Choose the system of inequalities whose solution is represented by the graph.

Answer: 2.632

Step-by-step explanation:

Given : The probability that the population has a particular genetic mutation = 1 % = 0.01

Let X be a random variable representing the number of people with genetic mutation in a group of 700 people.

Now, X follows the binomial distribution with parameters:

[tex]n=700;\ p=0.01[/tex]

The standard deviation for binomial distribution is given by :-

[tex]\sigma=\sqrt{np(1-p)}\\\\=\sqrt{700\times0.01(1-0.01)}\\\\=2.6324893162\approx2.632[/tex]

Hence, the standard deviation = 2.632

Answer: 8359

Step-by-step explanation:

The formula for sample size needed for interval estimate of population proportion :-

[tex]n=p(1-p)(\frac{z_{\alpha/2}}{E})^2[/tex]

Given : The significance level : [tex]\alpha=1-0.95=0.05[/tex]

Critical value : [tex]z_{\alpha/2}}=z_{0.025}=\pm1.96[/tex]

Previous estimate of proportion : [tex]p=0.32[/tex]

Margin of error : [tex]E=0.01[/tex]

Now, the required sample size will be :-

[tex]n=0.32(1-0.32)(\frac{1.96}{0.01})^2=8359.3216\approx8359[/tex]

Hence, the required sample size = 8359

To estimate the proportion of adults with high-speed Internet access with a 95% confidence level and a margin of error of 0.01, a sample size of 752 should be obtained.

To estimate the proportion of adults who have high-speed Internet access with a 95% confidence level and a margin of error of 0.01, we can use the formula:

Sample Size = (Z^2 * p * (1-p)) / (E^2)

Where Z is the Z-score corresponding to the desired confidence level, p is the estimated proportion from a previous study, and E is the desired margin of error.

With a previous estimate of 0.32, a confidence level of 95% (corresponding Z-score of 1.96), and a margin of error of 0.01, the sample size required would be:

(1.96^2 * 0.32 * (1-0.32)) / (0.01^2) = 752

A sample size of 752 should be obtained to achieve the desired confidence level.

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Answer:

Option A) (-14, -4)

Step-by-step explanation:

we know that

If a ordered pair lie on the circumference of a circle , then the ordered pair must satisfy the equation of the circle

we have

[tex](x+10)^{2}+(y+1)^{2}=25[/tex]

Verify each ordered pair

case A) we have  (-14, -4)

substitute the value of x and the value of y in the equation and then compare the results

[tex](-14+10)^{2}+(-4+1)^{2}=25[/tex]

[tex](-4)^{2}+(-3)^{2}=25[/tex]

[tex]25=25[/tex] ----> is true

therefore

The ordered pair is on the circumference of the circle

case B) we have  (4,14)

substitute the value of x and the value of y in the equation and then compare the results

[tex](4+10)^{2}+(14+1)^{2}=25[/tex]

[tex](14)^{2}+(15)^{2}=25[/tex]

[tex]421=25[/tex] ----> is not true

therefore

The ordered pair is not on the circumference of the circle

case C) we have  (-14,4)

substitute the value of x and the value of y in the equation and then compare the results

[tex](-14+10)^{2}+(4+1)^{2}=25[/tex]

[tex](-4)^{2}+(5)^{2}=25[/tex]

[tex]41=25[/tex] ----> is not true

therefore

The ordered pair is not on the circumference of the circle

case D) we have  (-4,14)

substitute the value of x and the value of y in the equation and then compare the results

[tex](-4+10)^{2}+(14+1)^{2}=25[/tex]

[tex](6)^{2}+(15)^{2}=25[/tex]

[tex]261=25[/tex] ----> is not true

therefore

The ordered pair is not on the circumference of the circle

Answer:

3.9 mi/h

Step-by-step explanation:

If the boy is rowing perpendicular to the current, the two vectors form a right triangle.

AB represents the downstream current, BC is the speed across the river, and AC is the ground speed of the boat

AC^2 = 2.4^2 + 3.1^2 =5.76 + 9.61 = 15.37

AC = sqrt(15.37) = 3.9 mi/h

The boat's speed over the ground is 3.9 mi/h.

