The number of outfits that Gianna can buy given her budget is 8.
How many outfits can she buy?The first step is to determine the total cost of the items bought so far
Total cost = price of the bicycle + cost of the bicycle reflectors + cost of the bike gloves
Cost of the bicycle reflectors = cost of one reflector x 2
Cost of the bicycle reflectors = $10.01 x 2 = $20.02
Total cost = $20.02 + $356.46 + $20.72 = $397.20
Amount that is left to buy the outfits = amount Gianna has - total cost
$760 - $397.20 = $362.80
Number of outfits she can buy = amount left / cost of one outfit
Number of outfits she can buy = $362.80 / $45.35
Number of outfits she can buy = 8
Here is the complete question:
Gianna has $760 to spend at a bicycle store for some new gear and biking outfits. assume all prices listed include tax. she buys a new bicycle for $356.46. she buys 2 bicycle reflectors for $10.01 each and a pair of bike gloves for $20.72. she plans to spend some of all of the money she has left to buy new biking outfits for $45.35 each. How many outfits can she buy ?
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log((4x)/(8))=log(x-5)
The given logarithmic equation solved for x is x = 10
Solving Logarithmic equationsFrom the question, we are to solve the given logarithmic equation.
The given logarithmic equation is
log((4x)/(8)) = log(x - 5)
To solve the given logarithmic equation, we will determine the value of the unknown variable.
The unknown variable in the equation is x.
From one of the rules of logarithm, we have that
If logₓY = logₓZ
Then,
Y = Z
Thus,
From log((4x)/(8)) = log(x - 5)
We can write that
(4x)/(8) = (x - 5)
Now, solve for x
(4x)/(8) = (x - 5)
Multiply both sides by 8
8 × (4x)/(8) = (x - 5) × 8
4x = 8x - 40
Subtract 8x from both sides of the equation
4x - 8x = 8x - 8x - 40
-4x = -40
Multiply both sides by -1
-1 × -4x = -1 × -40
4x =40
Divide both sides by 4
4x/4 = 40/4
x = 10
Hence, the solution of the equation is x = 10
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what are the factors of 28?
Answer:
1, 2, 4, 7, 14 and 28
Step-by-step explanation:
1 x 28 = 28
2 x 14 = 28
4 x 7 = 28
Answer:
1, 2, 4, 7, 14 and 28
Step-by-step explanation:
Someone please help me out on this ( this is due tonight )
Answer the 2 question in the photo!
Answer:
1. 190 degrees
2.
For the red triangle
-2,4, -4,2 -2,1
For the blue triangle
-2,-5 -5,-5 -7,-4
I don't know if this is correct but I hope this helps :)
i need help with my math work
Answer: I believe y=1x+0 (or y=x)
Step-by-step explanation: if you copy the slope and make the line go through (2,2), you get this line.
3³× (3⁴} ⁰.⁵ simplified
Thank you
Step-by-step explanation:
so, it is
3³ × (3⁴)^(0.5) ?
remember, when multiplying exponents of the same base, we add the exponents : e.g.
a⁵ × a³ = a⁸
when we have exponents in exponents we multiply the exponents : e.g.
(a³)⁴ = a¹²
now, also remember the priorities of mathematical operations :
1. brackets
2. exponents
3. multiplications and divisions
4. additions and subtractions
now, let's look at our expression again :
3³ × (3⁴)^(0.5)
since we only want to simplify and not to calculate, we leave (3⁴) alone, because the only thing we could do would be to actually calculate 3⁴.
so,
(3⁴)^(0.5) = 3^(4×0.5) = 3²
and then,
3³ × 3² = 3^(3+2) = 3⁵
so, the simplified expression is 3⁵.
which is 243 ...
Find the amount (future value) of ordinary annuity $1000 a year for 10 years at 10%/year compounded annually.
a.
$15,500
b.
$15,937
c.
$16,456
d.
$16,845
The future value of ordinary annuity $1000 a year for 10 years at 10% year compounded annually is $15937.
The value of a sum of money that will be paid on a specified date in the future is known as its future value. Since each payment is made at the end of a period, the formula for the future value of an ordinary annuity refers to the value on a specified future date of a series of periodic payments.
Given,
R=$1000, n=10, i=10%=10/100=0.1
The formula to calculate the future value is
FV=R[(1+i)^n-1]/i
[tex]FV=R(\frac{(1+i)^{n} -1}{i})[/tex]
[tex]FV=1000(\frac{(1+0.1)^{10} -1}{0.1})[/tex]
[tex]FV=1000(\frac{(1.1)^{10} -1}{0.1})[/tex]
[tex]FV=1000(\frac{1.593742}{0.1})[/tex]
[tex]FV=1000\times15.9374[/tex]
[tex]FV=15937.4[/tex]
Future Value approximately equal to $15937.
Therefore, the future value of the ordinary annuity $100 a year for 10 years at 10% compounded annually is $15937, Option c is the correct answer.
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Multiply. 3√2 ⋅ 2√8 ⋅ 3√. 6√ Enter your answer, in simplest radical form, in the box.
Answer:
the answer i think it is 432
Actual Unemployment Rate = 8%
Natural Unemployment Rate = 5%
What is the Cyclical Unemployment rate?
The Cyclical Unemployment rate is 3%.
What is unemployment?Unemployment simply means a scenario where those who are willing and able to work can't find suitable jobs.
Actual Unemployment Rate = 8%
Natural Unemployment Rate = 5%
The Actual Unemployment rate will be:
= Cyclical Unemployment Rate + Natural Unemployment Rate
8% = 5% + C
C = 8% - 5%
C = 3%
C = Cyclical Unemployment rate
The unemployment is 3%.
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A new car is purchased for 27,100 dollars. The value of the car depreciates at a rate of 7% per year. Which equation represents the value of the car after 6 years?
In exponential relations, we can represents given values like this:
[tex]f(x)=a*c^x[/tex]
c = growth/decay factora = starting point/y-interceptSolving the QuestionWe're given:
27,100 dollars = starting pointDecay factor = 7% per year⇒ Plug this information into [tex]f(x)=a*c^x[/tex]:
[tex]f(x)=27,100*(0.93)^x[/tex]
Why input 0.93 and not 0.07? Let's think of it this way: To calculate the new price of the car after one year, we find 93% of 27,100.
The dependent variable is the price (y) and the independent variable is the time in years (x).
f(x) = pricex = timeTherefore, to find the value of the car after 6 years, we plug in 6 as x:
[tex]f(x)=27,100*(0.93)^6[/tex]
Answer[tex]V=27,100*(0.93)^6[/tex]
Convert to vertex form. State the vertex. f(x)=-3x^2+12x-7
The vertex form of the quadratic equation is f(x) = -3(x - 2)² + 5. The coordinates of the vertex are (2, 5).
We are given a quadratic function. The equation of the quadratic function is f(x) = -3x² + 12x - 7. We need to convert the equation to vertex form. We can convert a quadratic equation to its standard vertex form by "completing the square" method. The calculations are done below.
f(x) = -3x² + 12x - 7
f(x) = -3(x² - 4x) - 7
f(x) = -3(x² - 4x + 2² - 2²) - 7
f(x) = -3(x² - 4x + 2²) - 7 + 3*2²
f(x) = -3(x - 2)² - 7 + 12
f(x) = -3(x - 2)² + 5
The coordinates of the vertex are (2, 5).
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change this root into a power
Answer:
I think it would be 12^1/4
Step-by-step explanation:
I hope this is what you were asking for :)
11. Choose the correct answer.
Which theorem or postulate could be used to prove the congruence of the triangles
Find the quotient 2 divided by 3/7
[tex]2\div \cfrac{3}{7}\implies \cfrac{2}{1}\div \cfrac{3}{7}\implies \cfrac{2}{1}\cdot \cfrac{7}{3}\implies \cfrac{14}{3}\implies 4\frac{2}{3}[/tex]
The quotient for the expression is 4.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
2 ÷ [tex]\frac{3}{7}[/tex]
= 2 / (3/7)
= (2 x 7) / 3
= 14/3
Now,
3 ) 14 ( 4
12
2
Remainder = 2
Quotient = 4
Thus,
The quotient is 4.
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PLSS HELP find x, y and z
The values of x, y and z in the angles are as follows
x = 30 degreesy = 15z = 150 degreesHow to find the angles on parallel line cut by a transversal?When parallel lines are cut by a transversal line, angle relationship are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles.
The parallel lines forms angles relationships.
Therefore,
x = 2y (alternate angles)
z = 2x + 90 (alternate angles)
Using substitution,
z = 2(2y) + 90
z = 4y + 90
x + 2x + 90 = 180 (sum of angles on a straight line)
3x = 180 - 90
3x = 90
x = 90 / 3
x = 30°
Hence,
30 = 2(y)
y = 30 / 2
y = 15
z = 4(15)+ 90
z = 60 + 90
z = 150°
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The perimeter of a rectangle i 202020 centimeter. The length i 666 centimeter. What i the area of the rectangle?
quare centimeter
The area of the rectangle is, 24 square centimeter.
What is area?
Area is a mathematical concept that expresses the size of a region on a planar or curved surface. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
Let, the perimeter of the rectangle is 20 centimeter.
The length is 6 centimeter.
Suppose the width of the rectangle is y.
So,
Perimeter = 2(6) + 2(y)
20 = 12 + 2y
8 = 2y
y = 4
Hence, the width of the rectangle is 4 centimeter.
Since,
Area of rectangle = length x width
A = 6 x 4
A = 24
Therefore, the area of the rectangle is, 24 square centimeter.
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Grace and her dad are planning to attend the state fair. An adult ticket is $15. The price of an adult ticket is one half the price of a student ticket plus $8. Write an equation to determine how much grace will pay for a student ticket.
1/2 x + 8 = 15 Grace will pay for a student ticket
the question requests the cost of a "student ticket." Because we don't know, let's assume the student ticket price is "x" dollars.
Because we know from the question that "the price of an adult ticket is half the price of a student ticket plus $8.00," we can represent the adult ticket price as follows:
1/2 x + 8
If we also get "An adult ticket costs $15.00" from the question, we can write the equation as:
1/2 x + 8 = 15
Grace will pay for a student ticket
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Emma recorded the weight of her kitten in ounces on certain days for 24 days. The data are shown in the scatter plot
Answer:
what are the instructions
Step-by-step explanation:
please repost with instructions
what are the two related linear equations for |x – 2| = 5.
The two related linear equations for |x – 2| = 5 are x - 2 = 5 and x - 2 = -5
How to determine the related equations?From the question, we have the equation to be
|x - 2| = 5
This equation is an absolute value function
The general rule of an absolute value function is that:
An equation represented as y = |x| can be expressed as y = x or y = -x
Using the above guideline as a guide, we have the following representation of |x – 2| = 5
x - 2 = 5 and x - 2 = -5
Hence, the equations are x - 2 = 5 and x - 2 = -5
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These marbles are placed in a bag and two
of them are randomly drawn.
What is the probability of drawing two
yellow marbles if the first one is placed back
in the bag before the second draw?
Give your answer as a ratio, reduced to
simplest terms.
?
Hint: Multiply the probability of the 1st Event by the
probability of the 2nd Event to get your answer
Answer:
There are 10 marbles, 2 are yellow
The probability would be 2:10 but in simplest form 1:5
The probability of picking both the same = 1:5 x 1:5 = 1:25
Step-by-step explanation:
I need Help pleaseeeeeeeeeeeeeeee
Answer:
D
Step-by-step explanation:
500 user in a day that mean in 2 days you get 1000 user cause the double of 500 is 1000
9 A rectangle and a square have the same area. The length
of the rectangle is 70 feet more than two times its width. The
length of a side of the square is 30 feet. Set up an equation to
find the dimensions of the rectangle. What are the dimensions
of the rectangle? Include units of measurement.
Answer:
Step-by-step explanation: If the square is 30 ft on one side the other side must be too. So 30x30 = 900. Now, we know the rectangle must also be 900 in area. So, the width must be 10feet and the length must be 90ft because 10x90 is also 900. How I got the length? I did 10x2+70.
Complete the following statement. Write your answer as a decimal or whole number.
% of $58 = $58
Answer: 1.72
Step-by-step explanation:
Write an equation for the trend line shown on the scatter plot.
An equation for the trend line shown on the scatter plot is y = 5x + 15.
How to find an equation for the trend line?In order to determine a linear equation for the trend line (line of best fit) that models the data points described in the scatter plot above, we would have to calculate the slope of this line.
By critically observing the scatter plot, we can reasonably and logically deduce the following points through which the trend line passes through:
Points (x, y) = (2, 25)
Points (x, y) = (6, 45)
Mathematically, the slope of any straight line can be calculated by using this formula;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (45 - 25)/(6 - 2)
Slope, m = 20/4
Slope, m = 5.
At point (2, 25), a linear equation for the trend line can be calculated by using the point-slope form:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x represents the length of trip (in days).y represents the weight (lbs).Substituting the given parameters into the formula, we have;
y - y₁ = m(x - x₁)
y - 25 = 5(x - 2)
y - 25 = 5x - 10
y = 5x - 10 + 25
y = 5x + 15.
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Write an absolute value equation representing all numbers x whose distance from 1 is 11 units.
The absolute value equation representingnumbers all x whose distance from is 11 units is
|1 - x| = 11 What is absolute value?Without taking direction into account, absolute value describes how far away from zero a certain number is on the number line.
A number can never have a negative absolute value.
How to write the absolute value equationThe equation is written in the form below
|1 - x| = 11
removing the absolute value sign
1 - x = ± 11
solving for x for positive value
1 - x = 11
1 - 11 = x
x = -10
solving for x for negative value
1 - x = -11
1 + 11 = x
12 = x
The absolute value equation as required is |1 - x| = 11 the values of is 12 or -10
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Malik wrote a total of 4 pages over 2 hours. How many hours will Malik have to spend this week in order to have written a total of 16 pages? Solve using unit rates.
Answer:
8 hours
Step-by-step explanation:
if it takes 2hrs to do 4 pages it takes an hour to do 2 pages
2*8=16
1*8=8
8 hours
hope it helps
Given (x – 1)^2 = 50, select the values of x.
x = –49
x = 51
x = 1+5√2
x = 1-5√2
Answer:
[tex]x=1+5\sqrt{2}, 1-5\sqrt{2}[/tex]
Step-by-step explanation:
[tex](x-1)^2=50 \\ \\ x-1=\pm 5\sqrt{2} \\ \\ x=1 \pm 5\sqrt{2}[/tex]
I need help please!!
Answer:
9/14 (9 over 14)
Step-by-step explanation:
If 5x to the power of 7 times s = 20x to the power of 4, which expression is equivalent to z
The expression that is equivalent to x is ∛4/s
How to determine the equivalent of x?In this question, the mathematical statement of the equation is given as
5x to the power of 7 times s = 20x to the power of 4
When the mathematical statement is represented as an equation, we have the following representation
5x⁷ * s = 20x⁴
Divide both sides by x⁴
So, we have the following representation
5x⁷/x⁴ * s = 20x⁴/x⁴
Evaluate the quotients
This gives
5x³ * s = 20
Divide both sides by 5
x³ * s = 4
So, we have
x³ = 4/s
Take the cube root of both sides
x = ∛4/s
Hence, the solution is x = ∛4/s
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1024,-256,64,-16, 3rd term
The next term of the given geometric series is the fifth term which is; a₅ = 4
What is the nth term of the geometric series?We are given the geometric series as;
1024, -256, 64, -16,.....
The formula to find the nth term of a geometric series is;
aₙ = ar^(n - 1)
where;
a is first term
r is common ratio
n is position of term
Thus, from the given series, we have that;
a = 1024
r = -256/1024
r = -1/4
Thus, the formula for the nth term of the series is;
aₙ = 1024(-¹/₄)^(n - 1)
Next term is the fifth term and so we have;
a₅ = 1024(-¹/₄)^(5 - 1)
a₅ = 1024(-¹/₄)^(4)
a₅ = 4
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kelsey has a bag full of jellybeans that weighs 3 1/2 pound. She gave her friend 1/3 of the bag. if she paid $2.58 per pound of jellybeans, how much money did she spend on the amount of jellybeans she gave away?
(PLUS 25 POINTS)
Answer: $3.01
Step-by-step explanation:
1. You first have to find out how much she spent for ALL the jellybeans, you find this by multiplying the pounds by the cost per pound.
(7/2)*(2.58)
Kelsey spent $9.03 for the 3 1/2 pound bag of jellybeans
2. You now have to find out how much she spent for 1/3 if the bag. You do this by multiplying the total cost by 1/3.
(1/3)(9.03)
3.01
ANSWER: Kelsey spent $3.01 on the amount of jellybeans she gave away.