pls help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Pls Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer 1

The length of the other diagonal of the kite is: 50 cm

What is the Area of a Kite?

We want to find the area of the given kite but It should be noted that:

The hypotenuse is usually the slanted line part in a triangle.

Area of a kite = pq/2

where:

p and q are diagonals

We are given:

Area of Kite = 180 cm²

Length of diagonal = 16 cm

Thus:

16q = 180

q = 180/16

q = 50 cm

This gives us the length of the other diagonal of the kite

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Related Questions

The density of milk is 1.03g/cm3. What is the mass of 405 cm3 of milk?

Answers

The mass of the 405 cm³ milk is 417.15 grams.

What is the mass of the milk?

Density is simply  the mass of a substance per unit volume.

It is expressed mathematically as;

p = m / v

Where m is mass and v is volume.

Given that:

Density of the milk p =  1.03g/cm³

Volume of the milk v = 405 cm³

Mass m = ?

Plug the values into the above formula and solve for mass m.

p = m / v

m = pv

m = 1.03g/cm³ × 405 cm³

m = 417.15 g

Therefore, the value of the mass is 417.15 grams.

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Simplify
| 2(11-3)/2|^2

Answers

Answer:

To simplify the expression |2(11-3)/2|^2, we follow the order of operations (parentheses, exponents, multiplication and division from left to right, and addition and subtraction from left to right).

First, simplify the expression inside the absolute value:

2(11-3)/2 = 2(8)/2 = 16/2 = 8

Now, simplify the absolute value of 8, which is simply the magnitude of 8:

|8| = 8

Finally, square the result:

8^2 = 8 * 8 = 64

Therefore, the simplified value of |2(11-3)/2|^2 is 64.

Step-by-step explanation:

1. The list of rational numbers below are
ordered from greatest to least.
15, 6.7, , 100%, -55%,
Which of the following numbers could NOT be
the missing value in the list above?
A. -80%
C.-2.6
B. -1
D. - 180%
-2.5

Answers

Answer:

The list of rational numbers below are ordered from greatest to least.

15, 6.7, , 100%, -55%,

To determine which of the following numbers could NOT be the missing value in the list above, we need to determine the correct order of the numbers in the list.

First, we can convert the percentages to decimals:

100% = 1

-55% = -0.55

Now we can order the numbers from greatest to least:

15, 6.7, 1, -0.55, x

We know that x is a rational number, so it can be expressed as a fraction. We can eliminate answer choices C and D because they are not rational numbers.

Next, we can compare x to the other numbers in the list. We know that x must be less than 6.7, so we can eliminate answer choice A.

That leaves us with answer choice B, -2.5. This number could be the missing value in the list, so the answer is B.

The values in the table show the relationship between times
measured in seconds and distances measured in meters.
Seconds
5
10
15
20

Meters
20
40
60
80
What is the unit rate, In meters per second, of the relationship
shown in the table?
Enter your answer in the box.
meters per second

Answers

the unit rate is 4 meters per second, meaning that for every second that passes, the distance increases by 4 meters.

The table shows the relationship between time and distance time is measured in seconds and distance is measured in meters.

The table provides us with the data points of time and distance allows us to examine the relationship between these two variables.

The table as time increases the distance also increases.

This suggests that there is a positive relationship between time and distance.

The unit rate of the relationship tells us how much distance changes for every unit of time.

The unit rate is 4 meters per second meaning that for every second that passes, the distance increases by 4 meters.

The relationship shown in the table is not necessarily a linear relationship.

A linear relationship would mean that the distance changes by the same amount for each unit of time.

The increase in distance is not constant over time.

From 5 seconds to 10 seconds the distance increases by 20 meters but from 10 seconds to 15 seconds the distance increases by 20 meters again and from 15 seconds to 20 seconds the distance increases by 20 meters yet again.

The table provides us with a snapshot of the relationship between time and distance and by examining the data we can identify patterns and relationships that can help us understand the behavior of these variables.

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car cost #450,000 and its being sold for #540,000. find the profit as a percentage of the cost price​

Answers

The profit as a percentage of the cost price​ is 20%

Finding the profit as a percentage of the cost price​

From the question, we have the following parameters that can be used in our computation:

Car cost #450,000It;s being sold for #540,000.

