Mathematics College

What is the value of X

Answers

Answer 1

Answer:

∠JKL = 159

∠JKM = 43

∠MKL = 116

Step-by-step explanation:

Step 1: Define a equation for the angles

∠JKL = ∠JKM +∠MKL

Step 2: Substitute the values in for the angles

(10x - 11) = (43) + (8x-20)

Step 3: Solve for x

10x - 11 = 43 + 8x - 20

2x = 34

x = 17

Step 4: Substitute x = 17 back into angle to solve

∠JKL = 10(17) - 11

=170 - 11

=159

∠JKM = 43

∠MKL = 8x - 20

= 8(17) - 20

= 136 - 20

=116

Answer 2

Answer:

17=x

JKM =43

MKL = 116

JKL= 159

Step-by-step explanation:

JKM + MKL = JKL

43+ 8x-20 = 10x-11

Combine like terms

23+8x = 10x-11

Subtract 8x from each side

23 +8x-8x = 10x-8x-11

23 = 2x-11

Add 11 to each side

23+11 = 2x-11+11

34 = 2x

Divide by 2

34/2 = x/2

17=x

JKM =43

MKL = 8x-20 = 8*17 -20 = 116

JKL= 10x-11 = 10*17 -11 = 159

Related Questions

A line slope of 2 passes through the point (4,8). What is the equation in slope-intercept form?

Answers

The equation would be Y=2x

A right triangle has vertices (−7,9),(3,9),(−7,−15). Find the perimeter of the triangle.

Answers

The perimeter of a triangle is 60 units if the right triangle has the vertices (-7, 9), (3, 9), (-7, -15).

What is meant by perimeter?

The perimeter calculation has various practical uses. A calculated perimeter is the length of fencing required to encircle a yard or garden. The circumference (perimeter) of a wheel/circle specifies how far it will roll in one revolution.

If the lengths of the triangle's sides are a, b, and c, the perimeter is the sum of their lengths:

P = a + b + c

The distance formula can be used to calculate any of the side lengths. However, because two of the sides are parallel to the axes, their lengths may be simply calculated by subtracting coordinates.

If the points are designated A, B, and C in that sequence, the two right-angle sides are as follows:

c = AB

= 3 -(-7)

= 10

b = AC

= 9 -(-15)

= 24

The Pythagorean theorem states that the third side of the relation can be found:

a² = b² +c²

a² = 10² +24² = 676

a=√676

a= 26

Now we can plug these numbers into the perimeter formula:

P = a + b + c = 26 + 24 + 10

P = 60

As a result, the perimeter of a triangle is 60 units.

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g In a multiple choice exam, there are 5 questions and 4 choices for each question (a, b, c, d). Nancy has not studied for the exam at all and decides to randomly guess the answers. What is the probability that: (a) the first question she gets right is the 5th question

Answers

Answer:

81 / 1024

Step-by-step explanation:

First, let's find the total number of ways that Nancy can choose random choices for the questions. This would be 4 * 4 * 4 * 4 * 4 = 4⁵ = 1024 because there are 4 choices and 5 questions. In order for first question she gets right to be the 5th question, she has to get the first 4 questions wrong. Therefore, since there are 4 choices for each question and only 1 of them is right, she has 4 - 1 = 3 options for the first 4 questions and only 1 option for the 5th one, so the total number of "successful" ways Nancy can do this would be 3 * 3 * 3 * 3 * 1 = 81. Therefore, the probability is 81 / 1024.

100 megatons+234 help please

Answers

Answer:

we know,

1 megaton=1000kg

100 megaton=100000

now,

total weight=100000+234

=100234.

A password contains three digits, such as 175. How many different passwords can be formed?

Answers

Answer: There are 1000 different passwords.

Step-by-step explanation:

Given: A password contains three digits.

Number of digits from 0 to 9 = 10

Using fundamental principle of counting,

The number of different passwords = (Number of choices for digits) x (Number of choices for digits) x (Number of choices for digits)

= (10) x (10)x (10)

=1000

Hence, there are 1000 different passwords.

Dan invests £11125 into his bank account. He receives 3.3% per year simple interest. How much will Dan have after 4 years? Give your answer to the nearest penny where appropriate.

