If 1 x 10^a + 2 x 10^b + 3 x 10^c + 4 x 10^d = 24130 and a≠b≠c≠d, then what does a/2 + b/4 + c/8 + d/16 equal?

To carry out the vertical analysis of an income statement, set the Revenue as the base figure to 100% for each line item.

Vertical analysis of a financial statement compares each line item on the financial statement as a percentage of a base figure.

The base figure is the revenue in the income statement or the total assets in the balance sheet.

The formula for vertical analysis is given as a financial statement line item divided by the total base figure X 100.

Examples of vertical analysis can be shown with AT$T and Verizon below:

                                                       AT&T        Percent

Revenue                                     $132,447        100%

Cost of Services (Expenses)         60,611        45.8% ($60,611/$132,447 x 100)

Selling & Marketing Expense      39,697       30.0%  

Depreciation & other expenses 20,393        15.4%

Operating Income                       $11,746         8.9%

                                                     Verizon      Percent

Revenue                                     $127,079       100%

Cost of Services (Expenses)         49,931        39.3% ($49,931/$127,079 x 100)

Selling & Marketing Expense        41,016       32.3%

Depreciation & other expenses   16,523       13.0%

Operating Income                      $19,599       15.4%

Thus, we have performed the vertical analysis of AT$T and Verizon above.

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Income Statements of AT&T and Verizon (in millions) are:

                                                       AT&T         Verizon

Revenue                                     $132,447     $127,079

Cost of Services (Expenses)         60,611          49,931

Selling & Marketing Expense      39,697          41,016

Depreciation & other expenses 20,393          16,523

Operating Income                       $11,746       $19,599

Answer:

When making homemade ice cream in a hand-cranked freezer, the tub containing the ice cream mix is surrounded by a brine (water/salt) solution. To freeze the ice cream mix rapidly so that smooth and creamy ice cream results, the brine solution should combine crushed ice and rock salt in a ratio of 5 to 1.

Answer: P=212*(1.240)n

Step-by-step explanation:

1) Find the % growth

263-212= 51

51/212 = 0.240566037735849

2) Add 1 to the decimal as the population isn't decreasing but increasing.

0.240566037735849 + 1 = 1.240

3) Fill in the equation

P=212*(1.240)n

Data:

Students: 180

Half male.

Male students: 180/2=90

Male teachers: 2

Ratio of male teachers to male students:

You can write the ratio in three different forms:

The maturity value is the sum of the interest and the principal. The formula for calculating interest is expressed as

I = PRT

where

I is the interest after time t

P is the principal or initial amount

R is the interest rate

T is the time in years

From the information given,

P = 10800

R = 8/100 = 0.08

T = 8 months

We would convert 8 months to years. Recall,

12 months = 1 yr

8 months = 8/12 = 0.67

Thus,

t = 0.67 yr

By substituting these values into the formula, we have

I = 10800 x 0.08 x 0.67

I = 578.88

Thus,

Maturity value = 10800 + 578.88

Maturity value = $11378.88

Answer:

  17%

Step-by-step explanation:

You want the percentage represented by a tip of $10.34 on a dinner bill of $61.66.

A percentage is a fraction that has been multiplied by 100%:

  10.34/61.66 × 100%

  ≈ 0.168 × 100%

  ≈ 17%

The tip was about 17% of the original bill.

1) As we were told of the half-life formula along with the data, we can write out the following to get the remains after 170 years:

2) So, according to this model we can tell there will be left approximately

The common difference in the given arithmetic sequence is 8.

So, formula for common differences:

Now, insert terms in the formula as follows:

Therefore, the common difference in the given arithmetic sequence is 8.

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The cost of the watch which sold at 130% of its cost and sale price is $39 is equal to $30.

As given in the question,

Sale price of the watch for which dealer sold = $39

Let $'x' be the cost of the watch with which dealer purchase

A dealer sold a watch 130% of its cost

Required expression to show the given condition of a dealer is given by:

   130% of x = $39

⇒ (130 /100) × x = $39

⇒ x = ( 39 × 100 ) / 130

⇒ x = $30

Therefore, the cost of the watch which sold at 130% of its cost and sale price is $39 is equal to $30.

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The one digit numbers that when added to 746 gives a digit in the ones place of the sum which is less than the ones digit in 746 are;

4, 5, 6, 7, 8, or 9

Place values is the value a digit in a number posseses based on its position in the number

The given parameters of the number are;

The number of digits in the number = 1

The ones digit of the sum of the number and 746 is less than the ones digit in 746, which is 6

Therefore;

The value of the number when added to 746 can be expressed as 7xy

Where;

y < 6

The process of adding two numbers involves the addition of the numbers based on their place values such that the ones digit part of the result is placed as the output while the 1 in a result that is 10 or more is added to the next higher place value number to the left of the added digits

Therefore, to have a value of the digit in the ones place less than 6, we can have;

746 + 0 = 746

746 + 1 = 747

746 + 2 = 748

746 + 3 = 749

The possible one digit numbers that gives a sum with a ones digit less than 6 when added to 746 therefore includes; 4, 5, 6, 7, 8, and 9

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Option A, Y- axis is the line of reflection used to map the preimage to its image.

The graph shows that if the graph is folded by a y-axis, Point G will cross Point G', which is two coordinates away from the y-axis.

Point F will cross point F', which is four coordinates away from the y-axis.

Points H will cross point H', which is in negative coordinates and 7 coordinates away from the y-axis.

Mirror images are symmetrical from any axis, which might be the x-axis or the y-axis. Flipping geometry refers to reflection. Mirror reflection is a type of reflection. When lines reflect an image, reflection lines form. A form is said to mirror another shape if each of its points is equidistant from each of the other shape's points.

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Answer:

-5x1/2= -2.5 14x1/8= 1.75

Step-by-step explanation:

-2.5+1.75=-0.75

Answer:

-3/4

Step-by-step explanation:

Plug in values of x and y into expression:

[tex]-5(\frac{1}{2})+14(\frac{1}{8})=[/tex]

[tex]-\frac{5}{2} +\frac{14}{8}=[/tex]

Find common denominator:

[tex]-\frac{5*4}{2*4} +\frac{14}{8}=[/tex]

[tex]-\frac{20}{8} +\frac{14}{8}=\frac{14}{8}-\frac{20}{8}=[/tex]

Solve numerator:

[tex]14-20=-6[/tex]

So,

[tex]=-\frac{6}{8}=-\frac{3}{4}[/tex]

Answer:

−1≤x<3

Step-by-step explanation:

−4≤3x−1<8

−4≤3x−1and3x−1<8

3x−1≥−4and3x−1+1<8+1

3x≥−3and3x<9

x≥−1andx<3

−1≤x<3

Let's begin by listing out the given information:

the probability of having exactly 2 boys in 3 births AND having exactly 2 girls in 3 births is 3/8.

the possible outcomes are

BBB,BBG,BGB,GBB,BGG,GBG,GGB,GGG

wherein 3 meet the requirement. There are 8 possible outcomes, all equally likely (if we assume each gender is equally likely). Hence the choice is 3/8.

We can also think about it in at least one more way: You identified all the possible ways to get 2 boys and one girl. Since the events are disjoint, we can add up the probabilities

P(2 boys, 1 girl)=P(BBG)+P(BGB)+P(GBB)

          =[tex]\frac{1}{2} X\frac{1}{2} X \frac{1}{2}[/tex]+ [tex]\frac{1}{2} X\frac{1}{2} X \frac{1}{2}[/tex] + [tex]\frac{1}{2} X\frac{1}{2} X \frac{1}{2}[/tex]

          = 3/8.      

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If  the interest rates suddenly rise by 2 percent,  the percentage change in the price of these bonds are : 19.73%, 16.56%.

