Answer:
i
Step-by-step explanation:
The square root of -1 is i which is an imaginary number
A hardware store buys 300 feet of nylon rope. The store sells the rope by the inch. A customer can purchase 40 inches of the rope for $1.60. The store sells all of the rope and makes a profit of $54. How much did the store pay for the rope in dollars per inch.
Pls answer this question it’s important..
Answer:
0.025 $/in.
Step-by-step explanation:
The store bought 300 ft of rope.
1 ft = 12 in.
300 ft * 12 in./ft = 3600 in.
The store bought 3600 inches of rope.
The store sells 40 inches of rope for $1.60. We can find the selling unit price of rope in dollars per inch.
($1.60)/(40 in.) = $0.04/in.
The store sells the rope at a price of $0.04 per inch.
The store sold all the rope at $0.04/in.
3600 in. * $0.04/in. = $144
The store sold all the rope for $144.
The profit was $54 for selling ll the rope.
$144 - $54 = $90
The bought the rope for $90.
The cost is dollars per inch is
($90)/(3600 in.) = 0.025 $/in.
Which of the following exponential regression equations best fits the data shown below?
Answer:
The correct option is D.
Step-by-step explanation:
The general exponential regression equations is
[tex]y=ab^x[/tex] .... (1)
where, a is initial value and b is growth factor.
Using graph calculator, we get
[tex]a=3.5349151766\approx 3.53[/tex]
[tex]b=4.37391527533\approx 4.37[/tex]
[tex]R^2=0.99878148[/tex]
Put the value of a and b in equation (1), to find the exponential regression equation.
Substitute a=3.53 and b=4.37 in equation (1).
[tex]y=(3.53)(4.37)^x[/tex]
[tex]y=3.53(4.37)^x[/tex]
The exponential regression equations that best fits the data is [tex]y=3.53(4.37)^x[/tex].
Therefore the correct option is D.
John and his son are building a boxcar for a group competition. According to the rules of the competition, the length of the car must be 3 inches greater than its width. Also, the width of the car must be at least 2 inches greater than the radii of the wheels. When they signed up for the competition, they were given a kit containing everything they needed to build the car except for the base and the wheels. According to the rules of the competition, they must spend no more than $50. The cost of the base will be $0.50 per square inch and the cost of each of the 4 wheels will be $2.25 per inch of radius. If x represents the width of the car and y represents the radii of the wheels, then which of the following systems of inequalities can be used to determine the length and width of the car and the radii of the wheels?
The system of inequalities to determine the dimensions and budget of the boxcar, according to the given restrictions in the problem, are: x + 3 >= length, x >= y + 2, and 0.50*x*(x+3) + 4 * 2.25 * y <= 50.
Explanation:The subject of this question is Mathematics, specifically the topic of inequalities. From the problem, we can create a system of inequalities based on the restrictions specified. We are told that the length of the car must be 3 inches greater than its width, which is represented by x, so one inequality is x+3 >= length. Second, the width of the car must be at least 2 inches greater than the radii of the wheels, represented by y, so we have another inequality, x >= y + 2.
Lastly, we need to account for the monetary constraint. The cost of the base is $0.50 per square inch, so the cost is 0.50*x*(x+3), and the cost of each of the 4 wheels is $2.25 per inch of radius, so the total cost is 4 * 2.25 * y. The total spending must not exceed $50, so our final inequality is 0.50*x*(x+3) + 4 * 2.25 * y <= 50. Therefore, the system of inequalities that can be used to determine the length, width of the car and the radii of the wheels is:
x + 3 >= length
x >= y + 2
0.50*x*(x+3) + 4 * 2.25 * y <= 50
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A coffee distributor needs to mix a(n) House coffee blend that normally sells for $10.50 per pound with a Kenya coffee blend that normally sells for $12.80 per pound to create 40 pounds of a coffee that can sell for $10.67 per pound. How many pounds of each kind of coffee should they mix?
Answer: They must mix
______pounds of the House Blend
______pounds of the Kenya Blend.
Round your answers to the nearest whole number of pounds.
Answer:
They must mix
37 pounds of the House Blend
3 pounds of the Kenya Blend.
