Describe how to solve d = rt for t

To find the equilibrium price, we need to determine the price at which the quantity demanded is equal to the quantity supplied. In other words, we need to find the price where D(p) = S(p).

Given the demand function D(p) = 1628 - 16p and the supply function S(p) = -4 + 8p, we can set them equal to each other:

1628 - 16p = -4 + 8p

Simplifying the equation, we combine like terms:

24p = 1632

Dividing both sides by 24, we find:

p = 68

Therefore, the equilibrium price is $68. At this price, the quantity demanded (D(p)) and the quantity supplied (S(p)) are equal, resulting in a market equilibrium.

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The probability that fewer than 60 out of a random sample of 500 adults will work from home is 0.03

In the given probability case we have;

What is the likelihood that, out of a random sample of 500 persons, fewer than 60 will work from home if 15% of adults in a particular country do so?

Let,

P = 15% = 0.15

n = 500

By considering the binomial distribution case the formula is given by

P( X = x ) = ⁿCₓ * Pˣ * (1 - P)ⁿ⁻ˣ

P( X ≤ 60 ) = ⁿCₓ * Pˣ * (1 - P)ⁿ⁻ˣ

                 = ⁶⁰∑ₓ=₀ (⁵⁰⁰Cₓ) (0.15)ˣ (1 - 0.15)⁵⁰⁰⁻ˣ

                 = 0.031

                 ≅ 0.03

Hence, the probability that fewer than 60 out of a random sample of 500 adults will work from home is 0.03

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Answer

\(\frac{573}{400}\)

step-by-step explanation:

\(\frac{1.4325}{1}\) ×  \(\frac{10000}{10000}\)  =  \(\frac{14325}{10000}\)

Simplify

\(\frac{14325}{10000}\) ÷\(\frac{25}{25}\) = \(\frac{573}{400}\)

Answer:

ANSWER

see attachment.

EXPLANATION

The graph of

f(x) = \sin( x) - 2f(x)=sin(x)−2

is the graph of

f(x) = \sin(x)f(x)=sin(x)

shifted down 2 units.

We first of all graph the basic sine function:.

y=sinx

and shift the graph down by 2 units to obtain the graph in the attachment.

A function assigns the values. The graph of the function f(x)=sin(x/2) is plotted as shown below.

A function assigns the value of each element of one set to the other specific element of another set.

The graph of the function f(x)=sin(x/2) is plotted as shown below. The graph of the function passes through the origin of the graph. Also, the nature of the graph of the function is cyclic.

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Answer:

3/5

Step-by-step explanation:

There are 20 discs in total. We need to find the probability of picking out either a red or yellow disc. There are 6 red discs and 6 yellow discs, a total of 12. This means that our chances of picking out a red or yellow disc from the bag is 12/20, which can be simplified to 3/5.

Answer:

3/5 or 60%

Step-by-step explanation:

Total disks: 6+3+6+5= 20

red+yellow disks: 6+6=12

red+yellow/total disks=12/20

FRACTION:

simplify: 12/20=6/10=3/5

3/5 probability of a red or yellow disk

PERCENTAGE:

12/20=60/100

60% chance of red or yellow

With 95% confidence the population mean μ is between 48.02 and 51.98. To construct confidence interval for the population mean, we need sample mean ,sample standard deviation, sample size additionally.

Assuming we have this information, we can use the following formula to calculate the confidence interval:

Confidence interval = sample mean +/- (t-critical * (sample standard deviation / square root of sample size))

where t-critical is the value from the t-distribution with n-1 degrees of freedom that corresponds to the level of significance (alpha) and sample size (n).

For example, if we have a sample size of 100, a sample mean of 50, a sample standard deviation of 10, and a level of significance of 0.05 (two-tailed test), the t-critical value for a 95% confidence interval would be 1.984.

Plugging these values into the formula, we get:

Confidence interval = 50 +/- (1.984 * (10 / √(100))) = (48.02, 51.98)

Interpreting the confidence interval, we can say with 95% confidence that the population mean m is between 48.02 and 51.98. This means that if we were to repeat the sampling process many times and calculate the confidence interval for each sample, we would expect 95% of these intervals to contain the true population mean.

In addition to providing a range of plausible values for the population mean, the confidence interval also provides information about the precision of the estimate. The wider the confidence interval, the less precise the estimate is likely to be. The narrower the confidence interval, the more precise the estimate is likely to be.

The width of the confidence interval depends on the sample size, sample standard deviation, and level of significance. A larger sample size, a smaller sample standard deviation, or a higher level of significance will all result in a narrower confidence interval.

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Complete question is:

Filling cola bottles Refer to Exercise 80 . Construct and interpret a 95% confidence interval for the population mean μ. What additional information does the confidence interval provide?

Answer:

A (0,6)  B (6, 1)  C (2,2)

Step-by-step explanation:

A (4, 4)

  [-4, 2]

Subtract 4 - 4 = 0 and then add 4+2 since both of them are positive. Do it for all of the coordinates

Image Coordinates:

A----->A¹(0,6)

B----->B¹(2,3)

C----->C¹(-2,4)

Answer:

-10.7°F.

Steps used to get answer:

1. Use this rule: a-b= -(b-a)

-(26-15.3)

2. Use the algorithm method.

  5 10

 26.0

- 15.3

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

   10.7

3. After simplification, we have:

−(26−15.3)=−10.7

4. Therefore, 15.3-26=-10.7

−10.7°F.

Done by NeighborhoodDealer

Answer:184yards

Step-by-step explanation:

First of all, the formulae for finding the perimiter is 2xlength + 2xwidth

which can also be written as 2l + 2w

solution:

=2l + 2w

=2x33 + 2x59

=66 + 118

= 184

Therefore the perimeter of the rectangle is 184yards.

Answer:

21

Step-by-step explanation:

Since the girls have the same age, let their age be x.
Then, their average is

\(\frac{x+x}{2} = \frac{2x}{2} = x\)

Let \(S_{i}\) denote the age of 'i' girls.
Then, \(S_{8} = S_{6} + x + x - eq(1)\)

Also, we have,

\(\frac{S_{8}}{8} =15 - eq(2)\)

\(\frac{S_{6}}{6} =13 - eq(3)\)

Then eq(2):

(from eq(1) and eq(3))

\(\frac{S_{6} + 2x}{8} =15\\\\\frac{13*6 + 2x}{8} = 15\\\\78+2x = 120\\\\2x = 120-78\\\\x = 21\)

The average of the other two girls with equal age​ is 21

Answer:

x=18.75

Step-by-step explanation.

We have to realize that this is a line. A line has 180 degrees.

Therefore we can make the equation;

(6x+30)+2x=180

8x+30=180

8x=150

x=18.75

please mark as branliest

Answer:

x=18.75

Step-by-step explanation:

We can see that these 2 angles are on a straight line, meaning that these 2 angles must add up to 180°.

We can set up an equation:

180=(6x+30)+2x

combine like terms

180=8x+30

subtract 30 from both sides

150=8x

divide both sides by 8

x=18.75

Hope this helps! :)

Answer:

y = 6/5 x -3

Step-by-step explanation:

Standard equation of a line is expressed as;

y = mx+b

Slope m = y2-y1/x2-x1

Given the coordinates  (0, -3)and (-5, 3)

Slope m = 3-(-3)/-5-0

Slope m = 6/5

Since the line cuts the y axis at y = -3, hence b = -3

GEt the required equation;

Recall that y = mx+b

y = 6/5 x + (-3)

y = 6/5 x -3

This gives the required equation

Answer: −6/5x-3

Step-by-step explanation: DeltaMath

The ordered pair of point C' after a rotation of 180º around the origin to create pentagon A'B'C'D'E' is given as follows:

C'(5,2).

The function rule for the five more known rotation rules are given as follows:

The coordinates of point C on the pentagon are given as follows:

C(5,2).

For the rotation of 180º, we change the signal of each component of the coordinate, hence it is given as follows:

C'(5,2).

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No, it is not as a result of all whole numbers are integers, thus there's no number that's not associate degree whole number.

The whole numbers area unit the numbers while not fractions and it's a group of positive integers and nil. it's diagrammatical by the image “W” and also the set of numbers area unit . Zero as a full represents nothing or a null worth.These numbers area unit positive integers as well as zero and don't embody aliquot or decimal elements (3/4, 2.2 and 5.3 don't seem to be whole numbers). Also, arithmetic operations like addition, subtraction, multiplication and division area unit attainable on whole numbers.

 Hence , it is not possible.

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\(\huge\sf \fcolorbox{purple}{redblush}{ Question : - }\)

R = {(-2, 4), (1, 3), (0, -4), (3, 2)}?

Domain of relation is (-2, 1,0,3}

so option 1st is correct

Based on the information, the probability will be:

P(X=7) = 0.03

P(X>=6) = 0.30

P(X=3 or 4) = 0.30

Probability is a measure that quantifies the likelihood of an event occurring. It is represented as a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain to happen. The probability of an event can also be expressed as a percentage between 0% and 100%.

To calculate the probability of an event, you need to know the total number of possible outcomes and the number of favorable outcomes. The probability of an event A happening, denoted as P(A), is given by:

P(A) = (Number of favorable outcomes)/(Total number of possible outcomes)

P(X=7) = 0.03

P(X>=6) = P(X=6) + P(X=7)+ P(X=8) = 0.16+0.03+0.11 = 0.30

P(X=3 or 4) = P(X=3) + P(X=4) = 0.16+0.14 = 0.30

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Answer: $ 6160

Step-by-step explanation:

Total money he will pay back = Principal + Interest

Simple interest = Principal x Rate x Time

i.e. Total amount need to pay = Principal + (Principal x Rate x Time)

= Principal (1+ Rate x Time)

Given: Principal =  $5,500, Rate = 3%=0.03 , Time = 4 years

Total amount need to pay = \(5500(1+(0.03)(4))\)

\(= 5500(1+0.12)\\= 5500(1.12)\\=\$6160\)

Hence,  the total amount he will have to pay back to the bank = $ 6160

Where k = 24g and m is the mass of the object.