The profit is the difference beyween the selling price and the coste price

So, we have

Profit = 540000 - 450000

Evaluate

Profit = 90000

Next, we have

Percentage = Profit/Cost price * 100

This gives

Percentage = 90000/450000* 100

Evaluate

Percentage = 20%

Hence, teh percentage is 20%

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Answer:

Step-by-step explanation:

To find the profit as a percentage of the cost price, we need to calculate the profit first.

Profit = Selling price - Cost price

Profit = #540,000 - #450,000

Profit = #90,000

Now we can calculate the profit percentage as follows:

Profit percentage = (Profit / Cost price) x 100

Profit percentage = (#90,000 / #450,000) x 100

Profit percentage = 20%

Therefore, the profit as a percentage of the cost price is 20%.

ELS, an S corporation, reported a business loss of $1,000,000. Ethan, ELS’s sole shareholder, is involved in ELS’s daily business activities, and he reports $1,200,000 of taxable income from sources other than ELS. What must you know in order to determine how much, if any, of the $1,000,000 loss Ethan may deduct in the current year? How would your answer differ when the CARES Act applied. Explain.

Answers

The tax deduction is explained below.

We need to take into account a few things in order to establish how much, if any, of the $1,000,000 loss Ethan may deduct in the current year.

We need to know Ethan's basis in his ELS shares, or shareholder basis. Shareholder basis, which is changed yearly based on numerous criteria such as income, losses, donations, and payouts, symbolizes the investment a shareholder has in the S corporation.

Ethan might be entitled to deduct the loss up to the amount of his basis if his basis is positive.

We must assess if Ethan is covered by the at-risk regulations. The shareholder's amount at risk in the S corporation is the only amount that can be deducted for losses under the at-risk regulations.

If Ethan is subject to these rules, his loss deduction could be limited based on his at-risk amount.

A few tax provisions were temporarily changed as a result of the CARES Act. The CARES Act specifically altered the exclusions for business losses for non-corporate taxpayers, including individual S company shareholders. Ethan might not be able to deduct the $1,000,000 loss because of restrictions on company losses that existed prior to the CARES Act.

The excess business loss limitation for non-corporate taxpayers was temporarily suspended under the CARES Act.

This meant that Ethan and other individual shareholders could write off business losses without being constrained by the prior cap of $250,000 ($500,000 for married taxpayers filing jointly).

Therefore, regardless of any restrictions that could have existed before to the passage of the CARES Act, Ethan would be permitted to deduct the entire $1,000,000 loss in the current year if the CARES Act is applicable.

Taxpayers were temporarily helped by being able to deduct losses from other income. It's crucial to remember that the CARES Act was passed in reaction to the COVID-19 outbreak and that some of its requirements could not be in force at the moment.

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please show work I don't understand how to do this ​

Answers

Answer: x= 3

Step-by-step explanation:

We solve the given equation to obtain value of x

Step 1: We open the bracket:

8x-6-8=4+2x

Step 2: We transform terms with x to left hand side and constants to the right hand side and change their signs

8x-2x=4+6+8

6x=18

x=18/6

Thus, x=3

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Compare the linear relationships.

Linear equation A: y=58x
Linear equation B is partially represented by the points in this table.

x
y

12
623

13
729

14
779

Which linear equation has the greater slope? Why?

Select the option that correctly answers both questions.

Responses

Equation B has the greater slope. It has a slope of 623,
and equation A has a slope of 58,
which is smaller.
Equation B has the greater slope. It has a slope of 6 and 2 thirds textsf comma and equation A has a slope of 5 eighths textsf comma which is smaller.

Equation A has the greater slope. It has a slope of 58,
and equation B has a slope of 59,
which is smaller.
Equation A has the greater slope. It has a slope of 5 eighths textsf comma and equation B has a slope of 5 ninths textsf comma which is smaller.

Equation A has the greater slope. It has a slope of 59,
and equation B has a slope of 58,
which is smaller.
Equation A has the greater slope. It has a slope of 5 ninths textsf comma and equation B has a slope of 5 eighths textsf comma which is smaller.

Equation B has the greater slope. It has a slope of 59,
and equation A has a slope of 58,
which is smaller.

Answers

Compare the linear relationships shows that

Equation B has the greater slope. It has a slope of 106, and Equation A has a slope of 58, which is smaller.

