Penny charges $5 per hour for babysitting, plus a flat fee of $12 for her travel expenses. Charlene charges $3 per hour for babysitting, plus a flat fee of $18 for her travel expenses.
Write an equation that could be used to determine the number of hours each babysitter must work to earn the same amount *

Form the given five quadratics , the one representing the repeated roots is equal to option d. 25x² - 30x + 9 and repeated roots are 3/5 or 3/5.

Quadratics representing repeated roots has discriminant equals to zero.

Standard quadratic equation is:

ax² + bx + c = 0

Discriminant 'D' = b² - 4ac

option a. -x²+ 18x + 81

Discriminant

'D' = 18² - 4(-1)(81)

      = 324 + 324

      = 648

D>0 has distinct roots.

option b. 3x²- 3x - 168

Discriminant

'D' = (-3)² - 4(-3)(-168)

      = 9 - 2016

      = -2007

D< 0 has distinct roots.

option c. x²- 4x -  4

Discriminant

'D' = (-4)² - 4(1)(-4)

      = 16 + 16

      = 32

D>0 has distinct roots.

option d. 25x²- 30x + 9

Discriminant

'D' = (-30)² - 4(25)(9)

      = 900 - 900

      = 0

D = 0 has repeated roots.

Repeated roots are:

x = ( -b ±√D ) / 2a

  = [-(-30)±√0 ]/ 2(25)

  = 30/ 50

  = 3/5.

option e.  x² - 14x + 24

Discriminant

'D' = (-14)² - 4(1)(24)

      = 196 - 96

      = 100

D>0 has distinct roots.

Therefore, the quadratics which represents the repeated roots are given by option d. 25x² - 30x + 9 and its repeated roots are 3/5 or 3/5.

The above question is incomplete, the complete question is:

One of the five quadratics below has a repeated root. (There other four have distinct roots.) What is the repeated root?

a. -x²+ 18x + 81

b. 3x² - 3x - 168

c. x² - 4x - 4

d. 25x² - 30x + 9

e. x² - 14x + 24

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Answer:

Josephine

Step-by-step explanation:

2 criteria was given to pass an exam:

1. At least, a mean mark of 40% must be achieved in the exam consisting of 4 papers

2. Score at least, 33% in each paper.

From the table given, and considering these two criteria, James definitely didn't pass the examination. He scored below 33% in one of the 4 papers. James scored 30% in Maths

Calculated the mean score for John and Josephine to determine if they meet the first criteria of having at least a mean score of 40%.

Mean score of John = (35 + 36 + 42 + 44) ÷ 4 = 39.25%

Mean score for Josephine = (60 + 55 + 38 + 75) ÷ 4 = 57%

Josephine passed the examination because she had a mean score of 57%, and also scored 33% and above in each test.

Answer:

parellel planes do not intersect

non-coplanar also dont

Answer:

y=x+0z

y=x+0z-5

Step-by-step explanation:

By far the easiest way to do it is using linear equations

we know that

y=x and

y=x-5

don't ever touch

so we can graph it on 3D and we get

and like the lines the planes don't touch

Answer:

Area = 8/25 or 0.32 or 32/100

Area = B

Step-by-step explanation:

L = 8/10

w = 4/10

Area = 8/10 * 4/10 = 32 / 100 = 0.32

Note:

32/100 = 8/25

Answer:

29

Step-by-step explanation:

Answer:

58⁰

Step-by-step explanation:

So its given that angle BAD and angle DAC are equal

BAD+DAC=CAB

29+29= 58⁰

Answer:

0,3 I think

Step-by-step explanation:

if you ever need help with questions like these, m a t h w a y works for me

If you are trying to determine if an input variable may affect your key characteristic (output variable) by examining the

correlation between variables, you should use the tool: D. Scatter plot diagram. therefore, option D.Scatter plot

diagram is correct.

A scatter plot diagram is a graphical representation of the relationship between two variables. It can help you visualize

the correlation between the input and output variables, making it easier to determine if there is a potential cause-and-

effect relationship.

