Sherri saves nickels and dimes in a coin purse for her daughter. The total value of the coins in the purse is $0.70. The number of nickels is two less than six times the number of dimes. How many nickels and how many dimes are in the coin purse?

The probability that a worker selected at random makes between $300 and $350 is 0.1359 Or 13.6%.

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.

Given, Weekly wages at a certain factory are normally distributed.

Mean(\(\overline{x}\)) = 400, S.D(\(\sigma\)) = 50.

Now, Since the wages are normally distributed we know,

\(z = \frac{x - \overline{x}}{\sigma}\).

Therefore,

z = (300 - 400)/50.

z = - 2.

And

z = (350 - 400)/2.

z = - 1.

Now, from the z-table,

P(z ≤ - 2) = 0.0228 and P(z ≤ - 1) = 0.1587.

Combining the two we have P( - 2 ≤ z ≤ - 1) =  0.1587 - 0.0228.

P( - 2 ≤ z ≤ - 1) = 0.1359.

As a result, the likelihood that a randomly chosen employee will earn between $300 and $350 is 0.1359, or 13.6%.

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It is not possible to find a combination using addition and multiplication of the given single-digit numbers that totals exactly 100 while keeping the same order.

To combine the single-digit numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 using only addition and multiplication so that they total 100 while keeping the same order, we can form the following expression:

1 + 2 + 3 + 4 + 5 + 6 + 78 + 9

In this expression, we group the numbers 7 and 8 together to form 78. Then, we add all the other numbers from 1 to 6 and the number 9. Adding them up, we get:

1 + 2 + 3 + 4 + 5 + 6 + 78 + 9 = 108

Unfortunately, the sum obtained from this expression is 108, not 100 as required.

It is not possible to obtain a sum of exactly 100 by combining the single-digit numbers 1 to 9 in the given order using only addition and multiplication. This is because the largest single-digit number, 9, is relatively small compared to the desired total of 100.

Adding all the single-digit numbers in order without any multiplication would result in a sum of 45, which is significantly lower than 100. Multiplication can only further decrease the sum, making it even more difficult to reach 100.

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The probability of winning this game is 0.003

Let us name p to be the probability of winning the game.

We have the expected value to be 100

100 = probability of winning + 1-p x loss

win = 100000 - 200

We then input in the formula

100 = p*99800 +(1-p) x -200

100 = 99800p - 200 + 200p

Collect like terms

100 + 200 = 99800 + 200p

300 = 100000p

Divide through by 100000

This give the

Probability of winning =  0.003

The probability of winning the game is very low hence I would not play.

The factors that would influence the decision are:

A game has an expected value to you of ?$100. It costs ?$200 to? play, but if you win you receive? $100,000 (including your ?$200 ?bet), for a net gain of ?$99,800. What is the probability of? winning

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The dimensions we will tell the shop to use are ⇒ Volume =  10 x 10 x 5 foot

The surface area of the box = \(225\) \(ft^{2}\)

Weight of the metal = 1125 kg

According to the question,

Given value = \(500\) \(ft^{3}\) tanks is to be built which has to be a square-based rectangle steel holding tank.

For this, we have to know the total surface area of the box,

Surface area (A) = 4 x sides of the rectangle + square base -- equation 1

Let's take the width of the square base = p

And let height = h

Since we know that,

Rectangle sides = p x h

Square base ⇒ p x p = \(p^{2}\)

Substituting these values in equation 1,

Surface area ( A ) = 4 x ( p x h ) + \(p^{2}\) ---- equation 2

The formula for calculating the volume of the box,

V = p x p x h

V = \(p^{2}\) x h --- equation 3

Referring to the question that the value of the volume is already given such that volume = \(500\) \(ft^{3}\)

So, V = \(500\) \(ft^{3}\)

Putting the value of V in equation 3,

500 = \(p^{2}\) x h

h = \(\frac{500}{p^{2} }\) ---- equation 4

Substituting the value of h from equation 4 to equation 2,

A = 4 x ( p x \(\frac{500}{p^{2} }\) ) + \(p^{2}\)

⇒ A = \(\frac{2000}{P}\) + \(p^{2}\)

We will be taking the derivative of the above equation,

⇒ A' = - \(\frac{2000}{p^{2} }\) + 2p

Now we will be minimizing A,

⇒ 0 = - \(\frac{2000}{p^{2} }\) + 2\(p\)

⇒ \(\frac{2000}{p^{2} }\) = 2\(p\)

