Answer:
$84.00
Step-by-step explanation:
You want the original price of a tennis racquet if its final price after a 25% discount and 7% tax is $67.41.
Price with taxTax add 7% to the price, so multiplies it by (1 +7%) = 1.07
DiscountThe 25% discount subtracts 25% of the original price, so multiplies it by ...
(1 -25%) = 1 -0.25 = 0.75
Final priceThen the final price is computed as ...
final price = (original price)·(0.75)·(1.07)
Dividing by the coefficients of the original price, we find it to be ...
original price = (final price)/(0.75 · 1.07) = $64.71/(0.75·1.07) = $84.00
The original price of the racquet is $84.00.
what is a Pythagoras theorem
The Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.
What is mathematical representation of Pythagoras theorem?From the given Pythagoras theorem above, the mathematical representation of the theorem would be written below as follows;
C² = a²+b²
Where:
'C' represents the hypotenuse which is the longest part of the triangle and is always diagonal connecting the two other points.'a' represents the perpendicular length that forms the angle 90° of the right angle triangle.'b' represents the base of the triangle.Learn more about Pythagorean formula here:
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If f(-5)=7 identify a point on the graph of f
Answer:
If f(-5) = 7, then the point P(-5, 7) will be on the graph of f
where -5 is the x-coordinate and 7 is the y-coordinate
Step-by-step explanation:
Suppose a network has 37 servers of which 8 fail. How many possibilities are there for the 8 that fail?
The number of possibilities for 8 of 37 servers to fail is 38608020
How to determine the ways of selection?From the question, we have
Total number of servers, n = 37
Numbers to servers that fail, r = 8
The number of ways for 8 serves to fail is calculated using the following combination formula
Total = ⁿCᵣ
Where
n = 37 and r = 8
Substitute the known values in the above equation
Total = ³⁷C₈
Apply the combination formula
ⁿCᵣ = n!/(n - r)!r!
So, we have
Total = 37!/29!8!
Evaluate
Total = 38608020
Hence, the number of ways is 38608020
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if you take away 25 from a number you will be left with two and halftimes 30. what is the number?
A manufacturer has two options for making cube-shaped boxes. The cost is calculated by multiplying the surface area of the box by the cost per square inch of the cardboard. Answer parts a through c below.
The quadratic functions are: f(x) = 0.03x² for Design A and g(x) = 0.024x² for Design B.
Describe Quadratic functions?A quadratic function is a type of polynomial function of the form f(x) = ax² + bx + c, where a, b, and c are constants and x is the variable. In a quadratic function, the highest power of the variable is 2.
The graph of a quadratic function is a parabola, which is a U-shaped curve that opens either upwards or downwards depending on the sign of the coefficient a. If a > 0, the parabola opens upwards, and if a < 0, the parabola opens downwards. The vertex of the parabola, which is the point where the curve changes direction, is given by the coordinates (-b/2a, f(-b/2a)).
Quadratic functions have a wide range of applications in various fields such as physics, engineering, economics, and finance. For example, they can be used to model the motion of projectiles, the trajectory of a rocket, the shape of a bridge arch, the optimization of business profits, and the behavior of financial markets.
Let's assume that each side of the cube has a length of x inches. Then, the surface area of the cube is 6x² square inches.
a. For Design A with a cost of $0.005 per square inch, the total cardboard cost can be calculated using the quadratic function:
f(x) = 0.005(6x²) = 0.03x²
b. For Design B with a cost of $0.004 per square inch, the total cardboard cost can be calculated using the quadratic function:
g(x) = 0.004(6x²) = 0.024x²
Therefore, the quadratic functions are:
f(x) = 0.03x² for Design A
g(x) = 0.024x² for Design B
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The complete question is:
Reed has an aquarium that holds 12 gallons of
water. There are approximately 4 liters in one
gallon. Which measurement is closest to the
number of liters in Reed's aquarium?
