What the remainder when -3x^(4)-2x^(3)+5x^(2)-7x is divided by x-i

Answer:

r = 8 units

Step-by-step explanation:

The equation of the circle centered at the origin is x² + y² = r²

   x² + y² = 64

   x² + y² = 8²

      r = 8 units

Answer:

8

Step-by-step explanation:

An equation of a circle is depicted by the notation [tex](x-h)^2+(y-k)^2=r^2[/tex], where

- [tex](h,k)[/tex] is the center point of the circle

- [tex]r[/tex] is the radius (the span of units from the origin to the border of the circle)

In this unique problem, the center is the origin (0,0), so [tex]h[/tex] and [tex]k[/tex] respectively equal 0.

Since the equation of the circle is [tex]x^2+y^2=64[/tex] , we must square root 64 since it's in it's [tex]r^2[/tex] form to obtain the value of [tex]r[/tex], which is the radius.

[tex]\sqrt{64}[/tex]=±8

Despite mathematically, -8 or 8 will work in this case, you cannot have a negative radius; therefore, the radius of the circle is 8.

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The correct graph that shows a line on the scatter plot that fits the data is the one with a line drawn through the points (1,7 and 2,6).

What is  Graph?

In mathematics, a graph is a visual representation of a set of objects, called vertices or nodes, that are connected by lines or arcs, called edges or links. Graphs are commonly used to represent and analyze relationships between different entities, such as people, places, or things.

here, we have,

The vertices in a graph can represent anything, such as cities on a map, people in a social network, or molecules in a chemical reaction. The edges between vertices represent the connections or relationships between them. For example, in a social network graph, the edges might represent friendships between people, while in a transportation network, the edges might represent roads or train tracks connecting different cities.

Graphs are used in many areas of mathematics and science, including computer science, physics, biology, and social science. They are a powerful tool for analyzing and visualizing complex systems and relationships, and have many practical applications, such as in route planning, network analysis, and social network analysis.

The correct graph that shows a line on the scatter plot that fits the data is the one with a line drawn through the points (1,7 and 2,6).

The graph of the quadratic function is on the image at the end, there we can see that the ball takes 7.8 seconds to return to the ground.

We know that the height of the ball is modeled by the quadratic function:

h(x) = -5x² + 39x + 0.24

Where x represents the time in seconds.

To do this, we need to use a graph of the quadratic function, when  we have the graph, we need to identify the zeros of the quadratic (when the height is zero, the ball is in the ground).

On the image at the end you can see the graph, there you can see that we have a zero at x = 7.8, it means that the ball takes 7.8 seconds to return to the ground.

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As, a1/a2 = b1/b2 = c1/c2 = 2 .Thus, the given system of equations forms the identical lines.

A list of numbers x, y, z, etc. that simultaneously make all of the equations true is the solution of a system of equations. A system of equations' solution set is the whole of all possible answers. Finding all answers using formulas containing a certain number of parameters is known as solving the system.

For the given system of equations:

6x - y - 2 = 0

here, coefficients a1 = 6, b1 = -1 and constant c1 = -2

Now,

3x - 1/2y - 1 = 0

here, coefficients  a2 = 3, b2 = -1/2 and constant c2 = -1

taking the ratios:

a1/a2 = 6/3 = 2

b1/b2 = -1/(-1/2)  = 2

c1/c2 = -2/(-1) = 2

As, a1/a2 = b1/b2 = c1/c2 = 2 .Thus, the given system of equations forms the identical lines.

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The total number of students Surveyed was 160, with 56 studying French and 104 studying Language X.

Assuming that there are only two foreign languages in the survey, French and another language (let's call it Language X), we can proceed with the given data.

French: 16, 12, 28
Totals: 40, 40, 80

Step 1: Analyze the given data.

The given data shows that there are three groups of students who are studying French:
- Group 1: 16 students
- Group 2: 12 students
- Group 3: 28 students

The total number of students in each group is:
- Group 1: 40 students
- Group 2: 40 students
- Group 3: 80 students

Step 2: Calculate the number of students studying Language X.

To determine the number of students studying Language X in each group, subtract the number of students studying French from the total number of students in each group:
- Group 1: 40 - 16 = 24 students
- Group 2: 40 - 12 = 28 students
- Group 3: 80 - 28 = 52 students

Step 3: Summarize the results.

In summary, the survey conducted by Christy found the following results:
- French: 16 students in Group 1, 12 students in Group 2, and 28 students in Group 3
- Language X: 24 students in Group 1, 28 students in Group 2, and 52 students in Group 3

The total number of students surveyed was 160, with 56 studying French and 104 studying Language X.

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The total number of seats available for the baseball game can be calculated by adding the number of box and club seats available whch is found to be 25,200.

