Which exponential function matches the table?

Answer:

277

Step-by-step explanation:

PEMDAS

E: 3^3 (3x3x3) = 27

M: 27x10 = 270

A: 270+7 = 277

Answer:

x/2=12

Step-by-step explanation:

I think your option B must be x/2 not x2.

In this case, both 1 and 2 are located on the real axis, so their imaginary components are zero.

To determine the value of i, we are given that 21 = 5 + 2,52 = 3, and 3 = 1 + di.

Let's solve for i step by step:

Start with the equation 21 = 5 + 2,52 = 3.

Subtract 5 from both sides to isolate the term with i:

21 - 5 = 2,52 = 3 - 5

16 = 2,52 = -2

Now, let's solve for i in the equation 3 = 1 + di.

Subtract 1 from both sides:

3 - 1 = 1 + di - 1

2 = di

We can rewrite di as i * d. So, the equation becomes:

2 = i * d

From the equation 16 = 2,52 = -2, we know that d = -2.

Substitute the value of d into the equation 2 = i * d:

2 = i * (-2)

Now, we solve for i:

Divide both sides by -2:

2 / (-2) = i * (-2) / (-2)

-1 = i

Therefore, the value of i is -1.

Now, let's plot 1 and 2 on the complex plane:

Plotting 1:

The complex number 1 is located on the real axis, which means it has no imaginary component. It can be represented as the point (1, 0) on the complex plane.

Plotting 2:

The complex number 2 is also located on the real axis, with no imaginary component. It can be represented as the point (2, 0) on the complex plane.

So, the plot of 1 and 2 on the complex plane would look like this:

o (2, 0) - 2

|

o (1, 0) - 1

Please note that the complex plane is a two-dimensional plane with the real axis representing the real numbers and the imaginary axis representing the imaginary numbers. In this case, both 1 and 2 are located on the real axis, so their imaginary components are zero.

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The utility’s percent change from 2010 to 2020 is a decrease of 4.07%

How many years are between 2010 and 2020?

There are 10 years in between 2010 and the year 2020, which means that the total decline over a period of 10 years is the annual decrease multiplied by 10.

Total decrease in 10 years=2.6*10

Total decrease in 10 years=26.0

Utility industry jobs in 2020=639.5-26.0

Utility industry jobs in 2020=613.5

The percentage change 2010-2020=(2020 jobs/2010 jobs)-1

The percentage change 2010-2020=(613.5/639.5)-1

The percentage change 2010-2020=-4.07%

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How much a statistic varies from one sample to another is known as the sampling variability of a statistic.

Testing variability arises due to the reality that exceptional samples of the same size can produce special values of a statistic, although the samples are described from the same populace. the quantum of slice variability depends on the scale of the sample, the variety of the populace, and the unique statistic being calculated.

The end of statistical conclusion is to apply the data attained from a sample to make consequences about the population, while counting for the slice variability of the statistic. ways similar as thesis checking out and tone belief intervals do not forget the sampling variability of a statistic to make redundant accurate consequences about the populace.

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Answer: D) 15.7

Step-by-step explanation:

Start with the formula C=2 πr

Then solve for r r=C2π = 98.62·π = 15.69(7)204

The radius of the circle is 15.7 mm.

The route or boundary that encircles any shape in mathematics is defined by the shape's circumference.

The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area. The length of a straight line drawn from the centre of a circle equals the diameter of that circle.

We have,

The circumference of Circle = 2πr

Also, The circumference of a circle is 98.596 millimeters.

So, circumference of Circle = 2πr

98.596 = 2πr

98.596 = 6.28r

r= 98. 596 / 6.28

r = 15.7 mm

Thus, the radius is 15.7 mm.

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Final Answer: \(b = -1\)

Steps/Reasons/Explanation:

Question: \(7b - 2/5 = 6b - 7/5\) equations with variables on both sides: decimals & fractions.

Step 1: Subtract \(6b\) from both sides.

\(7b - \frac{2}{5} - 6b = -\frac{7}{5}\)

Step 2: Simplify \(7b - \frac{2}{5} - 6b\) to \(b - \frac{2}{5}\).

\(b - \frac{2}{5} = -\frac{7}{5}\)

Step 3: Add \(\frac{2}{5}\) to both sides.