Answer:
48
Step-by-step explanation:
12*4=48
write an equivilant fractions for 3 3/4 and 1 2/3 using a common denominator iready
The requried equivalent fraction for the equivalent fraction to 3 3/4 and 1 2/3, is 45/12, and 20/12.
To find a common denominator for 4 and 3, we can multiply them together to get 12.
So, we can convert 3 3/4 as:
3 3/4 = 12/4 + 3/4 = 15/4
Similarly, we can convert 1 2/3 as:
1 2/3 = 5/3
Therefore, the equivalent fractions for 3 3/4 and 1 2/3 using a common denominator of 12 are:
15/4 = 45/12 and 5/3 = 20/12
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Set up a proportion and solve for x
Thus value of x in the given the proportion is 7.
How to find the value of x?Here, both triangles are congruent due to sss congruency,
Thus,
6 : 12
6k = 12
k = 12/6
k = 2
Also, The expressions are
(x+2) : 3x - 3
(x+2)k = 3x - 3
(x+2)2 = 3x - 3
2x + 4 = 3x - 3
3x - 2x = 4 + 3
x = 7
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what is the most effluence first step to isolate the variable term on one side of this equation -9x=-4x+5
Christina is buying a $170,000 home with a 30-year mortgage. She makes a $20,000 down payment.
Use the table to find her monthly PMI payment.
A. $51.25
B. $37.50
C. $23.75
D. $42.50
The monthly PMI Payment for Christina's loan is $37.50.The correct answer is option B.
To determine Christina's monthly PMI (Private Mortgage Insurance) payment, we need to find the corresponding interest rate for her loan-to-value (LTV) ratio. The LTV ratio is calculated by dividing the loan amount by the property value.
The loan amount can be calculated by subtracting the down payment from the property value:
Loan amount = Property value - Down payment
= $170,000 - $20,000
= $150,000
Now we can calculate the LTV ratio:
LTV ratio = Loan amount / Property value * 100
= $150,000 / $170,000 * 100
= 88.24%
Since Christina is obtaining a 30-year mortgage, we need to look at the interest rates for LTV ratios between 85.01% and 90%. According to the table, the interest rate for this range is 0.30%.
To calculate the PMI payment, we multiply the loan amount by the PMI rate and divide it by 12 months:
PMI payment = (Loan amount * PMI rate) / 12
= ($150,000 * 0.30%) / 12
= $450 / 12
= $37.50
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The Probable question may be:
Christina is buying a $170,000 home with a 30-year mortgage. She makes a $20,000 down payment.
Use the table to find her monthly PMI payment
Base to loan% = 95.01% to 97%,90.01% to 95%,85.01% to 90%,80.01% to 85%.
30-year fixed-rate loan = 0.55%,0.41%,0.30%,0.19%
15-year fixed-rate loan = 0.37%,0.28%,0.19%,0.17%.
A. $51.25
B. $37.50
C. $23.75
D. $42.50
i can you help me build the equation
i can graph it though :)
Answer:
x + 5y ≤ 30
Step-by-step explanation:
Function tables are?
Answer:
a table that describes a function by displaying inputs and corresponding outputs in tabular form
Step-by-step explanation:
Find the area of the triangle
Answer:
84mm
Step-by-step explanation:
Formula of a triangle:
A =bh/2
A=14(12)/2
A=168/2
A=84mm
3926 use each digit once, make the largest 4-digit number
Answer:
9632 is the largest number
Theprofit(indollars)earnedbysellingwappletreesisrepresentedby w2 − 4w + 14. The profit (in dollars) earned by selling w pear trees is
represented by 2w + 10. Write a polynomial that represents how much more profit is earned by selling w apple trees than w pear trees.
\(w^2 - 6w + 4\) is a polynomial that represents how much more profit is earned by selling w apple trees than w pear trees.
