Answer:
See below
Step-by-step explanation:
Period = 1/2 year total 4years = 8 periods
i = interest per period in decimal form = .12/2 = .06
initial deposit = ?
Final value = 60 000
60 000 = ? ( 1 + .06)^8
? = 37644.74
Converting between fractions, decimals, and percentsUse the definition of the word percent to write each percent as a fraction and then as a decimal.
Answer:
See below for the completed table
Explanation:
A percentage is a number or ratio written as a fraction of 100. It is usually denoted using the symbol %.
To convert from percentage to fraction, divide the percentage by 100.
[tex]25\%=\frac{25}{100}[/tex]You can then convert the fraction to a decimal where:
[tex]\frac{25}{100}=0.25\text{ (In decimal form)}[/tex]Using the method described above, we calculate for the other values on the table:
[tex]\begin{gathered} 50\%=\frac{50}{100}=0.5 \\ 100\%=\frac{100}{100}=1 \\ 1\%=\frac{1}{100}=0.01 \\ 37.5\%=\frac{37.5}{100}=0.375 \\ 110\%=\frac{110}{100}=1.1 \\ \frac{1}{2}\%=\frac{0.5}{100}=0.005 \end{gathered}[/tex]The completed table is attached below.
Divide using synthetic division. Write down the answer as a polynomial.x^3-5x^2-2x+24=0; (x+2)
we are given the following polynomial:
[tex]x^3-5x^2-2x+24=0[/tex]we are asked to use synthetic division by:
[tex]x+2[/tex]first we need to find the root of "x + 2":
[tex]\begin{gathered} x+2=0 \\ x=-2 \end{gathered}[/tex]Now we do the synthetic division using the following array:
[tex]\begin{bmatrix}{1} & {-5} & {-2} \\ {\square} & {\square} & {\square} \\ {\square} & {\square} & {\square}\end{bmatrix}\begin{bmatrix}{24} & {} & {} \\ {\square} & {} & {} \\ {\square} & {} & {}\end{bmatrix}\begin{cases}-2 \\ \square \\ \square\end{cases}[/tex]Now we lower the first coefficient and multiply it by -2 and add that to the second coefficient:
[tex]\begin{bmatrix}{1} & {-5} & {-2} \\ {\square} & {-2} & {\square} \\ {1} & {-7} & {\square}\end{bmatrix}\begin{bmatrix}{24} & {} & {} \\ {\square} & {} & {} \\ {\square} & {} & {}\end{bmatrix}\begin{cases}-2 \\ \square \\ \square\end{cases}[/tex]Now we repeat the previous step. We multiply -7 by -2 and add that to the next coefficient:
[tex]\begin{bmatrix}{1} & {-5} & {-2} \\ {\square} & {-2} & {14} \\ {1} & {-7} & {12}\end{bmatrix}\begin{bmatrix}{24} & {} & {} \\ {\square} & {} & {} \\ {\square} & {} & {}\end{bmatrix}\begin{cases}-2 \\ \square \\ \square\end{cases}[/tex]Now we repeat the previous step. we multiply 12 by -2 and add that to the next coefficient:
[tex]\begin{bmatrix}{1} & {-5} & {-2} \\ {\square} & {-2} & {14} \\ {1} & {-7} & {12}\end{bmatrix}\begin{bmatrix}{24} & {} & {} \\ {-24} & {} & {} \\ {0} & {} & {}\end{bmatrix}\begin{cases}-2 \\ \square \\ \square\end{cases}[/tex]The last number we got is the residue of the division, in this case, it is 0. Now we rewrite the polynomial but we subtract 1 to the order of the polynomial:
[tex]\frac{x^3-5x^2-2x+24}{x+2}=x^2-7x+12[/tex]In order to earn extra money during the summer, Trevor is working as a house painter. The
amount of money he earns depends on the number of houses he paints.
m = the amount of money Trevor earns
h = the number of houses Trevor paints
Which of the variables is independent and which is dependent?
h is the independent variable and m is the
dependent variable
m is the independent variable and h is the
dependent variable
Submit
The correct answer to this question is that m is the dependent variable and h is the independent variable.
