Find the unknown angle measure.

Answer:

A. 16

Step-by-step explanation:

Answer:

\(\boxed{V=lwh}\)

Step-by-step explanation:

The formula for volume of a cuboid is:

\(V=lwh\)

\(volume = length \times width \times height\)

Answer:

V = l w h

Step-by-step explanation:

Volume of a Cuboid = Length × Width × Height

Where l = length, w = width and h = height

step 1

Verify if the figures are similar

Remember that, if two figures are similar, then the ratio of its corresponding sides is proportional

so

In this problem we have two squares, and the squares are always similar figures

step 2

Find the scale factor

the scale factor is the ratio between corresponding sides

In this problem we have a reduction, because the figure I is smaller than figure II

the scale factor is equal to

scale factor=1/3

therefore

the answer is

scale factor 1/3 and it is a reduction (figure II to figure I)

Part 2

look at shape 111 in graph 2, is there a dilation that maps shape 11 onto shape 111? I'd so, what is the scale factor and is it an enlargement or a reduction

Figure II to figure III ------> is a reduction

so the scale factor is

scale factor=2/3

the answer is

Yes, there is a dilation

It is a reduction

scale factor=2/3

Part 3

is there a dilation that maps shape 111 onto shape 11? if so what is these scale factor and us it an enlargement or a reduction

REmember that

All the squares are similar

so

Yes, there is a dilation

Figure III to Figure II ------> it is an enlargement

scale factor=3/2=1.5

Part 4

is shape 1 similar to shape 11? why or why not?

Yes, they are similar

because, all the squares are always similar

that means, that the ratio of its corresponding sides is proportional

Part 5

is shape 11 similar to shape 111? why or why not?

Yes, they are similar

because, all the squares are always similar

that means, that the ratio of its corresponding sides is proportional

Part 6

if shape 1 is similar to shape 11 and shape 11 is similar to shape 111, what does that mean for shape 1 and shape 111?

yes , they are similar

shape 1 and shape 111 are similar because if you multiply the length of square 1 by the scale factor (2) you obtain the length of square 111

Answer:

Simplifying

4x + -7 = -2x + -5

Reorder the terms:

-7 + 4x = -2x + -5

Reorder the terms:

-7 + 4x = -5 + -2x

Solving

-7 + 4x = -5 + -2x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2x' to each side of the equation.

-7 + 4x + 2x = -5 + -2x + 2x

Combine like terms: 4x + 2x = 6x

-7 + 6x = -5 + -2x + 2x

Combine like terms: -2x + 2x = 0

-7 + 6x = -5 + 0

-7 + 6x = -5

Add '7' to each side of the equation.

-7 + 7 + 6x = -5 + 7

Combine like terms: -7 + 7 = 0

0 + 6x = -5 + 7

6x = -5 + 7

Combine like terms: -5 + 7 = 2

6x = 2

Divide each side by '6'.

x = 0.3333333333

Simplifying

x = 0.3333333333

Step-by-step explanation:

Answer:

x = - 1

Step-by-step explanation:

Let's solve

4x + 7 = 2x + 5

Subtract 2x from both sides.

4x + 7 −2x = 2x + 5 −2x

2x + 7 = 5

Subtract 7 from both sides.

2x + 7 − 7 = 5 −7

2x = −2

Divide both sides by 2.

2x / 2 = −2 / 2

x = −1

Answer:

109 cm

Step-by-step explanation:

The Circumference of a circle, C is given as ;

2πr

Where, r = Radius

Radius, r = 17.4 cm

C = 2 * 3.14 * 17.4

C = 109.272 cm

C = 109 cm (nearest whole number)

Answer:

74 is already in the simplest form. It can be written as 1.75 in decimal form (rounded to 6 decimal places).

Step-by-step explanation:

Answer:

no solution

Step-by-step explanation:

25y² +36 = 24

(5y + 6) (5y + 6)

roots -6/5, -6/5

solution is always a positive root

A mathematically indication example would be to solve the equation 3x + 2 = 14 for the value of x. The solution would be 4.

