65 out of the 100 boys like basketball ______________ ___________ 2. 15 out of 100 girls joined the swimming _____________ ____________ team

Answer:

B = x = 44 degrees

Step-by-step explanation:

Interior angles of a triangle = 180 degrees.

There are 2 congruent sides so the angle to the right of 67 degrees is also 67 degrees

180 - 2(67) = 46 degrees (the third angle of the triangle)

x + 46 degrees = 90 degrees ( complementary angles)

x = 44 degrees

Michael needs to analyze the population data, demographics of the city, and the competition in the area to determine whether or not to open a new store.

Michael is trying to determine where to open two new store locations. He has population data to determine the amount of revenue he will receive for each location.

He is charged a $1000 fee for opening a new store at a certain location. However, he is unsure whether the population of the city would be large enough to warrant opening a new store at that location.

The first step that Michael needs to take is to analyze the population data that he has.

Based on the population data, he needs to make an informed decision about whether or not to open a new store at that location. This would require him to take into consideration the average income of the population as well as the demographics of the city.

Another important factor that Michael needs to take into consideration is the competition in the area. If there are already several stores in the area, then opening a new store might not be a good idea.

This is because the competition would be too high and he would not be able to generate enough revenue to make up for the cost of opening a new store.

However, if there are no stores in the area, then Michael might consider opening a new store. This would require him to invest a significant amount of money, but he could also generate a significant amount of revenue in return.

Additionally, he needs to take into consideration the cost of opening a new store and whether or not he can generate enough revenue to make up for that cost.

Overall, Michael needs to carefully analyze all the data that he has before making an informed decision about where to open new store locations.

In conclusion, Michael needs to analyze the population data, demographics of the city, and the competition in the area to determine whether or not to open a new store. If the population is large enough and there is no competition in the area, then he should consider opening a new store. However, if there is already a significant amount of competition in the area, then he should avoid opening a new store.

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Step-by-step explanation:

please mark me as brainlest

Ok, the equation of the line also known as linear function has the form:

Where x,y indicate coordinates, a is the slope and b the intercept. Given two point

While linear regression can be a useful tool for prediction, it is important to consider the quality of the data, assess the linearity assumption, and be cautious when extrapolating beyond the observed data range.

This is an example of using linear regression to predict the weight of a kitten at a specific time (10 weeks in this case) based on the given linear model ŷ = 1.7 + 1.48t.

Using linear regression to make predictions is a common practice and can provide reasonable estimates in many cases. However, whether it is considered a best practice for prediction depends on various factors. Here are a few considerations:

Data quality: The accuracy and reliability of the predictions heavily depend on the quality of the data used to build the linear model. If the data used for training the model is representative and accurately reflects the underlying relationship, the predictions are likely to be more reliable.

Linearity assumption: Linear regression assumes a linear relationship between the predictor variable (in this case, time) and the response variable (kitten weight). If the relationship is not truly linear, the predictions may be less accurate. It is important to assess the linearity assumption and consider alternative models if needed.

Extrapolation: When making predictions outside the range of the observed data (such as predicting the weight at 10 weeks when the data only goes up to 8 weeks), caution should be exercised. Extrapolating beyond the observed range can introduce more uncertainty and may lead to less accurate predictions.

In summary, while linear regression can be a useful tool for prediction, it is important to consider the quality of the data, assess the linearity assumption, and be cautious when extrapolating beyond the observed data range.

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Answer:

4\(x^{2}\)-16x+8

Step-by-step explanation:

4(x - 2)(x - 2) - 8 = 4(\(x^{2}\) - 4x + 4) - 8 = 4\(x^{2}\) - 16x + 16 - 8 = 4\(x^{2}\) - 16x + 8.

Answer:

\(f(x) = 4x^2 -16x + 16\)

Step-by-step explanation:

f(x)=4(x-2)² Simplify.

f(x) = 4x^2 - 16x + 16

Form f(x)=ax²+bx+c.

f(x) = 4x^2 - 16x + 16

Answer:

18

Step-by-step explanation:

169-79=90

90/5=18

Answer:

F(x)=-x^2-4x-1

Step-by-step explanation:

According to PEMDAS, do the exponent part for the parentheses, sense it goes first.

F(x)= -(x^2+4x+4)+3

Then distribute the - sign

F(x)= -x^2-4x-4+3

Then you simplify

F(x)= -x^2-4x-1

Answer:

Hello,

Step-by-step explanation:

do I remind you of the formula  (a+b)²=a²+2ab+b²

\(f(x)=-(x+2)^2+3\\\\=-(x^2+4x+4)+3\\\\=-x^2-4x-4+3\\=-x^2-4x-1\)

Sorry i haven't see the sign minus before the parenthesis.

