A triangle is placed in a semicircle with a radius of 4 mm, as shown below. Find the area of the shaded region.
Use the value 3.14 for it, and do not round your answer. Be sure to include the correct unit in your answer.

Answer:

k ≥ 24

Step-by-step explanation:

ᵏ⁄₄ ≥ 6

Multiply each side by 4

ᵏ⁄₄ *4 ≥ 6*4

k ≥ 24

Answer:

k≥24

Step-by-step explanation:

k/4≥6

Use the multiplication property of equality by multiplying both sides by 4 to get

k≥24

If this is wrong or if I did something wrong, please tell me so I can learn the proper way, I am just treating this like a normal problem

Thank you

Answer:

504 ways.

Step-by-step explanation:

In this case, order matters. If Amy were lead, Bob were record keeper, and Charles were researcher, that would be different than if Bob were lead, Charles were record keeper, and Amy were researcher. So, we will be using a permutation formula to compute.

The formula is n! / (n - k)!, where n is the total number of people (9), and k is the number you are selecting (3).

9! / (9 - 3)! = 9! / 6! = (9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (6 * 5 * 4 * 3 * 2 * 1) = 9 * 8 * 7 = 72 * 7 = 504 ways.

Hope this helps!

Answer:

Well if (a,b) is in Quadrant IV which is the last quadrant the a or x is a positive number and the b or y is a negative number.

Answer:

a should be a positive number

b should be a negative number

Answer:

12 and 7

Step-by-step explanation:

The area of the first  triangle is

A = 1/2 bh

A = 1/2 ( 14*6)

A = 42

The area of the second triangle must equal 42

Varying inversely means as the height increases, the base must decrease at the same rate

Lets try 12 and 7

A = 1/2 (12*7)

A = 42

The height of the new triangle increased and the base decreased

Answer:

[tex]\boxed{12 \: \mathrm{and} \: 7}[/tex]

Step-by-step explanation:

Solve for the area of first triangle.

[tex]\frac{bh}{2}[/tex]

[tex]b=base\\h=height[/tex]

[tex]\frac{14 \times 6}{2}[/tex]

[tex]\frac{84}{2} =42[/tex]

The area of second triangle is same as the first triangle.

The area of second triangle is 42 units².

The base varies inversely with the height.

[tex]b \propto \frac{1}{h}[/tex]

As the value of b increases, the value of h decreases.

[tex]\frac{12 \times 7}{2}=42[/tex]

The answer is b = 12 and h = 7.

Answer:

The answer is below

Step-by-step explanation:

Twenty-five blood samples were selected by taking every seventh blood sample from racks holding 187 blood samples from the morning draw at a medical center. The white blood count (WBC) was measured using a Coulter Counter Model S. The mean WBC was 8.636 with a standard deviation of 3.9265. (a) Construct a 90% confidence interval for the true mean using the FPCF. (Round your answers to 4 decimal places.) The 90% confidence interval is from to

Answer:

Given:

Mean (μ) = 8.636, standard deviation (σ) = 3.9265, Confidence (C) = 90% = 0.9, sample size (n) = 25

α = 1 - C = 1 - 0.9 = 0.1

α/2 = 0.1/2 = 0.05

From the normal distribution table, The z score of α/2 (0.05) corresponds to the z score of 0.45 (0.5 - 0.05) which is 1.645

The margin of error (E) is given by:

[tex]E=z_{\frac{\alpha}{2} }*\frac{\sigma}{\sqrt{n} }\\ \\E=1.645*\frac{3.9265}{\sqrt{25} }=1.2918[/tex]

The confidence interval = μ ± E = 8.636 ± 1.2918 = (7.3442, 9.9278)

The 90% confidence interval is from 7.3442 to 9.9278

Answer:

Step-by-step explanation:

even function are symmetrical about the y axis or f(-x)=f(x)

odd function are symmetrical about the origin -f(-x)=f(x)

f(x)=x^6 + 10x^4-11x^2+19

f(-x)=(-x)^6+10(-x)^4+11(-x)^2+19=x^6 + 10x^4-11x^2+19

the function is even

Answer:

The demand function is  [tex]\mathbf{D(x) = 1200(\sqrt{25-x^2})+ 124000}[/tex]

Step-by-step explanation:

A firm has the​ marginal-demand function [tex]D' x = \dfrac{-1200}{\sqrt{25-x^2 } }[/tex].

