The annual sales after 7 years is $ 855.3556
Solution:
The growth function is given as:
[tex]y = a(1+r)^t[/tex]
Where,
y is the future value
a is the initial value
r is the growth rate
t is the number of years
From given,
a = 650
t = 7
[tex]r = 4 \% = \frac{4}{100} = 0.04[/tex]
Therefore,
[tex]y = 650(1 + 0.04)^7\\\\y = 650(1.04)^7\\\\y = 650 \times 1.315931\\\\y = 855.3556[/tex]
Thus the annual sales after 7 years is $ 855.3556
0.05 is 1/10 the value of
A. 5
B. 0.005
C. 0.5
D. 50
Answer:
C.
Step-by-step explanation:
as 0.05 is 1/10 of a number, multiplying 0.05 by 10 will give you the number that when divided by 10 will give you 0.05. Hence just multiply 0.05 by 10 and you get 0.5.
Dividing decimals
0.7 divided by 0.1995
Final answer:
When dividing 0.7 by 0.1995, it is crucial to perform the calculation accurately and round it according to the significant figures of the original numbers. Calculators will provide an exact answer, but understanding significant figures is necessary for a correctly rounded result.
Explanation:
Dividing Decimals
When we divide 0.7 by 0.1995, we have to handle decimals properly. It's similar to how a calculator operates but with an understanding of significant figures. The division of decimals can be tricky because calculators give an exact numerical value, which may not respect the precision of the input numbers.
For instance, if we divide 12.2 by 1.7 using a calculator, we get many decimal places. But based on the initial data's significant figures, we must round our answer appropriately. Similarly, if we divide 1.9436 by various powers of 10, we get:
1.9436 ÷ 100 = 0.019436
1.9436 ÷ 1000 = 0.0019436
When dividing by powers of 10, we move the decimal point to the left for each power. In more complex divisions or when your calculator presents more decimals than necessary, it is important to round the answer to the correct number of significant figures.
Please explain and show me how to do question 8 please, I’m dying and I have a test!
Answer:
So linear means equal so you’ll put x on one side and 750 plus 10% on one side and add an equal sign in the middle
I’m really terrible at explaining things but I hope this helped
What is the equation of the line that is parallel to the given
line and passes through the point (-2, 2)?
y=1/5x+4
y =1/5x+12/5
y=-5+4
y=-5x12/5
Answer:
[tex]y=\frac{1}{5}x+\frac{12}{5}[/tex]
Step-by-step explanation:
Complete Question: What is the equation of line that is parallel to the line [tex]y=\frac{1}{5}+4[/tex] and passes through [tex](-2,2).[/tex]
[tex]Let\ the\ equation\ of\ line\ is\ y=mx+c\\\\Since\ it\ is\ parallel\ to\ the\ line\ y=\frac{1}{5}x+4,\ the\ slope\ of\ both\ the\ lines\ will\ be\ same.\\\\Slope\ of\ y=\frac{1}{5}x+4\ is=\frac{1}{5}\\\\m=\frac{1}{5}\\\\Equation: y=\frac{1}{5}x+c\\\\It\ passes\ through\ (-2,2),\ This\ point\ will\ satisfy\ the\ equation.\\\\2=\frac{1}{5}\times (-2)+c\\\\c=2+\frac{2}{5}\\\\c=\frac{12}{5}\\\\The\ Equation\ is: y=\frac{1}{5}x+\frac{12}{5}[/tex]
To find the equation of a line parallel to a given line and passing through a given point, use the point-slope form of a line.
Explanation:To find the equation of a line parallel to the given line, we need to remember that parallel lines have the same slope. The given line has a slope of 1/5. So, the parallel line will also have a slope of 1/5. We can use the point-slope form of a line to find the equation. The point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Plugging in the values, we get:
y - 2 = 1/5(x + 2)
To simplify the equation, we can multiply through by 5 to get rid of the fraction:
5y - 10 = x + 2
Finally, we can rearrange the equation to the standard form:
x - 5y = -12
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9(x + 8) +63
what is the answer?