The tool that you should use to examine the correlation between variables is D. Scatter plot diagram.

A scatter plot diagram is a graphical representation that displays the relationship between two variables.

The x-axis represents the input variable, while the y-axis represents the output variable.

By plotting the data points on the scatter plot diagram, you can visually analyze the correlation between the variables.

If there is a strong positive or negative correlation between the variables, it suggests that the input variable may affect

the key characteristic (output variable).

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D. Scatter plot diagram is the tool that should be used to examine the correlation between variables to determine if an input variable may affect your key characteristic (output variable).

The scatter plot diagram is a graphical representation that displays the relationship between two variables, and it is commonly used to identify patterns, trends, and correlations between variables. By examining the scatter plot diagram, you can determine whether there is a positive, negative, or no correlation between the variables, which can help you to identify potential cause-and-effect relationships.
 To determine if an input variable may affect your key characteristic (output variable) by examining the correlation between variables, you should use:

A scatter plot diagram is a graphical tool that helps visualize the relationship between two variables, allowing you to identify any correlation between the input and output variables.

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The requried Burger Quick is able to estimate its wait time more consistently because it has a smaller IQR. Option A is correct.

A straightforward method of expressing statistical data on a plot in which a rectangle is drawn to represent the second and third quartiles, with a vertical line inside to indicate the median value.

Here,
Burger Quick is able to estimate its wait time more consistently because it has a smaller interquartile range (IQR). The IQR is a measure of the spread of the middle 50% of the data and is calculated as the difference between the third quartile (Q3) and the first quartile (Q1). The smaller the IQR, the more consistent the data is around the median, which is represented by the line within the box in the box plot.

In this case, Burger Quick has a smaller IQR (8.0) compared to Super Fast Food (7.0), indicating that the wait times at Burger Quick are more consistent around the median. The range, which is the difference between the maximum and minimum values, is not a good measure of consistency as it is affected by outliers.

Therefore, based on the given information, Burger Quick is able to estimate its wait time more consistently because it has a smaller IQR.

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Answer:

£169

Step-by-step explanation:

255/3 = £85

110 x 50 p = 5500 p

255 - 110 = 145 coins which are 20 p

145 x 20 p = 2900 p

5500 p = £55

2900 p = £29

£85 + £55 + £29 = £169

Answer:

I sun 169 ofc

Step-by-step explanation:

Answer:

x = 7

Step-by-step explanation:

x-7 = 0

add 7 on both sides - X-7+7 = 0+7

x=7

Mark me brainliest please

The probability of an individual buying the product given they have seen the ad is 0.10. The probability of an individual buying the product given they have not seen the ad is 0.05. Therefore, the probability of an individual having seen the ad given they have bought the product is 0.83, rounded to 3 decimal places.

The probability of an individual buying the product given they have seen the ad is 0.10, which means that 10% of individuals who have seen the ad will buy the product. The probability of an individual buying the product given they have not seen the ad is 0.05, which means that 5% of individuals who have not seen the ad will buy the product. Therefore, the probability of an individual having seen the ad given they have bought the product is the ratio of the two. This can be expressed as the probability of an individual having seen the ad given they have bought the product divided by the probability of an individual having not seen the ad given they have bought the product. This can be calculated as (0.80/0.10) / (1-0.80/0.05) = 0.83, rounded to 3 decimal places. This implies that there is an 83% probability that an individual has seen the ad if they have bought the product. This is because 80% of people have seen the television ads for the product, and only 10% of those who have seen the ad buy the product, whereas only 5% of those who have not seen the ad buy the product.

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3.13

47/15=3.13333333333333333333333... and to the nearest hundredth would be 3.13. let me know if im wrong, i love feedback!  

In this case, the monthly payment for the car loan would be approximately $1,299.13.

To calculate the monthly payment for a bank loan using Excel, you can use the PMT function.

