Abiodun walks 5km due north,then12km due east.How far ia he from the starting point?

Answer:

Para encontrar el valor de la expresión 6 - (3x + 1) + 2x^2 cuando x = 4, sustituimos el valor de x en la expresión y evaluamos:

6 - (3x + 1) + 2x^2

= 6 - (3 * 4 + 1) + 2 * 4^2

= 6 - (12 + 1) + 2 * 16

= 6 - 13 + 32

= -7 + 32

= 25

Por lo tanto, cuando x = 4, el valor de la expresión 6 - (3x + 1) + 2x^2 es igual a 25.

Step-by-step explanation:

To determine which company has higher salaries, you can use the mean, median, or mode as measures of center. Let's calculate each of these measures for the given data:

Company A salaries: 45,000, 55,000, 53,000, 51,000, 49,000, and 42,000.

Mean (Average):

To calculate the mean, sum up all the salaries and divide by the total number of salaries.

Mean of Company A salaries = (45,000 + 55,000 + 53,000 + 51,000 + 49,000 + 42,000) / 6 = 295,000 / 6 = 49,167

Median:

To find the median, you arrange the salaries in ascending order and find the middle value. If there is an even number of values, you take the average of the two middle values.

Arranging the Company A salaries in ascending order: 42,000, 45,000, 49,000, 51,000, 53,000, 55,000

Median of Company A salaries = (49,000 + 51,000) / 2 = 50,000

Mode:

The mode represents the value(s) that appear most frequently in the dataset.

In Company A salaries, all the values occur only once, so there is no mode.

Now let's calculate the same measures for Company B salaries:

Company B salaries: 54,000, 39,000, 51,000, 52,000, 44,000, and 48,000.

Mean of Company B salaries = (54,000 + 39,000 + 51,000 + 52,000 + 44,000 + 48,000) / 6 = 288,000 / 6 = 48,000

Arranging the Company B salaries in ascending order: 39,000, 44,000, 48,000, 51,000, 52,000, 54,000

Median of Company B salaries = (48,000 + 51,000) / 2 = 49,500

Mode of Company B salaries = There are no repeating values, so there is no mode.

To summarize:

- Mean of Company A salaries: $49,167

- Median of Company A salaries: $50,000

- Mode of Company A salaries: No mode

- Mean of Company B salaries: $48,000

- Median of Company B salaries: $49,500

- Mode of Company B salaries: No mode

Based on these measures of center, we can see that the mean and median salaries of Company A are slightly higher than those of Company B. However, since there is no mode in either dataset, we cannot consider the mode as a determining factor in this case.

The amount of money that Jane Doe get to take home after taxes in 2017 is A. $48500

Based on the W-2 form above, Jane Doe's gross pay was $50,000. She had $6,835 in federal income tax withheld, $725 in state income tax withheld, and $1,000 in FICA taxes withheld. This means that her net pay was $48,500.

Net pay = Gross pay - Total taxes withheld

Net pay = $50,000 - ($6,835 + $725 + $1,000)

Net pay = $48,500

Therefore, amount of money that Jane Doe get to take home after taxes in 2017 is A. $48500

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1. The price of a pair of gloves (x) is $8.50, and the price of a hat (y) is $6.50.

2. Aaliyah invested $7,200 in the mutual fund that rose 6% and $2,800 in the mutual fund that rose 9%.

1. Let's assume the price of a pair of gloves is represented by 'x' and the price of a hat is represented by 'y'.

From the given information, we can establish the following equations based on Cody and Tor's purchases:

Equation 1: 2x + 4y = 43.00 (Cody's purchase)

Equation 2: 2x + 2y = 30.00 (Tor's purchase)

To solve this system of equations, we can use a method like substitution or elimination.

Using the substitution method, we can rearrange Equation 2 to express x in terms of y:

2x = 30.00 - 2y

x = 15.00 - y

Now, we substitute this value of x into Equation 1:

2(15.00 - y) + 4y = 43.00

30.00 - 2y + 4y = 43.00

2y = 43.00 - 30.00

2y = 13.00

y = 6.50

Substituting this value of y back into Equation 2 to find x:

2x + 2(6.50) = 30.00

2x + 13.00 = 30.00

2x = 30.00 - 13.00

2x = 17.00

x = 8.50

Therefore, the price of a pair of gloves (x) is $8.50, and the price of a hat (y) is $6.50.