The amount of money Trevor earns can be formulated in the form of linear equation. A Linear equation is the one which can be expressed in the form of y = ax + b where y is dependent, and x is independent variable whereas a, b are coefficients. According to question amount of money Trevor earns will depend on the number of houses he paints. If m is the amount of money Trevor earns and h is the number of houses Trevor paints. This can be formulated as
m = hx + b and in this expression, m is dependent variable and h is independent variable as his earning will depend on the number of houses he paints.
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Premises:
If I'm a student, then I go to school. If I go to school, then I learn.
Conclusion:
If I'm a student, then I learn.
This is an example of the Law of
?
Answer:
it's wh question I think
Can you please help? I think it is ODD. Do you agree?
Given,
The function is:
[tex]f(x)=x+\frac{12}{x}[/tex]Taking x = -x then,
[tex]\begin{gathered} f(-x)=-x+\frac{12}{-x} \\ =-x-\frac{12}{x} \\ =-(x+\frac{12}{x}) \\ =-f(x) \end{gathered}[/tex]The function is odd.
The measure of two complementary angles are in ratio 2:3. What is the measure of the smaller angle
ANSWER
36°
EXPLANATION
Let a and b be the measures of the two angles. We know that they are complementary, so their measures add up to 90°. Also, we know that the quotient between their measures is 2/3,
[tex]\begin{gathered} a+b=90 \\ \frac{a}{b}=\frac{2}{3} \end{gathered}[/tex]Solve the second equation for a,
[tex]a=\frac{2}{3}b[/tex]Replace a with this expression in the first equation,
[tex]\frac{2}{3}b+b=90[/tex]Add like terms,
[tex]\frac{5}{3}b=90[/tex]Solving for b,
[tex]b=90\cdot\frac{3}{5}=54[/tex]So the other angle is,
[tex]a=\frac{2}{3}b=\frac{2}{3}\cdot54=36[/tex]Hence, the measure of the smaller angle is 36°.
Use four rectangles to estimate the area between the graph of the function f(x) = V3x + 5 and the x-axis on the interval[0, 4] using the left endpoints of the subintervals as the sample points. Round any intermediate calculations, if needed, to noless than six decimal places, and round your final answer to three decimal places.
Answer:
12.123
Step-by-step explanation:
You want the area under the curve f(x) = √(3x+5) on the interval [0, 4] estimated using the left sum and four subintervals.
Riemann sumWhen the interval [0, 4] is divided into four equal parts, each has unit width. That means the area of the rectangle defined by the curve and the interval width will be equal to the value of the curve at the left end of the interval.
The area we want is the sum ...
f(0) +f(1) +f(2) +f(3)
As the attachment shows, that sum is ...
area ≈ 12.123 . . . square units
__
Additional comment
The table values in the attachment are rounded to 7 decimal places. Trailing zeros are not shown. Actual values used have 12 significant digits, as the total shows.
Such a sum is called a Riemann sum, named for a German mathematician. Four such sums are commonly used, and further refinements are possible. Those are the left sum (as here), the right sum, the midpoint sum, and a sum using a trapezoidal approximation of the rectangle area.
For left, right, and midpoint sums, n function values are required for n subintervals. When the trapezoidal approximation is used, n+1 function values are required.
David has a coin collection. He keeps 9 of the coins in his box, which is 2% of the collection. How many total coins are in his collection?
Work Shown:
x = total number of coins
2% of x = 0.02x = 9 coins in the box
0.02x = 9
x = 9/0.02
x = 450 coins total
Need help please with this
Answer: It would be Answer D
Step-by-step explanation: He Subtracted from both sides in an incorrect order
A flower garden is shaped like a circle. Its diameter is . A ring-shaped path goes around the garden. The width of the path is .The gardener is going to cover the path with sand. If one bag of sand can cover , how many bags of sand does the gardener need? Note that sand comes only by the bag, so the number of bags must be a whole number. (Use the value for .)
The number sand bags required are 84 approximately.
Given, we have:
Diameter of garden = 38 yd
Width of path = 5 yd
Diameter of garden with path = 38 + 2 x 5 = 48 yd
We need to find area of path.
Area of path = Area of garden with path - area of garden
Area of path = π × 48²/4 - π × 38²/4
Area of path = 7234.56/4 - 4534.16/4
Area of path = 1808.64 - 1133.54
Area of path = 675.1 yd²
Area covered by one sand bag = 8 yd²
Number of sand bags required = Area of path/Area covered by one sand bag
=675.1/8
= 84.38 ≈ 84
Number of sand bags needed = 84
Therefore, number of sand bags required are 84.
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1/2 ^1/2 please show the steps
The value of [tex](\frac{1}{2} )^{\frac{1}{2} }[/tex] is 0.707.
1÷2 = 0.5
Given, [tex](\frac{1}{2} )^{\frac{1}{2} }[/tex]
Could be written like, [tex](0.5)^{0.5}[/tex] or √(1 ÷ 2) or √(0.5)
So the value of √(0.5) is 0.707.
Another way is to factorize each integer as the product of its primes using the square root prime factorization method. Follow these methods to find the square root of a certain number using prime factorization:
Step 1: Divide the supplied integer by its decimal equivalent.
Step 2: If the connected components are identical, a pair is generated.
Step 3: Choose one of the pair members for her.
Step 4: Multiply the prime numbers you got by picking one from each pair.
Step 5: This product is the square root of the specified number.
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A and B are sets of real numbers defined as follows.A = {x|x≤ 2}XB = {x|x < 7}Write A UB and An B using interval notation.If the set is empty, write 0.
The given sets are
[tex]\begin{gathered} A=\lbrace x:x,x\leq2\rbrace \\ \\ B=\lbrace x:x,x<7\rbrace \end{gathered}[/tex]That means A is all real numbers from 2 to negative infinity, and B is all real numbers between 7 and positive infinity
[tex]\begin{gathered} A=(-\infty,2] \\ \\ B=(7,\infty) \end{gathered}[/tex]Then we can find the union and intersection
[tex]\begin{gathered} A\cup B=(-\infty,2]\cup(7,\infty) \\ OR \\ A\cup B=(-\infty,\infty)-(2,7] \end{gathered}[/tex]I will draw a sketch to show you the intersection
We can see that there is NO intersection between A and B, then
[tex]\begin{gathered} A\cap B=\lbrace\rbrace \\ A\cap B=0 \end{gathered}[/tex]Solve this inequality
[tex]\boxed{ \large\displaystyle\text{$\begin{gathered}\sf \bf{-8\leq 10-2x < 28 } \end{gathered}$} }[/tex]
Separate the inequality compound in the inequality system.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{{\left\{ \begin{array}{r}10-2x\geq -8 \\ 10-2x < 28 \ \end{array} \right.} } \end{gathered}$} }[/tex]
We solve to: 10 - 2x < 28Order the unknown terms to the left side of the equation.[tex]\boxed{\bf{-2x < 28-10 }}[/tex]
Calculate the sum or difference.
[tex]\boxed{\bf{-2x < 18 }}[/tex]
Divide both sides of the equation by the coefficient of the invariable.[tex]\boxed{\bf{x > -\frac{18}{2} }}[/tex]
Clear the common factor
[tex]\boxed{\bf{x > -9} }}[/tex]
We solve to: 10 - 2x ≥ -8Order the unknown terms to the left side of the equation.
[tex]\boxed{\bf{-2x\geq -8-10 }}[/tex]
Calculate the sum or difference.
[tex]\boxed{\bf{-2x\geq -18 }}[/tex]
Divide both sides of the equation by the coefficient of the invariable.
[tex]\boxed{\bf{x\leq \frac{-18}{-2} }}[/tex]
Determine the sign of multiplication and division.
[tex]\boxed{\bf{x\leq \frac{18}{2} }}[/tex]
Clear the common factor
[tex]\boxed{\bf{x\leq 9}}[/tex]
[tex]\boxed{ \large\displaystyle\text{$\begin{gathered}\sf \bf{x > -9 \ and \ x\leq 9 } \end{gathered}$} }[/tex]
We find the intersection.
Answer = [tex]\boxed{ \large\displaystyle\text{$\begin{gathered}\sf \bf{-9 < x\leq 9 } \end{gathered}$} }[/tex]
Alternative forms: x ∈ (-9, 9]which situation can be represented by this inequality1.25x -6.50 > 50 A. Caleb has a balance of 6.50$ in his savings account and deposits 1.25$ each week. What is X the number of weeks must deposit 1.25$ in order to have a balance of more than 50$ in his savings account?B. Caleb earns 1.25% interest on the balance in his checking account and has to pay a monthly charge of 6.50$. What is X the balance that Caleb must have in his checking account in order to have an ending balance greater than 50$ after interest and fees.C. Caleb charges 1.25$ for gasoline plus 6.50$ per hour for mowing lawns. What is X the number of hours he has to mow lawns to earn more than 50$D. Caleb spends 6.50$ on supplies for a lemonade stand and sells each cup of lemonade for 1.25$. what is X the number of cups of lemonade Caleb must sell to earn profit of more than 50$
We need to find a situation that can be represented by the inequality below:
[tex]1.25\cdot x-6.5>50[/tex]This means that there must be a variable for which each unit has a value of 1.25. There must be a fixed cost of 6.5, because we are subtracting that value and the end goal must be to have more than 50.
The only option for which this applies is the option D.
Caleb spent a fixed amount of 6.5, he earns 1.25 for each lemonade he sells and he wants to have a profit of more than 50.
What is the area of the shaded triangle?The area of the shaded triangle is in. 2
The area of the shaded triangle is equal to:
[tex]A=\frac{1}{2}bh[/tex]the base of the shaded triangle is 4 in and the height is 5 in, then:
[tex]\begin{gathered} A=\frac{1}{2}(4)(5) \\ =\frac{1}{2}\cdot20 \\ =10 \end{gathered}[/tex]Therefore the shaded area is 10 squared inches.
Can Some one please help me match the congruence statements below!
Assume that AGHI ALMN. Which of the following congruence statements
are correct? Check all that apply.
A. ZN=21
B. ZL 41
C. ME ZH
☐ D. GH = LM
E. IG= LM
F. IH NM
The following congruence statements a, b, e, f are correct.
Triangle congruence: If all three corresponding sides and all three corresponding angles seem to be equal in size, two triangles are said to be congruent.
When two triangles are congruent, their sides and corresponding angles are identical.
Therefore, if GHI is congruent to LMN, then GH =LM, HI=MN and GI=LN, and also angle G=angle L, Angle H=angle M, while angle I = angle N, therefore the correct answers is f) ∠M= ∠H, (a) GH = LM b) ∠L=∠G. and e)IH=NM.
Therefore, option a, b, e, f are correct.
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Given that Kelsey has already made 10 pendants how many additional pendants must she make and sell to make a profit of 50 dollars?
Part a: Kelsey should make 36 pendants
Part b: Kelsey needs to make 26 more pendants
Rent of the booth at the craft fair = $200
The material cost of each pendant = is $7.80
The selling cost of each pendant = is $13.50
Let Kelsey make x number of pendants
Formulating the inequality equation we get:
Selling cost of each pendant*Number of pendants >= Rent of the booth + Material cost of each pendant*Number of pendants
= 13.50x >= 200 + 7.80x
Solving the inequality we get:
13.50x >=200+7.80x
5.70x >= 200
x >= 35.08
So, she should make a total of 36 pendants
Considering that she has already made 10 pendants. She needs 26 more pendants.
Although a part of your question is missing, you might refer to this full question: Kelsey makes pendants that she would like to sell at an upcoming craft fair. She must pay $200 to rent a booth at the craft fair. The materials for each pendant cost $7.80, and she plans to sell each pendant for $13.50. To make a profit, she must make more money than she spends. Kelsey has already made 10 pendants. Part A: Write and solve an inequality to show how many pendants Kelsey should make. Show the steps of your solutions. Part B: Given that Kelsey has already made 10 pendants, how many additional pendants must she make and sell to make a profit?
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The field inside a running track is made up of a rectangle 84.39 m long and 73 m wide, together with a half-circle at each end. The running lanes are 9.76 m Wide all the way around.What is the area of the running track that goes around the field? Round to the nearest square meter.
To find the area of the running track that goes around the field, we need to follow the formula:
area of running track = outside area - inside area
1. Outside Area:
outside area = area of rectangle + 2× area of the semi- circle
= 92.52× 84.39 + π × 46.26² = 14527.32m²
2. Inside Area:
inside area = area of rectangle + 2× area of the semi- circle
= 73 × 84.39 + π × 36.5² = 10343.74m²
So, area of running track = 14527.32 m² - 10343.74m² = 4183.58m² ≈ 4184m²
n
4 Which expression is equivalent to 8.508 ÷ 70.9?
A 8.508 709
B 85.08 709
C 850.8 709
D 8,508 709
5 What is the value of 0.5 ÷ 0.8? Show your work.
Answer:
a because 8.508
Step-by-step explanation:
0.625 so it easy 0.5:0.8
What does the fundamental theorem of algebra state about the equation 2x2−x+2 = 0?Question 5 options:The fundamental theorem of algebra tells you that the equation will have two complex roots since the leading coefficient of the equation is 2. The roots arex = 1 ± i7.−−√The fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots are x = 1 ± i7.−−√The fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots arex = 1±i15√4.The fundamental theorem of algebra tells you that the equation will have two complex roots since the leading coefficient of the equation is 2. The roots arex = 1±i15√4.
Given
Equation
[tex]2x^2-x+2=0[/tex]Procedure
The fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots are
[tex]x=\frac{1}{4}\pm\frac{\sqrt[]{15}}{4}[/tex]The discriminant b^2 - 4ac < 0
so, there are two complex roots.
2(3x+6)-96=6(2x-4)-56Which value of x makes the equation true?A. X=-2B. x=-2/3C. x=2D. x=3
Given equation:
[tex]2(3x+6)-96=6(2x-4)-56[/tex]Solve the equation to find the value of x,
[tex]\begin{gathered} 2(3x+6)-96=6(2x-4)-56 \\ 2(3x)+2(6)-96=6(2x)-6(4)-56 \\ 6x+12-96=12x-24-56 \\ 6x-84=12x-80 \\ -84+80=12x-6x \\ -4=6x \\ x=\frac{-4}{6} \\ x=-\frac{2}{3} \end{gathered}[/tex]Hence, x=-2/3
Answer: option B) is correct
Answer:
2(3×+6) is 96 _6 by (2×4=5) with A.X
From a group of 6 people, you randomly select 5 of them.
What is the probability that they are the 5 oldest people in the group?
Give your answer as a fraction
The probability that they are the 5 oldest people in the group is 1/6.
Given that we have a group of 6 people, and we randomly select 5 of them.
We need to find the probability that they are the 5 oldest people in the group.
The total number of ways to select 5 people from a group of 6 people is given by 6C5 which is equal to 6.
This means that there are only 6 possible outcomes when we randomly select 5 people from a group of 6 people.
We know that the 5 oldest people in the group can be selected only in one way.
So, the number of favorable outcomes is 1.
Hence, the probability of selecting the 5 oldest people from the group when 5 people are randomly selected is: Probability = favorable outcomes/total outcomes Probability = 1/6
Therefore, the probability that they are the 5 oldest people in the group is 1/6.
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How many 1/4 pound hamburgers could be made from 5 1/2 pounds of hamburger meat?
Given:
Total amount of hamburger meat = 5½ pounds
Let's find how many ¼ pound hamburgers could be made from 5½ pounds of hamburger meat.
To find how many pound hamburger could be made divide 5½ by ¼.