Using this formula to find the current price of a bond

P=C×1-1(1+YTM)^n/YTM +F /(1+YTM)^n

Where:

P =Current price of a bond

C = Coupon payment,

YTM = Yield to maturity

n = Time to maturity

F =Face value of a bond

The Faulk Corp. bond

C = Coupon rate / number  of payments per year × face value = 4% / 2×$1,000 = $20

n = 13 years = 36 half-year periods

YTM = 7% annually = 7% / 2 = 3.5% semiannually

F = $1,000

hence,

P=20× 1- 1/(1+0.035)^26/0.035 +1,000/ (1+0.035)^36

P=20× 1- 1/(1.035)^36/0.035 +1,000/ (1.035)^36

P= $405.81 + $289.83

P=$695.61

Assuming the annual YTM rises by 2%, the semiannual YTM = 9% / 2 = 4.5%.

Price of the Faulk Corp. bond:

P=20× 1- 1/(1+0.045)^36/0.045 +1,000/ (1+0.045)^36

P=20× 1- 1/(1.045)^36/0.045 +1,000/ (1.045)^36

P= $353.32 +$205.03

P=$558.38

Percentage change:

Percentage change = $558.38 - $695.61/$695.61×100%

Percentage change =19.73%

Gonas Company bond:

C =Coupon rate / number of payments per year× face value = 10% / 2 × $1,000 = $50

n = 18 years = 36 half-year periods,

YTM = 7% annually = 7% / 2 = 3.5% semiannually

F = $1,000

P=50× 1- 1/(1+0.035)^26/0.035 +1,000/ (1+0.035)^36

P=50× 1- 1/(1.035)^36/0.035 +1,000/ (1.035)^36

P= $1,014.52 + $289.83

P=$1,304.35

Assuming the annual YTM rises by 2%, the semiannual YTM = 9% / 2 = 4.5%, bond :

P=50× 1- 1/(1+0.045)^36/0.045 +1,000/ (1+0.045)^36

P=50× 1- 1/(1.045)^36/0.045 +1,000/ (1.045)^36

P= $883.30 +$205.03

P=$1,088.33

Percentage change:

Percentage change = $1,088.33 - $1,304.35/$1,304.35×100%

Percentage change =16.56%

Therefore the percentage change in the price of these bonds are : 19.73%, 16.56%.

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The correct option regarding the continuity of f(x) at x = 2 is given by:

B. lim x -> 2 f(x) exists, but f(2) exist.

A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is, if these three conditions are respected:

[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]

For this problem, the denominator of the function is:

8cos(0.5πx) + 2x²

At x = 2, the denominator of the function is:

8cos(0.5π(2)) + 2(2)² = 8cos(π) + 8 = -8 + 8 = 0 (as cos(π) = -1).

Then the function does not exist at x = 2, as the denominator is of 2.

From the graph of the function given at the end of the answer, we have that the lateral limits are as follows:

Since the lateral limits are equal, the limit exists, hence option B is correct.

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Answer:

[tex]t = 18.9[/tex]

Information given :

We know that:

- Element X is a radioactive isotope such that every 20 years, its mass decreases by half

- the initial mass of a sample of Element X is 770 grams

And we must find how long it would be until the mass of the sample reached 400 grams

Step-by-step explanation:

To find it, we need to use the following formula:-

[tex]A(t) = A(0)(0.5)^{\frac{t}{20} }[/tex]

- A(0) is the initial amount

From given information, A(0) = 770 grams

Now, replacing the value in t :

[tex]A(t) = (770)(0.5)^{\frac{t}{20} }[/tex]

Then, we must solve for t :-

[tex]400 = 770(0.5)^{\frac{t}{20} } \\\frac{400}{700}= (0.5)^{\frac{t}{20} } \\\\ 0.51948 = (0.5)^{\frac{t}{20} } \\\\log(0.51948) = log((0.5)^{\frac{t}{20} }) \\\\\\log(0.519,48) = \frac{t}{20} log (0.5)\\t=\frac{20*log(0.519,48)}{log(0.5)} \\t=\frac{20(-0.284431}{-0.301029} \\giving\\t=18.9[/tex]

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Cheers !