⇒ 2000 = 2\(p^{3}\)

⇒ 1000 = \(p^{3}\)

⇒ p = \(\sqrt[3]{1000}\)

⇒ p = 10 foot

Substituting the value of p in equation 4,

⇒ h = \(\frac{500}{10^{2} }\)

⇒ h = \(\frac{500}{100}\)

⇒ h = 5 foot

Substituting values in the area of the square box,

A = 4 x (10 x 5) + \(5^{2}\)

A = 200 + 25

A = 225 \(ft^{2}\)

The weight of the metal,

⇒ weight = A x weight per square foot

⇒ weight = 225 x 5

⇒ weight = 1125 kg

Therefore, The dimensions we will tell the shop to use are ⇒ Volume =  10 x 10 x 5 feet

The surface area of the box = 225 \(ft^{2}\)

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Take into account that for horizontal lines, the equation of the graph has the general form y = c, where c is the value of y where x = 0, or the y-intercept.

As you can notice in the given line and based on the previous description, you have:

y = 1

1 foot = 12 inches = 1/12

21/1 x 1/12 = 21/12 = 1.75 feet

Answer: 1.75 feet

Answer: A

Step-by-step explanation:

-5+-5+-5+-5=-20

-4+-4+-4+-4=-16

5+5+5+5+5=25

4+4+4+4+4=20

The questions asks for -5 x 4 = -20

The area of the square is 1084 square inches.

The area of a square can be calculated as the square of the sides of a given figure. A square is always a rectangle, parallelogram, a rhombus and a quadrilateral but its reverse statement may or may not be true.(ie it is not always necessary that a rectangle is a square or a parallelogram is a square or a rhombus is a square).

The area of a square = side x side

Given;

One side of square= 33inches

Area of square= A^2

=33x33

=1089

Therefore, the area will be 1089m^2

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The answer is:

g(x + 1) = 6x + 1

g(4x) = 24x -5

Work/explanation:

To evaluate, I plug in x + 1 into the function:

\(\sf{g(x)=6x-5}\)

\(\sf{g(x+1)=6(x+1)-5}\)

Simplify

\(\sf{g(x+1)=6x+6-5}\)

\(\sf{g(x+1)=6x+1}\)

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

Do the same thing with g(4x)

\(\sf{g(4x)=6(4x)-5}\)

\(\sf{g(4x)=24x-5}\)

Hence, these are the answers.

Answer:

x+5

Step-by-step explanation:

Answer:

The first is 18.

The second is less than (<).

Step-by-step explanation:

Hope this helps <3

Answer:

1. 18

2. C

Step-by-step explanation:

1. 7/42=1/6 3•6=18

2. 3/7 is greater than 3/8

The dimensions of the rectangular garden to maximize the area is length = width = 75 meters.

Let l be the length and w be the width of the rectangular garden.

We need to find the dimensions of the rectangular garden of greatest area that can be fenced off (all four sides) with 300 meters of fencing.

The perimeter of the  rectangular garden = 300 meters

We know that the perimeter of the rectangle =2(length + width)

300 = 2(l + w)

l + w = 150               .......(1)

Now, the maximum area of a  rectangular garden is when Length  = width

So, for equation 1

l + l = 150

l = 75 meters

So, w = 75 meters

And the area of the rectangular garden = length * width

                                                               = 75 * 75

                                                               = 5625 m²

So the maximum area of the  rectangular garden is 5625 m²

Therefore, the dimensions of the garden to maximize the area is length = width = 75 meters and maximum area is  5625 m²

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Answer:

b . all of the other ones look the same and that one is the different one

Answer:

B

Step-by-step explanation:

A proportional relationship graph should be a straight line, no curves.

The list of elements in the sets are as follows:

A.  A ∩ B = {2, 9}

B. B ∩ C = {2, 3}

C. A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}

D. B ∪ C = {2, 3, 5, 7, 9, 10}

Set are defined as the collection of objects whose elements are fixed and can not be changed.

Therefore,

universal set = U = {1,2,3, 4, 5, 6, 7, 8, 9, 10​}

A = {1, 2, 7, 8, 9}

B = {2, 3, 5, 9}

C = {2, 3, 7, 10}

Therefore,

A.

A ∩ B = {2, 9}

B.

B ∩ C = {2, 3}

C.

A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}

D.

B ∪ C = {2, 3, 5, 7, 9, 10}

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Hello there!

