A mini-golf course is determining the par score for each of its holes. The dot plot shows the number of strokes required to place a ball in the ninth hole for a sample of 31 players. A number line going from 1 to 9. 2 dots are above 1. 3 dots are above 2. 4 dots are above 3. 5 dots are above 4. 5 dots are above 5. 3 dots are above 6. 2 dots are above 7. 0 dots are above 8. 1 dot is above 9. Which measure of center is best to use to determine the expected number of strokes required for the ninth hole? a. The mean is the best choice because the data is nearly symmetrical. b. The median is the best choice because data is clustered. c. The mean is the best choice because the data is skewed to the right. d. The median is the best choice because the data is skewed to the left.

Step-by-step explanation:

√(m + n) = √m + √n

Square both sides:

m + n = m + 2√(mn) + n

Simplify:

0 = 2√(mn)

mn = 0

The equation is only true if either m or n (or both) is 0.

Final answer:

The square root of the sum of two numbers is not equal to the sum of the square roots of those numbers.

Explanation:

No, √m+n is not equal to √m + √n for all values of m and n. This is because of the nature of square roots and how they interact with addition. Taking the square root of a sum is not the same as the sum of the square roots. For example, for m = 4 and n = 9, √4 + √9 = 2 + 3 = 5, but √(4 + 9) = √13, which is not equal to 5. This example illustrates how the two expressions yield different results, emphasizing the importance of understanding the properties of square roots in mathematical operations.

First bag has 47 coins and second bag has 49 coins and third bag has 51 coins and fourth bag has 53 coins

Solution:

Given that,

Total number of coins = 200

Number of bags = 4

I put the coins into each bag so that each bag has 2 more coins than the one before

Therefore,

Each bag has 2 more coins than the one before. Based on this we can say,

Let "x" be the number of coins put in first bag

Then, x + 2 is the number of coins put in second bag

Then, x + 4 is the number of coins put in third bag

Then, x + 6 is the number of coins put in fourth bag

We know that,

Total number of coins = 200

[tex]x + x + 2 + x + 4 + x + 6 = 200\\\\4x + 12 = 200\\\\4x = 200-12\\\\4x = 188\\\\x = 47[/tex]

Thus,

Coins put in first bag = x = 47

Coins put in second bag = x + 2 = 47 + 2 = 49

Coins put in third bag = x + 4 = 47 + 4 = 51

Coins put in fourth bag = x + 6 = 47 + 6 = 53

Thus number of coins in each bag are found

Final answer:

By setting up an algebraic equation to distribute 200 coins into 4 bags with each bag having 2 more coins than the previous one, we find the number of coins in each bag are 47, 49, 51, and 53, respectively.

Explanation:

The question involves distributing 200 coins into 4 bags so that each subsequent bag has 2 more coins than the previous one. To find out how many coins are in each bag, let's denote the number of coins in the first bag as x. Consequently, the second bag would have x + 2 coins, the third bag x + 4 coins, and the fourth bag x + 6 coins. The total number of coins across all bags would be x + (x + 2) + (x + 4) + (x + 6) = 200.

Simplifying the equation, we get 4x + 12 = 200, which simplifies further to 4x = 188. Dividing both sides by 4 yields x = 47. Therefore, the number of coins in each bag, starting from the first to the fourth, are 47, 49, 51, and 53, respectively.

Answer:

The answer to your question is below

Step-by-step explanation:

c)  6x + 4x - 6 = 24 + 9x

     6x + 4x - 9x = 24 + 6

     x = 30                       This equation has one solution, it's an identity

d) 25 - 4x = 15 - 3x + 10 - x

    -4x + 3x + x = 15 + 10 - 25

   0 = 0                           It has infinite number of solutions, it is an identity

e)  4x + 8 = 2x + 7 + 2x - 20

    4x - 2x - 2x = 7 - 20 + 8

                  0 = -5          It has no solution it is a contradiction

Answer:

Estimated Average Requirement (EAR)

Step-by-step explanation:

The Estimated Average Requirement (EAR) is the average amount of daily intake value which is estimated to meet the needs of 50% of the healthy individuals.

