Select the correct answer.
Given: p || q, and r || s.

Linear pair theorem that is angle 1 is supplementary to angle 2 moves down to angle 2 equals angle 6. As for parallel lines cut by a transversal, corresponding angles are congruent. This moves down to blank box with question mark.

Prove: ∠1 and ∠14 are supplementary angles.

Two vertical parallel lines p and q runs through two horizontal parallel lines r and s to form 16 angles numbered from 1 to 16.

What is the next step in the proof? Choose the most logical approach.

A.
Statement: ∠6 ≅ ∠14
Reason: For parallel lines cut by a transversal, corresponding angles are congruent.

B.
Statement: ∠6 ≅ ∠7
Reason: Vertical Angles Theorem

C.
Statement: ∠6 and ∠5 are supplementary.
Reason: Linear Pair Theorem

D.
Statement: m∠6 + m∠8

Reason: angle addition

Answer: -5x^2 + 2

Step-by-step explanation:

Answer:

It should be 42.4

In mathematics, a sequence is an ordered list of elements, often denoted by brackets or parentheses.

The term "a sequence of length n" refers to a sequence that contains a specific number of elements, where the number of elements is denoted by "n."

When the domain of a function is the set of natural numbers (N), it is called an infinite sequence. An infinite sequence can be thought of as an ordered list that continues indefinitely.

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Answer: Mind showing the picture?

Step-by-step explanation:

55-15=40

40÷10=4

There is one adult and 4 children going to the movies

Answer:

Step-by-step explanation:

3

Answer:

0.07 ; 0.65 ; 0.00064339296875 ; 3.02 * 10^-12

Step-by-step explanation:

Given :

Number of monkeys, n1 = 10

Probability of fall, off ; p(m) = 35% = 0.35

Number of kangaroos, n2 = 5

Probability of fall, off : p(k) = 20% = 0.2

1.) A monkey and kangaroo falls off;

p(m) * p(k) = 0.35 * 0.2 = 0.07

2.) probability that monkey will not fall off;

1 - p(m) = 1 - 0.35 = 0.65

3.) probability that a monkey falls off every one of seven nights :

P(m) = 0.35 ; for 7 nights ;

0.35 *0.35 * 0.35 * 0.35 * 0.35 * 0.35 * 0.35 = 0.35^7 = 0.00064339296875

4.)

P(x ≥ 1) = p(1) + p(2) +... + p(10)

Using binomial probability calculator :

n = 7*10 = 70 ; p = 0.35

P(x ≥ 1) = 70C1 * 0.35^1 * 0.65^69 = 3.02 * 10^-12

Answer:

3/5 x +1 and 7.5 x -7

Step-by-step explanation:

any equation in the form y= mx+b is linear the other 2 in this question are not in this form thus they are not linear

In the given function H(p) = p/5 + 15, the independent variable is "p" ,

The independent variable in this function is denoted by "p." The independent variable can also be referred to as the input variable, which means that it is the value that is inputted into the function to produce an output. In this specific function, "p" represents the price of a good or service.

It is important to distinguish between the independent and dependent variables in a function. The dependent variable is denoted by "H(p)" in this case, and it is the output of the function. The value of the dependent variable is determined by the independent variable. In this function, "H(p)" represents the total cost of the good or service, which is dependent on the price "p." p is the input variable representing the price of the good or service.

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Answer:

Sister's age: 4

Brother's age: 12

Answer:

\(54\)

Step-by-step explanation:

Formula for average A of two numbers m and n is:

\(A=\frac{m+n}{2}\)

Substitute the value m=36 and n=72

\(A=\frac{36+72}{2}\)

This is equivalent to:

\(A=\frac{108}{2}\)

The average is:

\(A=54\)

2304 times 3 goes into 6912 and gives the remainder as 0.

The numerator number in the given division number 6912 by 3 is known as a dividend, and the denominator number is known as a divisor. As a result, 6912 is the dividend number and 3 is the divisor number.

Division is one of the four fundamental mathematical operations, along with addition, subtraction, and multiplication. Division is defined as the splitting of a large group into smaller groups so that each group has an equal number of items. In mathematics, it is an operation used for equal grouping and equal sharing.

Division is a basic arithmetic operation in which a larger number is divided into smaller groups with the same number of items. For example, how many total groups will be formed if 30 students must be divided into groups of 5 students for a sporting event? Such problems are easily solved by using the division operation. Here, we must divide 30 by 5. 30 5 = 6 will be the result. As a result, there will be six groups of five students each.