2. Let's assume Aaliyah invested an amount represented by 'x' in the mutual fund that rose 6% and an amount represented by 'y' in the mutual fund that rose 9%.

From the given information, we can establish the following equations based on the rise in investment:

Equation 1: 0.06x + 0.09y = 684 (rise in investment)

Equation 2: x + y = 10,000 (total investment)

To solve this system of equations, we can use a method like substitution or elimination.

Using the substitution method, we can rearrange Equation 2 to express x in terms of y:

x = 10,000 - y

Now, we substitute this value of x into Equation 1:

0.06(10,000 - y) + 0.09y = 684

600 - 0.06y + 0.09y = 684

0.03y = 84

y = 2800

Substituting this value of y back into Equation 2 to find x:

x + 2800 = 10,000

x = 10,000 - 2800

x = 7200

Therefore, Aaliyah invested $7,200 in the mutual fund that rose 6% and $2,800 in the mutual fund that rose 9%.

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Answer:

Step-by-step explanation:

Willis’s mistake is that he used the differences of 6, 10 and 14 instead of the differences of 7, 17 and 31. For a linear function, the y values should have a constant rate of change and not the differences.

The graph of this relation is four points on the coordinate plane (see attached diagram).

Hence option D is true.

Since we know that,

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

And a function is a special relation,

where each input x has a single output y.

This relation is not a function, because for one x (x=-1),

Here are two different possible y (y=3 or y=2).

If you consider the graph, you can see that there will be vertical line passing through the points (-1,3) and (-1,2).

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Answer:

Step-by-step explanation:

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

Volume = π * radius^2 * height

Given:

Volume = 20π cm^3

Height = 5 cm

We can rearrange the formula to solve for the radius:

radius^2 = Volume / (π * height)

radius^2 = (20π) / (π * 5)

radius^2 = 4

radius = 2

Now, we can find the diameter by multiplying the radius by 2:

diameter = 2 * radius

diameter = 2 * 2

diameter = 4

Therefore, the diameter of the cylinder is 4 cm.

Let's evaluate the probability based on the given information.

The number of ways to choose 6 men from 26 can be calculated as:

C(26, 6) = 26! / (6! * (26-6)!) = 26! / (6! * 20!) = 230,230.

The number of ways to choose 6 women from 29 can be calculated as:

C(29, 6) = 29! / (6! * (29-6)!) = 29! / (6! * 23!) = 177,100.

The total number of possible outcomes is the combination of selecting 6 men and 6 women from the given pool of 26 men and 29 women:

Total outcomes = C(26, 6) * C(29, 6) = 230,230 * 177,100 = 40,795,315,300.

Therefore, the probability of selecting exactly 6 men and 6 women from the given pool is:

Probability = 1 / Total outcomes = 1 / 40,795,315,300 ≈ 2.45 x 10^-11.

Hence, the probability is approximately 2.45 x 10^-11.

Step-by-step explanation:

Unclear what you are asking

here is one possibility

3^2  - 4^5

9    - 1024 = - 1015

Here is another possibility

(3^(2-4) )^5    =  = (3^(-2))^5 =   3 ^-10 =    1/59049      

Answer:

1. 176,500 centimeters

2. 940,000 centimeters

3.42,000,000 grams

Step-by-step explanation:

Convertion:

1.1.1

1765m to cm

1 meter = 100 centimeters

Therefore, 1765 meters =1765*100 centimeters = 176,500 centimeters

1.1.2

9.4 km to cm

1 kilometer = 1000 meters

First convert it into m.

9.4 kilometers = 9.4*1000 meters = 9400 meters

then in cm

1 meter = 100 centimeters

Therefore, 9400 meters = 9400*100 centimeters = 940,000 centimeters

1.1.3

4.2 tons to grams

1 ton = 1000 kilograms

First convert it into kilogram

1 kilogram = 1000 grams

Therefore, 4.2 tons = 4.2*1000 kilograms = 4200 kilograms

then in grams

4200 kilograms = 4200*1000 grams = 42,000,000 grams

I hope this helps! Let me know if you have any other questions.

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

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To calculate the rate at which the mixture is being poured, we divide the amount of mixture poured (in kilograms) by the time it takes (in minutes):

In this case, the amount of mixture poured is 50 kg, and the time taken is 8 minutes. Plugging these values into the formula, we have:

Dividing 50 kg by 8 min gives us:

Therefore, the mixture is being poured at a rate of 6.25 kilograms per minute.

