Write the place of 3 in the given number.
812.536

Answer:

They are the same length, and they intersect. Hope this helps!

Solution:

Given that;

The students hold a carwash.

They charge $5 per car. And, if they wash 23 cars, te

Answer:

the last 3

Step-by-step explanation:

math

We need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit which is compounded semi-annually.

To solve this problem, we can use the formula for the future value of an annuity:

\(FV = P * ((1 + r)^n - 1) / r\)

Where:

FV is the future value of the annuity

P is the periodic payment or deposit amount

r is the interest rate per period

n is the number of periods

In this case, the deposit amount is $726.56, the interest rate is 6.45% compounded semi-annually, and the future value is $31,300. We need to find the number of deposits (n).

We can rearrange the formula and solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Substituting the given values:

n = log((31,300 * 0.03225) / (726.56 * 0.03225 + 31,300)) / log(1 + 0.03225)

Using a calculator or software, we find that n ≈ 9.989.

Therefore, we need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit.

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On the first line the distributive property was used. This property says that the product of a constant with a sum of two numbers is equal to the sum of the products.

On the third line the "associative" property was used. This property says that if you have the sum of three numbers the order at which you sum them doesn't affect the results.

The expected value of the discrete distribution, for each case, is given as follows:

a) Amount won by one entry: $0.075.

b) If the cost is the cost of a postage stamp:  -$0.525.

The expected value of a discrete distribution is obtained with the sum of each outcome multiplied by it's probabillity.

In this problem, the distribution for the prizes is given as follows:

Hence the expected value for the prizes is:

E(X) = 10,000,000 x 1/300,000,000 + 350,000 x 1/150,000,000 + 50,000 x 1/10,000,000 + 20,000 x 1/1,000,000 + 400 x 1/200,000 + 75 x 1/6,000 = $0.075.

The cost of a postage stamp is of $0.6, hence the expected value considering this cost would be of:

0.075 - 0.6 = -$0.525.

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Answer:

El sistema de ecuaciones para calcular la cantidad de niños y adultos que acudieron a la función es:

x+y=270

175x+200y=88,250

Step-by-step explanation:

La información proporcionada indica que a la función entran 470 asistentes entre adultos y niños y con esta información puedes decir que la suma de niños y adultos que entran a la función es igual a 470:

x+y=270, donde

x es el número de niños

y es el número de adultos

Además, se indica que se recaudaron $88,250 y tienes los precios de cada entrada por lo que puedes expresar que la suma de los resultados de multiplicar cada precio por la cantidad de personas que entraron por ese precio es igual a $88,250:

175x+200y=88,250

De acuerdo a esto, la respuesta es que el sistema de ecuaciones para calcular la cantidad de niños y adultos que acudieron a la función es:

x+y=270

175x+200y=88,250

The values of b and a for the logarithmic function in this problem are given as follows:

The logarithmic function in the context of this problem has the format given as follows:

\(y = b\log_3{x + a}\)

The vertical asymptote is at x = -4, hence:

\(y = b\log_3{x - 4}\)

When x = 5, y = -1, hence the parameter b is obtained as follows:

\(-1 = b\log_3{5 - 4}\)

0.477b = -1

b = -1/0.477

b = -2.1.

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Answer: Minimum (s, h): (3, -5)

Maximum (s, h): (2, -2.5)

Explanation:

To locate the absolute extrema of the function h(s) = 5/(s - 4) on the closed interval [2, 3], we need to find the minimum and maximum values of the function within that interval.

First, let's evaluate the function at the endpoints of the interval:

h(2) = 5/(2 - 4) = -5/2 = -2.5

h(3) = 5/(3 - 4) = -5

Next, we need to find the critical points of the function within the interval (where the derivative is either zero or undefined). To do this, we differentiate the function:

h'(s) = -5/(s - 4)^2

Setting the derivative equal to zero, we get:

-5/(s - 4)^2 = 0

This equation has no solutions since the numerator is never zero.

Now, we check for any points where the function is undefined. In this case, the function is undefined when the denominator is zero:

s - 4 = 0

s = 4

Since s = 4 is not within the interval [2, 3], it does not affect the extrema within the interval.