The area is equal to 324π square units.

To find the area of a circle with radius 18 units, we can use the formula for the area of a circle, which is given by A = πr^(2), where r is the radius.

Given that the radius is 18 units, we can plug this value into the formula:

A = π(18)^2

Now, square the radius:

A = π(324)

Next, multiply 324 by π:

A = 324π

Therefore, the area of the circle with radius 18 units is 324π square units.

Now, let's compare the options with the given options:

a) 18π units^(2)- This is incorrect, as we calculated the area to be 324π square units.

b) 36π units^(2)- This is also incorrect, as our calculated area is 324π square units.

c) 9π units^(2)- This is incorrect, as our calculated area is 324π square units.

d) 324π units^(2)- This is the correct option , as we calculated the area to be 324π square units.

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The total number of defective iphones from a batch of 16,530 iphones is equal to 513 .

Total  number of iphones examined by quality-control inspector =290

Total number of iphones in a batch = 16,530

Number of iphones defective out of 290 = 9

Let us consider x be the number of defective iPhones in the batch of 16,530 iPhones.

Use proportions to find out how many defective iPhones there will be in a batch of 16,530 iPhones.

The proportion of defective iPhones in the sample of 290 iPhones is,

= 9/290

Proportion of defective iPhones in a batch of 16,530 iPhones,

Set up a proportion,

9/290 = x/16530

To solve for x, we can cross-multiply,

⇒ 9 x 16530 = 290 x

⇒ 148,770 = 290 x

⇒ x = 513

Therefore, there will be approximately 513 defective iPhones in a batch of 16,530 iPhones.

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The number 0. 7653765376537653 is rational number.

What is rational and irrational number?

 Perfect squares like 4, 9, 16, 25, and other integers are included in the category of rational numbers. Surds like 2, 3, 5, 7, and so forth are examples of irrational numbers. Rational numbers have whole integers for both their numerator and their denominator, meaning that their denominator is not equal to zero. All whole numbers, fractions, and decimal numbers that finish or repeat are considered rational numbers. Any number that is not rational—that is, any number that cannot be divided by a fraction—is considered to be irrational.

Here the given number is

=>0.7653765376537653

It consists repeated numbers and we can also convert into fraction value.

Hence it is a rational number.

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Answer:

16 pots

Step-by-step explanation:

We first need to find out the amount of dirt that can be filled into a single flowerpot.

We use the formula to find the cylinder's volume.

π\(r^{2}\)\(* h\)

Height is equal to ten, Radius is equal to 7.

49π \(* 10\)

≈ 1539.38

25,000 divided by 1539.38

≈ 16.24

He can fill 16 pots fully.

The fraud triangle is a model that describes the three key factors that must be present for fraud to occur: opportunity, rationalization, and pressure.

These factors are often represented as the three sides of a triangle, with fraud being the result at the center.

Opportunity refers to the ability of an individual to commit fraud, either due to a lack of internal controls or the ability to override existing controls. Rationalization refers to the mental process by which an individual justifies the fraudulent behavior to themselves, often by convincing themselves that it is not really wrong or that they have a valid reason for doing it. Pressure refers to the external factors that motivate an individual to commit fraud, such as financial difficulties, job insecurity, or a desire to meet performance targets.

In summary, the fraud triangle indicates that all three conditions of opportunity, rationalization, and pressure must be present for fraud to be perpetrated.

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Answer:

discriminant =b^2 -4ac

= (12)^2 -4(-4)(-9)

=0

Thus, the total length of lap covered to get the seven different obstacles is found as: 52 units.

the Pythagorean theorem is used to calculate the distance between two locations using the distance formula. The Pythagorean theorem can be rewritten as d = √((x2 - x1)²+(y2 - y1)²)  to calculate the separation between any two locations.

Given data:

Points on  y-axis and an x-axis are given,

M(-3,5), F(8,5), G(8,2), H(3,2), I(3,-5), J(-8,-5), K(-8,-2), and L(-3,-2).

Starting and ending point is F.

Points lies between the starting and ending are-

F ,G, H, I, J, K, L, M, F

Total length = sum of all length

d = √((x2 - x1)²+(y2 - y1)²)

FG =  √((8 - 8)²+(2 - 5)²)

FG =  √9

FG =  3

GH =  √((8 - 3)²+(2 - 2)²)

GH  =  √25

GH =  5

HI =  √((3 - 3)²+(2 + 5)²)

HI  =  √49

HI  =  7

IJ =  √((3 + 8)²+(-5 + 5)²)

IJ =  √121

IJ =  11

JK =  √((-8 + 8)²+(-2 - 5)²)

JK =  √9

JK =  3

KL =  √((-8 + 3)²+(-2 + 2)²)

KL =  √25

KL =  5

LM =  √((-3 + 3)²+(-2 - 5)²)

LM =  √49

LM =  7

MF =  √((8 + 3)²+(+5 - 5)²)

MF =  √121

MF =  11

Total length = 3 + 5 + 7 + 11 + 3 + 5 + 7 + 11

Total length = 52 units

Thus, the total length of the lap covered to get the seven different obstacles is found as: 52 units.