C) To solve the differential equation y" = 1 + (y')^2 by using the substitution u = y', we can rewrite the equation as:

u' = y"

Substituting for y" using the given equation, we get:

u' = 1 + u^2

This is a separable differential equation. We can separate the variables and integrate both sides:

∫ du/(1 + u^2) = ∫ dx

arctan(u) = x + C

Substituting back for u = y', we get:

arctan(y') = x + C

where C is the constant of integration. To find the particular solution, we need an additional condition, such as an initial condition.

D) The equation for the motion of the mass attached to the spring is:

m y" = -k y

where m is the mass of the object, k is the spring constant, and y is the displacement from the equilibrium position. We can solve this equation using the standard method of finding the characteristic equation:

m r^2 + k = 0

r^2 = -k/m

r = ±√(-k/m)

Since the mass is initially released from rest, we have y'(0) = 0. This means that u(0) = y'(0) = 0.

Also, the initial displacement is y(0) = 8 inches, and the equilibrium position is at y = 0. This means that the initial condition for the differential equation is y(0) = 8, and we can find the constant k using the given information:

F = k y

where F is the force exerted by the mass on the spring. At the equilibrium position, the force is balanced by the weight of the mass, so we have:

k (0) = mg

where g is the acceleration due to gravity. Since the mass weighs 24 pounds, which is equivalent to 384 ounces, we have:

k (0) = (384/16) g = 24 g

So the spring constant is k = 24g.

Substituting into the general solution for y(t) gives:

y(t) = A cos(√(k/m) t) + B sin(√(k/m) t)

Using the initial condition y(0) = 8, we get:

8 = A cos(0) + B sin(0) = A

So we have:

y(t) = 8 cos(√(k/m) t) + B sin(√(k/m) t)

To find B, we differentiate y(t) with respect to time:

y'(t) = -8√(k/m) sin(√(k/m) t) + B√(k/m) cos(√(k/m) t)

Using the initial condition y'(0) = 0, we get:

0 = B√(k/m) cos(0) = B√(k/m)

So we have B = 0.

Therefore, the solution to the differential equation is:

y(t) = 8 cos(√(k/m) t)

where k = 24g and m is the mass of the object.

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Answer:

C

Step-by-step explanation:

It's C because i majored in mathmatics in college and ended with a A

Answer:

Step-by-step explanation:

Let x be a random variable representing the number of the members of a men’s club that wear black vests to their club meetings. This is a binomial distribution since the outcomes are two ways. It is either they wear black or red. The probability of success, p = 70/100 = 0.7

The probability of failure, q would be 1 - p = 1 - 0.7 = 0.3

a) Number of samples, n = 10

We want to determine P(x ≤ 8)

From the binomial distribution calculator,

P(x ≤ 8) = 0.851

Answer:

The probability that at least 8 of the vest worn will be black is 0.75490

Step-by-step explanation:

The parameters given are;

The percentage of black vest worn = 70%, p₀ = 0.7

Number of men in sample, n = 10

Required  number of men who wore black = 8

Proportion of sample \(\hat p\) = 8/10 = 0.8

The z score of a proportion is given by the relation;

\(z = \dfrac{\hat p - p_0}{\sqrt{\dfrac{p_0(1 - p_0)}{n} } }\)

Plugging in the vales, we have;

\(z = \dfrac{0.8 - 0.7}{\sqrt{\dfrac{0.7(1 - 0.7)}{10} } } = 0.69\)

From the z table we have probability = p(z < 0.69) = 0.75490

The probability that at least 8 of the vest worn will be black = 0.75490.

Answer: I believe it is -3.3x + 1.2

Explanation:

Add like terms.

Answer:

20

Step-by-step explanation:

As they are similar, correspondence sides are in common ratios:

Apply cross product property

Multiply the numbers

Divide both sides of the equation by 5

Calculate

Answer:

its called a calculator division and multiplication

Step-by-step explanation:

Answer:

Step-by-step explanation:

1) Use multiplication distributive property \((xy)^a=x^ay^a\)

= \(\frac{(x^4)^2y^2}{3}\)

2) Use Power rule \((x^a)^b = x^{ab}\)

= \(\frac{x^8y^2}{3}\)

Answer:

y=5

Step-by-step explanation:

The curve stops at the y value of 6. And we need a horizontal line for the asymptote, so we don't need an x value only a y-value. So the y-value is 5 on the y-axis, which means your equation will be y=5.

-Hope this helped

Answer:

23.86700

Step-by-step explanation:

You cannot compare two marginal distributions to see if the corresponding two are related . So, the statement is false .

The answer to the stated question is false . No , you cannot compare two marginal distributions to see if the corresponding two variables are related.

The given question is related to probability and statistics.

Coming to probability distribution , it is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events.

The marginal distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset. It gives the probabilities of various values of the variables in the subset without reference to the values of the other variables.

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Square is consider as the king of all the quadrilaterals.

Explanation:

Square is consider as the king of all the quadrilaterals:

Therefore, square shape is consider as the king of all the quadrilaterals.

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Answer:

The probability of them picking granola is 1/3

The probability of them choosing juice is 1/4

Step-by-step explanation:

Hope it helps :)