Find the demand function given that D = 16,000 when x = $4 per unit.

What we are required to do  is to find the demand function D(x);

If we integrate D'(x) with respect to x ; we have :

[tex]\int\limits \ D'(x) \, dx = \int\limits{\dfrac{-1200 x}{\sqrt{25-x^2}} } \, dx[/tex]

[tex]D(x) = \int\limits{\dfrac{-1200 x}{\sqrt{25-x^2}} } \, dx[/tex]

Let represent   t  with [tex]\sqrt{25-x^2}}[/tex]

The differential of t with respect to x is :

[tex]\dfrac{dt}{dx}= \dfrac{1}{2 \sqrt{25-x^2}}}(-2x)[/tex]

[tex]\dfrac{dt}{dx}= \dfrac{-x}{ \sqrt{25-x^2}}}[/tex]

[tex]{dt}= \dfrac{-xdx}{ \sqrt{25-x^2}}}[/tex]

replacing the value of  [tex]\dfrac{-xdx}{ \sqrt{25-x^2}}}[/tex]  for dt in   [tex]D(x) = \int\limits{\dfrac{-1200 x}{\sqrt{25-x^2}} } \, dx[/tex]

So; we can say :

[tex]D(x) = \int\limits{\dfrac{-1200 x}{\sqrt{25-x^2}} } \, dx[/tex]

[tex]D(x) = 1200\int\limits{\dfrac{- x}{\sqrt{25-x^2}} } \, dx[/tex]

[tex]D(x) = 1200\int\limits \ dt[/tex]

[tex]D(x) = 1200t+ C[/tex]

Let's Recall that :

t  = [tex]\sqrt{25-x^2}}[/tex]

Now;

[tex]\mathbf{D(x) = 1200(\sqrt{25-x^2}})+ C}[/tex]

GIven that:

D = 16,000 when x = $4 per unit.

i.e

D(4) = 16000

SO;

[tex]D(x) = 1200(\sqrt{25-x^2}})+ C[/tex]

[tex]D(4) = 1200(\sqrt{25-4^2}})+ C[/tex]

[tex]D(4) = 1200(\sqrt{25-16}})+ C[/tex]

[tex]D(4) = 1200(\sqrt{9}})+ C[/tex]

[tex]D(4) = 1200(3}})+ C[/tex]

16000 = 1200 (3) + C

16000 = 3600 + C

16000 - 3600 = C

C = 12400

replacing the value of C = 12400 into [tex]\mathbf{D(x) = 1200(\sqrt{25-x^2}})+ C}[/tex], we have:

[tex]\mathbf{D(x) = 1200(\sqrt{25-x^2})+ 124000}[/tex]

∴ The demand function is  [tex]\mathbf{D(x) = 1200(\sqrt{25-x^2})+ 124000}[/tex]

Answer:

0.2006

Step-by-step explanation:

The probability the first calculator is defective is 42/62.

The probability the second calculator is defective is 41/61.

The probability the third calculator is defective is 40/60.

The probability the fourth calculator is defective is 39/59.

The probability all four calculators are defective:

(42/62) (41/61) (40/60) (39/59) = 0.2006

Answer:

Option b and d

Step-by-step explanation:

With the following data,

H0:p=0.11

Ha:p≠0.11

The p-value was determined to be 0.106 and significance level of 0.05.