Answer:
9x +135
Step-by-step explanation:
9(x + 8) +63 (by PEDMAS distribute 9 into parentheses first)
= x(9) + 8(9) +63
= 9x + 72 + 63
= 9x +135 [ =9(x+15) ]
Answer: 9x+135
Step-by-step explanation:
9(x + 8) +63
9x+72+63
9x+(72+63)
9x+135
Hope this helps, now you know the answer and how to do it. HAVE A BLESSED AND WONDERFUL DAY! As well as a great Valentines Day! :-)
- Cutiepatutie ☺❀❤
Jake has a rectangular garden that measures 12 feet by 14 feet. He wants to increase the area by 50% and plans to increase each dimension by equal lengths, x. Which equation could be used to determine the value of x?
In order to increase the area of a rectangular garden that measures 12 feet by 14 feet by 50% Jake must increase each dimension by equal lengths, x:
[tex]x\approx 2.9ft[/tex]
Explanation:First of all, let's calculate the area of the original rectangular garden:
[tex]A=b\times h \\ \\ b:base \\ \\ h:height \\ \\ \\ b=12ft \\ \\ h=14ft \\ \\ \\ A=12(14) \\ \\ A=168ft^2[/tex]
Jake wants to increase the area by 50%, so the new area would be:
[tex]A'=168(1.5) \\ \\ A'=252ft^2[/tex]
He wants to increase the area by 50% and plans to increase each dimension by equal lengths, x, so this is represented by the figure below, therefore:
[tex](12+x)(14+x)=252 \\ \\ 168+12x+14x+x^2-252=0 \\ \\ x^2+26x-84=0 \\ \\ \\ Using \ quadratic \ formula: \\ \\ x=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ a=1 \\ \\ b=26 \\ \\ c=-84 \\ \\ \\ x=\frac{-26 \pm \sqrt{26^2-4(1)(-84)}}{2(1)} \\ \\ x=\frac{-26 \pm \sqrt{1012}}{2} \\ \\ \\ Two \ solutions: \\ \\ x_{1}=-13+\sqrt{253} \approx 2.9\\ \\ x_{2}=-13-\sqrt{253} \approx -28.9 \\ \\ x_{2} \ is \ discarded \ because \ it \ can't \ be \ negatives[/tex]
Finally:
In order to increase the area of a rectangular garden that measures 12 feet by 14 feet by 50% Jake must increase each dimension by equal lengths, x:
[tex]x\approx 2.9ft[/tex]
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Find the missing value so that the two points have a
slope of -
(-2,y) and (0, -4)
Answer:
y = -2
Step-by-step explanation:
Use the formula for slope: [tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
"m" means slope, and we know it is -1.
Decide which points will be point 1 and point 2
Point 1 (-2, y) x₁ = -2 y₁ = y
Point 2 (0, -4) x₂ = 0 y₂ - -4
Substitute the "x" and "y" values into the formula
[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m = \frac{-4-y}{0-(-2)}[/tex] Simplify
[tex]-1 = \frac{-4-y}{2}[/tex] Remember m = -1. Get rid of the fraction
[tex]2*-1 = 2*\frac{-4-y}{2}[/tex] Multiply both sides by 2
[tex]-2 = \frac{2(-4-y)}{2}[/tex] The "2"s cancel out on the right
[tex]-2 = -4-y[/tex] Start isolating "y"
[tex]-2 +4= -4-y + 4[/tex] Add 4 to both sides
[tex]2= -y[/tex]
[tex]2/-1= -y/-1[/tex] Divide both sides by -1 to isolate "y"
-2 = y Answer
y = -2 Variable on left side
Three vertices of parallelogram WXYZ are X(–2,–3), Y(0, 5), and Z(7, 7). Find the coordinates of vertex W
Final answer:
The coordinates of vertex W of parallelogram WXYZ, given vertices X(-2,-3), Y(0, 5), and Z(7, 7), are W(9, 15). This is found by calculating vector ZW as equal to vector XY and adding ZW to the coordinates of Z.
Explanation:
The coordinates of vertex W of parallelogram WXYZ can be found by using the properties of parallelograms. In a parallelogram, opposite sides are equal in length and parallel. Given vertices X(-2,-3), Y(0, 5), and Z(7, 7), we can first find the vector representation from X to Y and from Y to Z:
XY = Y - X = (0 - (-2), 5 - (-3)) = (2, 8)YZ = Z - Y = (7 - 0, 7 - 5) = (7, 2)To find the vector from Z to W, which we'll call ZW, we use the fact that ZW must be parallel and equal in length to vector XY. Therefore:
ZW = XY = (2, 8)Now we add vector ZW to the coordinates of Z to find W:
W = Z + ZW = (7, 7) + (2, 8) = (9, 15)Thus, the coordinates of vertex W are (9, 15).