Looking for a mathematically indication example, we can consider a simple mathematical equation with one variable and solve it.

The equation would be 3 x + 2 = 14.

So we can solve for the equation to be :

3x + 2 - 2 = 14 - 2

3x = 12

3 x / 3 = 12 / 3

x = 4

In conclusion, the mathematically indication example would be 3x + 2 = 14 and the value of x would be 4.

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The complete square form of - 3x² + 33 = 48x is [x + 8]² = 75

To do this, we add and subtract a constant term to the quadratic expression to make it a perfect square.

In this case, we use the formula x² + 2bx + b² = (x + b)² to rewrite the quadratic expression as a perfect square trinomial, and then we solved for the variable by isolating the squared term and taking the square root.

Here we have

- 3x² + 33 = 48x

Keep 'x' terms on one side and constant terms sides on another side

=> - 3x² - 48x = - 33

Divide by - 3 on both sides

=> -3(x² + 4x)/3 = - 33/3  

=> x² + 16x = 11      

Take half of the 'x' term and square it and add on both sides

=> x² + 2(8x) (x) + (8)² = 11 + (8)²  

Which is in the form of x² + 2bx + b² = (x + b)²

=> [x + 8]² = 75

Therefore,

The complete square form of - 3x² + 33 = 48x is [x + 8]² = 75

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Answer: b = 11.62

Step-by-step explanation:

We can use this formula to solve for b:

\(b^{2} =\) \(\sqrt{c^{2}-a^{2} }\)

\(b^{2} =\) \(\sqrt{12^{2}-3^2 }\)

\(b^2= \sqrt{144-9}\)

= 11.61895004

We can round that to 11.62.

Hope this helped!

The Central tendency is typically located to the right of the tallest bar.

In a skewed left distribution, the central tendency is typically located to the right of the tallest bar. Skewed left distributions, also known as negatively skewed distributions, are characterized by a tail that extends towards the left side of the distribution.

The central tendency refers to the measure that represents the center or average of a distribution. It provides information about the typical or central value around which the data points tend to cluster. Common measures of central tendency include the mean, median, and mode.

In a skewed left distribution, the mean is usually influenced by the long tail on the left side of the distribution. This tail pulls the mean towards lower values, resulting in a lower mean compared to the median. Therefore, the mean will typically be located to the left of the tallest bar in a skewed left distribution.

On the other hand, the median is less affected by the skewness of the distribution and is relatively robust to extreme values. It represents the value that separates the lower 50% of the data from the upper 50%. In a skewed left distribution, the median will be located closer to the tallest bar or even slightly to the right of it.

The mode, which represents the most frequently occurring value in a distribution, may or may not be influenced by the skewness depending on the shape of the distribution. It can be located anywhere along the distribution, and its position is not necessarily tied to the location of the tallest bar.

To summarize, in a skewed left distribution, the central tendency is typically located to the right of the tallest bar. The median is usually closer to the tallest bar or slightly to the right, while the mean is influenced by the skewness and tends to be located to the left of the tallest bar.

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The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.

The correct answer choice is option B.

Malcolm's gift card = $50.

Cost Malcolm's car wash per visit = $7

Martha's gift card = $180

Cost Martha's car wash per visit = Difference between gift card balance of first and second visit

= $180 - $160

= $20

How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7

= $13

Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13

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Answer:

Part A:

1. Computation of Basic EPS

Basic EPS = (Net Income - Preferred Dividends) / Weighted Average Shares Outstanding²

Net Income = $120,000

Preferred Dividends = 4% x $50,000 = $2,000

Weighted Average Shares Outstanding = 100,000 (assuming no change in common stock during the year)

Basic EPS = ($120,000 - $2,000) / 100,000

Basic EPS = $1.18

2. Individual dilution/anti-dilution with decision making

We need to check if any of the convertible securities or stock options are dilutive or anti-dilutive by comparing their impact on EPS with the basic EPS.

