In the triangle below, with right angle I, suppose that m< J= (2x+22)° and m < K = (5x-2)
Find the degree measure of each angle in the triangle.

m < I =
M< J =
m < K =

Answer: There are 52 cards in a standard deck and half of them, 26 in all, are red.

Suppose that you are drawing 4 cards without replacement from a thoroughly shuffled deck. You have 26 cards choose 4 over 52 choose 4.

∴  P(pulling 4 cards from deck) =  (264)(524)

Equation of the line is y = 3/2x + 3.

Y = mx+b, where m is the slope and b is the y-intercept, is the formula for the slope-intercept form (the point where the line crosses the y-axis). The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation. The "slope-intercept" form is one of the most popular methods. It is so named because it makes the slope and y-intercept of the equations in the equation more clear. The number that is placed before the x is the slope.

Given,

Slope intercept form:

Formula:

y = mx + b

Where m = slope

2y - 3x = 6

2y = 6 + 3x

Equation:

y = 3 + 3/2x

y = 3/2x + 3

Equation of the line is y = 3/2x + 3.

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The quadratic function whose only zero is -13 is h(x) = x² + 26x + 169

From the question, we are to write a quadratic function whole only zero is -13.

Since -13 is the only zero of the function,

Then,

x = -13 twice

This means that (x + 13) is a factor of the function

Since x = -13 twice,

Then,

The quadratic function h is

h(x) = (x + 13)(x + 13)

Expand the quadratic function by distributing

h(x) = x(x + 13) + 13(x + 13)

h(x) = x² + 13x + 13x + 169

h(x) = x² + 26x + 169

Hence, the function is h(x) = x² + 26x + 169

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Answer: I would say a half of beef is cheaper the pounds are different maybe subtract a half from five

Step-by-step explanation:

Answer: Yes

Step-by-step explanation:It can because math works like that.

Answer:

Step-by-step explanation:

Thanks

Answer:

The answer you are looking for is 0.35 foot per second.

Step-by-step explanation:

Formula = divide the speed by 20

(Or in this case 7 divided by 20).

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Answer:

See below

Step-by-step explanation:

Eight minus unknown quantity 'x' equals two.

a) 25 % of customers receive the service for​ half-price.

b) The guaranteed time​ limit should be of 16 minutes.

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score.

When the distribution is normal, we use the z-score formula.

The p-value is the probability that the value of the measure is smaller than X, which is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

we have that mean of 15 minutes and a standard deviation of 4 minutes.

​(a) Longer than 20 minutes is 1 subtracted by the p value of Z when X = 20. So

[tex]Z = \dfrac{{x} - \mu}{\sigma}[/tex]

Z = (20 - 15)/4

Z = 5/4

Z = 1.25

1.25 has a pvalue of 0.25

1 - 1.25= 0.25

25 % of customers receive the service for​ half-price.

(b)  The time limit should be the 100 - 7 = 93th percentile, which is X when Z has a pvalue of 0.93.  So X when Z = 0.25.

[tex]Z = \dfrac{{x} - \mu}{\sigma}[/tex]

0.25= (x- 15)/4

x = 16

The guaranteed time​ limit should be of 16 minutes.

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The ordered pairs that are solutions to the linear equation x + 2y = 4 are given as follows:

The linear function in this problem is defined as follows:

x + 2y = 4.

To complete the ordered pairs, we take the given coordinate and then solve for the missing coordinate .

For the first ordered pair, the given coordinate is of x = -3, hence we have to solve for y when x = -3, thus:

-3 + 2y = 4.

2y = 7.

y = 7/2

y = 3.5.

Hence the ordered pair is:

(-3, 3.5).

For the second ordered pair, the given coordinate is of y = -7, hence we have to solve for x when y = -7, thus:

x + 2y = 4.

x - 14 = 4

x = 18.

Hence the ordered pair is:

(18, -7).

The ordered pairs that we have to complete are given as follows:

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Using the triangle rule, the length of the third side falls between 5 cm and 29 cm.

In the given question,

The measurements of two sides of a triangle are 12 cm and 17 cm.

We have to find which side length could be the measurement of the third side of the triangle.

We know that,

The sum of the length of any two sides is always greater than the third side.

The given sides of triangles are 12 cm and 17 cm.

Hence, the length of the third side should be shorter than the total of the other two sides,

12 + 17 = 29 cm.