Here's how to do it:

1. Open Excel and create a new spreadsheet.

2. In cell A1, enter the loan amount: -40000 (negative because it's an outgoing payment).

3. In cell A2, enter the annual interest rate: 9%.

4. In cell A3, enter the loan duration in years: 3.

5. In cell A4, enter the formula to calculate the monthly payment: =PMT(A2/12, A3*12, A1).

6. The result in cell A4 will be the monthly payment.

So, in this case, the monthly payment for the car loan would be approximately $1,299.13.

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Answer:

At the average rate of making profit, it will take slightly more than 30 hours for the business to reach a profit goal of $500. (30.075)

Step-by-step explanation:

a) It is not clear what linear equation is desired. We are given enough information to write an equation relating the number of bracelets produced by each worker to the time it takes.

Let n represent the number of bracelets Danica produces. Let r represent the number of bracelets Darrelle produces. Let h represent time in hours.

.. r/3 = h/4 ... Darrelle produces 3 bracelets in 4 hours

.. 4r - 3h = 0 ... equation in standard form

.. r = (3/4)h ... equation in slope-intercept form (the intercept is 0)

.. n/5 = h/2 ... Danica produces 5 bracelets in 2 hours

.. 2n - 5h = 0 ... equation in standard form

.. n = (5/2)h ... equation in slope-intercept form

b) We have no idea what special functions were discussed in the course. Of course these equations can be graphed. (2-dimensional equations are easily graphed.)

c) A profit function can be written in terms of the number of bracelets produced. Then it can be solved to find when (h=?) profit is equal to $500.

.. Let p represent the total profit from production of bracelets.

.. p = 10.50*r + 3.50*n ... profit in terms of bracelets produced

.. p = 10.50*((3/4)h) + 3.50*((5/2)h) ... profit in terms of hours, where both work the same hours

.. p = 16.625 h

.. 500 = 16.625 h ... we want to find hours until $500 profit

.. 500/16.625 = h ≈ 30.0752

At the average rate of making profit, it will take slightly more than 30 hours for the business to reach a profit goal of $500.

_____

If you work out the timing of when bracelets are finished, assuming they are made at a constant rate, you find that there will be 23 of Darrelle's bracelets and 76 of Danica's bracelets finished in 30 hours and 40 minutes. These will yield a profit of $507.50. After another 8 minutes, Danica will have finished bracelet 77 to add another $3.50 to the profit total.

The given expressions, when A=1, B=0, and C=1, X evaluates to 1.001; when A=B=C=1, X evaluates to 1.111; and when A=B=C=0, X evaluates to 0.000. These evaluations are based on the given values of A, B, and C, and the notation ¯¯¯¯¯¯BC represents the complement of BC.

To evaluate the expression X = A.¯¯¯¯¯¯BC, we substitute the given values of A, B, and C into the expression.

(a) For A = 1, B = 0, and C = 1:

X = 1.¯¯¯¯¯¯01

To find the complement of BC, we replace B = 0 and C = 1 with their complements:

X = 1.¯¯¯¯¯¯01 = 1.¯¯¯¯¯¯00 = 1.001

(b) For A = B = C = 1:

X = 1.¯¯¯¯¯¯11

Similarly, we find the complement of BC by replacing B = 1 and C = 1 with their complements:

X = 1.¯¯¯¯¯¯11 = 1.¯¯¯¯¯¯00 = 1.111

(c) For A = B = C = 0:

X = 0.¯¯¯¯¯¯00

Again, we find the complement of BC by replacing B = 0 and C = 0 with their complements:

X = 0.¯¯¯¯¯¯00 = 0.¯¯¯¯¯¯11 = 0.000

In conclusion, when A = 1, B = 0, and C = 1, X evaluates to 1.001. When A = B = C = 1, X evaluates to 1.111. And when A = B = C = 0, X evaluates to 0.000. The evaluation of X is based on substituting the given values into the expression A.¯¯¯¯¯¯BC and finding the complement of BC in each case.