The game of baseball can be used to teach various mathematical concepts, such as probability, statistics, graphing, estimation, and basic arithmetic. The game can also be used to introduce concepts such as geometry and trigonometry, as well as to build problem-solving skills.

The total number of seats available can be calculated by adding the number of box and club seats available, which is

12,600 + 5400 = 18,000.

This total can then be multiplied by the respective percentages of the other two categories to get the total number of seats available.

For instance, the total number of bleacher seats available can be calculated by multiplying 12,000 by 18%.

12,000 x 0.18 = 2,160

Similarly, the total number of grandstand seats available can be calculated by multiplying 12,000 by 42%.

12,000 x 0.42 = 5,040

Hence, the total number of seats available for the baseball game is

18,000 + 2,160 + 5,040 = 25,200.

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The Julia needs to sell at least 1,819 subs to break even each month with the new upscale repositioning of her sub shop.

1- To break even, Julia needs to cover all her costs which include labor costs, insurance, rent, and utilities along with the cost of ingredients and packaging.
Total fixed costs = Labor costs + Insurance + Rent + Utilities = $7,000 + $900 + $800 + $300 = $8,000
Total variable cost per sub = Average cost of ingredients/packaging = $1.15

To break even, Julia needs to sell enough subs to cover her fixed costs and variable costs.

Breakeven point = Fixed costs / (Price per sub - Variable cost per sub)
Breakeven point = $8,000 / ($6 - $1.15) = 1,778.26

Therefore, Julia needs to sell at least 1,779 subs to break even each month.

2- If Julia is able to lower the average cost of ingredients and packaging per sub to $0.95, then the new variable cost per sub becomes $0.95. All other costs remain the same.

Breakeven point = Fixed costs / (Price per sub - Variable cost per sub)
Breakeven point = $8,000 / ($6 - $0.95) = 1,723.68

Therefore, Julia needs to sell at least 1,724 subs to break even each month with the new lower cost of ingredients and packaging.

3- If Julia raises the price per sub to $10 and the variable cost per sub rises to $4.22, the new breakeven point becomes:

Breakeven point = Fixed costs / (Price per sub - Variable cost per sub)
Breakeven point = $8,000 / ($10 - $4.22) = 1,818.18

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The lateral surface area of the triangular prism is 275.5 sq. mm.

"Being to the side" is the definition of the term "lateral." A triangular prism's lateral area is equal to the sum of its side faces' areas (which are 3 rectangles). Specifically, it is the total surface area less the surface areas of the two bases. Also called the lateral surface area (LSA). Due to the two dimensions involved in its calculation, we measure it in square units.

The lateral surface area of the triangular prism is given as:

LSA = (a + b + c)h

Here, the value of a = 7.5, b = 10.5, and c = 11mm, and h = 9.5mm.

Substitute the values:

LSA = (7.5 + 10.5 + 11) (9.5)

LSA = 275.5 sq. mm

Hence, the lateral surface area of the triangular prism is 275.5 sq. mm.

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The equation in slope-intercept form for the line that passes through the point (-8,7) and has a slope of 3/2 is y = (3/2)x + 19.

Step-by-step explanation:

use the formula for completing the square

Answer:

y=(11-8p)xz

Step-by-step explanation:

xyz+8p=11

xyz=11-8p

y=(11-8p)xz

Answer:

0; п; 1,5п; 2п.

Step-by-step explanation:

all the details are provided in the attachment.

Step-by-step explanation:

y= -3/3 is equivalent to -1

so y = -1

it located on the negative y-axis

where y= -1

According to the question we can say that the area to the right of z = 2.00 is 0.0228 or 2.28%.

a. To find the percentage of adults in the USA with stage 2 high blood pressure, we need to find the area under the normal distribution curve to the right of 160.

Using a standard normal distribution table or a statistical software, we can find that the z-score corresponding to 160 systolic blood pressure is:

z = (160 - 117) / 22 = 2.00

The area to the right of z = 2.00 is 0.0228 or 2.28%. Therefore, around 2.28% of adults in the USA have stage 2 high blood pressure.

b. To find how many people out of a sample of 2000 would be expected to have systolic blood pressure greater than 160, we can use the same z-score from part (a) and the standard normal distribution formula:

z = (x - μ) / σ

Rearranging the formula to solve for x, we get:

x = z * σ + μ

Substituting the values, we get:

x = 2.00 * 22 + 117 = 161.4

So the expected number of people with systolic blood pressure greater than 160 out of a sample of 2000 is:

2000 * (1 - P(Z < 2.00)) = 2000 * (1 - 0.9772) = 45.6

Rounding up, we can expect about 46 people to have systolic blood pressure greater than 160 out of a sample of 2000.

c. To find the percentage of adults in the USA who qualify for stage 1 high blood pressure, we need to find the area under the normal distribution curve between 140 and 160.

