The cost of the camera if Sharon paid $78 sales tax at a rate of 6.5% is $1200
What was the cost of the camera?
Amount of sales tax = $78
Sales tax rate = 6.5%
Cost of the camera = x
.
Amount of sales tax = Sales tax rate × Cost of the camera
78 = 6.5% × x
78 = 0.065 × x
78 = 0.065x
Divide both sides by 0.065
x = 78/0.065
x = 1200
Therefore, the camera cost $1200
Let X and Y be the following sets: X={0,12,23} Y={3,12,15} Which of the following is the set X \ Y?
Please can you show working out if possible
Answer:
Step-by-step explanation:
X={0,12,23}
Y={3,12,15}
X \ Y = { 0 , 23}
X/Y means the element should be only in X. We have remove the element in X if it is in Y
In this 0 and 23 is only in X
12 is X and Y. So it wont come in X/Y
The set X \ Y represents the difference of two sets, indicating all the elements that are in set X but not in set Y. For X={0, 12, 23} and Y={3, 12, 15}, the elements that are in X but not in Y are '0' and '23', so X \ Y = {0, 23}.
Explanation:In set theory, the notation X \ Y represents the difference of two sets. This indicates all the elements that are in set X but not in set Y. In this case:
X={0, 12, 23}, Y={3, 12, 15}
So the elements that are in X but not in Y are '0' and '23'.
Therefore, X \ Y = {0, 23}.
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Sharon purchased a used car for $24,600. The car depreciates exponentially by 8% per
much will the car be worth after 5 years? Round your answer to the nearest penny.
Answer:
The value of car after 5 years of exponentially depreciation is $16,213.36
Step-by-step explanation:
The initial amount of the car = i = $24,600
The depreciates rate of interest applied = r = 8%
Let The value of car after n years = A
The number of years = n = 5 years
Now,According to question
The value of car after n years = initial price of car × [tex](1-\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
Or, The value of car after 5 years = i × [tex](1-\dfrac{\textrm r}{100})^{\textrm n}[/tex]
Or, $A = $24,600 × [tex](1-\dfrac{\textrm 8}{100})^{\textrm 5}[/tex]
Or, $A = $24,600 × [tex](0.92)^{5}[/tex]
Or, $A = $24,600 × 0.65908
Or, $A = $16,213.36
So, The value of car after 5 years = A = $16,213.36
Hence , The value of car after 5 years of exponentially depreciation is $16,213.36 . Answer
Find the distance from the point (-6,8) to the line y=-3x+10. Round distance to nearest hundredths.
The distance from the point (-6,8) to the line y=-3x+10 is calculated using the distance formula which yields a value of approximately 6.32, when rounded to the nearest hundredths.
Explanation:The subject of this question is mathematics, specifically it pertains to finding the distance between a point and a line. The distance between a point (x1, y1) and a line ax + by + c = 0 can be calculated using the formula: distance = |ax1 + by1 + c|/sqrt(a²+b²). In your case, the given point is (-6,8) and the line is y = -3x + 10, which can be rewritten as 3x + y - 10 = 0. Therefore, a = 3, b = 1, c = -10, x1 = -6, and y1 = 8.
Substituting these values into the distance formula: distance = |3*(-6) + 1*(8) - 10|/sqrt((3)² + (1)²) = |-18 + 8 - 10|/sqrt(10) = |-20|/sqrt(10) = 20/sqrt(10) = 6.32, rounded to the nearest hundredths.
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What is the area of the shaded triangle?
8mm 10mm 31mm 6mm 24mm
Answer: 96mm²
Step-by-step explanation:
c=31 mm
m=6mm
b=8mm
d=10mm
l=24 mm
-----------------------
c=31 mm
a=24+6=30 mm
b=8mm
A of ΔM=30*8/2=
120 mm²
A of ΔS=b*m/2=8*6/2=24mm²
Area od shaded triangle is=area of ΔM-area ofΔS=120-24=96mm²
identify the vertex for
f(x)=4x^2-8x-4
Answer:
Step-by-step explanation:
You could complete the square to do this, or you could just evaluate the h coordinate using the simple formula
[tex]h=-\frac{b}{2a}[/tex]
then find k by subbing that h value into the equation for x to find y which is the same as k. In our quadratic, a = 4, b = -8, and c = -4.
[tex]h=\frac{-(-8)}{2(4)}=1[/tex]
Now sub that value into the quadratic to find y (k):
[tex]4(1)^2-8(1)-4=4-8-4=-8[/tex]
The vertex of the quadratic is (1, -8)
Trevor Has $178 in his bank account at the start of the week. He makes one withdrawal during the week. At the end of the week, Trevor Gets a notice from the bank that he has a negative balance of -$62. Write and solve an equation to determine how much money Trevor Took out in his withdrawal.
the answer that is correct and shows work gets the crown! good luck and happy new year!
Answer:
Equation: 178 - x = - 62
Explanation:
Start of the wee: 178
One withdrawal: x
End of the week: -62
178 - x = -62
Simplify both sides of equation
178−x=−62
178+−x=−62
−x+178=−62
Subtract 178 from both sides
−x+178−178=−62−178
−x=−240
Divide both sides by -1
-x / -1 = -240 / -1
x=240
Trevor withdrew $240 from his bank account. This was calculated by setting up an equation with his initial positive balance and final negative balance, and solving for the withdrawal amount.
To determine how much money Trevor withdrew from his bank account, we can set up an equation representing the transactions in his account. Let x represent the amount of money withdrawn. We start with Trevor's initial balance, subtract the withdrawal, and set that equal to his final negative balance:
Initial balance - Withdrawal = Final balance
178 - x = -62
To solve for x, we add x to both sides to get the withdrawal amount on its own and then add 62 to both sides to isolate x:
178 - x + x = -62 + x
178 = x - 62
178 + 62 = x
240 = x
So, Trevor withdrew $240 from his bank account.
Three of these expressions give the distance between point A and point B on the number line
Which expression does NOT
A. |7.4-3.5|
B. |7.5+3.5|
C. |- 3.5-7.5|
D. |7.5-(-3.5)|
Answer:
Option A does not give the right expression.
Step-by-step explanation:
On the number line if there are two points P(a) and Q(b) given by coordinates a and b, then the distance between those two points will be given by
d = |a - b| ......... (1)
which is independent of the position of the points.
Therefore, if point A is at - 3.5 and point B is at 7.5, then the distance between point A and point B will be given by |7.5+3.5| or |- 3.5-7.5| or |7.5-(-3.5)|, but not by |7.4-3.5|.
Hence, option A does not give the right expression. (Answer)
Find the midpoint of the line segment whose endpoints are (3,7) and (9,3)
Answer:
The midpoints are ( 6, 5 ).
Step-by-step explanation:
Given that the endpoints are A ( 3, 7) and B (9, 3)-
As we know that-
If a line segment AB is with endpoints ( [tex]x_{1}, y_{1}[/tex] ) and ( [tex]x_{2}, y_{2}[/tex] then the mid points C are-
C = ( [tex]\frac{ x_{1} + x_{2} }{2}[/tex], [tex]\frac{ y_{1} + y_{2} }{2}[/tex] )
Here,
A ( 3, 7 ) and B ( 9, 3 )-
Then the midpoints C are-
C = ( [tex]\frac{ 3 + 9}{2}[/tex], [tex]\frac{ 7 + 3 }{2}[/tex] )
C= ( 12/2 , 10/2 )
C = ( 6, 5 )
Hence the midpoints are (6, 5).
Simplify: -7x+6y - 6x
Answer:
-13x + 6y
Step-by-step explanation:
combine like terms
-7x + 6y - 6x
-7x - 6x = -13x
-13x + 6y
Answer:
Step-by-step explanation:
-7x+6y-6x
Solution:
Put like terms together from left to right; that is the equation will assume a new order from -7x+6y-6x to
-7x-6x+6y
Sum the figures with like terms
= -13x+6y (answer)
Karen bought a hat for $15.62,$15.62, which was 22%22% of her money. How much money did Karen have to start?
1) $71.00
2) $710.00
3) $343.64
4) $140.85
Option 1: $71.00 is the correct answer
Step-by-step explanation:
Let x be the money Karen started with:
Then
22% of x is $15.62
Mathematically writing
[tex]15.62 = 22\%\ of\ x\\15.62 = 0.22 * x\\x = \frac{15.62}{0.22}\\x = 71[/tex]
Hence,
Karen had $71.00 to start.
Option 1: $71.00 is the correct answer
Keywords: Percentage, percent
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PLEASE HELP ASAP!!! WILL MARK BRAINLIEST!!!!
Put a positive factor back into the square root:
[tex]\sqrt[-5]{0.6}[/tex]
Solve for x
(2x-a)/b=(ax+1)/c, if ab ≠ 2c
Answer:
Part 1) [tex]-\sqrt{15}[/tex]
Part 2) [tex]x=\frac{b+ac}{2c-ab}[/tex]
Step-by-step explanation:
Part 1) we know that
To put factor back into the square root, we have to put squared value
we have
[tex]-5\sqrt{0.6}[/tex]
Remember that
[tex]5=\sqrt{5^2}[/tex]
substitute in the expression above
[tex]-5\sqrt{0.6}=-\sqrt{(5^2)(0.6)}=-\sqrt{25*0.6}=-\sqrt{15}[/tex]
Part 2) we have
[tex]\frac{2x-a}{b}=\frac{ax+1}{c}[/tex]
Solve for x
That means----> Isolate the variable x
Multiply in cross
[tex](2x-a)c=(ax+1)b[/tex]
Apply distributive property
[tex]2cx-ac=abx+b[/tex]
Group terms
[tex]2cx-abx=b+ac[/tex]
Factor x left side
[tex]x(2c-ab)=b+ac[/tex]
Divide by (2c-ab) both sides
[tex]x=\frac{b+ac}{2c-ab}[/tex]
the local music activities coordinator sold 300 tickets to the orchestra concert. student tickets were $4 and the adult tickets were $6 if the total sales were $1600 how many student tickets were sold
There were 100 student tickets sold
Step-by-step explanation:
The given is:
The local music activities coordinator sold 300 tickets to the orchestra concertStudent tickets were $4The adult tickets were $6The total sales were $1600We need to find how many student tickets were sold
Assume that the number of student tickets is x and the number of adult tickets is y
∵ The number of student tickets is x
∵ The number of adult tickets is y
∵ They sold 300 tickets
∴ x + y = 300 ⇒ (1)
∵ The price of the student ticket = $4
∵ The price of the adult ticket = $6
∵ The total sales = $1600
- Add the prices of the students tickets and the adult tickets
and equate the sum by the total sales
∴ 4x + 6y = 1600 ⇒ (2)
Now we have a system of equation to solve it
Multiply equation (1) by -6 to eliminate y
∵ -6x - 6y = -1800 ⇒ (3)
- Add equations (2) and (3)
∴ -2x = -200
- Divide both sides by -2
∴ x = 100
There were 100 student tickets sold
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Find the least common denominator for these two rational expressions -4/a^2 and 5/3a
Answer:
3a²
Step-by-step explanation:
least common denominator of a² and 3a
a² = a *a
3a = 3 * a
least common denominator = 3 * a*a =3a²
Answer:
The answer is 3a², where a ≠ 0
Step-by-step explanation:
1. Let's review the information provided to us to answer the question correctly:
Rational expressions are 4/a² and 5/3a
2. Find the least common denominator for these two rational expressions.
Denominators of the expressions are:
a² and 3a ⇒ a² = a * a, 3a = 3 * a
The least common denominator will be:
3a², where a ≠ 0
3a²/a² = 3 and 3a²/3a = a
simplify the expression-
4+ -9r–1
Answer: -9r+3
Step-by-step explanation:
In order to simplify this expression, all you have to do is combine the like terms. However, because there is an addition and a subtraction sign next to each other, we have to multiply them together to find which sign will stay.
Positive x Positive = Positive
Positive x Negative = Negative <---
Negative x Negative = Positive
Because we know that multiplying a negative sign by a positive sign will give us negative, we have to keep the subtraction sign and remove the addition sign. This leaves us with 4-9r-1. All that is left to do is simplify.
Combine the like terms: 4-1 = 3
Answer: -9r+3
Hope this helps!
Answer:
-9r + 3.Step-by-step explanation:
Group Like Terms:
A: -9r + 4 - 1,
Add/Subtract numbers:
A: -9r + 3.If you have any questions feel free to comment below.
Best of Luck to you.
-13(6x-15)+6x>8x-11 Solve.
Answer:
x<103/40
Step-by-step explanation:
-13(6x-15)+6x>8x-11
-78x+195+6x>8x-11
-78x-8x+6x+195>-11
-78x-2x>-11-195
-80x>-206
80x>206
x>206/80
x>103/40
x<103/40
How does the stargate find the x, y, z position to its six alignment points?
Duante's bedroom is a rectangular prism. The area of the floor is 90 square feet, and the height of the bedroom is 12 feet. What is the volume of Duante's bedroom?
The volume of Duante's bedroom is 1080 cubic feet.
Given that, the area of the floor is 90 square feet, and the height of the bedroom is 12 feet.
What is a rectangular prism?A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases. A cuboid is also a rectangular prism. The cross-section of a cuboid and a rectangular prism is the same.
Volume of a rectangular prism = Area of a base × Height.
Here, volume of a rectangular prism = 90 × 12
= 1080 cubic feet
Therefore, the volume of Duante's bedroom is 1080 cubic feet.
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1. Simplify f(g(x)) in terms of x if f(x) = x² - 1 and g(x) = 2 x + 3.
In this question, you're plugging in g(x) into f(x) to simplify.
You would plug the g(x) equation into the x variable in the f(x) equation.
Plug g(x) into f(x):
(2x+3)² - 1
Solve:
(2x+3)² - 1
Use FOIL:
F = First
O = Outsides
I = Insides
L = Last
4x² + 12x + 9 - 1
Combine like terms:
4x² + 12x + 8
Answer:
4x² + 12x + 8
Use Order of Operations. (2/5 x 30) x 6 to the second power - 3 to the second power
Answer:
Step-by-step explanation:
(2/5 * 30) * 6^2 - 3^2 Reduce 2/5 * 30
180 * 6^2 - 3^2 Raise the bases of the power
180 *36 - 9 Multiply 36 and 180
6480 - 9 Subtract 9
6471
If your speed limit was 70 miles a an hour how long will it take you to travel 140 miles with no traffic
It will take you 2 hours since ur going 70 mph divide the 140 mph by 70mph . Hope this helps :)
Which number is NOT a multiple of the number 4?
A. 4
B. 18
C. 40
D. 88
Answer:
b.18
Step-by-step explanation:
18/4=4.5
Answer: The answer would be b, or 18. 4x4.5 is 18, but you are not multiplying it by a whole number. so it CAN'T be B.
Hope this helps!
The line has a slope of -2 and passes through
the point (4, -3).
Answer:
Step-by-step explanation:
Which has the greatest value?
Answer:
f(6)
Step-by-step explanation:
Answer:
f(2)
Step-by-step explanation:
which expression is equivalent to the pic
Answer:
OPTION A: [tex]$ \frac{1}{2^{15}} $[/tex]
Step-by-step explanation:
We should know that:
[tex]$ (a^b)^c = a^{b . c} $[/tex]
So, [tex]$ (2^3)^{-5} = 2^{3 . (-5)}} $[/tex]
[tex]$ = 2^{-15} $[/tex]
This is equivalent to [tex]$ \frac{1}{2^{15}} $[/tex]
Hence, OPTION A is the answer.
Complete the scaling for each number line or set of axes
a)The scale of the number line is 1 unit represents 8 units.
b) On both x and y axes 1 unit represents 4 units.
How to find scale of a graph.
a) The difference between 64 and 32 is
= 64 - 32 = 32
On the number line there are 4 divisions between 32 and 64
Each division = 32/4 = 8
Therefore,the scale of the number line is 1 unit represents 8 units.
b) vertical axis (y axis)
From 0 to 12 there are 3 divisions
Each unit of the division = 12/3 = 4
Therefore, 1 unit represents 4 units on the y axis.
Horizontal axis (x axis)
From 0 to 20, there are five divisions
Each division = 20/5 = 4
Therefore, each 1 unit of division represents 4 unit
Complete question
A set is _____ under an operation (such as addition, etc) if any elements of that set always generate element IN set, when the operation is performed on them help need this answer now
Answer:
Closed.
Step-by-step explanation:
if an=5n-3 find the common difference
Answer:
d = 5
Step-by-step explanation:
The common difference d of an arithmetic sequence is
d = a₂ - a₁ = a₃ - a₂ = [tex]a_{n}[/tex] - [tex]a_{n-1}[/tex]
Given
[tex]a_{n}[/tex] = 5n - 3
Generate the first 2 terms of the sequence by substituting n = 1, n = 2
a₁ = 5(1) - 3 = 5 - 3 = 2
a₂ = 5(2) - 3 = 10 - 3 = 7
d = 7 - 2 = 5
There are 4 red and 6 green marbles in a jar. What is the probability of drawing two green marbles, with replacement?
2/5
9/25
3/5
4/25
SELECT EACH CORRECT ANSWER
The probability of drawing two green marbles, with replacement is [tex]\frac{9}{25}[/tex]
Solution:Given that There are 4 red and 6 green marbles in a jar
To find: probability of drawing two green marbles, with replacement
The probability of an event is given as:
[tex]\text {probability }=\frac{\text { number of favourable outcomes }}{\text { total number of possible outcomes }}[/tex]
Here total number of possible outcomes = 4 red + 6 green marbles = 10
Favourable outcome is drawing two green marbles with replacement
So favourable outcome = 6
So probabilty of choosing green marble:
[tex]probability = \frac{6}{10} = \frac{3}{5}[/tex]
Now given that with replacement, so we get
[tex]\text { probability }=\frac{3}{5} \times \frac{3}{5}=\frac{9}{25}[/tex]
Thus probability is [tex]\frac{9}{25}[/tex]
Find the slope that passes through (3,1) and (5,8)
Answer:
[tex]\large\boxed{slope=\dfrac{7}{2}=3.5}[/tex]
Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have two points (3, 1) and (5, 8).
Substitute:
[tex]m=\dfrac{8-1}{5-3}=\dfrac{7}{2}[/tex]
Answer:
[tex]\boxed{\bold{Slope \ \frac{7}{2} \ = \ 3.5 }}[/tex]
Explanation:
Slope Intercept Form: y = mx + b
Slope Formula: [tex]\bold{\frac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\bold{\left(x_1,\:y_1\right)=\left(3,\:1\right),\:\left(x_2,\:y_2\right)=\left(5,\:8\right)}[/tex]
[tex]\bold{m=\frac{8-1}{5-3}}[/tex]
[tex]\bold{m=\frac{7}{2}}[/tex]
[tex]\bold{Slope \ in \ fraction \ form: \frac{7}{2} }[/tex]
[tex]\bold{Slope \ in \ decimal \ form: \ 3.5}[/tex]
An advertisement for the state fair will be painted on one of four silos along the highway into town. The silos are in the shape of cylinders. Only the lateral area of the silo will be painted, not the top and bottom. If it costs $1.20 per square foot to paint the sides of the silo, which silo will cost the least to paint?
Recall the formula LA=2 pi rh.
A. Silo A
B. Silo B
C. Silo C
D. Silo D
===============================================
How I got that answer:
r = radius
h = height
LA = lateral surface area of cylinder
LA = 2*pi*r*h
Let's find the lateral surface area of each silo. The smallest lateral surface area will lead to the lowest total cost.
-------------
Silo A
LA = 2*pi*r*h
LA = 2*pi*6*60
LA = 720pi
-------------
Silo B
LA = 2*pi*r*h
LA = 2*pi*8*50
LA = 800pi
-------------
Silo C
LA = 2*pi*r*h
LA = 2*pi*10*34
LA = 680pi
-------------
Silo D
LA = 2*pi*r*h
LA = 2*pi*12*20
LA = 480pi
-------------
If we ignore the "pi" terms for each of the four answers above, we see that 480 is the smallest value. Silo D has the smallest lateral surface area at 480pi square feet.
-------------
Side note: to determine the total cost, you multiply the surface area by the cost per square foot ($1.20)
For example, the total cost to paint silo D is
cost = (surface area)*(price per square foot)
cost = (480*pi)*(1.20)
cost = 1809.557
cost = 1809.56
This section is optional as your teacher isnt requiring you to find the actual costs, but rather just the silo with the least amount of area. You could go the longer route to find each surface area, compute the total cost, and then compare the total costs. You should find that silo D's cost is the lowest.