Macon has 32 rocks in his collection. He has 4 times as many rocks as his brother. How many rocks does Macon’s brother have?
Answer:
8
Step-by-step explanation:
macon has 4 TIMES as many as his bro, so just divide 4.
32 / 4 = 8
What are the zeros of the quadratic equation y=5(2x-1)(x+3)
Answer:
x = 1/2 or -3
Step-by-step explanation:
to find the zeros, we need to find the values of x which would cause y to become zero,
i.e solve x for :
5(2x-1)(x+3) = 0 (divide both sides by 5)
(2x-1)(x+3) = 0
hence either
2x-1 = 0 (add 1 to both sides)
2x = 1 (divide both sides by 2)
x = 1/2 --> first zero
or
x+3 = 0 (subtract 3 from both sides)
x = -3 ----> 2nd zero
Rashid is standing 15 feet away from a tree. The height of the tree is 15 feet. What is the measure of ∠θ, which is the angle of elevation from Rashid's feet to the top of the tree?
You apply the formula of tan^-1(15÷15) wich gives you 45 degrees
Solve for x: 3(x + 1) = 2(x - 1)
Answer:
x = -5
Step-by-step explanation:
3(x + 1) = 2(x - 1)
Distribute on both sides.
3x + 3 = 2x - 2
Subtract 2x from both sides.
x + 3 = -2
Subtract 3 from both sides.
x = -5
Answer:
The answer you are looking for is x = -5.
Step-by-step explanation:
First, start by distributing the 3 and 2. This will remove the parentheses. The way you do this is by multiplying each number or variable inside the parentheses by the number outside the parentheses.
3x + 3 = 2x - 2
Next, get the variable to one side. One way to accomplish this is by subtracting 2x from each side.
x + 3 = -2
Lastly, move the numbers to one side. Do this by subtracting 3 from both sides.
x = -5
There you go. Your answer is now in the simplest form. Confirm the answer is as simple as plugging in -5 for x in the original equation.
calculate correct to three significant figures length of Arc with subtend an angle of 70 degrees at the centre of circle of radius 4 cm
Answer:
4.89 cm
Step-by-step explanation:
Formula for arc length = (angle/360)×2×pi×r
(70/360)×2×pi×4 = 4.89cm
Joaquin reshaped the dough into another three dimensional shape that could have a circular cross section.What is one shape Juaquin could have made?
Answer:
Sphere
Step-by-step explanation:
Mary took out a student loan for $15000 at 4% simple interest. How much interest will she pay in 10 years? suppose she paid it off in 8 years instead of 10 years. how much would she save in interest? :)
Simple interest formula:
Total = principal x (1 + rate x years)
10 years:
Total = 15,000(1+0.04x10)
Total = $21,000
8 years:
Total = 15000(1+0.04x8)
Total = $19,800
Savings = 21,000 - 19,800 = $1,200
reduce 36/60 to simplest terms
Answer:3/6
Step-by-step explanation:
Kim drew a map of the Mississippi River. The scale was 3 centimeters represents 120 miles. The actual length of the Mississippi River is 2,320 miles. What is the river on the map
To represent the actual length of the Mississippi River, which is 2,320 miles, on a map with a scale of 3 cm per 120 miles, the river would be 58 cm long on the map.
Explanation:The question concerns calculating the scale representation of the actual length of the Mississippi River on a map. According to the given scale, 3 centimeters on the map represents 120 miles in reality. The actual length of the Mississippi River is 2,320 miles. To find the length of the Mississippi River on the map, we use the scale ratio to set up a proportion.
First, we calculate the scale ratio which is 3 cm to 120 miles. This means 1 cm represents 40 miles (120 miles ÷ 3 cm). To find how many centimeters represent 2,320 miles, we divide the actual miles by the miles each centimeter represents. Therefore, 2,320 miles ÷ 40 miles/cm equals 58 cm. Thus, the Mississippi River would be represented as 58 cm long on Kim's map.
