Answer:
A depreciation of 14.3% leaves you with 85.7%, right? Each year's value is 85.7% of the tear before.
So, 6500(0.857)3 = $4091.25
Given the following geometric sequence, find the common ratio: {225, 45, 9, ...}.
1/5
-5
-1/5
5
Answer:
1/5
Step-by-step explanation:
a=225
45/225=1/5
The formula for GP is Tn=ar^n-1
The ratio of the measures of the sides of a triangle is 2:11:15. If the perimeter of the triangle is 168 inches, find the length of the longest side.
Answer: 90
Step-by-step explanation:
Let the sides have lengths 2n, 11n, and 15n.
Since the perimeter is 168, 2n+11n+15n=168, meaning that n=6.
So, the longest side is 15(6)=90 inches.
Evaluate the expression 120n+160,500120n+160,500 when n=32n=32.
Answer: The answer should be 164,340.
paul says x/y can result in either positive or negative quotient. is paul correct? explain why or why not.
Answer:
Dividing by same signs give a positive answer.
Dividing by different signs give a negative answer.
Step-by-step explanation:
Quotient is just a term for the answer given by a division problem.
positive/positive = positive
positive/negative = negative
negative/positive = negative
negative/negative = positive
Which transformations are needed to change the parent cosine function to y = 0.35 cosine (8 (x minus startfraction pi over 4 endfraction))? vertical stretch of 0.35, horizontal stretch to a period of 16 pi, phase shift of startfraction pi over 4 endfraction units to the right vertical compression of 0.35, horizontal compression to a period of 4 pi, phase shift of startfraction pi over 4 endfraction units to the left vertical compression of 0.35, horizontal compression to a period of startfraction pi over 4 endfraction, phase shift of startfraction pi over 4 endfraction units to the right vertical stretch of 0.35, horizontal stretch to a period of startfraction pi over 4 endfraction, phase shift of startfraction pi over 4 endfraction units to the right
The transformations that are needed to change the parent cosine function to y = 0.35×cos(8(x-π/4)) are:
vertical stretch of 0.35horizontal compression of period of [tex]\pi/4[/tex]phase shift of [tex]\pi/4[/tex] to rightHow does transformation of a function happens?The transformation of a function may involve any change.
Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.
If the original function is [tex]y = f(x)[/tex], assuming horizontal axis is input axis and vertical is for outputs, then:
Horizontal shift (also called phase shift): Left shift by c units: [tex]y = f(x+c)[/tex]earlier)Right shift by c units: [tex]y = f(x-c)[/tex]output, but c units late)Vertical shift:Up by d units: [tex]y = f(x) + d[/tex]Down by d units: [tex]y = f(x) - d[/tex]Stretching:Vertical stretch by a factor k: [tex]y = k \times f(x)[/tex]Horizontal stretch by a factor k: [tex]y = f(\dfrac{x}{k})[/tex]For this case, we're specified that:
y = cos(x) (the parent cosine function) was transformed to [tex]y = 0.35\cos(8(x-\pi/4))[/tex]
We can see its vertical stretch by 0.35, right shift by [tex]\pi/4[/tex]horizontal stretch by 1/8
Period of cos(x) is of [tex]2\pi[/tex] length. But 1.8 stretching makes its period shrink to [tex]2\pi/8 = \pi/4[/tex]
Thus, the transformations that are needed to change the parent cosine function to y = 0.35×cos(8(x-π/4)) are:
vertical stretch of 0.35horizontal compression to period of [tex]\pi/4[/tex] (which means period of cosine is shrunk to [tex]\pi/4[/tex] which originally was [tex]2\pi[/tex] )phase shift of [tex]\pi/4[/tex] to rightLearn more about transformation of functions here:
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Answer: vertical compression of 0.35, horizontal compression to a period of StartFraction pi Over 4 EndFraction, phase shift of StartFraction pi Over 4 EndFraction units to the right
Step-by-step explanation:
Tom knows that in his school 10 out of every 85 students are left-handed.
There are 391 students in Tom's school.
how many students in Tom's school are left handed?