The EAR is estimated on the basis of specific conditions of adequacy, and are derived from a careful study of the literature.

The major parameters which is selected for the criterion are reduction of disease risk.

Answer:

81.85% of the workers spend between 50 and 110 commuting to work

Step-by-step explanation:

We can assume that the distribution is Normal (or approximately Normal) because we know that it is symmetric and mound-shaped.

We call X the time spend from one worker; X has distribution N(μ = 70, σ = 20). In order to make computations, we take W, the standarization of X, whose distribution is N(0,1)

[tex] W = \frac{X-μ}{σ} = \frac{X-70}{20} [/tex]

The values of the cummulative distribution function of the standard normal, which we denote [tex] \phi [/tex] , are tabulated. You can find those values in the attached file.

[tex]P(50 < X < 110) = P(\frac{50-70}{20} < \frac{X-70}{20} < \frac{110-70}{20}) = P(-1 < W < 2) = \\\phi(2) - \phi(-1)[/tex]

Using the symmetry of the Normal density function, we have that [tex] \phi(-1) = 1-\phi(1) [/tex] . Hece,

[tex]P(50 < X < 110) = \phi(2) - \phi(-1) = \phi(2) - (1-\phi(1)) = \phi(2) + \phi(1) - 1 = \\0.9772+0.8413-1 = 0.8185[/tex]

The probability for a worker to spend that time commuting is 0.8185. We conclude that 81.85% of the workers spend between 50 and 110 commuting to work.

Final answer:

To have a monthly income of $2600, the salesman needs to make total sales of $29,616.67, considering his base salary of $925 and a 6% commission for sales over $1700.

Explanation:

The question asks us to calculate how much a local salesman needs to sell to have a monthly income of $2600. The salesman receives a base salary of $925 and earns a commission of 6% for all sales over $1700.

To solve this, we need to figure out the total sales that would give the salesman an extra $1675 ($2600 total desired income minus the $925 base salary), knowing that he only gets a commission on the amount over $1700.

Let's denote the total amount in sales that the salesman needs to make as S.

The commission is only applied to the amount exceeding $1700, so the equation can be set up as follows:

Therefore, the salesman would need to sell $29,616.67 worth of goods in a month to have a total monthly income of $2600.

Answer:

11 different combinations

Step-by-step explanation:

A salesman packed 3 shirts and 5 ties.

With one shirt, he could wear all 5 ties = 5 combinations

With another shirt, he could wear 4 ties  = 4 combinations

With the third shirt, he could wear only 2 ties= 2 combinations

number of different combinations= [tex]5+4+2=11[/tex]

so answer is 11

Answer: right-tailed

Step-by-step explanation:

By considering the given information , we have

Null hypothesis : [tex]H_0: p\leq0.6[/tex]

Alternative hypothesis : [tex]H_a: p>0.6[/tex]

The kind of test (whether  left-tailed, right-tailed, or​ two-tailed.) is based on alternative hypothesis.

Since the given alternative hypothesis([tex]H_a[/tex]) is right-tailed , so out test is a right-tailed test.

Hence, the correct answer is "right-tailed".

ANSWER: True

EXPLANATION:

The statement is true. Any correctly constructed frequency distribution is valid. However, some choices for the categories or classes give more information about the shape of the distribution.

Answer:

-6

Step-by-step explanation:

=======================================

The tangent of an angle is the ratio of the opposite over adjacent sides.

tan(angle) = opposite/adjacent

tan(theta) = 4/3

This means that

opposite = 4 and adjacent = 3

This only happens when angle P is the reference angle. In other words,

tan(P) = 4/3

Answer:

The total number of buns Mrs Klein made = 400

Step-by-step explanation:

Question

Mrs Klein made fruit buns. She sold 3/5 of it in morning and 1/4 of the remaining in the afternoon. If she sold 200 more buns in the morning than afternoon, how many buns did she make?

Given:

Mrs Klein sold  [tex]\frac{3}{5}[/tex]  of the buns in the morning.

Mrs Klein sold [tex]\frac{1}{4}[/tex]  of the remaining buns in the evening.

