combine the exponential expressions to produce a single exponential expression. (2 points)

396,667.5 is the total of all whole numbers between 1 and 890.

To find the sum of the whole numbers from 1 to 890, we can use the formula for the sum of an arithmetic series:

S = n(a1 + an) / 2

Where S is the sum, n is the number of terms, a1 is the first term, and an is the last term. In this case, n = 890, a1 = 1, and an = 890. Plugging these values into the formula, we get:

S = 890(1 + 890) / 2

S = 890(891) / 2

S = 793335 / 2

S = 396667.5

Therefore, the sum of the whole numbers from 1 to 890 is 396,667.5.

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Answer:

The answer is 0 Lil Bro

Step-by-step explanation:

Hope that helps with you Middle school work!

The equation of the parabola will be;

y = (x - 3)² + 1

What is mean by Parabola?

A parabola is a set of points in the plane which are equidistant from the directrix and focus.

Given that;

The vertex of the parabola = (3 , 1)

A parabola passes through the point (2,2).

Now,

Since, The equation of parabola in vertex form is;

y = a (x - h)² + k

Where, (h , k) are vertex of the parabola.

So, The equation of parabola with vertex (3, 1) will be;

y = a (x - 3)² + 1

And, It passes through the point (2,2).

So we substitute the value of (2, 2) in place of (x, y) as;

2 = a (2 - 3)² + 1

2 = a + 1

a = 2 - 1

a = 1

Substitute the value of a in above equation, we get;

The equation of parabola as;

y = (x - 3)² + 1

Therefore, The equation of the parabola will be;

y = (x - 3)² + 1

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Answer:

E= ( 3, -2 )

D= ( 2, -5 )

F= ( 6, -4)

Step-by-step explanation:

I dont know how to explain it sorry but try out Khan academy its a website that will help you understand everything in any subject

The area of the triangle is 3.535533, whose vertices are  (0,0,0), (1,3,−1), and (2,1,1) .

Explanation: -

To find the area of the triangle with vertices (0,0,0), (1,3,-1), and (2,1,1), you can use the formula for the area of a triangle in 3D space:

Area = 0.5 * ||AB x AC||

Here, AB and AC are the vectors representing the sides of the triangle, and "x" denotes the cross product.

STEP 1:- Find the vectors AB and AC:
AB = B - A = (1,3,-1) - (0,0,0)

     = (1,3,-1)
AC = C - A = (2,1,1) - (0,0,0)

     = (2,1,1)

STEP 2: - Compute the cross product AB x AC:
AB x AC = (3 * 1 - (-1) * 1, -(1 * 1 -(- 1 )* 2), 1 * 1 - 3 * 2)
AB x AC = (3 + 1, 3, 1 - 6)

              = (4, 2, -5)

STEP 3: - Compute the magnitude of the cross product ||AB x AC||:
||AB x AC|| = √(4² + (-3)² + (-5)²)

                  = √(16 + 9 + 25)

                  = √50

                  =7.071060

STEP 4: - Calculate the area of the triangle:
Area = 0.5 * ||AB x AC|| = 0.5 * (7.071060)

Therefore, the area of the triangle is 3.535533.

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Answer:

72

Step-by-step explanation:

you is correct good job

The circumference of the circle in terms of π whose radius is given would be = 63π. That is option D.

To calculate the circumference of a circle, the formula that should be used would be given below.

That is;

circumference of circle= 2πr

The radius = 31½

circumference = 2×π × 31½

= 2×π× 63/2

= 63π

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Answer:

10

Step-by-step explanation:

When you increase the x-value by one, the y-value decreases by 2. If you decrease the x-value by 1 which would be 0, then add 2 to the y-value which is 10, that would be the y-intercept

Answer:10!!

Step-by-step explanation:

Using the zero product property

To use the zero product property to determine the values of x for which the expression equals 0, we need to set each factor equal to 0 and solve for x.

Setting each factor equal to 0 gives us:

x+7 = 0 or x-2 = 0

Solving each equation for x, we get:

x = -7 or x = 2

Hence, the values of x are x=-7 and x=2.

Setting each factor equal to 0 gives us:

2x+7 = 0 or x-6 = 0

Solving each equation for x, we get:

x = -7/2 or x = 6

Hence, the values of x  are x=-7/2 and x=6.

Setting each factor equal to 0 gives us:

-3x+11 = 0 or 4x+18 = 0

Solving each equation for x, we get:

x = 11/3 or x = -9/2

Hence, the values of x  are x=11/3 and x=-9/2.

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The mean absolute deviation (MAD) of Han's recorded data is 6 pages. To calculate the mean absolute deviation (MAD) of the data, we first need to find the mean of the data set. We can do this by adding up all the values and dividing by the total number of values.

In this case, Han recorded the number of pages he read for five days. From the dot plot, we can see that he read 20 pages on day 1, 30 pages on day 2, 40 pages on day 3, 25 pages on day 4, and 35 pages on day 5.

