The distance between two places of interest is 2/3km. I go 1/4 of this distance on foot. How far is still to go?​

Step-by-step explanation:

It wants u to cross and multiply so what i would do is put both of them together and multiply across and when u get the answers that u multiply u then divide to see what was the lowest and what the greatest ratio was so for me i would gi with a

The length of each piece is 10 in and 8 in.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The total length of the string = 18 in

One piece = x + 2

Another piece = x

Now,

Solve for x.

x + 2 + x = 18

2x + 2 = 18

2x = 18 - 2

2x = 16

x = 8

Now,

One piece = 8 + 2 = 10 in

Another piece = 8 in

Thus,

The length of each piece is 10 in and 8 in.

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140.55 pounds will be sold approximately each week at the optimal price of $0.67/lb.

To find the price elasticity of demand for bananas at $0.20/lb, we need to use the formula:

According to the given data:

E(p) = -p(q'/q(p))

where q' is the derivative of q(p) with respect to p.

First, we need to find q'(p):

\(q'(p) = -225e^(1.5(5-p))\)

Then, we can plug in the values:

E(0.20) = -0.20(q'(0.20)/q(0.20))

= \(-0.20(-225e^(1.5(5-0.20)) / 100e^(1.5(5-0.20)))\)

= 2.70

Therefore, the price elasticity of demand for bananas at $0.20/lb is 2.70.

To find the price elasticity of demand for bananas at $1/lb, we can use the same formula:

E(p) = -p(q'/q(p))

First, we need to find q'(p):

\(q'(p) = -225e^(1.5(5-p))\)

Then, we can plug in the values:

E(1) = -1(q'(1)/q(1))

= \(-1(-225e^(1.5(5-1)) / 100e^(1.5(5-1)))\)

= 0.68

Therefore, the price elasticity of demand for bananas at $1/lb is 0.68.

To find the price that maximizes revenue, we need to find the value of p that makes revenue, R(p), maximum.

Revenue is given by:

R(p) = pq(p)

= \(p100e^(1.5(5-p))\)

To maximize revenue, we need to find the critical point of R(p) by taking its derivative and setting it equal to zero:

\(R'(p) = 100e^(1.5(5-p)) - 150pe^(1.5(5-p)) = 0\)

Simplifying this expression, we get:

\(2e^(1.5(5-p)) - 3pe^(1.5(5-p)) = 0\)

2 = 3p

p = 2/3

Therefore, the price that maximizes revenue is $0.67/lb.

To find the maximum revenue per week, we can plug this price back into the revenue equation:

\(R(2/3) = (2/3)*100e^(1.5(5-2/3))\)

= $167.56

Therefore, the maximum revenue per week is $167.56.

To find how many pounds will be sold each week at the optimal price of $0.67/lb, we can plug this price back into the demand equation:

\(q(2/3) = 100e^(1.5(5-2/3))\)

= 140.55

Therefore, approximately 140.55 pounds will be sold each week at the optimal price of $0.67/lb.

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Answer:

i believe the answer would be option D

Step-by-step explanation:

Answer:

\(x= \dfrac{\pi}{3}, \;\;x=\dfrac{5 \pi}{3}\)

Step-by-step explanation:

Given trigonometric equation:

\(2 \tan\left(\dfrac{x}{2}\right)- \csc x=0\)

To solve the equation for x in the given interval [0, 2π), first rewrite the equation in terms of sin x and cos x using the following trigonometric identities:

\(\boxed{\begin{minipage}{4cm}\underline{Trigonometric identities}\\\\$\tan \left(\dfrac{\theta}{2}\right)=\dfrac{1-\cos \theta}{\sin \theta}$\\\\\\$\csc \theta = \dfrac{1}{\sin \theta}$\\ \end{minipage}}\)

Therefore:

              \(2 \tan\left(\dfrac{x}{2}\right)- \csc x=0\)

\(\implies 2 \left(\dfrac{1-\cos x}{\sin x}\right)- \dfrac{1}{\sin x}=0\)

  \(\implies \dfrac{2(1-\cos x)}{\sin x}- \dfrac{1}{\sin x}=0\)

\(\textsf{Apply the fraction rule:\;\;$\dfrac{a}{c}-\dfrac{b}{c}=\dfrac{a-b}{c}$}\)

\(\dfrac{2(1-\cos x)-1}{\sin x}=0\)

Simplify the numerator:

\(\dfrac{1-2\cos x}{\sin x}=0\)

Multiply both sides of the equation by sin x:

\(1-2 \cos x=0\)

Add 2 cos x to both sides of the equation:

\(1=2\cos x\)

Divide both sides of the equation by 2:

\(\cos x=\dfrac{1}{2}\)

Now solve for x.