Considering all the information, we can conclude:

The minimum value of h(s) on the interval [2, 3] is -5, which occurs at s = 3.

The maximum value of h(s) on the interval [2, 3] is -2.5, which occurs at s = 2.

Therefore, the absolute extrema are:

Minimum (s, h): (3, -5)

Maximum (s, h): (2, -2.5)

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Yes, the line shown on the scatter plot is a good line of fit because the line follows the pattern.

What is a line of best fit?

The straight line that best depicts the overall picture of what the collected data is showing is known as the line of best fit, also known as a trendline or a linear regression. It aids in determining whether the two things under study are related or have a correlation. This trendline aids in our ability to forecast upcoming developments involving the data under study.

The line models a positive association is incorrect, because the plot has a negative slope which means that it has a negative association.

The data does not have a linear association is wrong because it can seen that the plot does show that most of the points are clustered around a path that would be a line through the points.

It is not necessary for a line of best fit to go through any of the original points so line does not pass through any of the data points is also incorrect.

Therefore, the line is a good fit as it follows the pattern.

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Answer:

Hope this help :)

Step-by-step explanation:

The actual distance between the two cities is 288 miles.

A scale drawing is a smaller version of a larger image / city. The scale drawing is reduced by a constant ratio.  This means that the scale drawing of the two cities would be smaller than the actual cities.

The scale is used to keep the proportion of the dimensions between the scale drawing and the original diagram similar. This means that the scale drawing of the two cities would be smaller than the actual cities.

The actual distance between the two cities = (3 x 24) ÷ 1/4

= 3 x 24 x 4 = 288 miles

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Answer:

Step-by-step explanation:

A=3.14 x 22m x 22m

A=69.08m x 22m

A=1519.76m2 (squared po yan)

A catalytic ozone destruction cycle requires no atomic oxygen and it incorporates the photochemical decomposition of ClONO₂ to Cl and NO₃, and photochemical decomposition of the later to NO and O₂. The overall reaction is NO + O₃ → NO₂ + O₂

In the lower stratosphere, a proposed mechanism for ozone destruction in the late spring over northern latitudes begins with the photochemical decomposition of ClONO₂ to Cl and NO₃. This reaction is catalyzed by sunlight in the lower stratosphere. The photodissociation of NO₃ is the next step in the cycle, and it results in the production of NO and O₂.

The NO then reacts with O₃ in the following reaction: NO + O₃ → NO₂ + O₂The NO₂ that is produced then reacts with atomic oxygen to form NO₃, and the cycle starts again with the photodissociation of ClONO₂. The NO that is produced during the reaction between NO₂ and O₃ can also react with atomic oxygen to form NO₂, which can then go on to form NO₃.However, the catalytic cycle that has been proposed requires no atomic oxygen to be present. The NO that is produced during the reaction between NO₂ and O₃ reacts with more O₃ to form NO₃ and O₂: NO + O₃ → NO₂ + O₂NO₂ + O₃ → NO₃ + O₂The NO₃ that is produced in this reaction can then go on to react with more O₃, starting the cycle over again. Thus, the overall reaction for the catalytic ozone destruction cycle is:NO + O₃ → NO₂ + O₂NO₂ + O₃ → NO₃ + O₂NO₃ + O₃ → NO + 2O₂The cycle continues as long as the necessary reactants are available.

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Answer:

Distance from point AA to point BB = 189.3 feet

Step-by-step explanation:

Let the distance from point AA to the base of the lighthouse be represented by x, and the distance from point BB to the base of the lighthouse be represented by y. So that;

distance from point AA to point BB = x - y

To determine the value of x, applying the required trigonometric function;

Tan θ = \(\frac{opposite}{sdjacent}\)

Tan 13 = \(\frac{102}{x}\)

x = \(\frac{102}{Tan 13}\)

  = 441.81 feet

x = 441.8 feet

To determine the value of y;

Tan 22 = \(\frac{102}{y}\)

y = \(\frac{102}{Tan 22}\)

  = 252.46

y = 252.5 feet

Thus,

distance from point AA to point BB = 441.8 - 252.5

                                                           = 189.3 feet

Answer:

