During their team meeting, both managers shared their findings. Complete the statement describing their combined results.



Select the correct answer from each drop-down menu.



The initial number of video views was ____ the initial number of site visits, and the number of video views grew by _____ the number of site visits.



The difference between the total number of site visits and the video views after 5 weeks is _____.



More than


the same as


fewer than



a smaller factor than


the same factor as


a larger factor than



20,825


52,075


15,625


36,450

The law of sines is solved and the triangle is given by the following relation

Given data ,

From the law of sines , we get

a / sin A = b / sin B = c / sin C

a)

C = 135° C = 45₁ B = 10°

So , the measure of triangle is

A/ ( 180 - 35 - 10 ) = A / 35

And , a/ ( sin 135/35 ) = sin 35 / a

On simplifying , we get

a = 36.50

Hence , the law of sines is solved

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The value of x is 6 and the perimeter is 52 unints

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

The figure

If the lines that appear to be tangent are tangent, then we have the following equation

x + 2 = 8

Evaluate the like terms

x = 6

The perimeter is the sum of the side lengths

So, we have

Perimeter = x + 2 + 8 + 5 + 5 + 9 + 9 + 4 + 4

This gives

Perimeter = 6 + 2 + 8 + 5 + 5 + 9 + 9 + 4 + 4

Evaluate

Perimeter = 52

Hence, the perimeter is 52 unints

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If the first cube has a volume of 125 cm³ and the second cube has a volume of 343 cm³, the difference in the area of one face of the second cube and the area of one face of the first cube is 24cm². The answer is B. 24 cm².

To find the difference in the area of one face of each cube, we first need to find the side length of each cube. Since the volume of a cube is equal to the side length cubed (V = s³), we can find the side length by taking the cube root of the volume.

For the first cube:
Volume = 125 cm³
Side length = cube root of 125 = 5 cm

For the second cube:
Volume = 343 cm³
Side length = cube root of 343 = 7 cm

Next, we find the area of one face of each cube. The area of one face of a cube is equal to the side length squared (A = s²).

Area of one face of the first cube:
A1 = 5² = 25 cm²

Area of one face of the second cube:
A2 = 7² = 49 cm²

Finally, find the difference in the area of one face of each cube:
Difference = A2 - A1 = 49 cm² - 25 cm² = 24 cm²

The answer is B. 24 cm².

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The point of intersection between the two given equations is (3, -2).

The problem is asking to find the point of intersection between the two given equations:

y = (1/3)x - 3 ............... (equation 1)

y = -x + 1 ............... (equation 2)

To solve for the intersection point, we can set the two equations equal to each other:

(1/3)x - 3 = -x + 1

Simplifying and solving for x:

(1/3)x + x = 1 + 3

(4/3)x = 4

x = 3

Now that we know x = 3, we can substitute it into either of the two original equations to find y:

Using equation 1: y = (1/3)x - 3 = (1/3)(3) - 3 = -2

Using equation 2: y = -x + 1 = -(3) + 1 = -2

Therefore, the intersection point is (3, -2).

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The equation provided, "e3r + 6e2x + 7e et - 64 pestle da," is not an integral expression and does not have a variable of integration.

Additionally, the requested answer, "] +0," does not make sense in the context of the question. Please provide a complete and accurate question for me to assist you with. Hi! Based on your terms provided ("Integrals", "substitution", and "find"), I understand that you are looking to solve an integral using substitution. However, the integral you provided appears to have some typographical errors. Please provide the correct integral, and I'll be happy to help you solve it.

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The FICA tax will be $3595.5 on an income of $47,000.

Given that the principal amount = $47,000

Given that the FICA is taxed at the percentage of 7.65%

To findout the FICA tax we have to findout the 7.65% of money from the principal money $47,000.

The formula for finding the Y% of money from Z amount is = [tex]\frac{y}{100}[/tex] * Z

From the above formula, we can find the FICA tax.

FICA tax = [tex]\frac{7.65}{100}[/tex] * 47000 = 0.0765 * 47000 = 3595.5.

From the above solution, we can conclude that the FICA tax on an income of $47,000 is $3595.5

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The benchmark fractions are the most common fraction.

Such as 1/2, 0, 3/8 etc.

Mixed fractions are a type of fraction in which there is a whole number part and a fractional part. for example 17/3 would be 5 2/3 as a mixed fraction

There are 26 zeros in this number when it is written in standard notation. The correct answer is option (A). The mass of the sun is estimated to be 1.9891 x 10³⁰kg. To determine the number of zeros in this number when written in standard notation, we need to first convert it to standard form.

