A cash bix of$1 and $5 bills is worth $45. The number of $1 bills is three more than the number of $5 bills. Hiw many each bill does it contain?

Step-by-Step Explanation

[tex]5 = \sqrt{r - 3} \\ = > (5) ^{2} = {( \sqrt{r - 3)} }^{2} \\ = > 25 = r - 3 \\ = > r = 25 + 3 = 28[/tex]

Answer

r = 28

Hope it helps.

If you have any query, feel free to ask.

The 3 dimensional figure has 6 vertices , 9 edges and 5 faces.

Vertices in shapes are the points where two or more line segments or edges meet (like a corner). Edges are the line segments that join one vertex to another and are also where the shape’s faces meet. Faces are the flat surface of a solid shape.

Given here: A figure with 3 rectangular faces and 2 triangular faces.

We know, Vertices are the corners of the three-dimensional shape, where the edges meet. Faces are flat surfaces and edges are the lines where two faces meet.

The vertices of the figure are A,B,C,D,E,F And edges as AB,BC,CF,FA,EB,DC,AE,FD,ED

And the faces are as follows

rectangular faces- AFDE, ABCF, EDCB

Triangular faces- EAB, DFC

Hence, The 3 dimensional figure has 6 vertices , 9 edges and 5 faces.

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I spend around 0 hours watching television( as I don't have a T.V.) and around 2-3 hours on internet.

Around 1-2 hours I am all by myself.

As one of the famous quote says-" Time is nothing but a stubborn illusion." but the very importance of time is a topic that we cannot even fathom to compare it. It's not something we can buy, not something we can control but a process that decays everything. Since we humans live for a very short amount of time, we should use it more wisely than money.

I spend around 0 hours watching television( as I don't have a T.V.) and around 2-3 hours on internet and Around 1-2 hours I am all by myself.

Our lives are significantly influenced by time. We gain the good habit of structuring and organizing our day-to-day activities with time. You can acquire knowledge and experience over time if you better appreciate time. Because you can't change the passage of time, it is the most valuable resource.

The minutes are represented by a two-digit number that ranges from 00 to 59, and the hour is represented by a two-digit number that ranges from 00 to 23 (or 24). The hour and the minute are separated by a colon: 00:15

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On an average, about 2.13 people region will need to get selected in order to find that one person who carries the genetic trait.

Random selection is a very important process in research methodology. The purpose of random selection is to increase the generalizability of the results as when we draw a random sample from a large population, it is less likely to be subject to bias.

Since 47 percent of the people in the population are carrying the gene, the probability of random selection will be 0.47. But we need to also consider how many trials will be unsuccessful. Therefore, we will use the mean,

1/0.47 = 2.127 ≅ 2.13

--The given question is incomplete, the complete question is

"According to a recent survey, 47 percent of the people living in a certain region carry a certain genetic trait. People from the region will be selected at random one at a time until someone is found who carries the genetic trait. On average, how many people from the region will need to be selected to find one person who carries the genetic trait?"--

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The standard deviation for the given data, can be found to be 3. 97

To find the standard deviation, you first need to find the mean of the data as:

= Sum of the numbers / Sample number

= ( 16 + 10 + 5 + 7 + 13 ) / 5

= 51 / 5

= 10. 2

The variance can then be found from this data, the mean, and a variance calculator to be 15.76.

The standard deviation is:

= √ 15.76

= 3. 97

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This equation can be resolved by simplifying it appropriately. Solve it by combining like terms.

To solve this problem

2a^(3) -4a^( 2)-6a-1-4a^( 3)+6a^( 2)-11a-3

Firstly, take away the ones that are 1 and 3 from it.

