Please help ASAP
Find the sum of 2 x^2 + 3 x - 4, 8 - 3 x , and -5 x^2 + 2.
A. -3 x2 - 2
B. -7 x2 - 2
C. -3 x2 + 6
D. -7 x2 - 6 x - 2

To find the combined rate of all the individuals working together, you must add the individual rates.

When calculating the combined rate of individuals working together, you need to add up the individual rates. Each worker contributes their own rate of work or productivity, and by adding these rates together, you can determine the combined rate at which they are working collectively.

This allows you to assess the overall efficiency and output of the team or group. By summing up the individual rates, we have better understanding of the overall productivity and performance of the group.

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The total value of the loan with quarterly compounded interest is approximately $45,288.38, while the total value of the loan with monthly compounded interest is approximately $45,634.84. The difference in total interest accrued is approximately $346.46.

Part A: To determine the total value of the loan with quarterly compounded interest, we can use the formula for compound interest:

A = P(1 + r/n)^(nt),

where:

A is the total value of the loan,

P is the principal amount (initial loan amount),

r is the interest rate (in decimal form),

n is the number of times interest is compounded per year,

and t is the number of years.

Given:

P = $20,000,

r = 9% or 0.09,

n = 4 (quarterly compounding),

t = 10 years.

Substituting the values into the formula, we have:

A = 20000(1 + 0.09/4)^(4*10).

Calculating this value, we find:

A ≈ $45,288.38.

Therefore, the total value of the loan with quarterly compounded interest is approximately $45,288.38.

Part B: To determine the total value of the loan with monthly compounded interest, we follow the same formula but with a different value for n:

n = 12 (monthly compounding).

Substituting the values into the formula, we have:

A = 20000(1 + 0.09/12)^(12*10).

Calculating this value, we find:

A ≈ $45,634.84.

Therefore, the total value of the loan with monthly compounded interest is approximately $45,634.84.

Part C: The difference between the total interest accrued on each loan can be calculated by subtracting the principal amount from the total value of each loan.

For the loan with quarterly compounding:

Total interest = Total value - Principal

Total interest = $45,288.38 - $20,000

Total interest ≈ $25,288.38.

For the loan with monthly compounding:

Total interest = Total value - Principal

Total interest = $45,634.84 - $20,000

Total interest ≈ $25,634.84.

The difference between the total interest accrued on each loan is approximately $346.46.

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Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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As given by the question

There are given that the triangle.

Now,

For finding the missing side, use the tangent and cosine function.

Hence, the tangent and cosine functions are to be used to find the sides.

Now,

For find the angle, use sine function:

Then,

Hence, the angle of the given triangle is 71.8 degrees.

The area of the segment is 9( π-2) units²

The area of a figure is the number of unit squares that cover the surface of a closed figure.

A segment is the area occupied by a chord and an arc. A segment can be a major segment or minor segment.

Area of segment = area of sector - area of triangle

area of sector = 90/360 × πr²

= 1/4 × π × 36

= 9π

area of triangle = 1/2bh

= 1/2 × 6²

= 18

area of segment = 9π -18

= 9( π -2) units²

therefore the area of the segment is 9(π-2) units²

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Answer:

The 99% confidence level for the proportion of all adult Americans who watched streamed programming up to that point in time is (0.514, 0.566). This means that we are 99% sure that the true proportion of all American adults surveyed said they have watched digitally streamed TV programming on some type of device is between 0.514 and 0.566.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the z-score that has a p-value of \(1 - \frac{\alpha}{2}\).

A poll reported that 54% of 2342 American adults surveyed said they have watched digitally streamed TV programming on some type of device.

This means that \(\pi = 0.54, n = 2342\)

99% confidence level

So \(\alpha = 0.01\), z is the value of Z that has a p-value of \(1 - \frac{0.01}{2} = 0.995\), so \(Z = 2.575\).