In standard form, the number is expressed as a decimal between 1 and 10 multiplied by a power of 10. To convert the given number to standard form, we move the decimal point 30 places to the right because the exponent is positive 30. This gives us 1989100000000000000000000000000. As we can see, there are 27 digits in this number. Therefore, there are 27-1=26 zeros in this number when it is written in standard notation.

In conclusion, the answer is A, 26. This type of question is commonly asked in science and engineering, where large or small numbers are expressed in scientific notation for convenience. Understanding how to convert between scientific notation and standard form is important for anyone studying or working in these fields.

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The distance between the two scout patrols is approximately 11.66 kilometers.

We can see that the situation forms a right triangle with the hypotenuse representing the distance between the two scout patrols. Let's call this distance d.

Each patrol initially hikes 5 kilometers in opposite directions. This means that the distance between them at this point is 10 kilometers (5 km + 5 km).

Then, each patrol turns 90 degrees to their right and hikes 6 kilometers. This means that they travel along the legs of the right triangle, which have a length of 6 kilometers.

Using the Pythagorean theorem, we can solve for the hypotenuse:

d² = 10² + 6²

d² = 136

d ≈ 11.66 km

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According to the question the  graph the line -3x + 5y = 15, we can start by solving for y:

-3x + 5y = 15

5y = 3x + 15

y = (3/5)x + 3

As an algebraic framework that depicts a specific function by joining a collection of points, a graph is defined. It establishes a pairwise connection among the items. The graph is made up of nodes (vertices) linked by edges. (lines).

Briefing :

Now we have the equation in slope-intercept form (y = mx + b) where the slope is 3/5 and the y-intercept is 3.

To graph the line, we can start at the y-intercept (the point (0, 3)) and then use the slope to find additional points. Since the slope is 3/5, we can move up 3 units to the right 5 units to get to the point (5, 6), and down 3 units to the left 5 units to get to the point (-5, 0). Connect these points to get the line.

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(a) The elasticity at p = $50 and q = 4502 is 2.778.

(b) The elasticity is elastic.

(c) An increase in price would result in a decrease in revenue.

(a) To find the elasticity when p = $50 and q = 4502, we first need to find the partial derivatives of q with respect to p and then use the elasticity formula:

Demand: 2p²q = 10000 + 9000p²

Partial derivative of q with respect to p: 4pq = 18000p

When p = $50 and q = 4502:

4(50)(4502) = 900800

Elasticity:

e = (p/q) * (dq/dp) = (50/4502) * (900800/18000) = 2.778

(b) To determine what type of elasticity this is, we look at the value of the elasticity calculated in part (a). Since the elasticity is greater than 1, we know that this is an elastic demand.

(c) To determine how the revenue would be affected by an increase in price, we need to look at the relationship between elasticity and revenue. If demand is elastic,

Then an increase in price will result in a decrease in total revenue, and if demand is inelastic, then an increase in price will result in an increase in total revenue.

Since we know that the demand is elastic (from part (b)), we can conclude that an increase in price will lead to a decrease in revenue.

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Answer:

C = 52

Step-by-step explanation:

sin(c/4) = sin(104/8)

sin(c/4) = 0.22495

c/4 = 13

c = 52

The average rate of change is -0.1295, under the condition the given exponential decay function is f (t) = 2(0. 95).

In order to find the average rate of change from x=0 to x=4 for the given exponential decay function [tex]f(t) = 2(0.95)^{t}[/tex], we need to find the slope of the line that passes through the points (0,f(0)) and (4,f(4)).

f(0) = 2(0.95)⁰ = 2

f(4) = 2(0.95)⁴ ≈ 1.482

The slope of the line passing through these two points is:

(f(4) - f(0))/(4 - 0)

= (1.482 - 2)/4

≈ -0.1295

Therefore, the average rate of change from x=0 to x=4 is approximately -0.1295.

An exponential decay function is a form of a function that reduces at a constant rate over time. It is a type of  mathematical model used to present many real-world phenomena such as radioactive decay, population growth, and the depreciation of assets.

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Answer:

a = 3

b = 1

c = 5

d = 2

Step-by-step explanation:

To find the prime factorization of 600, we can use trial division by dividing by the smallest prime numbers until we reach a prime factor:

600 ÷ 2 = 300

300 ÷ 2 = 150

150 ÷ 2 = 75

75 ÷ 3 = 25

25 ÷ 5 = 5

Therefore, the prime factorization of 600 is:

600 = 2^3 × 3^1 × 5^2

So, a = 3, b = 1, c = 5, and d = 2.