The ground speed is found to be approximately 3.92 miles per hour.

we use the Pythagorean theorem to solve this problem.

Step-by-step solution:

This demonstrates how mathematical principles can be applied to real-world scenarios, such as navigating a boat across a river with a current.

Answer:

The average price of a gallon of orange increased by $0.03 each month.

Step-by-step explanation:

It is 11 months between October 2013 and September 2014 so the price after 11 months =

f(11) = 6.12 + 0.03(11)

= 6.12 + 0.33

= $6.45.

This is an increase of 0.33 / 11 = 0.03 / month.

Answer:

  Both A and B . . . . . and 2 more answers

Step-by-step explanation:

Completing the square, you get

  tan²(x) -tan(x) +0.25 = 2.25 . . . . . add 0.25

  (tan(x) -0.5)² = 1.5²

  tan(x) = 0.5 ± 1.5 = {-1, 2}

For tan(x) = -1, the solutions are ...

  x = arctan(-1) = 135°, 315°

For x = 2, the solutions are ...

  x = arctan(2) ≈ 63.435°, 243.435°

Answer:

Cos function should be used for the determination of the length of the hypotenuse.

Answer:

  B)  108π cm^2

Step-by-step explanation:

We assume the circumference measurement is the same as it would have been before the fruit was cut. In that case, the radius is found from ...

  C = 2πr . . . . . . . . . formula relating circumference and radius

  12π cm = 2πr . . . . substitute given information

  6 cm = r . . . . . . divide by 2π

The surface area of a hemisphere is 3 times the area of the circular face:

  S = 3πr^2

  S = 3π(6 cm)^2 = 108π cm^2

The surface area of the grapefruit half is 108π cm^2.

Answer:

B) 108π cm2

Step-by-step explanation:

If a grapefruit is approximately spherical and Jane cuts the grapefruit in half and determines that the circumference of the resulting hemisphere is 12π centimeters, the surface area of one-half of the cut grapefruit is 108π cm2.

Formula: 2πr

S = 3π(6 cm)^2

Answer:

20,000 ft

Step-by-step explanation:

This is a linear equation.  The negative sign in front of the 1100 indicates that the line is going from upper left to lower right, the path a plane would definitely travel when it is landing.  The 1100 is the speed at which the plane is traveling down.

The standard form of a linear equation is y = mx + b where m is the rate of change (which is the same as the slope), and b is the y-intercept, which is found by replacing x with 0 and solving for y.  This is also known as the "starting point" for a linear situation.  Since the t in our equation represents the time that has gone by since the plane started its descent in hours, if we replace x with 0, we are effectively saying that NO time has gone by (and the plane has not yet begun to descend).  That means that the plane begins its descent at 20,000 feet in the air.

Answer:

6

Step-by-step explanation:

To solve, first plug in 4 as your x value for your g(x) equation.

[tex]g(4)=\sqrt{4-3} \\g(4)=\sqrt{1} \\g(4)=1[/tex]

Next, plug in the value of g(4) into your f(x) equation for x.

[tex]f(1)=-1+7\\f(1)=6[/tex]

Answer:

D. 1, 3, 5, and 7 are congruent / 2, 4, 6, and 8 are congruent

Step-by-step explanation:

Vertical angles (such as 5 and 7) are congruent.

This means that angles 5 and 7 are congruent,

angles 1 and 3 are congruent,

angles 6 and 8 are congruent,

and angles 2 and 4 are congruent.

Answer:

197,8879 N.

Step-by-step explanation:

The magnitude of the horizontal force exerted on the statue can be calculated using trigonometric functions.

The question given says that Nancy is pushing the statue with a force of 120 N at a 60° angle to the horizontal and Harry is pulling the statue with a force of 180 N at a 40° angle with the horizontal.

With that information can be calculated the horizontal force exerted on the statue by Nancy, the horizontal force exerted on the statue by Harry and, adding that results, the total horizontal magnitude can be calculated.

The cosine function can be used to calculate the horizontal component of the forces exerted by Nancy and Harry, to determine the horizontal component of the force exerted on the statue.