Since the p value (0.106) is great than 0.05, then we will fail to reject the null hypothesis and conclude that There is sufficient evidence to conclude the proportion of people over 65 years of age in a certain city is 11%

Answer:

m∠N = 51°

m∠M = 31°

m∠O = 98°

Step-by-step explanation:

It is given that ΔMNO is an isosceles triangle with base NM.

m∠N = (4x + 7)° and m∠M = (2x + 29)°

By the property of an isosceles triangle,

Two legs of an isosceles triangle are equal in measure.

ON ≅ OM

And angles opposite to these equal sides measure the same.

m∠N = m∠M

(4x + 7) = (2x + 29)

4x - 2x = 29 - 7

2x = 22

x = 11

m∠N = (4x + 7)° = 51°

m∠M = (2x + 9)° = 31°

m∠O = 180° - (m∠N + m∠M)

         = 180° - (51° + 31°)

         = 180° - 82°

         = 98°

Answer:

Statistical concepts are used in quality testing. Companies make many products on a daily basis and every company should make sure that they sold the best quality items.

Step-by-step explanation:

pls keep brainly questions only school related thank you!

Answer:

you will start to ascend at the rate of 1.6

Step-by-step explanation:

Walking south, it's the negative part of a coordinate, so the unit vector at this point is; u = (0,-1)

We are told that the equation z = 1600 − 0.005x² − 0.01y²

Therefore, we have;

∇z = ((δ/δx)i + (δ/δx)j)(1600 − 0.005x² − 0.01y²)

This gives;

∇z = -0.005(2x)i - 0.01(2y)j

∇z = <-0.01x - 0.02y>

coordinates are (120, 80, 1464).

Thus;

∇z(120, 80, 1464) = <-0.01(120), - 0.02(80)> = <-1.20, -1.60>

D_uf = <-1.20, -1.60> × <0, - 1>

D_uf = 0 + 1.6

D_uf = 1.6

So, you will start to ascend at the rate of 1.6

Answer:

2.28% of babies born in the United States having a low birth weight.

Step-by-step explanation:

The complete question is: In the United States, birth weights of newborn babies are approximately normally distributed with a mean of μ = 3,500 g and a standard deviation of σ = 500 g. What percent of babies born in the United States are classified as having a low birth weight (< 2,500 g)? Explain how you got your answer.

We are given that in the United States, birth weights of newborn babies are approximately normally distributed with a mean of μ = 3,500 g and a standard deviation of σ = 500 g.

Let X = birth weights of newborn babies

The z-score probability distribution for the normal distribution is given by;

                          Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean = 3,500 g

            [tex]\sigma[/tex] = standard deviation = 500 g

So, X ~ N([tex]\mu=3500, \sigma^{2} = 500[/tex])

Now, the percent of babies born in the United States having a low birth weight is given by = P(X < 2500 mg)

   P(X < 2500 mg) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{2500-3500}{500}[/tex] ) = P(Z < -2) = 1 - P(Z [tex]\leq[/tex] 2)

                                                                 = 1 - 0.97725 = 0.02275 or 2.28%

The above probability is calculated by looking at the value of x = 2 in the z table which has an area of 0.97725.

Answer:

The z-score for 2,500 is -2. According to the empirical rule, 95% of babies have a birth weight of between 2,500 g and 4,500 g. 5% of babies have a birth weight of less than 2,500 g or greater than 4,500 g. Normal distributions are symmetric, so 2.5% of babies weigh less than 2,500 g.

Step-by-step explanation:

did the assignment on edge:)

Answer: There is no sufficient evidence to support the claim that loaded die behaves differently than a fair die

Step-by-step explanation:

Find explanations in the attached file

Answer:

0.65463

Step-by-step explanation:

From the given question:

It is stated that 2% of the parts are defective (D) out of 50 parts

Therefore the probability of the defectives;

i.e  p(defectives) = [tex]\dfrac{N(D)}{N(S)}[/tex]

p(defectives) = [tex]\dfrac{2}{50}[/tex]

p(defectives) = 0.04

The probability of the failure is the P(Non-defectives)

p(Non-defectives) =  1 - P(defectives)

p(Non-defectives) =  1 - 0.04

p(Non-defectives) =  0.96

Also , Let Y be the number of non -defective out of the 52 stock parts.