The given set of questions are solved under the condition of  parametric equations x(t)=sin(3t) and y(t)=cos(3t) .

Hence, the length of the curve from t= 0 to t= π is 3π.

Now,

A. To evaluate the velocity, we need to perform the derivative of x(t) and y(t) concerning t.

x'(t) = 3cos(3t)

y'(t) = -3sin(3t)

Therefore,  the velocity vector is

v(t) = <3cos(3t), -3sin(3t)>

B. To define the acceleration, we need to evaluate  the derivative of v(t) concerning t.

a(t) = v'(t) = <-9sin(3t), -9cos(3t)>

C. To describe  the speed, we need to calculate  the magnitude of the velocity vector.

|v(t)| = √((3cos(3t))² + (-3sin(3t))²)

= 3

D. In order to find the number of times at which the particle stops, to find when the speed is equal to zero.

|v(t)| = 0 when cos(3t) = 0

sin(3t) = 0.

Therefore,

cos(3t) = 0 when t = (π/6) + (nπ/3),

here n = integer.

sin(3t) = 0 when t = (nπ/3),

here n = integer.

E. To calculate the length of the curve from t=0 to t=π by performing  calculus

L = ∫[a,b] √((dx/dt)² + (dy/dt)²) dt

Therefore, a=0 and b=π.

L = ∫[0,π] √((3cos(3t))² + (-3sin(3t))²) dt

 = ∫[0,π] 3 dt

 = 3π

The given set of questions are solved under the condition of  parametric equations x(t)=sin(3t) and y(t)=cos(3t) .

Hence, the length of the curve from t=0 to t=π is 3π.

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The complete question is

A particle moves along a path in the xy-plane. the path is given by

the parametric equations x(t)=sin(3t) and y(t)=cos(3t), help with

steps A-E

a. Find the velocity

b. Find the acceleration.

c. Find the speed and simplify your answer completely.

d. Find any times at which the particle stops. Thoroughly explain your answer.

e. Use calculus to  find the length of the curve from t=0 to t = π , show your work.

Answer: 7

Step-by-step explanation:

Answer:

y=|x-2|-2

Step-by-step explanation:

Go onto desmos and you can ask it to graph an equation to test your answers.

The least-squares regression line of height versus age will have a slope of 0.8 .  Was true statement option (2)

The correlation coefficient (r) measures the strength and direction of a linear relationship between two variables, in this case, height and age. A correlation coefficient of 0.8 indicates a strong positive linear relationship between height and age. The slope of the least-squares regression line represents the change in the height of a child for each one-unit increase in age.

Therefore, a slope of 0.8 indicates that for each one-year increase in age, the expected increase in height is 0.8 units. The other options are not correct or relevant based on the given information.

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Full Question: the height and age of each child in a random sample of children was recorded. the value of the correlation coefficient between height and age for the children in the sample was 0.8 . based on the least-squares regression line created from the data to predict the height of a child based on age, which of the following is a correct statement?

responses on average,

Yes. The null hypothesis is that the changes in the course did not have a significant impact on the DFW rate. The chi-squared statistic is 44.63, with 2 degrees of freedom, and the p-value is less than 0.001.

1. Yes, it is likely that the changes in the gateway course had an impact on the DFW rate, as the rate decreased from 42.1% in Year 1 to 19.4% in Year 3.

2. The null hypothesis is that the changes in the course did not have a significant impact on the DFW rate, while the alternative hypothesis is that the changes did have a significant impact on the rate.

3. The chi-squared statistic is 44.63, with 2 degrees of freedom, and the p-value is less than 0.001. This indicates that there is a significant relationship between the year the course was given and the DFW rate, providing evidence to reject the null hypothesis in favor of the alternative hypothesis that the changes made to the course had a significant impact on the DFW rate.

The p-value of less than 0.001 indicates strong evidence against the null hypothesis, as it is less than the significance level of 0.1.

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The car depreciated at an annual rate of approximately 45.81%.

In 2016, Dave bought a new car for $15,500, and its current value is $8,400. To find the annual depreciation rate, we'll use the formula A(t) = P(1 ± r)t, where A(t) is the future value, P is the initial value, r is the annual rate, and t is the time in years.

Here, A(t) = $8,400, P = $15,500, and t = 1 (one year). We are solving for r, the annual depreciation rate.

$8,400 = $15,500(1 - r)¹

To isolate r, we'll first divide both sides by $15,500:

$8,400/$15,500 = (1 - r)

0.541935 = 1 - r

Now, subtract 1 from both sides:

-0.458065 = -r

Finally, multiply both sides by -1 to find r:

0.458065 = r

To express r as a percentage, multiply by 100:

0.458065 x 100 = 45.81%

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The car depreciated at an annual rate of 12.2%.