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a) To find the mean and variance of the difference in sample means, we can use the properties of sampling distributions. The mean of the difference in sample means is equal to the difference in population means:

Mean of the difference in sample means = Mean(Jack Creek) - Mean(Cataract Creek) = 1000 - 970 = 30

The variance of the difference in sample means is calculated by summing the variances of the two samples, divided by their respective sample sizes:

Variance of the difference in sample means = (Variance(Jack Creek) / Sample Size of Jack Creek) + (Variance(Cataract Creek) / Sample Size of Cataract Creek)

Variance of Jack Creek = (standard deviation of Jack Creek)^2 = 40^2 = 1600

Variance of Cataract Creek = (standard deviation of Cataract Creek)^2 = 20^2 = 400

Sample Size of Jack Creek = 30

Sample Size of Cataract Creek = 15

Variance of the difference in sample means = (1600 / 30) + (400 / 15) = 53.33 + 26.67 = 80

Therefore, the mean of the difference in sample means is 30 and the variance of the difference in sample means is 80.

b) To find the probability that the average amount of dissolved metals at Jack Creek is at least 50 more than the average amount at Cataract Creek, we can calculate the probability using the properties of the normal distribution.

Let X be the average amount of dissolved metals at Jack Creek and Y be the average amount at Cataract Creek.

We need to find P(X - Y >= 50). This can be rephrased as P(X >= Y + 50).

Using the properties of normal distributions, we can standardize the random variables X and Y:

Z = (X - Mean(X)) / (Standard Deviation(X)) = (X - 1000) / 40

W = (Y - Mean(Y)) / (Standard Deviation(Y)) = (Y - 970) / 20

Now we can rephrase the probability in terms of Z and W:

P(X >= Y + 50) = P(Z >= (W + 50 - 1000) / 40) = P(Z >= (W - 950) / 40)

To find this probability, we can look up the corresponding value in the standard normal distribution table or use statistical software.

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From the given circle image, we can say that the two lengths that must form the ratio of 1:2 is; d. AH:HI

From the image attached, we are given that Point A is the center of the circle.

Let us access each of the options to find out which one of the two lengths must form a ratio of 1:2;

Option a. HI:EF

We see that both HI and EF are diameters of the circle. Thus, their ratio cannot be equal to 1:2.

Option b. EF:AD

We see that EF is the diameter while s the radius, we can say that;

Diameter = 2 × Radius

Thus;

EF : AD = 2:1

Option c: AD : AH

We see that both D and AH are radius and as such their ratio can never be 1:2.

Option d : AH:HI

We see that AH is the radius while HI is the diameter. Thus, their ratio will be; AH:HI = 1:2

Option e; BC:HI

We see that BC is a chord and we are not given its' length and so we can't ascertain if it forms a ratio of 1:2 with HI

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Answer:

Looks like at (3,21) the graph intersects, meaning both values are equal to one another.

Step-by-step explanation:

A o option

-(-45)

hope it helps

The value of the trigonometric identities are;

1. cos R = 15/17

cos S = 8/17

2. cos R = 12/13

cos S = 5/13

Trigonometric Identities are simply seen as the equalities involving trigonometry functions.

It also holds true for all the values of variables given in the equation.

There are various distinct trigonometric identities involving the side length as well as the angle of a triangle. They are;

We have cosine represented as;

cos θ = adjacent/hypotenuse

For the first triangle, we have;

cos R = 30/34 = 15/17

cos S = 16/34 = 8/17

For the second triangle;

cos R = 24/26 = 12/13

cos S = 10/26 = 5/13

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Step-by-step explanation:

Number of green and white jelly beans

= Number of green + Number of white

= 4 + 2 = 6.

Probability = Number of green and white jelly beans / Total number of jelly beans * 100%

= 6 / (4 + 2 + 5) * 100% = 54.55%.

The probability that you pick a green jelly bean or a white jelly bean should be 54.55%.

Since there are 4 green jelly beans, 2 white jelly beans and 5 purple jelly beans in a jar

So here the probability is

\(= 6\div (4 + 2 + 5)\)

= 54.55%

Therefore, The probability that you pick a green jelly bean or a white jelly bean should be 54.55%.

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The signed area under the curve using Left Riemann sum is 4242.083 units² and using Right Riemann sum is 4492.917 units².