F= (120 N cos 60°) + (180 N x cos 40°)

F= 197,8879 N

To find the magnitude of the horizontal force exerted on the statue, we need to resolve the forces applied by Nancy and Harry into their horizontal components. Nancy's horizontal force is 60N and Harry's horizontal force is 137.48N. The magnitude of the horizontal force exerted on the statue is 197.48N.

To find the magnitude of the horizontal force exerted on the statue, we need to resolve the forces applied by Nancy and Harry into their horizontal components.

Nancy is pushing the statue with a force of 120N at a 60° angle to the horizontal, so the horizontal component of her force is 120N * cos(60°) = 60N.

Harry is pulling the statue with a force of 180N at a 40° angle with the horizontal, so the horizontal component of his force is 180N * cos(40°) = 137.48N.

To find the magnitude of the horizontal force exerted on the statue, we sum up the horizontal components of both forces: 60N + 137.48N = 197.48N.

Answer: 3.5308

Step-by-step explanation:

Claim : The firm's professionals volunteer an average of more than 15 hours per month.

i.e.  [tex]\mu>15[/tex]

Null hypothesis : [tex]H_0:\mu\leq15[/tex]

Alternative hypothesis : [tex]H_1:\mu>15[/tex]

Sample size : [tex]n=24[/tex]

The sample mean : [tex]\overline{x}=16.6\text{ hours}[/tex]

Sample standard deviation : [tex]\sigma=2.22\text{ hours}[/tex]

The test-statistics for the population mean is given by :-

[tex]z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

i.e. [tex]z=\dfrac{16.6-15}{\dfrac{2.22}{\sqrt{24}}}=3.5307960256\approx3.5308[/tex]

Hence, the correct value of the test statistic for the appropriate hypothesis test is 3.5308.

A t-statistic can be computed using the formula: (sample mean - population mean) / (standard deviation / sqrt(sample size)). Applied to the given scenario, it would test the hypothesis of average volunteer hours vs the claimed 15 hours/month.

In this scenario, you are being asked to conduct a one-sample t-test.

Set up your null hypothesis (H0), which assumes no effect, so that the true volunteer hours would be equal to 15 hours/month, and the alternative hypothesis (Ha) would be that average volunteer hours are more than 15 hours/month.

The formula to calculate the t-statistic is: (sample mean - population mean) / (standard deviation / sqrt(sample size)). Using given values, it would look like this: (16.6 - 15) / (2.22 / sqrt(24))

Compute this, and the resulting value will be your t-statistic.

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Answer:

a = 2 and b = 2

Step-by-step explanation:

It is given a matrix multiplication,

To find the value of a and b

It is given that,

| 3  2 |  *  | -2 |    =   | a |

|-1  0 |     |  4 |         | b |

We can write,

a = (3 * -2) + (2 * 4)

 = -6 + 8

 = 2

b = (-1 * -2) + (0 * 4)

 = 2 + 0

 = 2

Therefore the value of  a = 2 and b = 2

Answer:

a=2 and b=2.

Step-by-step explanation:

The given matrix multiplication is

[tex]\begin{bmatrix}3&2\\ -1&0\end{bmatrix}\begin{bmatrix}-2\\ 4\end{bmatrix}[/tex]

We need to resulting vector matrix of this matrix multiplication.

[tex]\begin{bmatrix}3\left(-2\right)+2\cdot \:4\\ \left(-1\right)\left(-2\right)+0\cdot \:4\end{bmatrix}[/tex]

[tex]\begin{bmatrix}2\\ 2\end{bmatrix}[/tex]

It is given that [tex]\begin{bmatrix}a\\ b\end{bmatrix}[/tex] is resulting matrix.

[tex]\begin{bmatrix}2\\ 2\end{bmatrix}=\begin{bmatrix}a\\ b\end{bmatrix}[/tex]

On comparing both sides, we get

[tex]a=2,b=2[/tex]

Hence, a=2 and b=2.

Answer:

  D.  a1=23/100, r=1/100

Step-by-step explanation:

The repeating fraction can be written as the sum ...

