km bisects angle jkn, kn bisectss angle mkl, prove angle jkm = angle nkl

Explanation:

You have a right triangle with legs of 11 and 60. The hypotenuse is unknown.

Use the pythagorean theorem to find the hypotenuse.

\(a^2 + b^2 = c^2\\\\11^2 + 60^2 = c^2\\\\121 + 3600 = c^2\\\\3721 = c^2\\\\c^2 = 3721\\\\c = \sqrt{3721}\\\\c = 61\\\\\)

The ramp is exactly 61 inches long.

Answer:

68/100=17/25

Step-by-step explanation:

Since there are 2 digits in 68, the very last digit is the "100th" decimal place. So we can just say that 68 is the same as 68/100. terms by dividing both the numerator and denominator by 4. :D

Answer:

0.68=17/25

Step-by-step explanation:

first, turn it into a regular number which is as simple as dividing by 100, then you want to find a fraction which you first convert 0.68 into 68/100 and simplifying it gives you 17/25.

Answer:

It would take Samantha 6 hours to drive 105 miles.

Step-by-step explanation:

This question can be solved by proportions.

After 4 hours she had traveled 70 miles.

This means that she travels 70/4 = 17.5 miles per hour.

How many hours would it take Samantha to drive 105 miles?

17.5 miles per hour, so for 105 miles:

105/17.5 = 6

It would take Samantha 6 hours to drive 105 miles.

Answer:

C, (–7.5, –5)

Step-by-step explanation:

Answer:

---------------------------------------

Let the cost of the meal be x.

Adding a tip of 19%:

Answer:

Wyatt should multiply with 1.19.

Step-by-step explanation:

Forming the expression,

→ 1 + (19% of 1)

Now the required number is,

→ 1 + (19% of 1)

→ 1 + ((19/100) × 1)

→ 1 + (19/100)

→ 1 + 0.19 = 1.19

Hence, required number is 1.19.

The correct answer is,

C. 60(x - 3) = 45x.

This equation is based on the information that the 45 expensive wood costs $3.00 more than the 60 cheap wood. In other words, if the price of the 60 cheap wood is x, the price of the 45 expensive wood is x + 3.

Since,  Algebra involves working with numbers, equations, and variables to solve real-world problems and understand abstract relationships.

Now, To solve this equation, we must use algebra and solve for x.

First, we multiply both sides of the equation by 4/5. This gives us:

48x + 36 = 45x

-36 = 3x

Finally, we divide left side of the equation by 3, giving us the final solution:

x = -12

Therefore, the price of the 60 cheap wood is $12, and the price of the 45 expensive wood is $15.

that is, 60 (x - 3) = 45x

This equation shows the correct relationship between the two types of wood that the contractor purchased.

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Answer:

22

Step-by-step explanation:

f(x)=9

g(x)=13

13+9=22

Answer:

3 hours

Step-by-step explanation:

To solve this we can first find out how many minutes is 1/5th of an hour which is: 12 mins.

Now we know it will take 15 sets of 12 minutes to water the full lawn so we can multiply 15*12 to get our answer.

15*12 = 180

Now we divide 180 (minutes) by 60 (minutes) to find out how many hours that is:

180/60 = 3 hours

Hope this helped! If possible please leave a thanks so I can continue to help out others :),

comment if you have any questions.

Answer:

3 hours

Step-by-step explanation:

1/5 of an hour is 12 minutes.

So 1/15 of a lawn takes 12 minutes to water.

Next you multiply 15, how many times 1/15 of a lawn is watered, and multiply it by 12, the time it takes to water 1/15 of a lawn.

So you would get 180 minutes.

Finally you convert it to hours. To do this, you divide it by 60, how many minutes in and hour, and should get an answer of 3 hours.

Hope this helps!

Answer:

angle a is 110

angle B is 110

angle C is 70

Answer:

684π

Step-by-step explanation:

It is two parts: half of a sphere and one cylinder.

Sphere volume formula: V=4/3πR³, r=12/2=6, r³=216

                                      v=4/3π216

                                      v=288π

Half of sphere:  288π/2=144π

Cylinder volume: V=πr²h, r=12/2=6, r²=36, h=15,

                           V=π*36*15=540π

So, total is 144π+540π=684π

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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The adjusted bank balance after reconciling is Br. 5,224.42.

To prepare the bank reconciliation, we have to analyze the differences between the bank statement balance and the company's ledger balance.

Details

Bank statement balance of Br. 4,964.47 at July 31.

Add: Deposit made after banking hours Br. 410.90

New balance: Br. 5,375.37.

Deduct Erroneously charged check of Br. 79

New balance Br. 5,296.37.

Deduct Outstanding checks:

Check No. 801 of Br. 100.00 (issued on June 15).