Considering that the third side must be less than the difference between the first two sides,

17 – 12 = 5 cm

So, the length of the third side falls between 5 cm and 29 cm.

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The values of each variable are ∠d=71°, ∠c=87°, arc a=121°, arc b=53°.

A circle is a shape formed by all points on a plane that are at a fixed distance from the center. It is the curve sketched out by a point moving in a plane such that its distance from a particular point remains constant. The radius is the distance between any point on a circle and the center. The radius must usually be a positive integer. Degenerate case is a circle with r=0. Except when otherwise specified, this article is about circles in Euclidean geometry, and specifically the Euclidean plane.

1) Measure of ∠d

∠d+109°=180°

∠d=71°

2) Measure of ∠c,

∠c+93°=180°

∠c=87°

3) Measure of arc a is,

109°=1/2[97°+arc a]

218°=97°+arc a

arc a=121°

4) Measure of arc b,

87°=1/2[121°+arc b]

174°=121°+arc b

arc b=53°

Therefore, the values of each variable are ∠d=71°, ∠c=87°, arc a=121°, arc b=53°.

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0.065=x/5800

x=$377; that is the dollar value of the decrease

The account is now worth $5423.

The simplified expression of the expression given as -3x+16+5x+8 is 2(x + 12)

From the question, the equation is given as

-3x+16+5x+8

To start with, we need to rewrite the expression

So, we have the following representation

-3x + 16 + 5x + 8

The above expression is not an equation

Instead, it is an expression

This is so because there is no equality symbol i.e. = in the expression

So, we collect the like terms

-3x  + 5x + 8 + 16

Solving further, we need to evaluate the like terms

So, we have the following equation

-3x  + 5x + 24

Evaluate the like terms again

So, the equation becomes

2x + 24

The above expression cannot be further simplified, however, it can still be factored

Factor out 2 from the expression

This gives

2(x + 12)

Hence, the solution is 2(x + 12)

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Answer:

Let the number of apples and bananas bought be x and y respectively.

x + 5 = y ------ equation (1)

0.75x + 0.50y = 7.50 ------ equation (2)

Substitute equation (1) into equation (2):

     0.75x + 0.50(x+5) = 7.50

0.75x + 0.50x + 2.50 = 7.50

                          1.25x = 5

                               ∴x = 4

Substitute x = 4 into equation (1):

∴y = 4+5

    = 9

∴David bought a total of 4 apples and 9 bananas.

By using the formula of average speed, it can be inferred that

My average speed is 14 miles per hour

What is average speed?

Speed of an object is the distance covered by the object per unit time

Average speed is calculated by dividing the total distance covered by the total time taken

Length of one block = 560 feet = [tex]\frac{560}{5280}[/tex] miles

Number of blocks = 33

Total distance = [tex]\frac{560}{5280} \times 33\\[/tex]

                        = [tex]\frac{7}{2}[/tex] miles

Total time = 15 minutes = [tex]\frac{15}{60}[/tex] hours = [tex]\frac{1}{4}[/tex] hours

Average speed = [tex]\frac{\frac{7}{2}}{\frac{1}{4}}[/tex] = [tex]\frac{7}{2} \times 4[/tex] = 14 miles per hour

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The missing value is 22

Direct proportion is the relation between two quantities or values where the ratio of the two will always equal a constant value. The symbol used for proportion is the symbol '∝'.

When two quantities are in direct proportion, if we increase one value, then the other will also increase, and if we decrease one value then the other value will also decrease.

Here we have  

x -    1     2    3     4      5

y -  -2    4    10    16     ?      

As we see the value of x is directly proportional to y  

For every 1 unit value of x, the y value is increasing 6 units

For more Understand observe the following

at x = 1  => y = -2

at x = 2 => y = -2 + 6 = 4  

at x = 3 => y = -2 + 2(6) = 10

Therefore,

The relation between x and y can derive as given below

=> y = - 2 + (x-1)6

=> y = - 2 + 6x -6  

=> y = 6x - 8  

at x = 5 => y = 30 - 8 =22

Therefore,

The missing value is 22

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The percent of Americans that had central heterochromia is A. 0061%.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

In this case, it's estimated that only around 200,000 Americans have central heterochromia and the population of the United States

was 327,750,000 people.