The theoretical probability of selecting the letter T is 1/4.

Probability is the possibility of happening an event.

Given the four letters M, A, T, and H.

Note that the letter T occurs 1 time, therefore, the probability of selecting the letter T is:

[tex]\sf P=\dfrac{1}{4}[/tex]

Hence, the theoretical probability of selecting the letter T is 1/4.

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The correct statement regarding the reflection rules in this problem is given as follows:

D. g(x) is a reflection of f(x) over the x-axis.

The functions f(x) and g(x) in the context of this problem are defined as follows:

The entire function was multiplied by -1, meaning that the signal of the function was exchanged, hence the function was reflected over the x-axis.

As the function was reflected over the x-axis, the correct option in the context of the problem is given by option D.

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Answer:

$941.65

Step-by-step explanation:

We have to find the sales tax of the camera.

tax rate = 9.5%

listed price = $859.95

           [tex]\sf Sales \ tax = tax \ rate * listed \ price[/tex]

                         = 9.5 % * 859.95

                        = 0.095 * 859.95

                        = $81.70

To find the total cost, add the sales tax to the listed price.

Total cost = 859.95 + 81.70

                = $941.65

Answer:

Step-by-step explanation:

To solve for m/MNP if m/MNO = 132° and m/PNO = 40°, we can use the fact that the sum of the angles in a triangle is 180 degrees.

First, we can find the measure of angle MNO:

m/MNO + m/PNO + m/MNP = 180

132 + 40 + m/MNP = 180

m/MNP = 8

Copy

Therefore, m/MNP = 8 degrees.

I hope this helps! Let me know if you have any other questions.

The probability of 12 women jurors being chosen is approximately 0.000342 or 0.0342%.

To calculate the probability of selecting 12 women jurors out of a pool of 26 men and 29 women, we need to consider the total number of possible combinations and the specific combination of interest.

The total number of ways to choose 12 individuals from a pool of 55 (26 men + 29 women) is given by the combination formula:

C(55, 12) = 55! / (12! * (55-12)!) = 22579284062370.

The number of ways to choose 12 women from a pool of 29 is given by the combination formula:

C(29, 12) = 29! / (12! * (29-12)!) = 7726160.

Therefore, the probability of selecting 12 women jurors is the ratio of the number of ways to choose 12 women to the total number of possible combinations:

P(12 women jurors) = C(29, 12) / C(55, 12) ≈ 7726160 / 22579284062370 ≈ 0.000342.

Hence, the probability of 12 women jurors being chosen is approximately 0.000342 or 0.0342%.

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His total earnings for a total sale of 7,000​ could be 1450sh

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

Salary = 400

Commission = 15%

using the above as a guide, we have the following:

Total earnings = 400 + 15% * Total sales

So, we have

Total earnings = 400 + 15% * 7000

Evaluate

Total earnings = 1450

Hence, the total earnings is 1450

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Question

Simon earned 400sh weekly for goods sold and a commission of 15%

What could be his earnings for a total sale of 7,000​.

The tangent from the external point are equal, so the x value is 3 units.

7) The measure of the arc XW is 180-105=75

8) The measure of the arc VWY is 105+75+85 = 265

9) We know that, tangent from the external point are equal

In circle C, AB=AD

26=8x+2

8x=24

x=24/8

x=3 units

10) 9x-3=7x+5

9x-7x=5+3

2x=8

x=8/2

x=4

Therefore, the tangent from the external point are equal, so the x value is 3 units.

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Answer:

Step-by-step explanation:

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

Volume = π * radius^2 * height

Given:

Volume = 627.8 cm^3

Height = 19.5 cm

π (pi) = 3.14

Substituting the given values into the formula:

627.8 = 3.14 * radius^2 * 19.5

Simplifying the equation:

627.8 = 60.93 * radius^2

To solve for the radius, we can divide both sides of the equation by 60.93:

radius^2 = 627.8 / 60.93

radius^2 = 10.29

Taking the square root of both sides:

radius ≈ √10.29

Rounding to the nearest tenth:

radius ≈ 3.2

Therefore, the approximate radius of the cylinder is 3.2 cm.

Answer:

3.2

Step-by-step explanation:

The volume of a cylinder is:

Vol = pi•r^2•h

Fill in what is given.