The car depreciated in value over time, so we want to find the rate of decrease. We can use the formula:

A(t) = P(1 - r)t

where A(t) is the current value of the car, P is the original price of the car, r is the annual rate of depreciation, and t is the time elapsed in years.

We can plug in the given values and solve for r:

$8,400 = $15,500(1 - r)⁵

Dividing both sides by $15,500, we get:

0.54 = (1 - r)⁵

Taking the fifth root of both sides, we get:

(1 - r) = 0.878

Subtracting 1 from both sides, we get:

-r = -0.122

Dividing both sides by -1, we get:

r = 0.122

Multiplying by 100 to express as a percentage, we get:

r = 12.2%

Therefore, the car depreciated at an annual rate of 12.2%.

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The critical value for a right-tailed test of a population mean at α=0.10 level of significance with 20 degrees of freedom is 1.325.

The critical value for a left-tailed test of a population mean at the α=0.10 level of significance based on a sample size of n=15 is -1.345.

The critical value(s) for a two-tailed test of a population mean at the α=0.01 level of significance based on a sample size of n=11 is -2.718 and 2.718.

To find the critical values, we need to use a t-distribution table or a statistical software that provides the critical t-values for a specific level of significance and degrees of freedom.

For part (a), since it's a right-tailed test, the critical value will be positive, and we need to look for the t-value that corresponds to an area of 0.10 to the right of the mean in the t-distribution table. With 20 degrees of freedom, the critical value is 1.325.

For part (b), since it's a left-tailed test, the critical value will be negative, and we need to look for the t-value that corresponds to an area of 0.10 to the left of the mean in the t-distribution table. With 15 degrees of freedom, the critical value is -1.345.

For part (c), since it's a two-tailed test, we need to split the significance level equally between the two tails. We need to find the t-values that correspond to an area of 0.005 to the left of the mean and 0.005 to the right of the mean in the t-distribution table. With 11 degrees of freedom, the critical values are -2.718 and 2.718.

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Answer:

89

Step-by-step explanation:

construct the formula to obtain the total of marks in first 9 tests:

79 = x/9

79 * 9 = 711

x = 711

so to get 80% in the next test we construct this formula:

80 = 711 + y / 9 + 1

the value we get for y is 89

to confirm the answer, 711+89/10 gives us 80, which is the correct value we want

To find the vector a = AB, we subtract the coordinates of point A from the coordinates of point B:

a = B - A = (-2,4,3) - (4,-6,-3) = (-2-4, 4+6, 3+3) = (-6, 10, 6)
The vector a can be written as a column vector with angle brackets: a = < -6, 10, 6 >.
To find the vector AB (a), we need to subtract the coordinates of point A from the coordinates of point B. Here's the calculation:

a = B - A
a = (-2, 4, 3) - (4, -6, -3)
Now, subtract each corresponding coordinate:

a = (-2 - 4, 4 - (-6), 3 - (-3))
a = (-6, 10, 6)
So, the vector AB (a) is <-6, 10, 6>.

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Based on the information, the three numbers are 14, 34, and 70.

Based on the information, the second number = 3x - 8

The third number is five times the first number, which can be written as:

third number = 5x

The sum of the three numbers is 118, so we can write an equation:

x + (3x - 8) + 5x = 118

9x - 8 = 118

Adding 8 to both sides:

9x = 126

x = 236 / 914

Now we can use this value of x to find the other two numbers:

second number = 3x - 8 = 3(14) - 8 = 34

third number = 5x = 5(14) = 70

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The coordinates for H’I’D’E’ after a reflection over the y-axis include the following:

H' (-1, 4).

I' (-2, -1).

D' (-4, -3).

D' (-5, 3).

In Mathematics and Geometry, a reflection over or across the y-axis or line x = 0 is represented and modeled by this transformation rule (x, y) → (-x, y).

By applying a reflection over the y-axis to the coordinate of the given quadrilateral HIDE, we have the following coordinates:

(x, y)                             →                 (-x, y).

Coordinate H = (1, 4)   →  Coordinate H' = (-(1), 4) = (-1, 4).

Coordinate I = (2, -1)   →  Coordinate I' = (-(2), -1) = (-2, -1).

Coordinate D = (4, -3)   →  Coordinate D' = (-(4), -3) = (-4, -3).

Coordinate E = (5, 3)   →  Coordinate D' = (-(5), 3) = (-5, 3).