and we need Y ≥ 50

P( Y ≥ 50) , n = 52 , p = 0.96

P( Y ≥ 50) = P(50 ≤ Y ≤ 52) = P(Y = 50, 51, 52)

= P(Y = 50) + P(Y =51) + P(Y=52)    (disjoint events)

P(Y = 50) = [tex](^{52}_{50}) ( 0.96)^{50}(1-0.96)^2[/tex]

[tex]P(Y = 50) = 1326 (0.96)^{50}(0.04)^2[/tex]

P(Y = 50) = 0.27557

P(Y = 51) =[tex](^{52}_{51}) ( 0.96)^{51}(1-0.96)^1[/tex]

[tex]P(Y = 51) = 52(0.96)^{51}(0.04)^1[/tex]

P(Y = 51) = 0.25936

(Y = 52) =[tex](^{52}_{52}) ( 0.96)^{52}(1-0.96)^0[/tex]

[tex]P(Y = 52) = 1*(0.96)^{52}(0.04)^0[/tex]

P(Y = 52) = 0.1197

∴

P(Y = 50) + P(Y =51) + P(Y=52) = 0.27557 + 0.25936 + 0.1197

P(Y = 50) + P(Y =51) + P(Y=52) = 0.65463

Answer:

As X → - ∞ , y → ∞ and as x→ ∞ , y → ∞

Step-by-step explanation:

let f(x) = y = 3x² - 5x + 2

y = 3x² - 5x + 2

= x ( 3x - 5 ) + 2

y = ∞ ( 3 ( ∞ - 5 ) ) + 2

= ∞ (∞ ) + 2

y = ∞

y → ∞ as x → ∞

Now,

as x → - ∞

y = x ( 3x - 5 ) + 2

= ∞ ( 3 ( - ∞ ) - 5 ) + 2

= - ∞ ( - ∞ ) + 2

∞² + 2 = ∞

Hence , Option C is the correct answer.

Answer:

Mathematically you can use the following V = ⁴⁄₃πr³

π = pi

r = radius

To do this you would need a set of scales, a jug, some water, a pen, a ruler and some paper.

ωα√

Answer:

45

Step-by-step explanation:

Both angles (2x+45) and x together form a straight angle which measures 180 degrees.

Together should make you think of adding the angle measurements.

So we have that (2x+45)+x should be 180 degrees.

The equation we want to solve is:

(2x+45)+x=180

2x+45+x=180

(2x+x)+45=180

3x+45=180

3x=180-45

3x=135

x=135/3

x=45

Let's confirm that x is 45.

(2x+45) with x=45:

(2*45+45)

(3*45)

135

So (2x+45)+x at x=45 gives us:

135+45

180

Answer has been confirmed.

Answer:

[tex]\boxed{x = 45}[/tex]

Step-by-step explanation:

=> [tex]x+2x+45 = 180[/tex] (Angles on a straight line add up to 180 degrees)

=> [tex]3x+45 = 180[/tex]

Subtracting 45 to both sides

=> 3x = 180-45

=> 3x = 135

Dividing both sides by 3

=> x = 45

Answer: -4/3

Step-by-step explanation:

Formula to find a slope of two given points is

y(sub2) - y(sub1) / x(sub2) - x(sub1)

Plug the values in to get the answer.

-2 - 2 / -1 - (-4)

-4/3

Answer:

13.33

Step-by-step explanation:

As in the attached diagram,  we can see that the points belong to  [tex]\mu\pm \sigma[/tex] interval

Data provided in the question as per the details below:

[tex]\mu_{\bar x}[/tex] = 440

[tex]\mu_{\bar x} + \sigma_{\bar x}[/tex] = 480

So,

[tex]\sigma_{\bar x}[/tex] = 480 - 440

= 40

Now the standard deviation of the population is

[tex]V(\bar{x}) = \frac{\sigma}{\sqrt n} \\\\ = \frac{40}{\sqrt 9}[/tex]

= 13.33

Hence, the standard deviation of the population for which the sample is drawn is 13.33

Answer:

multiplying the equation A

Step-by-step explanation:

3c=d-8 ####### *4

+ c=4d + 8

After that you will get the value of c and d.