The lower limit of this interval is:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.54 - 2.575\sqrt{\frac{0.54*0.46}{2342}} = 0.514\)

The upper limit of this interval is:

\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.54 + 2.575\sqrt{\frac{0.54*0.46}{2342}} = 0.566\)

The 99% confidence level for the proportion of all adult Americans who watched streamed programming up to that point in time is (0.514, 0.566). This means that we are 99% sure that the true proportion of all American adults surveyed said they have watched digitally streamed TV programming on some type of device is between 0.514 and 0.566.

Answer:

16 If you see me

Step-by-step explanation:

Answer:

The height of the tree if the point on the ground is 28 feet from the tree is 91.5 ft.

The angle of elevation is given 73°. The distance between the point on the ground and the tree is 28 feet.

What is a trigonometric function?

In mathematics, the trigonometric function is a function that deals with the sides of the right-angled triangle and angles.

sin, cos, tan, cosec, sec, and cot are the basic function of trigonometric.

We know that tan Ф = perpendicular / Base

tan 73° = h / 28

tan 73° × 28 = h

3.27 × 28 =h

h = 91.5 ft

Therefore, the height of the tree if the point on the ground is 28 feet from the tree is 91.5 ft.

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Step-by-step explanation:

Answer:

71.57

Step-by-step explanation:

since she already has 18 cups flour she needs 6 cups of sugar

The value of the missing angle x is: 38°

We know that the sum of angles in a triangle is 180 degrees and as such:

∠DAE = 180 - (82 + 68)

∠DAE = 30°

Now, we know that alternate angles are congruent. Thus:

∠DAE ≅ ∠ADC = 30°

Opposite angles of a parallelogram are equal (or congruent) Consecutive angles are supplementary angles to each other (that means they add up to 180 degrees).

Thus:

∠BAE = ∠BDE = 82 + 30

= 112°

Thus:

∠ABC = ∠ACB = 68°

Thus:

∠BAC = 180 - 2(68)

∠BAC = 44°

Thus:

x = 112 - (44 + 30)

x = 112 - 74

x = 38°

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Answer:

m∠1 = 110° and m∠2 = 70°

Step-by-step explanation:

m∠1 = 110° since vertical angles

To find m∠2, m∠1 and m∠2 must add to 180°

m∠1 + m∠2 = 180°

110° + m∠2 = 180°

m∠2 = 70°

The equation of the line of best fit is \(y = -\frac{5}{6}x + \frac{82}{3}\) and

We start by drawing an approximated line of best fit (see attachment)

From the attached graph, we have the following points:

(x, y) = (4, 24) and (28, 4)

The equation of the line of best fit is then calculated as:

\(y = \frac{y_2 -y_1}{x_2 -x_1} * (x - x_1) + y_1\)

This gives

\(y = \frac{4 -24}{28 -4} * (x - 4) + 24\)

Evaluate the difference

\(y = -\frac{20}{24} * (x - 4) + 24\)

Simplify

\(y = -\frac{5}{6} * (x - 4) + 24\)

Expand

\(y = -\frac{5}{6}x + \frac{10}{3} + 24\)

Evaluate the sum

\(y = -\frac{5}{6}x + \frac{10 + 24*3}{3}\)

\(y = -\frac{5}{6}x + \frac{82}{3}\)

Hence, the equation of the line of best fit is \(y = -\frac{5}{6}x + \frac{82}{3}\)

The time spent on TV is given as:

x = 15

So, we have:

\(y = -\frac 56 * 15 + \frac{82}3\)

Evaluate the product

\(y = -\frac{75}6 + \frac{82}3\)

Evaluate the sum

\(y = \frac{-75+164}6\)

This gives

\(y = \frac{89}6\)

Simplify

y = 15

Hence, the amount of time spent during homework is 15 hours for a student that spent 15 hours on TV

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Answer:

24$

Step-by-step explanation:

The side lengths of the triangle are x = 12.375 cm , y = 8.475 cm   .

Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle.

The basic trigonometric ratios formulas are given below,

sin θ = Perpendicular/Hypotenuse

cos θ = Base/Hypotenuse

tan θ = Perpendicular/Base

sec θ = Hypotenuse/Base

cosec θ = Hypotenuse/Perpendicular

cot θ = Base/Perpendicular

According to the question

Hypotenuse of the triangle r = 15 cm

Perpendicular for ∠ θ  =  y

Base for ∠ θ  =  x

sin(θ)=0.565

cos(θ)=0.825

Now, using trigonometric ratio

sin θ = \(\frac{Perpendicular}{Hypotenuse}\)

sin(θ)=0.565  (given)

0.565 = \(\frac{y}{r}\)

0.565 * r = y

y = 0.565 * 15

y = 8.475 cm  

cos θ = \(\frac{Base}{Hypotenuse}\)

cos(θ)=0.825

0.825 = \(\frac{x}{r}\)

0.825 * r = x

x = 0.825 * 15

x = 12.375 cm

Hence, the side lengths of the triangle are x = 12.375 cm , y = 8.475 cm.

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  .

Juliet will earn the same amount of money whether she chooses a monthly salary of ​$1900 from the company or a base salary of ​$1800 plus a ​5% commission on furniture sales if her sales amount to $2000.

To find the amount of sales for which the two salary choices are equal, we set the equation for the base salary plus commission equal to the equation for the flat monthly salary. The equation can be written as:

1800 + 0.05x = 1900

where x is the amount of furniture sales in dollars.

Simplifying and solving for x, we get:

0.05x = 100

x = 2000

If she sells less than $2000 of furniture, she will earn more with the flat monthly salary of $1900. If she sells more than $2000 of furniture, she will earn more with the base salary plus commission. This calculation provides an important decision-making tool for Juliet, as she can tailor her salary choice based on her expected sales for the month.

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The only true statement about the domain of the given function is:

B. f(x) is negative for all x < -5

The domain of a function is defined as the set of values that we can possibly plug into our function. This set is the x values in a function such as f(x).

Now, we are given the function as:

f(x) = \(\frac{2}{x^{2} } + 3x - 10\)

When x < -5, we have:

f(-4) = \(\frac{2}{(-4)^{2} } + 3(-4) - 10\)

f(-4) = -21.875

This suggests that for all values below x = -5 will result in negative values

When x > 2

f(3) = \(\frac{2}{3^{2} } + 3(3) - 10\)

f(3) = -0.78

Thus, it will get positive for higher values but it can also be negative as seen here.

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The height of second floor above the first floor in the given problem is 20 foot.

Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.

In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).

The slant side is called hypotenuse.

From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.

From that angle (suppose its measure is θ),

\(\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}\\\)

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We are given that;

The length of escalator= 40foot

The angle of escalator from horizontal axis= 30°

Now,

Sinx= perpendicular/hypotenuse

Sin30= x/40

1/2=x/40

x=40/2

x=20

Therefore, by using trigonometric ratios the answer will be 20 foot.

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Based on the given responses, the student who factored 20x^6 = (2x)(10x^5) correctly is Andrei. Therefore, the correct answer is (Choice A) Andrei.

Among the given responses, the student who factored 20x^6 = 20, x to the power of 6 correctly is Andrei. Andrei's factorization is (2x)(10x^5), which correctly represents the original term 20x^6. Therefore, the correct answer is (Choice A) Andrei.

Amit's factorization is (4x^3)(5x^3), which is incorrect because it breaks down the term into two factors with the same exponent, while the original term has an exponent of 6.

Andrew's factorization is (20x^2)(x^3), which is also incorrect as it does not accurately represent the original term 20x^6.

Hence, the only student who correctly factored 20x^6 = 20, x to the power of 6 is Andrei.

The right answer is A. Andrei who factored 20x^6 = (2x)(10x^5) correctly.

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The final rule for g(x) is g(x) = 3|3x| + 12.

To stretch the graph of f(x) = −|3x| − 4 vertically by a factor of 3, we multiply the function by 3. This will result in a vertical stretching of the graph.

So, the rule for g(x) is g(x) = 3f(x).