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Carla Lopez deposits $1,900 per year into her retirement account and the funds have an average earnings rate of 7 percent. The task is to calculate the future value of her retirement account after 40 years.

To calculate the future value of Carla's retirement account, we can use the formula for the future value of an ordinary annuity, which is:

\(Future Value = Payment *[(1 + interest rate)^n - 1] / interest rate\)

Here, the payment is $1,900, the interest rate is 7 percent (or 0.07), and n is the number of years until her retirement, which is 40.

Substituting these values into the formula, we get:

\(Future Value = $1,900 * [(1 + 0.07)^{40} - 1] / 0.07\)

Calculating this expression will give us the future value of Carla's retirement account. However, it mentions using "Exhibit 1-8," which is not provided in the question.

Therefore, without the specific information from Exhibit 1-8, it is not possible to provide the exact value of Carla's retirement account.

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The probability that Marta makes at least 2 of the 3 free throws is 0.972

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

Proportion of throws = 90%

Number of throws = 3

The probability that Marta makes at least 2 of the 3 free throws is calculated as

Probability = P(2) + P(3)

Each individual probability can be calculated using

P(x) = nCx * p^x * (1 - p)^(n - x)

Substitute the known values in the above equation, so, we have the following representation

Probability = 3C2 * (0.9)^2 * (1 - 0.9)^1 + 3C3 * (0.9)^3 * (1 - 0.9)^0

Evaluate the expressions

Probability = 0.243 + 0.729

So, we have

Probability = 0.972

Hence, the probability is 0.972

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Answer:

sin2αcos2β + cos2αsin2β

Step-by-step explanation:

Given that

sin(A+B) = sinA cos B + cos A sinB

According to the question;

sin(2α+2β) = sin2αcos2β + cos2αsin2β

where A =  2α and B = 2β

Answer:

D. -18x + 4

Step-by-step explanation:

\(-6(3x-\frac{2}{3})\)

\(-6\cdot \:3x+6\cdot \frac{2}{3}\)

\(-18x + 4\)

Answer:

\({ \tt{ - 6(3x - \frac{2}{3}) }} \\ \\ = { \tt{ - 18x + ( \frac{2}{3} \times 6) }} \\ \\ = { \tt{ - 18x + (2 \times 2)}}\\ = { \boxed{ \tt{ - 18x + 4}}}\)

The new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees are approximately (4.993, 2.048).

To find the new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees, we can use the rotation formula:

x' = x * cos(theta) - y * sin(theta)

y' = x * sin(theta) + y * cos(theta)

Where (x, y) are the original coordinates, (x', y') are the new coordinates after rotation, and theta is the angle of rotation in radians.

Converting the angle of rotation from degrees to radians:

theta = 5 degrees * (pi/180) ≈ 0.08727 radians

Plugging in the values into the rotation formula:

x' = 5 * cos(0.08727) - 2 * sin(0.08727)

y' = 5 * sin(0.08727) + 2 * cos(0.08727)

Evaluating the trigonometric functions and simplifying:

x' ≈ 4.993

y' ≈ 2.048

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Answer:

Step-by-step explanation:

a) Just work backwards!

Instead of adding 4, subtract by 4

Instead of multiplying by 3, divide by 3

22 - 4 / 3 = x

b)

22 - 4 = 18

18 / 3 = 6

Therefore, x = 6

The expression and the length of ribbon that she needs for both pillows is \(4(2x^{2} +4x-6)\) , 130 inches .

Given:

The side length of the pillow is 2x2+1 inches. She plans to make a similar pillow, including the ribbon, whose side length is 4x-7 inches.

The length of ribbon :

= 4(\(2x^{2} +1\)) + 4(4x - 7)

= 4(2\(x^{2} +1\)+4x - 7)

= 4(\(2x^{2} +4x-6\))

The length at x = 3.5 is,

= 4(2(\(3.5^{2}\))+4(3.5) - 6)

= 4(24.5+14-6)

= 4(24.5+8)

= 130 inches.

Therefore the expression and the length of ribbon that she needs for both pillows is \(4(2x^{2} +4x-6)\) , 130 inches .