How to compare the slopes

Equation A is given as y = 58x

The slope is 58

For Equation B  

Slope of Equation B = (change in y) / (change in x)

= (729 - 623) / (13 - 12)

= 106 / 1

= 106

Comparing the slopes, we can see that the slope of Equation B (106) is greater than the slope of Equation A (58)

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Luke is going to invest $7,600 and leave it in an account for 5 years. Assuming the
interest is compounded daily, what interest rate, to the nearest tenth of a percent,
would be required in order for Luke to end up with $8,900?

Answers

The nearest tenth of a percent an interest rate of 4.5% would be required for Luke to end up with $8,900 after 5 years with daily compounding.

The formula for compound interest to solve the problem:

A = [tex]P(1 + r/n)^{(nt)[/tex]

A is the final amount, P is the initial principal, r is the interest rate, n is the number of times the interest is compounded per year and t is the time in years.

P = $7,600

A = $8,900

t = 5 years

n = 365 (compounded daily)

The interest rate r.

Rearrange the formula and solve for r:

r = [tex]n[(A/P)^{(1/(nt))} - 1][/tex]

Substituting the values we know:

r = [tex]365[(8,900/7,600)^{(1/(5 \times 365))} - 1][/tex]

≈ 4.5%

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5) Use the figure to answer the
following question.
Which expression can be used to find the volume of the figure below?
2 cm
Choose 1 answer:
A
B
8 cm
7 cm 1 cm
6 cm
cm x 7 cm x 1 cm) + (1 cm x 6 cm x 8 cm)
cm x 8 cm x 7 cm) + (1 cm x 6 cm x 8 cm)
cm x 7 cm) + (8 cm x 6 cm)
Option A above
O Option B above
O Option C above
*
1 point

Answers

An expression that can be used to find the volume of the figure include the following: B. (2 cm × 8 cm × 7 cm) + (1 cm × 6 cm × 8 cm).

How to calculate the volume of a rectangular prism?

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.

By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have the following;

Volume of figure = (2 cm × 8 cm × 7 cm) + (1 cm × 6 cm × 8 cm)

Volume of figure = 112 cm³ + 48 cm³

Volume of figure = 160 cm³

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in how many different ways can 7 floats line up for the homecoming parade

Answers

Step-by-step explanation:

7!  =  7 P 7 = 5040 ways

7 choices for first

6 choices for 2nd

5 choices for 3rd

4 chouces for 4th

3

2

1

           7 x 6 x 5 x 4 x 3 x 2 x 1 = 7!

it takes 16 people to play a 30 minute rugby game. How many people would it take to play an hour game

Answers

I’m pretty sure u would double the number of people since it doubled the time
It would take 32 people

John deposited $600 into a savings account at an interest rate of 5% per year. How much interest will he earn in 3 years? What will be his account balance, including interest, after 3 years?

Answers

Answer:

$690

Step-by-step explanation:

To find the interest earned in three years, we can use the interest formula

Interest = Principal x Rate x Time

- Principal = $600 (the amount John deposited)

- Rate = 5% per year (as a decimal, this is 0.05)

- Time = 3 years

Interest = $600 x 0.05 x 3 = $90

Therefore, John will earn $90 in interest over 3 years.

To find his account balance, including interest, after 3 years, we can simply add the interest earned to the original principal:

Account balance = Principal + Interest

Account balance = $600 + $90 = $690

Therefore, John's account balance, including interest, after 3 years will be $690.

Answer:

Simple interest: 690, compound interest: 694.5

Step-by-step explanation:

Simple interest  = PRT/100 = 600*5*3/100 = 90 = 600+90 = 690

compound interest = P(1+r/100)^n = 600(1+5/100)^3 = 694.5

Your answer depends on if its simple or compound interest if not said so either of the answers I have given to you is right :)

If we rent a truck and pay a $75/day fee plus $.20 for every mile we travel, write a linear equation that would express the total cost per day using to represent the number of miles we travel. Graph this function on your graphing calculator and find the total cost for one day if we travel 70 mi

Answers

Answer: $89 for one day and 70 miles

Step-by-step explanation:

Bernard can save $315 per month that he puts into a savings account
earning 7% annual interest. How much will he have saved after 4
years? show your work

Answers

After 4 years of saving $315 per month at 7% annual interest rate, Bernard will have saved approximately $10,864.11.

To calculate the amount that Bernard will have saved after 4 years, we can use the formula for compound interest:

A = P(1 + r/n[tex])^{(nt)[/tex]

Where:

A = the amount of money Bernard will have saved after 4 years

P = the amount of money Bernard is putting into savings each month = $315

r = the annual interest rate = 7% = 0.07

n = the number of times interest is compounded per year (monthly compounding in this case) = 12

t = the number of years = 4

Substituting the given values into the formula, we get:

A = 315(1 + 0.07/12[tex])^{(12\times 4)[/tex]

A = 315(1.00583333[tex])^{48[/tex]

A = 315(1.31564)

A = $10,864.11

Therefore, after 4 years of saving $315 per month at 7% annual interest rate, Bernard will have saved approximately $10,864.11.

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Can someone help me with thissss

The revenue generated by a company manufacturing lawn mowers is R= -0.5x^2+91x, where x represents the number of mowers produced. The cost to produce the mowers is C= 38x+300,where x is the number of mowers produced.
Find the profit polynomial (Hint: Profit = Revenue - Cost) that describes the total profit generated by the company manufacturing lawn mowers based on the number of mowers produced.

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

Give the profit earned if 53 mowers are sold. ------------

add work please

Answers

The profit function is given as follows:

P(x) = -0.5x² + 53x - 300.

The profit if 53 mowers are sold is given as follows:

P(53) = -$1,598.5. (loss).

How to obtain the profit function?

The profit function is obtained as the subtraction of the revenue function by the cost function, as follows:

P(x) = R(x) - C(x).

The functions for this problem are given as follows:

R(x) = -0.5x² + 91x.C(x) = 38x + 300.

Hence the profit function is given as follows:

P(x) = -0.5x² + 91x - (38x + 300)

P(x) = -0.5x² + 53x - 300.

The profit if 53 mowers are sold is given as follows:

P(53) = -0.5(53)² + 53(2) - 300

P(53) = -$1,598.5.

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If trapezoid JKLM is translated using the rule (x, y) → (x + 3, y − 3) and then translated using the rule (x, y) → (x − 1, y + 1) to create trapezoid J″K″L″M″, what is the location of L″?

Answers

Answer:

L'' = (6, - 5 )

Step-by-step explanation:

the translation rule (x, y ) → (x + 3, y - 3 ) means

add 3 to the original x- coordinate and

subtract 3 from the original y- coordinate

then

L (3, - 2 ) → L'' (3 + 3, - 2 - 3 ) → L'' (6, - 5 )

i really need the answer to this, can anyone help me please?

Answers

The value of total area of the shape is,

⇒ 82 cm²

We have to given that;

Figure of shape is shown.

Since, Figure is made by three rectangles.

And, Area of rectangle is,

A = length x width

Hence, The area of upper rectangle is,

A = 3 x 8

A = 24 cm²

Area of middle rectangle is,

A = (11 - (3 + 5)) x (8 - 2)

A = 3 × 6

A = 18 cm²

Area of lower rectangle is,

A = 5 x 8

A = 40 cm²

Thus, The value of total area of the shape is,

⇒ 24 + 18 + 40 cm²

⇒ 82 cm²

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Post Test: Polygons 4 Given: ΔMNO Prove: The medians of ΔMNO are concurrent. Given triangle of sides M (x1, y1), N (x2, y2) and O (x3, y3) point to the same triangle on the graph of x-axis and y-axis, with M prime (0, 0), O prime (2t, 0) and N prime (2r, 2s) has a midpoint s formed by connecting Prime PQR Proof: Statements Reasons 1. ∆MNO Given 2. Use rigid transformations to transform ΔMNO to the congruent ΔM'N'O' so that M' is at the origin and M'O' lies on the x-axis in the positive direction. Rigid transformations result in congruent shapes. 3. Any property that is true for ΔM'N'O' will also be true for ΔMNO. Definition of congruence 4. Let r, s, and t be real numbers such that the vertices of ΔM'N'O' are M'(0,0), N'(2r,2s), and O'(2t,0). Defining constants 5. Let P', Q', and R' be the midpoints of M'N', N'O', and M'O', respectively. Defining points 6. P' = (r,s); Q' = (r + t,s); R' = (t,0) ? 7. Definition of slope 8. Applying point-slope formula 9. and intersect at point S . Algebra 10. Point S lies on . The coordinates of S satisfy the equation of . 11. All three lines share point S. Follows from 9 and 10 12. The medians are concurrent. Definition of concurrent lines Which reason completes the proof for step 6? A. Definition of midsegment B. Definition of slope C. Definition of midpoint D. Definition of median

Answers

A reason that completes the proof for step 6 include the following: A. Definition of midsegment.

What is a midsegment?

In Mathematics and Geometry, a midsegment can be defined as a type of line segment that is typically used for connecting the midpoints of two (2) sides of a triangle.

In order to prove that a midsegment is parallel to the median, it is imperative that the definition of the midsegment must be applied.

According to the definition of the midsegment, which states that a line segment connects the midpoints of the two (2) sides of a given triangle (ΔMNO), we can logically deduce the following:

P' = (r, s)

Q' = (r + t, s)

R' = (t, 0)

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

please help I'm confused, what's the area of the entire quadrilateral?

Answers

Answer:

62.25

Step-by-step explanation:

this quadrilateral is a trapizoid

A = (a+b)/2 * h

a = x

b = 2.4+4.2+x

h = 7.5

we know x is 5 so we just plug it in

after doing that we get 62.25

Tina has volunteered at the pet shelter 4 more times than Kai. Tina has volunteered 16
times Which equation represents this situation?
A. 16+k-4
B. 16k-4
C. K+4=16
D. 4K=16

Answers

The correct answer is option C: [tex]\(k + 4 = 16\).[/tex] This linear equation represents the relationship between Tina and Kai's volunteer times.

To represent the given situation, the equation that correctly represents the relationship between Tina's volunteer times (Tina = 16) and Kai's volunteer times (Kai = k) is:

[tex]\[Tina = Kai + 4\][/tex]

In this equation, Tina's volunteer times are represented by "Tina," and Kai's volunteer times are represented by "Kai." Since Tina has volunteered 4 more times than Kai, we add 4 to Kai's volunteer times to get the total number of times Tina has volunteered.

Substituting the given values, we have:

[tex]\[16 = k + 4\][/tex]

This equation represents the fact that Tina has volunteered [tex]16[/tex] times, which is equal to Kai's volunteer times (k) plus the additional 4 times that Tina volunteered.

Simplifying the equation:

[tex]\[k + 4 = 16\][/tex]

This equation is equivalent to the original equation and represents the relationship between Tina and Kai's volunteer times. Hence, the correct answer is option C: [tex]\(k + 4 = 16\).[/tex]

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The weather table predicts the chance of rain for five days.


Day of the Week Chance of Rain
Monday 70%
Tuesday 10%
Wednesday 40%
Thursday 50%
Friday 60%

Answers

Friday has a 60% chance of rain. This indicates a relatively high Probability of rainfall, making it more likely to experience wet conditions on Friday.

The weather table provides information on the chance of rain for five consecutive days, starting from Monday to Friday. Here are the details:

Day of the Week | Chance of Rain

----------------|---------------

Monday          | 70%

Tuesday         | 10%

Wednesday    | 40%

Thursday        | 50%

Friday             | 60%

According to the table, Monday has the highest chance of rain with a probability of 70%. This indicates that there is a relatively high likelihood of rain occurring on Monday. However, it does not guarantee that it will rain, as there is still a 30% chance of a dry day.

On Tuesday, the chance of rain drops significantly to 10%. This suggests that it is highly unlikely for rain to occur on Tuesday, with a higher probability of dry weather.

Wednesday shows a moderate chance of rain at 40%. This indicates a somewhat higher possibility of precipitation compared to Tuesday but not as high as Monday.

Thursday follows with a 50% chance of rain. This suggests an even chance of rain or no rain, making it relatively uncertain.

Finally, Friday has a 60% chance of rain. This indicates a relatively high probability of rainfall, making it more likely to experience wet conditions on Friday.

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You and some friends buy hamburgers
and milkshakes for lunch. A hamburger
costs $1.50 and a milkshake costs $2.00.
The total bill for 12 items is $21.50.
How many hamburgers and how many
milkshakes did your group buy?
(Please hurry and show work.)