She sold 200 more buns in the morning than afternoon.

To find the total number of buns she make.

Solution:

Let the total number of buns be  =  [tex]x[/tex]

Number of buns sold in the morning will be given as =  [tex]\frac{3}{5}x[/tex]

Number of buns remaining = [tex]x-\frac{3}{5}x[/tex]

Number of buns sold in the evening will be given as =  [tex]\frac{1}{4}(x-\frac{3}{5}x)[/tex]

Difference between the number of buns sold in morning and evening = 200

Thus, the equation to find [tex]x[/tex] can be given as:

[tex]\frac{3}{5}x-\frac{1}{4}(x-\frac{3}{5}x)=200[/tex]

Using distribution:

[tex]\frac{3}{5}x-\frac{1}{4}x+(\frac{1}{4}.\frac{3}{5}x)=200[/tex]

[tex]\frac{3}{5}x-\frac{1}{4}x+\frac{3}{20}x=200[/tex]

Multiplying each term with the least common multiple of the denominators to remove fractions.

The L.C.M. of 4, 5 and 20  = 20.

Multiplying each term with 20.

[tex]20\times \frac{3}{5}x-20\times\frac{1}{4}x+20\times\frac{3}{20}x=20\times 200[/tex]

[tex]12x-5x+3x=4000[/tex]

[tex]10x=400[/tex]

Dividing both sides by 10.

[tex]\frac{10x}{10}=\frac{4000}{10}[/tex]

∴ [tex]x=400[/tex]

Thus, total number of buns Mrs Klein made = 400

Answer:

tm = tₐ = -m/k ㏑{ [mg/k] / [v₀ + mg/k] }

Xm = Xₐ = (v₀m)/k - ({m²g}/k²) ㏑(1+{kv₀/mg})

Step-by-step explanation:

Note, I substituted maximum time tm = tₐ and maximum height Xm = Xₐ

We will use linear ordinary differential equation (ODE) to solve this question.

Remember that Force F = ma in 2nd Newton law, where m is mass and a is acceleration

Acceleration a is also the rate of change in velocity per time. i.e a=dv/dt

Therefore F = m(dv/dt) = m (v₂-v₁)/t

There are two forces involved in this situation which are F₁ and F₂, where F₁ is the gravitational force and F₂ is the air resistance force.

Then, F = F₁ + F₂ = m (v₂-v₁)/t

F₁ + F₂ = -mg-kv = m (v₂-v₁)/t

Divide through by m to get

-g-(kv/m) = (v₂-v₁)/t

Let (v₂-v₁)/t be v¹

Therefore, -g-(kv/m) = v¹

-g = v¹ + (k/m)v --------------------------------------------------(i)

Equation (i) is a inhomogenous linear ordinary differential equation (ODE)

Therefore let A(t) = k/m and B(t) = -g --------------------------------(ia)

b = ∫Adt

Since A = k/m, then

b = ∫(k/m)dt

The integral will give us b = kt/m------------------------------------(ii)

The integrating factor will be eᵇ = e ⁽k/m⁾

The general solution of velocity at any given time is

v(t) = e⁻⁽b⁾ [ c + ∫Beᵇdt ] --------------------------------------(iiI)

substitute the values of b, eᵇ, and B into equation (iii)

v(t) = e⁻⁽kt/m⁾ [ c + ∫₋g e⁽kt/m⁾dt ]

Integrating and cancelling the bracket, we get

v(t) = ce⁻⁽kt/m⁾ + (e⁻⁽kt/m⁾ ∫₋g e⁽kt/m⁾dt ])

v(t) = ce⁻⁽kt/m⁾ - e⁻⁽kt/m⁾ ∫g e⁽kt/m⁾dt ]

v(t) = ce⁻⁽kt/m⁾ -mg/k -------------------------------------------------------(iv)

Note that at initial velocity v₀, time t is 0, therefore v₀ = v(t)

v₀ = V(t) = V(0)

substitute t = 0 in equation (iv)

v₀ = ce⁻⁽k0/m⁾ -mg/k

v₀ = c(1) -mg/k = c - mg/k

Therefore c = v₀ + mg/k  ------------------------------------------------(v)