From inspection of the attached unit circle, we can see that the values of x for which cos x = 1/2 are π/3 and 5π/3. As the cosine function is a periodic function with a period of 2π:

\(x=\dfrac{\pi}{3} +2n\pi,\; x=\dfrac{5\pi}{3} +2n\pi \qquad \textsf{(where $n$ is an integer)}\)

Therefore, the values of x in the given interval [0, 2π), are:

\(\boxed{x= \dfrac{\pi}{3}, \;\;x=\dfrac{5 \pi}{3}}\)

A. The margin of error for a 99% confidence interval is $$2,320.75.

B. The confidence interval for the mean starting salary of college graduates who have taken a statistics course is CI = $42,462.25 to $47,103.75

PART A.

The margin of error (ME) is determined using the formula:

ME= z ∗ σ/√n

where:

z is the z-score for the desired confidence level

σ is the population standard deviation

n is the sample size

For a 99% confidence level, the z-score is 2.576. The population standard deviation is $10,272, and the sample size is 130.

Substituting these values into the formula, we have:

ME =  2.576 ∗ 10272/√130

ME = $2,320.75

PART B

The confidence interval (CI) is determined using the formula:

CI = \(\bar{x}\) ± ME

where:

\(\bar{x}\) is the sample mean

ME is the margin of error

The sample mean is $44,783, and the margin of error is $2,320.75.

Substituting the values into the formula, we get:

CI= 44783 ± 2320.75

CI = $42,462.25 to $47,103.75

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Answer:

x = 6

y = - 3

Step-by-step explanation:

x * y = - 18

x - y = 9. 3-y-y = 9. 3 -2y = 9.

-2y = 9-3

y = 6/-2

y = -3

x + y = 3. x = 3-y

x * -3 = - 18

x = -18/-3

x = 6

Answer:

Attached is an example of a circle with a radius of 5 and a diameter of 10.

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The equation f(x)=40-1.25x gives Aisha's savings as a function of the amount of birdseed she buys.

In the equation f(x)=40-1.25xf(x) x represents the number of pounds of birdseed she buys at $1.25 per pound.

Here's what each part of the equation means:

$40 is the total amount of money Aisha has.

$1.25 is the cost per pound of birdseed.

x is the number of pounds of birdseed she buys.

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Sum of the interior angles of a rectangular polygon of 18 sides​ IS 2880°

Given,

Rectangular polygon of 18 sides.

The sum of the measures of the interior angle of any polygon is the number of sides minus 2 multiplied by 180.

Then,

S=(n-2)*180°

n = Number of sides

So,

S=(18-2)(180°)

S=16(180°)

S=2880°

A polygon with 18 sides has an interior angle sum of 2880 degrees.

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The minimum length of pipe required to deliver water to points A and B is approximately 20.375 miles.

We are given that a water pumping station is to be built on a river at point P in order to deliver water to points A and B. The design requires that LAPD = /BPC so that the total length of piping that will be needed is a minimum. We need to find this minimum length of pipe.

The given figure is shown below: \(AB = 10 \ miles\)\(BC = 6 \ miles\)\(CP = 12 \ miles\). We are given that \(LAPD = LCPB\).

Now, we need to find the minimum length of pipe required for delivering the water to points A and B.The total length of the pipe, \(L_{total} = LA + AB + BP\)Since \(LAPD = LCPB\), we can say that\(AP^2 + PD^2 = BP^2 + PC^2\).

From the triangle ACP, we can say that\(AC^2 = AP^2 + PC^2\). So, we can substitute AP^2 + PC^2 with AC^2 to get\(AP^2 + PD^2 = BP^2 + AC^2\)Now, we can substitute AP = AC - PC and BP = BC + PC in the above equation to get\((AC - PC)^2 + PD^2 = (BC + PC)^2 + AC^2\).