Answer:
46 are left handed
Step-by-step explanation:
divide 10 by 85 and you get 0.11764705882352941176470588235294 then multiply that by 391 and you get 46
You have decided to purchase a car for $22,346. 16. The credit union requires a 10% down payment and will finance the balance with a 5. 4% annual interest loan for 36 months. The sales tax in your city is 7. 6%, and the license and title charges are $125. 13. Determine the amount that the credit union will finance you for. Round your answer to the nearest cent. A. $24,179. 10 c. $21,761. 20 b. $24,169. 60 d. $21,752. 64.
The amount that the credit union will finance is $24169.60
We have given that the cost of the car is $22,346. 16
and the credit union required 10% down payment
and sale tax=7.6%
The license and title charges are $125. 13.
We have to determine that the amount that the credit union will
finance Now we have sale tax 7.6% for $22,346. 16
Therefore, we get
[tex]\frac{7.6}{100} \times 22,346. 16=1698.31[/tex]
What is the amount that the credit union finance ?credit union finance=cost of car+sales tax+the license and title charges.
[tex]=22346.16+1698.31+12.13\\=24169.60[/tex]
Therefore, the amount that the credit union will finance is $24169.60
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A parallelogram with a right angle that is not a rectangle.
Answer:
One is a rhombus.
Step-by-step explanation:
Find the area of the triangle. Enter your answer in the box. 27 mm 12 mm 14 mm sq mm
Answer:
84 cm^2
Step-by-step explanation:
The area of a triangle is calculated using the following formula:
1/2 * b*h (b: base, h: height)
1/2 * 14 * 12 = 84 the area is indicated with cm^2 so the answer is 84 cm^2
Determine the value of y, if x is −8. y=x 2 +4
Step-by-step explanation:
given: x = -8,
putting value of x in given equation,
y=(-8)2+4
y= -16+4
y=-12
I am thinking of a number. The sum of its digits is divisible by 2. My number is a multiple of 11. My number is greater than 4 x 5 but less than 7 x 8+ 23. The number is a multiple of 3. What is my number? Is it possible to have more than one answer?
Answer:
66
Step-by-step explanation:
Number:xy
20<xy<79
Multiples of 2,3,11
The least common multiple of this number is 66.
18 less than the quotient of a number and -5 is greater than 3
Step-by-step explanation:
x = "a number"
x/-5 - 18 > 3
Please Help! Which of the following methods is not used to prove triangles are congruent?
Answer:
AAA is not a congruency postulate because it could only prove that triangles are similar, not congruent.
Step-by-step explanation:
Fine the area of the circle. Round to the nearest tenth. Use 3.14 for pie.
Answer:
the answer is 379.9m²
Step-by-step explanation:
half of 22 is ll time 3.14 equals 379.94. to the nearest tenth is 379.9
someone, please help me out with these two problems, it's trig.
Answer:
2nd problem
The sum of the angles of the triangle is 180°.
B= 90°
Simplest radical form please !!Need answers asap
Answer:
11) [tex]5\sqrt{7}[/tex] yd
12) [tex]2\sqrt{10}[/tex] cm
13) 9 ft
14) [tex]\sqrt{95}[/tex] cm
15) [tex]5\sqrt{5}[/tex] km
16) [tex]\sqrt{39}[/tex] yd
A student’s work to simplify a radical is shown below. Select the statement which best applies to the sample mathematical work.
Answer: D
Step-by-step explanation:
A flat-bottomed ice cream waffle cup is shaped like a 72 mm tall cone with a 42 mm diameter opening at the top, but with the bottom 24 mm of the cone replaced by a flat waffle bottom with a 14 mm diameter. to the nearest square millimeter, what area of waffle does the cone have?
a.) 4002
b.)4398
c.)4552
d.)4157
The area of waffle in the cone is the amount of space covered by the waffle
The cone has 5630 square millimeter of waffle
How to determine the surface area?
The surface area of a cone is calculated using:
A = πr * (r+[tex]\sqrt{[/tex](h^2 + r^2))
For the complete 72 mm tall cone, we have:
Height (h) = 72 mm
Radius (r) = 42 mm/2 = 21 mm
So, the surface area is:
A = πr * (r+[tex]\sqrt{[/tex](h^2 + r^2))
A = 3.142 * 21 * (21+[tex]\sqrt{[/tex](72^2 + 21^2))
Evaluate
A = 3.142 * 21 * (21+75)
A = 6334.272
When the cone is cut at the top, we have:
Height (h) = 24 mm
Radius (r) = 14 mm/2 = 7 mm
So, the surface area is:
A = πr * (r+[tex]\sqrt{[/tex](h^2 + r^2))
A = 3.142 * 7 * (7+[tex]\sqrt{[/tex](24^2 + 7^2))
Evaluate
A = 3.142 * 7 * (7 + 25)
A = 703.808
Calculate the difference (d) between the areas
d = 6334.272 - 2.5*703.808
Evaluate
d = 5630.464
Approximate
d = 5630
Hence, the cone has 5630 square millimeter of waffle
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What is the distance between (4, 6) and (4, -1) ?
7 units
5 units
4 units
I don't know
The distance between points (4,6) and (4,-1) is 7 units.
Given The coordinates of the end points of line (4,6) and (4,-1).
Distance is the measurement about how far things are present on the surface. It is usually calculated in some units known as km, m, etc.
The distance between two points can be calculated as under:
Distance=[tex]\sqrt{(x2-x1)^{2} +(y2-y1)^{2} }[/tex] where the coordinates are (x1,y1),(x2,y2).
To calculate the distance we need to put the values of coordinates in the formula:
Distance between (4,6) and (4,-1)=[tex]\sqrt{(4-4)^{2} +(-1-6)^{2} }[/tex]
=[tex]\sqrt{(0)^{2}+(-7)^{2} }[/tex]
=[tex]\sqrt{0+49}[/tex]
=[tex]\sqrt{49}[/tex]
=7
Hence the distance between (4,6) and (4,-1) is 7 units.
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#SPJ10
Answer:
it would be 7 units :)
Step-by-step explanation: cuz im smart and said so
You make commission working at Footlocker. On Saturday you sold
$1,500 worth of merchandise and made $120 in commission. On
Sunday you sold $1,300 worth of merchandise. If you made the same percent commission,how much did you earn on Sunday?
A. $8
B. $86. 66
C. $104
D. $1,039. 99
Answer:
C. $104
Step-by-step explanation:
First, we need to figure out what percent $120 is of $1500.
120 ÷ 1500 = 0.08 = 8%. So, $120 is 8% of $1500, and this is the percentage that'll be used to calculate Sunday's commission.
0.08 (8%) × 1300 = 104
Thus, you earned $104 on Sunday.
The diagram shows a plan for the rectangular house with an attached porch. The combined area of the house and the porch is 733ft2. What is the value of x? Show your work. The numbers are 59ft, 13ft, 6 ft, 7ft, 9ft is the porch, x ft
The value of x in the diagram is 8 feet that makes the combined area of the house and the porch to be 733 ft²
How to calculate area?
Combined area = big rectangle + smaller rectangle - triangle
Hence:
733 = (13 * (59 - x)) + (x * 9) - 0.5(9 - 7) * (x - 6)
733 = 767 - 13x + 9x - x + 6
x = 8 feet
The value of x in the diagram is 8 feet that makes the combined area of the house and the porch to be 733 ft²
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20 points!!!Solid metal support poles in the form of right
cylinders are made out of metal with a density of 5.2
g/cm². This metal can be purchased for $0.35 per
kilogram. Calculate the cost of a utility pole with a
radius of 19 cm and a height of 620 cm. Round your
answer to the nearest cent. (Note: the diagram is not
drawn to scale)
Density is mass per unit volume. The cost of the metals from the calculations performed is $1280.
What is density?Density is defined as the ratio of the mass of an object to its volume. We have the following information;
Mass of the metal = ?