Answer:

16

Step-by-step explanation:

\( |x| = x \: \: \: if \: \: x \: \geqslant 0 \\ |x| = - x \: \: \: if \: \: \: x \: \leqslant 0\)

-12 < 0 so |-12| = -(-12) = 12

4 > 0 so |4| = 4

|-12| + |4| = 12 + 4 = 16

Answer:

16

Step-by-step explanation:

Hello! This question is looking for the absolute value of integers. The absolute value is the distance the number has from zero. For example, -12 as twelve numbers away from zero, twelve away in the negative direction. The absolute value of -12, then, is just twelve. An easy way to remember this is to take away the negative sign when taking the absolute value, since an absolute value can never be negative. The absolute value sign is represented by a squarish bracket [ and ].

This question says to find the absolute value of each integer and then add the two. First we have [-12]. This is 12 away from zero, and we can take away the - sign from the asked integer and we get 12.

The second integer given is 4, and when we take the absolute value of 4, [+4], we get positive four. This is because four is four spaces away from zero on the number line.

Thus, we have +12 and +4 as are values to add since they are the absolute values and we can form this equation

12+4=16

Thus, the answer is 16.

Hope this helps! Remember the hint, when something has brackets like that or asks for the absolute value, take away a negative sign and make it positive! Have a great day!

Answer:

r = 1

Step-by-step explanation:

Use the distributive property to multiply −6 by −3+5r.

18−30r=−5−7r

Add 7r to both sides.

18−30r+7r=−5

Add −30r and 7r to get −23r.

18−23r=−5

Subtract 18 from both sides.

−23r=−5−18

Subtract 18 from −5 to get −23.

−23r=−23

Divide both sides by −23.

r=−23/−23​

Divide −23 by −23 to get 1.

r=1

Answer: \(f^{-1} (x) = \sqrt{x} +1\)

Step-by-step explanation:

\(y = x^2 - 2x + 1\)

We know straight away the inverse will be a square root function. We also know that this inverse will have a restriction on the domain, (because you can only take the square root of a positive number).

So, to find the inverse, first we'll switch the x and y and solve for y:

\(x = y^2 - 2y +1\)

\(x = (y-1)^2\), (factor!)

±\(\sqrt{x} = y - 1\)

So, the inverse "function" is:

\(f^-1(x)\) = ±\(\sqrt{x} +1\)

But theres an issue here!

If we tried graphing this, this "function" would not pass the vertical line test, so its not really a function at all!

We need to restrict the domain to only include the values that are above the x axis.

So our final inverse function is:

\(f^{-1} (x) = \sqrt{x} +1\)

The equations of the three altitudes of triangle ABC include the following:

A triangle can be defined as a two-dimensional geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.

A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.

Mathematically, the slope of a straight line can be calculated by using this formula;

\(Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}\)

Also, the point-slope form of a straight line is given by this equation:

y - y₁ = m(x - x₁)

Assuming the following parameters for triangle ABC:

For the equation of altitude AM, we have:

Slope of BC = (2 - 8)/(4 - 0)

Slope of BC = -6/4

Slope of BC = -3/2

Slope of AM = -1/slope of BC

Slope of AM = -1/(-3/2)

Slope of AM = 2/3.

The equation of altitude AM is given by:

y - y₁ = m(x - x₁)

y - 0 = 2/3(x - (-2))

3y = 2(x + 2)

3y = 2x + 4

3y - 2y - 4 = 0.

For the equation of altitude BN, we have:

Slope of CA = (2 - 0)/(4 - (-2))

Slope of CA = 2/6

Slope of CA = 1/3

Slope of BN = -1/slope of CA

Slope of BN = -1/(1/3)

Slope of BN = -3.

The equation of altitude BN is given by:

y - y₁ = m(x - x₁)

y - 8 = -3(x - 0)

y - 8 = -3x

y + 3x - 8 = 0.

For the equation of altitude CL, we have:

Slope of AB = (8 - 0)/(0 - (-2))

Slope of AB = 8/2

Slope of AB = 4

Slope of CL = -1/slope of AB

Slope of CL = -1/4

The equation of altitude CL is given by:

y - y₁ = m(x - x₁)

y - 2 = -1/4(x - 4)

4y - 2= -(x - 4)

4y - 2= -x + 4

4y + x - 2 - 4 = 0.

4y + x - 6 = 0.

