What is the equation of the line that passes through the point (8,6)
and has a slope of frac{1}{4}

In a family with five girls and the probability of a boy being born is 1/2, the probability of the next child being a boy is still 1/2.

The previous births do not affect the probability of the next birth since each birth is an independent event.

The probability of an event occurring is determined by the ratio of the number of favorable outcomes to the total number of possible outcomes. In this case, the event of interest is the birth of a boy.

Since each birth is an independent event, the probability of having a boy on any given birth is always 1/2, regardless of the previous children born.

In the given scenario, the family already has five girls. This information is not relevant to the probability of the next child being a boy. The gender of the previous children does not affect the probability of the next child being a boy or a girl.

Therefore, the probability of the next child being a boy remains 1/2, as it is for any independent birth event.

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Answer:

x = \(\frac{3}{4}\)

Step-by-step explanation:

Given

\(\frac{3}{4(x+2)}\) = \(\frac{x}{x+2}\)

multiply numerator/ denominator of \(\frac{x}{x+2}\) by 4, thus

\(\frac{3}{4(x+2)}\) = \(\frac{4x}{4(x+2)}\)

Since the denominators are common , equate the numerators, that is

4x = 3 ( divide both sides by 4 )

x = \(\frac{3}{4}\)

Answer:

Length = 16 yds

Width = 13 yds

Step-by-step explanation:

P = 2w + 2l

l = w + 3

58 = (2w + 2(w + 3))

58 = 4w + 6

52 = 4w

w = 13

L = w + 3

= 13 + 3

= 16

The length and width of the rectangle are 16,13yd.

The Length and Width of the rectangle can be found as:

The length of the rectangle is 3yds longer than the width which means length = w+3

and the perimeter is given by 58yd

Let W be the width and L be the length

We know that the perimeter of a rectangle is 2(L+w)

The perimeter of a rectangle is defined as the sum of all the sides of a rectangle

2(w+w+3)=58

2(2w+3)=58

2w=29-3

w=13

then the length of the rectangle will be w+3

                                                              13+3 = 16

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Standard Deviation statistic of the sampling distribution is used in calculating the margin of error for a confidence interval of the population mean.

Basically, the margin of error is stated as follows:

Error margin, E = Z* (Standard deviation)

Therefore, the calculation of the margin of error does not employ the mean at all.

The margin of error is computed using the standard deviation.

The term "standard deviation" reveals that a measurement of the data's dispersion from the mean. While a high standard deviation indicates that the data are more spread or dispersed, a low standard deviation suggests that the data are clustered or gathered around the mean.

It depicts the average deviation of each score from the mean. A high standard deviation in a normal distribution denotes that values are often far from the mean, while a low standard deviation denotes that values are grouped together around the mean.

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The no-arbitrage price today of a 5-year $1,000 US Treasury note with a 2% coupon rate and a 4.25% yield to maturity is approximately $908.44, closest to option B: $900.53.

To determine the no-arbitrage price of a 5-year $1,000 US Treasury note with a coupon rate of 2% and a yield to maturity (YTM) of 4.25%, we can use the present value of the future cash flows.First, let's calculate the annual coupon payment. The coupon rate is 2% of the face value, so the coupon payment is ($1,000 * 2%) = $20 per year.The yield to maturity of 4.25% is the discount rate we'll use to calculate the present value of the cash flows. Since the coupon payments occur annually, we need to discount them at this rate for five years.

Using the present value formula for an annuity, we can calculate the present value of the coupon payments:PV = C * (1 - (1 + r)^-n) / r,

where PV is the present value, C is the coupon payment, r is the discount rate, and n is the number of periods.

Plugging in the values:PV = $20 * (1 - (1 + 0.0425)^-5) / 0.0425 = $85.6427.

Next, we need to calculate the present value of the face value ($1,000) at the end of 5 years:PV = $1,000 / (1 + 0.0425)^5 = $822.7967.