18 3/4

Step-by-step explanation:

Answer:

18 3/4 or 75/4

Step-by-step explanation:

Assume all of the statistics used have a normal sampling distribution. Use 3 decimal places. Below are the steps of calculation:(a) For a 98% confidence interval for a population mean based on n = 11 observations with known: We know that margin of error formula = Zα/2 σ/√n, Where Zα/2 is the quantile of the normal distribution at α/2, σ is the population standard deviation and n is the sample size. In this case, α = 0.02, n = 11 and Zα/2 = 2.326. The sample size is small, and therefore we assume a normal distribution. Using the formula above, we obtain: margin of error = Zα/2 σ/√n = 2.326 σ/√11(b) For a 98% confidence interval for a population mean based on n = 11 observations with unknown. We know that margin of error formula = tα/2 s/√n. Where tα/2 is the quantile of the t-distribution at α/2, s is the sample standard deviation and n is the sample size. In this case, α = 0.02, n = 11 and tα/2 = 2.718. The sample size is small, and therefore we assume a normal distribution.

Using the formula above, we obtain: margin of error = tα/2 s/√n = 2.718 s/√11(c) For a 90% confidence interval for a population proportion, p, based on n = 11 observations. We know that margin of error formula = Zα/2 √((p(1-p))/n)Where Zα/2 is the quantile of the normal distribution at α/2, n is the sample size, and p is the sample proportion. In this case, α = 0.1, n = 11 and Zα/2 = 1.645.Using the formula above, we obtain: margin of error = Zα/2 √((p(1-p))/n) = 1.645 √((p(1-p))/11)(d) For a 92% confidence interval based on n = 14 observations for the slope parameter. We know that margin of error formula = tα/2 * SE. Where tα/2 is the quantile of the t-distribution at α/2, and SE is the standard error of the estimate. In this case, α = 0.08, n = 14 and tα/2 = 1.771.

Using the formula above, we obtain: margin of error = tα/2 * SE = 1.771 * SE. Therefore, the correct quantile for the margin of error of each confidence interval is as follows:(a) 2.670(b) 2.570(c) 0.512(d) 1.564.

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Answer and Step-by-step explanation:

The least common multiple (LCM) of 15 and 24 can be found using the prime factorization of 15 and 24 which is...

The prime factorization of 15 is... 3 x 5.

The prime factorization of 24 is... 2 x 2 x 2 x 3.

Eliminate the duplicate factors of the two, then multiply them once with the remaining factors of the lists to get LCM (15,15) = 120.

Hope this helped you out! Have a wonderful day! <3

The puck travelled a distance of 53.8 meters when the puck is 120 centimeters before the opponent's goal and puck travelled a distance of 56.2 meters when the puck is 120 centimeters after the opponent's goal.

Given that the distance to the opponent's goal from the player's current position is 55 meters. And after the shot, the puck is 120 centimeters from his opponent's goal.

We need to find out how many meters the puck travelled.

Also given there are 100 centimeters in 1 meter.

So, 55 meters = 55 × 100 centimeters

⇒ 55 metets = 5500 centimeters

Now, we are given that the puck is 120 centimeters from the opponent’s goal. It is not clear whether the puck landed before or after the goal post. So, considering both cases.

Case 1: the puck is 120 centimeters beyond the opponent's goal.

So, the distance travelled by the puck is

5500 centimeters + 120 centimeters = 5620 centimeters

Divide 5620 by 100 to convert centimeters to meters.

The puck travelled a distance of 5620 cm or 56.2 meters.

Case 2: the puck is 120 centimeters before the opponent's goal.

So, the distance travelled by the puck is

5500 centimeters - 120 centimeters = 5380 centimeters

Divide 5380 by 100 to convert centimeters to meters.

The puck travelled a distance of 5,380 cm or 53.8 meters.

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Answer:

A

Step-by-step explanation:

since there are 3 corresponding sides shown, the SSS similarity theorem can be utilized.

The formula D = inv (A) returns the inverse of a symbolic matrix A. The symbol will be \(A^{-1}\).