Using the standard normal distribution formula and z-scores, we get:

z1 = (140 - 117) / 22 = 1.05

z2 = (160 - 117) / 22 = 1.95

Using a standard normal distribution table or a statistical software, we can find the area to the left of z1 and z2, and then subtract the two areas to get the area between z1 and z2:

P(z1 < Z < z2) = P(Z < z2) - P(Z < z1) = 0.9744 - 0.8531 = 0.1213

Therefore, approximately 12.13% of adults in the USA qualify for stage 1 high blood pressure.

d. To find the systolic blood pressure corresponding to the 30th percentile, we need to find the z-score that has an area of 0.30 to its left.

Using a standard normal distribution table or a statistical software, we can find the z-score that corresponds to the area 0.30:

z = -0.52

Using the standard normal distribution formula and the given mean and standard deviation, we can solve for the systolic blood pressure:

x = z * σ + μ = -0.52 * 22 + 117 = 105.16

Therefore, if you are in the 30th percentile for blood pressure among US adults, your systolic blood pressure is approximately 105.16.

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Answer: I can help you!

Step-by-step explanation:

Answer and explanations

Answer:

rational function is:

f(x) = (x² - 4x - 5) / (x - 9)

To find f(5), we substitute x = 5:

f(5) = (5² - 4(5) - 5) / (5 - 9) = (-10) / (-4) = 5/2

To find f(9), we substitute x = 9:

f(9) = (9² - 4(9) - 5) / (9 - 9) = undefined

The function value f(9) is undefined because the denominator becomes zero, which makes the expression undefined.

To find f(7), we substitute x = 7:

f(7) = (7² - 4(7) - 5) / (7 - 9) = (-10) / (-2) = 5

Therefore, the function values are:

f(5) = 5/2

f(9) = undefined

f(7) = 5

Since this is a right circular cylinder, the 8-feet height is irrelevant because we should expect the water's height to rise at a steady rate of 0.032481 feet/min.

When the ratio of the output to the input remains constant at any particular point along the function, the rate of change is said to be constant.

The slope is another name for the steady rate of change.

The height of 8 feet is unimportant because, because this is a right circular cylinder, we should anticipate that the height of the water will increase at a constant rate.

[tex]V=\pi*r^2*h\\\\V=\pi*7^2*h\\\\V=\pi*49h\\\\\frac{dV}{dh} =49\ \pi \\\\\frac{dV}{dt}*\frac{dt}{dh}=49\ \pi \\\\5*\frac{dt}{dh} =49\pi\\\\\frac{dt}{dh} =\frac{49}{\frac{\pi}{5} } \\\\\frac{dt}{dh} =\frac{5}{\frac{49}{\pi} } \\\\\frac{dt}{dh} = 0.032481\ feet/min[/tex]

Since this is a right circular cylinder, the 8-feet height is irrelevant because we should expect the water's height to rise at a steady rate of 0.032481 feet/min.

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Answer:

Step 1: Find the previous balance.

After 8 payments, the remaining balance on the loan is $2,237.27. Therefore, the previous balance would be the balance before the 8th payment.

Total number of payments = 24

Number of payments already made = 8

Number of payments remaining = 24 - 8 = 16

Using the given monthly payment, we can find the balance before the 8th payment:

PV = PMT x [(1 - (1 + r/n)^-n*t)/(r/n)]

where PV is the present value or previous balance, PMT is the monthly payment, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time period in years.

Plugging in the given values, we get:

PV = $147.37 x [(1 - (1 + 0.075/12)^(-12*2))/(0.075/12)]

PV = $3,090.60

Therefore, the previous balance was $3,090.60.

Step 2: Find the interest for the 9th month.

We know that the balance at the end of the 8th month was $2,237.27. We can use this and the given interest rate to find the interest for the 9th month.

Interest = Balance x (Annual interest rate/12)

Interest = $2,237.27 x (0.075/12)

Interest = $13.99

Step 3: Find the final payment.

To find the final payment, we need to add the interest for the 9th month to the monthly payment and subtract it from the remaining balance.

Final payment = Remaining balance + Interest for 9th month - Monthly payment

Final payment = $2,237.27 + $13.99 - $147.37

Final payment = $2,103.89

Therefore, the final payment is $2,103.89.

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68% of the data values will be within one standard deviation (0.6) of the mean.

95% of the data values will be within 2 standard deviations (1.2) of the mean.

99.7% of the data values will be within 3 standard deviations (1.8) of the mean.