Finally, we sum up the present values of the coupon payments and the face value:No-arbitrage price = $85.6427 + $822.7967 = $908.4394.

Rounding to the penny, the no-arbitrage price is $908.44, which is closest to option B: $900.53.

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To find the price at which the designer will sell the maximum number of shirts, we need to determine the vertex of the quadratic function representing the number of shirts sold.

The equation for the number of shirts sold is given by:

S = -4x^2 + 80x - 76

This is a quadratic function in the form of:

S = ax^2 + bx + c

To find the price at which the maximum number of shirts is sold, we need to locate the vertex of the quadratic function. The x-coordinate of the vertex can be found using the formula:

x = -b / (2a)

In this case, a = -4 and b = 80. Plugging in these values, we can calculate the x-coordinate:

x = -80 / (2*(-4))

x = -80 / (-8)

x = 10

Therefore, the designer will sell the maximum number of shirts at a price of $10. Hence, the correct option is c) $10.

Answer:

22

Step-by-step explanation:

f(2) : 2*2 = 4 ,  4+4 = 8

f(5) ; 2*5 = 10 ; 10+4 = 14

8+14 = 22

Answer:

f(2) = 8, f(5) = 14.

Step-by-step explanation:

in f(2), 2 will replace x. in f(5),  5 will replace x.

f(2)= 2(2) + 4.

f(2)= 4 + 4.

f(2)= 8

f(5)= 2(5) + 4

f(5)= 10+ 4

f(5)= 14

Answer:15.32258064516

Step-by-step explanation:

15.32258064516

Answer:

I think it is 636 pounds

Step-by-step explanation:

if I'm right plz give me brainliest

Time taken by Matilda on each project is \(5\frac{7}{12}\) hours.

According to the question we have been given that,

Total time taken by Matilda to complete the consulting projects = \(16\frac{3}{4}\) hours

First we will convert it into simple fraction which is

         \(16\frac{3}{4} = \frac{67}{4} \\\) hours

Number of consulting projects = 3

And Matilda spends same amount of time to each of the project.

To find the time she spend on each project is by using unitary method

that is,            3 projects = \(\frac{67}{4}\) hours

                      1 project = \(\frac{67}{4} / 3\)

                                     = 67/12

                                     = \(5\frac{7}{12}\) hours

Hence time taken by Matilda on each project is \(5\frac{7}{12}\) hours.

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Here, to find the minimum radius of convergence R of power series solutions about the ordinary point x = 0 and x = 1, for the differential equation (x^2 - 2x + 10)y" + xy' - 4y = 0, we can use the formula R = 1/limsup |an|^1/n.

Step:1 At x = 0, the power series solution is y = c_0 + c_1x + c_2x^2 + c_3x^3 + ... + c_nx^n + ... , and the coefficients an are given by c_n = (-1)^(n-1)*(n-1)!/[(x^2-2x+10)n!]. Thus, the minimum radius of convergence R at x = 0 is R = 1/limsup |c_n|^1/n.
Step:2 Similarly, at x = 1, the power series solution is y = c_0 + c_1(x-1) + c_2(x-1)^2 + c_3(x-1)^3 + ... + c_n(x-1)^n + ..., and the coefficients an are given by c_n = (-1)^(n-1)*(n-1)!/[((x-1)^2-2(x-1)+10)n!]. Thus, the minimum radius of convergence R at x = 1 is R = 1/limsup |c_n|^1/n.

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Answer:

X,y=83/52 ,45/26

Step-by-step explanation:

just  look up your answer and you will find the step by step. Hopefully this helped :)

24 weeks of data must be randomly sampled to estimate the mean weekly sales.

The data is ∝=0.10

\(\sigma=\$ 1200, E=\$ 400$\)

The margin of error is given by this formula:

\($$M E=z_{\alpha / 2} \frac{\sigma}{\sqrt{n}}$$\)

And on this case we have that ME =400 and we are interested in order to find the value of n, if we solve n from equation.