Check No. 888 of Br. 10.25 (issued on July 24).

Check No. 890 of Br. 294.50 (issued on July 27).

Check No. 891 of Br. 205.00 (issued on July 30).

Total outstanding checks: Br. 609.75.

New balance: Br. 4,686.62.

Deduct: Incorrectly charged amount of Br. 120.

Add: Correct amount of Br. 210.

Add: Proceeds from the collection Br. 500.

Add: Interest earned on the account balance  Br. 24.75.

Deduct: Returned check of Br. 10

Deduct: Fee charged by the bank for handling the collection Br. 5.00.

Deduct: Check from customer John Br. 50.25.

Deduct the service charge by the bank for the month of July of Br. 12.70.

New balance: Br. 5,224.42.

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From the question, you can see that there is an increase in the number of population as the year increses. The exponential equation to represent this scenario is expressed as;

P(t) = P0e^kt

k is the constant of variation

P0 is the initial population

P(t) is the population after some time t

From the question;

We are given P0 =500

If in 1996, about 3550 participated in the Summer Olympics in Atlanta, this means;

at t = 11 (number of years between 1985 and 1996), P(t) = 3550

Substitute into the formula;

3550 = 500e^11k

find k;

Divide both sides by 500

3550/500 = 500e^11k/500

7.1 = e^11k

Apply ln to both sides

ln 7.1 = lne^11k

ln 7.1 = 11k

k = ln 7.1/11

k = 1.9601/11

k = 0.17819

k = 0.18

The resulting exponential equation will be;

P(t) = 500e^0.18t

The correct option is A. k = 0,18; P(t) = 500e^0.18t

Answer: Hello the options related to your question is missing attached below are the missing options.

A.) The probabilities of the RVs may be equal

B.) The sum of the probabilities of the RVs exceed 1

C.) This is an impossible occurrence

D.) The probabilities of the RVs must be equal

E.) None of the above

answer:

The probabilities of the RVs may be equal ( A )

Step-by-step explanation:

Given that the value of the  population mean and the value of probability mass function of a set of random variables are similar

For the Random Variables : 100,200,300,400

The Probability mass function of RV = ( 100 + 200 + 300 + 400 ) / 4

Hence  The probabilities of the RVs may be equal

The probability that a point chosen at random lies on the shaded region is given as follows:

4/7.

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.

The area of the shaded region in this problem is given as follows:

4² = 16.

The total area of the figure is given as follows:

16 + 2 x 1/2 x 3 x 4 = 28.

Hence the probability is given as follows:

16/28 = 4/7.

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The perimeter of the given shape as represented in the task content is; 29 cm.

It follows from the task content that the perimeter of the given shape on the centimeter grid as required is to be determined.

Since each grid line has 1cm as it's length;

The perimeter of the shape is the sum of all side lengths of the shape;

Perimeter, P = 6+2+3+2+2+1+3+2+2+2+2+1

P = 29 cm

Hence, the perimeter of the shape is; 29 cm.

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The quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).

A division is a process of splitting a specific amount into equal parts.

We have to find 3x³-2x²+7x+9 divided by x²-3x

3x³-2x²+7x+9 is the dividend and x²-3x is the divisor.

The steps to solve this are given below.

Step 1: Take the first digit of the dividend from the left. Check if this digit is greater than or equal to the divisor.

Step 2: Then divide it by the divisor and write the answer on top as the quotient.

Step 3: Subtract the result from the digit and write the difference below.

Step 4: Bring down the next digit of the dividend (if present).

Step 5: Repeat the same process.

Hence, the quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).

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Answer:

(2a^3a^4)^5 simplifies to 32a^35.

Step-by-step explanation:

To simplify (2a^3a^4)^5, we can use the properties of exponents which states that when we raise a power to another power, we can multiply the exponents. Therefore, we can rewrite the expression as:

(2a^3a^4)^5 = 2^5 * (a^3a^4)^5

Next, we can simplify the expression inside the parentheses by multiplying the exponents:

a^3a^4 = a^(3+4) = a^7

Substituting this into our expression, we get:

(2a^3a^4)^5 = 2^5 * (a^3a^4)^5 = 2^5 * a^35

Finally, we can simplify this expression by using the property of exponents that states that when we multiply two powers with the same base, we can add their exponents. Therefore, we can rewrite the expression as:

2^5 * a^35 = 32a^35

Therefore, (2a^3a^4)^5 simplifies to 32a^35.

The required measure of the angle ∠MON is given as 87°.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

Here,
For the given circle, the measure of arc MN is given in the form of an angle of 87° which consists of an angle MNO, so the measure of the section is equal to MON i.e.
∠MON = 87°

Thus, the required measure of the angle ∠MON is given as 87°.

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We can solve this by substitution method.