Answers

Answer:

£11564.54

Step-by-step explanation:

100 + 3.3 = 103.3%

103.3% = 1..013

£11125 x 1.013^3 = £11564.54

I hope this helped you!

simplify (1-√3)(⅓+√3) leaving your answer in the form p+q√3

Answers

Answer:

[tex]\frac{-8 +2\sqrt{3} }{3}[/tex]

Step-by-step explanation:

When working with surds we need to take note of the roots present there.

To expand this equation we can do it the following way noting that √3 X √3 = 3

Expanding (1-√3)(⅓+√3)

1 X 1/3 = 1/3

1 X √3 = √3

-√3 X 1/3 =-√3/3

√3 X √3 = 3

hence, expanding the equation, we have

1/3 + √3 -√3/3 + 3

We can simply group the like terms and add them up.

[1/3 +3] +[√3-√3/3]

10/3 + [tex]\frac{2\sqrt{3} }{3}[/tex]

= [tex]\frac{-8 +2\sqrt{3} }{3}[/tex]

If you roll a 6-sided die 4 times, what is the probability of one roll being a multiple of 3? A)2/3 B)16/81 C)145/1296 D)65/81 E)625/1296 (I really need help! Pls answer fast!)

Answers

Answer:

671/1296

The probability of rolling at least one six is therefore 1 − 625/1296 = 671/1296 ≈ . 517.

Step-by-step explanation:

Answer:

671/1296

Step-by-step explanation:

It is also known that customers will spend an average of $178 on additional maintenance. The standard deviation of the expenses is $50. If a simple random sample of 100 customers is taken: What is the probability that the sample mean will be between 166.75 and $170.50

Answers

Answer:

probability that the sample mean will be between 166.75 and $170.50 = 0.42816

Step-by-step explanation:

We are given;

Mean; μ = $178

Standard deviation; σ = $50

Now, we want to find the probability that the sample mean will be between $166.75 and $170.50.

Thus, we'll use the z-score formula;

z = (x - μ)/σ

So;

Lower limit of z is;

z = (166.75 - 178)/50

z = -0.225

Upper limit of z is;

z = (170.50 - 178)/50

z = -0.15

From the z-distribution table attached, the area between -0.225 and -0.15 is;

0.44038 - 0.01222 = 0.42816

Describe the relationship between the values of the two 7s in the number 3,772 what equation could you use to help describe the relationship

Answers

Answer:

y = 10x, which is the relationship between two 7 in the number 3772

Step-by-step explanation:

In the given number 3772

3 is at thousandth position its value is 3000 numerically

7 is at the hundredth position its value is 700 numerically

next 7 is at tens position its value is 70 numerically

and 2 is at unit position its value is 2 numerically

thus, 3772 can also be written as sum of number based on its position

3000

+700

+ 70

+ 2

___-

= 3772

Thus,

since Third 7 from left has value of 70

and Second 7 from left has value of 700

we know 70*10 = 700

Thus, 70 is 10 times to that 700

Thus, we can say that

value of Second 7 from left = 10*value of Third 7 from left

Thus,

let value of Second 7 from left be y

value of Third 7 from left be x

then

y = 10x, which is the relationship between two 7 in the number 3772

In 2003, the population of an African country was about 10.2 million people, which is 1 million more than 4 times the population in 1950. Enter and solve an equation to find the approximate population p (in millions) in 1950. An equation is . The approximate population in 1950 was million people.

Answers

In 1950 the proximate population was as 2.3 million

What is value of
X+8
Enter your answer in the box
2x-5
B
10
14
Plz help

Answers

Answer:

not 100% but i think x may be 23.5

Step-by-step explanation:

The values of (x+8) and (2x-5) are 35 and 49 respectively.

What is a triangle?

A triangle is defined as a two-dimensional shape with three sides, three interior angles, and three vertices.

Given a triangle, ABC

We have,

(x+8)/10 = (2x-5)/14

7x+56 = 10x-25

3x = 81

x = 27

X+8 = 35

2x-5 = 49

Hence, The values of (x+8) and (2x-5) are 35 and 49 respectively.

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What is the distance between point (6, -1) and point (5, 3) rounded to the nearest tenth?