\($$\begin{aligned}n & =\left(z_\alpha\right)^2 \times\left(\frac{\sigma}{E}\right)^2 . \\& =(1.645)^2 \times\left(\frac{1200}{400}\right)^2 \\& =2.706025 \times \frac{1440000}{160000} \\& =24.354225 \approx 24 \\n & =24 \\\end{aligned}$$\)

There are 24 weeks of data must be randomly sampled to estimate the mean weekly sales of a new line of athletic footwear.

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There are 3 cups of ketchup for every 1/2 cup of mustard, then the rate in cups of ketchup per cup of mustard is:

3÷1/2 = 3*2 = 6 cups of ketchup per cup of mustard

The process involves finding the complementary solution x_c(t) by solving the homogeneous equation, determining the particular solution x_p(t) using the method of variation of parameters, and combining them to obtain the general solution x(t).

1. The method of variation of parameters can be used to solve the initial value problem x' = axf(t), x(a) = xa, where a and f(t) are given functions. In this case, we have the values a = 4 - 2t and f(t) = 16t^2. We need to find the solution x(t) using the initial condition x(0) = 2.

2. To solve the initial value problem using the method of variation of parameters, we first find the complementary solution x_c(t) by solving the homogeneous equation x' = ax.

3. For the given a = 4 - 2t, the homogeneous equation becomes x' = (4 - 2t)x. By separation of variables and integration, we find the complementary solution x_c(t) = Ce^(2t - t^2).

4. Next, we find the particular solution x_p(t) by assuming a particular solution of the form x_p(t) = u(t)e^(2t - t^2), where u(t) is a function to be determined.

5. Differentiating x_p(t) and substituting it into the original differential equation, we can solve for u'(t) and determine the form of u(t). After finding u(t), we substitute it back into x_p(t).

6. Finally, the general solution is given by x(t) = x_c(t) + x_p(t). By substituting the values and integrating, we can obtain the specific solution x(t) for the given initial condition.

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The function rule that could be represented by the graph is given as follows:

y = 2x³ + x - 3.

The first step in defining the function is looking at it's y-intercept, which is the value of y when the graph of the function crosses the y-axis.

This value is of -3, hence the function can be defined as follows:

f(x) = ax^n + x - 3.

Then we look at the behavior of the function. It has an inflection point, as it is concave down and then it becomes concave up, hence:

Thus:

f(x) = ax³ + x - 3.

Then we look at the x-intercept, meaning that when x = 1, y = 0, this the leading coefficient is obtained as follows:

0 = a + 1 - 3

a = 2.

Thus the function is defined as follows:

y = 2x³ + x - 3.

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Answer:

13x + 5= -12

hope this helps :)

Answer:

So, first you need to set up a proportion and cross multiply. This allows you to  get an equation which you can solve for x.

Step-by-step explanation:

\(\frac{4}{5}\) × \(\frac{17}{x}\)  

Cross multiply to get 4x = 85

Next, isolate the x variable by dividing the 4 on both sides. This leaves you with x = 21.25.

Answer: x = 21.25

A: √50x^2 and d: √72x^2 are like radicals.

Like radicals are square roots with the same coefficient outside the radical. For example, √50x^2 and √72x^2 can be simplified to √2 * √25x^2, which makes them like radicals. Simplifying the expressions helps to see if they are alike.

Expressions such as √32x and √18n cannot be simplified to have the same coefficient outside the radical and hence, they are not like radicals.

In conclusion, only √50x^2 and √72x^2 are like radicals after simplification.

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Answer:

A&D

Step-by-step explanation:

Got it right on edge

Probability that the person selected at random from the sport centre of 125 people is a fraction of 1/4 or 0.25.

The probability of an event is the fraction of the required number of outcome divided by the number of possible outcomes.