[tex]0.\overline{23}=0.23+0.0023+0.000023+\dots[/tex]

The first term is a1 = 0.23 = 23/100, and each successive term is shifted 2 decimal places to the right, so is multiplied by the common ratio r=1/100.

Answer:

Step-by-step explanation:

Here, a1 = 0.23 and r = 0.01.  Thus, the sum of this infinite series will be

 a1          0.23          0.23

------- = ------------- = ----------- = 23/99.

1 - r      1 - 1/100      99/100

Check this by dividing 23 by 99 on a calculator.  Result:  0.23232323....

Answer:

D, J

Step-by-step explanation:

21)

recall for a linear equation in the form

y=mx + b, where m is the slope

the slope a a line that is perpendicular to the equation is given by m' = -1/m

in this case the line is given with the slope of 3/4

hence the slope of a perpendicular line must be,

-1 / (3/4) = -4/3  (Hence D is the answer)

22)

M is the midpoint between Q (a,d) and R (c,b). Using the midpoint formula (see attached), we find the coordinates of M to be:

M [ (a+c)/2 , (d+b)/2 ]

The distance between P(a,b) and M [ (a+c)/2 , (d+b)/2 ] is given by (see other attached formula):

√ [(a+c)/2 - a]² + [(d+b)/2 - b]²

= √ [(a+c)/2 - (2a/2)]² + [(d+b)/2 - (2b/2)]²

= √ [(a+c - 2a)/2]² + [(d+b-2b)/2]²

= √ [(c - a)/2]² + [(d-b)/2]² (J is the answer)

Answer:

The amount you need to invest in a year is $951.3

Step-by-step explanation:

Consider the provided information.

The future value can be calculated as:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Where, A represents future value, P represents Principal value, r represents interest rate in decimal, n represents number of time interest is compounded and t represents time in years.

Now use the above formula to find the money needed to invest i.e P.

Substitute, n = 12 , t = 1, A = 1000 and r = 5% or 0.05 in the above formula.

[tex]1000=P(1+\frac{0.05}{12})^{12 \times 1}[/tex]

[tex]1000=P(1.00417)^{12}[/tex]

[tex]1000=P(1.0512)[/tex]

[tex]P=951.3[/tex]

Thus, the amount you need to invest in a year is $951.3

977.38 -_- ..........

Answer:

[tex]\large\boxed{\bold{Q1.}\ \angle W,\ \angle Y,\ \angle X}\\\boxed{\bold{Q2.}\ \angle D>\angle E}[/tex]

Step-by-step explanation:

Q1.

2x + 9 > 2x + 1     subtract 2x from both sides

9 > 2    TRUE → ∠Y > ∠W

∠Y = (2x + 9) and ∠W = (2x + 1) are acute angles

∠X is right angle

right angle > acute angle

Therefore:

∠W < ∠Y < ∠X

Q2.

Angles B, C, and E are acute angles.

Angles A, D and F are obtuse angles.

obtuse angle > acute triangle

Therefore

∠D > ∠E

Answer:

[tex]W_{total} =  -56X + 68600[/tex]

Step-by-step explanation:

We wil define:

1) "x" as number of cans inside the truck.

2) "y" as number of bottles inside the truck.

We now that the amount of both cans and bottles inside the truck is "980". This quantity is equal to the sum of cans and bottles, so now we can write:

[tex]X+Y=980[/tex]

We will call this expression equation n° 1.

On the other hand, we know that the total weight is a sum of the weight of the cans and the weight of the bottles. The total weight of the cans, for example, is the result of  multiplying the numbers of cans in the truck with the weight of each can, like here: ([tex]W_{cans} = X * 14 oz[/tex]

So now we can write:

[tex]W_{total} = (X*14oz) + (Y*70oz)[/tex]

We well call this expression equation n° 2.

From equation n°1 we obtain "y", like this:

[tex]X + Y = 980\\Y = 980 - X[/tex]

And we replace it in equation n°2:

[tex]W_{total} = (X*14) + (Y * 70)\\\\W_{total}  = 14X + 70Y\\W_{total}  = 14X + 70(980-X)\\W_{total}  =  14X + 68600 - 70X\\W_{total} =  -56X + 68600[/tex]

Now we have the expression of the total weight considering the amount of cans in the truck.