Answers

Answer:

The answer is

4.1 units

Step-by-step explanation:

The distance between two points can be found using the formula

[tex] \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } [/tex]

where

( x1 , y1) and ( x2 , y2) are the points

From the question

The points are (6, -1) and (5, 3)

The distance between the points is

[tex] \sqrt{( {6 - 5})^{2} + ({ - 3 - 1})^{2} } [/tex][tex] = \sqrt{ {1}^{2} + ( { - 4})^{2} } [/tex][tex] = \sqrt{1 + 16} [/tex][tex] = \sqrt{17} [/tex]

= 4.123105

We have the final answer as

4.1 units

Hope this helps you

Does anyone know this?

Answers

Answer:

first option is right

Step-by-step explanation:

Find the a. MEAN and b. STANDARD DEVIATION for the data set. Round to two decimal places.
10) Country Number of Television Sets per 100 people
A 124
B 94
C 129
D 109
E 114
A) a. 115
b. 13.69
B)
a. 114
b. 13.69
C)
a. 114
b. 169
D) a. 113
b. 13.69
Provide an appropriate response.
11) If an adult male is told that his height is within 2 standard deviations of the mean of the normal distribution of heights of adult males, what can he assume?
A) His height measurement is in the same range as about 99.7% of the other adult males whose heights were measured.
B) His height measurement is in the same range as about 95% of the other adult males whose heights were measured.
C) He is taller than about 99.7% of the other men whose heights were measured.
D) He is taller than about 95% of the other men whose heights were measured. The scores on a driver's test are normally distributed with a mean of 100. Find the score that is:_____
12) Find the score that is 2 standard deviations below the mean, if the standard deviation is 26.
A) 126
B) 48
C) 152
D) 74
Suppose that prices of a certain model of new homes are normally distributed with a mean of $150,000. Use the 68-95-99.7 rule to find the percentage of buyers who paid:____
13) between $147,700 and $152,300 if the standard deviation is $2300.
A) 34%
B) 95%
C) 99.7%
D) 68%
14) more than $154,800 if the standard deviation is $2400.
A) 95%
B) 2.5%
C) 47.5%
D) 97.5%
A set of data items is normally distributed with a mean of 60. Convert the data item to a z-score, if the standard deviation is as given. 15) data item: 100; standard deviation:_____
a) 10
b) 40
c) 10
d) 4/3

Answers

Answer:

Explained below.

Step-by-step explanation:

(10)

The data set is:

S = {124, 94, 129, 109, 114}

The mean and standard deviation are:

[tex]\bar x=\frac{1}{n}\sum x=\frac{1}{5}\times [124+94+...+114]=114\\\\s=\sqrt{\frac{1}{n-1}\sum ( x-\bar x)^{2}}[/tex]

[tex]=\sqrt{\frac{1}{5-1}\times [(124-114)^{2}+(94-114)^{2}+...+(114-114)^{2}]}\\=\sqrt{\frac{750}{4}}\\=13.6931\\\approx 13.69[/tex]

The correct option is B.

(11)

According to the Empirical 95% of the data for a Normal distribution are within 2 standard deviations of the mean.

So, the adult male's height is in the same range as about 95% of the other adult males whose heights were measured.

The correct option is B.

(12)

Let the score be X.

Given:

μ = 100

σ = 26

[tex]X=\mu-2\sigma[/tex]

[tex]=100-(2\times 26)\\=100-52\\=48[/tex]

The correct option is B.

(13)

Let X be the prices of a certain model of new homes.

Given: [tex]X\sim N(150000, 2300^{2})[/tex]

Compute the percentage of buyers who paid between $147,700 and $152,300 as follows:

[tex]P(147700<X<152300)=P(\frac{147700-150000}{2300}<\frac{X-\mu}{\sigma}<\frac{152300-150000}{2300})[/tex]

[tex]=P(-1<Z<1)\\=0.68\\[/tex]

According to the 68-95-99.7, 68% of the data for a Normal distribution are within 1 standard deviations of the mean.

The correct option is D.

(14)

Compute the percentage of buyers who paid more than $154,800 as follows:

[tex]P(X>154800)=P(\frac{X-\mu}{\sigma}>\frac{154800-150000}{2400})[/tex]

[tex]=P(Z>2)\\=0.975\\[/tex]

According to the 68-95-99.7, 95% of the data for a Normal distribution are within 2 standard deviations of the mean. Then the percentage of data above 2 standard deviations of the mean will be 97.5% and below 2 standard deviations of the mean will be 2.5%.