Round to the nearest tenth, if necessary. Question: z2 = 361
options:
A.) 18, –18
B.) 180.5, –180.5
C.) 19, –19
D.) 19
The answer is option C) 19,-19
Step-by-step explanation:
Given, z² = 361
To eliminate the square of z, take square root on both sides
z = √361
The factor of 361 could not be an even number, since the last digit of 361 is odd. So, eliminate option A)The option B) is a larger number and it cannot be the answer. So, eliminate it.Try option C) works or not. (19)² = 19[tex]\times[/tex]19 = 361 and (-19)² = -19[tex]\times[/tex]-19 = 361.Therefore, z = √361 = ±19. option C) is the correct answer.[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{z^2 = 361}\\\\\large\text{Take the square root of the number 361}\\\\\mathsf{z = \pm \sqrt{361}}\\\\\large\text{Simplify it}\\\\\mathsf{z = -19\ or\ z = 19}\\\\\\\huge\text{Therefore your answer should be:}\\\huge\boxed{\mathsf{z = 19\ or\ z = -19 \ (Option\ C.)}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
How to solve for-6g + 36 = 12
Answer:
4
Step-by-step explanation:
-6g+36=12
-6g=12-36
-6g=-24
6g=24
g=24/6
g=4
Answer:
g= - 8
Step-by-step explanation:
Simplifying
-6g + -36 = 12
Reorder the terms:
-36 + -6g = 12
Solving
-36 + -6g = 12
Solving for variable 'g'.
Move all terms containing g to the left, all other terms to the right.
Add '36' to each side of the equation.
-36 + 36 + -6g = 12 + 36
Combine like terms: -36 + 36 = 0
0 + -6g = 12 + 36
-6g = 12 + 36
Combine like terms: 12 + 36 = 48
-6g = 48
Divide each side by '-6'.
g = -8
Simplifying
g = -8
A teacher's cabinet has 56 black dry erase markers and 14 red dry erase markers. Which proportion can be used to determine P the percent of dry erase markers that are red?
A=p\100 = 14\56
B=70 / 14 = 100 / p
C=p\14 = 56\100
D=70 / 56 = p\100
Answer:
D. 3b2 + 2b ≥ 56
Step-by-step explanation:
I just did the test too
The correct proportion to determine the percentage of red dry erase markers is 'p/100 = 14/56'. By cross-multiplying and simplifying, we find that 25% of the markers are red.
Explanation:In order to find the percent of dry erase markers that are red, it would be correct to use the proportion 'p/100 = 14/56'. This proportion represents 'p', the percent of red markers out of a total of 100, equal to the actual number of red markers (14) out of the total number of markers (56). Therefore, option A is correct. For example, if you cross-multiply and simplify, you can find the value of 'p' and hence the percentage ratio of red markers. Multiply 14 by 100 to obtain 1400 and then divide 1400 by 56 to obtain 25. Therefore, 25% of the dry erase markers are red.
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what is the fifth term of the geometric sequence? 5, 15 , 45, ...
The geometry sequence has the equation [tex]a(n)=5(3^{n-1})[/tex].
The 5 represents the first number of the sequence and the 3 represents the common ratio.
a(5) = [tex]5(3^{5-1})=5(3^{4})=5(81)=405[/tex]
answer: 405
Answer:
It is 405.
It is 405.
Write each in ax^b form where n can be either positive or negative integer
Answer:
a. [tex]$ x^{-5} $[/tex]
b. [tex]$ 3x^{-2} $[/tex]
c. [tex]$ \frac{4}{3}x^4 $[/tex]
Step-by-step explanation:
We have to know the two results to compute the problems.
1. [tex]$ x^a . x^b = x^{a + b} $[/tex]
2. [tex]$ \frac{x^c}{x^d} = x^c . x^{-d} = x^{c - d} $[/tex]
a. [tex]$ \frac{x^3}{x^8} $[/tex]
Using (2), we get: [tex]$ \frac{x^3}{x^8} = x^{3 - 8}[/tex]
[tex]$ \textbf{= x}^{\textbf{5}} $[/tex]
b. [tex]$ \frac{6x}{2x^3} $[/tex]
[tex]$ = 3\frac{x}{x^3} $[/tex]
[tex]\textbf{= 3x}^{\textbf{-2}} $[/tex]
c. [tex]$ \frac{28x^6}{21x^2} $[/tex]
[tex]$ = \frac{4}{3}x^{6 - 2} $[/tex]
[tex]$ = \frac{\textbf{4}}{\textbf{3}}\textbf{x}^{\textbf{4}} $[/tex]
Hence, the answer.
