A new car is purchased for 22300 dollars. The value of the car depreciates at 10.25% per year. What will the value of the car be, to the nearest cent, after 6 years?
Answer : The value of car will be, $11654.98
Step-by-step explanation:
Given,
Principle = $22300
Time = 6 years
Rate of depreciation = 10.25 %
Formula used :
[tex]A=P(1-\frac{R}{100})^t[/tex]
where,
A = amount
P = principle
R = rate of depreciation
T = time
Now put all the given values in the above formula, we get:
[tex]A=P(1-\frac{R}{100})^t[/tex]
[tex]A=\$ 22300(1-\frac{10.25}{100})^{6}[/tex]
[tex]A=\$ 11654.98[/tex]
Therefore, the value of car will be, $11654.98
if f(x)=x^2-x and g(x)=x+1, determine f (g(x)) in simplest from
Answer:
f(g(x)) = x^2 +x
Step-by-step explanation:
To find f(g)(x) , we substitute g(x) in for x in the function f(x)
f(x) = x^2 -x
f(g(x)) = g(x)^2 -g(x)
= (x+1)^2 - (x+1)
= (x+1)*(x+1) - (x+1)
FOIL the square
(x+1) (x+1)
First x*x = x^2
outer x*1 = x
inner 1*x = x
last 1*1 =1
Add them together
x^2 + x+x+1 = x^2+2x+1
f(g(x)) = (x+1)*(x+1) - (x+1)
= x^2+2x+1 -(x+1)
Distribute the -1
= x^2 +2x+1 -x-1
= x^2 +x
f(g(x)) is basically replacing the x with g(x).
So, f(x)=(g(x))^2 - g(x)
g(x), in turn, equals x+1
Replace g(x) with x+1
(x+1)^2 - (x+1)
Expand: x^2+x+x+1 - x - 1
Cancel out x and 1
f(g(x))=x^2+x
If you require factoring it's
f(g(x))=x(x+1)
A basket is filled with 7 white eggs and 14 brown eggs. Half of the brown eggs are cracked.
An egg is randomly selected from the basket. What is the probability that it is a cracked, brown egg?
Write your answer as a fraction.
. Sarah drove 77 miles on 3.6 gallons of gas. If her car holds 15 gallons of gas, which proportion would she use to find out how far she can drive her car on a full tank of gas? a. 3.6/15 = x/77 c. 3.6/77 = x/15 b. 77/x = 15/3.6 d. 77/3.6 = x/15
Final answer:
To find out how far Sarah can drive on a full tank of gas, the correct proportion is '77/3.6 = x/15'. This compares the known miles driven to gallons used, scaled up to a full tank of 15 gallons, representing the distance with 'x'. So the correct option is d.
Explanation:
The student is working on solving a proportion problem related to fuel consumption and driving distances. To find out how far Sarah can drive her car on a full tank of gas, we need to set up a proportion that compares miles driven to gallons used, and then scale it up to a full tank of gas.
Since Sarah drove 77 miles on 3.6 gallons of gas, we can compare this to a full tank of 15 gallons to find the total distance she can drive, represented by 'x'. The correct proportion is 77 miles to 3.6 gallons as 'x miles' is to 15 gallons.
The correct proportion is d. 77/3.6 = x/15, as it reflects the direct relationship between miles driven and gallons of fuel. When the gallons are increased from 3.6 to 15, we expect the miles that can be driven to increase proportionally.
2x+y=3 passes from origin. is this statement true or false
Answer:
the answer is false.
Step-by-step explanation:
Answer:
False
Step-by-step explanation:
2x+y=3
⇒ This equation can be written in the form of y = mx + c where m is the slope, c is the y-intercept and x and y are x and y coordinates respectively of the point where the the line passes.
2x+y=3
y = -2x + 3.
If the line passes through the origin (0,0), then c = 0. This is not the case in our eqation.
Again if the question passes through the origin, by substituting the point (0,0) in the question it would satify it.
2x+y=3 ⇒ 2(0) + 0 = 3
0 + 0 ≠ 3
0 ≠ 3
The statement is false.
The lowest temperature ever recorded is -89c. The highest temperature is 56.7c. What is the difference between the highest and the lowest recorded temperature
Answer:
The difference is 145.7
Step-by-step explanation:
89+56.7= 145.7
Answer:
-32.3
Step-by-step explanation:
I got -32.3 because when I subtracted -89 from 56.7 I got -32.3. If you don't know how to subtract integers it's simple, you just subtract 89 from 56.7 then choose the sign that has the greater absolute value. In this case -89 has the greater absolute value, so you take the negative sign.
