A TV studio has brought in 6 boy kittens and 8 girl kittens for a cat food commercial.
The director is going to choose 7 of these kittens at random to be in the commercial.
What is the probability that the director chooses 4 boy kittens and 3 girl kittens? Round your answer to three decimal places.

Using proportions, the ratios are given as follows:

a) 9:196.

b) 27:2744.

c) 3:14.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Considering the standard ratio of 3:14 units, we have that:

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The brackets or error bars shown at the top of each bar extend one standard error above and below each of the group means. For group 1, the error bar extends 3.9 units above and below the mean for group 1.

A researcher is investigating whether a reading intervention program improves reading comprehension for second graders. He collects a random sample of second graders
Group 1 consists of n₁ = 52 second graders who did not participate in the program. Their mean reading comprehension score is M₁ = 36.8.
Group 2 consists of n₂ = 56 second graders who did participate in the program. Their mean reading comprehension score is M₂ = 52.4.

Error bar, are the line through a point on a graph,axes, which emphasizes  the uncertainty or variation of the corresponding coordinate of the point.

We have the data,
σ = 25.24, n₁ = 52 M₁ = 36.8.

n₂ = 56  M₂ = 52.4.

Error bar  = M2-M1/n2-n1
      =  (52.4-36.8)/(56-52)
      =  3.9

Thus, the required value that will be put in black space is 3.9

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The center of mass is mathematically given as

[tex]\bar{x}=\left(\frac{44 e-100}{25 e-40}\right)\end{aligned}[/tex]

Determine the center of mass in one dimension:

Represent the masses at the respective distances.

[tex]\begin{|c|c|} Masses \ & \ \ \ \ \ \ \ \ \ \ \ \ \ \ Located at \\\rho=x^{3}+x \cdot e^{-x} & \ \ \ \ x \in(0,1)$ \\\end[/tex]

We calculate the total mass of the system.

[tex]\begin{aligned}m &=\int_{0}^{1} \rho \cdot d x \\& m =\int_{0}^{1}\left(x^{3}+x \cdot e^{-x}\right) \cdot d x \\&m =\left|\frac{x^{4}}{4}-(x+1) e^{-x}\right|_{0}^{1} \\&m =\left(\frac{5}{4}-\frac{2}{e}\right)\end{aligned}[/tex]

Step 03: Calculate the moment of the system.

[tex]\begin{aligned}M &=\int_{0}^{1}(\rho \cdot x) \cdot d x \\& M=\int_{0}^{1}\left(x^{4}+x^{2} \cdot e^{-x}\right) \cdot d x \\&M =\left|\frac{x^{5}}{5}-\left(x^{2}-2 x+2\right) \cdot e^{-x}\right|_{0}^{1} \\&M=\left(\frac{11}{5}-\frac{5}{e}\right)\end{aligned}[/tex]

we calculate the center of mass.

[tex]\begin{aligned}\bar{x} &=\left(\frac{M}{m}\right) \\& \bar{x}=\left\{\left(\frac{\left.11-\frac{5}{5}\right)}{\left(\frac{5}{4}-\frac{2}{e}\right)}\right\}\right.\\& \bar{x}=\left(\frac{11 e-25}{5 e}\right) \cdot\left(\frac{4 e}{5 e-8}\right) \\&\bar{x}=\left(\frac{44 e-100}{25 e-40}\right)\end{aligned}[/tex]

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The input and output table that works for both rules is input = 20 and output = 10.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let y represent the output and x represent the input.

From the first rule:

y = x/2

From the second rule:

y = x - 10

To work for both rules:

x/2 = x - 10

x = 2x - 20

x = 20

y = 20 - 10 = 10

The input and output table that works for both rules is input = 20 and output = 10.

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Using proportions, it is found that 78 students would prefer long jump.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Out of 300 students, 26% would prefer long jump, hence the amount is given by:

n = 0.26 x 300 = 78 students.

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Answer:

x<3−√11 /2 or x > 3 +√11/2

Step-by-step explanation:

Solve the inequality for x by finding a, b, and c of the quadratic then applying the quadratic formula.

If the equation is r = 3 +4cos(θ) then because b/a>1 the curve is a limacon with an inner loop.