If A is a non-singular square matrix, then \(A^{-1}\), often known as the inverse matrix of A, must exist if it is to satisfy the following property:

A\(A^{-1}\) =\(A^{-1}\)A = I, where I is the identity matrix.

Finding the minors and cofactors of the given matrix's components is one of the most crucial steps in determining its inverse. To comprehend this approach clearly, follow the steps listed below.

The following formula may also be used to find the inverse matrix:

\(A^{-1}\)= adj(A)/det (A).

The calculation for the inverted matrix is done.

Hence they are the symbol and methods to find the inverted matrix.

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Answer:

C

Step-by-step explanation:

The angles at point A have to be congruent so that you have two congruent angles. and one congruent side, which give SAA.

From the image, we can see than angle B and angle D are congruent. We also know that line AC is congruent to itself since it shared between the two triangles. Since we need one more angle, that angle has to be angle A.

Since Barry is going to post-secondary school for three years, a personal line of credit is vital to pay for his education.

It should be noted that when a individual collects a loan, the person will have to pay it back with an extra amount as interest.

In this case, it's important for him to use his personal line or credit rather than collecting a student loan from people. This isn't good in this scenario.

Therefore, since Barry is going to post-secondary school for three years, a personal line of credit is vital to pay for his education.

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Answer:

$60 for adults (x), $24 dollars for children (y)

Step-by-step explanation:

Solve using systems of equations

3x + y = $204

2x + 3y = $192

y = 204 - 3x

2x + 3( 204 - 3x) = 192

2x + 612 - 9x = 192

-7x + 612 = 192

420 = 7x

x = $60 for adults

y = 204 - 3(60)

y = $24 for children

Answer:

The answer would be Y= 1/4X -3

Step-by-step explanation:

Hope it was helpful .

Good luck ^.^

Answer:

-2/3

Step-by-step explanation:

Let us take the coordinates of any two points on the line, i.e.,

1. (0,3)

2. (3,1).

Slope

= Δy/Δx

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

= (1 - 3)/(3 - 0)

= -2/3

So, the slope is -2/3.

Answers:

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

Explanation:

x = Erin's true speed

Her true speed x is within 2 mph of 56 mph.

This means the interval for x is \(56-2 \le \text{x} \le 56+2\) which simplifies to \(54 \le \text{x} \le 58\)

She could be going as slow as 54 mph, or as fast as 58 mph, or something in between.

The expression |x-56| measures the distance from x to 56 on the number line. Recall absolute value is used to ensure the distance isn't negative.

We want this distance to be within 2 units, i.e. we want the distance to be 2 or smaller.

\(\text{distance on number line} \le 2\\\\|\text{x}-56| \le 2\)

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

Here's what the steps look like to solve that absolute value inequality

\(|\text{x}-56| \le 2\\\\-2 \le \text{x}-56 \le 2\\\\-2+56 \le \text{x}-56+56 \le 2+56\\\\54 \le \text{x} \le 58\\\\\)

For the second step, we use the rule that |x| < k is the same as -k < x < k where k is some positive number.

In the third step, I added 56 to all three sides to isolate x fully.

Based on the triangle proportionality theorem, the true proportion regarding the figure is: B. i/j = h/k

The triangle proportionality theorem states that when two sides of a triangle is intersected by a line that is parallel to the third side of a triangle, the two sides intersected are therefore divided in the same ratio.

TU is parallel to QR. Therefore, based on the triangle proportionality theorem, TU will divide QS and RS in the following ratio: B. i/j = h/k

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See attachment for the area model of the equation 4x^2+12x+9 = (2x+3)^2

Area models are shapes used to model or illustrate products, multiplications, divisions and quotients

The equation is given as:

4x^2+12x+9 = (2x+3)^2

Express (2x+3)^2 as the product of (2x+3) and (2x+3)

4x^2+12x+9 = (2x+3) * (2x+3)

The above means that the area model is a square.

So, the side lengths of the model must be equal, where the side lengths are 2x + 3 and the area of the square is 4x^2+12x+9

See attachment for the area model of the equation 4x^2+12x+9 = (2x+3)^2

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