Step-by-step explanation:
Let 'x' be House coffe and 'y' be Kenya Coffee. Then:
10.50x + 12.80y = 10.67(40)
Also, we knw that:
x + y = 40
Solving the system of equations above, we have that:
x ≈37.0435 ≈ 37 pounds
y ≈2.95652 ≈ 3 pounds
They must mix
37 pounds of the House Blend
3 pounds of the Kenya Blend.
a right pyramid with a square base has a base edge length of 24 feet and slant height of 20 feet the height of the pyramid is feet
Answer:
The height of the pyramid is 16 feet.Step-by-step explanation:
Look at the picture.
Use the Pythagorean theorem:
[tex]leg^2+leg^2=hypotenuse^2[/tex]
We have
[tex]leg=12ft,\ leg=H,\ hypotenuse=20ft[/tex]
Substitute:
[tex]12^2+H^2=20^2[/tex]
[tex]144+H^2=400[/tex] subtract 144 from both sides
[tex]H^2=256\to H=\sqrt{156}\\\\H=16\ ft[/tex]
Answer:
16 feet
Step-by-step explanation:
for edg
The u-drive rent-a-truck company plans to spend $8 million on 280 new vehicles. Each commercial van will cost $25,000 , each small truck $30,000 , and large truck $40,000. Past experience shows that they need twice as many vans as small truck. How many of each type of vehicle can they buy?
Answer:
1 large truck, 99 small trucks and 180 commercial vans
Step-by-step explanation:
Step 1 : Write the data.
Total amount: 8,000,000
Total trucks needed: 280
Cost of commercial van (x) = $25,000
Cost of small truck (y) = $30,000
Large truck = $40,000 (from my understanding, only 1 large truck has to be bought since the amount given for commercial vans and small trucks is for each of it.
Since they need twice as many vans as small trucks, commercial van will be 2y and small truck will be y
Step 2 : Form two equations
40,000 + 25000(x) + 30000(y) = 8,000,000
25000(x) + 30000(y) = 7960,000 (equation 1)
1(large truck) + x + y =280
x + y = 279 (equation 2)
Step 3 : Find the value of y
From equation 2:
x = 279 - y
From equation 1:
25000(x) + 30000(y) = 7960,000
25000(279 - y) + 30000(y) = 7960,000
-25000y + 30000y + 6975000 = 7960000
5000y = 985000
y= 98.5 rounded off to 99 small trucks
Step 4: Find value of x
x + y = 279
y = 279 - 99
y = 180 commercial vans
Step 5: Answer how many type of each vehicle can they buy.
They can buy:
1 large truck
99 small trucks
180 commercial vans
!!
PLEASE HELP ME ASAp!!!!!!
Answer:
The area of the prism: 404 square feet.
Step-by-step explanation:
The idea in this exercise is to find the areas of all the geometric figures, and then add them all.
Notice that we have four consecutive rectangles, two smaller with dimension 6 ft by 8 ft and two larger with dimension 11 ft by 8 ft. Then, combined area of this four rectangles is
A_1 = 6*8 + 6*8 + 11*8+11*8 = 48+48+88+88 = 272.
For the other two rectangles, notice that their bases has the same length (11 ft). Their height can obtained using the characteristics of the prism. In this case must be 6 ft, the same length of the base of the previous smaller rectangles. The, the combined area of this rectangle is
A_2 = 6*11 +6*11 = 66 + 66 = 132.
Finally, adding those two area we get the area of the prism: 404 square feet.
In The Diagram Below, BD is parallel to XY, What is the value of Y?
A.73
B.97
C.83
D.87
Answer: B.97
Step-by-step explanation:
When two parallel lines are intersected by a transversal line then the sum of adjacent angles is 180°.
From the given figure , BD is parallel to XY and a transversal intersecting it making a pair of adjacent angles 83° and y°.
[tex]83^{\circ}+y^{\circ}=180^{\circ}\\\\\Rightarrow\ y^{\circ}=180^{\circ}-83^{\circ}=97^{\circ}[/tex]
Hence, the value of y= 97.