627.8 = pi•r^2•19.5

use 3.14 for pi.

627.8 = 3.14•r^2•19.5

simplify.

627.8 = 61.23r^2

divide by 61.23

10.253 = r^2

sqrt both sides

sqrt10.253 = r

3.2 = r

Reema should use 3 hooks, with a distance of 7 inches between each hook, and each hook will be positioned 5 3/8 inches from the left edge of the wood.

To determine the number of hooks Reema should use, we first need to calculate the available space on the wood for the hooks.

The total length of the wall is 4 feet, which is equivalent to 48 inches. Reema wants to center the coat rack, so she will have an equal amount of space on either side.

Therefore, each side will have (48 - 28 1/4) / 2 = 9 3/8 inches of space.

Next, we need to determine the distance between the hooks.

Reema wants about 7 or 8 inches of space between each hook.

Let's choose 7 inches for consistency.

Since there will be (n - 1) spaces between n hooks, the total space taken by the spaces will be 7 [tex]\times[/tex] (n - 1) inches.

Now, let's subtract the space taken by the spaces from the available space on the wood: 9 3/8 - 7 [tex]\times[/tex] (n - 1) = 9 3/8 - 7n + 7 inches.

Reema wants the first and last hooks to be no less than 1 3/4 inches from either end of the wood.

Therefore, we subtract twice this distance from the remaining space: 9 3/8 - 7n + 7 - 2 [tex]\times[/tex] (1 3/4) = 9 3/8 - 7n + 7 - 3 1/2 inches.

Now we have the expression 9 3/8 - 7n + 7 - 3 1/2 inches representing the remaining space.

We want this value to be greater than or equal to zero, as it should not be negative.

Simplifying the expression, we have 18 7/8 - 7n - 3 1/2 inches ≥ 0.

Now we can solve this inequality to find the range of values for n, the number of hooks.

We can then determine the distance between the hooks by dividing the remaining space by the number of spaces, and the distance of each hook from the left edge of the wood by adding the space taken by the spaces to the distance between the hooks.

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Answer: (x+6)(x-3)

Step-by-step explanation:

y=x^2+3x-18

(x+6)(x-3 )

Answer: Obtuse Angle

Step-by-step explanation: A 90 degree angle is a right angle anything larger then a right angle is a obtuse angle.

Answer:

It would be called an obtuse angle

Step-by-step explanation: so you see if it was exactly 90 degrees it would be called a right angle. Anything above 90 (b91 92 93 etc...) degrees would be an obtuse angle and anything below 90 ( 89 88 87 etc..) would be an acute angle except an 180 degree angle would be a straight angle. Hope that helps!

have a wonderful Sunday!

Answer:

See below for answers and explanations

Step-by-step explanation:

a, b, and c are the coefficients of the quadratic, so a=1, b=6, and c=-12

(h,k) is the vertex of the parabola, so we must convert it to vertex form by completing the square:

[tex]y=x^2+6x-12\\y+21=x^2+6x-12+21\\y+21=x^2+6x+9\\y+21=(x+3)^2\\y=(x+3)^2-21[/tex]

Therefore, the vertex is (3,-21), which means h=-3 and k=-21.

The y-intercept is when x=0, or when the function passes through the x-axis:

[tex]y=x^2+6x-12\\y=0^2+6(0)-12\\y=-12[/tex]

Therefore, the y-intercept is -12 (also written as (0,-12) as an ordered pair).

The x-intercept is when y=0, or when the function passes through the y-axis:

[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\frac{-6\pm\sqrt{6^2-4(1)(-12)}}{2(1)}\\\\x=\frac{-6\pm\sqrt{36+48}}{2}\\\\x=\frac{-6\pm\sqrt{94}}{2}[/tex]

Therefore, the x-intercepts are (-6+√94)/2 and (-6-√94)/2.

Hope this helped!

The probability that event A or B takes place is 17/19

Probability is defined as the ratio of the required to the total possible outcomes of an event.

The probability of event A or B taking place can be defined as ;

P(A or B) = P(A) + P(B)

P(A) = 10/19

P(B) = 7/19

Hence,

P(A) + P(B) = 10/19 + 7/19

L.C.M of 19 and 19 = 1

P(A) + P(B) = (10 + 7)/19

P(A) + P(B) = 17/19

Therefore, the probability that event A or B takes place is 17/19

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