Given limacon with equation r=3+4cos(θ) and we have to answer how the quotient of a and b relate to the existence of an inner loop.

Equation is like a relationship between two or more variables expressed in equal to form and it is solved to find the value of variables.

formula of polar graph is similar to r= a+ b cos (θ).

Case 1. If a<b or b/a>1

then the curve is a limacon with inner loop.

Case 2. If a>b or b/a<1

Then the limacon does not have an inner loop.

Here given that [tex]r=3+4cos[/tex] (θ)

It is observed that , a<b or b/a>1

Therefore the curve is limacon with an inner loop.

Hence because b/a>1 the curve is a limacon with an inner loop.

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Answer:

The answer is B

Step-by-step explanation:

The value of x in the equation is x=-44.

The given equation is [tex]\frac{3}{4}\left(\frac{1}{4}x+8\right)-\left(\frac{1}{2}x+2\right)=\frac{3}{8}(4-x)-\frac{1}{4}[/tex].

An algebraic expression in mathematics is an expression that's made from variables and constants, together with algebraic operations (addition, subtraction, etc.). Expressions are made of terms.

Firstly, apply the distributive property as a(b+c)=ab+ac and get

[tex]\begin{aligned}\frac{3}{4}\times \frac{1}{4}x+\frac{3}{4}\times 8-\frac{1}{2}x-2&=\frac{3}{8}\times 4-\frac{3}{8}\times x-\frac{1}{4}\\ \frac{3x}{16}+6-\frac{x}{2}-2&=\frac{3}{2}-\frac{3x}{8}-\frac{1}{4} \end[/tex]

Now, rearrange the terms by taking variable terms on the left-hand side and constant terms on the right-hand side as

[tex]\frac{3x}{16}-\frac{x}{2}+\frac{3x}{8}=\frac{3}{2}-\frac{1}{4}-6+2[/tex]

Further, simplify the above expression by taking L.C.M as

[tex]\begin{aligned}\frac{3x-8x+6x}{16}&=\frac{6-1}{4}-4\\ \frac{x}{16}&=\frac{5-16}{4}\\ \frac{x}{16}&=\frac{-11}{4}\end[/tex]

Then, multiply both sides with 4 and get

[tex]\begin{aligned}4\times \frac{x}{16}&=4\times \frac{-11}{4}\\ \frac{x}{4}&=\frac{-11}{1}\end[/tex]

Furthermore, cross multiply both sides and get

[tex]x=-44[/tex]

Hence, the value of x in the equation which is given [tex]\frac{3}{4}\left(\frac{1}{4}x+8\right)-\left(\frac{1}{2}x+2\right)=\frac{3}{8}(4-x)-\frac{1}{4}[/tex] is x=-44.

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Answer: Addition property of equality

Step-by-step explanation:

Assuming you meant 3x-9=2x+5, it would be the addition property of equality since you are adding 9 to both sides.

The amount paid in tax based on the information is Rs 13500.

From the information given, the monthly salary is 45000. Therefore, the yearly salary will be:

= 45000 × 12

= 540000

Also, it's stated that the tax rate for first 450000 is 1% and next 100000 is 10%. Therefore, the amount that will be paid in tax will be:

= (450000 × 1%) + (90000 × 10%)

= 4500 + 9000

= 13500

Therefore, the amount paid in tax will be Rs 13500.

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The length of a square with diagonal of 10 cm is 5√2 cm.

Each angle in a square is 90 degrees.

Therefore, the diagonal form a right triangle with the length of the square.

The length of the square are equal.

Hence, using Pythagoras theorem,

let

x = length of square

x² + x² = 10²

2x² = 100

x² = 50

x = √50

x = 5√2

Therefore, the length of a square with diagonal of 10 cm is 5√2 cm.

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Using a calculator, the correlation coefficient is of 0.7649. Since the correlation is greater than 0.6, there is strong correlation.

Using a calculator, we insert the points (x,y) to find the coefficient. In this problem, the points are given as follows:

(1, 5), (4, 8), (8, 3), (13, 10), (19, 13)

The coefficient is of 0.7649. Since the correlation is greater than 0.6, there is strong correlation.

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Answer:

The scale factor would be 1/2.

Step-by-step explanation:

2 of the sides both are 4 units.

If you go to figure B, it got smaller.

So in this case, you would divide.

On figure B, 2 of the sides are 2 units.

If you did it in reverse, you would get 2 because 2 times 2 is 4.

But we divide, so 4/2 is 2, so the scale factor would be:

1/2

Hope this helped!

And brainliest pls :)

Answer:

?=3

Step-by-step explanation:

3=3/1

Flip 3/1 and you get

1/3

Rewriting the equation of the given line in slope-intercept form,

[tex]3x+6y=18\\\\x+2y=6\\\\2y=-x+6\\\\y=-\frac{1}{2}x+3[/tex]

This means the slope of the given line is -1/2.

As perpendicular lines have slopes that are negative reciprocals, the answer is 2.

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

Determine the slope of the line perpendicular to 3x+6y=18

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

[tex]\bf{\dfrac{3}{6}x+\dfrac{6}{6}y=\dfrac{18}{6}[/tex] | dividing the ENTIRE equation by 6, to make it easier to write in y=mx+b form

[tex]\bf{\dfrac{1}{2}x+y=3}[/tex] | subtract 1/2 x

[tex]\bf{y=-\dfrac{1}{2}x+3[/tex].

[tex]\cline{1-2}[/tex]

Now, perpendicular lines' slopes are opposite inverses of each other.

The opposite inverse of -1/2 is

                  = 2

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

                 [tex]\bf{=2}[/tex]

[tex]\LARGE\boxed{\bf{aesthetics\not1\theta l}}[/tex]

Answer:

See below

Step-by-step explanation:

Start by subtracting 5.2 from both sides of the equation

  so  "subtraction property of equality "    I suppose ......

then the next step would be divide both sides by 2.5  

  which would be division property of equality  

Answer: Subtraction Property of Equality

Step-by-step explanation:

- the subtraction property of equality is the rule that when you subtract the same number to or from both sides of an equation and get an equivalent equation

__________________________________________________________

- for this equation you would subtract 5.2 from the left-side of the equation and subtract it from 35.2 on the right side of the equation

      - this is to isolate n

- basically 2.5n = 30 since n is a variable and that number multiplied by 2.5 will equal 30

- so the new equation would be 2.5n = 30

- so then:  [tex]\frac{n}{2.5}[/tex] = [tex]\frac{30}{2.5}[/tex]  so n = 12

hope this helps :)

Answer: 123/32 or 3 27/32 sticks

Step-by-step explanation:

41/8*3/4 =

41*3/8*4 =

123/32 =

3 27/32

Using PEDMAS, the value of each expressions are:

a. 1 + 5 × 2 + (1 + 3)² = 27

b. 0.25 × 4³ - 1 = 15

c. 4 + 8(1/4 + 2) = 22

PEDMAS implies that you solve a problem first following the order, parentheses, exponent, division, multiplication, addition, and subtraction.

Let's evaluate the expressions using PEDMAS:

a. 1 + 5 × 2 + (1 + 3)²

1 + 5 × 2 + (4)²

1 + 5 × 2 + 16

1 + 10 + 16

= 27

b. 0.25 × 4³ - 1

0.25 × 64 - 1

16 - 1

= 15

c. 4 + 8(1/4 + 2)

4 + 8(9/4)

4 + 18

= 22.

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Answer: A

Step-by-step explanation:

[tex]C=2\pi r=2(\pi)(17) \approx 106.8[/tex]

The probability of an event is the measurement of the chance of that event's occurrence. The probabilities of considered events are:

Binomial distributions consist of n independent Bernoulli trials. Bernoulli trials are those trials that end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining to a binomial distribution with parameters n and p, then it is written as

X = B(n,p)

The probability that out of n trials, there'd be x successes is given by

P(X=x)  = [tex]^nC_xp^x(1-p)^{n-x}[/tex]

Since 10 people can be either diseased or not and they be so independent of each other (assuming them to be selected randomly) , thus, we can take them being diseased or not as outputs of 10 independent Bernoulli trials.

