Peter has a bag with 150 coins in it. He closed his eyes and pulled out 10. Three were quarters, 5 were dimes, and 2 were
nickels.
a What is the experimental probability that the coin is a
quarters
Fraction:
Decimal:
Percent:

The weight of the Avery's lunch box using given weights is equal to 0.92 pounds (rounded to two decimal places).

Total weight of the backpack= 2 2/3 pounds

                                                = 8/3 pounds

The weight of the each book =7/8 pounds.

Let x be the weight of the lunch box in pounds.

An equation that represents the total weight in Avery's backpack,

2(7/8) + x = 8/3

To solve for x, simplify and solve for x,

⇒14/8 + x = 8/3

Multiplying both sides by 24 the least common multiple of 8 and 3 to clear the fractions,

⇒42 + 24x = 64

Subtracting 42 from both sides,

⇒24x = 22

Dividing both sides by 24,

⇒x = 22/24

Simplifying the fraction,

⇒x = 11/12

     =  0.92 pounds (rounded to two decimal places).

Therefore, the  weight of the lunch box is equal to 0.92 pounds (rounded to two decimal places).

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After the hurricane and the disease, 48% of the original population of rats is left.

We have,

After the hurricane, 40% of the rats were wiped out, which means

100% - 40% = 60% of the rats survived.

Then, after the disease spread through stagnant water, 20% of the remaining rats were killed.

This means 100% - 20% = 80% of the rats that survived the hurricane are still left.

To find the percentage of the original population of rats that is left after both events, we multiply the percentages:

Percentage left = 60% * 80% = 0.6 * 0.8 = 0.48

Finally, we convert the decimal value back to a percentage:

Percentage left = 0.48 * 100% = 48%

Therefore,

After the hurricane and the disease, 48% of the original population of rats is left.

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Answer:

S= 11+4t

Step-by-step explanation:

Answer:

S= 11+4t .      

hope I'm write not sure

Step-by-step explanation:

The Measure of angle A is 120°, Measure of angle C = 120° and the Measure of angle D is 60°

In a parallelogram, opposite angles are congruent. Therefore, if the measure of angle A is 120°, then the measure of angle C is also 120°.

Since angle A and angle C are opposite angles, their adjacent angles are also congruent. This means that the measure of angle B is equal to the measure of angle Z.

Now, let's consider angle D. In a parallelogram, the sum of the measures of adjacent angles is always 180°. Since angle C is 120°, the adjacent angle D must be:

180° - 120°

= 60°.

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The number of terms in the given arithmetic sequence is n = 10. Using the given first, last term, and the common difference of the arithmetic sequence, the required value is calculated.

The general form of the nth term of an arithmetic sequence is

an = a1 + (n - 1)d

Where,

a1 - first term

n - number of terms in the sequence

d - the common difference

The given sequence is an arithmetic sequence.

First term a1 = \(1\frac{1}{2}\) = 3/2

Last term an = \(2\frac{1}{2}\) = 5/2

Common difference d = 1/9

From the general formula,

an = a1 + (n - 1)d

On substituting,

5/2 = 3/2 + (n - 1)1/9

⇒ (n - 1)1/9 = 5/2 - 3/2

⇒ (n - 1)1/9 = 1

⇒ n - 1 = 9

⇒ n = 9 + 1

∴ n = 10

Thus, there are 10 terms in the given arithmetic sequence.

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Disclaimer: The given question in the portal is incorrect. Here is the correct question.

Question: If the first and the last term of an arithmetic progression with a common difference are \(1\frac{1}{2}\), \(2\frac{1}{2}\) and 1/9 respectively, how many terms has the sequence?

Answer:

6:5

I guess that's the answer because 2*3/5

According to your solution of the given system of equations, the value of y is 7.

Simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.

Given a system of equation y = 2x + 11 and 3x + 2y = 8

From equation 1 we will substitute the value of y in the form of x in equation 2

=> 3x + 2(2x + 11) = 8

=> 3x + 4x + 22 = 8

=> 7x = 8 - 22

=> 7x = -14

=> x = -2

Substitute this value in equation 1

=> y = 2* -2 +11

=> y = -4 + 11

=> y = 7

therefore,  the value of the y is 7 from your solution of the system of equations given.

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Answer:

hi

Step-by-step explanation:

it wuold be nine

Answer: The ones place digit would be 9

The equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is y = (5/2) * x^2y + 1. This equation represents a curve where the y-coordinate is a function of the x-coordinate, satisfying the conditions.

To determine an equation of the curve that satisfies the conditions, we can integrate the slope function with respect to x to obtain the equation of the curve. Let's proceed with the calculations:

We have:

Point: (0, 1)

Slope: 5xy

We can start by integrating the slope function to find the equation of the curve:

∫(dy/dx) dx = ∫(5xy) dx

Integrating both sides:

∫dy = ∫(5xy) dx

Integrating with respect to y on the left side gives us:

y = ∫(5xy) dx

To solve this integral, we treat y as a constant and integrate with respect to x:

y = 5∫(xy) dx

Using the power rule of integration, where the integral of x^n dx is (1/(n+1)) * x^(n+1), we integrate x with respect to x and get:

y = 5 * (1/2) * x^2y + C

Applying the initial condition (0, 1), we substitute x = 0 and y = 1 into the equation to find the value of the constant C:

1 = 5 * (1/2) * (0)^2 * 1 + C

1 = C

Therefore, the equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is:

y = 5 * (1/2) * x^2y + 1

Simplifying further, we have:

y = (5/2) * x^2y + 1

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Answer: 1.25

Step-by-step explanation: Divide 1,200 in 7 days and the aswer is 1.25

The volume of the composite solid is approximately X cubic inches.

The composite solid consists of multiple interconnected shapes, including cylinders and rectangular prisms. To find its volume, we need to calculate the volume of each individual shape and then add them together.

First, let's calculate the volume of the cylinders. We have two cylinders with different dimensions. The formula to find the volume of a cylinder is V = πr²h, where "r" represents the radius of the base and "h" is the height. Calculate the volume of both cylinders and add them together.

Next, we have a rectangular prism. The formula to find its volume is V = lwh, where "l" represents the length, "w" is the width, and "h" is the height. Calculate the volume of the rectangular prism.

Now, sum up the volumes of the cylinders and the rectangular prism to find the total volume of the composite solid.

In the end, the volume of the composite solid is approximately X cubic inches. Remember to round your answer to the nearest tenth, as specified.

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The percent increase in the interstate highway system from 1960 to now is 381%.

option A.

The percent increase from 16,000 km to 77,000 km is difference between the old value and new value divided by the old value expressed in 100%.

percent increase =  100% x (new value - old value) / old value

percent increase = 100% x  (77,000 - 16,000) / 16,000

percent increase = 100% x 61,000 / 16,000

percent increase = 381.25%

Thus, the percent increase in the interstate highway system from 1960 to now is approximately 381%, which is option A.

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The cost of downloading 10 songs for Johnny is $30.

The cost of downloading music for Johnny can be represented by the expression 1.5x + 15, where x is the number of songs downloaded. To find the cost of downloading 10 songs, we can plug in x = 10 into the expression:

1.5 * 10 + 15 = 15 + 15 = 30

So, it will cost Johnny $30 to download 10 songs. This expression represents the total cost as the sum of a $30 $30 ($15 monthly fee) and a variable cost ($1.50 per song fee).

The fixed cost remains constant regardless of the number of songs downloaded, while the variable cost increases as more songs are downloaded.

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The number of hours worked by Anthony , Josh and Dominic is 2 hours , 0 hours and 5 hours respectively

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of hours worked by Anthony = A

Let the number of hours worked by Josh = J

Let the number of hours worked by Dominic = D

Total number of hours worked by Anthony , Josh and Dominic = 7 hours

So , A + J + D = 7   be equation (1)

Now ,

Dominic worked twice as many hours as Anthony did with an extra hour

So , D = 2A + 1   be equation (2)

And ,

Dominic worked 5 more hours than Josh did

So , D = 5 + J   be equation (3)

Simplifying be equation (2) and be equation (3) , we get

2A + 1 = 5 + J

Subtracting 5 on both sides , we get

J = 2A - 4   be equation (4)

Now ,

Substituting the values of equation (2) , equation (3) and equation (4) in equation (1) , we get

A + 2A - 4 + 2A + 1 = 7

5A - 3 = 7

Adding 3 on both sides , we get

5A = 10

Divide by 5 on both sides , we get

A = 2

Therefore , the number of hours Anthony worked is 2 hours

Now , Substituting the value of A in equation (4) , we get

J = 4 - 4

J = 0 hours

Therefore , the number of hours Josh worked is 0 hours

Now , Substituting the value of A in equation (2) , we get

D = 4 + 1

D = 5 hours

Therefore , the number of hours Dominic worked is 5 hours

Hence , The number of hours worked by Anthony , Josh and Dominic is 2 hours , 0 hours and 5 hours respectively

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Answer:

slope=-2

Step-by-step explanation:

7-3/0-2=

4/-2=

-2

The width for the second rectangle which is HIJK will be A. 24 inches.