If there are 189 children, then there are 189 divided 7 = 27 groups of 7 children.

As mentioned in the problem, for every 7 children, there are 2 caretakers therefore, there are a total of 2 x 27 = 54 caretakers in the local daycare.

So, in total, there are 189 children + 54 caretakers = 243 people in the daycare facility.

In the first case the equation has only one unique solution and in the second case the equation has many solutions.

We are given the equation a|x + b| + c = d and we need to determine the solution of this equation when a > 0 and c = d. The equation contains absolute value symbol which always gives a positive value. The equation can be written as

a|x + b| + c = d

a|x + b| = d - c, since c = d then we can write equation as

a|x + b| = 0, Now, a > 0

=> |x + b| = 0

=> x = -b that is only one unique solution.

Now, in second case a < 0 and c > d then

a|x + b| = d - c

If c > d, then the left-hand side of the equation becomes negative and also a < 0 so the right-hand side also becomes negative. So, the equation will have many solutions in this case.

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Step 1

Given; Austin has a granola recipe that requires 5/6 pounds of oats to make one batch of granola. if Austin uses 2 1/2 pounds of oats while making granola, how many batches has he made?

Step 2

Using ratio

Answer;

Answer:3

Step-by-step explanation:if austin has to make 1 granola with 5/6pounds but he is using only 5/2 pounds to make 1 granola so that he can make 3 granulas with 5/6

Answer:

19

Step-by-step explanation:

-3(-7)-2

21-2

19

it need to be at least 20 chqracters so ignore this the answer is at the top

Answer:

h(1) = 6

Step-by-step explanation:

h(1) will be

h(x) = 2x² + 4

h(1) = 2(1)² + 4 = 2 + 4

h(1) = 6

1 and 3

1 * 12 = 12

2 * 12 = 24

so 1 is true

7 * 5.14 = 36

9 * 5.14 = 46.26

so 2 is not true

7 * 4 = 28

2 * 4 = 8

so 3 is true

The three sides of the triangle will be 82, 63, and 41 feet.

Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees. The perimeter of the triangle is the sum of all three sides of the triangle.

That a flower bed is in the shape of a triangle with one side twice the length of the shortest​ side, and the third side 22 feet more than the length of the shortest side.

Let the three sides of the triangle be A, B, and C. Here A is the longest side B is the shortest side and C is the third side.

Perimeter = A + B + C

A = 2B and C = 22 + B

Put the values in the equation as solve:-

Perimeter = A + B + C

186 = 2B + B + 22 + B

186 = 4B + 22

4B = 186 - 22

4B = 164

B = 164 / 4

B = 41 feet

Longest side = 2B = 2 x 41 = 82 feet

Shirtest side = B = 41 feet

Third side = 22 + B = 22 + 41 = 63 feet

Therefore, the three sides of the triangle will be 82, 63, and 41 feet.

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EXPLANATION

Since we have four given scenarios, the only viable option is the third one because It's the only statement where we take a sample (1000 individuals of 1883 participants).

Answer:

[tex]\frac{-5}{2}[/tex]

Step-by-step explanation:

There are two blue dots on the graph.  It does not matter which dot you startr at.  Let's start at the bottom, right dot.  How many space up and to the left you do you have to move to get to the second dot?

You need to move 5 dots straight up.  Up is a positive direction.  Then you have to move 2 spaces left.  Left is a negative direction, so your slope will be negative.

- [tex]\frac{5}{2}[/tex]            [tex]\frac{-5}{2}[/tex]           [tex]\frac{5}{-2}[/tex]   All of these mean the same thing.