Find the unit rate to the nearest cent per ounce.
A 24-ounce box of cornflakes costs $4.59
Answer:
0.19125
Step-by-step explanation:
You divided 4.59 by the amount 24-oz
What is the definition of a parallelogram? What are the properties?
Answer:
A parallelogram is a quadrilateral whose opposite sides are parallel.
It's properties include:
- The opposite sides of a parallelogram are parallel.
- A diagonal of a parallelogram divides it into two congruent triangles.
- The opposite sides of a parallelogram are congruent.
- The opposite angles of a parallelogram are congruent.
- The consecutive angles of a parallelogram are supplementary.
- The diagonals of a parallelogram bisect each other.
a quadrilateral whose both pair of opposite side are equal and parallel to each other is called a parallelogram
PROPERTIES OF PARALLELOGRAM opposite sides are equal and parallel opposite angles are equal adjacent angle are supplementary diagonal of a parallelogram bisect each other[tex]AREA OF PARALLELOGRAM => BASE X HEIGHT = BXH [/tex]
any side of parallelogram can be chosen as the base of parallelogram the perpendicular dropped on that side from opposite vertex is known as height attitude
guys I need help.....
Answer:
.224 / 7 = .032
Step-by-step explanation:
.224 / 7
7 goes into 2 0 times with 2 left over
7 goes into 22 3 times with 1 left over
7 goes into 14 2 times with 0 left over
.224 / 7 = .032
Answer:
.032
Step-by-step explanation:
whats is the ratio of 3 dogs to 4 cats
Answer:
3 to 4
or
3:4
Step-by-step explanation:
Joy wants to buy strawberries and raspberries to bring to a party strawberries cost $1.60 per pound and raspberries cost $1 .75 per pound. if she only has $10 to spend on berries which equality represents the situation where she buys x pounds of strawberries and y pounds of raspberries ?
Answer: 1.60x + 1.75y is less than or equal to 10
Step-by-step explanation:
Since the strawberries cost $1.60 per pound, it would be x pounds times $1.60 for the total cost of strawberries. Since the raspberries cost $1.75 per pound, it would be y pounds times $1.75 for the total cost of the raspberries. The total cost of both, or 1.60x + 1.75y, must be equal to or less than 10 because she cannot spend over 10 dollars.
The situation can be represented by the equation 1.60x + 1.75y = 10, where x represents the pounds of strawberries and y represents the pounds of raspberries. To find out how many pounds of strawberries and raspberries Joy can buy, we can rearrange the equation and solve for x and y.
Explanation:The situation can be represented by the equation 1.60x + 1.75y = 10, where x represents the pounds of strawberries and y represents the pounds of raspberries. To find out how many pounds of strawberries Joy can buy, we can rearrange the equation to solve for x: x = (10 - 1.75y) / 1.60. Similarly, to find out how many pounds of raspberries Joy can buy, we can rearrange the equation to solve for y: y = (10 - 1.60x) / 1.75.
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The five fifth grade teachers ans six fourth grade teachers ordered 2 large pizzas all together. Each pizza costs $13.75. If they are going to spilt the cost evenly, how much will each person need to pay?
Answer:
80 Cents
Step-by-step explanation:
Answer: Each person will need to pay $1.25
Step-by-step explanation: $13.75 divided by the 11 people = $2.25
Perhaps brainliest?
what is the sum of 121/4+5 5/6 reduced to lowest terms thanks
Answer:18 1/12
Step-by-step explanation:i first added the whole numbers 12 and 5 to get 17; i then addled 1/4 and 5/6; i did this by finding a common denominator of both fractions and converted them into 6/24 and 20/24; i added them to get 26/24 which simplifies to 1 and 2/24, which equals 1 1/12; i added 1 to 17 and got 18, then added 1/12 to get 18 1/12
The sum of 121/4 and 5 5/6 is found by converting the mixed number to an improper fraction, finding a common denominator, adding the fractions, and simplifying if possible. The final answer is 433/12, which is already in its lowest terms.
The question asks for the sum of the numbers 121/4 and 5 5/6 reduced to the lowest terms. To answer this, we must first convert the mixed number to an improper fraction and then add it to the other fraction. Here's how to do it step by step:
Convert 5 5/6 to an improper fraction: 35/6.