Look at the second equation. If we rearrange to find 7x, we can substitute in the value into the first equation.

\(5y-7x=12\)

\(5y-7x-12=0\)

\(5y-12=7x\)

Therefore, \(7x=5y-12\)

Now replace the 7x in the first equation with 5y - 12:

\(2y+7x=-5\) (substitute in 7x = 5y - 12)

\(2y+(5y-12)=-5\)

\(7y-12=-5\)

\(7y=7\)

\(y=1\)

Now that we know y, we can find x by substituting in y = 1 into any equation we want. I will use the equation: 7x = 5y - 12

\(7x=5y-12\) (substitute in y = 1)

\(7x=5(1) -12\)

\(5x=5-12\)

\(7x=-7\)

\(x=-1\)

__________________________________________________________

Answer:

\(y=1\\x=-1\)

The value of the variable "x" is 11.

We have a triangle. The vertices of the triangle are K, L, and M. The side KM is extended from point M to point N. The measures of the angles MKL, LMN, and KLM are (3x + 19)°, (7x + 5)°, and (2x + 8)°, respectively. We need to find out the value of the variable "x".

The angles LMK and LMN form a linear pair. It means they are supplementary angles. The sum of the angles is 180°.

∠LMK + ∠LMN = 180°

∠LMK + (7x + 5)° = 180°

∠LMK = 180° - (7x + 5)°

In the triangle KLM, we will use the angle sum property of a triangle. The sum of all the angles in a triangle is equal to 180°.

∠K + ∠L + ∠M = 180°

(3x +19)° + (2x + 8)° + [180° - (7x + 5)°] = 180°

3x +19 + 2x + 8 + 180 - 7x - 5 = 180

-2x + 22 = 0

2x = 22

x = 11

Hence, the value of the variable "x" is 11.

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Answer: A discrete

Step-by-step explanation:

The standard error represents the average deviation of the sample means from the true population mean. Rounding this value to four decimal places, the standard error of X¯¯¯ is approximtely 0.6500 mpg.

A smaller standard error indicates that the sample means are more likely to be close to the population mean.To calculate the standard error of X¯¯¯, the mean from a random sample of 25 fill-ups by one driver, we can use the formula:

Standard Error (SE) = σ / sqrt(n),

where σ is the standard deviation and n is the sample size.

In this case, the standard deviation (σ) is given as 3.25 mpg, and the sample size (n) is 25.

Plugging in these values into the formula, we have:

SE = 3.25 / sqrt(25).

Calculating the square root of 25, we get:

SE = 3.25 / 5.

Performing the division, we find:

SE ≈ 0.65.

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Answer:  first choice is correct

Step-by-step explanation:

\(\sqrt{10} = 3.16\\\\ \sqrt{13} = 3.6\)

22/9 = 2.44

Therefore Point A is 22/9, Point B is \(\sqrt{10}\),  Point C is \(\sqrt{13}\)

Answer:

yes

the domain is greater than or equal to 0 and less than or equal to 4

the range is greater than or equal to 2 and less than or equal to 4

Step-by-step explanation:

Your on your own.. :/

Answer:

Step-by-step explanation:

The length of BD is 18.5 units.

In the given right triangle ABC, with altitude BD drawn to hypotenuse AC, we are given the lengths AD = 22 and DC = 15. We need to find the length of BD.

Let's consider triangle ABD. Since BD is the altitude, it divides the right triangle ABC into two smaller right triangles: ABD and CBD.

In triangle ABD, we have the following sides:

AB = AD = 22 (given)

BD = ?

Now, let's consider triangle CBD. In this triangle, we have the following sides:

BC = DC = 15 (given)

BD = ?

Since triangles ABD and CBD share the same base BD, and their heights are the same (BD), we can say that the areas of these triangles are equal.

The area of triangle ABD can be calculated as:

Area(ABD) = (1/2) * AB * BD

Similarly, the area of triangle CBD can be calculated as:

Area(CBD) = (1/2) * BC * BD

Since the areas of ABD and CBD are equal, we can equate their expressions:

(1/2) * AB * BD = (1/2) * BC * BD

We can cancel out the common factor (1/2) and solve for BD:

AB * BD = BC * BD

Dividing both sides of the equation by BD (assuming BD ≠ 0), we get:

AB = BC

In triangle ABC, the lengths AB and BC are equal, which implies that triangle ABC is an isosceles right triangle. In an isosceles right triangle, the leg's length are congruent, so AB = BC = AD = DC.

BD is equal to half of the hypotenuse AC:

BD = (1/2) * AC

Substituting the given values, we have:

BD = (1/2) * (AD + DC) = (1/2) * (22 + 15) = (1/2) * 37 = 18.5

Therefore, the length of BD is 18.5 units.

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