We shall determine the answer to the question as follows;

People in the sport centre = 125

People who used the 3 facilities = 6

People who accessed only gym = 59 - (6 + 11 + 19) = 26

People who accessed only track event = 55 - (6 + 11 + 24) = 14

People who accessed only swimming pool event = 70 - (6 + 19 + 24) = 21

People who accessed only gym and swimming pool events = 29 - 6 = 19

People who accessed only gym and track events = 17 - 6 = 11

People who accessed only swimming pool and track events = 30 - 6 = 24

Total number of people who accessed at least any one of the facilities = 121

The number of people who did not access any of the facility = 125 - 121 = 4, which is the number of possible outcomes for our required outcome.

Therefore, the probability that the person selected doesn't use any facility = 1/4

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Step-by-step explanation:

\( \frac{45}{40} = \frac{9}{x} \\ = > \frac{40}{45} = \frac{x}{9} \\ = > x = \frac{40}{45} \times 9 \\ = > x = \frac{40}{5} \\ = > x = 8\)

x = 8

Answer:

it's D

Step-by-step explanation:

D is the angle (answer)

Answer:

The symbol ≅ means congruent or approximately equal to. In this case, since we are referring to m∠1 and m∠5, we can decide that this sign means congruent/equal to each other.

Step-by-step explanation:

(4y-6) and 14 are vertical angles this they are equal

\(4y - 6 = 14\)

\(4y = 20\)

\(y = 5\)

Likewise, 5x-5 and 3x+17 are equal

\(5x - 5 = 3x + 17\)

\(2x = 22\)

\(x = 11\)

Please note that the degree measure is not 11 itself, that the value of the x variable,

In fact, if you plug in 11 for x.

The value of the variable will be

50 degrees

Answer:

376 units and 1,857 units

Step-by-step explanation:

The computation is shown below:

The number of units that company sells to break even is

Let us assume the number of units be x

$16,000  + $8.20x  = $50.75x

$16,000 = $50.75x - $8.20x

$16,000 = $42.55

x = $16,000 ÷ $42.55

= 376 units

Now in order to make the profit the number of units sold is

$50.65x - ($16,000 + $8.20x) = $95,000

$50.65x - $16,000 - $8.20x = $95,000

$42.55x = $95,000 - $16,000

$42.55x = $79,000

x = $79,000 ÷ $42.55

= 1,857 units

∠A = ∠C for every isosceles triangle and not only for this specific isosceles triangle.

We are given that:

AB = BC

Now, draw a angle bisector from point B to the line AC in a way that it intersects AC at D.

Now, we get that:

∠ABD = ∠CBD ( BD is the angle bisector)

BD = BD ( common line)

So, ΔABD ≅ Δ CBD ( SAS property)

So,

∠A = ∠ C ( CPCT rule)

Also, it will be true for every isosceles triangle.

Therefore, we get that, ∠A = ∠C for every isosceles triangle and not only for this specific isosceles triangle.

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Your question was incomplete. Please refer the content below:

There is an isosceles triangle with AB = BC. Prove that ∠A = ∠C.

Did we prove the conclusion true for every isosceles triangle or only for this specific isosceles triangle.

Without knowledge of all sides and angles, it is still possible to confirm that two triangles are comparable.

Given:

PQ/XY = QR/YZ and ∠Q ≅ ∠Y

To prove that, △PQR is similar to △XYZ.

Proof: Assume PQ > XY

Draw MN parallel to BC, we find that MQN similar to XYZ

QM/QP = QN/QR --- (1)[using the basic proportionality theorem]

Now △MQN and △XYZ are congruent thus, XY/QP = YZ/QR --- (2)

Since QM = XY from (1) and (2),

XY/QP = QM/QP = QN/QR = YZ/QR

Thus, QN = YZ by SAS congruence criterion.

△MQN ≅ △XYZ

But △MQN congruent to △XYZ,

Thus, △PQR is similar to △XYZ.

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The correct graph which represents the equation y = 1/2x - 1 is,

⇒ Graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The equation is,

⇒ y = 1/2x - 1

Now, After draw the equation we get;

Graph of a line passing through the points (-2, - 2) and (0, - 1).

Thus, The correct statement is,

⇒ Graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1.

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