Add 121/4 to 35/6. To do this, find a common denominator, which would be 12 in this case.
Convert both fractions to have the common denominator: 121/4 becomes 363/12, and 35/6 becomes 70/12.
Add the two fractions: 363/12 + 70/12 equals 433/12.
Reduce the fraction if possible. In this case, 433/12 is already in its lowest terms.
Therefore, the sum of 121/4 and 5 5/6 reduced to lowest terms is 433/12.
Is this a true proportion ? 3/4,8/12
Question
Is this a true proportion ? 3/4,8/12
Answer:
FalseStep-by-step explanation:
3/4 = 8/12
semplify
3/4 = 2/3
or you can solve in this way
3/4 = 8/12
0.75 = 0.66≈
If f(x) = x2 -1, what is the equation for f–1(x)?
Answer:
[tex]f^{-1}=+-\sqrt{x+1}[/tex]
Step-by-step explanation:
f(x) = x^2 -1
We need to find f^-1(x)
WE find inverse of f(x)
Replace f(x) with y
[tex]y= x^2 -1[/tex]
Replace x with y and y with x
[tex]x= y^2 -1[/tex]
Solve for y
add 1 on both sides , [tex]x+1= y^2[/tex]
To remove square , take square root on both sides
[tex]\sqrt{x+1} =\sqrt{y^2}[/tex]
[tex]\sqrt{x+1} =y[/tex]
[tex]y=+-\sqrt{x+1}[/tex]
Replace y with f^-1
[tex]f^{-1}=+-\sqrt{x+1}[/tex]
Answer:
Inverse function is
[tex]f^{-1}(x)=\pm \sqrt{x+1}[/tex]
Step-by-step explanation:
Given that [tex]f(x)=x^2-1[/tex]
Now using that equation of f(x), we need to find equation of the inverse function
[tex]f(x)=x^2-1[/tex]
[tex]f^{-1}(x)[/tex]
Step 1: Replace [tex]f^{-1}(x)[/tex] with y
[tex]y=x^2-1[/tex]
Step 2: Switchx and y
[tex]x=y^2-1[/tex]
Step 3: Solve for y
[tex]x=y^2-1[/tex]
[tex]x+1=y^2-1+1[/tex]
[tex]x+1=y^2[/tex]
[tex]y^2=x+1[/tex]
take square root of both sides
[tex]y=\pm \sqrt{x+1}[/tex]
Hence inverse function is
[tex]f^{-1}(x)=\pm \sqrt{x+1}[/tex]
A line with a slope of 4 passes through the point 2,1 what is the equation y=mx+b
The point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
We have the slope m = 4 and the point (2, 1). Substitute:
[tex]y-1=4(x-2)[/tex] use distributive property
[tex]y-1=(4)(x)+(4)(-2)[/tex]
[tex]y-1=4x-8[/tex] add 1 to both sides
[tex]\boxed{y=4x-7}[/tex]
You are the new warehouse manager and you have a facility that has 25 storage racks that are 25 feet long, 12 feet high and 3 feet wide. The boxes that you need to store are 15x8x10 inches and there are 5000 of the boxes. Do you have enough storage space?
Answer is shown in the attached image, in RED.
solve the inequality -8x-10>7x+20
Answer:
-2 > x
Step-by-step explanation:
-8x-10>7x+20
Add 8x to each side
-8x+8x-10>7x+8x+20
-10 > 15x+20
Subtract 20 from each side
-10 -20 > 15x+20-20
-30 > 15x
Divide by 15
-30/15 > 15x/15
-2 > x
As the figure shows Elton runs 500 m to point b first then he turns 100 degrees and runs another 350 m to point c how far is the distance from point a to c
Answer:
658.24 m
Step-by-step explanation:
Let A be the point from where Elton started. Connect points A and C, you get triangle ABC with AB=500 m, BC=350 m and m∠B=100°. Use the cosine rule to determine the length of the segment AC:
[tex]AC^2=AB^2+BC^2-2\cdot AB\cdot BC\cdot \cos \angle B,\\ \\AC^2=500^2+350^2-2\cdot 500\cdot 350\cdot \cos 100^{\circ},\\ \\AC^2=250000+122500-350000\cdot (-0.174),\\ \\AC^2\approx 433276.8622,\\ \\ AC\approx 658.24\ m.[/tex]
Answer:
658.24 m
Step-by-step explanation:
The figure makes a triangle with vertices abc.
Where ab = 500 m
bc = 350 m
The angle abc = 100°
Using the cosine rule we can find the distance ac.
ac² = 500²+350² - 2×500×350×cos100°
= 372,500 - -60,776.86
= 433,276.86
ac = √433,276.86
= 658.24 m
University Theater sold 465 tickets for a play. Tickets cost $23 per adult and $13 per senior citizen. If total receipts were $7145, how many senior citizen tickets were sold?
Answer:
355 senior citizen tickets were sold.
Step-by-step explanation:
Assuming a to the the ticket of adults and s to be the ticket of senior citizens, we can write two equations as:
[tex]a +s=465[/tex] --- (1)
[tex]23a+13s=7145[/tex] --- (2)
From equation 1, [tex]a=465-s[/tex].
Substitute [tex]a[/tex] in equation 2 to get:
[tex]23 (465-s) + 13s = 7145[/tex]
[tex]10695 - 23s +13s =7145[/tex]
[tex]-10s = -3550[/tex]
[tex]s = 355[/tex]
Therefore, there were 355 senior citizen tickets sold.
What is the value of (-3+3i)+(-2+3i)?
Answer:
The value is of given expression is -5+6i.
Step-by-step explanation:
The given expression is
[tex](-3+3i)+(-2+3i)[/tex]
It can be written as
[tex]-3+3i-2+3i[/tex]
Now combine like terms.
[tex](-3-2)+(3i+3i)[/tex]
[tex](-3-2)+(3+3)i[/tex]
Simplify each parenthesis.
[tex](-5)+(6i)[/tex]
[tex]-5+6i[/tex]
Therefore the value is of given expression is -5+6i.
which order pairs are solutions of the inequality -7y +2x ≤ 3
A (0,0)
B (1,1)
C (-3,5)
Answer: A & B
Step-by-step explanation:
-7y + 2x ≤ 3
(0, 0): -7(0) + 2(0) ≤ 3
0 + 0 ≤ 3
0 < 3 TRUE
(1, 1): -7(1) + 2(1) ≤ 3
-7 + 2 ≤ 3
-5 < 3 TRUE
(-3, 5): -7(-3) + 2(5) ≤ 3
21 + 10 ≤ 3
31 < 3 FALSE
solve
4x+6<-6
I could really use the help
Answer:
x < -3
Step-by-step explanation:
First subtract 6 from both sides of the inequality.
[tex]4x+6-6<-6-6[/tex]
[tex]4x<-12[/tex]
Divide 4 on both sides.
[tex]\frac{4x}{4} < \frac{-12}{4}[/tex]
[tex]x<-3[/tex]
Write the equation of the line with a slope of 17 and passing through the point (0,0)
Answer: y = 17x
Step-by-step explanation:
Note that the equation that will be used is: y = mx + b,in which m = slope and b = y-intercept.
Solve for b:
0 = 17(0) + b
Simplify:
0 = 0 + b
b = 0
Equation: y = 17(x)
~
ABOUT POINT SLOPE FORM:
y - Y1 = m (x - X1)m is the slopeY1 & X1 is a point on the lineThe form allows you to identify the slope & the point on the lineABOUT PROBLEM:
Since the slope is 17, it represents m in Poin Slope Form0 represents Y10 represents X1y - Y1 = m (x - X1)
y - 0 = 17 (x - 0) --- IN POINT SLOPE FORM
Hope this helps you!!! :)
do diagonals of a rhombus bisect the vertex angles???
Answer:
Yes, one of a rhombus's properties is that the diagonals bisect vertex angles.
The diagonals of a rhombus bisect the vertex angles.
Explanation:Yes, the diagonals of a rhombus bisect the vertex angles.
To understand this, we can consider that in a rhombus, the diagonals are perpendicular to each other, and when a diagonal bisects an angle, it creates two congruent triangles.
Therefore, the diagonals of a rhombus do indeed bisect the vertex angles.
What is the largest fraction 3/4 7/8 8/10 7/9?
Answer:
7/8 ths
Step-by-step explanation:
3 divided by 4 is .75
* 7 divided by 8 is .875
8 divided by 10 is .80
7 divided by 9 is .77
If you divide the fractions you can compare the values and the highest value is your largest fraction.
The fraction with largest value of numerator is largest fraction in the two or more fraction number with same denominator. The fraction 7/9 has the largest fraction.
Given information-
The set of the fraction given in the problem is,
[tex]\dfrac{3}{4}, \dfrac{7}{8}, \dfrac{8}{10}, \dfrac{7}{9}[/tex]
What is the order of fraction?The order of the fraction is arranging the fraction number from the smallest to the largest number.
The fraction with largest value of numerator is largest fraction in the two or more fraction number with same denominator.
To compare the fraction, make the denominator with same.
[tex]\dfrac{3}{4}, \dfrac{7}{8}, \dfrac{8}{10}, \dfrac{7}{9}[/tex]
To make the denominator same find out the least common factor of denominators which are 4,8,10 and 9 which is 360.
Multiply and divide with 360 in the given fractions to bring the 360 in denominator,
[tex]\dfrac{3\times360}{4\times360}, \dfrac{7\times360}{8\times360}, \dfrac{8\times360}{10\times360}, \dfrac{7\times360}{9\times360}[/tex]
[tex]\dfrac{270}{360}, \dfrac{315}{360}, \dfrac{288}{360}, \dfrac{315}{360}[/tex]
As the numerator 315 is the highest among all. Hence the fraction 7/9 has the largest fraction.
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These dot plox show the lenghs (in feet) from a sample of crocodiles and allogators
Answer:
C and D
Step-by-step explanation:
The Middles were the same length and the side of the alligator are slightly longer.
The correct options are:
C. Center-- The crocodiles have a greater median length than the alligators.
D. Spreads-- The lengths of the alligators are more spread out.
Step-by-step explanation:Median of the data--
The median is the central tendency of the data and it always exist in the middle of the data.
By looking at the data.
We observe that the Median of the data :
Crocodile lie at : 17
and that of the alligator lie at : 9
Hence, the median for the crocodile is more than for the alligators.
Spread--
The spread in the data means how far the data points are from the center of the data i.e. mean or median.
By looking at the data crocodile we observe that all the data points are close to the median.
whereas in the data alligator one of the data point is far from the median.
Hence, the spread in case of alligator is more as compared to that of crocodiles.
Solve, using the substitution method.
y = 2x + 6
3x – y = 6
There are an infinite number of solutions.
(12, 30)
(14, 12)
There is no solution.
The solution to the system of equations is (12, 30).
Option B is the correct answer.
What is a solution?Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.
We also find the solution in a system of equations using the substitution or elimination method.
Example:
2x + 4 = 8
The solution is x = 2.
We have,
To solve the system of equations using the substitution method,
We solve one equation for one of the variables and substitute the expression into the other equation.
Let's solve the first equation for y:
y = 2x + 6
Now, substitute y = 2x + 6 into the second equation and solve for x:
3x - y = 6
3x - (2x + 6) = 6
3x - 2x - 6 = 6
x = 12
Now that we have found x, we can substitute it back into either of the original equations to find y.
Let's use the first equation:
y = 2x + 6
y = 2(12) + 6
y = 30
Therefore,
The solution to the system of equations is (12, 30).
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Alexandria wants to go hiking on Saturday. She will choose from several parks considering these conditions:
• She wants to hike for 2 hours.
• She wants to spend no more than 6 hours away from home.
• She can average 65 miles per hour to and from the park.
Choose and solve the inequality that represents the possible distances from Alexandria’s home to a park that satisfies the conditions above.
Answer:
The correct answer for this problem is 200 miles.
Stephen Had $1200. He spent 40% of it. How much money did he spend?
[tex]p\%=\dfrac{p}{100}\\\\40\%=\dfrac{40}{100}=\dfrac{4}{10}=0.4\\\\40\%\ of\ \$1200\ is\ 0.4\cdot\$1200=\$480\\\\Answer:\ \text{He spend}\ \$480.[/tex]
Final answer:
To determine the amount Stephen spent from his $1200 at 40%, the percentage is converted to a decimal (0.40) and multiplied by $1200, resulting in $480 spent.
Explanation:
Stephen had $1200. To calculate the amount of money he spent after using 40% of his money, we need to find 40% of $1200. We can write this as 0.40 × $1200.
Step 1: Convert the percentage into a decimal: 40% = 0.40
Step 2: Multiply the decimal by the total amount of money Stephen had: 0.40 × $1200 = $480.
Hence, Stephen spent $480 out of his $1200.