The Hcf of 2 numbers O and L is the number O itself .This can be only true if

Check the picture below.

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-3}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~2 - (-3)~~)^2 + (~~3 - (-2)~~)^2} \implies d=\sqrt{(2 +3)^2 + (3 +2)^2} \\\\\\ d=\sqrt{( 5 )^2 + ( 5 )^2} \implies d=\sqrt{ 25 + 25 } \implies d=\sqrt{ 50 }[/tex]

The value of x is 3. Option B

It is important to note that the given shape is a parallelogram.

The properties of a parallelogram are;

Now, let's equate the sides, we have;

4x - 1 = 6x - 5

collect like terms

4x - 6x = -5 -1

Subtract like terms

-2x = -6

Make 'x' the subject of formula

x = -6/-2

x = 3

Hence, the value is 3

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Angle EBI and angle BCJ are congruent is proved as follow.

To prove that corresponding angles are congruent, we can use the transformation that takes angle EBI to angle BCJ.

Therefore, we can conclude that corresponding angles are congruent.

Alternatively, we can use the fact that if two lines are parallel, then the alternate interior angles are congruent and corresponding angles are congruent. Since AI and GJ are parallel, angle EBI and angle BCJ are congruent.

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The reasonable domain for the Funtion is 0 to 14 parts. So,the correct option is B.

This function's domain is the set of all potential input values for the variable p. Because the variable p reflects the number of components generated, it must be non-negative.

Because the function is defined for p is larger than or equal to 0, the domain includes all non-negative p values. Because the function is linear, it is defined for all non-negative real numbers; however, in this case, the company manufactures custom truck parts for big rigs.

Which means the company may have a limit on the number of parts it can produce; this limit is 14 parts, so the reasonable domain for this function is 0 to 14 parts.

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Answer:

3

Step-by-step explanation:

Experimental probability is based on the actual outcomes of an experiment (gathered by experimenting repeatedly).  

Theoretical probability is based on the possible outcomes (expected outcomes).

Probability formula

[tex]\boxed{\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}}[/tex]

Theoretical probability of flipping a head

A coin has two sides: one side is a "head", the other side is a "tail".

The number of ways flipping a head can occur is 1.

The total number of possible outcomes is 2.

Therefore, the theoretical probability of flipping a head is 1/2.

Theoretical probability of rolling a number less than 3

The cube has six sides labelled 1, 2, 3, 4, 5 and 6.

The number of ways that rolling less than 3 can occur is 2 (rolling 1 or 2).

The total number of possible outcomes is 6.

Therefore, the theoretical probability of rolling a number less than 3 is 2/6 = 1/3.

Therefore, the theoretical probability of flipping a head and rolling a number less than 3 is:

[tex]\sf P(head)\; and\; P(X < 3)=\dfrac{1}{2} \times \dfrac{1}{3}=\dfrac{1}{6}[/tex]

To calculate the number of actual outcomes and expected outcomes after 90 trials, multiply the number of trials by the probability for each outcome:

[tex]\textsf{Number of actual outcomes}=90 \times \dfrac{2}{15}=12[/tex]

[tex]\textsf{Number of expected outcomes}=90 \times \dfrac{1}{6}=15[/tex]

Therefore, the difference between the number of expected outcomes and the number of actual outcomes is:

[tex]\implies 15-12=3[/tex]

Note: If Olivia continued to flip the coin and roll the number cube, as the number of trials increased, we would expect the experimental probability of 2/15 to get nearer to the theoretical probability of 1/6 and so the difference between the number of actual and expected outcomes would become smaller.

Answer:

SEE ATTACHED

Step-by-step explanation:

For making of 60 biscuits the quantity and packs of butter required by Helen is :

a. The exact amount of butter is 480 grams to make 60 biscuits.

b. Number of packs of butter Helen needs to buy is 2 packs.

Amount of sugar need to make 15 biscuits = 60 grams

Flour is three time of sugar to make 15 biscuits = 60 × 3

                                                                               = 180 grams

Amount of flour to make 60 biscuits = 180 × 4

                                                            = 720 grams

Butter is two times as sugar  to make 15 biscuits= 60 × 2

                                                                                = 120grams

a. Exact amount of butter to make 60 biscuits is:

Butter required to make 60 biscuits = 120 × 4

                                                            = 480 grams

b. One pack is of 250 grams

Number of packs of butter she need to buy = 480 / 250

                                                                         = 1,92

                                                                         ≈ 2packs

Therefore, the quantity of butter and number of packs of butter is given by :

a. The exact amount of butter required to make 60 biscuits is 480 grams.

b. The number of packs she needs to purchase is 2 packs.