Thus, we have:
[tex]5\frac{1}{2}\div\frac{1}{4}[/tex]To perform the division, take the following steps:
Step 1:
Convert the mixed fraction to improper fraction
[tex]\frac{11}{2}\div\frac{1}{4}[/tex]Step 2:
Flip the fraction on the right and change the division symbol to multiplication
[tex]\begin{gathered} \frac{11}{2}\ast\frac{4}{1} \\ \\ =\frac{11\ast4}{2\ast1} \\ \\ =\frac{44}{2} \\ \\ =22 \end{gathered}[/tex]Therefore, 22 of ¼ pound of hamburger could be made from 5½ pounds of hamburger meat.
ANSWER:
22
A population doubles every 27 years. Assuming exponential growth find the following:help find continuous growth rate (a) The annual growth rate: 2.6(b) The continuous growth rate is____% per year help (numbers)
Given,
A population doubles every 27 years.
a. Let initial population be 1 and after 27 years it becomes 2.
Considering r as the rate of annuall growth we have,
[tex]\begin{gathered} 1(1+r)^{27}=2 \\ \Rightarrow27\ln (1+r)=\ln 2 \\ \Rightarrow\ln (1+r_{})=\frac{0.693}{27} \\ \Rightarrow1+r=1.0257 \\ \Rightarrow r=0.026 \end{gathered}[/tex]Thus annual growth rate is 2.6%
b. For continuous growth,
[tex]\begin{gathered} 1(e^{27x})=2 \\ \Rightarrow27x=0.693 \\ \Rightarrow x=0.025 \end{gathered}[/tex]The continuous growth rate is _2.5___% per year
For the function f(x), = 10 (√x + 9), find f-¹(x).
The inverse of the function f(x) = 10 (√x + 9) is f⁻¹(x) = (x - 90)² / 100
Given,
The function, f(x) = 10 (√x + 9)
We have to find the inverse of the function, f⁻¹(x)
Here,
f(x) = 10 (√x + 9)
f(x) = 10√x + 90
Replace f(x) with y.
y = 10√x + 90
Swap x with y;
x = 10√y + 90
Solve for y
That is,
x = 10√y + 90
x - 90 = 10√y
(x - 90) / 10 = √y
Square both sides
((x - 90) / 10)² = √y²
(x - 90)² / 100 = y
Replace y with f⁻¹(x)
That is,
f⁻¹(x) = (x - 90)² / 100
Therefore,
The inverse for the function f(x) = 10 (√x + 9) is f⁻¹(x) = (x - 90)² / 100
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Bob's Golf Palace had a set of 10 golf clubs that were marked on sale for $840. This was a discount of 10% off the original selling price.Step 2 of 4: If the golf clubs cost Bob's Golf Palace $390, what was their profit? Follow the problem-solving process and round youranswer to the nearest cent, if necessary.
Consider that the Bob's Golf Palace bought the set of golf clubs by $390.
Moreover, take into account that the golf clubs were markes on sale for $840.
The profit is only the difference between the marked on sale and the money Bob's Golf Palace payed:
$840 - $390 = $450
Hence, the profit was $450
Question Solve for d. d³ = 27
Answer:
d = 3
Step-by-step explanation:
I took different numbers, like 1 and 2, and multiplied them to themselves 3 times, for example, 2 x 2 x 2, but since that answer was wrong, I decided to try a different number, which was 3 and that was correct.
27 is The same as the product of four and a number
Answer:
6.75
Step-by-step explanation:
6.75x4 = 27 so if this is what was meant by this then heres your answer
hope this helped
have a good day ^^
Calculate the distance between the points L=(1, -8) and C=(9, -3) in the coordinate plane.
Round your answer to the nearest hundredth.
kintett. 41
Distance:
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ L(\stackrel{x_1}{1}~,~\stackrel{y_1}{-8})\qquad C(\stackrel{x_2}{9}~,~\stackrel{y_2}{-3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ LC=\sqrt{(~~9 - 1~~)^2 + (~~-3 - (-8)~~)^2} \implies LC=\sqrt{(9 -1)^2 + (-3 +8)^2} \\\\\\ LC=\sqrt{( 8 )^2 + ( 5 )^2} \implies LC=\sqrt{ 64 + 25 } \implies LC=\sqrt{ 89 }\implies LC\approx 9.43[/tex]