Answers

Answer:

5 burgers and 7 milkshakes

Step-by-step explanation:

1.5x5=7.5

2x7=14

7.5+14=21.5

WILL GIVE BRAINLIEST PLEASE HELP

Answers

Answer: line a is parallel to line b

Step-by-step explanation:

the only 2 lines they're talking abt are line a and line b

For which triangle does the Pythagorean Theorem
express the relationship between the lengths of its three
sides?
A
B
C
D

Answers

Pythagorean theorem is represented by triangle B.

Which triangle express the relationships according to Pythagorean theorem?

In this question we find four cases of triangle, of which we must determine what triangle can be explained by Pythagorean theorem. This theorem offers a relationship between the three sides of the triangle:

r² = x² + y²

Where:

x, y - Legsr - Hypotenuse.

Please notice that hypotenuse is the longest side of the triangle. Graphically speaking, there is a right triangle, that is, a triangle with one right angle. Then, triangle B express the relationship according to Pythagorean theorem.

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The melody in 12-bar blues often includes which feature, found in some work songs?

bebop

Oragtime

O call & response

Answers

Answer:

Hard bop energetic and emotional style of music developed in response to cool jazz and featured fast tempos, loud dynamics, and blues and gospel influences.

Step-by-step explanation:

A football is catapulted into the air so that its height h, in metres, after t seconds is h = -4.9t² +27t +
2.4 a) How high is the football after 1 second? b) For how long is the football more than 30 m high? c)
What is the maximum height of the football?

Answers

Answer:

a] 24.5; b] 2.8; c] 39.59.

Step-by-step explanation:

a. after t=1sec:

h(1)=-4.9*1²+27*1+2.4; ⇔h(1)=24.5 [m];

b. more than 30 [m] heigh:

-4.9t²+27t+2.4≥30; ⇔ 4.9t²-27t+27.6≤0; ⇔(t-1.35)(t-4.15)≤0;

Δt≈4.15-1.35=2.8 [sec];

c. maximum height:

h'(t)=-9.7t+27; ⇒ h'(t)=0, ⇒ -9.7(t-2.78)=0; ⇒ t=2.78 [sec], then

[tex]h_{max}=h(2.78)=-4.9*2.78^2+27*2.78+2.4=39.59[m].[/tex]

Solve for measure of angle a.
41
03
29°
a = [ ? ]°
If two chords intersect inside a circle: - bec

Answers

The measure of angle a is 35°

How to solve for measure of angle a?

The chord of a circle is the line segment joining any two points on the circumference of the circle.

The diameter is the longest chord of a circle which passes through the center of the circle.

For chords that meet inside of a circle, the measure of the angle formed is one-half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

Using the above concept (That is the given hint in the question), we can say:

∠a = (29 + 41)/2

∠a = 70/2

∠a = 35°

Therefore, the measure of angle a is 35°

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Complete Question

Check attached image

A wall 24 inches is conrete, 5 inches is brick, and 9 inches is limestone. What fracrion of the wall is concrete?

Answers

The fraction of the wall that is concrete is 12/19

What is a fraction?

A fraction is a mathematical representation of a part of a whole or a division of one quantity by another. It consists of two parts: a numerator and a denominator, separated by a horizontal line called a fraction bar or a division slash.

The numerator represents the number of parts or the quantity being considered, while the denominator represents the total number of equal parts or the divisor. The numerator and denominator are both whole numbers or integers.

In this problem, to determine the fraction that is concrete, we have to know the total length of the wall.

length of wall = 24 + 5 + 9 = 38 inches

The fraction of the wall that is concrete = 24 / 38 = 12/19

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Suppose that 10,000 barrels of nuclear waste are
Housed in a storage facility. Each barrel has a 1 in
100,000 chance of developing a leak in a given ye
If leaks in different barrels are independent events
what is the probability that at least 1 barrel developing
a leak over a 20 year period

Answers

The probability that at least one barrel develops a leak over a 20-year period is approximately 0.1813 or 18.13%.

How to calculate the probability

Since leaks in different barrels are independent, the probability that none of the 10,000 barrels develops a leak in a given year is:

0.99999¹⁰⁰⁰⁰ = 0.9048

Therefore, the probability that at least one barrel develops a leak in a given year is:

1 - 0.9048 = 0.0952

Now we can use the same approach to find the probability that no barrel develops a leak in 20 years:

0.99999²⁰⁰⁰⁰⁰ = 0.8187

Therefore, the probability that at least one barrel develops a leak over a 20-year period is:

1 - 0.8187 = 0.1813

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