In conclusion, we can infer and logically deduce that the equations of the three altitudes of triangle ABC include the following:

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Answer:

B and E

Step-by-step explanation:

the graph (Justine) shows the line

y = 2x

the line for Velma is

y = 4x

now we need to remember that the slope (inclination) of a line is the factor of x (so, 2 and 4 in the two line equations).

a slope is expressed as y/x and indicates how many units y changes when x changes a certain amount of units (like 1).

as described (and also confirmed by the graph) the x units are minutes, and the y units are meters.

so, as per her slope, Velma moves 4 meters in 1 minute.

and Justine moves 2 meters in 1 meter.

so, Justine is half as fast as Velma.

and therefore, Justine moves a shorter distance than Velma each minute.

Answer:

Step-by-step explanation:

B and E

Answer:

$350

Step-by-step explanation:

Let the bench cost $x

Then the garden table costs $x - 43

x + (x - 43) = 657

2x =  657 + 43

2x = 700

x = 350

The cost of the bench is $350.

Nice day to you!

The  examples of electrophilic substitution reactions are:

An atom that is connected to an aromatic ring is replaced with an electrophile in electrophilic aromatic substitution processes.

An electrophilic substitution reaction  can be seen as the chemical process in which an electrophile replaces the functional group belonging to a molecule. which can be regraded as the  atom of hydrogen which makes up the displace functional group.

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complete question;

What are electrophillic substitution reaction?

A.Halogenation

B.Redox reaction

C. Nitration.

D. Sulphonation.

The limit of [f(x) - f(2)]/[x - 2] as x approaches 2 is 20

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

f(x) = 5(x2 – 1)

Rewrite as

f(x) = 5(x² – 1)

The limit is given as

[f(x) - f(2)]/[x - 2]

Calculate f(2)

So, we have

f(2) = 5(2² – 1)

Evaluate

f(2) = 15

Substitute f(2) = 15 in [f(x) - f(2)]/[x - 2]

So, we have

[f(x) - f(2)]/[x - 2] = [5(x² – 1) - 15]/[x - 2]

Open the brackets

[f(x) - f(2)]/[x - 2] = [5x² – 5 - 15]/[x - 2]

Evaluate the like terms

[f(x) - f(2)]/[x - 2] = [5x² – 20]/[x - 2]

Factorize

[f(x) - f(2)]/[x - 2] = [5(x² – 4)]/[x - 2]

Express as difference of two squares

[f(x) - f(2)]/[x - 2] = [5(x – 2)(x + 2)]/[x - 2]

Divide

[f(x) - f(2)]/[x - 2] = 5(x + 2)

Limit x to 2

[f(x) - f(2)]/[x - 2] = 5(2 + 2)

Evaluate

[f(x) - f(2)]/[x - 2] = 20

Hence, the limit is 20

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Answer: 16.7%

Step-by-step explanation:

x/(root y) =x

root y is increased by 44%

x/(44+root y)=16.7%

The distance between two points in three-dimensional space is a measure of the separation between the two points. In this case, the two points are the center of a sphere and a point that the sphere passes through.

To find the distance, we can use the distance formula in three dimensions, which is an extension of the distance formula in two dimensions. The distance formula is:

d = √((x1 - x2)^2 + (y1 - y2)^2 + (z1 - z2)^2)

where (x1, y1, z1) is the center of the sphere and (x2, y2, z2) is the point that the sphere passes through. The square root of the sum of the squares of the differences between the corresponding coordinates gives the distance between the two points.

In this problem, the center of the sphere is not given, so it is not possible to calculate the distance between the sphere and the point. The center of the sphere is a crucial piece of information needed to solve this problem.

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Answer:

16

Step-by-step explanation:

3^x +1 = f(X)

2x-4 = g(x)

find f(2)-g(-1)

we substitute in function f(X) by value (2), and in function g(X) by value (-1)

1. 3^x +1 becomes 3^2+1 =9+1=10

2. 2(-1)-4= -2-4=-6

then f(2)-g(-1)

= 10-(-6) =10+6=16

Answer: An implicit function is a function, written in terms of both dependent and independent variables, like y-3x2+2x+5 = 0. Whereas an explicit function is a function which is represented in terms of an independent variable.

Step-by-step explanation: To find the implicit derivative,

Differentiate both sides of f(x, y) = 0 with respect to x.

Apply usual derivative formulas to differentiate the x terms.

Apply usual derivative formulas to differentiate the y terms along with multiplying the derivative by dy/dx.

Solve the resultant equation for dy/dx (by isolating dy/dx).