\(b = -\frac{7}{5} + \frac{2}{5}\)

Step 4: Simplify \(-\frac{7}{5} + \frac{2}{5}\) to \(-1\).

\(b = -1\)

~I hope I helped you :)~

On solving the problem, 160 square feet will be the area of the garden be  after he doubles the length and width.

A flat (2-D) surface's or an object's shape's total area is known as its area. On a piece of paper, use a pencil to draw a square. It is a 2-D figure. Its Area refers to the area that the shape occupies on the paper. Imagine that your square is now composed of smaller unit squares.

we have,

rectangular garden with an area = 40 square feet.

Each dimension of the rectangular has been increased by doubling.

Now

Area = L X W

if the area is doubled

= > (2XL)(2XW)

=>  ( 4 X L W)

= > 4X40

=>  160

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The increase in the mean for February compared to January is $3.00. We rounded the answer to the nearest penny, which is two decimal places.

To find the mean earnings for January, we add up all of Laurel's earnings and divide by the number of Fridays she babysat:

$20.50 + $30.75 + $28.00 + $25.25 = $104.50

$104.50 ÷ 4 = $26.125

So, Laurel earned an average of $26.13 for each Friday she babysat in January.

In February, she earned $12 more for babysitting four Fridays than she did in January, which means she earned:

$104.50 + $12 = $116.50

The mean for February can be found the same way:

$116.50 ÷ 4 = $29.125

So, the mean for February is $29.13.

To find the increase in the mean for February compared to January, we subtract the mean for January from the mean for February:

$29.13 - $26.13 = $3.00

Therefore, the increase in the mean for February compared to January is $3.00.

We rounded the answer to the nearest penny, which is two decimal places.

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To calculate the annual interest rate required to earn if you want a $600 per month contribution to grow to $45,000 in six years, we can use the formula for future value of an annuity: FV = PMT x [((1 + r)n - 1) / r]where,FV = future value of an annuityPMT = the payment you will make in each periodr = the interest rate per periodn = the number of periods.

Using the given values, we have:FV = $45,000PMT = $600n = 6 x 12 = 72 (since we are given in months, and there are 12 months in a year)r = ?To solve for r, we can use trial and error or a financial calculator. Here, we will use a financial calculator.

To solve this problem, we will use the formula for future value of an annuity:FV = PMT x [((1 + r)n - 1) / r]where,FV = future value of an annuity PMT = the payment you will make in each periodr = the interest rate per periodn = the number of periods.

We are given:FV = $45,000PMT = $600n = 6 x 12 = 72 (since we are given in months, and there are 12 months in a year)r = ?To solve for r, we can use a financial calculator or trial and error. Here, we will use a financial calculator. We enter the values into the financial calculator and solve for r. We get

:r = 8.81% (rounded to two decimal places)Therefore, the annual interest rate required to earn if you want a $600 per month contribution to grow to $45,000 in six years is approximately 8.81%.

The annual interest rate required to earn if you want a $600 per month contribution to grow to $45,000 in six years is approximately 8.81%.

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The domain of the function \(f(x) = \sqrt{\frac{1}{3}x + 2\) is (d) x  ≥ -6

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

\(f(x) = \sqrt{\frac{1}{3}x + 2\)

Set the radicand greater than or equal to 0

So, we have

1/3x + 2 ≥ 0

Next, we have

1/3x  ≥ -2

So, we have

x  ≥ -6

Hence, the domain of the function is (d) x  ≥ -6

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The cylinder with maximum volume has a radius of 6.5 feet and a height of 2.5 feet.

Let the radius and height of the cylinder be r and h, respectively. Since the cylinder is inscribed in the cone, its height and radius must satisfy the following conditions:

The height of the cylinder must be equal to the height of the cone, i.e. h = 2.5 feet.

The radius of the cylinder must be less than or equal to the radius of the base of the cone, i.e. r ≤ 6.5 feet.