Now, let's find the expression for g(x) using the given function f(x) = −|3x| − 4:

g(x) = 3f(x)

g(x) = 3(-|3x| - 4)

g(x) = -3|3x| - 12

This is the expression for g(x), which represents the transformed graph.

To reflect the graph of g(x) across the x-axis, we change the sign of the function. This means that the negative sign in front of the absolute value will become positive, and the positive sign in front of the constant term will become negative.

Therefore, the final rule for g(x) is g(x) = 3|3x| + 12.

Now, let's consider the graph of g(x). The graph will have the same shape as f(x), but it will be stretched vertically by a factor of 3 and reflected across the x-axis.

The original graph of f(x) = −|3x| − 4 is a V-shaped graph that opens downward and passes through the point (0, -4). The transformed graph of g(x) will have a steeper V-shape, opening downward, and passing through the point (0, 12) instead of (0, -4).

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The height of the hill is approximately 25.73 ft. Where v0 is the initial velocity (108 ft/s), g is the acceleration due to gravity \((-32.2 ft/s^2)\),

To find the height of the hill, we can use the formula for the vertical position of an object under constant acceleration:

h = h0 + v0t + 1/2at^2

where h is the final height, h0 is the initial height, v0 is the initial velocity, t is the time, and a is the acceleration due to gravity (-32.2 ft/s^2).

In this case, we are given that the initial height h0 is 3 ft, the initial velocity v0 is 108 ft/s, and the time t is 9.5 s. We want to find the height of the hill, which we can denote as h_hill. The final height is the height of the plain, which we can denote as h_plain and assume is zero.

At the highest point of its trajectory, the arrow will have zero vertical velocity, since it will have stopped rising and just started to fall. So we can set the velocity to zero and solve for the time it takes for that to occur. Using the formula for velocity under constant acceleration:

v = v0 + at

we can solve for t when v = 0, h0 = 3 ft, v0 = 108 ft/s, and a = -32.2 ft/s^2:

0 = 108 - 32.2t

t = 108/32.2 ≈ 3.35 s

Thus, it takes the arrow approximately 3.35 s to reach the top of its trajectory.

Using the formula for the height of an object at a given time, we can find the height of the hill by subtracting the height of the arrow at the top of its trajectory from the initial height:

h_hill = h0 + v0t + 1/2at^2 - h_top

where h_top is the height of the arrow at the top of its trajectory. We can find h_top using the formula for the height of an object at the maximum height of its trajectory:

h_top = h0 + v0^2/2a

Plugging in the given values, we get:

h_top = 3 + (108^2)/(2*(-32.2)) ≈ 196.78 ft

Plugging this into the first equation, we get:

h_hill = 3 + 108(3.35) + 1/2(-32.2)(3.35)^2 - 196.78

h_hill ≈ 25.73 ft

If the arrow is launched at t0, the equation describing velocity as a function of time would be:

v(t) = v0 - gt

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a) The number of bird feeders that the company must sell in a week to obtain the maximum profit = 100

b) Maximum profit = 3800

Maximum profit

Given that ,

f(x)=−0.40\(x^{2}\)+80x−200

f'(x) = -0.40 x \(2x\) + 80

      = - 0.80\(x + 80\)

f''(x) = - 0.80

a) For Maximum and minimum profit

f'(x) = 0

- 0.80\(x\) + 80 = 0

        0.80 \(x\)  = 80

                  \(x\) = 80 / 0.80

                     = 80 /80 x 100

                  \(x\) = 100

for x = 100 , f''(x) = -0.80

                   f''(x) < 0

Therefore, for x = 100 profit is maximum

Number of bird feeders = 100

b)Maximum profit

f(x) = -0.40 \(x^{2}\) + 80 \(x\) - 200

      = -0.40 x 100 x 100 + 8000 - 200

      = - 4000 + 8000 - 200

      = 4000 - 200

      = 3800

Therefore maximum profit = 3800

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Answer:

B and C are both in slope-intercept-form.

Step-by-step explanation:

Slope Intercept Form is --> y = mx + b, where m is the slope, and b is the y-intercept.

