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?
Answers
Question 1
Using scientific notation, we know a=2, b=4, c=1, and d=3. So,
[tex]\frac{a}{2}+\frac{b}{4}+\frac{c}{8}+\frac{d}{16}=1+1+\frac{1}{8}+\frac{3}{16}=37/16[/tex]
Question 2
[tex]a+13b=3(3a-b)\\\\a+13b=9a-3b\\\\16b=8a\\\\a=2b\\\\\therefore \frac{a^3}{b^3}=\frac{(2b)^3}{b^3}=\frac{8b^3}{b^3}=8[/tex]
Related Questions
Perform the following division: -48 / 5
A. 9.6
B. 8.1
C. -8.1
D. -9.6
Answers
Hope this helps!
How many solutions does the equation. a| x + b | + c = d have when a > 0 and c = d? When a < 0 and c > d ? Explain your reasoning.
Answers
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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What is the ratio of male teachers to male students?
Answers
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:
[tex]\begin{gathered} 2\colon90 \\ \\ 2\text{ to 90} \\ \\ \frac{2}{90} \end{gathered}[/tex]The Faulk Corp. has a bond with a coupon rate of 4 percent outstanding. The Gonas Company has a bond with a coupon rate of 10 percent outstanding. Both bonds have 18 years to maturity, make semiannual payments, and have a YTM of 7 percent. a. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds?
Answers
If the interest rates suddenly rise by 2 percent, the percentage change in the price of these bonds are : 19.73%, 16.56%.
Percentage changeUsing 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 bill for dinner was $61.66. You left $10.34 for the tip. What percentage of the original bill was the tip? Round your a
to the nearest whole percent.
Answers
Answer:
17%
Step-by-step explanation:
You want the percentage represented by a tip of $10.34 on a dinner bill of $61.66.
PercentageA 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.
What is the probability of having exactly 2 boys in 3 births AND having exactly 2 girls in 3 births? (Equal chance of any)
Answers
the probability of having exactly 2 boys in 3 births AND having exactly 2 girls in 3 births is 3/8.
What is the difference between permutation and combination in probability?For a list of data, where the order of the data is important, a permutation is used, while for a group of data, where the order of the data is irrelevant, a combination is used.Combinations exist when the order doesn't matter, but permutations exist when it does. A permutation could be described as an ordered combination. The following formula determines how many permutations of n objects, taken r at a time: P(n,r)=n!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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Classify each as corresponding, AIA, AEA, CIA,
or CEA
1)
3)
5)
X
y
2)
4)
++
Answers
or CEA
1)
3)
5)
X
y
2)
4)
++
Element X is a radioactive isotope such that every 20 years, its mass decreases by
half. Given that the initial mass of a sample of Element X is 770 grams, how long
would it be until the mass of the sample reached 400 grams, to the nearest tenth of a
year?
Answers
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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a fellow comrade,
Cheers !
For scenarios of statistical studies are given below. Decide which study is a sample statistic
Answers
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).
Find the common difference and the next two terms of the arithmetic sequence.11,19,27,35The common difference isWrite the next two terms in the sequence:11,19,27,35,?,?
Answers
The common difference in the given arithmetic sequence is 8.
What is an arithmetic sequence?An ordered group of numbers with a shared difference between each succeeding term is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6. The arithmetic mean can be calculated as one approach. Divide the total by the total number of values after adding up all the values. Add the numbers together, for instance: a + b + c + d and so on, if there is a set of "n" numbers.So, formula for common differences:
d = (aₙ₊₁ - aₙ)Now, insert terms in the formula as follows:
d = (aₙ₊₁ - aₙ)d = (19 - 11)d = 8Therefore, the common difference in the given arithmetic sequence is 8.
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A dealer sold a watch 130% of his cost. If the sale price was $39, how much did the cost the dealer? Please show your work.
Answers
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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Name the line of reflection used to map the preimage to its image.
Answers
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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Select all the equations where x = 3 is a solution.X-3 = 01 + x = 209 - x= 3O 6 = 2xOf = 3x2 = 9
Answers
Let's begin by listing out the given information:
[tex]undefined[/tex]Calc Limits. Attatched question.
Answers
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.
What is the continuity concept?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:
lim x -> -2^- f(x) = -infinity.lim x -> -2^+ f(x) = -infinity.Since the lateral limits are equal, the limit exists, hence option B is correct.
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4 ≤-3x - 1≤9
What is the compound inequality
Answers
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
Question four need to know what I did wrong I need to do it I need to understand
Answers
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.
Find the slope of the line graphed below.
Answers
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.
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. A small ice cream freezer requires 10 cups of crushed ice. How much rock salt should be mixed with the ice to create the necessary brine solution?
Answers
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.
If f(x) = -3x-2, g(x) = - 4x² + 7x-2, and h(x) = 2x² + 4, find h(1).
Answers
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
The number must be a one digit number, When the number is added to 746 the digit in the ones place of the sum is less than the ones digit in 746.
Answers
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
What is a place value?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
746 + 4 = 750; 0 < 6746 + 5 = 751; 1 < 6746 + 6 = 752; 2 < 6746 + 7 = 753; 3 < 6746 + 8 = 754; 4 < 6746 + 9 = 755; 5 < 6The 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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Beginning with 23 grams of a radioactive element whose half-life is 45 years, the mass y (in grams) remaining after t years is given byy = 23(1/2)^t/45, t ≥ 0.How much of the initial mass remains after 170 years? (Round your answer to three decimal places.)
Answers
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:
[tex]\begin{gathered} y=23(\frac{1}{2})^{\frac{t}{45}} \\ y=23(\frac{1}{2})^{\frac{170}{45}} \\ y=23(\frac{1}{2})^{\frac{170}{45}}^ \\ y\approx1.677 \end{gathered}[/tex]2) So, according to this model we can tell there will be left approximately
[tex]1.677g[/tex]Part 1 of 2
Your friend says that the solutions to the inequality 6x-19x≤52 are xs-4. Solve the inequality correctly. What error did your friend
make?
Answers
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?
Answers
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
[tex]\frac{\frac{5}{6}pounds\text{ of oats}}{2\frac{1}{2}pounds\text{ of oats}}=\frac{1\text{ batch of granola}}{x}[/tex][tex]\begin{gathered} \frac{5}{6}x=\frac{5}{2} \\ 10x=30 \\ x=\frac{30}{10} \\ x=3 \end{gathered}[/tex]Answer;
[tex]3\text{ batches}[/tex]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
When x =1/2 and y = 1/8, -5x + 14y =
Answers
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]
Determine which of the following proportions are true.I 1mi2hr=12mi24hrII 7min9cents=36min24centsIII
Answers
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
If f (x) = -3x - 2, find the value
ƒ(-7)
Answers
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
A flower bed is in the shape of a triangle with one side twice the length of the shortest side, and the third side is 22 feet more than the length of the shortest side. Find the dimensions if the perimeter is 186 feet.
Answers
The three sides of the triangle will be 82, 63, and 41 feet.
What is a triangle?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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how do i do vertical analysis
Answers
To carry out the vertical analysis of an income statement, set the Revenue as the base figure to 100% for each line item.
What is a vertical analysis?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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Question Completion: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
What is the maturity value given the following:$10,800 at 8% for 8 months
Answers
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
A population grows according to an exponential growth model. The initial population is 212 and the population after one year is 263.
Complete the formula where P is the population and n is the number of years.:
P=212*(___)n
Round your answer to three decimal places.
Answers
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