x 8.5 x 7

= 89.25

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Ms. Paquette used approximately 0.73 gallons of paint for one coat on the rectangular wall.

To determine how many gallons of paint Ms. Paquette used for one coat on the rectangular wall, we first need to calculate the total area of the wall.

Area of the wall = length x width
= 25.5 feet x 10 feet
= 255 square feet

Now, to find out how many gallons of paint are needed for one coat, we need to know the coverage rate of the paint. This information is usually provided on the paint can label. Let's assume that the coverage rate for the paint Ms. Paquette used is 350 square feet per gallon.

To calculate how many gallons of paint are needed, we can divide the total area of the wall by the coverage rate of the paint:

255 square feet ÷ 350 square feet per gallon = 0.7286 gallons

This means that Ms. Paquette used approximately 0.73 gallons of paint for one coat on the rectangular wall. Since paint is typically sold in 1-gallon containers, she would need to purchase at least one gallon of paint to complete one coat on this wall.

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The circumference of the tank is is 125.66m and the percentage of the circumference that is visible to the person is 10.24%.

a) To calculate the circumference of the cylindrical tank, using the formula C = 2πr, where C is the circumference and r is the radius of the tank. In this case, r = 20 m, so:

C = 2π(20 m) ≈ 125.66 m

b) To determine the percentage of the circumference visible to the person, we first need to calculate the angle (in degrees) that subtends the visible arc. This can be done using the inverse tangent function:

angle = atan(opposite/adjacent) = atan(20 m/60 m)

angle ≈ 18.43°

Since the visible arc is symmetrical on both sides, the total angle of the visible arc is twice the calculated angle:

total angle ≈ 36.86°

Now, calculate the percentage of the circumference that is visible by dividing the total angle by 360° and multiplying by 100%:

percentage = (36.86°/360°) × 100% ≈ 10.24%

So, the visible percentage of the circumference to the person is approximately 10.24%.

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The p-value is less than the significance level so reject the null hypothesis and concluded percentage of the students volunteer their time is different from receiving financial aid students.

Percentage of college students who volunteer their time = 20%

Perform a hypothesis test.

Null hypothesis H₀: p = 0.20,

where p is the proportion of college students who volunteer their time.

The alternative hypothesis is Hₐ: p ≠ 0.20.

Indicating that the proportion of college students who volunteer their time is different for students receiving financial aid.

57 out of 381 randomly selected students who receive financial aid volunteered their time.

Test the hypothesis,

Calculate the sample proportion of volunteers among the students receiving financial aid,

p₁ = 57 / 381

    = 0.149

Using Test statistic,

which follows a normal distribution under the null hypothesis .

Mean = 0  

Standard deviation σ = √(p(1-p)/n),

where p = 0.20 is the proportion under the null hypothesis

n = 381 is the sample size.

z

= (p₁ - p) /√(p×(1-p)/n)

= (0.149 - 0.20) / √(0.20(1-0.20)/381)

= -2.55

Using attached table of p-value from z-score.

Calculated test statistic of -2.55 corresponds to a p-value of 0.0054,

which is less than the significance level α = 0.01.

Reject the null hypothesis .

Therefore, we conclude that there is evidence to suggest that the percentage of college students who volunteer their time is different for students receiving financial aid.

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The above question is incomplete, the complete question is:

20% of all college students volunteer their time. is the percentage of college students who are volunteers different for students receiving financial aid? of the 381 randomly selected students who receive financial aid, 57 of them volunteered their time. what can be concluded at the α = 0.01 level of significance?

The p-value of the test is 0.017 > 0.01, which means that there is not convincing evidence that the mean time behind the whell for all U.S drivers is less than 51 minutes.

We are told that:

Time spent by U.S. drivers on average each day = 51 minutes behind the wheel

Thus, the null hypothesis is:

H₀: μ = 51

The alternate hypothesis is:

Hₐ: μ < 51

The formula for the test statistic is:

z = (x' - μ)/(σ/√n)

where:

x' is sample mean

n is sample size

μ is population mean

σ is standard deviation

Thus:

z = (46.4 - 51)/(18.8/√75)

z = -2.12

From online p-value from z-score calculator, we have:

The p-value of the test is referred to as the probability of finding a sample mean that is less than 46.4, which is the p-value of z when X = 46.4.

Looking at the z-table, z = -2.12 has a p-value of 0.017.

Decision:

The p-value of the hypotheses test is seen to be0.017 > 0.01.

Thus, this tells us that we don't have convincing evidence that the mean time spent behind the wheel for all U.S drivers is less than 51 minutes.

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The only option left is −5°F, which is colder than −3°F and thus could be the temperature on her thermometer this morning.

The temperature on Skylar's thermometer is measured using a scale that indicates the degree of hotness or coldness of the atmosphere. In this case, we know that the temperature on her thermometer last night was −3°F. The negative sign indicates that the temperature was below the freezing point of water.

We are asked to determine what the temperature could be on her thermometer this morning. Since we are told that the temperature is colder than −3°F, we can eliminate 0°F and 2°F as possible options, as they are warmer than −3°F.