Convertible Preferred: Each preferred share can be converted into 1.9 common shares (1,900 / 1,000). The conversion would increase the common shares outstanding by 1,900 and decrease the preferred dividends by $2,000.

EPS after conversion = ($120,000 - $0) / (100,000 + 1,900)

EPS after conversion = $1.16

Since this is lower than the basic EPS of $1.18, the convertible preferred is dilutive and should be included in the diluted EPS calculation.

Stock Options - A: Each option can be exercised at $12 to buy one common share when the average market price is $11. This means that the options are out of the money and would not be exercised by the holders. Therefore, they have no impact on EPS and are anti-dilutive.

Stock Options - B: Each option can be exercised at $7 to buy one common share when the average market price is $8. This means that the options are in the money and would be exercised by the holders. The exercise would increase the common shares outstanding by 4,000 and generate cash proceeds of $28,000 ($7 x 4,000). The cash proceeds can be used to buy back some common shares at the market price of $8. The number of shares bought back is 3,500 ($28,000 / $8). The net increase in common shares outstanding is 500 (4,000 - 3,500).

EPS after exercise = ($120,000 - $2,000) / (100,000 + 500)

EPS after exercise = $1.17

Since this is lower than the basic EPS of $1.18, the stock options - B are dilutive and should be included in the diluted EPS calculation.

Convertible Bonds: Each bond can be converted into 40 common shares (40,000 / 1,000). The conversion would increase the common shares outstanding by 40,000 and decrease the interest expense by $50,000 ($1,000,000 x 5%). The interest expense is net of tax, so we need to multiply it by (1 - tax rate) to get the after-tax amount. The tax rate is 30%.

EPS after conversion = ($120,000 - $2,000 + $50,000 x (1 - 0.3)) / (100,000 + 40,000)

EPS after conversion = $1.19

Since this is higher than the basic EPS of $1.18, the convertible bonds are anti-dilutive and should be excluded from the diluted EPS calculation.

3. Ranking of potential dilutors

We need to rank the potential dilutors from the most dilutive to the least dilutive based on their impact on EPS.

The most dilutive security is the convertible preferred with an EPS of $1.16.

The second most dilutive security is the stock options - B with an EPS of $1.17.

The least dilutive security is the convertible bonds with an EPS of $1.19.

4. Step-by-step inclusion of individual dilutors to arrive at reportable EPS with decision making.

We need to include the potential dilutors in order of their dilution until we reach a point where the next security would be anti-dilutive.

The first security to include is the convertible preferred.

EPS with convertible preferred = ($120,000 - $0) / (100,000 + 1,900)

EPS with convertible preferred = $1.16

The next security to include is the stock options - B.

EPS with stock options - B = ($120,000 - $0) / (100,000 + 1,900 + 500)

EPS with stock options

a) P(psychology student)  = 1/3. b) P(psychology or anthropology student)  = 5/6. c) P(not sociology student)= 5/6

(a) The probability of choosing a psychology student is the number of psychology students divided by the total number of students:

P(psychology student) = 4/(6+2+4) = 4/12 = 1/3

(b) The probability of choosing a psychology student or an anthropology student is the sum of the number of psychology and anthropology students divided by the total number of students:

P(psychology or anthropology student) = (4+6)/(6+2+4) = 10/12 = 5/6

(c) The probability of not choosing a sociology student is the number of non-sociology students divided by the total number of students:

P(not sociology student) = (6+4)/(6+2+4) = 10/12 = 5/6

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Answer:

  (a)  twenty-eight ninths, square root of nineteen, cube root of eighty-eight

Step-by-step explanation:

When ordering a list of numbers by hand, it is convenient to convert them to the same form. Decimal equivalents are easily found using a calculator.

The attachment shows the ordering, least to greatest, to be ...

  \(\dfrac{28}{9}.\ \sqrt{19},\ \sqrt[3]{88}\)

__

Additional comment

We know that √19 > √16 = 4, and ∛88 > ∛64 = 4, so the fraction 28/9 will be the smallest. That leaves us to compare √19 and ∛88, both of which are near the same value between 4 and 5.

One way to do the comparison is to convert these to values that need to have the same root:

  √19 = 19^(1/2) = 19^(3/6) = sixthroot(19³)

  ∛88 = 88^(1/3) = 88^(2/6) = sixthroot(88²)

The roots will have the same ordering as 19³ and 88².

Of course, these values can be found easily using a calculator, as can the original roots. By hand, we might compute them as ...

  19³ = (20 -1)³ = 20³ -3(20²) +3(20) -1 = 8000 -1200 +60 -1 = 6859

  88² = (90 -2)² = 90² -2(2)(90) +2² = 8100 -360 +4 = 7744

Then the ordering is ...

  28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Answer:

the ordering is

28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Step-by-step explanation:

The decay model is given as,

After t = 9433 years,

Thus amount of carbon left is 5 grams.

Step-by-step explanation:

Since the triangle is an equilateral one every angle equals 60

\(x+20 =60\)°

Subtract 20 from both sides

\(x=40\)°

divide both sides by 4

Brainliest please :)

Answer:

could be 16

Step-by-step explanation:

Answer:

Step-by-step explanation:

eight ten a.m.

Answer: The usual dose for an 18-month-old weighing 21 pounds is 48 mg of ibuprofen.

Step-by-step explanation: To find the usual dose of ibuprofen for a child, we need to follow these steps:

Therefore, the usual dose for an 18-month-old weighing 21 pounds is 48 mg of ibuprofen. Hope this helps, and have a great day! =)

Answer:

For me impossible can't understand

Answer:

a) P [ Y ≤ -12 ]  =  0,32997      or        P [ Y ≤ -12 ]  = 32,99 %

b) P [ Y > -1 ]  =  0,3707          or   P [ Y > -1 ]  =  37,07 %

c) P [ 34 ≤  Y  ≤  44]    =  0,1585      or     P [ 34 ≤  Y  ≤  44]    =  15,85 %

d) P [ Y > -4 ]  = 0,59871         or        P [ Y > -4 ]  = 59,87 %

Step-by-step explanation:

Normal Distribution:   N ( -8 ; 9 )

a) P [ Y ≤ -12 ]  = ( - 12  - (-8))/9

P [ Y ≤ -12 ]  =  - 4/9  = - 0,44

From  z-table for the z score -0,44 we get:

P [ Y ≤ -12 ]  =  0,32997      or        P [ Y ≤ -12 ]  = 32,99 %

b)  Normal Distribution:   N ( - 4 ; 9 )

P [ Y > -1 ]  =  1  - P [ Y ≤ -1 ]

P [ Y ≤ -1 ]  =  ( - 1 - ( - 4 ) ) / 9

P [ Y ≤ -1 ]  =  3 / 9  =  0,3333

From  z-table for the z score 0,33 we get:

P [ Y ≤ -1 ]  = 0,6293

P [ Y > -1 ]  =  1  - P [ Y ≤ -1 ]  =  1 - 0,6293

P [ Y > -1 ]  =  0,3707          or   P [ Y > -1 ]  =  37,07 %

c)  Normal Distribution:   N ( 40  ;  25  )

P [ 34 ≤  Y  ≤  44]

P [ 34 ≤  Y  ≤  44]    = P [  Y  ≤  44]  -  P [ Y ≤ 34 ]

 P [  Y  ≤  44]  = ( 44 - 40 ) / 25   = 0,16

From  z-table for the z score 0,16 we get:

P [  Y  ≤  44]  = 0,5636

P [ Y ≤ 34 ]  = ( 34  - 40 ) / 25   =  - 6 / 25   = -  0,24

From  z-table for the z score -0,24 we get:

P [ Y ≤ 34 ]  = 0,40517

Then

P [ 34 ≤  Y  ≤  44]    = P [  Y  ≤  44]  -  P [ Y ≤ 34 ]

P [ 34 ≤  Y  ≤  44]    =   0,5636 -  0,40517

P [ 34 ≤  Y  ≤  44]    =  0,1585      or     P [ 34 ≤  Y  ≤  44]    =  15,85 %

d)  Normal Distribution:   N ( -3  ;  4  )

P [ Y > -4 ]  =  1  -  P [ Y ≤ -4 ]

P [ Y ≤ -4 ]  =  ( - 4 - ( -3))/4  =  - 1/4  = - 0,25

From  z-table for the z score -0,25 we get:

P [ Y ≤ -4 ]  = 0,40129

P [ Y > -4 ]  =  1  -  0,40129

P [ Y > -4 ]  = 0,59871         or        P [ Y > -4 ]  = 59,87 %

Answer:

(657)

Step-by-step explanation:

Simplify the following:

3 (300 - 70/5 - (3×23 - (8 - 2×3)))

The gcd of -70 and 5 is 5, so (-70)/5 = (5 (-14))/(5×1) = 5/5×-14 = -14:

3 (300 + -14 - (3×23 - (8 - 2×3)))

-2×3 = -6:

3 (300 - 14 - (3×23 - (-6 + 8)))

8 - 6 = 2:

3 (300 - 14 - (3×23 - 2))

3×23 = 69:

3 (300 - 14 - (69 - 2))

| 6 | 9

- | | 2

| 6 | 7:

3 (300 - 14 - 67)

300 - 14 - 67 = 300 - (14 + 67):

3 ((300 - (14 + 67)))

| 1 |

| 6 | 7

+ | 1 | 4

| 8 | 1:

3 (300 - 81)

| | 9 |

| 2 | | 10

| | |

- | | 8 | 1

| 2 | 1 | 9:

3 (219)

3 (219) = (3×219):

(3×219)

3×219 = 657:

Answer: (657)

Answer:

18

Step-by-step explanation:

bc it is asking for the absolute value

Alaska occupies 17.22% of the surface area of the United States. Rounding to the nearest whole number, we get 17%. Hence, the answer is:17%

We are given that the surface area of the United States is 3.797 million square miles and the state of Alaska occupies 655,400 square miles. We need to determine what percentage of the surface area of the United States is occupied by Alaska using ratios.To find the percentage, we need to first find the ratio of Alaska's surface area to the surface area of the United States. We can do this by dividing the surface area of Alaska by the surface area of the United States. That is,655,400 / 3,797,000 = 0.1722We can express this ratio as a percentage by multiplying by 100. That is,0.1722 × 100 = 17.22%

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It will take 22 years for the account value to reach $7500 with an annual interest rate of 9% per year.

According to the question,

We have the following information:

2500 dollars is placed in an account with an annual interest rate of 9%.

We know that following formula is used to find simple interest:

Simple interest = principal*rate*time/100

Now, the simple interest on any amount will be equal to the total amount after interest minus the principal amount:

7500-2500

5000

So, we have the following expression:

(2500*9*t)/100 = 5000

Now, using cross multiplication method:

t = (5000*100)/(2500*9)

t = 200/9 years

t = 22.2 years

Now, the nearest year will be 22 years.

Hence, it will take 22 years for the account value to reach $7500 with an annual interest rate of 9% per year.

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Answer:

5^12

Step-by-step explanation:

This is called the "Power of Powers rule." When you are doing this rule, the inside exponent inside the parenthesis (the ^4 in this case) multiplies with the one outside the parenthesis, like this: 5^4*3 = 12.

However, if there is a base number next to the exponent outside the parenthesis that is a different number than the one inside the parenthesis, this method will not work. (Example: (5^4)5^3)

Important note: Anytime you are combining exponents through any rule, the base number must be the same to be able to combine.

Step-by-step explanation:

31 + 6x + x + 16 = 180

7x + 47 = 180

7x = 180 - 47

x = 133/7

x = 19