The percent of Americans that had central heterochromia will be:

= Those with the disease / Total population × 100

= 200,000 / 327,750,000 × 100

= 0.0061%

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A) The bunny population after every 2 months is f(T)=5T+20

B) The bunny population after 16 weeks is x=29.205

C) The number of months that the bunny population to reach 300 bunnies is 112 months.

All nationals present in, or temporarily absent from, a country, as well as aliens permanently settled in a country, are characterized as population. This indicator depicts the average number of people who live in a given location. The annual changes in population caused by births, deaths, and net migration during the year are referred to as growth rates.

Given,

0 months -------- 20 bunnies

2 years ------- 80 bunnies

In two years, bunnies are increased by,

=80-20

=60

2 years ------>60

1 year ------>30

A) f(T)=mT + b

1 year -----> 12 months -----> 30 bunnies

12/6 months ------>30/6 bunnies

2 months -----> 5 bunnies

f(T)= initial population+ increased population in two months

f(T)=20+5

f(T)==25

f(T)= 2.5T+20

f(T)=5T+20

Where T =time in months

B) For 10 years ------> 10 bunnies

52 weeks -------->30 bunnies

16 weeks ------?

x=(16*30)/52

x=29.205

C) 1 month -------> 2.5 bunnies

 ? ---------------->280 bunnies

x=280/2.5

x=112 months

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Answer:

A) The bunny population after every 2 months is f(T)=5T+20

B) The bunny population after 16 weeks is x=29.205

C) The number of months that the bunny population to reach 300 bunnies is 112 months.

What is meant by population?

All nationals present in, or temporarily absent from, a country, as well as aliens permanently settled in a country, are characterized as population. This indicator depicts the average number of people who live in a given location. The annual changes in population caused by births, deaths, and net migration during the year are referred to as growth rates.

Given,

0 months -------- 20 bunnies

2 years ------- 80 bunnies

In two years, bunnies are increased by,

=80-20

=60

2 years ------>60

1 year ------>30

A) f(T)=mT + b

1 year -----> 12 months -----> 30 bunnies

12/6 months ------>30/6 bunnies

2 months -----> 5 bunnies

f(T)= initial population+ increased population in two months

f(T)=20+5

f(T)==25

f(T)= 2.5T+20

f(T)=5T+20

Where T =time in months

B) For 10 years ------> 10 bunnies

52 weeks -------->30 bunnies

16 weeks ------?

x=(16*30)/52

x=29.205

C) 1 month -------> 2.5 bunnies

? ---------------->280 bunnies

x=280/2.5

x=112 months

The equation of the parallel line is y = (-3/2)x + 20

What does the term Slope of a Straight Line means?

A line's slope is defined as the change in y coordinate with respect to the change in x coordinate. The net y coordinate change is y, while the net x coordinate change is x.

Solution:

Firstly we need to find the slope of the given line 3x+2y = 14

Since, the equation is in the form ax + by = c

Therefore, by comparing we can say a = 3 and b = 2

Slope = -(b/a) = -3/2

Since we need to find the equation of the parallel line

So, the slope of the parallel line will be -3/2

y = mx + b

we know that the line passes through the point (8,8)

putting x,y = 8 and m = -3/2

8 = (-3/2)*8 + b

8 = -12 + b

b = 20

So, the equation of the parallel line is y = (-3/2)x + 20

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In  linear equation, option A,B,C are equal expect D .

What in mathematics is a linear equation?

The given equation is  3x -4y =21.

A.  (11, 3)

3(11) - 4(3) = 21

21 = 21 > equal

B.  (7, 0)

3(7) - 4(0) = 21

21 = 21 > equal

C.  (−1, −6)

3(-1) - 4(-6) = 21

21 = 21 > Equal

D.  (−3, 3)

3x – 4y = 21

3(-3) - 4(3) = 21

-21 = 21 > not equal

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a. The penalty Lorna must pay is $26.86.

b. The total amount Lorna must pay on February 27 is $2037.74.

Given that,

On December 14, 2017, Lorna Hall's $2,010.88 real estate tax was due. Because of her job loss, Lorna was unable to pay her taxes until February 27, 2018. Late payment fees are assessed at a rate of 6 1/2% regular interest.

We have to find

a. What is the fine Lorna is required to pay

b. How much will Lorna owe in total on February 27.

First,

We know that,

i=p×r×t

Here,

i is interest.

p is principal amount.

r is rate of interest

t is time.

So, p is $2010.88

r is 6 1/2%

t is 17+31+27= 75 days is 75/365

So,

i= 2010.88×6 1/2×75/365

i= $26.86

The penalty Lorna must pay is $26.86.

Second,

We know that,

Total amount= real estate tax due amount+ Penalty pay.

Total amount= $2010.88+$26.86

Total amount= $2037.74

The total amount Lorna must pay on February 27 is $2037.74.

Therefore, a. The penalty Lorna must pay is $26.86.

b. The total amount Lorna must pay on February 27 is $2037.74.

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Answer:

x = 12 m

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × width

here A = 44 , then

x × 3 [tex]\frac{3}{4}[/tex] = 44 ( change mixed number to improper fraction )

x × [tex]\frac{11}{3}[/tex] = 44 ( multiply both sides by 3 to clear the fraction )

11x = 132 ( divide both sides by 11 )

x = 12 m

13492928512 is the last term (7th term )of binomial expansion of the given expression so therefore it has no coefficient .

The binomial theorem is a way to bring the formulation to a finite power.

The binomial theorem is a effective extension device with packages in algebra, probability, and more.  A binomial is an algebraic expression containing  wonderful terms.

it has been attached below b'coz' that was not possible to type here

hope that image is clear .

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a) The test statistic is: t = -7.44.

b) The p-value is: < 0.0001.

c) The conclusion is that the null hypothesis is rejected.

d) The final conclusion is that there is sufficient evidence to conclude that the mean prediction error is different of zero.

From the pop-up shown at the complete problem given by the image at the end of the answer, the test statistic and the p-value are given as follows:

The conclusion regarding the null hypothesis is to reject the null hypothesis, as the test statistic has an absolute value less than the critical value, as we are using a two-tailed test, comparing if the mean is different of zero.

Considering that the null hypothesis is rejected, and also that the p-value is less than the significance level of 0.05, there is sufficient evidence to conclude that the mean prediction error is different of zero.

The pop-ups with the information of the test are given by the image at the end of the answer.

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The area of the shaded region is x=245 feet for both rectangle and circle.

The quantity area expresses the extent of a region on a plane or a curved surface. The area of a plane region or plane area refers to the area of a form or planar lamina, whereas surface area refers to the area of an open surface or the boundary of a three-dimensional object. Area can be defined as the amount of material of a given thickness required to make a model of the shape, or the amount of paint required to cover the surface with a single coat. It is the two-dimensional equivalent of the length of a curve or the volume of a solid.

The area of a shape can be calculated.

Area of shaded region=Area of rectangle-1/2(Area of circle)

=L×B-1/2(πr²)

=23×14-1/2((22/7)×7×7)

=322-77

=245 feet

Therefore, the area of the shaded region=245 feet

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Answer:

3/20

Step-by-step explanation:

3/5 : 4

3/5 x 1/4

3/20

Answer:

whats the question

The 30 feet by 15 feet dimension of the old stage and the 1,000 square feet of the new stage generates equations that gives the depth of the new stage;

An equation states the relationships between two expressions as being of the same value.

The width and depth of the concert hall for the old stage are 30 feet and 15 feet respectively

Area of the new stage = 1000 ft.²

The dimensions of the new stage are;

Width = 30 + x

Depth = 15 + x

Which gives;

(30 + x) × (15 + x) = 1,000

(30 + x) × (15 + x) - 1,000 = 0

x² + 45·x - 550 = 0

(x + 55)·(x - 10) = 0

The distance added to the width and length of the old stage, x = 10

The width of the new stage = 30 feet + 10 feet  = 40 feet

The depth of the new stage = 15 feet + 10 feet = 25 feet

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The linear equation we need to solve is:

$25.50*w = $309.99 - $131.49

And the solution is w = 7.

We know that the cost of the gaming chair is $309.99.

To buy this, you already have saved $131.49, and save another $25.50 per week, then the amount you have after w weeks is:

f(w) = $131.49 + $25.50*w

So the linear equation we need to solve is:

$131.49 + $25.50*w = $309.99

To solve this we need to isolate w.

$131.49 + $25.50*w = $309.99

$25.50*w = $309.99 - $131.49

w = ($309.99 - $131.49)/$25.50 = 7

So they can buy the chair after 7 weeks.

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