A jar contains only nickels and dimes. The jar contains a total of 21 coins. The value of all the coins is 1.65$. How many nickels and dimes are in the jar?

Answer:

\(m= \frac{6}{5}\)

Step-by-step explanation:

Slope can be calculated using following formula

\(m=\frac{y_2-y_1}{x_2-x_1}\)

Here

\((x_1, y_1) = (-5, -1) \ \ and \ \ (x_2, y_2) = (5, 11)\)

Slope m is given as

\(m=\frac{11-(-1)}{5-(-5)}\)

\(m=\frac{12}{10}\\m=\frac{6}{5}\)

The solution to the inequality -3(1 - z) < 9 is z < 4.

To solve the inequality -3(1 - z) < 9, we can follow these steps:

Distribute the -3 on the left side of the inequality:

-3 + 3z < 9

Combine like terms:

3z - 3 < 9

Add 3 to both sides of the inequality to isolate the variable:

3z < 12

Finally, divide both sides of the inequality by 3 to solve for z:

z < 4

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The evaluated integral is 55(z + 1) (x² - 1) ln(x² - 1) - 55(z + 1) (x² - 1) + C, where C is the constant of integration.

We have,

To evaluate the integral ∫ 110(z + 1) ln(x² - 1) dx, we will follow the integration rules step by step.

However, it seems there is a typo in the integral expression, as the absolute value notation "|" is not properly placed.

For now, I will assume that the absolute value notation is not necessary for the integral.

Let's proceed with the evaluation:

∫ 110(z + 1) ln(x² - 1) dx

To integrate this, we can apply the method of substitution.

Let's set u = x² - 1, then du = 2x dx.

Substituting these values, we have:

∫ 110(z + 1) ln(u) (1/2) du

Now, we can simplify and integrate:

(1/2) ∫ 110(z + 1) ln(u) du

To integrate ln(u), we use integration by parts.

Let's set dv = ln(u) du, then v = u ln(u) - ∫ (u) (1/u) du.

Simplifying the integral further:

(1/2) [110(z + 1) (u ln(u) - ∫ (u) (1/u) du)]

The term ∫ (u) (1/u) du simplifies to ∫ du, which is simply u.

(1/2) [110(z + 1) (u ln(u) - u)]

Substituting back u = x^2 - 1:

(1/2) [110(z + 1) ((x^2 - 1) ln(x² - 1) - (x² - 1))]

Now, we can perform the final integration:

(1/2) [110(z + 1) (x² - 1) ln(x² - 1) - 110(z + 1) (x² - 1)] + C

Simplifying further:

55(z + 1) (x^2 - 1) ln(x² - 1) - 55(z + 1) (x² - 1) + C

Therefore,

The evaluated integral is 55(z + 1) (x² - 1) ln(x² - 1) - 55(z + 1) (x² - 1) + C, where C is the constant of integration.

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Answer:

sample proportion of defective items

Step-by-step explanation:

The p-chart is a type of chart in which the sample is taken periodically from the production process, so as to determine if the population proportion of defective items in the sample falls within the control limits on the chart.

For a P-chart, as the sample size gets larger it turns more into a normal distribution making it possible to approximate the distribution of the proportion defective.

Answer:

-3(-1)=

Step-by-step explanation:

Answer:

3 + 7 = 10

Step-by-step explanation:

I hope this answers your question. :)

Answer: 3+7=10

Step-by-step explanation:

maybe this is it but this question is really unclear

Marci can get 7 free comic books if she buys 68 comics. Therefore, option A, "7 free comic books" is the correct answer.

According to the question, the Comic Depot gives one free comic book to customers when they purchase 9 comic books. This means that a customer who buys 9 comic books gets one comic book for free. If a customer buys 18 comic books, he/she will get two comic books for free, and so on. We can find the relationship between the number of comic books a customer buys and the number of free comic books he/she gets by using a unitary method.

Let x be the number of comic books Marci buys and let y be the number of free comic books she gets. Since Marci gets one free comic book for every nine comic books she buys, we have that:

y = (1/9) x.

Rearranging the equation above to solve for x, we have that:

x = 9y

We are asked to find the number of free comic books Marci can get if she buys 68 comic books. Thus, we substitute x = 68 into the equation above to find the number of free comic books y:

y = (1/9)68 = 7.56

Thus, Marci can get 7 free comic books.

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the probability that the average age of a randomly selected sample of 100 students will be less than 21.8 years is 0.0564 rounded to three decimal places. The final answer is 0.056.

The problem given can be solved by using the central limit theorem.

According to the central limit theorem, if the sample size is sufficiently large, then the sample mean will follow a normal distribution with a mean of μ and a standard deviation of σ/√n, where n is the sample size.Using this formula, we can find the probability that the average age of a randomly selected sample of 100 students will be less than 21.8 years. The formula is:

P(Z < (X-μ)/(σ/√n))

where Z is the standard normal distribution, X is the value we want to find the probability for, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, X = 21.8, μ = 22, σ = 2, and n = 100. Plugging these values into the formula, we get:

P(Z < (21.8-22)/(2/√100)) = P(Z < -1.58)

Using Excel or a standard normal distribution table, we can find that the probability of Z being less than -1.58 is 0.0564.

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The distribution of X₁ - 3X₂ is a normal distribution with mean μ₁ - 3μ₂ and variance s₁² + 9s²₂ - 6rhos₁s₂.

To find the distribution of X₁ - 3X₂, we need to find the mean and variance of this new variable.

The mean of X₁ - 3X₂ is:

E(X₁- 3X₂) = E(X₁) - 3E(X₂) = μ₁ - 3μ₂

The variance of X₁ - 3X₂ is:

Var(X₁ - 3X₂) = Var(X₁) + 9Var(X₂) - 6Cov(X₁,X₂)

Since X₁ and X₂ have a bivariate normal distribution with means μ₁ and μ₂, variances s₁ and s₂ and correlation rho, we know that:

Var(X₁) = s²₁

Var(X₂) = s²₂

Cov(X₁,X₂) = rhos₁ s₂

Substituting these values into the variance equation, we get:

Var(X₁ - 3X₂) = s₁² + 9s²₂ - 6rhos₁s₂.

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The most appropriate choice for function and subtraction of function will be given by-

(r-c)(x) = \(4x^2-8x-25\)

What is function and subtraction of function?

A function from A to B is a rule that assigns to each element of A a unique element of B

A is the domain set and B is the co-domain set.

Subtraction of function

Suppose f(x) and g(x) are two functions. Then

(f - g)(x) = f(x) - g(x)

Here,

r(x) = \(4x^2 + 2x\)

c(x) = \(10x+25\)

(r-c)(x) = r(x) - c(x) = \((4x^2+2x)-(10x +25)\)

                            = \(4x^2+2x -10x-25\)

                            = \(4x^2-8x-25\)

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Answer:

greater than

hope this helps! <3

Answer:

I'm so sorry I just really need some points

line 1 & 2 neither

line 1 & 3 perpendicular

line 2 & 3 parallel

Answer:

x = 12

y = -4

Step-by-step explanation:

Answer:

197

Step-by-step explanation:

-7 + 4 + 200 =

-3 + 200 =

197

Answer:

197

Step-by-step explanation:

=> (-7) + 4 + 200

=> -(7 - 4) + 200

=> -3 + 200

=> 200 - 3

=> 197

Answer: About 0.2 gallons

Step-by-step explanation: 4/18=0.2 repeating, so each person gets about 0.2 gallons.

Each of her friend will get 4 and a half gallons of juice.

Division is one of the four main arithmetical operations by which we find the equal distribution of something.

Given that, At Lara's party, 4 gallon of fruit punch are shared equally among 18 friend.

To find how much each of them got, we will divide total amount of punch  by total number friends

Amount of juice each of them gets, = 18/4 = 4.5

Hence,  Each of her friend will get 4 and a half gallons of juice.

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The product of 56.2 and 9.2057 to the appropriate number of significant digits is 517.00.

The significant digits in a number are the digits that contribute to its precision. When multiplying numbers, the result should be rounded to the same number of significant digits as the factor with the least number of significant digits.

In this case, 56.2 has three significant digits, and 9.2057 has five significant digits. The factor with the least number of significant digits is 56.2. Therefore, the product should be rounded to three significant digits.

Multiplying 56.2 by 9.2057 gives 517.38134. Rounding this result to three significant digits gives us 517.00. The trailing zeros after the decimal point are significant in this case as they indicate the precision of the result. Hence, the correct answer is 517.00.

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The boat must move 785.82 m closer to the cliff  for the angle of depression to become 19°.

We need to find how much closer to the cliff the boat must move for the angle of depression to change from 7° to 19°.

Calculate the distance from the boat to the base of the cliff at 7° angle of depression.
Using the tangent function, we have:
tan(angle) = height/distance
tan(7°) = 150m/distance
distance = 150m/tan(7°)

distance=1221.49

Calculate the distance from the boat to the base of the cliff at 19° angle of depression.
Using the tangent function, we have:
tan(angle) = height/distance
tan(19°) = 150m/distance
distance = 150m/tan(19°)

distance=435.6665

Calculate the difference between the two distances to find out how much closer the boat must move.
difference = distance at 7° angle of depression - distance at 19° angle of depression

Plugging in the values from Steps 1 and 2, we get:
difference = (150m/tan(7°)) - (150m/tan(19°))

difference=1221.49-435.6665

difference=785.8235

After calculating, we find that the boat must move approximately 785.82 meters closer to the cliff for the angle of depression to change from 7° to 19°.

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Answer: You can make more bracelets than necklaces. ✅

Step-by-step explanation:

You have 2.88 meters of copper wire and 5.85 meters of aluminum wire.

With 2.88 meters of copper wire, you can make 12 bracelets because each bracelet needs 0.24 meters of copper wire.

With 5.85 meters of aluminum wire, you can make 9 necklaces because each necklace needs 0.65 meters of aluminum wire.

So you can make 12 bracelets and 9 necklaces.

Therefore you can make more bracelets than necklaces.

I would have labeled the points as

(x1,y1) = (11,12)

(x2,y2) = (15,16)

then used the formula

m = (y2-y1)/(x2-x1)

However, your idea works as well. I don't see any errors with your steps. Nice work.

Answer:

Step-by-step explanation:

1/8=0.125

rounded to the nearest thousand is 0

The count of letter f (any case) in ' if fred is from a part of france, then of course fred's french is good', is 8.

A word, phrase, or sentence in which no letter of the alphabet appears more than once is known as a heterogram (from the prefix hetero-, meaning "different," and the suffix -gram, meaning "written"). The same idea has also been denoted by the phrases isogram and nonpattern word.

Language on Vacation: An Olio of Orthographical Oddities, written by Dmitri Borgmann in 1965, mentions the idea, however he refers to it as an isogram. Borgmann asserts that he "introduced" the term "isogram" in a 1985 essay. Although he uses the term "isogram" in the paper itself, he also offers the name "asogram" to prevent confusion with lines of constant value like contour lines.

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Answer:

2201.8348 ; 3 ; x / (1 + 0.01)

Step-by-step explanation:

1)

Final amount (A) = 2400 ; rate (r) = 6% = 0.06, time, t = 1.5 years

Sum = principal = p

Using the relation :

A = p(1 + rt)

2400 = p(1 + 0.06(1.5))

2400 = p(1 + 0.09)

2400 = p(1.09)

p = 2400 / 1.09

p = 2201.8348

2.)

12000 amount to 15600 at 10% simple interest

A = p(1 + rt)

15600 = 12000(1 + 0.1t)

15600 = 12000 + 1200t

15600 - 12000 = 1200t

3600 = 1200t

t = 3600 / 1200

t = 3 years

3.)

A = p(1 + rt)

x = p(1 + x/100 * 1/x)

x = p(1 + x /100x)

x = p(1 + 1 / 100)

x = p(1 + 0.01)

x = p(1.01)

x / 1.01 = p

x / (1 + 0.01)

Answer:

2201.8348 ; 3 ; x / (1 + 0.01)

Step-by-step explanation:

Hope this helps! (:

Answer:

y=3x+1 or Slope:3 and Y intercept: (0,1)

Step-by-step explanation:

Use the slope formula and the slope-intercept form to find the slope  m  and y-intercept  b .

Formula : y=mx+b

Answer:

the y intercept is (0,1) and the slope is 3

that means the  y = mx + b format would be:

y = 3x + 1

Answer:

7+3 = 10

Step-by-step explanation:

if I understand the problem strangeness right, and there is nothing missing in it, then this is the simple answer.

the difference of 12 and 9 is 12-9 = 3.

and then adding this 3 to 7 is 7+3 =10

Answer:

10

Step-by-step explanation:

The difference of 12 and 9 is 3.

Now,

If we add 7 to 3, the answer is 10.

Answer:

answer is

Step-by-step explanation:

Object distance (u) = -100cm  Focal length (f) = 50cm Image distance = v  By lens formula; 1v−1u=1f1v−1u=1f ⇒ 1v−1−100=1501v−1−100=150 ⇒1v=150−11001v=150−1100 ⇒1v=2−1100−11001v=2−1100−1100 v =100cm  Hence the image is formed at 100 cm behind the lens.  Object distance (u) = -100cm  Focal length (f) = -25cm  Image distance = v  By lens formula;Read more on Sarthaks.com - https://www.sarthaks.com/951256/an-object-is-kept-at-a-distance-of-100-cm-from-each-of-the-above-lenses-calculate-the?show=951265#a951265

Step-by-step explanation:

The axis of symmetry: is the line that makes the parabola split in exactly half and lines up with the vertex. For that parabola x=1 is the line of symetry.

The vertex is where the minimum of the graph is, on this graph you can eyeball it to be (1,-9)

The x-intercept is where y is 0 so that's where the lines intersex with the x-axis. (-2,0) and (4,0)

The y-intercept of the function is where x is 0 and where the parabola intersects with the y-axis. On this graph it would be (0,-8)

Hope that helps :)

Answer:

3 of the pyramids

Step-by-step explanation:

Given:

Hexagonal Prism

Hexagonal based pyramid

Required

How many of the pyramid will fill up the prism

To do this, we start by calculating the volumes of both shapes.

Let V1 be the volume of the hexagonal prism

\(V_1 = \frac{3\sqrt{3}}{2}a^2h\)

Where: a = base and h = height

Let V2 be the volume of the hexagonal based pyramid

\(V_2 = \frac{\sqrt{3}}{2}a^2h\)

Where: a = base and h = height

The number of the pyramid that can occupy the prism is calculated by dividing V1 by V2

\(Number = \frac{V_1}{V_2}\)

\(Number = \frac{3\sqrt{3}}{2}a^2h /\frac{\sqrt{3}}{2}a^2h\)

Convert division to multiplication

\(Number = \frac{3\sqrt{3}}{2}a^2h * \frac{2}{\sqrt{3}a^2h}\)

\(Number = \frac{3\sqrt{3}}{2} * \frac{2}{\sqrt{3}}\)

\(Number = \frac{3\sqrt{3}}{1} * \frac{1}{\sqrt{3}}\)

\(Number = \frac{3*1}{1} * \frac{1}{1}\)

\(Number = 3\)

Answer:

32

Step-by-step explanation:

Opposite angles are congruent, so Angle BAC is 58 degrees.

Line KL and FG are perpendicular (forms a 90 degree angle), so Angle ABC is 90 degrees.

Points ABC form a triangle, and the interior angles of a triangle must add up to 180 degrees.

Thus, 58 + 90 + Angle BCA = 180. Solving for BCA, we get 32 degrees. Since Angle GCJ is opposite to BCA, x is 32 degrees.

Below, you will learn how to solve the problem.

(a) To find the linear relationship y = mx + b between x = year and y = profit, we first need to find the slope (m) and the y-intercept (b).

The slope (m) is the change in y (profit) divided by the change in x (year):
m = (17 - 5)/(6 - 2)

m = 12/4

m = 3

Next, we can use one of the data points (2, 5) and the slope (3) to find the y-intercept (b):
5 = 3(2) + b
b = 5 - 6

b = -1

So the linear relationship between x = year and y = profit is:

y = 3x - 1

(b) To find the company's profit at the end of 3 years, we can plug in x = 3 into the equation:
y = 3(3) - 1

y = 8

So the company's profit at the end of 3 years is $8 million.

(c) To predict the company's profit at the end of 8 years, we can plug in x = 8 into the equation:

y = 3(8) - 1 = 23

So the company's profit at the end of 8 years is predicted to be $23 million.

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