Simplify 12 × 10 ^8/ 4 × 10^5 and leave in ordinary form
Answer:
3 x 10^3
Step-by-step explanation:
The first is to identify the operation to be performed, it is a quotient between two potency.
Being two potency of the same base number (10), the property says that the quotient of two potency of the same base subtracts its exponent, and the base remains the same.
The corresponding exponents are 8 and 5.
The subtraction is 8-5 = 3.
The whole number that accompanies the base is divided in a current way, that is 12/4. Therefore, the result is 3.
6. Jefferson purchased a jacket originally priced at $129 on sale for $90.30. What
was the percent of discount?
A. 70%
B. 30%
C. 50%
D. 39%
Final answer:
To find the percent of discount, subtract the sale price from the original price, divide by the original price, and multiply by 100. The percent of discount is 30%.
Explanation:
To find the percent of discount, we need to calculate the difference between the original price and the sale price, and then divide it by the original price and multiply by 100.
Original price - Sale price = $129 - $90.30 = $38.70
Percent of discount = ($38.70 / $129) * 100 = 30%
Therefore, the percent of discount is 30%, which is option B.
What is 20 plus -14?
Answer:
6
Step-by-step explanation:
Does the following table represent a proportional relationship, and if so what is the proportion of the cost for a box of cereal to the size of the box?
Cost for a box of cereal $2.20 $2.64 $3.30 $4.84
Size of box (in ounces) 10 12 15 22
yes, $0.22 per ounce
yes, $4.55 per ounce
yes, $0.44 per ounce
no it is not proportional
Answer:
A
Step-by-step explanation:
I'm not entirely sure but please let me know if I'm right
Answer: yes
Step-by-step explanation: 2.20 divided by 10 is .22, so one ounce is 22 cents. 2.64 divided by 12 is .22, 3.30 divided by 15 is .22, and 4.84 divided by 10 is .22. All the costs are the same per ounce, so it is a proportional relationship of .22.
Solve: 8y - 6x = 48 / 2y = 3/2x - 12
Nicole has five times as many stickers in her sticker collection as her sister her sister has 32 stickers how do you stickers does Nicole have
Answer:
160 stickers
Step-by-step explanation:
32 x 5=160
Answer:
160
Step-by-step explanation:
Let x = sister's number of stickers
Then 5x = Nicole's number of stickers
x = 32
5x = 5 × 32 =160
Nicole has 160 stickers.
One of the roots of the quadratic equation x^2−5mx+6m^2=0 is 36. Find the greatest possible value of the second root.
Answer:
The greatest possible value of the second root will be 54.
Step-by-step explanation:
The given quadratic equation is x² - 5mx + 6m² = 0
So, we have to find the values of variable x.
Now, x² - 5mx + 6m² = 0
⇒ x² - 3mx - 2mx + 6m² = 0
⇒ x(x - 3m) - 2m(x - 3m) = 0
⇒ (x - 3m)(x - 2m) = 0
So, x = 3m and 2m.
Now, if 3m = 36
Then, m = 12 and the other root will be x = 2m = 24.
Again, if 2m = 36
Then, m = 18 and the other root will be x = 3m = 54.
So, if one root of the equation is 36 then, the greatest possible value of the second root will be 54. (Answer)
HELP
A gardener is planting two types of trees:
Type A is 2 feet tall and grows at a rate of 25 inches per year.
Type B is 10 feet tall and grows at a rate of 9 inches per year.
Algebraically determine exactly how many years it will take for these trees to be the same height.
Answer:
It will take 1/2 of a year or 6 months for these trees to be the same height.
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Type A is 2 feet tall and grows at a rate of 25 inches per year.
Type B is 10 feet tall and grows at a rate of 9 inches per year.
2. Algebraically determine exactly how many years it will take for these trees to be the same height.
x = Number of years
Type A = 2 + 25x
Type B = 10 + 9x
Let's solve for x, using the following equation:
Type A = Type B
2 + 25x = 10 + 9x
25x - 9x = 10 - 2
16x = 8
x = 8/16 = 1/2
It will take 1/2 of a year or 6 months for these trees to be the same height.
Let's prove it, this way:
2 + 25x = 10 + 9x
2 + 25 (1/2) = 10 + 9 (1/2)
2 + 25/2 = 10 + 9/2
29/2 = 29/2
14.5 = 14.5