*** IMPORTANT: there is a character similar to an "A" that i can't erase, maybe is a mistake from brainly. Do not consider it as part of the solution.

I assume the question is to find [tex](g\circ f)(-4)[/tex]

[tex](g\circ f)(x)=(-2x-5)^4\\\\(g\circ f)(-4)=(-2\cdot(-4)-5)^4=3^4=81[/tex]

Answer:

  x = 8.75

Step-by-step explanation:

The measure of angle C is half the measure of arc RS, so ...

  6x = (1/2)(105)

  x = 105/12 = 8.75 . . . . divide by 6

Answer:

[tex]x=8.75[/tex]

Step-by-step explanation:

We have been given a circle. We are asked to find the value of x for our given circle.

Upon looking at our given circle, we can see that angle RCS is an inscribed angle of arc RS.

We know that measure of an inscribed angle is half the measure of its intercepted arc, so we can set an equation as:

[tex]m\angle RCS=\frac{\widehat{RS}}{2}[/tex]

[tex]6x^{\circ}=\frac{105^{\circ}}{2}[/tex]

[tex]6x^{\circ}=52.5^{\circ}[/tex]

[tex]\frac{6x^{\circ}}{6}=\frac{52.5^{\circ}}{6}[/tex]

[tex]x^{\circ}=8.75^{\circ}[/tex]

[tex]x=8.75[/tex]

Therefore, the value of x is 8.75 for the given circle and option A is the correct choice.

Answer:

  Case I, Case II

Step-by-step explanation:

For cases III and IV, you need the Law of Cosines.

The Law of Sines can be used when you have at least one side and the angle opposite. If you know two angles of a triangle, you know all three, so the given angles don't necessarily have to be opposite the given side if two angles are known.

The Laws of Sines can be applied to solve Case I and Case II.

Answer:

x=105÷7

Step-by-step explanation:

You have to split the candy with 7 people and you can't split people

For this case we have that the variable "x" represents the amount of candies that each child touches.

If there are a total of 105 candies and they want to be distributed equally among 7 children, then we have the following expression:

[tex]x = \frac {105} {7}[/tex]

Thus, the correct option is:

"x = one hundred five divided by seven"

Answer:

OPTION B

Answer:

The answer in the procedure

Step-by-step explanation:

we know that

The volume of a rectangular pyramid is equal to

[tex]V=\frac{1}{3}LWH[/tex]

where

L is the length of the rectangular base

W is the width of the rectangular base

H is the height of the pyramid

If the pyramid is scaled proportionally by a factor of k

then

the new dimensions are

L=kL

W=kW

H=kH

substitute and find the new Volume V'

[tex]V'=\frac{1}{3}(kL)(kW)(kH)[/tex]

[tex]V'=\frac{1}{3}(k^{3})LWH[/tex]

[tex]V'=(k^{3})\frac{1}{3}LWH[/tex]

[tex]V'=(k^{3})V[/tex]

The new volume is equal to the scale factor k elevated to the cube multiplied by the original volume

Answer:

V = πr2h

V' = π × (k × r)2 × (k × h)

   = π × k2 r2 × kh

   = k3 × πr2h

   = k3 × V

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\bold{Q1}\\\\5x^2-50x+120=5(x^2-10x+24)=5(x^2-6x-4x+24)\\\\=5\bigg(x(x-6)-4(x-6)\bigg)=5(x-6)(x-4)\\\\\bold{Q2}\\\\64x^2-1=(8x)^2-1^2=(8x-1)(8x+1)\\\\\text{Used}\ a^2-b^2=(a-b)(a+b)[/tex]

Answer:

see explanation

Step-by-step explanation:

1

Given

5x² - 50x + 120 ← factor out 5 from each term

= 5(x² - 10x + 24)

To factor the quadratic

Consider the factors of the constant term (+ 24) which sum to give the coefficient of the x- term ( - 10)

The factors are - 4 and - 6, since

- 4 × - 6 = 24 and - 4 - 6 = - 10, hence

x² - 10x + 24 = (x - 4)(x - 6) and

5x² - 50x + 120 = 5(x - 4)(x - 6) → d

2

64x² - 1 ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b)

64x² = (8x)² ⇒ a = 8x and b = 1

64x² - 1

= (8x)² - 1² = (8x - 1)(8x + 1) → b

Answer:

  none of the above

Step-by-step explanation:

The applicable relationship is ...