The above question is incomplete, the complete question is :

Helen has to buy all the butter she needs to make 60 biscuits. She buys the butter in 250g packs.

(i) What is the exact amount of butter she needs?

(ii) How many packs of butter will she have to buy?

Figure is attached.

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A population is a person or object that is a member of the sample being studied while a sample is the entire group that is being studied.

In a research study, a sample is a relatively small group of people from whom data is collected. The population is the bigger group to whom the information is then generalized.

All citizens, whether they are living there permanently or are only visiting, are referred to as the "people."

This indicator shows the average population density of a given area. The annual population fluctuations brought on by births, deaths, and net migration are known as growth rates.

A population is any large group that has at least one attribute in common. Not all populations are made up of people.

Populations can include, but are not limited to, people, animals, groups, organizations, buildings, houses, trucks, farms, and things.

Of the 7.8 billion people on the planet, 1%, or around 78 million individuals, would be there. One percent of the 7.8 billion people on the planet, or 78 million people, live there.

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Complete question -

A person or object that is a member of the group being studied is called ______.

They needed a total of 8 weeks to save the same amount of money, and after 8 weeks, everyone would have $200.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given, Harper and Joe want to buy season passes for Disneyland but neither of them has the $1,300 needed to purchase a pass.

Since Harper decides to get a job that pays $25 a week. She has nothing saved right now. Joe already has $80 and plans to save $15 of her weekly allowance.

To save up for the season pass:

Harper needs = 1300$

Since, She earns 25$ a week

Harper needs total weeks = 1300/25

Harper needs total weeks = 52 weeks

joe also needs 1300 $

Since, joe already has $80 and plans to save $15 of her weekly allowance.

Joe needs total weeks = (1300 -80)/15

Joe needs total weeks = 81.33

To have the same amount of money saved up:

Let "x" be the weeks they required to save the equal money:

25 *x = 80 + 15*x

10*x = 80

x = 8

Everyone will have = 25 * 8

Everyone will have = 200$

Therefore, they required total of 8 weeks to have the same amount of money saved up and everyone will have 200$ after 8 weeks.

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The circumference of the Super Pizza is 56.52 inches  and approximate area of the Super Pizza 253.34 inches2.

To calculate the circumference of the Super Pizza
Circumference = π x diameter
Circumference = 3.14 x 18
Circumference = 56.52 inches

To calculate the area of the Super Pizza
Area = π x radius2
Area = 3.14 x (18/2)2
Area = 3.14 x 81
Area = 253.34 inches2

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Answer:

-3(x - 3) (x + 1)

Step-by-step explanation:

Let's check

-3(x - 3) (x + 1)

(-3x + 9) (x + 1)

-3[tex]x^{2}[/tex] -3x + 9x + 9

-3[tex]x^{2}[/tex] + 6x + 9

Answer:

-3(x-3)(x+1)

Step-by-step explanation:

A common factor that all three numbers share is that they are divisible by 3, so we can factor 3 out. Typically, I take out the negative first:

-3([tex]x^2-2x-3[/tex]) (always remember to change signs!)

Now, we are left with [tex]x^2-2x-3[/tex], and to factor that out, we need to find two numbers that add up to -2 and multiply to -3. These two numbers will be 1 and -3, so we can write our factor like this:

(x-3)(x+1)

Let's add back in the -3 from earlier to complete our factoring:

-3(x-3)(x+1)

The ratio of sedans to sports coupes on the lot is 2:3, which can also be expressed as 3:2, 3:4, or 4:3. This means that there are two sedans for every three sports coupes, or three sedans for every two sports coupes, etc.

The ratio of sedans to sports coupes on the lot can be expressed as a fraction, which is the number of sedans divided by the number of sports coupes. In this case, there are 24 sedans and 18 sports coupes, which can be written as 24/18. This fraction can be simplified to 2/3, which is equivalent to the ratio 2:3. This ratio can also be expressed as 3:2, 3:4, or 4:3, which means that there are two sedans for every three sports coupes, three sedans for every two sports coupes, three sedans for every four sports coupes, or four sedans for every three sports coupes. In summary, the ratio of sedans to sports coupes on the lot is 2:3, which can also be expressed in several other ways.

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Answer:

First question: 452.2

Second question: 267.9

Step-by-step explanation:

Not a hundred percent sure on second ques

a1 is a linear combination of w1, w2, and w3, and is thus a vector in w.

a. No, b is not in fa 1; a 2; a 3g. There are 3 vectors in fa 1; a 2; a 3g.

b. Yes, b is in w. There are 4 vectors in w.

c. To show that a1 is in w, we need to show that a1 is a combination of the vectors in w. We can do this by constructing a linear combination of the vectors in w that results in a1. In this case, we can take w1 = (2, 4, 1, 0), w2 = (4, 0, 3, 2), and w3 = (2, 6, 3, 3). Now we can set up a linear combination of these vectors, with coefficients c1, c2, and c3, to equal a1. Thus, we have: c1(2, 4, 1, 0) + c2(4, 0, 3, 2) + c3(2, 6, 3, 3) = (2, 0, 0, 0). Solving for c1, c2, and c3, we get c1 = 2, c2 = -2, and c3 = 0. Therefore, a1 is a linear combination of w1, w2, and w3, and is thus a vector in w.

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Answer:

53700

Step-by-step explanation:

Depreciation of every year is 8%, 2016-2017-18-19-20 - 4 years

in the beginning of 2017 it'll be 0.92*75000

so it'll be (1-8%)^4 = 0.71639

multiply by 75000 = 53729.  to the nearest 100 = 53700

The probability that the student will be a student who lives on campus is 0.24

In math the term probability is referred as the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions.

Here we have given that one full-time student who is a freshman or sophomore is selected at random.

Here we need to find the probability that the student will be a student who lives on campus.

Here we know that the probability that a student is a sophomore is calculated as,

=> P(S) = 19/42 = 0.45.

Whereas the probability that a student has a freshman is calculated as,

=>P(H)=25/42=0.6.

Then the probability that the student will be a student who lives on campus is calculated as,

=> P(H∩S)=P(S)+P(H)−P(S∪H)

Apply the values then simplify this one then we get,

=> 0.45+0.6−(42−8)/42=0.24

Complete Question:

Suppose that a certain college class contains 42 students and then if one full-time student who is a freshman or sophomore is selected at random, what is the probability that the student will be a student who lives on campus?

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Answer: The coefficient of determination, r^2, is a measure of how well a linear regression model fits the data. It is calculated by squaring the linear correlation coefficient, r. In this case, r^2 = 0.845^2 = 0.7146. This tells us that 71.46% of the variation in the data is explained by the regression line, while 28.54% is unexplained.

The coefficient of determination, r^2, is a measure of how well a linear regression model fits the data. It is calculated by squaring the linear correlation coefficient, r. In this case, r^2 = 1^2 = 1. This tells us that 100% of the variation in the data is explained by the regression line, and 0% is unexplained.

The standard error of estimate (SEE) for a linear regression model is a measure of the average difference between the predicted values and the actual values. In this case, we can use the formula SEE = sqrt(SSE/n) where SSE is the sum of the squared differences between the predicted and actual values, and n is the number of observations. The given equation is y = -2.5x, so we can use this equation to find the predicted values and then calculate the SSE and SEE.

The standard error of estimate (SEE) for a linear regression model is a measure of the average difference between the predicted values and the actual values. In this case, we can use the formula SEE = sqrt(SSE/n) where SSE is the sum of the squared differences between the predicted and actual values, and n is the number of observations. The given equation is y = 1.523x + 6.343, so we can use this equation to find the predicted values and then calculate the SSE and SEE by using the given data.

Answer:

rate = 7%

Step-by-step explanation:

From the question

Principal = $1,800

Time = 7 years

simple interest = $882

Rate = ?

rate = 100 × ST

P × T

rate = 100 × $882

$1,800 × 7

rate = $88200

12,600

rate = 7%

Answer:They use the process of photosynthesis to transform water, sunlight, and carbon dioxide into oxygen, and simple sugars that the plant uses as fuel. These primary producers form the base of an ecosystem and fuel the next trophic levels

Step-by-step explanation:

The majority of human physical, mental, and personality factors have a mean in the middle of the distribution, where there are also the most cases. For example, in baseball, the rookie of the year often has a poor second season.

Correct answer is b) regression to the mean.