Substitute equation (v) into (iv)

v(t) = [v₀ + mg/k] e⁻⁽kt/m⁾ - mg/k ----------------------------------------(vi)

Now at maximum height Xₐ, the time will be tₐ

Now change V(t) as V(tₐ) and equate it to 0 to get the maximum time tₐ.

v(t) = v(tₐ) = [v₀ + mg/k] e⁻⁽ktₐ/m⁾ - mg/k = 0

to find tₐ from the equation,

[v₀ + mg/k] e⁻⁽ktₐ/m⁾ = mg/k

e⁻⁽ktₐ/m⁾ = {mg/k] / [v₀ + mg/k]

-ktₐ/m = ㏑{ [mg/k] / [v₀ + mg/k] }

-ktₐ = m ㏑{ [mg/k] / [v₀ + mg/k] }

tₐ = -m/k ㏑{ [mg/k] / [v₀ + mg/k] }

Therefore tₐ = -m/k ㏑{ [mg/k] / [v₀ + mg/k] } ----------------------------------(A)

we can also write equ (A) as tₐ = m/k ㏑{ [mg/k] [v₀ + mg/k] } due to the negative sign coming together with the In sign.

Now to find the maximum height Xₐ, the equation must be written in terms of v and x.

This means dv/dt = v(dv/dx) ---------------------------------------(vii)

Remember equation (i) above  -g = v¹ + (k/m)v

Given that dv/dt = v¹

and -g-(kv/m) = v¹

Therefore subt v¹ into equ (vii) above to get

-g-(kv/m) = v(dv/dx)

Divide through by v to get

[-g-(kv/m)] / v = dv / dx -----------------------------------------------(viii)

Expand the LEFT hand size more to get

[-g-(kv/m)] / v = - (k/m) / [1 - { mg/k) / (mg/k + v) } ] ---------------------(ix)

Now substitute equ (ix) in equ (viii)

- (k/m) / [1 - { mg/k) / (mg/k + v) } ] = dv / dx

Cross-multify the equation to get

- (k/m) dx = [1 - { mg/k) / (mg/k + v) } ] dv --------------------------------(x)

Remember that at maximum height, t = 0, then x = 0

t = tₐ and X = Xₐ

Then integrate the left and right side of equation (x) from v₀ to 0 and 0 to Xₐ respectively to get:

-v₀ + (mg/k) ㏑v₀ = - {k/m} Xₐ

Divide through by - {k/m} to get

Xₐ = -v₀ + (mg/k) ㏑v₀ / (- {k/m})

Xₐ = {m/k}v₀ - {m²g}/k² ㏑(1+{kv₀/mg})

Therefore Xₐ = (v₀m)/k - ({m²g}/k²) ㏑(1+{kv₀/mg}) ---------------------------(B)

The question is about an object projected upwards under gravity and a certain resistance. The equations of motion will be non-linear due to the nature of the resistance. Solving these equations metaphorically or numerically will yield the maximum height and time taken to reach that height.

The subject matter here is mechanics which falls under Physics. Given that there is a body of constant mass m projected upwards with an initial velocity v0 and the medium being passed through provides a resistance of k|v|, the equations of motion under this resistance will be non-linear.

The question here pertains to the calculations related to an object moving upwards under a given resistance and gravity. To obtain the maximum height achieved by the body xm and the time taken to reach that tm, we employ the trick of non-dimensionalisation. First, we observe the units of all physical quantities and using this, we can introduce reduced physical quantities which are dimensionless.

Unfortunately, these non-linear equations don’t have a neat analytical solution, and methods of approximation or numerical techniques might be necessary to solve them for particular initial conditions.

https://brainly.com/question/35147838

#SPJ3

Answer:

The type of sample is Stratified sampling.

Step-by-step explanation:

Consider the provided information.

Types of sampling.

Here the population is divided into groups of males and females therefore it is stratified sampling.

Hence, the type of sample is Stratified sampling.

Unfortunately you are incorrect. The answer is actually tan(y) = 20/21

The tangent of an angle is the ratio of the opposite and adjacent sides.

tan(angle) = opposite/adjacent

tan(K) = JL/LK

tan(y) = 20/21

----------------------

Side note: the tangent of angle x would be the reciprocal of this fraction since the opposite and adjacent sides swap when we move to angle J

tan(angle) = opposite/adjacent

tan(J) = LK/JL

tan(x) = 21/20

Answer:

The code is attached. I used python to define the function and matplotlib library to plot the histogram.

Step-by-step explanation:

Answer:

d. dog

Step-by-step explanation:

The BCG matrix is a tool used to assess the performance of the products of an organization on the basis of market share and market growth.

Basically there are 4 classes of products namely; Star, cash cow, question mark and dog.

Dogs are product with low market share and low growth.

Question mark have high growth but low market share while cash cows are the products with high mark share but low growth.

Stars are products with high market share and high market growth.

Hence dog is a poor performer that has only a small share of a slow-growth market. Option d.

Answer:

a. [1,2]

[tex] m= \frac{9-0}{2-1}=9[/tex]

b. [1,3.5]

[tex] m =\frac{17-0}{3.5-1}=6.8[/tex]

c. [1,5]

[tex] m =\frac{0-0}{5-1}=0[/tex]

d. [0,3.5]

[tex] m =\frac{17-(-5)}{3.5-0}=6.29[/tex]

So then we can conclude that the highest slope is for the interval [1,2] and that would be our solution for the fastest average rate.

a. [1,2]

[tex] m= \frac{9-0}{2-1}=9[/tex]

Step-by-step explanation:

Assuming that we have the figure attached for the function. For this case we just need to quantify the slope given by:

[tex] m = \frac{\Delta y}{\Delta x}[/tex]

For each interval and the greatest slope would be the interval on which the volume of the box is changing at the fastest average rate

a. [1,2]

[tex] m= \frac{9-0}{2-1}=9[/tex]

b. [1,3.5]

[tex] m =\frac{17-0}{3.5-1}=6.8[/tex]

c. [1,5]

[tex] m =\frac{0-0}{5-1}=0[/tex]

d. [0,3.5]

[tex] m =\frac{17-(-5)}{3.5-0}=6.29[/tex]

So then we can conclude that the highest slope is for the interval [1,2] and that would be our solution for the fastest average rate.

a. [1,2]

[tex] m= \frac{9-0}{2-1}=9[/tex]

The correct answer is A. [1,2].

To determine over which interval the volume of the box changes at the fastest average rate, we need to find the average rate of change of the volume function ( V(x) ) over the given intervals and compare them.
The volume ( V(x) ) of the box is given by:
[tex]\[ V(x) = (x + 1)(5 - x)(x - 1) \][/tex]
We first need to express ( V(x) ) in a simplified form. Let's expand the expression:
[tex]\[ V(x) = (x + 1)(5 - x)(x - 1) \]\[ V(x) = (x + 1)(x^2 - 6x + 5) \]\[ V(x) = x(x^2 - 6x + 5) + 1(x^2 - 6x + 5) \]\[ V(x) = x^3 - 6x^2 + 5x + x^2 - 6x + 5 \]\[ V(x) = x^3 - 5x^2 - x + 5 \][/tex]
Now, we calculate the average rate of change over each interval. The average rate of change of ( V(x) ) over an interval ([a, b]) is given by:
[tex]\[ \text{Average Rate of Change} = \frac{V(b) - V(a)}{b - a} \][/tex]
We need to compute this for each interval provided.
1. Interval [1, 2]:
[tex]\[ V(1) = (1 + 1)(5 - 1)(1 - 1) = 0 \]\[ V(2) = (2 + 1)(5 - 2)(2 - 1) = 3 \times 3 \times 1 = 9 \]\[ \text{Average Rate of Change} = \frac{V(2) - V(1)}{2 - 1} = \frac{9 - 0}{2 - 1} = 9 \][/tex]
2. Interval [1, 3.5]:
[tex]\[ V(1) = 0 \]\[ V(3.5) = (3.5 + 1)(5 - 3.5)(3.5 - 1) = 4.5 \times 1.5 \times 2.5 = 16.875 \]\[ \text{Average Rate of Change} = \frac{V(3.5) - V(1)}{3.5 - 1} = \frac{16.875 - 0}{3.5 - 1} = \frac{16.875}{2.5} = 6.75 \][/tex]
3. Interval [1, 5]:
[tex]\[ V(1) = 0 \]\[ V(5) = (5 + 1)(5 - 5)(5 - 1) = 6 \times 0 \times 4 = 0 \]\[ \text{Average Rate of Change} = \frac{V(5) - V(1)}{5 - 1} = \frac{0 - 0}{5 - 1} = 0 \][/tex]
4. Interval [0, 3.5]:
[tex]\[ V(0) = (0 + 1)(5 - 0)(0 - 1) = 1 \times 5 \times -1 = -5 \]\[ V(3.5) = 16.875 \]\[ \text{Average Rate of Change} = \frac{V(3.5) - V(0)}{3.5 - 0} = \frac{16.875 - (-5)}{3.5 - 0} = \frac{16.875 + 5}{3.5} = \frac{21.875}{3.5} \approx 6.25 \][/tex]
Comparing these average rates of change:
[tex]\([1, 2]\): 9\\ \([1, 3.5]\): 6.75\\ \([1, 5]\): 0\\ \([0, 3.5]\): 6.25[/tex]
The interval where the volume of the box is changing at the fastest average rate is [tex]\([1, 2]\)[/tex], with an average rate of change of 9.
Therefore, the correct answer is: A.[tex]\([1, 2]\)[/tex].