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Lizzie's divisibility test states that a number n is divisible by a certain number m if and only if the alternating sum of its two-digit chunks is divisible by m.

Lizzie's divisibility test involves breaking a positive integer into two-digit chunks, finding the alternating sum of these chunks, and then determining if the result is divisible by a certain number m.

To apply the test:

To prove that this is a divisibility test for m, you need to show that n is divisible by m if and only if the result of the alternating sum is divisible by m.

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If the surface area of a can with a particular volume is minimized when the height of the can is 22 cm, we would expect the radius of the can to be the same as the height, given that a cylinder has the smallest surface area when its height and radius are equal.

The surface area of a can with height h and radius r can be given by the formula:

A = 2πr² + 2πrh

The volume of the can is given by:

V = πr²h

If we differentiate the surface area with respect to r and equate it to zero to find the critical point, we get:

dA/dr = 4πr + 2πh(dr/dr) = 0

Simplifying this expression, we get:

2r + h = 0

Since we know that the height of the can is 22 cm, we can substitute h = 22 in the equation to get:

2r + 22 = 0

Solving for r, we get:

r = -11

Since the radius of the can cannot be negative, we discard this solution. Therefore, the radius of the can should be equal to its height, which is 22 cm.

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Answer:  In bold

Step-by-step explanation:

The formula they gave is a rate

Let's solve for the rate first.

This equation is done for 3 years 2018-2021  that's why ^3

3.55 =  2.90(1+x)³                 >divide both sides by 2.90

1.224 = (1+x)³                         > take cube root of both sides

1.0697 =  1+x

x= .0697

so let's make our generic formula

[tex]y = 2.90(1+.0697)^{t}[/tex]        let t be years and let y=  price  

Let's calculate 2018, so this would be year 0

[tex]y = 2.90(1+.0697)^{0}[/tex]

y=$2.90   this is for 2018

They already gave you 2021 price

y=$3.55   this is for 2021

Rate of increase is .0697 

In 2025

That's 7 years=t

[tex]y = 2.90(1+.0697)^{7}[/tex]

y=$4.65    for 2025

Answer:

j: 0, m: (-4)

Step-by-step explanation:

RECALL:

Rational function is the func. expressed by polynomials p(x) and q(x) as:

p(x)/q(x) where q(x) is non-zero

j(m+4) must be non zero, or

j(m+4)≠0

j≠0 and m+4≠0

j≠0 and m≠(-4)

The planes intersect at the point (-19/21, -11/14, 1).

To determine how, if at all, the planes intersect, we need to solve the system of equations given by the three planes:

[2T/3A] 2x + 2y + z - 10 = 0

5x + 4y - 4z = 13

3x – 2z + 5y - 6 = 0

We can use elimination to solve this system. First, we can eliminate z from the second and third equations by multiplying the second equation by 2 and adding it to the third equation:

5x + 4y - 4z = 13

6x - 4z + 10y - 12 = 0

11x + 14y - 12 = 0

Next, we can eliminate z from the first and second equations by multiplying the first equation by 2 and subtracting the second equation from it:

4x + 4y + 2z - 20 = 0

-5x - 4y + 4z = -13

9x - y - 6z - 20 = 0

Now we have two equations in three variables. To eliminate y, we can multiply the second equation by 14 and subtract it from the first equation:

11x + 14y - 12 = 0

-70x - 56y + 56z = -182

-59x - 42z - 12 = 0

Finally, we can substitute this expression for x into one of the previous equations to find z:

3(59/42)z - 12/42 - 2y - 10 = 0

177z - 60 - 84y - 420 = 0

177z - 84y - 480 = 0

Now we have two equations in two variables, z and y. We can solve for y in terms of z from the second equation:

y = (177/84)z - (480/84)

Substituting this expression for y into the third equation, we can solve for z:

177z - 84[(177/84)z - (480/84)] - 480 = 0

177z - 177z + 480 - 480 = 0

This equation simplifies to 0=0, which means that z can be any value. Substituting z=1 into the expression for y, we get:

y = (177/84)(1) - (480/84) = -11/14

Substituting z=1 and y=-11/14 into the expression for x, we get:

x = (59/42)(1) - (12/42) + 2(-11/14) + 10 = -19/21

Therefore, the planes intersect at the point (-19/21, -11/14, 1).

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The number of bracelets that can be made using all the colors one time only is 720.

Given that Diana is making bracelet with 6 different colors we need to find the number of bracelets that can be made using all the colors one time only,

Since there are 6 beads so, the number of bracelets can be made = 6!

= 720

Hence the number of bracelets that can be made using all the colors one time only is 720.

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