Density of the metal = 5.2 g/cm3
height of the metal = 620 cm
radius of the metal = 19 cm
Volume of a cylinder = πr^2h = 3.142 * (19)^2 * 620 cm = 703242cm^3
Mass = density * volume = 5.2 g/cm3 * 703242cm^3
= 3657 Kg
If the cost is $0.35 per kilogram, then 3657 Kg costs; 3657 Kg * $0.35
= $1280
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Identify the solution of the inequality |4x − 2| > 14 and the graph that represents it.
The solution to the inequality |4x − 2| > 14 is x > 4 and x < -3
What is an inequality?
An inequality is an expression that shows the non equal comparison of two or more numbers and variables.
Given the inequality:
|4x − 2| > 14
Hence:
4x - 2 > 14 or -(4x - 2) > 14
x > 4 or x < -3
The solution to the inequality |4x − 2| > 14 is x > 4 and x < -3
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The area of the squared garden is 625 sq. m, what is its perimeter ? (Ans: 100 m)
Answer: Area of square = a*a(where a is length of one side) Putting value a x a=625 cm2 a= 25 Perimeter will be 4 x a 4 x 25 = 100 cm
Step-by-step explanation:
[tex]\sf\huge\underline{Given:-}[/tex]
Area of the square field [tex]\sf{= 625 m^2}[/tex]
[tex]\sf\huge\underline{To\: Find:-}[/tex]
[tex]\rightarrow[/tex] Perimeter of the square garden.
[tex]\sf\huge\underline{Formula \:Used:-}[/tex]
Area of square [tex]\sf{= side^2}[/tex]
Perimeter of square [tex]\sf{= 4×side}[/tex]
[tex]\sf\huge\underline{Solution:-}[/tex]
As we know,
[tex]\rightarrow[/tex] Area of square [tex]\sf{= side^2}[/tex](putting the given value of area)
[tex]\rightarrow[/tex] [tex]\sf{Side^2}[/tex] [tex]\sf{= 625}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{Side}[/tex][tex]\sf{= \sqrt{625}}[/tex]
[tex]\rightarrow[/tex][tex]\sf{Side}[/tex][tex]\sf{= 25cm}[/tex]
So, From here we got the side of the square garden that is, 25cm.
Now,
[tex]\rightarrow[/tex]Perimeter of square [tex]\sf{= 4×side}[/tex](Putting the value of side)
[tex]\rightarrow[/tex] Perimeter of square [tex]\sf{= 4×25}[/tex]
[tex]\rightarrow[/tex]Perimeter of square [tex]\sf{= 100cm}[/tex]
Therefore, perimeter of the square garden = 100cm.
Dr. Bayer measured the masses of newborn twins. Baby A weighs 2.8 kilograms. Baby B weighs 2,950 grams. What is the difference between the masses of these newborn twins in grams? OPTIONS
Convert 2.8 kilograms into 2800 grams.
Baby A weighs 2800 grams, baby B weighs 2950 grams -> The difference between the masses = 2950 - 2800 = 150 grams.
Which expression represents 4 fifths t(negative 10 t)? –8t 46 over 5 46 over 5 –8t2
Answer:
is this a multiple choice question? if so can you retype it out to show the separate answer choices because im having trouble reading your question.
Step-by-step explanation:
Answer:
–8t^2 or DStep-by-step explanation:
Took the test and got it right.
Which expression is equivalent to (o)(5)?
Of(5) g(5)
Of(5) + g(5)
O5f(5)
05g(5)
an unknown number is increased by -3. the result is -8
find the unknown number
Answer:
The unknown number is -5.
Step-by-step explanation:
-3 + -5 = -8
-8 - -3 = -5
-8 - -5 = -3
I’m not entirely sure with this question, anyone can please help?
Step-by-step explanation:
3x + 4 = 72 - x
3x - x = 72 - 4
2x = 68
x = 39
The circumference of the hub cap of a tire is 77.62 centimeters. Find the area of this hub cap. Use
3.14 for it.
PLEASE HELP ME
[tex]\textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=77.62 \end{cases}\implies 77.62=2\pi r\implies \cfrac{77.62}{2\pi }=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2\qquad \qquad A=\pi \left( \cfrac{77.62}{2\pi } \right)^2\implies A=\cfrac{77.62^2}{4\pi }\implies A\approx 479.69[/tex]