After solving this equation, we get\(AC = \frac {37}{8}\) and \(PC = \frac {27}{8}\)Now, we can calculate the length of pipe required as follows: \(L_{total} = LA + AB + BP = 10 + 6 + \frac {27}{8} = \boxed{20.375 \ miles}\). Therefore, the minimum length of pipe required to deliver water to points A and B is approximately 20.375 miles.

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The equation Hats 2030=230.09+23x represents a linear relationship between the number of years since 2010 (x) and the projected number of hats sold in the year 2030.

The slope of the equation, 23, indicates that for each additional year since 2010, the projected number of hats sold in 2030 increases by 23. The y-intercept of the equation, 230.09, represents the projected number of hats sold in 2030 if x is equal to zero (i.e., in the year 2010). This equation can be used to forecast future hat sales based on past trends and can help businesses and organizations plan for inventory and production needs. However, it is important to note that unforeseen events, changes in consumer behavior, and other factors can impact actual hat sales and should be considered when making business decisions.

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div( curl( grad f )) - scalar field; the divergence of a vector field is a scalar field

A quantity with both direction and magnitude, particularly when used to depict the distance between two points in space.

In a scalar field, each point in a space—possibly actual space—is assigned a single integer.

According to the given information

(a) You can only determine the curl of a vector field; curl f is meaningless.

(b) grad f - vector field; when you take a gradient of something , it results in a vector field

(c) div F - scalar field; take the divergence of a vector field, it results in a scalar field

(d) A vector field is produced by the operation curl(grad f) on a vector field.

(e) grad F - meaningless; gradients are only used for scalar fields

(f) grad( div F ) - vector field; the gradient of a scalar field is a vector field

(g) div( grad f ) - scalar field; if you take divergence of a vector field, the result is a scalar field

(h) Grad (div f) is useless; one cannot take a scalar field's divergence into account.

(i) vector field; a vector field is a vector field's curl (curl F).

(j) div(div F) is useless; it is impossible to calculate a scalar field's divergence.

(k) ( grad f ) x ( div F ) - meaningless; you cant cross a scalar field by a vector field !

(l) The divergence of a vector field is a scalar field, and its formula is div(curl(grad f))

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Answer:

-59

Step-by-step explanation:

x+41=-18

x= -18-41

x = -59

Answer:

I believe the answer would be A. $200.00

Step-by-step explanation:

This is because if jay has 12 cars that he paid 3,500$ each for, the total cost would have been $42,000.

And the current price is 4,200$ for each car.

If you add 200$ to each 4,200$ car, you get 4,400$

After, you take the amount for each car (4,400) and multiply it by 12 (the amount of cars purchased) and you get 52,800.

You then need to subtract the recent cost of 12 cars (52,800) by 42,000$ (the original cost for 12 cars) and you will get $10,800.

52,800-42,000=10,800

therefore, A.$200.00 would be the correct answer

I'm not sure if all calculations are correct, but I hope this helps! :)

The average value of the cars must rise by $200 for the combined value of the 12 cars to be exactly $10,800 more than what Jay paid for them. Therefore, the correct answer is A. $200.00.

To find out how much more the average value of the cars must rise for the combined value to be $10,800 more than what Jay paid for them, we need to calculate the difference between the current combined value and the total price Jay paid, and then divide it by the number of cars.

Given:

Number of cars (n) = 12

Price Jay paid for each car (P) = $3,500

Current worth of each car (W) = $4,200

Total price Jay paid (T) = n * P = 12 * $3,500 = $42,000

Current combined value of the cars (C) = n * W = 12 * $4,200 = $50,400

Difference in value = C - T = $50,400 - $42,000 = $8,400

Additional increase needed = $10,800 - $8,400 = $2,400

To find the average increase needed per car, we divide the additional increase by the number of cars:

Average increase per car = Additional increase / Number of cars = $2,400 / 12 = $200

Therefore, the average value of the cars must rise by $200 for the combined value of the 12 cars to be exactly $10,800 more than what Jay paid for them.

The correct answer is A. $200.00.

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The number of ways that the student can choose the question to answer is; 30 ways

We are given that;

Number of questions in Section A = 5 questions

Number of questions in section B = 3 questions

Number of questions to be answered from section A = 3 questions

Number of questions to be answered from section B = 2 questions

The formula for probability combination is;

nCr = n!/(r!(n - r)!)