Answer:

Multiply equation A by -4

Step-by-step explanation:

3c = d - 8

c = 4d + 8

Multiply equation A by -4.

-12c = -4d + 32

c = 4d + 8

Add the equations.

-11c = 40

Variable d is eliminated.

Answer:

A)$ 45

B) $105

Step-by-step explanation:

Bag and a belt cost $255

Let bag = x

Let belt = y

X+y= 255 equation 1

Let total money be z first

Remaining money= z-255

X-30 = z-255

Y +15 = z-255

Equating the left side of the equation

X+30 = y+15

X-y= 45 equation 2

Solving simultaneously

X+y= 255

X-y= 45

2x = 300

X= 150

If x= 150

150-y= 45

150-45= y

105=y

Bag = $150

Belt = $105

Bag Is 150-105 more than the belt

150-105= $45

Answer:

[tex](x+4)^2+(y-4)^2=9[/tex]

Step-by-step explanation:

From the graph, we need to identify two things: the center of the circle and the radius of the circle.

From this graph, we find that the center of the circle is at (-4,4) and the radius of the circle is 3.

Recall that the format for the equation of a circle is [tex](x-x_1)^2+(y-y_1)^2=r^2[/tex]

Now, we can put our know information into this equation and simplify to get our answer

[tex](x-(-4))^2+(y-4)^2=3^2\\\\(x+4)^2+(y-4)^2=9[/tex]

Answer:

the car overtake the truck at time 11:40 am.

Step-by-step explanation:

We have both vehicules going at constant speed from city a to city b. The distance is unknown, but can be written as d.

We will express the time in hours (and decimals of hours).

The truck speed can be calculated estimating the time between arrival and start:

- The arrival time is 1.15 pm. This is t2=13.25.

- The starting time is 9:15 am. This is t1=9.25.

The truck took t2-t1=13.25-9.25=4 to go from city a to b.

The average speed is then:

[tex]v_t=\dfrac{\Delta x}{\Delta t}=\dfrac{d}{4}[/tex]

We can write the equation for the position x(t) for the truck as:

[tex]x(t)=x_0+v_t\cdot t=x_0+\dfrac{d}{4}t\\\\\\x(13.25)=x_0+\dfrac{d}{4}(13.25)=d\\\\x_0=d-3.3125d=-2.3125d\\\\\\x(t)=-2.3125d+0.25d\cdot t[/tex]

For the car we have:

- The arrival time is 12:45 am. This is t2=12.75.

- The starting time is 10 am. This is t1=10.

The car took t2-t1=12.75-10=2.75.

The average speed is then:

[tex]v_c=\dfrac{\Delta x}{\Delta t}=\dfrac{d}{2.75}[/tex]

We can write the equation for the position x(t) for the car as:

[tex]x(t)=x_0+v_c\cdot t=x_0+\dfrac{d}{2.75}t\\\\\\x(12.75)=x_0+\dfrac{d}{2.75}(12.75)=d\\\\x_0=d-4.6363d=-3.6363d\\\\\\x(t)=-3.6363d+0.3636d\cdot t[/tex]

The time at which the car overtake the car is the time when both vehicles have the same position:

[tex]x(t)/d=-2.3125+0.25\cdot t = -3.6363+0.3636\cdot t\\\\-2.3125+3.6363=(0.3636-0.25)t\\\\1.3238=0.1136t\\\\t=1.3238/0.1136\approx11.65[/tex]

The car overtakes the truck at t=11.65 hours or 11:39 am.

Hey there! I'm happy to help!

If the number of red marbles is 6 more than double the number of black marbles, we can create this equation, with r representing the red marbles and b representing the black marbles.

r=2b+6

We also know that r+b=33, and if we know that r is equal to 2b+6, we can just replace r with that and then solve for b.

2b+6+b=33

We combine like terms.

3b+6=33

We subtract six from both sides.

3b=27

We divide both sides by 3.

b=9

Now we just subtract 9 from 33 to see how many red ones there are.

33-9=24

So, there are 24 red marbles and 9 black marbles.

Now, let's see which of these options are correct.

The equation r+b=33 represents the total number of marbles.

This is true because r plus b is equal to the total, which is 33.

The equation r=2b+6 can be used to find the number of red marbles.

This is true because it we used this r-value to find how many black marbles there were.

The equation r=2b+6 represents the total number of marbles.

This is false because it does not have the total number, which is 33.

The equation r=b=33 can be used to find the number of red marbles.

This is true because we plugged in the r-value to solve for b with this equation.

There are 9 red marbles in the bag.

This is false. There are 24 red marbles.

There are 9 black marbles in the bag.

This is true.

There are 24 black marbles in the bag.

This is false. There are 9 black marbles.

There are 24 red marbles in the bag.

This is true.

Have a wonderful day! :D

Answer:

1,2,4,6,8

Step-by-step explanation:

Answer:

z = 70°

y = 103°

Step-by-step explanation:

From the picture attached,

110° + z° = 180° [Supplementary angles]

z = 180 - 110

z = 70°

Since sum of interior angles of a polygon = (n - 2)×180°

where n = number of sides of the polygon

For a quadrilateral (n = 4),

Sum of interior angles = (4 - 2) × 180°

                                     = 360°

z° + y° + 100° + 87° = 360°

70° + y° + 187° = 360°

y = 103°

Therefore, measure of the angles x = 70° and y = 103°.

Hey there! :)

Answer:

4√3 in.

Step-by-step explanation:

Given:

-Equilateral triangle

-Side lengths of 8 in

Find the altitude using the Pythagorean Theorem (c² = a² + b²) where:

'a' is the shorter leg, or half of the base to find the altitude

'b' is the altitude

'c' is the Hypotenuse, or 8 in.

Therefore:

8² = 4² + b²

64 = 16 + b²

48 = b²

b = √48 or 4√3 in.

Therefore, the altitude of the triangle is 4√3 in.

Answer:

x = log (7)/ 2log 5

Step-by-step explanation:

25^ x = 7

Replace 25 with 5^2

5^ 2x = 7

Take log  on each side

log (5 ^2x) = log ( 7)

We know that log a^ b = b log a

2x  log 5 = log (7)

Divide each side by log 5

2x  log 5/ log 5= log (7)/ log 5

2x = log (7)/ log 5

Divide each side by 2

x = log (7)/ 2log 5

Answer:

Likely

Step-by-step explanation: Mathematically it is likely because there are 4 options certain is the thing that will defiantly happen so it would be 4/4. The impossible thing would be 1/4 this is because 1/4 is the smallest so it is obviously going to be impossible. Likely would be 3/4 and unlikely would clearly be 2/4

Answer:

it is likely

Step-by-step explanation:

it is not certant because it is not 4/4 but it is not impossible because its not 0/4 so the answer is likely 3/4

Step-by-step explanation:

It is given that,

Total length of a board is 65 inches

It is sawed into two pieces such that one piece is 7 inches shorter than twice the length of the other piece.

Let x is the length of other piece and y is the length of first piece such that,

y = 2x-7 ....(1)

Also,

x+y = 65 .....(2)

Put the value of y from equation (1) to equation (2) such that,

x+2x-7 = 65

3x=65+7

3x=72

x = 24 inches

Put the value of x in equation (1)

y = 2(24)-7

y = 41 inches

So, the length of first piece is 41 inches while the length of other piece is 24 inches.