  C = 2πr

Solving for r, we get

  r = C/(2π) ≈58. (367 cm)/(2·3.14159) ≈ 58.41 cm . . . . no matching choice

_____

When the problem does not include a correct answer choice, I usually suggest you ask your teacher to show you the working of it.

18cm I hope this helps

Answer:

$120.

Step-by-step explanation:

The amount he sells the tool kit for  = 80 + 20% of 80

= 80 + 16

= $96.

Let m be the marked price, then

m - 0.20m = 96

0.8m = 96

m = $120.

To make a 20 percent profit on tool kits costing $80, with a 20 percent discount applied, Harry should mark the tool kits for $120.

The subject of this question is profit calculation. This is a common topic in Mathematics, particularly in the field of business or financial mathematics. In order to understand this question, we need to consider the cost price with the profit margin and the discount offered.

In this case, if Harry buys tool kits for $80 and wants to make a 20 percent profit on his cost, he must initially price the tool kits in a way that both his profit is covered and the customer sees a discount of 20 percent.

Firstly, we calculate the 20 percent profit which is given by 0.2 x $80 = $16. This implies that the price before applying discount should be $80 (cost price) + $16 (profit) = $96.

Now, if Harry gives a 20% discount, the price $96 represents the 80% (100%-discount) of the final price (let's call it X). Therefore, we can write this as 0.8*X = $96. Solving for X gives X = $96 / 0.8 = $120. So, Harry should mark the tool kits for $120.

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Answer:

Ruhana and her team should refurbish 15 tv sets and 20 dvd players each week to minimize the cost.

Step-by-step explanation:

For the given situation let the number of tv sets be x and number of dvd players be y.

Now we have to minimize the cost as it costs $75 to refurbish a tv set and $40 to refurbish a dvd player.

i.e. Minimize z=75x+40y

it gives subject to the constraints

4x+2y≥100......(1)(100 hours each week. It takes 4 hours to refurbish a tv set and 2 hours to refurbish a dvd player.)

x+y≥35.......(2)(weekly sales target is to refurbish at least 35 tv sets or dvd players.)

To plot equation (1) we need to find coordinates of points lying on line (1)

put x=0 gives 2y=100⇒y=50

put y=0 gives 4x=100⇒x=25

So we got points (0,50) and(25,0) for (1)..............(3)

Similarly for equation (2)

put x=0 gives y=35

put y=0 gives x=35

so we got points (0,35) and(35,0) for (2).................(4)

with the help of (3) and (4) we plot the following graph (assume x≥0 and y≥0)

The unbounded feasible region determined by constraints gives the corner points as A(0,50),B(15,20)and C(35,0).

from  we get the value of z is minimum at point B (15,20) .

hence we got our optimal solution at B (15,20), where x is the number of tv sets and y is the number of dvd players  .therefore Ruhana and her team should refurbish 15 tv sets and 20 dvd players each week to minimize the cost.

Answer:

Explanation:

You can convert the percent markup into a multiplicative factor in this way:

Base price:                     15,800 . . . (cost to the seller)

Percent mark up:           115% . . .  (based on the cost to the seller)

Sale price:                      15,800 + 115% of x = 15,800 + 115 × 15,800 /100 =

                                        = 15,800 + 1.15 × 15,800 = 15,800 (2.15) = 33,970

The markup is:

And the percent markup based on the sale price is:

            = 53.49 %

Rounding to the nearest tenth percent that is 53.5 %.

Answer:

  a.  0.6975

  b.  0.833625

Step-by-step explanation:

a. The probability of both drives failing is 0.55² = 0.3025, so the probability that both drives won't fail is 1 -0.3025 = 0.6975.

__

b. The probability of all three drives failing is 0.55³ = 0.166375, so the probability that all three drives won't fail is 1 -0.166375 = 0.833625.