Both B and C have a slope (-6/4 for B, -3/2 for C) and both have a y-intercept (8/4 or 2).

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98% confidence interval for the proportion of all american adults who would report having earned money by selling something online in the previous year by using z-score. The correct answer is (0.1859, 0.2133)

The point estimate for the proportion of American adults who earned money by selling something online in the previous year is:

p-hat = 914/4579 = 0.1995

To construct a 98% confidence interval for the population proportion, we can use the formula:

p-hat ± z*(sqrt(p-hat*(1-p-hat)/n))

where z is the z-score associated with the desired confidence level (98% corresponds to a z-score of 2.33), and n is the sample size. Plugging in the values, we get:

0.1995 ± 2.33*(sqrt(0.1995*(1-0.1995)/4579))

Simplifying this expression, we get:

(0.1859, 0.2133)

Therefore, the correct answer is (0.1859, 0.2133). This means we are 98% confident that the true proportion of American adults who earned money by selling something online in the previous year lies between 0.1859 and 0.2133.

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The net force on the cart is 62N

and the vertical component =36.64 N

the horizontal component= 50N

What is revolution of vector?

The process of splitting a vector into its components is called resolution of the vector. We resolve a vector into two components which are. component along the x-axis called horizontal component. component along the y-axis called vertical component

30N tension on the cart is westward which mean the vertical component will be 0 and the horizontal component will be 30N.

40N tension isN 30° E which means

the vertical component= 40 sin60=36.64N

Horizontal component= 40 cos 60= 20N

sum of vertical = 36.64N +0= 36.64N

sum of horizontal= 30N+20N= 50N

60° was used for tension 40N because the angle of vector must always lie on the horizontal axis

therefore the net force F is obtained by using Pythagoras theorem

F= √(50^2+36.64^2)

= 62N to the nearest whole number.

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Complete Question:

Sammi wanted to create a dot plot based on this tally chartin which step, if any, did Sammi make a mistake creating his dot plot? (See attached pictures showing the chart tally and the 3 steps)

A. Sammi made a mistake in Step 1 because his number line did not include all numbers in the data set.

B. Sammi made a mistake in Step 2 because he chose a title without knowing if the table represents the number of hours read per week.

C. Sammi made a mistake in Step 3 because he did not correctly plot each dot above the appropriate place on the number line.

D. Sammi did not make a mistake.

Answer:

B. Sammi made a mistake in Step 2 because he chose a title without knowing if the table represents the number of hours read per week.

Step-by-step Explanation:

Taking a good look at Sammi's tally alongside the 3 steps he took, we can tell if he made any mistake or not.

=> Option A is incorrect because Sammi plotted correctly a number line that included all values in the data set. The values from the tally chart shows 3 to 6 hours.

=> Option B is correct, Sammi made a mistake in step 2 as he fails to state an appropriate title that corresponds with what the dots he wants to plot represents.

=> Option C is incorrect because from the tally chart, we can see that Sammi correctly plotted each dot accordingly above where each supposed to be in the number line.

Therefore, we can conclude that Sammi made a mistake in Step 2. Our answer is B.

Answer:

b

Step-by-step explanation:

i did edge 2022

The value of the angle B from the trigonometric ratios is 53.13 degrees

The Pythagorean theorem is a powerful tool for solving various problems involving right triangles. It allows us to find the length of a missing side in a right triangle when the lengths of the other two sides are known. It is also used to identify whether a triangle is a right triangle or not.

We have that;

TanB = 4/3

B= Tan-1(4/3)

B = 53.13 degrees

Hence we are going to have by the use of tan that the angle is 53.1 degrees

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Answer:

b = -17

Step-by-step explanation:

-2b - 12 = 22

     +12     +12

-2b = 34

-2b/-2    34/-2

b = -17

Answer:

-17

Step-by-step explanation:

-2B-12=22

-2B-2 (+12)=22+12 (add 12 to both sides to isolate the variable

-2B=24

-2B/-2=24/-2 (divide by -2 to isolate the variable)

B=-17