The correct option is D.

(15)

The z-score is given as follows:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

20 points! Each month, Sal must pay for car insurance and fuel to drive a vehicle. Sal's parents agree to pay p percent of his car expenses. The cost of car insurance is the same every month, but the cost of fuel depends on d, the number of miles Sal drives. The expression (1−p)(0.10d+60) represents how much Sal must pay toward his monthly car expenses. Which part of the expression represents the percentage of the monthly expenses that Sal must pay? 0.10d + 60 1−p 60 0.10d

Answers

Answer:

1 - p

Step-by-step explanation:

The cost of insurance is constant, this is 60.The cost of fuel is 0.10d as d is the number of miles.The only variable left is 1-p which represents the percentage of expenses

So the answer is:

1 - p

Answer:

1-p

Step-by-step explanation:

I took the test and this was the answer.

Which number best represents the slope of the graphed line?

Answers

Answer: A

Explanation:

-5

Because the slope rise 5 and run to the left once.

If a slope run to right it means positive
If a slope run to left it means negative

Answer:

the answer is A.

Step-by-step explanation:

for every time you move over one in the x axis you move down 5 on the y axis

pt 2 6-7 Pleaseee Helpp

Answers

Answer:

w = 15

Step-by-step explanation:

x ___w___ = 3 x 5

w = 15

Hi there! Hopefully this helps!

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

Answer: w = 15~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

[tex]\frac{w}{5} = 3[/tex]

Multiply both sides by 5.

[tex]w = 3 \times 5[/tex]

Multiply 3 and 5 to get, you guessed it, 15!

A(n) ___
is a numerical summary of a population.

Answers

Answer:

parameter

Step-by-step explanation:

need help with this question

Answers

Answer:

25) -76

26) -23

27) 21

28) 8

Step-by-step explanation:

25) (-32)-44=-32-44=-76

26) (-12)+(-11)=-12-11=-23

27) 2+15+4=17+4=21

28) 16+(-13)+5=16-13+5=3+5=8

Step-by-step explanation:

Hope it helps u mate

plz mark it as brainlist

the projected number of employed writers and authors in 2016 is 153,000. 12.4% of those will have some college experience but no degree, and 84.1% will have a bachelors degree or higher. If this holds true, how many more writers and authors with bachelors degree will be there than those with only some college experience and no degree?

Answers

Answer:

Step-by-step explanation:

12.4% 153000 = 12.4/ 100 * 153000 = 0.124 * 153000 = 1897

84.1% 153000 = 84.1/100 * 153000 = 0.841 * 153000 = 128673

The difference (and the answer) is 128673 - 1897 = 126776

Note: 3.5% are not accounted for. They probably just sat down and wrote.

determine whether y = 4x+5 and y= 1/4x-2 are perpendicular

Answers

Answer:

No, they are not perpendicular

Step-by-step explanation:

Perpendicular lines will have opposite reciprocal slopes, meaning that the slopes will have opposite signs and be the reciprocals of each other.

We can see that the slopes of the lines are not opposite reciprocals.

4 and 1/4 are not opposite reciprocals because they do not have opposite signs.

if m<2, then m<1 is...

Answers

Answer:

Step-by-step explanation:

m<1 and m<2 are complementary angles because the sum of two angles = 90° and since m<1 = m<2

90 ÷ 2 = 45

A past survey of students taking a standardized test revealed that % of the students were planning on studying engineering in college. In a recent survey of students taking the SAT, % of the students were planning to study engineering. Construct a % confidence interval for the difference between proportions by using the following inequality. Assume the samples are random and independent.