Similarly, −1°F is only slightly colder than −3°F, so it is unlikely to be the temperature on Skylar's thermometer this morning. Therefore, the only option left is −5°F, which is colder than −3°F and thus could be the temperature on her thermometer this morning.

It is important to note that temperature can have a significant impact on our daily lives. Extreme cold temperatures can cause frostbite, hypothermia, and other health hazards, while hot temperatures can lead to dehydration, heat exhaustion, and heat stroke. It is important to dress appropriately and take necessary precautions when the temperature is too low or too high.

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For the g(x) functions provided, here are their key features:

g(x) = (x + 2)(x − 1)(x − 2)

End behavior: As x approaches negative or positive infinity, g(x) approaches positive infinity.

Y-intercept: g(0) = -4

Zeros: x = -2, 1, 2

Ray and Kelsey could both be accurate, all depending on the stated third-degree polynomial function.

It is conceivable for a third-degree polynomial to present up to three zeros, thus corroborating Kelsey's point that the function can have up to three intersection points with the x-axis maximum. Moreover, it can even occur that this function possesses a repeatable zero, causing a fourth interception.

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The box plot that represents these data is Option B because the centre of measure falls on 4.

To find the median, we first arrange the study hours in ascending order:

2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 7.

From here, we have 15 numbers, so the median is the 8th number in the list which is 4.

As the median study hours for Mr. Jeffer's math class is 4 hours per week, then, the box plot that represents these data is B because the centre of measure falls on 4.

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Answer:

Pens=13

Pencils=27

Step-by-step explanation:

1. Pens = x, Pencils = y

x+y=40

2. y+5 & x-5 --> y=4x

3. Rearrange the x+y=40 to y=40-x. Then substitute y=4x and y=40-x to 4x=40-x.

4. Solve. 4x=40-x, 5x=40, x=8

5. Plug in x=8 to y=4x -> y=32.

6. Reverse the y+5 & x-5. y=27, x=13.

Answer:

the answer for this problem would be -20

Answer:

-20

Step-by-step explanation:

The easiest way to do it is to change -3 3/7 and 5 5/6 into improper fractions. To do that, let’s take -3 3/7 for example. You would add the numerator by the whole number, and then multiply the denominator by the whole number. Getting you -24/7, the other number would be 35/6 then you multiply the two getting you -840/42, which it turned back into a proper fraction by dividing the two numbers, you would get -20. Hope this helps!

The best estimate of the volume of this cylindrical water dispenser is 2940 in³. The correct option is b.

To estimate the volume of the cylindrical water dispenser, we can use the formula for the volume of a cylinder, which is given by V = πr²h, where V is the volume, π is a mathematical constant approximately equal to 3.14, r is the radius, and h is the height.

Given that the radius of the water dispenser is 7 inches and the height is 20 inches, we can substitute these values into the formula:

V = π(7²)(20)

V = π(49)(20)

V ≈ 3.14 × 49 × 20

V ≈ 3.14 × 980

V ≈ 3075.2 in³

From the given options, the closest estimate to the calculated volume of approximately 3075.2 in³ is option B: 2940 in³. While it is not an exact match, it is the closest estimate among the options provided.

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The group of natural numbers is a subset of the whole numbers.

What is Whole number ?

Whole numbers are a set of numbers that includes all positive integers (1, 2, 3, ...) and zero (0). They do not include negative numbers or fractions. Whole numbers are often used to count objects or represent quantities that cannot be divided into smaller parts.

Out of the given options, the group of natural numbers is the only one that is a subset of whole numbers. The other options - Rational numbers, Real numbers, Irrational numbers, and Integers - are not subsets of the whole numbers.

Rational numbers include fractions and decimal numbers, which can be expressed as a ratio of two integers, including non-whole numbers.

Real numbers include all rational and irrational numbers, including non-whole numbers. Irrational numbers are non-repeating, non-terminating decimals that cannot be expressed as a fraction. Integers include both positive and negative whole numbers, as well as zero.

The subset of whole numbers is called natural numbers.

Therefore, the group of natural numbers is a subset of the whole numbers.

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Ferris wheel has the same diameter as The Colossus is g(t) = 40 cos (π/45 t) +50. So, correct option is A.

To determine which of the given functions represents a Ferris wheel with the same diameter as The Colossus, we need to use the fact that the diameter of a Ferris wheel is equal to the amplitude of the sinusoidal function that models its height.

The amplitude of the function f(t) = 40 sin (π/45 t) +48 is 40, so the diameter of The Colossus is 40 feet. We need to find the function that also has an amplitude of 40.

Looking at the given answer choices, we see that function g(t) has an amplitude of 40 cos (π/45 t) +50, which is equal to 40. This means that the Ferris wheel represented by function g(t) has a diameter of 40 feet, the same as The Colossus.

Functions h(t), j(t), and k(t) all have amplitudes that are less than 40, so they represent Ferris wheels with smaller diameters than The Colossus.

Therefore, the answer is A.

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