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The value of c is 0 guaranteed by the Mean Value Theorem for Integrals for the function 2x+1 on the interval [3,6].

Mean value theorem states, roughly, that for a given planar arc between two endpoints, there is at least one point at which the tangent to the arc is parallel to the secant through its endpoints.

Given.

Function is 2x+1 on the interval [3,6]

f(x)=2x+1

f(x) continuous on [3, 6] and differentiable on (3, 6) so the MVT applies here.

f(3)=7

f(6)=13

Average rate of change of f on [3,6]

= (13-7) / (6-3) = 6/3=2

To find the c-value guaranteed by the MVT, such that the instantaneous rate of change when x = c is 2, we differentiate, set f'(x) = 2, and solve:

f'(x) = 2 and x = 1.

c = 0 is the only c-value in the interval at which the instantaneous rate of change = the average rate of change.

Hence, the value of c is 0 guaranteed by the Mean Value Theorem for Integrals for the function 2x+1 on the interval [3,6].

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Answer:

\(\Large\boxed{\sf x = 19.2}\)

Step-by-step explanation:

Here a right angled triangle is given to us and we need to find out the value of x . The measure of one of the sides is 24 and one of the acute angle is 53° .

So here we may use the ratio of sine as ,

\(\sf\qquad\longrightarrow sin\theta =\dfrac{p}{h} \\\\\)

• On substituting the respective values ,

\(\sf\qquad\longrightarrow sin53^\circ =\dfrac{x}{24}\\\\\)

Substitute the value of sin 53° = 4/5 ,

\(\sf\qquad\longrightarrow \dfrac{4}{5}=\dfrac{x}{24} \\\\\)

Cross multiply ,

\(\sf\qquad\longrightarrow x =\dfrac{24*4}{5} \\\\\)

Simplify,

\(\sf\qquad\longrightarrow \frak{\pink{x =19.2}} \\\\\)

\(\rule{200}4\)

Here we use trigonometric ratios

\(\\ \rm\hookrightarrow sin\theta=\dfrac{Perpendicular}{Hypotenuse}\)

\(\\ \rm\hookrightarrow sin53=\dfrac{x}{24}\)

\(\\ \rm\hookrightarrow 0.8(24)=x\)

\(\\ \rm\hookrightarrow x=19.2\)

The net pay is the amount left after taxes and deductions have been removed from the gross pay.

Her monthly gross pay is: $4111.93

The deductions are:

\(\mathbf{FIT = \$102}\)

\(\mathbf{SIT = 3.2\%}\)

\(\mathbf{CIT = 1.8\%}\)

Let her gross pay be x.

So, we have:

\(\mathbf{Net = x - FIT - x \times SIT - x \times CIT}\)

So, we have:

\(\mathbf{3804.33 = x - 102 - x \times 3.2\%- x \times 1.8\%}\)

Express percentage as decimals

\(\mathbf{3804.33 = x - 102 - x \times 0.032- x \times 0.018}\)

\(\mathbf{3804.33 = x - 102 - 0.032x - 0.018x}\)

Add 102 to both sides

\(\mathbf{3906.33 = x - 0.032x - 0.018x}\)

\(\mathbf{3906.33 = 0.95x}\)

Divide both sides by 0.95

\(\mathbf{4111.93 = x}\)

Rewrite as:

\(\mathbf{x = 4111.93 }\)

Hence, her monthly gross pay is: $4111.93

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Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

The exact value of the given expression of tan 15 ° can be found to be 1 / √3.

When given a tangent degree, you can find the exact value by relating it to the Sine and Cosine values as shown below :

tan ( x ) = sin ( x ) / cos ( x )

Given that x is 15 degrees, we have :

tan ( 15 ) = sin ( 15 ) / cos ( 15 )

The values of sine and cosine :

sin(30) = 1/2

cos(30) = √3/2

This means the relation is:

tan ( 15 ) = sin ( 15 ) / cos ( 15)

= ( 1 / 2 ) / (√3 / 2 )

= 1 / √3

=  0.2679

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Solve for x.

2x + 9 = 33

2x = 24

x = 12

A. x = 7.5

B. x = 12

C. x = 21

D. x = 84

Answer:

\(2x + 9 = 33 \\ 2x = 33 - 9 \\ 2x = 24 \\ x = \frac{24}{2} \\ x = 12\)

Answer: An = 114 + (n - 1)-6

Step-by-step explanation:

Per 5 weeks there is  reduction of 30 patients. Divide by the common factor (5) and you see that per 1 week, there is a reduction of 6 patients. Going back in time to see what the first term was, you can create a explicit formula for this  function.

Hope this helps. Brainliest would be nice!

Answer:

f(x) = −6x + 120

Step-by-step explanation:

I JUST TOOK THE TEST

Answer:

9 integers between 2023 and 5757 that have 12, 20, and 28 as factors.

Step-by-step explanation:

An integer that has 12, 20, and 28 as factors must be divisible by the least common multiple (LCM) of these numbers. The LCM of 12, 20, and 28 is 420. So we need to find the number of integers between 2023 and 5757 that are divisible by 420.

The first integer greater than or equal to 2023 that is divisible by 420 is 5 * 420 = 2100. The last integer less than or equal to 5757 that is divisible by 420 is 13 * 420 = 5460. So the integers between 2023 and 5757 that are divisible by 420 are 2100, 2520, ..., 5460. This is an arithmetic sequence with a common difference of 420.

The number of terms in this sequence can be found using the formula for the nth term of an arithmetic sequence: an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, d is the common difference, and n is the number of terms. Substituting the values for this sequence, we get:

5460 = 2100 + (n - 1)420 3360 = (n - 1)420 n - 1 = 8 n = 9

So there are 9 integers between 2023 and 5757 that have 12, 20, and 28 as factors.

Answer:

6x +4 where x is amount for standard call

Step-by-step explanation:

Answer:

4c+6

Step-by-step explanation:

Right on my test

Answer: 21:9 and 42:18

Step-by-step explanation:

14:6 at its most basic form is 7:3, so find anything that could be equal to this if a number is multiplied on both sides.

21:9 is our simplified ratio multiplied by 3 on both sides.

42:18 is our simplified ratio multiplied by 6 on both sides.

But, the final ratio doesn't work, because 7 and 3 respectively cannot multiply to 13 and 8 with the same value.

The number of total bears counted in 2002 will be: A. 1060 bears.

To determine the total bear estimate, we will use the mark-recapture formula. In this formula, we equate the number of the population to MC/R where:

M = Number marked initially

C = Number captured in the second sample

R = The recaptured number

Also, R/C = M/N

For the given problem,

M = 2008

C = 38

R = 72

So, N =  2008 * 38/72

= 1059 approximately 1060 bears.

So, the bear population will amount to 1060.

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Answer:

Answer is explained in the photo

Answer:

2

Step-by-step explanation:

1+1=2

Thank you for coming to my TED Talk

Answer:

22

Step-by-step explanation:

Answer:

A = 2184 cm²

Step-by-step explanation:

the area (A) of the figure is calculated as

A = \(\frac{1}{2}\) h(b₁ + b₂)

where h is the perpendicular height between the bases b₁ and b₂

here h = 42 , b₁ = 52 , b₂ = 52 , then

A = \(\frac{1}{2}\) × 42 × (52 + 52) = 21 × 104 = 2184 cm²

Answer:

A = 2184 cm2

Step-by-step explanation:

Area of a parallelogram:

\(A = b*h\)

\(b=52,h=42\)

\(A=(42)(52)=2184cm^{2}\)

Hope this helps.

Answer:

Step-by-step explanation:

Step 1:First Make 3/4 and 5/6 into like fractions.Find the L.C.M of 4 and  

            6,which is 12.

            3*3/4*3=9/12

             5*2/6*2=10/12

Step 2:Subtract 9/12 from 10/12,which is 1/12.

Answer:

x < -3 or x > 2

Step-by-step explanation:

x² + x - 6 > 0

Convert the inequality to an equation.

x² + x - 6 = 0

Factor using the AC method and get:

(x - 2) (x + 3) = 0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x - 2 = 0

x = 2

x + 3 = 0

x = -3

So, the solution is x < -3 or x > 2

Answer:

  $142.32, profit on sale of the policy

Step-by-step explanation:

You want to know the expected value of a $280,000 life insurance policy sold for $270, if the probability the insured will live for the year is 0.999544.

The insurance company expects to have to pay the $280,000 death benefit for 0.000456 of the policies issued. That means their expected payout on any one policy is ...

  0.000456 × $280,000 = $127.68

The company gets a premium of $270 for the policy, so the expected value of the policy to the company is ...

  $270 -127.68 = $142.32

The expected value of the policy to the company is $142.32.

This represents its profit from sale of the policy.

__

Additional comment

Of course, the company has expenses related to the policy, perhaps including a commission to the agent selling it, and expenses related to handling claims. That is to say that not all of the difference between the premium and the average death benefit is actually profit. It is what might be called "contribution margin."

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