To find the mean, we add up all the values:

20 + 30 + 40 + 25 + 35 = 150

And then divide by the total number of values (which is 5 in this case):

150 / 5 = 30

So the mean of Han's recorded data is 30 pages per day.

Next, we need to find the deviation of each value from the mean. We can do this by subtracting the mean from each value:

|20 - 30| = 10
|30 - 30| = 0
|40 - 30| = 10
|25 - 30| = 5
|35 - 30| = 5

The absolute values are used because we only care about the distance from the mean, not whether the values are above or below the mean.

Then, we add up all the deviations:

10 + 0 + 10 + 5 + 5 = 30

And divide by the total number of values (which is still 5):

30 / 5 = 6

So the mean absolute deviation (MAD) of Han's recorded data is 6 pages.

In summary, to find the MAD of a set of data, we need to find the mean of the data, find the deviation of each value from the mean (using absolute values), add up all the deviations, and divide by the total number of values.

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The hypotheses for the test are H₀: σ₁² = σ₂² and H₁: σ₁² ≠ σ₂². This is a two-tailed test to assess if there is a difference in the standard deviations of sound levels between the areas designated as "casualty doors" and operating theaters. The claim being investigated is whether or not there is a difference in the standard deviations.

The hypotheses for the test are:

H₀: σ₁² = σ₂² (There is no difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

H₁: σ₁² ≠ σ₂² (There is a difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

This hypothesis test is a two-tailed test because the alternative hypothesis is not specifying a direction of difference.

To substantiate the claim that there is a difference in the standard deviations, we will conduct a two-sample F-test at a significance level of 0.10, comparing the variances of the two groups.

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Answer:

4 units

Step-by-step explanation:

The length of the shorter side is equal to the difference in y-coordinates of two vertically opposite vertices. The y-coordinates of the vertices (-1, -5) and (3, -5) are both -5, so the vertical side between them is not the shorter side. The y-coordinates of the vertices (3, -7) and (-1, -7) are both -7, so the vertical side between them is the shorter side. The difference in the x-coordinates of these two vertices is 3 - (-1) = 4, so the length of the shorter side is 4 units.

Answer: Your answer is 2

Step-by-step explanation: I did the k12 quiz here's proof

Answer: 0.000036

Step-by-step explanation:

When multiplying a number by 10 to the power of a positive exponent (e.g. 10 3 ), move the decimal in the number that many spaces to the right (e.g. 4.5 ⋅ 10 3 = 4500 ).

When multiplying a number by 10 to the power of a negative exponent (e.g. 10 − 4 ), move the decimal in the number (the absolute value of) that many spaces to the left (e.g. 4.5 ⋅ 10 − 4 = 0.00045 ).

For 3.6 ⋅ 10 − 5 , move the decimal five spaces to the left: 0.000036

Answer:

12742.84$

Step-by-step explanation:

11798 (the price) + 11796 x 0.08 (8% interest)=12742.84

Answer:

Step-by-step explanation:

Example: (1 2/3) (2 3/5)

Turn to improper fractions

1 2/3= 5/3   2 3/5= 13/5

5/3 x 13/5=?

5x13= 65

3x5= 15

Simplify/divide: 65/15 = 4 1/3

Another example. (2 5/6)(3)

Improper fraction:  2 5/6= 17/6

Turn Whole number to fraction: 3= 3/1

17/6 x 3/1

17x3= 51

6x1= 6

51/6

Simplify/divide: 8 1/2

Answer:

61m/h

Step-by-step explanation:

488/8 (to get the number of miles PER HOUR) = 61 miles/ hour

Answer:

The missing fraction is 6/12

(you can further simplify this but the question requires that you don't do that)

Step-by-step explanation:

To add fractions easily, their denominators should have the same value, so the denominator should be 12,

Then, to get 16 in the numerator, we need to find a number that on adding to 10, gives 16, or,

10 + x = 16

x = 16 - 10

x = 6

So, the numerator should be 6

so we get the fraction, 6/12

We can also solve it in an alternate way,

\(10/12 + x = 16/12\\x = 16/12 - 10/12\\x = (16-10)/12\\x = 6/12\)

Answer:

Step-by-step explanation:

yes but that is just me go to my page for why i think that

The statement 'when finding a minimum in a linear programming problem, it is possible to find more than one minimum value' is True.

In this question, we have been given a statement - 'when finding a minimum in a linear programming problem, it is possible to find more than one minimum value.'

We need to state whether it is true or false.

We know that, the minimum value of the objective function Z = ax + by in a linear programming problem can also occur at more than one corner points of the feasible region.

Therefore, when finding a minimum in a linear programming problem, it is possible to find more than one minimum value.

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Based on the provided scenario, the statement can be classified as: b. This is a nonsampling error that causes bias.

Nonsampling errors refer to errors that occur in data collection, processing, or analysis that are not related to the sampling method.

The scenario described, where individuals may not provide truthful answers due to fear of their responses being shared with law enforcement officials, introduces a bias in the collected data.

This bias occurs because the reported data does not accurately represent the true prevalence of illicit drug use in the population.

The fear of legal consequences leads to a systematic deviation from the true values, which is a form of bias.

Therefore, option b is the correct classification for this scenario.

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Answer: 4135 over 1 or 8270 over 2

Step-by-step explanation:

The equation in terms of x (rs) is rs + 3 * rs = 32. By solving this equation, we found that rs = 8 and st = 24.

To find rs and st, we need to write an equation in terms of x using the given information and then solve for x.

Let's suppose that rs and st are two line segments, and x represents the length of rs. To find the lengths of rs and st, we can set up an equation based on the given information.

From the problem, we know that the length of st is three times the length of rs. This can be expressed as:

st = 3 * rs

Additionally, the total length of rs and st is 32 units. Mathematically, this can be represented as:

rs + st = 32

Now, we can substitute the value of st from the first equation into the second equation:

rs + 3 * rs = 32

Simplifying this equation, we have:

4 * rs = 32

To solve for rs, we divide both sides of the equation by 4:

rs = 32 / 4

rs = 8

Hence, we have found that rs is equal to 8 units.

To find the length of st, we can substitute the value of rs into the first equation:

st = 3 * rs

st = 3 * 8

st = 24

Therefore, the length of st is 24 units.

In summary, the equation in terms of x (rs) is rs + 3 * rs = 32. By solving this equation, we found that rs = 8 and st = 24.

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the equation of the tangent line to the graph of \(f(x) = -4x \cdot e^x\) at the point \((a, f(a))\) for \(a = 3\) is \(y = -16e^3x + 60e^3\).

To find the equation of the tangent line to the graph of \(f(x) = -4x \cdot e^x\) at the point \((a, f(a))\) for \(a = 3\), we need to determine the slope of the tangent line and the point of tangency.

Step 1: Find the slope of the tangent line

The slope of the tangent line can be found by taking the derivative of \(f(x)\) with respect to \(x\). Let's compute it:

\(f'(x) = \frac{d}{dx} (-4x \cdot e^x)\)

Using the product rule, we have:

\(f'(x) = -4e^x - 4xe^x\)

Step 2: Find the point of tangency

To find the point of tangency, substitute \(x = a\) into \(f(x)\). In this case, \(a = 3\), so we evaluate \(f(a)\):

\(f(3) = -4(3) \cdot e^3\)

Step 3: Determine the equation of the tangent line

Now that we have the slope of the tangent line and the point of tangency, we can use the point-slope form of a linear equation to find the equation of the tangent line. The point-slope form is given by:

\(y - y_1 = m(x - x_1)\)

where \((x_1, y_1)\) is a point on the line and \(m\) is the slope of the line.

Substituting the values we found into the equation, we have:

\(y - f(3) = f'(3)(x - 3)\)

\(y - (-4(3) \cdot e^3) = (-4e^3 - 4(3)e^3)(x - 3)\)

Simplifying:

\(y + 12e^3 = (-4e^3 - 12e^3)(x - 3)\)

\(y + 12e^3 = -16e^3(x - 3)\)

\(y = -16e^3x + 48e^3 + 12e^3\)

\(y = -16e^3x + 60e^3\)

Therefore, the equation of the tangent line to the graph of \(f(x) = -4x \cdot e^x\) at the point \((a, f(a))\) for \(a = 3\) is \(y = -16e^3x + 60e^3\).

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Answer:

Triangle 2

Step-by-step explanation:

The translation is a type of transformation, where the figure is just translated or simply moved from its original place.

The figure is not rotated or dilated but simply moved.

Here, we can see that only figure or triangle 2 is like the triangle ABC. Other triangles have undergone other transformations.

So, the correct answer is triangle 2.

~Hope this helps~

Answer: The area of each slice of pizza can be calculated by finding the area of the whole pizza and dividing it by the number of slices.

The radius of the pizza is half of the diameter, so the radius is 20/2 = 10 inches.

The area of the whole pizza can be calculated using the formula for the area of a circle:

Area = π × radius^2

Area = π × 10^2

Area = 100π square inches

Since there are 8 slices, each slice has an area of:

100π square inches / 8 = 12.5π square inches

Therefore, the area of the 5 slices that Chris ate is:

5 × 12.5π square inches = 62.5π square inches

This is approximately equal to 196.35 square inches, when rounded to two decimal places.

Step-by-step explanation:

Answer:

0.875

Step-by-step explanation:

Answer:

47/4  or 11.75 = m

Step-by-step explanation:

-47 -2.5 = -2.5 - 1.7m - 2.3m

Combine like terms

-49.5 = -2.5 -4m

Add 2.5 to each side

-49.5 +2.5 = -2.5+2.5 -4m

-47 = -4m

Divide each side by -4

-47/-4 = -4m/-4

47/4 = m

11.75 = m

Answer:

Step-by-step explanation: