Select the equivalent expression. ma") =? 62 Cou Choose 1 answer: 62 А Sol a 20 b B ( Line 1 С a12.68

Answer: Yes, it is a function

Step-by-step explanation:

Answer:

ACD

Step-by-step explanation:

PLZZ mark brainliest!!

Answer:

D i think i havent done this in a while

Step-by-step explanation:

Step-by-step explanation:

31 + 6x + x + 16 = 180

7x + 47 = 180

7x = 180 - 47

x = 133/7

x = 19

Answer:

6/7

Find a number that goes into both numbers ie 2 which goes in 6 and 7 times respectively

Answer:

144

Step-by-step explanation:

divide 50 by 3 and then multiply by 9

That we subtract \(2 \times $P(A_1$ and A_2$ and A3_3)\) because this prοbability was cοunted twice in the intersectiοns. Plugging in the given prοbabilities, we get: \(\rm P(X=2) = 0.01 + 0.01 + 0.06 - 2 \times 0.01 = 0.06\).

Prοbability is a measure οf the likelihοοd οf an event οccurring. It is a number between 0 and 1, where 0 means the event is impοssible and 1 means the event is certain tο happen.

The calculatiοn fοr P(X=0) is cοrrect. Hοwever, the calculatiοn fοr P(X=1) is nοt cοrrect.

Tο calculate P(X=1), we need tο cοnsider the prοbability that exactly οne defect is present. This can happen in three ways: A1 οnly, A2 οnly, οr A3 οnly. Therefοre, we can calculate:

\(\rm P(X=1) = P(A1) - P(A_1\ and\ A_2) - P(A_1 \ and\ A_3) + P(A_2) - P(A_2\ and\ A_3)} \rm + P(A_3) - P(A_1 \ and\ A_3)}\)

Plugging in the given prοbabilities, we get:

\($$P(X=1) = 0.17 - 0.01 - 0.06 + 0.07 - 0.01 + 0.13 - 0.06 = 0.13\)

Tο calculate P(X=2), we need tο cοnsider the prοbability that exactly twο defects are present. This can happen in three ways: A1 and A2, A2 and A3, οr A1 and A3. Therefοre, we can calculate:

\($$ P(X=2) = P(A_1 $and A_2) + $P(A_2 $ and A_3) + $P(A_1 $ and A_3) - 2$ \times $P(A_1 $ and A_2 $ and A_3)$$\)

Therefοre, that we subtract \(2 \times $P(A_1$ and A_2$ and A3_3)\) because this prοbability was cοunted twice in the intersectiοns. Plugging in the given prοbabilities, we get:

\($$ P(X=2) = 0.01 + 0.01 + 0.06 - 2$ \times 0.01 = 0.06.\)

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Answer:

Lucy has ridden 25% of the course so far. This means she has completed a quarter of the total distance.

Step-by-step explanation:

To determine the percentage of the course Lucy has ridden so far, we can use the following formula:

Percentage = (Distance ridden / Total distance) * 100

Given that the total distance of the bike course is 88 miles and Lucy has

ridden 22 miles, we can substitute these values into the formula:

Percentage = (22 miles / 88 miles) * 100

Simplifying the equation:

Percentage = (1/4) * 100

Percentage = 25

Therefore, Lucy has ridden 25% of the course so far. This means she has completed a quarter of the total distance.

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Answer:

2160 square units

Step-by-step explanation:

Given data

Radius= 6 units

Angle= 120°

Area of the sector is given as

Area of sector= r^2* ∅/2

Area of sector= 6^2*120/2

Area of sector= 36*60

Area of sector= 2160 square units

A. x² - 200 gives the amount of money the interior designer will make decorating the house as a function of hours he works.

B. He will earn 1,875 if he works for 50 hours.

C. The difference quotient is equal to 2x.

The solution has been obtained by using functions.

What is a function?

Function is a kind of relation, or rule, that associates a single input with a single, predetermined output.

We are given two functions

f(x) = 49x² – 200

which represents the amount of money he earns per room decorated

g(x) = (1/7)x

which represents the number of rooms the interior designer decorates

A. The amount of money the interior designer will make decorating the house as a function of hours he works will be given by evaluating f(x) in g(x).