Let we say

Success= Probability of a diseased person tagged as diseased by the clinic

Failure = Probability of a diseased person tagged as not diseased by the clinic.

Then,

P(Success) = p = 72% = 0.72 (of a single person)

P(Failure) = q = 1-p = 0.28

Let X be the number of people diagnosed diseased by the clinic out of 10 diseased people. Then we have: X ≈ B(n+10,P=0.73)

Calculating the needed probabilities, we get:

a) P(At leased 8 have disease) = P(X≥8) =P(X=8) + P(X=9) + P(X=10)

P(X≥8) = [tex]^{10}C_8(0.73)^8(0.28)^2+^{10}C_9(0.73)^9(0.27)^1+^{10}C_{10}(0.73)^{10}(0.27)^0[/tex]

P(X≥8) ≈ 0.2548 + 0.1456 + 0.0374 ≈ 0.4378

b)  P(At most 4 have the disease) = P(X≤4) = P(X=0) + P(X=1)+P(X=2)+P(X=3)+P(X=4)

P (X ≤ 4) =

[tex]^{10}C_0(0.73)^0(0.27)^{10}+^{10}{C_1(0.73)^1(0.27)^9+^{10}{C_2(0.73)^2(0.27)^8+^{10}C_3(0.73)&^3(0.27)^7 \\[/tex]

[tex]+^{10}C_4(0.73)^4(0.27)^6[/tex]

P (X ≤ 4) = 0.000003 + 0.000076+0.00088+0.00604+0.02719

P (X ≤ 4) =  0.0342

Thus,

The probabilities of considered events are:

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Answer:

D. all real numbers greater than or equal to 0

Step-by-step explanation:

The range is the set of y-values.

Answer: 44.2

Step-by-step explanation:

108.29*2/4.9=44.2

Answer:

B

Step-by-step explanation:

y² - 12y + 32

consider the product of  factors of the constant term (+ 32) which sum to give the coefficient of the y- term (- 12)

the factors are - 4 and - 8 , since

- 4 × - 8 = + 32 and - 4 - 8 = - 12 , then

y² - 12y + 32 = (y - 4)(y - 8)

Answer:

B. (y-4)(y-8)

Step-by-step explanation:

Given equation: y² - 12y + 32. Essentially, we are going to find two numbers that multiply to 32 and add up to -12.

1) Pull out the factors of 32 and find the pair that multiply to 32 and add up -12.

They are: -8 and -4.

2) Rewrite the b of the original quadratic equation as a sum, then factorise by grouping.

y² - 8y - 4y +32

y(y - 8) - 4(y - 8)

(y - 4)(y -8)

The perimeter of the shaded region is 8π cm and the area of the shaded region is 32(π - 2) cm² or 36.53 square cm.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

We have shown a square in which a one-fourth circle is shown and making an ellipse.

The perimeter of the circle = 2πr = 2π(8) = 16π cm

The perimeter of the one-fourth is circle = (16π)/4 = 4π cm

The perimeter of 2 one-fourth circle = 2(4π) = 8π cm

The area of the one-fourth circle = (1/4)πr² = (1/4)π(8)² = 16π square cm

The area of the right-angle triangle = (1/2)(8)(8) = 32 square cm

The area of the shaded region = 2(16π - 32) = 36.53 square cm

or

= 32(π - 2)cm²

Thus, the perimeter of the shaded region is 8π cm and the area of the shaded region is 32(π - 2) cm² or 36.53 square cm.

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The population of Charlotte is 661,000.

Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred.

The population of Charlotte = number of unemployed people / percentage of unemployed

26,440 / 0.04 = 661,000

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The area of polygon MNOPQR = (Area of a rectangle that is 15 square units + Area of a rectangle that is 2 square units)

From the information about the polygon MNOPQR, side MN is parallel to side RQ and also the side MR is parallel to side PQ

With a perpendicular line drawn from point O on the side RQ, which intersects with line  RQ at point S.

We can then  divide the  polygon into two different rectangles

MNSR  with A₁ as its area

OPQS  with A₂ as its area

For rectangle MNSR, line MN is 5 units and line MR is 3 units

The formula for area of a rectangle is given as;

A₁ = (length)×(width)

Substitute the values

A₁ = 5 × 3

A₁ = 15 square units

For rectangle MNSR, line MN= line RS and line MR = line NS,

We have RS= 5 units and NS= 3 units

So, line SQ= RQ- RS = 7-5 = 2 units

Also,  OS= NS - NO = 3- 2 = 1 unit

Let's substitute the values

A₂ = 2 × 1

A₂ = 2 square units

Therefore, the area of polygon MNOPQR = (Area of a rectangle that is 15 square units + Area of a rectangle that is 2 square units)

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Answer and Explanation:

First, solve for x in both inequalities:

4x − 1 > 7                         5x − 1 < −6

4x > 8                             5x < −5

x > 2                               x < −1

Because this is an OR problem, determine if there is any overlap. (See the attached image for details.) There is not, so the answer is no solution or Ø.

If one finalist is randomly selected for a prize then the probability that person will be selected is 6.25%.

Given A person is one of 16 finalists and one finalist is randomly selected for a prize.

Probability is the likeliness of happening an event among all the events possible. The formula of calculating probability is number of events possible/total outcomes.

The value of probability lies between 0 and 1. It cannot be negative because there might be chances of something and sometimes not so the value be 0.

Total finalists=16

Probability=1/16

When we convert it in percentage it will be 1*100/16

=6.25%

Hence the probability that person  will be selected is 6.25%.

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Answer:

1) 150 mph

2) 90 mph

3) 3 mph

Explanation:

1) The trains move at a constant speed, and after 5 hours they are 750 miles apart. 750/5=150

2) The faster train is 1.5 faster than the slower train, and we know their combined speed is 150 mph. 150/5=30, and 30x3=90.

3) We know that both trains combined travel 150 mph. 450/150=3.

Based on the data given, the speeds and time taken are as follows:

Speed is the ratio of distance covered and time taken.

1)The distance covered by the two trains in 5 hours = 750 miles.

The trains move at a constant speed and their combined speed will be:

Combined speed = 750/5

Combined speed = 150 mph

2) The train heading south has a speed 1.5 times faster than the other train heading north.

Ratio of speeds = 3 : 2

Speed of faster train 150 x 3/5 = 90 mph

3) The combined speed of the trains = 150 mph

Distance to be covered = 450 miles

Time taken = 450/150

Time taken = 3 hours

In conclusion, the speed of the two trains are determined from the distance travelled and time taken.

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Answer:

Vertex form: [tex]y=\frac{1}{2}(x-2)^2-3[/tex]

Standard Form: [tex]y=0.50x^2-2x-1[/tex]

Step-by-step explanation:

Well the vertex form of an equation is given in the form: [tex]y=a(x-h)^2+k[/tex] where (h, k) is the vertex, and by looking at the graph, you'll see the vertex is at (2, -3). So plugging this into the equation gives you: [tex]y=a(x-2)^2-3[/tex]. Now to find a which will determine the stretch/compression, you can substitute any point in (besides the vertex, because that'll result in (x-2) being 0). So I'll use the point (0, -1) which is the only point I think I can accurately determine by looking at the graph (besides (4, -1) since it's symmetric). Anyways I'll plug this in

Plug in (0, -1) as (x, y)

[tex]-1 = a(0-2)^2-3[/tex]

calculate inside the parenthesis

[tex]-1 = a(-2)^2-3[/tex]

square the -2

[tex]-1 = 4a-3[/tex]

Add 3 to both 3 to both sides

[tex]2 = 4a[/tex]

divide both sides by 4

[tex]a=\frac{1}{2}[/tex]

This gives you the equation: [tex]y=\frac{1}{2}(x-2)^2-3[/tex]

To convert this into standard form you simply expand the square binomial, you can use the foil method to achieve this, but it generally expands to: [tex](a+b)^2=a^2+2ab+b^2[/tex].

Original equation:

[tex]y=\frac{1}{2}(x-2)^2-3[/tex]

expand square binomial:

[tex]y=\frac{1}{2}(x^2-4x+4)^2-3[/tex]

Distribute the 1/2

[tex]y=0.50x^2-2x+2-3[/tex]

Combine like terms:

[tex]y=0.50x^2-2x-1[/tex]