Complete question :

Answer: she has 30 pages left to read.

Step-by-step explanation:

Let x represent the total number of pages in the book which Lilla is reading.

Lilla read 1/5 of her book last week. This means that the number of pages that she read last week is

1/5 × x = x/5

This week she read 3 times as much as she read last week. This means that the number of pages that she read this week is

3 × x/5 = 3x/5

The number of pages that she has left to read would be

x - 3x/5

= (5x - 3x)/5 = 2x/5

b. There are 75 pages in Lilla's book. It means that the number of pages that she has left to read would be

(2 × 75)/5 = 150/5

= 30

Final answer:

Lilla read 4/5 of her book after two weeks and has 1/5, or 15 pages, left to read of her 75-page book.

Explanation:

Lilla read 1/5 of her book last week. This week she read 3 times as much as she read last week. To express how much of her book Lilla has left to read, let us denote the total amount of the book as 1 (or 100%).

a. The amount she read this week would be 3 times 1/5, which is 3/5. Thus, the total amount Lilla read over the two weeks is 1/5 + 3/5, which simplifies to 4/5 of the book. Therefore, the expression for the amount of the book Lilla has left to read is 1 - 4/5, which simplifies to 1/5 of the book.

b. Lilla's book has 75 pages. To find out how many pages she has left to read, we calculate 1/5 of 75. This is done by multiplying 75 by 1/5:

75  imes 1/5 = 75/5 = 15 pages

Therefore, Lilla has 15 pages left to read.

Answer:

Current balance in Marcelo's account = $132.63

Step-by-step explanation:

Given:

Initial amount in Marcelo's bank account = $49.13

Amount paid in two fees = $32.50 each

Amount added by two deposits = $74.25 each

To find balance in dollars in Marcelo's account.

Solution:

Total amount paid in fees = [tex]2\times \$32.50=\$65[/tex]

Total amount deposited = [tex]2\times \$74.25=\$148.50[/tex]

The balance in Marcelo's account can be represented as:

⇒ Initial balance - Amount given in fees + Amount deposited

⇒ [tex]\$49.13-\$65+\$148.50[/tex]

⇒ [tex]\$132.63[/tex]

Thus, balance in Marcelo's account now = $132.63

Answer: 132.63

Step-by-step explanation:

I copied the other guy lol thanks for the points

Final answer:

To determine the gross earnings for 40 hours worked at a pay rate of $6.50 per hour, multiply the pay rate by hours. The gross earnings would be $260.00.