So,

f(g(x)) = 49((1/7)x)² – 200

f(g(x)) = x² - 200

B. Since, the house requires 50 hours of work, this means that x = 50.

Substituting this in f(g(x)) = x² - 200, we get

f(g(50)) = 50² - 200

f(g(50)) = 1,875

C. The difference quotient for the function is as follows

\(\lim_{h \to \ 0}\frac{f(x+h) -f(x)}{h}\)

\(\lim_{h \to \ 0}\frac{(x+h)^{2}-200-x^{2}+200}{h}\)

\(\lim_{h \to \ 0}\frac{x^{2} + 2xh + h^{2}-x^{2}}{h}\)

= 2x

Hence, x² - 200 gives the amount of money and he earns 1,875 if he works for 50 hours. The difference quotient is equal to 2x.

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Answer

925 students brought their lunch.

Explanation

First let's rewrite the equation.

You know that "of" means multiply and "is" means equal.

Okay, so let's break it down.

The question says, "At your school, 74% of students brought their lunch at the cafeteria. There are 1250 students in the school."

This means that 74% of 1250 students brought their lunch at the cafeteria.

You are trying to find how many students brought their lunch. This will be x.

So the equation would be this.

74% × 1250 = x

74% is 0.74.

0.74 × 1250 = x

0.74 × 1250 = 925

So 925 students brought their lunch.

Answer:

6 groups

Step-by-step explanation:

Division: 30/5 = 6

Multiplicatio: 6 times 5 = 30

hope it helps, have a nice day~

Answer:

x = - \(\frac{3}{4}\) , x = 1

Step-by-step explanation:

4x² = x + 3 ← subtract x + 3 from both sides

4x² - x - 3 = 0 ← in standard form

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 4 × - 3 = - 12 and sum = - 1

the factors are - 4 and + 3

use these factors to split the x- term

4x² - 4x + 3x - 3 = 0 ( factor the first/second and third/fourth terms )

4x(x - 1) + 3(x - 1) = 0 ← factor out (x - 1) from each term

(x - 1)(4x + 3) = 0 ← in factored form

equate each factor to zero and solve for x

4x + 3 = 0 ( subtract 3 from each side )

4x = - 3 ( divide both sides by 4 )

x = - \(\frac{3}{4}\)

x - 1 = 0 ( add 1 to both sides )

x = 1

solutions are x = - \(\frac{3}{4}\) , x = 1

The Correl function is the easiest way to for calculating correlation between two variables.

What is correlation ?

correlation can be defined as the measure of relation between two variables.

In case you want to measure of degree the power of a dating between two variables, you can accomplish that through using a complicated or on line calculator. you could additionally placed your mathematical abilities to apply and calculate it through hand. while calculating a correlation coefficient via hand.

To find correlation using data points are as follows  :

Determine your data sets.

Calculate the standardized value for your x variables.

Calculate the standardized value for your y variables.

Multiply and find the sum.

Divide the sum and determine the correlation coefficient.

Hence, The Correl function is the easiest way to for calculating correlation between two variables.

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The distance to cover on the next training day is 29/36 mile

Sarah trained longer by 1/4 miles

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

Total distance = 7 1/4 miles

Days = 9

So, we have

Distance = (7 1/4)/9

Evaluate

Distance = 29/36

Here, we have

The dot plot

The total distance here is

Total = 1/4 * 2 + 1/2 * 1 + 1 * 5

Total = 6

7 1/4 miles is greater than 6 miles, by 1/4 miles

Hence, Sarah trained longer

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Answer:

When two springs are compressed by the same amount, the spring with a higher spring constant will have more potential energy. The potential energy stored in a spring is given by the equation:

U = (1/2)kx^2

where U is the potential energy, k is the spring constant, and x is the displacement from the equilibrium position.

If we compress two springs by the same amount, x, then the potential energy stored in each spring will be:

U1 = (1/2)k1x^2

U2 = (1/2)k2x^2

where k1 and k2 are the spring constants of the first and second spring, respectively.

Since x is constant for both springs, we can compare U1 and U2 by comparing k1 and k2. The spring with a higher spring constant will have more potential energy because it requires more force to compress it by the same amount.

To justify this answer further, we can use Hooke's Law which states that the force required to compress or stretch a spring is proportional to its spring constant. Therefore, a spring with a higher spring constant will require more force to compress it by the same amount than a spring with a lower spring constant. This means that more work is done on the higher spring constant spring during compression, resulting in more potential energy being stored in it.

The theoretical probability of spinning red is given as follows:

1/3.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For the spinner in this problem, 2 out of 6 regions are red, hence the theoretical probability is given as follows:

2/6 = 1/3.

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The angles of the triangle are 125 degrees, 20 degrees, and 35 degrees.

A triangle is a closed geometric shape with three sides, three angles, and three line segments. Three non-collinear points are joined by line segments to create the simplest polygon, which has three non-collinear points.

Triangles can be categorized according to the size of their sides and angles. Triangles can be categorized as equilateral (all sides are equal in length), isosceles (both sides are equal in length), or scalene based on their sides (all sides are different in length). Triangles can be categorized as acute (all angles are less than 90 degrees), obtuse (one angle is greater than 90 degrees), or right (one angle is greater than 90 degrees) (one angle is exactly 90 degrees).

In any triangle, the sum of the three interior angles is always 180 degrees. Therefore, we can write:

a + b + c = 180

Substituting the given values, we get:

(6x-1) + 20 + (x+14) = 180

Simplifying and solving for x, we get:

7x + 33 = 180

7x = 147

x = 21

Now that we have the value of x, we can substitute it back into the expressions for the angles to find their values:

angle a = (6x-1) = (6*21-1) = 125 degrees

angle b = 20 degrees

angle c = (x+14) = (21+14) = 35 degrees

Therefore, the angles of the triangle are 125 degrees, 20 degrees, and 35 degrees.

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let's firstly convert the mixed fraction to improper fraction and proceed from there.

\(\stackrel{mixed}{2\frac{1}{4}}\implies \cfrac{2\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{9}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{9}{4}\div \left(\cfrac{3}{8}\div \cfrac{1}{2} \right)\implies \cfrac{9}{4}\div \left(\cfrac{3}{8}\cdot \cfrac{2}{1} \right)\implies \cfrac{9}{4}\div \left(\cfrac{3}{4} \right) \\\\\\ \cfrac{9}{4}\cdot \left(\cfrac{4}{3} \right)\implies \cfrac{9}{3}\cdot \cfrac{4}{4}\implies 3\cdot 1\implies \text{\LARGE 3}\)

The series is given to be:

The nth term is given to be 1704.

The formula to calculate the nth term is given to be:

where a₁ is the first term and d is the common difference.

The sum of the sequence can be calculated using the formula:

From the series, we have:

Therefore, the sum of the nth term can be calculated as shown below:

Using the quadratic formula to solve, we have:

Since the number cannot be negative or a decimal/fraction, the term number will be 24.

Answer:

72

Step-by-step explanation:

replace the variable of x with 6 in the equation.

Answer:

There are 4 treatments

Step-by-step explanation:

In this study, there are four treatments. Each sample from 1 to 3 was subjected to each treatments which in this case are the methods; Lind's Method, Szabo's Method, Carl's Method and Manley's Method.

Thus, the methods in this study are the treatments the samples are subjected to.

Answer:

No {false}

Step-by-step explanation:

All congruent figures are similar, but not all similar figures are congruent. (It is like a theory, don't forget it)

Answer:

3.5

Step-by-step explanation:

Answer:

the answer is 0.2857142857.

Hope that helps

Answer: you just need to do A=bh

Step-by-step explanation:

So you need to multiply the base by the height

Answer:

\(\frac{-11}{8}\)

Step-by-step explanation:

1) To find tan m = 1/2 on a calculator, you need to take the inverse to find m.

\(tan^{-1}\)(1/2) is about 26°.

So, m = 26°

2) To find tan n = -6 on a calculator, you also need to take the inverse.

\(tan^{-1}\)(-6) is -80, which is positive 280°. (360° - 80° = 280°)

n = 280°

3) SO, the exact value of tan(m + n) would be tan(26° + 280°), which is tan(306°).

tan(306°) is about -1.376.

The closest answer to -1.376 is the third answer choice, which is -11/8.

Answer:

y = 1/2x + 4

Step-by-step explanation:

Answer:

y = 1/2x + 4

Step-by-step explanation:

To find the 1/2 you can see that is is between the box, and cannot be negative because it is going up not down. To find y-interceptive, you start where the line starts and until you hit a y value; which is 4.

Answer:

Step-by-step explanation:

Given that:

A small-business Web site contains 100 pages and 60%, 30%, and 10%  of the pages contain low, moderate, and high graphic content, respectively.

. A sample of four pages is selected without replacement,

Let  X and Y denote the number of pages with moderate and high graphics output in the sample

We are meant to determine

a)  \(f_{XY}(x, y)\)  from the given data in the question;

However; the probability mass function can be expressed via the relation:

\(f_{XY}(x,y) = \dfrac{(^{30} _x ) ( ^{10} _y ) (^{60} _ {4-x-y} ) }{ ( ^{100}_4)}\)

We can now have a table shown as :

\(X|Y\)                0           1               2              3              4          Total    \(f_X(x)\)

0              0.1244     0.0873     0.02031    0.0018     0.0001   0.234

1               0.2618     0.13542   0.02066    0.00092    0         0.419

2              0.1964     0.0666    0.00499       0              0         0.268

3              0.0621     0.01035     0                 0              0         0.073

4              0.0069       0              0                0              0          0.007

Total \(F_Y(y)\)   0.6516   0.2996   0.0460      0.0028  0.0001    1

b) \(f_X(x)\)

The marginal distribution definition of \(f_X(x)\)\(= P(X=x)\)

\(f_X(x)\) \(= \sum P(X=x, Y=y)\)

From the table above ; the corresponding values of \(f_X(x)\)  are :

X           0           1         2          3           4

\(f_X(x)\)    0.234   0.419  0.268   0.073    0.007

( since \(f_X(x)\) represent the vertical column)

c) E(X)

By using the expression \(E(x) = \sum ^4 _{x= 0} x f_X(x)\)

we have:

E(X) = \(0*0.234+1*0.419+ 2*0.268+3*0.073+4*0.007\)

E(X) = 0 + 0.419 + 0.536 + 0.218 + 0.028

E(X) = 1.202

d) fyß(y)

Using the thesis of conditional Probability; we have :

\(P(A|B) = \dfrac{ P(A,B) }{ P(B) }\)

The conditional probability for the mass function is then:

\(f_{Y|X=3}(y) = \dfrac{f_{XY}(3,y)}{f_{X}(x)}\)

where;

\(f_X(3) = 0.0725\)

values of \(f_{XY} (3,y)\) for every y ∈ (0,1,2,3,4)

Therefore; the mass function is:

\(Y|{_X_3}:\left[\begin{array}{ccccc}0&1&2&3&4\\0.857&0.143&0&0&0\\ \end{array}\right]\)

e) E(Y | X = 3)

By using the expression \(E(Y|X=3) = \sum ^4 _{y= 0} y f_{y \beta} \ (y|x)\)

we have:

⇒ \(0 * 0.857 + 1*0.143 +0 +0+0\)

= 0.143

The value of E(Y | X = 3) = 0.143

g) Are X and Y independent?

To Check if X and Y independent; Let assume if \(f_{XY}(x,y) = f_X(x)f_{Y}(y)\) ; then we can say that X and Y are independent.

From the above previous table :

\(f_{(XY)} (0.4) = 0.0001\)

\(f_X (0)\) = 0.1244 + 0.087268+0.02031+ 0.001836 + 0.0001

\(f_X (0)\)  = 0.234

\(f_X (4)=0.0001 +0+0 \\ \\ = 0.001\)

\(f_{X}(0) f_Y(4) = 0.234*0.0001\)

\(f_{X}(0) f_Y(4) = 0.00002\)

We conclude that \(f_{(XY)} (0.4) \neq f_X(0) f_Y(y)\); As such X and Y are said to be  non - independent.