Number of ways of answering from section A = ⁵C₂

Number of ways of answering from section B = ³C₂

Thus, the number of ways that the student can choose the question to answer from the 8 questions in total is;

⁵C₂ * ³C₂

= 5!/(2!(5 - 2)!) * 3!/(2!(3 - 2)!)

= 10 * 3

= 30 ways

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Answer: 30%

Step-by-step explanation:
12/40 = 3/10 = 0.30

0.30*100 = 30%

Answer:

3/12

Step-by-step explanation:

Theres 12 possibilities and she has 3 numbers which means each number has a 1 out of 12 chance of winning the prize. Molly has three numbers so she has a probability of 3/12 to win a prize.

The polynomial expression that represents the perimeter is (3x^3 +3x -148)ft and the value is 182ft

Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates. We can perform arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable.

Perimeter of the triangle is the sum of the sides of the triangle which is = 2x^2 -120 + x^2 -5x +8x -28

Perimeter = (3x^2 +3x -148)ft

when x = 10

Perimeter = 3(10)^2 +3(10) -148 = 182ft

In conclusion the expression  (3x^2 +3x -148)ft is the expression for the perimeter of the triangle and the value is 182ft

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Answer:

x²-5x-50

Explanation:

Given the expression:

First, expand:

Next, open the bracket:

Finally, simplify:

Answer:

9.05

Step-by-step explanation:

make gallons into quarts

quar prefix in many languages means 4

1 gallon is 4 quarts

3 gallons is 4 times 3 -> 12 quarts

just by seeing 108 and 12 the answer will be around 9

108.90 ÷ 12 = 9.05

The mean and the standard deviation, from the frequency table, are given as follows:

The frequency table gives the number of times that each observation appears.

The mean of a data-set is given by the sum of all observations divided by the number of observations, hence it is given as follows:

Mean = (1 x 13 + 2 x 12 + 3 x 5)/(13 + 12 + 5) = 1.73.

The standard deviation is given by the square root of the sum of the difference squared between each observation and the mean, divided by the number of observations, hence it is given as follows:

Standard deviation = sqrt((13 x (1 - 1.73)² + 12 x (2 - 1.73)² + 5 x (3 - 1.72)²)/30) = 0.73.

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1

1-

1-

_________________________________________________________

Answer:

Step-by-step explanation:

1 = 27

2 = 36

2 = 1,000

Answer:

3^3 = 27

6^2 = 36

10^3 = 1000

Answer:

The null hypothesis must be rejected

Step-by-step explanation:

Here the P value is less than 0.05

which means that the test results are statistically significant and there are sufficient evidence to reject the null hypothesis and accept the alternative hypothesis.

Hence, the null hypothesis must be rejected.

Answer:

5.5hr

Step-by-step explanation:

Distance=550Km

Speed=100Km/hr

Speed=(Distance/Time)

Time=(Distance/Speed)

Time=550/100=5.5hr

Factor of polynomial m are 0,   6n⁴.

What is polynomial in maths?

A polynomial is an expression in mathematics made up of variables (also known as indeterminates) and coefficients, and it only uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of the variables. The polynomial x2 4x + 7 is an illustration of one with a single indeterminate x.

= 30m³n⁴ - 5m⁴

= 5m³(6n⁴ - m )

let 5m³(6n⁴ - m ) = 0

       5m³ = 0

         m = 0

 6n⁴ - m = 0

      m =   6n⁴

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The required length of the base of the triangular pane of glass is 22 inches.

We know that the formula for the area of a triangle is:

Area = 1/2 * base * height

We are given that the height of the triangular pane of glass is 32 inches and the area is 352 square inches. Substituting these values into the formula, we get:

352 = 1/2 * base * 32

Multiplying both sides by 2 and dividing by 32, we get:

base = 22

Therefore, the length of the base of the triangular pane of glass is 22 inches.

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The answer is 369,072. This is the total number of copies sold to date.

An expression that uses symbols to represent the relationship between two or more values.

This is calculated by solving the equation 9.7% × x = 35,800, where x is the total number of copies sold to date.

To solve this equation, we first need to convert the percentage to a decimal.

To do this, we divide 9.7 by 100, giving us 0.097.

We can then multiply both sides of the equation by this decimal, giving us 0.097x = 35,800.

We can then solve for x by dividing both sides of the equation by 0.097. This gives us x = 369,072. This is the total number of copies sold to date.

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