Explanation:

To calculate the gross earnings given the pay rate and hours worked, we use a simple multiplication. However, there is an additional consideration mentioned in Exercise 3.1, which states that the employee should receive 1.5 times the hourly rate for hours worked above 40 hours. Therefore, the calculation involves two steps if the number of hours exceeds 40.

Calculation:

In this particular case, the student only worked 40 hours at a pay rate of $6.50 per hour. Using the first formula, the gross earnings would be:
Gross Earnings = $6.50/hour × 40 hours = $260.00

Answer:

36

Step-by-step explanation:

Given that

[tex]R_n = R_{n+1} +3[/tex] is given

First term is 15

This is an arithmetic series with a =15 and d =3

If n is the number of terms, then we have

Sum of n terms = 36 xn = 36n

But as per arithmetic progression rule

[tex]S_n = \frac{n}{2} [2a+(n-1)d]\\= \frac{n}{2} [30+(n-1)3]=36n[/tex]

[tex]72 = 30+3n-3\\n-=15[/tex]

When there are n terms we have middle term is the 8th term

Hence median is 8th term

=[tex]a_8 = 15+7(3) \\=36[/tex]

Answer: the company's annual profit if the price of their product is $32 is $3041

Step-by-step explanation:

A company's annual profit, P, is given by P = −x²+ 195x − 2175, where x is the price of the company's product in dollars.

To determine the company's annual profit if the price of their product is $32, we would substitute x = 32 into the given equation. It becomes

P = −32²+ 195 × 32 − 2175

P = −1024 + 6240 − 2175

P = $3041

Answer:

It's A

Step-by-step explanation:

Trust Me

DC=14

Explanation

consider triangle ADB

<BAD=54°

sin<BAD=opposite side/ hypotenuse

sin 54°=BD/BA

BD=BA sin 54°=20*0.8=16

consider triangle BDC

cos <BCD=adjacent side/hypotenuse

=DC/BC

cos 28°=DC/BC

DC=cos28°  *BC

=0.88*16=14.08

Answer:

  x = -2.4

Step-by-step explanation:

  f(x) = -1/4x -3

  x = -1/4x -3 . . . . .  the desired value of f(x)

  5/4x = -3 . . . . . . . add 1/4x

  x = -12/5 . . . . . . . multiply by 4/5, the inverse of 5/4

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Check

  -1/4(-2.4) -3 = 0.6 -3 = -2.4 = x . . . . answer checks OK

Step-by-step explanation:

Diameter, D = 42 feet

Circumference = πD = π x 42 = 131.95 feet

Number of rotations per minute = 3

Total time = 5 minutes

Total rotations = 5 x 3 = 15

Distance traveled per rotation = 131.95 feet

Distance traveled in 15 rotations = 15 x 131.95 = 1978 feet

Option C is the correct answer.

- We´re gonna work with two separate triangles:

-The first one is the larger triangle (40º angle) and a vertical side that represents the ENTIRE height, b, of the tower.

Larger triangle with height b: tan 40°= [tex]\frac{b}{87}[/tex] ; .8390996312 = [tex]\frac{b}{87}[/tex];  b≈73.00166791

-The second one the smaller triangle (25º angle) and a vertical side, a, that represents the height of the first (bottom) section of the tower.

Smaller triangle with height a: tan 25°= [tex]\frac{a}{87}[/tex] ; ..4663076582 = [tex]\frac{a}{87}[/tex];  a≈40.56876626

-Then you need to solve for the vertical heights (b and a) in the two separate triangles.

-The needed height, x, of the second (top) section of the tower will be the difference between the ENTIRE height, b, and the height of the first (bottom) section, a. You will need to subtract.

In both triangles, the solution deals with "opposite" and "adjacent" making it a tangent problem.

Difference (b - a): 73.00166791 - 40.56876626 = 32.43290165 ≈ 32 feet

Answer:

Step-by-step explanation:

AB:AC=4:5

AB:BC=4:5-4 OR 4:1

So B divides AC in the ratio 4:1

Answer:

the opportunity cost of producing each additional car REMAINS CONSTANT