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Answer:

Step-by-step explanation:2x2+1 inches. She plans to make a similar pillow, including the ribbon, whose side length is 4x-7 inches. What

expression can be used for the length of ribbon that she needs for both pillows, and what is the length if x = 3:5?

Answer:

y=-x+5

Step-by-step explanation:

Hope this helps!

And can I have brainliest!

Answer:

C.) 12.4

Step-by-step explanation:

The square root of 155 needs to be found.

It's about 12.4498996.

Thinking that your options are supposed to be decimals, the closest rounded answer would be C.

To determine the equation of the tangent plane and normal line of the given curve at the point P(2, -3, 18), we need to find the partial derivatives of the function f(x, y, z) = x^2 + y^2 - 2xy - x + 3y - z - 4.

Taking the partial derivatives with respect to x, y, and z, we have:

fx = 2x - 2y - 1

fy = -2x + 2y + 3

fz = -1

Evaluating these partial derivatives at the point P(2, -3, 18), we find:

fx(2, -3, 18) = 2(2) - 2(-3) - 1 = 9

fy(2, -3, 18) = -2(2) + 2(-3) + 3 = -7

fz(2, -3, 18) = -1

The equation of the tangent plane at P is given by:

9(x - 2) - 7(y + 3) - 1(z - 18) = 0

Simplifying the equation, we get:

9x - 7y - z - 3 = 0

To find the equation of the normal line, we use the direction ratios from the coefficients of x, y, and z in the tangent plane equation. The direction ratios are (9, -7, -1).Therefore, the equation of the normal line passing through P(2, -3, 18) is:

x = 2 + 9t

y = -3 - 7t

z = 18 - t

where t is a parameter representing the distance along the normal line from the point P.

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By using the concept of Probability, 0.771 is the probability by which worker 1 will outproduce worker 2

Let Xi be the random variable representing the number of units the first worker produces in day i.

Define X = X₁+ X₂ + X₃ + X₄ + X₅ as the random variable representing the number of units the first worker produces during the entire week.

We know that Mean =(Sum of all quantities)/(Number of quantities)

Mean=75 and number of quantities =5(given)

Therefore, from the formula

=>Sum of all quantities=75×5

or We can Say that X₁+ X₂ + X₃ + X₄ + X₅=375--------------------------------(eq1)

Now, talking about the standard deviation of first worker

We know that standard deviation = \(\frac{\sqrt{(Each quantity - Mean)^{2} } }{\sqrt{Total Number of quantities} }\)

We are given standard deviation of first worker as 20,

Therefore 20×\(\sqrt{Total Number of quantities}\) = \(\sqrt{(Eachquantity -Mean)^{2} }\)

20√5 = √[(X₁ - Mean)²+(X₂ - Mean)²+(X₃ - Mean)²+(X₄ - Mean)²+(X₅ - Mean)²]-(eq2)

Therefore, from eq1 and eq2,

we get Mean(µx) =375 and standard deviation(σ\(x\)) =20√5

Similarly, define random variables Y₁, Y₂, . . . , Y₅ representing the number of units produces by the second worker during each of the five days and define Y = Y₁ + Y₂ + Y₃ + Y₄ + Y₅.

From the Mean formula,

we get  Y₁ + Y₂ + Y₃ + Y₄ + Y₅=(65×5)--------------------------------(eq3)

Standard deviation of second worker = 21(given),

So using the standard deviation formula, we get

Therefore 21×\(\sqrt{Total Number of quantities}\)=\(\sqrt{(Eachquantity -Mean)^{2} }\)

21√5=√[(Y₁ - Mean)²+(Y₂ - Mean)²+(Y₃ - Mean)²+(Y₄ - Mean)²+(Y₅ - Mean)²]-(eq4)

Therefore, from eq3 and eq4,

we get Mean(µy) =325 and standard deviation(σy) =21√5

Of course, we assume that X and Y are independent. The problem asks for P(X > Y ) or in other words for P(X − Y > 0).

It is a quite surprising fact that the random variable U = X −Y , the difference between X and Y ,is also normally distributed with mean µU = µx−µy = 375−325 = 50 and standard deviation σu ,where σ\(u^{2}\) = σ\(x^{2}\)+σ\(y^{2}\) =400·5+441·5 = 841·5 = 4205

It follows that  σu=√4205.

Now probability of first worker(P₁)=375/√4205

probability of second worker(P₂) =325/√4205

We can clearly see P₁>P₂

Difference in Probability of both workers(P)=P₁-P₂

=>P=[(375/√4205)-(325/√4205)]

=>P=50/√4205

=>P=50/64.84

=>P=0.771

Hence, probability by which worker 1 will outproduce worker 2 is 0.771.

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