Answer:

2%

Step-by-step explanation:

(sales tax/ cost before tax) x 100%

(6.20 ÷ 310) x 100

0.02 x 100%

= 2

so the answer is 2%

Generally, insurance helps the policyholder to transfer the A. Risk from their bank account to the insurance company.

Insurance risk refers to the exposure of a policyholder to financial loss and consequent inability to meet their liabilities.

Insurance risks are transferable to insurance companies who pool resources together from many policyholders to meet and spread the risks.

Insurance does not transfer money, insurance, or health to the insurance company, but it transfers risk.

Thus, the correct option is Option A.

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The boat is 1189 feet away from the lighthouse at position A, and the angle between the boat and the beacon light is 10°. The distance between point A and point B is 2811.4 feet.

The boat is 1189 feet away from the lighthouse at position A, and the angle between the boat and the beacon light is 10°.

As a result, if h is the lighthouse's height, we have:

tan 10 = h/1189

h = 1189.tan 10

h = 209.7 feet

The elevation angle at position B is 3°. The following equation provides the distance (d) from the lighthouse:

tan 3 = h/d

d = h/tan 3 = 4000.4 feet

Therefore, the distance between points A and B is 400.4 - 1189

= 2811.4 feet

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Answer:407.7669

Step-by-step explanation:

Answer:

y = 16000(0.86)^t

Step-by-step explanation:

y = 16000(0.86)^t

The length of the arc AD is approximately 5.24 cm.

What is the length of an arc in circle?

Length of arc = (angle of arc / 360°) x (circumference of circle)

Here, the angle of arc is given as 60° and the radius of the circle is given as 5 cm.

So, the circumference of the circle can be found as:

circumference of circle

[tex]= 2 \times π \times radius \\ = 2 \times π \times 5 \\ = 10π cm[/tex]

Using the formula for length of arc, we can find the length of AD as

length of AD = (angle of arc / 360°) x (circumference of circle)

= (60° / 360°) x (10π cm)

= (1/6) x (10π cm)

= (5/3)π cm

≈ 5.24 cm

Therefore, the length of the arc AD is approximately 5.24 cm.

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Correct question is "There is a circle with centre O and AD is an arc. Now radius of the circle is 5 cm and angle of arc is 60° then what is the length of the arc AD ?"

Debido a restricciones de longitud, los límites de la función aparecen descritos en la explicación de esta pregunta.

En este problema debemos determinar los límites de un punto y los límites laterales de la función. El limite de un punto se determina mediante la evaluación directa de la función, mientras los límites laterales de la función se determinan viendo a que valor tiende la función.

A continuación, determinamos los límites de las funciones:

Caso 1:

Subcaso A (x = 1)

f(x) = - 1

Subcaso B (x = 5)

f(x) = 1

Subcaso C (x = 3⁻)

f(x) → - ∞

Subcaso D (x = 3⁺)

f(x) → + ∞

Subcaso E (x = 3)

No existe

Case 2:

Subcaso A (x = 0)

f(x) = 0

Subcaso B (x = - 2)

f(x) = 0.5

Subcaso C (x = 3⁻)

f(x) → - ∞

Subcaso D (x = - 3⁺)

f(x) → + ∞

Subcaso E (x = - 3)

No existe

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The solution of given derivative of y = √(arctan(x)) is:

 Y' = 1 / (2√arctan(x)(1 + x²))

In general, the term "differentiate" means to distinguish or recognize the differences between two or more things or concepts.

In mathematics, differentiation refers to the process of finding the rate at which a function changes with respect to one of its variables. It is a fundamental concept in calculus and involves calculating the derivative of a function. The derivative gives us the slope of a tangent line to the curve of the function at a specific point

To differentiate Y = √arctan(x), we need to use the chain rule and the formula for differentiating the arctan function, which is:

d/dx arctan(x) = 1 / (1 + x²)

Using the chain rule, we have:

Y = √arctan(x)

Y = [tex](arctan(x))^(1/2)[/tex]

Y' =[tex](1/2)(arctan(x))^(-1/2) * d/dx (arctan(x))[/tex]

Y' = [tex](1/2)(arctan(x))^(-1/2) * (1 / (1 + x^{2} ))[/tex]

Putting it all together, we have:

Y' = (1 / 2√arctan(x)) * (1 / (1 + x²))

Simplifying the expression, we get:

Y' = 1 / (2√arctan(x)(1 + x²))

Therefore, the derivative of Y = √arctan(x) is:

Y' = 1 / (2√arctan(x)(1 + x²))

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Point K and F

Looking at the data, you can see that most of the data points form close to a line- if you were to draw a line of best fit through the data, you would see that it would be quite close to most points on the graph. This is the trend of the graph, it is linear.

However, you can see thaf K and F do not come close to this trend at all and are therefore outliers since they do not fall close to the line.