Regression to the mean is the propensity of outcomes that are extreme by chance on the first measurement to move closer to the average when tested a second time. Results that are susceptible to regression to the mean are those that are vulnerable to some degree of chance. When exceptional scores are the result of chance or a fluke, it's improbable that those extreme scores will be obtained again.

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Answer:

5

Step-by-step explanation:

(2x4)-(3x1)

=(8)-(3)

= 5

So its  5

Answer:

Step-by-step explanation:

Let the 3 angles be x , 2x , and 3x

notice x:2x:3x = 1:2:3

we know x+2x+3x = 180

6x = 180

x = 30

so the largest angle is 3(30) or 90 degrees

The vector u can be expressed as a sum of n and p when n= (-33/10, 11/10) and p= (-7/10, -21/10).

To find the vector p that is parallel to v, we need to project u onto v. We can use the formula for projection:

p = (u . v) / (||v||^2) * v

where . represents dot product and ||v|| represents the magnitude of v.

First, we need to find the dot product of u and v:

(-4,-1) . (1,3) = -4*1 + -1*3 = -4 + -3 = -7

Next, we need to find the magnitude of v:

||v|| = sqrt(1^2 + 3^2) = sqrt(1 + 9) = sqrt(10)

Then, we can plug these values into the projection formula:

p = (-7) / (sqrt(10))^2 * (1,3) = (-7/10) * (1,3) = (-7/10, -21/10)

So the vector p that is parallel to v is (-7/10, -21/10)

To find the vector n that is orthogonal to v, we can subtract p from u:

n = u - p = (-4,-1) - (-7/10, -21/10) = (-4 + 7/10, -1 + 21/10) = (-33/10, 11/10)

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Answer:

Refer to the step-by-step

Step-by-step explanation:

Since ∠1 and ∠2 are alternate exterior angles, m∠2=108°

In parallelogram lmno measure of angle m m∠M = 80°

In a parallelogram, opposite sides and opposite angles are congruent to each other.

⇒ m∠N = m∠L and m∠M = m∠O ..........(1)

Also, the sum of any two consecutive angles of a parallelogram is supplementary that is 180°

⇒ m∠M + m∠L = 180°  ...........(2)

Now, using equation (1)

m∠N = m∠L

⇒ 5x = 3x + 40

⇒ 5x - 3x = 40

⇒ 2x = 40

⇒ x = 20

⇒ m∠N = m∠L = 5x = 100°

Now, from equation (2)

m∠M + m∠L = 180°

⇒ m∠M + 100 = 180

⇒ m∠M = 80°

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Five repetitions should be done for each exercise in the preparation drill.

Preparation drills are an important part of any fitness routine, as they allow the muscles and joints to be prepared for the workout ahead. Doing the correct number of repetitions for each exercise in the preparation drill is key to getting the most out of the workout. Generally, five repetitions is recommended for each exercise. This should give the body just enough time to get used to the exercise while still providing enough of a challenge. Doing too many repetitions may lead to fatigue or overstretching, leading to injury. Doing too few repetitions may not be enough to prepare the body and prevent injury. Five repetitions is the ideal number for most preparation drills.

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32 rows are needed in the truth table that we would use to evaluate a logical statement in five variables

As per the given data:

If we have a logical statement in five variables then we have to determine how many rows we need in the truth table that you would use to evaluate it.

It is calculated by both from truth table and by using the formula.

A table with rows and columns is created for a compound statement, and the number of rows depends on the number of statements.

As we know that the formula for number of rows need in the truth table.

Number of rows = [tex]2^{n}[/tex]

Where n = Number of variables

Here given number of variables are 5.

n = 5

  [tex]2^{n}[/tex] = [tex]2^{5}[/tex]

= 32

Therefore 32 rows are needed in the truth table.

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Time in Line to Buy Groceries is Quantitative-Discrete type of data. So the option C is correct.

We can observe data in a straightforward integer format or monitor quantitative discrete data in a real line at regular intervals.

We need to utilize an integer time point, which cannot be a decimal, to keep track of time while standing in line for groceries. It cannot be delivered in 2.45 days because a grocery store is unable to provide a delivery schedule in fractions.

The correct solution is therefore quantitative discrete.

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The complete question is:

Identify the type of data that would be used to describe a response.

Time in Line to Buy Groceries

A. Qualitative (Categorical)

B. Quantitative - Continuous

C. Quantitative - Discrete