The given curve is y = x + 8 and the interval [0, 50].

We need to find the signed area under the curve using Left and Right Riemann sums with 100 rectangles.

For the Left Riemann sum, we use the left endpoint of each rectangle to find the height of the rectangle, and for the Right Riemann sum, we use the right endpoint of each rectangle to find the height of the rectangle.

Using Left Riemann Sum:

Let Δx be the width of each rectangle.Δx = (50 - 0) / 100 = 0.5 units

Let xi be the left endpoint of the i-th rectangle.

i = 0 corresponds to x = 0, i = 1 corresponds to x = 0.5, i = 2 corresponds to x = 1, and so on.

Therefore, xi = i ΔxThe height of the rectangle is given by f(xi) = xi + 8

Therefore, the signed area under the curve using Left Riemann sum is:

F = Σ [f(xi) Δx] i=0 to i=100F

= Σ [(i Δx + 8) Δx] i=0 to i=100F

= Σ [i (Δx)² + 8Δx] i=0 to

i=100F = Σ (0.25i² + 4) i=0 to

i=100F = Σ (0.25i²) i=0 to

i=100 + Σ 4 i=0 to

i=100

Using the formula for sum of squares, we get:

F = 0.25 Σ i³ i=0 to i=100 + 4(101)F

= 0.25[(100/2)² (101/2)²] + 404F = 4242.083 units²

Using Right Riemann Sum: Using the same method as above,

we get the height of the rectangle as f(xi+1)

= xi+1 + 8

Therefore, the signed area under the curve using Right Riemann sum is: F = Σ [f(xi+1) Δx] i=0

to i=100F

= Σ [(i Δx + 8 + Δx) Δx] i=0

to i=100F = Σ [(i+1) (Δx)² + 8Δx] i=0 to

i=100F = Σ (0.25i² + 0.75i + 4) i=0 to i

=100F = Σ (0.25i²) i=0 to

i=100 + Σ (0.75i) i=0 to

i=100 + Σ 4 i=0 to i=100

Using the formula for sum of squares and sum of first n natural numbers, we get:

F = 0.25 Σ i³ i=0 to

i=100 + 0.75 Σ i² i=0 to

i=100 + 404F = 0.25[(100/2)² (101/2)²] + 0.75[(100)(101)(201)/6] + 404F

= 4492.917 units²

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Answer:

\(6x+20\)

Step-by-step explanation:

\(2*3x=6x\)

\(2*10=20\)

The multidimensional Taylor expansion is a mathematical tool that allows us to approximate a scalar-valued function of multiple variables (such as a loss function with multiple weights) around a specific point in parameter space.

The Taylor expansion involves the use of the gradient vector (which contains the first partial derivatives of the function evaluated at the expansion point) and the Hessian matrix (which contains all the second partial derivatives of the function evaluated at the expansion point).

By truncating the expansion after a certain number of terms, we can obtain increasingly accurate approximations of the function around the expansion point, which can be useful for optimization or other purposes.

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Answer: 12

Step-by-step explanation:

Since value of y varies directly with x, we introduce a constant, k which will give:

y = kx

If x = 4, then y = 20 we then calculate the value of k.

y = kx

20 = 4k

k = 20/4

k = 5

We then find the value of x when y = 60. This will be:

y = kx

60 = 5x

x = 60/5

x = 12

The value of x is 12 when y is 60

True. The coefficient of variation is a better measure of risk than the standard deviation if the expected returns of the securities being compared differ significantly.

The coefficient of variation (CV) is a relative measure of risk that takes into account the standard deviation and the mean of a distribution. It is a better measure of risk than the standard deviation when comparing securities with significantly different expected returns because it adjusts for the differences in the means.

The CV is calculated as the ratio of the standard deviation to the mean, and it allows for the comparison of the risk of investments with different expected returns on a standardized basis. Therefore, it is a useful tool for investors who want to compare the risk of investments that have different levels of expected returns. However, it should be noted that the CV has limitations and should not be the sole measure of risk used in investment analysis.

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