To maximize the volume of the cylinder, we can use the formula for the volume of a cylinder:

V = πr^2h

Substituting h = 2.5, we get:

V = 2.5πr^2

Now, we can express the volume of the cylinder in terms of a single variable, r. To do this, we use the fact that the cylinder is inscribed in the cone, so the cross-sectional area of the cylinder is a fraction of the cross-sectional area of the cone. Specifically, the ratio of the areas is equal to the square of the ratio of the radii:

r/6.5 = h/2.5

Solving for h, we get:

h = 2.5r/6.5

Substituting into the formula for the volume of the cylinder, we get:

V = 2.5πr^2 = 2.5πr^2(h/2.5) = πr^2(2r/6.5)

Simplifying, we get:

V = (4π/13)r^3

To find the value of r that maximizes V, we can take the derivative of V with respect to r and set it equal to zero:

dV/dr = (4π/13)3r^2 = 0

Solving for r, we get:

r = 0

This is not a valid solution since r must be greater than zero. Therefore, we must look for a maximum value of V on the interval 0 < r ≤ 6.5.

To do this, we can evaluate V at the endpoints of the interval and at any critical points in the interior. Since we already know that there are no critical points, we just need to evaluate V at the endpoints:

V(0) = 0

V(6.5) = (4π/13)(6.5)^3 ≈ 724.06

Therefore, the cylinder with maximum volume has a radius of 6.5 feet and a height of 2.5(6.5/6.5) = 2.5 feet.

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If there is sufficient evidence to reject a null hypothesis at the 10% level, then there is sufficient evidence to reject it at the 5% level.

What is hypothesis testing?

A statistical hypothesis test is a technique for determining if the available data are sufficient to support a specific hypothesis. We can make probabilistic claims regarding population parameters through hypothesis testing.

Here,

We have to find the correct statement about hypothesis testing.

We concluded that  If there is sufficient evidence to reject a null hypothesis at the 10% level, then there is sufficient evidence to reject it at the 5% level.

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Answer:

In this case, B is true.

Whether to use a one-sided or a two-sided test is typically decided BEFORE the data are gathered, not after.

Be careful while reading the options on the quiz, because depending on the question you get, the options may be worded slightly differently. Because of the wording, the answer may be different as well (on the FLVS quiz, I got different answer choices for this question). Be careful and read cautiously!

Have a great day.

Answer:

C

Step-by-step explanation:

Third letter of English lexicon

The set of points that form a line are called a pattern. This pattern is created by a series of points that share a common direction and form a straight line. It is important to recognize these patterns in order to better understand and analyze data.

A pattern is a repeated sequence or arrangement of something. In geometry, a line is a set of points that extend infinitely in both directions. These points are arranged in such a way that they share a common direction and form a straight line. The set of points that form a line are called a pattern because they follow a specific sequence and arrangement.

Recognizing patterns is important in many fields, including mathematics, science, and engineering. By analyzing patterns, we can better understand the underlying structures and processes that shape the world around us. For example, in data analysis, recognizing patterns can help us identify trends and make predictions about future outcomes.

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The distance traveled by the little boy is 150.72 feet.

Distance is the measure of the length between two points.

To calculate the total distance traveled by the little boy, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the distance traveled by the little boy is 150.72 feet.

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The department's sales per square foot are $51.16 per square foot.

Division is the process of dividing a number by a given number.

Given that, the supermarket had sales last week of $15349, and the area of the department is 300 square feet.

The sales per square foot are:

(total sales)/ (total area)

= 15349/300

= 51.16

Hence, the department's sales per square foot are $51.16 per square foot.

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The least common multiple refers to the common multiple for the give numbers.

Among the answer choice, number 3 makes more sense. All the product of the common factors is the LCM.

Answer:

2 - 9 - 36

= - 43

Step-by-step explanation:

(hope it's Help)

Step-by-step explanation:

I assume we are simplifying

1) -6k+7k = k

2) 12r-8-12 = 12r-20

3) n-10+9n-3 = 10n-13

4) -4x-10x = -14x

Answer:

A = 13.23 m²

Step-by-step explanation:

A = bh

Where,

A = area of the parallelogram

b = base of the parallelogram

h = height of the parallelogram

From the question, assume

b = 2.1 m

h = 6.3 m

A = bh

= 2.1 m × 6.3 m

= 13.23 m²

A = 13.23 m²

The weight that separates the top 4% is x = 7.87 (round nearest hundredth) .

The weight that separates the bottom 4% is x = 7.63 (round nearest hundredth).

The majority of the observations are centred around the middle peak of the normal distribution, which is a continuous distribution of probability that really is symmetrical around in its mean.

The probability for values that are farther from of the mean tapered down equally both in directions.