Answer:it is 83
Step-by-step explanation:
What is 16 percent of 65
Answer:
10.4
Step-by-step explanation:
The way to find percentage is by multiplying the number you want to find the percentage of by the percentage and divide it by 100
So, in the case of 16% of 65
we multiply 65 by 16 =1040
then we divide by 100
Hence 1040/100=10.40
which is same as 10.4
HOPE IT HELPS....
The solution of the expression 16 percent of 65 is 10.4.
A percentage is a ratio that may be written as a fraction of 100.
A fraction is a ratio between two quantities. The upper part is called numerator and the lower part is called denominator.
A collection of constants, variables connected using one or more arithmetic operator is called an expression.
This can be simplified as:
[tex]\dfrac{16}{100} \times65 = 10.4[/tex] in decimal form.
Thus, 16 percent of 65 is 10.4
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Which of the pairs of ratios are equivalent? A) 12: 24, 50 :100 B) 16 to 3,27 to 5 C) 22/1, 68/3 D) 3/7, 17/35
Answer:
A
Step-by-step explanation:
equivalent because each are 1:2
Final answer:
After simplifying each pair of ratios, only 12: 24, and 50:100 (Pair A) are equivalent ratios, as both simplify to 1:2. The other pairs are not equivalent since their simplified forms are different.
Explanation:
To determine which of the pairs of ratios are equivalent, we can simplify each ratio or convert them to fractions and simplify to see if they have the same value. Let's look at each pair:
A) 12: 24 simplifies to 1:2. 50 :100 also simplifies to 1:2. Therefore, these ratios are equivalent.B) 16 to 3 is the same as the fraction 16/3. 27 to 5 is the same as the fraction 27/5. These ratios are not equivalent as their simplified forms (16/3 and 27/5) are different.C) 22/1 is simply 22. 68/3 when divided is approximately 22.67. These ratios are not equivalent because 22 does not equal 22.67.D) 3/7 is a fraction and does not simplify further. 17/35 simplifies to 1/2 when divided by 17. These ratios are not equivalent because 3/7 is different from 1/2.From the above, only the pair A) 12: 24, 50:100 are equivalent ratios.
if f || k and k || m, then blank
Answer:
f || m
Step-by-step explanation:
If f is parallel to k and k is parallel to m
then f must be parallel to m
Koalas absorb only 25% of the fiber they eat. A koala absorbed 10.5 ounces of fiber in one day. How many ounces of fiber did he eat that day?
42 ounces
Step-by-step explanation:In this question, it is asking how many ounces of fiber did the Koala eat that day.
In order to solve this question, we would need to gather some important information from the question.
Important Information:
Koalas absorb only 25% of fiber they eatKoala absorbed 10.5 ounces of fiber in 1 dayWith the information above, we can solve the question.
We know that koalas only absorb 25% of fiber. We also know that a koala absorbed 10.5 ounces of fiber.
This means that the 10.5 ounces is 25% of fiber. This is 1/4 of the fiber it ate.
Now, we just need to find the other 3/4.
We could just multiply 10.5 by 4 to find how much fiber it ate that day.
[tex]10.5*4=42[/tex]
When you multiply, you should get 42.
This means that the Koala ate 42 ounces of fiber that day.
I hope this helps you out.Good luck on your academics.Have a fantastic day!Answer:
42
Step-by-step explanation:
We seek the answer to the question "10.5 ounces is 25% of what number?" If we call the unknown number of ounces x, we have the equation 10.5=0.25x. Dividing both sides by 0.25, we have x=10.5/0.25=42 ounces of fiber.
Prove that f(x)=x+3/2 and g(x)=2x-3are inverse
To prove that two functions are inverse, we need to show that applying one function and then the other will result in the original input. By evaluating f(g(x)) and g(f(x)), we can confirm that f(x) = x + 3/2 and g(x) = 2x - 3 are inverse functions.
Explanation:To prove that two functions f(x) and g(x) are inverse, we need to show that applying one function and then the other will result in the original input. In other words, f(g(x)) = x and g(f(x)) = x. Let's check if this holds true for the functions given:
First, let's find f(g(x)):Since f(g(x)) = x and g(f(x)) = x, we can conclude that f(x) = x + \frac {3}{2} and g(x) = 2x - 3 are indeed inverses of each other.
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f(x) and g(x) are inverse functions.
To prove that f(x) = x + 3/2 and g(x) = 2x - 3 are inverses, find their compositions and show they equal x, establishing them as inverse functions.
To prove that f(x) = x + 3/2 and g(x) = 2x - 3 are inverses:
Find the composition of f(g(x)) and g(f(x)).Show that f(g(x)) = x and g(f(x)) = x for all x.Thus, f(x) and g(x) are inverse functions.
ZE is the angle bisector of measure YEX and the perpendicular bisector of GF, GX is the angle bisector of measure YGZ and the perpendicular bisector of EF, FY is the angle bisector of measure ZFX and the perpendicular bisector of EG. Point A is the intersection of EZ, GX, and FY.
Answer:
C
Step-by-step explanation:
The center of inscribed circle into triangle is point of intersection of all interior angles of triangle.
The center of circumscribed circle over triabgle is point of intersection of perpendicular bisectors to the sides.
Circumscribed circle always passes through the vertices of the triangle.
Inscribed circle is always tangent to the triangle's sides.
In your case angles' bisectors and perpendicular bisectors intesect at one point, so point A is the center of inscribed circle and the center of corcumsribed circle. Thus, these circles pass through the points X, Y, Z and G, E, F, respectively.
Write a function rule that gives the total cost c(p) of p pounds of sugar if each pound costs $0.59.
c(p) = 0.59p
c(p) = 59p
c(p) = p + 0.59
Answer:
c(p) = 0.59p
Step-by-step explanation:
We multiply the number of pounds of sugar, p, time the cost per pound ,.59, to get the total cost
c(p) = .59*p
Answer: c(p) = 0.59p
Step-by-step explanation:
Match the polygons formed by the set of points with their perimetersrounded to the nearest hundredth. Please help ASAP taking a test . Thank you so much in advance
Answer:
Polygon ABCDE = 50 units
Polygon FGHIJ = 23.4 units
Polygon KLMNO = 19.24 units
Polygon UVWXY = 38 units
Step-by-step explanation:
In order to find the perimeter, we have to find lengths of all sides of given points
The distance formula will be used to find the lengths
[tex]d = \sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2} }[/tex]
where (x_1,y_1) are coordinates of first point and (x_2,y_2) are coordinates of second point)
So,
For A(1,1), B(6,13), C(8,13), D(16,-2) and E(1, -2)
AB = 13 units
BC = 2 units
CD = 17 units
DE = 15 units
EA = 3 units
Perimeter of polygon ABCDE = 13+2+17+15+3 = 50 units
For F(14,-10), G(16,-10), H(19,-6), I(14,-2) and J(11,-6)
FG = 2 units
GH = 5 units
HI = 6.40 units
IJ = 5 units
JF = 5 units
Perimeter of polygon FGHIJ = 2+5+6.40+5+5 = 23.4 units
For K(4,2), L(8,2), M(12,5), N(6,5) and O(4,4)
KL = 4 units
LM = 5 units
MN = 6 units
NO = 2.24 units
OK = 2 units
Perimeter of polygon KLMNO = 4+5+6+2.24+2 = 19.24 units
For P(7,2), Q(12,2), R(12,6), S(7,10) and T(4,6)
PQ= 5 units
QR= 4 units
RS=6.40 units
ST= 5 units
TP = 5 units
Perimeter of polygon PQRST = 5+4+6.40+5+5 = 25.40 units
For U(4,-1), V(12, -1), W(20,-7), X(8, -7) and Y(4,-4)
UV = 8 units
VW = 10 units
WX = 12 units
XY = 5 units
YU = 3 units
Perimeter of polygon UVWXY = 8+10+12+5+3 = 38 units
Alvin throws the football to a receiver who jumps up to catch the ball. The height of the ball over time can be represented by the quadratic equation -4.9t2 + 7.5t + 1.8 = 2.1 . This equation is based on the acceleration of gravity -4.9 m/s2, the velocity of his pass is 7.5 m/s and releases the football at a height of 1.8 meters, and the height where the receiver catches the ball of 2.1 meters. Put the equation in standard form and then solve by using the quadratic equation.
Answer:
The standard form of the equation is 49t² - 75t + 3 = 0
The solution of the equations are 1.49 and 0.041
Step-by-step explanation:
* Lets explain how to solve the problem
- The standard form of the quadratic equation is ax² + bx + c = 0,
where a , b , c are constant and a can not be 0
∵ The quadratic equation is -4.9t² + 7.5t + 1.8 = 2.1
- Lets make the left hand side equal to 0
∵ -4.9t² + 7.5t + 1.8 = 2.1 ⇒ subtract 2.1 from both sides
∴ -4.9t² + 7.5t - 0.3 = 0 ⇒ multiply each term by -10
∴ 49t² - 75t + 3 = 0
* The standard form of the equation is 49t² - 75t + 3 = 0
∵ ax² + bx + c = 0
∴ a = 49 , b = -75 , c = 3
- Lets use the formula [tex]x=\frac{-b+-\sqrt{b^{2}-4ac}}{2a}[/tex] to solve
the equation
∴ [tex]x=\frac{-(-75)+\sqrt{(-75)^{2}-4(49)(3)}}{2(49)}=1.49[/tex]
∴ [tex]x=\frac{-(-75)-\sqrt{(-75)^{2}-4(49)(3)}}{2(49)}=0.041[/tex]
* The solution of the equations are 1.49 and 0.041
The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 6 to 5. Ir there were 3822 yes votes, what was the total
number of votes?
total votes
Answer:
The total number of votes was [tex]7,007[/tex]
Step-by-step explanation:
Let
x -----> the number of yes votes
y -----> the number of no votes
we know that
[tex]\frac{x}{y} =\frac{6}{5}[/tex]
isolate variable y
[tex]y=\frac{5}{6}x[/tex] -----> equation A
[tex]x=3,822[/tex] -----> equation B
Substitute equation B in equation A and solve for y
[tex]y=\frac{5}{6}(3,822)=3,185[/tex]
therefore
To find out the total number of votes sum the number of yes votes plus the number of no votes
[tex]3,822+3,185=7,007[/tex]
Answer: 7,007 votes :)
Step-by-step explanation:
Hope that helps
Which principle must a government follow in order to be considered a
democracy?
Step-by-step explanation:
The political equality of all citizens is an essential principle of democracy. In ademocracy, the just powers of government are based upon the consent of the governed.
D) leaders Must be selected by the citizens rather than inheriting power. (Apex)
a photo with a length of 3 inches and a width of 5 inches is enlarged to a poster size. the poster and the photo are similar. the length of the poster is 21 inches. what is the width of the poster? (answers there^^)
Answer:
J. 35 inches
Step-by-step explanation:
Write a proportion:
3 / 5 = 21 / x
Cross multiply:
3x = 105
Divide:
x = 35
The width of the poster is 35 inches.
The width of the poster is 35 inches.
What is the ratio proportion?Proportion is an equation that defines that the two given ratios are equivalent to each other. In other words, the proportion states the equality of the two fractions or the ratios.
A photo with a length of 3 inches and a width of 5 inches is enlarged to poster size.
The poster and the photo are similar. the length of the poster is 21 inches.
Let x be the width of the poster.
The width of the poster is given by;
[tex]\rm \dfrac{Length \ of \ photo}{Width \ of \ photo}=\rm \dfrac{Length \ of \ poster}{Width \ of \ poster}\\\dfrac{3}{5}=\dfrac{21}{x}\\\\3 \times x =21 \times 5\\\\3x=105\\\\x=\dfrac{105}{3}\\\\x=35[/tex]
Hence, the width of the poster is 35 inches.
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(3,1.5) and (5, 2.5) what is the slope of the line through these two points?
The slope of the line through given two points is [tex]\frac{1}{2}[/tex]
What is the formula of slope ?
If (x₁, y₁) & (x₂, y₂) are two given points on a line.
Then the slope of the line (m) = [tex]\frac{y_{2} -y_{1} }{x_{2}- x_{1} }[/tex]
What is the required slope ?Given points on a line are (3, 1.5) & (5, 2.5)
∴ Slope of the line (m) = [tex]\frac{y_{2} -y_{1} }{x_{2}- x_{1} }[/tex]
= [tex]\frac{2.5-1.5}{5-3}[/tex]
= [tex]\frac{1}{2}[/tex]
So, the required slope is [tex]\frac{1}{2}[/tex]
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You need 300 mL of a 65% alcohol solution. On hand, you have a 50% alcohol mixture. How much of the 50% alcohol mixture and pure alcohol will you need to obtain the desired solution?
You will need
____ mL of the 50% solution
and
______ mL of pure alcohol.
Answer:
You will need 220 mL of the 60% solution and 80 mL of pure alcohol.
Step-by-step explanation:
Let 'x' be the amount of 50% alcohol solution and y the amount of pure alcohol.
Therefore:
(0.5x + y)/300 = 0.65 ⇒ 0.5x + y = 190
x + y = 300
Solving the sistem of equations:
x = 220 and y = 080
Therefore, You will need
220 mL of the 60% solution
and 80 mL of pure alcohol.
I Need The Answer Please Help!!
Answer:
33°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Subtract the sum of the 2 given angles from 180 for ∠1, that is
∠1 = 180° - (116 + 31)° = 180° - 147° = 33°
What is a factorial and what is the purpose of it?
Answer:
Step-by-step explanation:
Factorial is used to multiply any natural number with all the numbers smaller than it. It is denoted by n! (n is the natural number)
where n! = n*(n-1)*(n-2)*(n-3)*(n-4) so on....
For example if we take factorial of 5.
Then,
5!= 5*(5-1)*(5-2)*(5-3)*(5-4)
= 5*4*3*2*1
= 120
It is used for the questions which asks us to order a number of things or in how many ways you can arrange something....
Factorial is a key function in mathematics used to calculate permutations and arrangements. It represents the number of ways objects can be arranged within a set number. Factorial is essential in combinatorics and probability theory.
Factorial is a mathematical function denoted as n! and calculated as the product of all positive integers up to n.
The purpose of factorial is to represent the number of ways in which a set of objects can be arranged or permutations can be made within a set number of objects.
Factorial is extensively used in mathematics, especially in combinatorics and probability theory.
1
what is sin 62° ? apexxx
Answer:
D. 15/17
Step-by-step explanation:
Sine is opposite/hypotenuse and the opposite side to 62 degrees is 15 while the hypotenuse is 17
The value of sin 62° will be equal to 15/17.
What is trigonometry?Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.
The formula for sin angle is given as:-
SinФ = Perpendicular / Hypotenuse
From the figure, Perpendicular is 15 and the hypotenuse is 17 so the value will be:-
Sin62° = 15 / 17
Therefore the value of sin 62° will be equal to 15/17.
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Identify the two rational numbers 2.7182818459, 2.777777, square root 3, -7/3
Answer:
2.777777 and -7/3
Step-by-step explanation:
2.7182818459 cannot be written in fraction form therefore it is irrational.
2.777777 is rational because it can be written as the fraction 25/9
The square root of 3 is 1.7320508075688772, this number cannot be written as a fraction so it is irrational.
-7/3 is rational because it is already in fraction form.
Answer:
2.777777 and -7/3
Step-by-step explanation:
If a number can be defined in the form of p/q where q≠0, then it is called rational number.
If a decimal number is repeating then it is a rational number because it can be written in the form of p/q.
For example: 1.222, 3/5, 2.5, -1/2, 4.0707007...
All real numbers which are not rational numbers are called irrational numbers.
For example: 0.2357835.., √2, π.
In the given numbers,
Rational numbers = 2.777777, -7/3
Irrational numbers = 2.7182818459 and √3
Therefore the two rational numbers are 2.777777 and -7/3.
A (5, 3), B (2, 1), and C (-2, 4) are the coordinates of a triangle's vertices. If the triangle is reflected over the x-axis, what are the coordinates of the image?
Answer:
A(5,3) ->A'(5,-3)
B(2,1) ->B'(2,-1)
C(-2,4) ->C'(-2,-4)
Step-by-step explanation:
If a point is reflected over the x-axis, it ends up on the opposite side of the x-axis with the same distance from the x-axis.
So what that means is the x-coordinate will stay the same and the y-coordinate will be opposite of what it was.
So if we reflect each of your points through the x-axis you will get:
A(5,3) ->A'(5,-3)
B(2,1) ->B'(2,-1)
C(-2,4) ->C'(-2,-4)
Answer:
(5,-3) (2,-1) (-2,-4)
Step-by-step explanation:
When reflection over the x-axis the rule is (x,y) becomes (x, -y)
so your x will stay the same but your y will change
Which is greater than 4.026?
A. 4.020
B. 4.030
C. 4.021
D. 4.006
Answer:
b
Step-by-step explanation:
Answer:
B. 4.030
Step-by-step explanation:
We need to compare 4.026 with the numbers int he four choices.
All number have the same whole number part, 4.
To compare them, all you need to do is compare the decimal part.
All numbers have 3 places after the decimal point, so the decimal parts are all in thousandths.
A. 4 and 20 thousandths
B. 4 and 30 thousandths
C. 4 and 21 thousandths
D. 4 and 6 thousandths.
The number you are given is 4 and 26 thousandths.
Of all the thousandths in the choices, only 30 thousandths is greater than 26 thousandths, so 4.030 is the only number greater than 4.026.
Two different cars each depreciate to 60% of their respective original values. The first car depreciates at an annual rate of
10%. The second car depreciates at an annual rate of 15%. What is the approximate difference in the ages of the two cars?
A. 1.7 years
B. 2.0 years
C. 3.1 years
D. 5.0 years
Answer: A) 1.7 Years
Step-by-step explanation:
Answer:
A. 1.7 years
Step-by-step explanation:
Let [tex]P_1[/tex] be the original value of first car,
Since, the car depreciates at an annual rate of 10%,
Let after [tex]t_1[/tex] years the value of car is depreciated to 60%,
That is,
[tex]P_1(1-\frac{10}{100})^{t_1}=60\%\text{ of }P_1[/tex]
[tex]P_1(1-0.1)^{t_1}=0.6P_1[/tex]
[tex]0.9^{t_1}=0.6[/tex]
Taking ln on both sides,
[tex]t_1ln(0.9) = ln(0.6)[/tex]
[tex]\implies t_1=\frac{ln(0.6)}{ln(0.9)}[/tex]
Now, let [tex]P_2[/tex] is the original value of second car,
Since, the car depreciates at an annual rate of 15%
Suppose after [tex]t_2[/tex] years it is depreciated to 60%,
[tex]P_2(1-\frac{15}{100})^{t_2}=60\%\text{ of }P_2[/tex]
[tex]P_2(1-0.15)^{t_2}=0.6P_2[/tex]
[tex]0.85^{t_2}=0.6[/tex]
Taking ln on both sides,
[tex]t_2ln(0.85) = ln(0.6)[/tex]
[tex]\implies t_2=\frac{ln(0.6)}{ln(0.85)}[/tex]
[tex]\because t_1-t_2=\frac{ln(0.6)}{ln(0.90)}-\frac{ln(0.6)}{ln(0.85)}[/tex]
[tex]=1.70518303046[/tex]
[tex]\approx 1.7[/tex]
Hence, the approximate difference in the ages of the two cars is 1.7 years,
Option 'A' is correct.
Exponential functions have the form f(x)=b^x. What type of an exponential function would you have (increasing or decreasing) if the value of b is greater than one?
Answer:
Increasing
Step-by-step explanation:
Let's see what happens if we choose a value for b greater than 1.
Let's try b=2.
[tex]f(x)=2^x[/tex].
I'm going to keep increasing x. If y increases, the the function is increasing. If y decreases, the function is decreasing.
Let's start with x=1.
[tex]y=2^1=2[/tex]
Now x=2.
[tex]y=2^2=4[/tex]
The y's got higher as you increased x so the function is increasing.
The function keep increasing for the varying value of x, hence the exponential function is increasing
Given the exponential function f(x) = [tex]b^x[/tex]
We are to check if the function is increasing or decreasing if b is greater than 1
Let b = 2 and x = 1
[tex]f(1) = 2^1\\f(1) = 2[/tex]
Let b = 2 when x = 2
[tex]f(2)=2^2\\f(2)=4[/tex]
Let b = 2 when x = 3
[tex]f(3)=2^3\\f(3)=8[/tex]
You can see that the function keep increasing for the varying value of x, hence the exponential function is increasing
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