2a^(3) -4a^( 2)-6a-4a^( 3)+6a^( 2)-11a-4

Then combine like terms

2a^(3) -4a^( 2)-6a-4a^( 3)+6a^( 2)-11a-4

-2a^(3) -4a^( 2)-6a+6a^( 2)-11a-4

Then mix related terms owing a^(2)

-2a^(3) -4a^( 2)-6a+6a^( 2)-11a-4

-2a^(3) +2a^( 2)-6a-11a-4

Combine like terms having ( a )

-2a^(3) +2a^( 2)-6a-11a-4

-2a^(3) +2a^( 2)-17a-4

Consequently, the answer to this issue is

-2a^(3) +2a^( 2)-17a-4

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False. While large neural networks (NNs) can often outperform traditional learning algorithms in certain tasks, this is not always the case.

The performance of a large NN depends on the size of its training dataset, the type of problem it is being used to solve, the amount of data preprocessing and feature engineering that has been done, the size of the network, the type of optimisation algorithm being used, and the quality of the hyperparameters used. There is no single formula or calculation that can be used to determine which type of algorithm will be better than another.

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The maximum and minimum value of the function subject to the given constraint is f(0,0) = 0.

What are Lagrange multipliers?

Lagrange's multiplier is a mathematical technique used to find the maximum or minimum value of a function subject to certain constraints. It is named after Joseph-Louis Lagrange, who first introduced the method in the 18th century.

To use Lagrange multipliers to find the maximum and minimum values of the function f(x, y) = y^2 - x^2 subject to the constraint 1/4x^2 + y^2 = 64, we need to first set up the Lagrange function:

L(x, y, λ) = y^2 - x^2 + λ(1/4x^2 + y^2 - 64)

We then find the partial derivatives of L with respect to x, y and λ:

∂L/∂x = -2x + λ(1/2x) = 0

∂L/∂y = 2y + λ(y) = 0

∂L/∂λ = 1/4x^2 + y^2 - 64 = 0

Solving these equations, we find the following solutions:

x = 0, y = 0, λ = -8

x = 8√2, y = 8√2, λ = 4

x = -8√2, y = -8√2, λ = 4

Now, we need to check these solutions to see if they satisfy the constraint 1/4x^2 + y^2 = 64. Only the first solution x = 0, y = 0 satisfies the constraint.

Hence, the maximum and minimum value of the function subject to the given constraint is f(0,0) = 0.

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The proportion of all CEOs of medium and large companies who have MBAs is between 27.9% and 33.5%.

The formula we use is the Wilson Score Interval, which is a modified version of the Binomial Proportion Confidence Interval.

In this formula, we will use the following variables:

n = 344 (the total number of CEOs surveyed)

X = 97 (the number of MBAs)

z = 1.96 (the z-value corresponding to a 95% confidence level)

We then calculate the confidence interval as follows:

Lower Bound = (X + (z^2/2))/(n + z^2) - (z * SQRT((X * (1-X))/(n + z^2) + (z^2/4)) / (n + z^2)

Upper Bound = (X + (z^2/2))/(n + z^2) + (z * SQRT((X * (1-X))/(n + z^2) + (z^2/4)) / (n + z^2)

Plugging in the values for n, X, and z, we get the following confidence interval:

Lower Bound = 0.279

Upper Bound = 0.335

Therefore, we can be 95% confident that the proportion of all CEOs of medium and large companies who have MBAs is between 27.9% and 33.5%.

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The area of  trapezoid having side lengths of 14 inches & 8 inches and height 12 inches is,  132 In.²

An area is total space occupied by two-dimensional or flat surfaces. In other words we can say that it is a number of unit squares present in a closed figure. We use various units for measurement of area like, cm², m², ft², mm².

Given that,

A trapezoid,

segment lengths,

AB = 8 in.

BE  = 12 in.

DF = 3 in.

FE  = 8 in.

EC  = 3 in.

Total length of side 1 =   AB = 8 in.

Total length of side 1 =   DF + FE + EC

                                   =    3 + 8 + 3

                                   =    14 in.

Height  = 12 in.

Area of trapezoid  = 1/2(Sum of sides) x distance between them

                              = 1/2(8 + 14) x 12

                              =  132 In.²

Hence, the area is  132 In.²

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The surface area S is given by the definite integral of the function :

|r(t) X r'(t)| over the interval [1], which can be approximated by numerical integration methods.