Now, use z-chart to find the z-value for that separates the top 4% and the bottom 4%.

The values of z = +1.75 and z = -1.75

Let the weight of the machines be 'x'.

Use the formula for z- value

z = (x -  μ)/ σ

Where,

σ  is standard deviation =  0.07 ounces.

μ is mean = 7.75 ounces.

Substitute all the values and calculate the weight.

case 1: when z = +1.75

1.75 = (x - 7.75)/0.07

x  = (1.75×0.07) + 7.75

x = 7.872

x = 7.87 (round nearest hundredth)

case 2: when z = -1.75

-1.75 = (x - 7.75)/0.07

x  = (-1.75×0.07) + 7.75

x = 7.6275

x = 7.63 (round nearest hundredth)

Therefore,

x = 7.87 (round nearest hundredth) is weight which separates top 4%.

x = 7.63 (round nearest hundredth) is weight which separates bottom 4%.

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Look at the explanation to understand the answer.

Step-by-step explanation:

Step 1.

Rewrite (a2) in a2 + 6 so the a is before 2

(a2 + 6) + (4a + 6) ⇒ (2a + 6) + (4a + 6)

Step 2.

We'll need to organize 2a + 6 + 4a + 6 into groups of like terms, so we can combine them easier.

They're two groups of like terms in the expression.

First group: 2a and 4a

Second group: 6 and 6

Now, rewrite it so the 6 is added by the other 6.

2a + 4a + 6 + 6

Step 3.

We'll need to combine like terms in 2a + 4a + 6 + 6 by adding all the numerical coefficients and copying the literal parts, if any. No numerical coefficient implies value of 1. Numerical 'like' terms will be added.

We already know the groups with like terms.

First group: 2a and 4a

Second group: 6 and 6

Let's solve.

2a + 4a = 6a

6 + 6 = 12

Combine 6a and 12 up and you'll get your answer.

6a + 12 is the answer.

Answer:

1/2 or 0.5 (same value, different form)

Step-by-step explanation:

Ok...since I can't actually graph it, we can make a table out of it....

x      y

7     -1

9      0

From -1 to 0, we add 1 (this is for the y section)

From 7 to 9, we add 2 (this is for the x section)

Now all we have to do is divide the y with the x

y/x = 1/2

The slope will be 1/2 (fraction form) 0.5 (decimal form)

Hope this helped!

The values of a=60, b=750, c=3, a+b+c= 813 as determined by Pythagorean Theorem..

What is Pythagorean Theorem?

A geometric theorem states that the square of a right triangle's hypotenuse equals the sum of the squares of its other two sides.

Call the circle's center O, the unicorn's tether point A, and the final spot where the rope reaches tower B. Triangle OAB is a right triangle since BA is a tangent line at point B and OB is a radius. We determine the horizontal component of AB has length \(4\sqrt{5}\) using the Pythagorean Theorem.

The cylinder is "unrolled" to become a flat surface. Let C be the rope's bottom tether, D the point below A on the ground, and E the point directly beneath B. Triangles CDA and CEB share characteristics of right triangles. The Pythagorean Theorem states that CD=8cdotsqrt6.

Let x represent the size of CB.\(CD=8\cdot\sqrt{6}\)

\(\[\frac{CA}{CD}=\frac{CB}{CE}\implies \frac{20}{8\sqrt{6}}=\frac{x}{8\sqrt{6}-4\sqrt{5}}\implies x=\frac{60-\sqrt{750}}{3}\]\)

Therefore,

a=60, b=750, c=3,a+b+c= 813 as determined by Pythagorean Theorem.

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The sum of all the angles that are labeled in the given vertex is 294°

In a single vertex, the three angles around the vertex are given as 55°, 64°, and 175°

We have to find the sum of all the angles that are labeled in the given single vertex.

A vertex is a point two or more lines meets.

It is the corner of a geometrical shape.

Example:

A square has 4 corners so it has 4 vertexes.

A cube has 8 corners so it has 8 vertexes.

We will add all the different angles in the single vertex as shown in the figure below.

Let,

Angle A = 55°

Angle B = 64°

Angle C = 175°

The sum of all the angles that are labeled is:

= Angle A + Angle B + Angle C

= 55° + 64° + 175°

= 294°

The sum of all the angles that are labeled in the given vertex is 294°

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