From the diagram, it should be noted that rectangle ABCD is similar to rectangle HIJK. Therefore it should be noted that the relationship between the width and length is expressed as:

= Width / Length

= 12/16

= 3/4

Therefore, the width for the second rectangle will be:

= 3/4 × 3.2

= 2.4

In conclusion, the correct option is A.

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The line which is having same y intercept as the line which passes through points (-4,0) and (0,3) is y=2x+3.

Given Points through which the line passes through are (-4,0) and (0,3)

We have to find the equation whose y intercept is equal to the y intercept of the line whose points given above.

First of all we have to find the y intercept of the line which passes through (-4,0) and (0,3). Equation of line is :

y-y1=(y2-y1)/(x2-x1)*(x-x1)

y-0=(3-0)/(0+4)  *(x+4)

y=3/4(x+4)

y -intercept exists where x=0

put x=0

y=3

So the options are:

By putting the value of x in all options we will find

y=-4

y=-3

y=3

y=4

So the third option is correct.

Hence the line whose y-intercept matched with the given line is y=2x+3.

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Answer:

a

Step-by-step explanation:

Answer:

Step-by-step explanation:

Isosceles triangle, the given angles are congruent

Answer:

n = 4

Step-by-step explanation:

6n - 3 = n + 17

5n = 20

n = 4

The positive root of the equation \(4cos(x) - x^4\) using Newton's method is 0.866966.

We begin with an initial guess \(x_{0}=1\), and we can iteratively define the calculation using the formula:

\(x_{i+1}= x_{i} - \frac{ f(x_{i})}{f'(x_{i})}\)

where \(f(x)=4cos(x) - x^4\)and f'(x) is the derivative of f(x).

So, \(f'(x) = -4sin(x) - 4x^3.\)

We repeat this process, using the previous approximation to find the next one, until we reach the desired accuracy.

In each iteration, we substitute the current approximation into the formula to refine our estimate.

Iteration 1: \(x_{1}= x_{0}- f(x_{0})/f'(x_{0})= 1 - \frac{ (4cos(1) - 1^4)}{(-4sin(1) - 4(1)^3)}= 1.576\)

Iteration 2: \(x_{2}= x_{1} - f(x_{1})/f'(x_{1}) = 1.1576 - \frac{(4cos(1.1576) - 1.1576^4)}{(-4sin(1.1576) - 4(1.1576)^3)} = 1.2055\)

Iteration 3: \(x_{3}= x_{2} - f(x_{2})/f'(x_{2}) = 1.2055 - \frac{4cos(1.2055-(1.2055)^4)) }{(-4sin(1.2055) - 4(1.2055)^3)} = 1.2080\)

After several iterations, we get that the positive root of the equation \(4cos(x) - x^4\) is approximate x ≈ 0.866966, accurate to six decimal places.

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Answer:

yes your right

Step-by-step explanation:

not a line not a line segment and not a triangle

good job

Answer:

yes it's correct

Step-by-step explanation:

Because none of the other answer choices would fit the description for the question

       Hence, OPTION (C) is your answer:  X  =  44

Step-by-step explanation:

       √x + 5 - 3 = 4

        √x +  5   =  3  +  4

        √x +  5   =   7

         (√x  +   5)2     =     (7)2

            x   +   5         =   49

        x   -  44     =   0

             +44      =   44

       X                =   44

       Hence,  X  =  44

        Equation: √x  +  5  =  7

      √(44)  +  5  =  7

    √49  =   7

            Hence,   x   =   44

        I hope this helps!

The matrix product \(y1′(t)=[915−4−7]y1(t)\)is evaluated to show that y1(t) is a solution to the system y′=Py is as follows:

\(y1(t) = [2e^(3t) - 8e^(-t), 3e^(3t) - 20e^(-t)]\) Thus, y1′(t) is given by\(y1′(t) = [6e^(3t) + 8e^(-t), 9e^(3t) + 20e^(-t)]y1′(t) = [9 15 6 9] [2e^(3t) - 8e^(-t) 3e^(3t) - 20e^(-t)].\)

Therefore, y1′(t) = Py1(t) hence, y1(t) is a solution to the system y′=Py.b. The matrix product\(y2′(t)=[915−4−7]y2(t)\) is evaluated to show that y2(t) is a solution to the system y′=Py is as follows:\(y2(t) = [-4e^(3t) + 2e^(-t), -6e^(3t) + 5e^(-t)]\)Thus, \(y2′(t) is given byy2′(t) = [-12e^(3t) - 2e^(-t), -18e^(3t) - 5e^(-t)]y2′(t) = [9 15 6 9] [-4e^(3t) + 2e^(-t) -6e^(3t) + 5e^(-t)].\)

Therefore, y2′(t) = Py2(t) hence, y2(t) is a solution to the system y′=Py.c. The Laplace transform of the following initial value is:

y′′ + y = {sin(πt), 0, 0 ≤ t < 1 y(0) = 0, y′(0) = 0\(y′′ + y = {sin(πt), 0, 0 ≤ t < 1 y(0) = 0, y′(0) = 0\) Taking the Laplace transform of both sides gives u\(s L{y′′ + y} = L{sin(πt)}\)Now, \(L{y′′} + L{y} = L{sin(πt)} ⇒ s^2 Y(s) - s y(0) - y′(0) + Y(s) = π/2(s^2 + π^2)\)

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Answer:

Step-by-step explanation:

1. 10^2+7^2=x^2

x=sqrt(149)

2. 21^2-19^2=x^2

x=sqrt(80)

3. This is all pythagorean theorem busywork, a^2+b^2=c^2 where c is the hypotenuse of the triangle.  I think from my examples you should be able to figure the rest out.

The coefficients obtained by the student may be less efficient and have larger standard errors compared to the professor's regression.

If the student enters each observation twice, resulting in a sample size of 100 instead of the original 50, the assumption of independent observations is violated in Ordinary Least Squares (OLS) regression. The OLS assumption assumes that the observations are independent, meaning that the value of one observation does not depend on the value of another observation.

In this case, the student's dataset contains repeated observations, which introduces dependence between observations. This violation of the independence assumption can lead to biased and inconsistent parameter estimates in the regression analysis.

Regarding the slope coefficients, if the student runs a regression using the duplicated data, the estimated coefficients may be different from the professor's regression. The duplication of observations inflates the sample size, potentially affecting the precision and accuracy of the estimates.

However, the direction and overall relationship between the variables may still be captured by the student's regression, although the estimates may not be as reliable.

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Part A

we have the equation

(x-13)^2+(y-4)^2=16

Rewrite as

(x-13)^2+(y-4)^2=4^2

so

The center of the circle is the point (13,4)

The radius of the circle is 4 units

using a graphing tool

Part B

Remember that

If an ordered pair lies on the circle, then the ordered pair must satisfy the equation of the circle

so

Verify each ordered pair

Hunter (11,4)

For x=11 and y=4

substitute in the equation of the circle

Is not true

so

Hunter is not in the spotlight

Joe (8,5)

x=8 and y=5

Is not true

so

Joe is not in the spotlight

Mason (15,5)

x=15 and y=5

Is not true

Mason is not in the spotlight

Answer:

Step-by-step explanation:

Given

Temperature = 12 degrees below 0

Required

Represent as an integer

12 degrees below 0 means that the temperature is less than 0.

This can then be expressed as:

\(Temperature = 0 - 12\)

\(Temperature = - 12\)

Hence, the integer that represents this scenario is -12

The probability that between 31.2% and 50.4% of the students in the sample will be minority students is approximately 0.7154, or 71.54%.

To solve this problem, we can use the normal approximation to the binomial distribution, assuming that the sample size is large enough. The mean (μ) of the binomial distribution is given by n * p, where n is the sample size and p is the probability of success. In this case, the sample size is 100 and the probability of success is 0.36.

μ = n * p = 100 * 0.36 = 36

The standard deviation (σ) of the binomial distribution is given by the square root of n * p * (1 - p).

σ = √(n * p * (1 - p)) = √(100 * 0.36 * (1 - 0.36)) ≈ 4.16

To calculate the probability between 31.2% and 50.4%, we need to convert these percentages into z-scores using the formula:

z = (x - μ) / σ

where x is the observed value, μ is the mean, and σ is the standard deviation.

For 31.2%:

z1 = (31.2 - 36) / 4.16 ≈ -1.06

For 50.4%:

z2 = (50.4 - 36) / 4.16 ≈ 3.37

Next, we need to find the cumulative probabilities associated with these z-scores using a standard normal distribution table or calculator. The cumulative probability can be interpreted as the area under the normal curve up to a given z-score.

P(31.2% ≤ x ≤ 50.4%) = P(-1.06 ≤ z ≤ 3.37)

Using a standard normal distribution table or calculator, we can find the corresponding cumulative probabilities:

P(-1.06 ≤ z ≤ 3.37) ≈ 0.8577 - 0.1423 ≈ 0.7154

Therefore, the probability that between 31.2% and 50.4% of the students in the sample will be minority students is approximately 0.7154, or 71.54%.

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Answer:

10 gallons were poured out

Step-by-step explanation:

2/3's of the 15 gallons of water is 10 gallons. Therefore 10 gallons were poured out.