The confidence interval is __

Answers

Complete Question

The complete question is shown on the first uploaded image

Answer:

The 95% confidence interval is [tex]-0.00870 <p_1 -p_2 < -0.007297[/tex]

Step-by-step explanation:

From the question we are told that

The first sample size is [tex]n_1 = 1068000[/tex]

The first proportion [tex]\r p_1 = 0.084[/tex]

The second sample size is [tex]n_2 = 1476000[/tex]

The second proportion is [tex]\r p_2 = 0.092[/tex]

Given that the confidence level is 95% then the level of significance is mathematically represented as

[tex]\alpha = (100 - 95)\%[/tex]

[tex]\alpha = 0.05[/tex]

From the normal distribution table we obtain the critical value of [tex]\frac{ \alpha }{2}[/tex] the value is

[tex]Z_{\frac{\alpha }{2} } =z_c= 1.96[/tex]

Now using the formula from the question to construct the 95% confidence interval we have

[tex](\r p_1 - \r p_2 )- z_c \sqrt{ \frac{\r p_1 \r q_1 }{n_1} + \frac{\r p_2 \r q_2 }{n_2} } <p_1 -p_2 < (\r p_1 - \r p_2 )+ z_c \sqrt{ \frac{\r p_1 \r q_1 }{n_1} + \frac{\r p_2 \r q_2 }{n_2} }[/tex]

Here [tex]\r q_1 = 1 - \r p_1[/tex]

=> [tex]\r q_1 = 1 - 0.084[/tex]

=> [tex]\r q = 0.916[/tex]

and

[tex]\r q_2 = 1 - \r p_2[/tex]

=> [tex]\r q_2 = 1 - 0.092[/tex]

=> [tex]\r q_2 = 0.908[/tex]

[tex](0.084 - 0.092 )- (1.96)* \sqrt{ \frac{0.092* 0.916 }{1068000} + \frac{0.084* 0.908 }{1476000} } <p_1 -p_2 < (0.084 - 0.092 )+ (1.96)* \sqrt{ \frac{0.084* 0.916 }{1068000} + \frac{0.092* 0.908 }{1476000} }[/tex]

[tex]-0.00870 <p_1 -p_2 < -0.007297[/tex]

Please help. Will select brainliest.

Answers

Answer:

Heptagon: D

Spetagon: D

Nonagon: B

Luke is 5 years younger than 3 times Sydney's age, s. In this situation, what does 3s represent?
0 Luke's age
O Sydney's age
o three times Luke's age
O three times Sydney's age

Answers

Answer:

Step-by-step explanation:

'3s' represents 'three times Sydney's age.'

Answer:

three times Sydney's age

Step-by-step explanation:

i took a test on this

Choose the function that correctly identifies the transformation of f(x) = x2 shifted two units down and one unit to the left. g( x) = ( x + 1) 2 + 2 g( x) = ( x - 1) 2 + 2 g( x) = ( x + 1) 2 - 2 g( x) = ( x - 1) 2 - 2

Answers

Answer:

g(x)= (x +1)^2 -2

Step-by-step explanation:

Pre Calc Introduction to Derivatives-Using Limits Help!

Answers

Answer:

Attachment 1 : Option A,

Attachment 2 : Option D,

Attachment 3 : Option B,

Attachment 4 : Instantaneous rate of change will be 24

Step-by-step explanation:

"Remember that we can solve such questions by finding the derivative first"

1 : Let's consider this approach a bit differently. If we were to graph this function, we would see that the point (-2,26) would lie on the curve having a negative slope.

The rate of change would thus be negative, eliminating choices b and d. And, the slope of this function would be much greater than 4 due to the coefficient of " 5 " in f(x) = 5x² + 6. Hence our answer will be option a.

2 : f'(5) = - 2 * 5 + 4,

f'(5) = - 10 + 4 = - 6

Your solution is option d.

3 : f'(2) = 12 / 2 + 1 / - 3,

f'(2) = 12 / 3 / - 3 = 4 / - 3,

f'(2) = - 4 / 3

Your solution is option b.

4 : Here again we can apply the power rule, where using constant multiple rule and derivative of a constant, you can quickly find the derivative of g .

g'(t) = 3(2x¹) + 0 = 6t,

And now we can evaluate the derivative at that value of t.

g'(4) = 6(4) = 24 - hence the instantaneous rate of change at t = 4, will be 24

2. What is the sum of the three solutions (find the values for x, y, and z, then add the answers)?
2x + 3y − z = 5 x
− 3y + 2z = −6
3x + y − 4z = −8
please show steps

Answers

Answer:

x = 30/7 , y = 46/7 , z = 48/7

Step-by-step explanation:

Solve the following system:

{2 x + 3 y - z = 5 x | (equation 1)

2 z - 3 y = -6 | (equation 2)

3 x + y - 4 z = -8 | (equation 3)

Express the system in standard form: