8
LO
5
15
4
1
In the figure shown above, all the corners form right angles. What is the area of the figure in squ
O 33 square units
O 66 square units
O 70 square units
O 120 square units

The equations used are:

Longest side = a

Shortest side = 1/2 x a = 1/2a

Third side = a - 1

The shortest side is 8 inches, the longest side is 16 inches and the third side is 15 inches.

The perimeter of a triangle is the sum of the length of the three sides of the triangle.

Let the following expressions represent the lengths of the sides of the triangle:

Longest side = a

Shortest side = 1/2 x a = 1/2a

Third side = a - 1

Perimeter = a + 1/2a + a - 1 = 39

a + 1/2a + a = 39 + 1

2a + 1/2a = 40

2 1/2a = 40

5/2a = 40

a = 40 x 2/5

a = 16 inches

Shortest side = 1/2 x 16 = 8 inches

Third side = 16 - 1 = 15 inches

To learn more about triangles, please check: https://brainly.com/question/22949981

#SPJ1

To find the missing angle measure, we need to use the fact that the sum of angles in a triangle is 180 degrees. Let's denote the missing angle as x. We know that one angle is 38 degrees and another angle is 12.5 degrees.Therefore, the missing angle measure is 129.5 degrees.

By subtracting these two angles from 180 degrees, we get:

180 - 38 - 12.5 = 129.5

Without additional information, it is not possible to determine the remaining parts of the triangle. We would need the lengths of at least one side or the measures of other angles to solve for the missing parts.

The given information states that AC is equal to AB minus mzB. Without knowing the values of AB and mzB, we cannot determine the exact length of AC. We would need additional information to solve for the length of AC.Therefore, the missing angle measure is 129.5 degrees.

For more such questions on angle

https://brainly.com/question/30759856

#SPJ11

Answer:

y intercept= (0,-3)

slope= 2/1 or simplified 2

Step-by-step explanation:

Answer:

(0.5455 ; 0.7545)

Step-by-step explanation:

Given that:

Sample size, n = 80

Baseball fans, x = 52

Proportion, p = x/n = 52 / 80 = 0.65

Using the relation :

Confidence interval :

p ± Zcrit√[(p(1 -p))/n]

Zcrit at 95% = 1.96

Lower boundary: p - Zcrit√[(p(1 -p))/n]

0.65 - 1.96√[(0.65(1 -0.65))/80]

0.65 - 1.96√[(0.65(0.35))/80]

0.65 - 1.96 * √0.00284375

0.65 - (1.96 * 0.0533268)

0.65 - 0.104520528

= 0.545479472

Upper boundary: p + Zcrit√[(p(1 -p))/n]

0.65 + 1.96√[(0.65(1 -0.65))/80]

0.65 + 1.96√[(0.65(0.35))/80]

0.65 + 1.96 * √0.00284375

0.65 + (1.96 * 0.0533268)

0.65 + 0.104520528

= 0.754520528

(0.5455 ; 0.7545)

ANSWER

P(no eggs) = 67%

P(toast) = 33%

P(cereal and orange juice) = 17%

P(cereal or orange juice) = 83%

EXPLANATION

Aaron starts his day with either orange juice or apple juice followed by cereal, toast or scrambled eggs.

This means that he makes two sets of choices.

The first set is between Orange juice or apple juice.

The second set is between Cereal, Toast or Scrambled eggs.

a) The probability that Aaron chooses a breakfast with no eggs.

In the second set, there are 3 possible choices.

The probability of choosing a breakfast with eggs is:

P(eggs) = 1/3

So, the probability of choosing a breakfast with no eggs is:

P(no eggs) = 1 - 1/3

P(no eggs) = 2/3

In percentage:

P(no eggs) = 2/3 * 100

P(no eggs) = 67%

b) The probability that Aaron chooses a breakfast with toast.

The probability of choosing a breakfast with toast is:

P(toast) = 1/3

P(toast) = 1/3 * 100 (in percentage)

P(toast) = 33%

c) The probability that Aaron chooses a breakfast with cereal and orange juice.

To find this, we have to find the probability that he chooses a breakfast with cereal, the probability that he chooses a breakfast with orange juice and then find the product.

P(cereal) = 1/3

P(orange juice) = 1/2 (since he has two options in the first set)

So, the probability that he will choose a breakfast with cereal and orange juice is:

P(cereal and orange juice) = 1/3 * 1/2

P(cereal and orange juice) = 1/6

P(cereal and orange juice) = 1/6 * 100 (in percentage)

P(cereal and orange juice) = 17%

d) The probability that Aaron chooses a breakfast with cereal or orange juice.

To find this, we have to find the probability that he chooses a breakfast with cereal, the probability that he chooses a breakfast with orange juice and then add them together.

P(cereal) = 1/3

P(orange juice) = 1/2

P(cereal or orange juice) = 1/3 + 1/2

P(cereal or orange juice) = 5/6

P(cereal or orange juice) = 5/6 * 100 (in percentage)

P(cereal or orange juice) = 83%

Based on the annuities calculated, he should choose option 1.

Present value = $35,000 + (Annuity amount * Present value of an ordinary annuity of $1)

= $35,000 + ($9,400 * (5%,6))

= $35,000 + ($9,400 * 5.07569)

= $35,000 + 47,711

= $82,711

Present value = (Annuity amount * Present value of an ordinary annuity of $1)

= $17,700 * (5%,6)

= $17,700 * 5.07569

= $89,840

Alex should choose Option 1

Future value annuity = Annuity amount * Future value of an ordinary annuity of $1

= $180,000 * (6%,10)

= $180,000 * 13.1808

= $2,372,544

Learn more about annuity on:

https://brainly.com/question/5303391

#SPJ1

If a triangle has one side length of 9cm and another side of .12cm . The 3 possible answers for the third side​ are:  17, 20, and 21.

To determine the possible lengths for the third side of the triangle, we can use the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side.

Using this theorem, the possible lengths for the third side can be found by checking which of the following inequalities hold:

   9 + 12 > x

   9 + x > 12

   12 + x > 9

Simplifying these inequalities, we get:

   x > -3 (always true)

   x > -9 (always true)

   x > -3 (always true)

Therefore, the possible lengths for the third side of the triangle must satisfy x > -9, which eliminates the answer 3 (which is less than 9 - 12 = -3).

The possible lengths for the third side are:

   9 + 12 > x, so x < 21

   9 + x > 12, so x > -3

   12 + x > 9, so x > -3

Therefore, the possible lengths for the third side of the triangle are:

   17 (9 + 12 = 21, which is greater than 17)

   20 (9 + 12 = 21, which is greater than 20)

   21 (9 + 12 = 21, which is equal to 21)

So, the three possible lengths for the third side of the triangle are 17, 20, and 21.

Learn more about length here:https://brainly.com/question/2217700

#SPJ1

The complete question is:

A triangle has one side length of 9

centimeters (cm) and another side length of 12

cm.

Which answers are possible lengths for the third side?

Select three that apply

17

22

9

21

20

3

Answer:

1

+

sec

2

(

x

)

sin

2

(

x

)

=

sec

2

(

x

)

Start on the left side.

1

+

sec

2

(

x

)

sin

2

(

x

)

Convert to sines and cosines.

Tap for more steps...

1

+

1

cos

2

(

x

)

sin

2

(

x

)

Write  

sin

2

(

x

)

as a fraction with denominator  

1

.

1

+

1

cos

2

(

x

)

⋅

sin

2

(

x

)

1

Combine.

1

+

1

sin

2

(

x

)

cos

2

(

x

)

⋅

1

Multiply  

sin

(

x

)

2

by  

1

.

1

+

sin

2

(

x

)

cos

2

(

x

)

⋅

1

Multiply  

cos

(

x

)

2

by  

1

.

1

+

sin

2

(

x

)

cos

2

(

x

)

Apply Pythagorean identity in reverse.

1

+

1

−

cos

2

(

x

)

cos

2

(

x

)

Simplify.

Tap for more steps...

1

cos

2

(

x

)

Now consider the right side of the equation.

sec

2

(

x

)

Convert to sines and cosines.

Tap for more steps...

1

2

cos

2

(

x

)

One to any power is one.

1

cos

2

(

x

)

Because the two sides have been shown to be equivalent, the equation is an identity.

1

+

sec

2

(

x

)

sin

2

(

x

)

=

sec

2

(

x

)

is an identity

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

B brainlist

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

i got it correct on the iready quiz

The graph of the line does not change except only in the y - intercept. The slope of the line remains same.

        y = mx + c

        [m] : slope of line.

        [c] : y - intercept

Given is a graph that shows the relationship between time and the distance a train travels.

From the graph, we can write the coordinates as -

(1, 60) and (2, 120)

So, we can write the slope of the line as -

m = (120 - 60)/(2 - 1)

m = 60/1

m = 60

Therefore, the slope of the line given in the graph will be 60 miles/hr.

To solve more questions on functions, expressions and polynomials, visit the link below -

brainly.com/question/17421223

#SPJ2

Thus, the probability of getting triangle when the 20 faced dice is rolled is obtained as: 1/2.

Events related with the experiment are the results of a random experiment.

For the given data:

probability = favourable events / total events

Then,

probability of getting triangle = 10/ 20 = 1/2

Thus, the probability of getting triangle when the 20 faced dice is rolled is obtained as: 1/2.

Know more about the unbiased events

https://brainly.com/question/25670011

#SPJ1

Correct Question:

A die has 20 sides shown as​ follows: ​10 triangles, 3 ​circles, and 7 squares. The probability of rolling a triangle is​ ___ ?

Answer:

Step-by-step explanation:

Set up an equation:

7x + 10x + 13x = 100000 and solve for x:

30x = 100000 so

x = 3333.33

Anna gets 7(3333.33) = 23333.31

Louise gets 10(3333.33) = 33333.33

Lacey gets 13(3333.33) = 43333.29

9514 1404 393

Answer:

  C)  30

Step-by-step explanation:

The marked angles are supplementary to each other.

  140° + (x +10)° = 180°

  x = 30 . . . . . . divide by °, subtract 150

Answer:

Step-by-step explanation:

Ramesh will bear a total medical expense of RM1,760, and the insurance company will cover RM2,900.

1. Ramesh's deductible is RM1,500 per year. This means that he is responsible for paying the first RM1,500 of medical expenses before the insurance coverage kicks in.

2. For the first treatment, the medical cost was RM700. Since this amount is less than the deductible, Ramesh will have to pay the entire RM700 out of pocket.

3. For the second treatment, the medical cost was RM2,000. Since Ramesh has already met his deductible with the first treatment, the insurance company will cover a portion of the expenses. Ramesh will be responsible for 20% of the remaining RM500 (RM2,000 - RM1,500), which amounts to RM100. The insurance company will cover the remaining 80% of RM500, which amounts to RM400.

4. For the third treatment, the medical cost was RM1,700. Again, since Ramesh has already met his deductible, the insurance company will cover a portion of the expenses. Ramesh will be responsible for 20% of the entire cost, which amounts to RM340 (20% of RM1,700). The insurance company will cover the remaining 80% of RM1,700, which amounts to RM1,360.

5. To calculate the total medical expenses borne by Ramesh, we add up the amounts he is responsible for in each treatment: RM700 + RM100 + RM340 = RM1,140.

6. The total medical expenses covered by the insurance company can be calculated by adding up the amounts they pay in each treatment: RM400 + RM1,360 = RM1,760.

7. Finally, to find the overall amount borne by Ramesh and the insurance company, we sum up the individual expenses: Ramesh's expenses + insurance company's expenses = RM1,140 + RM1,760 = RM2,900.

For more such questions on expense, click on:

https://brainly.com/question/2292799

#SPJ8

Answer:

20x+80

10/21

Step-by-step explanation:

Answer:

20x+80

10/21

Step-by-step explanation:

20*x+20*4

20x+80

\(\frac{5}{7}*\frac{2}{3}\)

5*2=10

7*3=21

\(\frac{10}{21}\)

The y-intercept of the linear model is 211,400, which represents the estimated number of automobiles in the town in the year 2015 (when the independent variable is zero).

To find the y-intercept of the linear model, we need to determine the value of the dependent variable (the number of automobiles) when the independent variable (the number of years since 2015) is equal to zero.

Let's first find the slope of the line, which represents the rate of change of the number of automobiles per year:

slope = (change in number of automobiles) / (change in number of years)

slope = (2420 - 1890) / (2020 - 2015) = 106 automobiles per year

Now we can use the point-slope form of a linear equation to find the y-intercept:

y - y1 = m(x - x1)

where y1 is the value of the dependent variable when the independent variable is x1. In this case, x1 = 2015, y1 = 1890, and m = 106 (the slope we just calculated).

y - 1890 = 106(x - 2015)

To find the y-intercept, we can set x = 0:

y - 1890 = 106(0 - 2015)

y - 1890 = -213,290

y = 211,400

for such more question on linear model

https://brainly.com/question/9753782

#SPJ11

The number of tourists who visited the city at the end of February that year is 4x.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

The number of tourists visiting the city doubles every month, which means the number of tourists at the end of January is 2 times the number of tourists at the beginning of January, or 2x.

Similarly, the number of tourists at the end of February is 2 times the number of tourists at the end of January, or 2(2x) = 4x.

Therefore,

The number of tourists who visited the city at the end of February that year is 4x.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ2

The graph of a proportional relationship can be described as a graph that always starts at point zero and is always a straight line graph.

A straight line graph is defined as the type of graph that is also called a linear graph which shows a relationship between two or more quantities that uses a graphical form of representation.

There are some characteristics that shows that a graph is of proportional relationship which include the following:

Learn more about graph here:

https://brainly.com/question/25184007

#SPJ1

Answer:

76

Step-by-step explanation:

j and k are the same size and every triangle equals 180

64+64=128

180-128=52

L=52

l and m are the same

52+52=104

180-104= 76

n=76

The end behavior of the function is as x tends to infinity, f(x) tends to zero. It is power function.

The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.

The degree and the leading coefficient of a polynomial function given is determine the end behavior of the graph.

Given that function has a vertical asymptote at x = -5 and x = 3 , a point discontinuity at x = 2.

The end behavior of f(x) goes to 0 as x goes to negative infinity and f(x) goes to 0 as x goes to positive infinity.

The domain is (-inf, -5)U(-5, 2)U(2, 3) U (3,inf).

Hence, we can conclude that the end behavior of the function is as x tends to infinity, f(x) tends to zero.

Learn more about the end behavior of function here:

brainly.com/question/11808280

#SPJ1

The two numbers from the equations are 16 and -52

The first number is 16

The second number is -52

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first number be = x

Let the second number be = y

So , the equation will be

Let the sum of two numbers be = -36

And the equation will be

x + y = -36   be equation (1)

Let the difference of two numbers be = 68

And the equation will be

x - y = 68   be equation (2)

Subtracting equation (1) from equation (2) , we get

On simplifying the equation

2x = 32

Divide by 2 on both sides of the equation , we get

x = 16

The equation will be

Substituting the value of x in the equation , we get

x + y = -36

16 + y = -36

Subtracting 16 on both sides , we get

y = -52

Hence , the two numbers are 16 and -52

To learn more about equations click :

https://brainly.com/question/10413253

#SPJ6

Answer:

\(\huge\boxed{\sf 18^{-3}}\)

Step-by-step explanation:

\(\displaystyle \frac{18^4}{18^7}\)

So, the expression becomes:

= \(18 ^{4-7}\)

= \(18^{-3}\)

\(\rule[225]{225}{2}\)

Answer:

x = - 6

Step-by-step explanation:

x² + 12x + 36 = 0 ( subtract 36 from both sides )

x² + 12x = - 36

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(6)x + 36 = - 36 + 36

(x + 6)² = 0 ( take square root of both sides )

x + 6 = \(\sqrt{0}\) = 0 ( subtract 6 from both sides )

x = - 6

The mechanical advantage of the given machine is 40, Velocity ratio is 80 and efficiency is 0.5.

The given question is concerned with finding the mechanical advantage, velocity ratio and efficiency of a weight lifting machine.

The problem has provided the following information:

Weight of the object, W = 1 kN = 1000 NEffort applied, E = 25 NHeight through which the object is lifted, h = 100 mm = 0.1 m Distance through which the effort is applied, d = 8 m

We know that, mechanical advantage = load/effort = W/E and velocity ratio = distance moved by effort/distance moved by the load.Mechanical advantage

The mechanical advantage of the given machine is given by; Mechanical advantage = load/effort = W/E= 1000/25= 40Velocity ratioThe velocity ratio of the given machine is given by;

Velocity ratio = distance moved by effort/distance moved by the load.= d/h = 8/0.1= 80EfficiencyThe efficiency of the given machine is given by;

Efficiency = (load × distance moved by load) / (effort × distance moved by effort)Efficiency = (W × h) / (E × d)= (1000 × 0.1) / (25 × 8)= 0.5

Therefore, the mechanical advantage of the given machine is 40, velocity ratio is 80 and efficiency is 0.5.

For more questions on Velocity .

https://brainly.com/question/25749514

#SPJ8

Answer:

I dont speak math sorry

Step-by-step explanation:

Answer:

I think 7 would be the estimate if im wrong this is the specific number 6 13/15

Step-by-step explanation:

Answer:

She will need aproximately 7 cups

Step-by-step explanation:

First, you add 3 1/5 and 3 2/3 which is 6.86666666667

Just round that answer up and that'll give you seven

The two-way frequency table that correctly shows the marginal frequencies is Table B.

A two-way frequency table is used to display the frequencies of two categories of variables collected from a single group. We are asked to find the two-way frequency table that correctly shows the marginal frequencies and to do this, we can see that in the second table, the sum of men who participated in the survey amounted to

12 + 86 = 98

Now the total number of adults that participated in the survey was 200. This means that the number of women was 102. That is;

200 - 98 = 102

The only table that represents the number of women as 98 is table B and this makes it the correct choice.

Learn more about a two-way frequency table here:

https://brainly.com/question/16148316

#SPJ1

Answer:

a=0

Step-by-step explanation:

If this is what you are asking, and if I understand it correctly, 8*8=64 and not 8, but 8*0=0, therefore 0 is a solution.