To find the surface area of the surface generated by the given equations, we need to first find the cross-sectional area of the surface at every point of t and then integrate it over the interval. To do this, we need to find the vector r(t) = (x(t),y(t)) and its derivative r'(t) = (x'(t),y'(t)) which gives the tangent vector to the curve at t. The cross-sectional area of the surface at t is given by the magnitude of the vector cross product of the vectors r(t) and r'(t) and is written as |r(t) X r'(t)|. Then the surface area S is given by the definite integral of this cross-sectional area over the interval [1].

The definite integral can be solved analytically or numerically, however, the final answer would be the integration of the function |r(t) X r'(t)| over the interval [1], which is not possible to solve analytically, so we use numerical integration methods.

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The constant term is the term independent of a variable, which is [tex]15[/tex].

The coefficient of [tex]x[/tex] is the constant being multiplied by [tex]x[/tex] in the term with [tex]x[/tex] as the only variable, which is [tex]17[/tex].

ex=1+x2+x3/2!+x4/3!  is the Taylor series centered.

The function itself evaluated at a = 0 as well as the first three derivatives are therefore required to determine the first four terms using this formula (because the 0t h derivative equals the function itself).

The fourth derivative can be used to determine the next term as the fourth derivative is required to obtain four non-zero terms using this function and the 0th term is zero. This is likely why the first four derivatives were chosen.

f(0)=0(e0)=0

ex=1+x+x2/2!+x3/3!

ex=x(1+x+x2/2!+x3/3!)

ex=1+x2+x3/2!+x4/3!

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The y-intercept of the given line is 100.

What is the y-intercept?

The y-intercept is the point at which the line crosses the y-axis, which occurs when x = 0. To find the y-intercept, we can plug in x = 0 into the equation of the line.

We can write the equation of the line in the form y = mx + b, where m is the slope of the line and b is the y-intercept.

We can find the slope m using the point slope formula:

m = (y2 - y1) / (x2 - x1) = (148-100)/(42-0) = 48/42 = 4/3

Now we can substitute the point (0,100) into the equation of the line:

y = (4/3)x + b

100 = (4/3) * 0 + b

b = 100

So the y-intercept is (0,100)

Hence, the y-intercept of the given line is 100.

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We can conclude that the resistors from Manufacturer 1 have better mean resistance than Manufacturer 2.

What is the null hypothesis?

In statistics, the null hypothesis is a statement or assumption that there is no relationship or difference between certain populations or variables. It is typically represented by the symbol H0. The null hypothesis is used as a starting point for statistical hypothesis testing, which is a method used to determine whether the null hypothesis can be rejected or not based on sample data.

Given that the specialist has purchased 35 resistors from Manufacturer 1 with a mean of 150 ohms and a standard deviation of 2 ohms, and Manufacturer 2 offers a sample of 40 resistors with a mean of 148 ohms and a standard deviation of 2.5 ohms, we can assume that the two samples are independent and normally distributed.

To compare the means of the two samples, we can use a t-test for the means of two independent samples. The t-test will allow us to determine whether the difference in means between the two samples is statistically significant, or if it could have occurred by chance.

The null hypothesis of the t-test would be that there is no difference in means between the two samples, or that the mean of the Manufacturer 1 sample is equal to the mean of the Manufacturer 2 sample. The alternative hypothesis would be that there is a difference in means, or that the mean of the Manufacturer 1 sample is not equal to the mean of the Manufacturer 2 sample.

The t-value can be calculated using the formula:

t = (x1-x2)/sqrt((s1^2/n1) + (s2^2/n2))

where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Once the t-value is calculated, we can look up the t-value in a t-table to find the corresponding p-value. The p-value represents the probability of obtaining a t-value as extreme as the one calculated, assuming the null hypothesis is true.

If the p-value is less than the chosen significance level (usually 0.05), we would reject the null hypothesis and conclude that there is a statistically significant difference in means between the two samples

Hence, we can conclude that the resistors from Manufacturer 1 have better mean resistance than Manufacturer 2.

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Answer:

y = x - 4

Step-by-step explanation:

You can take any x input value from the chart and it's output and sub it into the equation

Assume (_) = z

Let's take the first input and output

6 = 10 + z

Z= - 4

Now sub z into the equation,

y = x - 4

The more appropriate average score for the two groups of adolescents is 1.83.

The appropriate average score for the two groups of adolescents can be computed using the following formula: (Group1 score + Group2 score) / 2.

For example, in the first row, the Group 1 score is "Lots" and the Group 2 score is "Little". The average score for this row would be (3 + 1) / 2 = 2.

In the second row, the Group 1 score is "Little" and the Group 2 score is "Somewhat". The average score for this row would be (1 + 2) / 2 = 1.5.

Similarly, for the remaining 8 rows, the average scores can be calculated as follows:

Row 3: (1 + 2) / 2 = 1.5

Row 4: (1 + 1) / 2 = 1

Row 5: (1 + 2) / 2 = 1.5

Row 6: (1 + 3) / 2 = 2

Row 7: (1 + 3) / 2 = 2

Row 8: (1 + 2) / 2 = 1.5

Row 9: (1 + 2) / 2 = 1.5

Row 10: (3 + 2) / 2 = 2.5

Therefore, the more appropriate average score for the two groups of adolescents is 1.83.

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Answer:Equation (1):

-8x + 4y = 24

Equation (2):

-7x + 7y = 28

Simplify the equation:

Equation 1 can be simplify by 4:

-2x + y = 6

Equation 2 can be simplify by 7:

-x + y = 4

Add x to both sides of the equation 2:

y = x + 4

Substitute equation 2 into 1:

x + 4 - 2x = 6

x - 2x = 6 - 4

- x = 2

x = - 2.

Substitute - 2 for x in equation 2:

y = - 2 + 4

y = 2.

Therefore, (x, y) = (- 2, 2)

The medians of a triangle connect the midpoints of each side and intersect at the centroid of the triangle.

Medians of a triangle are lines that connect the midpoints of each side of the triangle to the opposite vertex. This means that they divide the triangle into two halves, each with an area that is equal to half of the area of the entire triangle. The medians of a triangle with vertices (a1, a2, a3) intersect at a point known as the centroid of the triangle, which is located at the intersection of the three medians. The centroid can be found by taking the average of the three vertices, or by finding the intersection of the three medians. The centroid is the point at which the three medians of the triangle intersect and is the center of gravity for the triangle. In other words, it is the point that all three medians will intersect at.

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Answer:

8 days

Step-by-step explanation:

We know

A project should take no more than 60 hours, which means the number of hours should [tex]\leq[/tex] 60 hours.

John can spare 7.5 hours per day to work on the project.

Let x represent the number of days; we have the equation

7.5x [tex]\leq[/tex] 60

x [tex]\leq[/tex] 8

So, the maximum number of days it will take him to finish is 8 days.

The value of p = (125i + 10005)/5

=> p = 25i + 2001

Now, According to the question:

Let's know:

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

Karl was attempting to calculate economic figures.

The given equation is:

fp - w = 10000

f = 5 and w = 5 + 125i

To solve for the value of p.

(-125i - 5) + 5 p = 10000

Add 5 + 125i to both sides:

5 p + ((-125 i - 5) + 125 i + 5) = 125 i + 5 + 10000

(-125 i - 5) + (125 i + 5) = 0:

5 p = 10000 + 5 + 125 i

10000 + 5 + 125 i = (10000 + 5) + 125 i = 10005 + 125 i:

5 p = 125 i + 10005

Divide both sides of 5 p = 125 i + 10005 by 5:

(5 p)/5 = (125 i + 10005)/5

p = (125i + 10005)/5

Hence, The value of p = (125i + 10005)/5.

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Answer:

2x+3y=1470

Step-by-step explanation:

The statements that complete the proof are:

From the question, we have the following parameters that can be used in our computation:

The incomplete two-column proof

Given that

QS || RT and ∠R ≅ ∠T

We have

∠Q ≅ ∠T because alternate inerior angles are equal

By the reflexive property, we have

ΔQST ≅ ΔQST

This implies that

ΔQTS ≅ ΔTQR

Lastly, we have: ∠QTS ≅ ∠TQR

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The coefficient of variation in heights is 0.0432 (the or) 4.32 %.

The coefficient of variation in weights is 0.1733 (or) 17.33 %.

Variation in heights is less than variation in weights of thirteen-year-old girls.

For given Height data

Mean for heights will be sum of all the heights divided by total number of heights.

= [tex]\frac{59.4 +61.2+ 62.1 +64.7 +60.1 +58.3 +64.6 +63.7 +66.1}{9}[/tex]
= 62.2444

Standard Deviation for heights

When we have n number of observations and the observations are

[tex]\mathrm{x}_1, \mathrm{x}_2, \ldots \ldots \mathrm{x}_n[/tex], then the mean deviation of the value from the mean is determined as [tex]$$\sum_{i=1}^n\left(x_i-\bar{x}\right)^2$$[/tex]

=2.6908

(a) coefficient of variation in heights:

Standard deviation is the positive coefficient of the variance.

[tex]=\frac{\text { Standard Deviation }}{\text { Mean }}[/tex]

[tex]=\frac{2.6908}{62.2444}[/tex]

= 0.0432 (or) 4.32 %

(b) Coefficient of variation in weights is:

[tex]=\frac{\text { S.D }}{\text { mean }}[/tex]

[tex]=\frac{18.0831}{104.3333}[/tex]

= 0.1733 or 17.33 %

(c) Coefficient of variation in heights is 0.0432 (or) 4.32 %

Coefficient of variation in weights is 0.1733 or 17.33 %

0.0432 (or) 4.32 %  < 0.1733 or 17.33 %

Variation in heights < Variation in weights.

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Answer:

1 [tex]\frac{15}{18}[/tex]

Step-by-step explanation:

Re-write the problem:

5x3    -4 x 2          15   -8

——————      =  —-   —-      =

6x 3   9 x 2          18     18

15 - -8

———         =   1 [tex]\frac{15}{18}[/tex]

 18

Answer: The two numerical expressions that correctly represent the phrase "twice the sum of nine and four" are:

2 * (9 + 4) = 2 * 13 = 26

2(9 + 4) = 2(13) = 26

Both expressions use the correct mathematical operations to represent the phrase "twice the sum of nine and four" and both will yield the same result of 26.

Step-by-step explanation:

The second side of triangle has the length is 12cm.

Given data :

We know that,

BY p Pythagorean theorem,

a² + b² = c²

9² + b² = 15²

b² = 15² - 9²

b² = 144

b = 12

Therefore,

The second side means the hypotenuse is equal to 12cm.

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The probability of X being greater than 0 is 1.

P(X>0)=1-P(X≤0)

=1-φX+Y(-∞)=1-e^(-2*(-∞))-0.24*2*(-∞)-0.09*e^(-2*(-∞))

=1-0-0-0=1

Since x and y are identically independent random variables, P(X>0)=1-P(X≤0).

The moment generating function of x+y is given as φX+Y(t)=e2t+0.24.2t+0.09e2t.

To find P(X>0), we need to calculate P(X≤0). This can be done by putting t=-∞ in the moment generating function.

Therefore, P(X>0)=1-φX+Y(-∞)=1-e^(-2*(-∞))-0.24*2*(-∞)-0.09*e^(-2*(-∞))=1-0-0-0=1

The probability of X being greater than 0 is 1.

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Answer:

12

Step-by-step explanation:

There are 6 common factors of 12 and 60, that are 1, 2, 3, 4, 6, and 12. Therefore, the greatest common factor of 12 and 60 is 12.

The problem that can be solved is 2x + 3y = 5 and x + y = 2 & the solution to th system is (1, 1)

From the question, we are to

Create a problem that can be modeled and solved using systems of linear equations

A problem that can be solved using graph is as follows:

2x + 3y = 5

x + y = 2

Next, we plot and attach the graph

The point of intersection on the graph is the solution

This means that the solution is (1. 1)

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