The profit earned by selling w pear trees is 2w + 10
To find the difference in profit, we need to subtract the profit earned by selling w pear trees from the profit earned by selling w apple trees:
\((w^2 - 4w + 14) - (2w + 10)\)
Simplifying the expression:
\(w^2 - 6w + 4\)
Therefore, the polynomial that represents how much more profit is earned by selling w apple trees than w pear trees is \(w^2 - 6w + 4\).
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Evaluate, show your steps tysm :)
~giving brainliest~
Answer:
-9/25
Step-by-step explanation:
-1^10 = -1
since (-1)(-1)(-1)(-1)(-1)(-1)(-1)(-1)(-1)(-1) = -1
Anything to the power of 0 is 1 so -22^0 = 1
Now our equation is -1 + 1 -(3/5)^2
Simplifying this:
0 -9/25 =
-9/25
Answer:
in fraction: 41/25
= 1.64
Step-by-step explanation:
\((-1)^{10} =1\)
\((-22)^{0} =1\)
\((\frac{3}{5} )^{2} =\frac{9}{25}\)
Then
\(1+1-\frac{9}{25} =2-\frac{9}{25} =\frac{50}{25} -\frac{9}{25} =\frac{41}{25}\)
decimal: 1.64
Hope this helps
11. The circumference of a circle is 53.38 centimeters.
What is the area in square centimeters? Use 3.14 for .
( Please explain how you got your answer )
Answer:
A = 226.87 square cm
Step-by-step explanation:
We know that the circumference is given by the formula
C = πd, where
C is the circumference,and d is the diameter of the circleStep 1: First, we must find the diameter of the circle by plugging in 53.38 for C and 3.14 for π and simplifying:
53.38 = 3.14d
17 = d
Thus, the diameter of the circle is 17 cm
Step 2: We know that the diameter is simply twice the radius, r. Thus, we can find the radius by dividing the diameter by 2:
d = 2r
d/2 = r
17/2 = r
8.5 = r
Thus, the radius of the circle is 8.5 cm.
Step 3: The formula for area of a circle is given by the formula
A = πr^2, where
A is the area in square units, and r is the radius.Thus, we can plug in 8.5 for r and 3.14 for π to find the area of the circle:
A = 3.14(8.5)^2
A = 3.14(72.25)
A =226.865
Thus, the area is 226.865 square cm. You can use the exact answer, the answer rounded to the nearest hundredth (A = 226.87 square cm), or the answer rounded to the nearest tenth (A = 226.9 cm)
The area of a rectangle is 9.1 square centimeters. The length is 2.6 centimeters. What is the width?
Taylor's sister is 7 years less than twice Taylor's age,a. The sum of Taylor's age and her sister's age is 41. Which equation represents this relationship
1) a + (7 - 2a) = 41
2) a + (2a-7)=41
3) 2a-7=41
4) a = 2a - 7
Explain why the other 3 choices are incorrect.
By simplifying a system of equations we will see that the correct option is the second one:
(2a - 7) + a = 41
Which equation represents this relationship?
Let's define the variables:
a = Taylor's Age.s = Sister's Age.We have the statements:
"Taylor's sister is 7 years less than twice Taylor's age"
s = 2*a - 7
"The sum of Taylor's age and her sister's age is 41"
s + a = 41
So we have a system of equations:
s = 2a - 7
s + a = 41
Replacing the first equation in the second one we get:
(2a - 7) + a = 41
So the correct option is the second one, that is the equation that represents this relationship.
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Which of the following is an example of the identity property of 1?
Answer:
Option B
Step-by-step explanation:
The identity property of 1 states that any number multiplied by one would be the same number.
\(a * 1 = a\)
Option B shows that (11/25) multiplied by one would be (11/25). The product would same as the multiplicand in this scenario.
Option B would be the most appropriate answer for the question.
Hope this helps.
On average, Peter goes through three fish hooks in order to catch 7 fish. How many hooks can he expect to use if he needs to catch 189 fish?
By solving a proportional relation, we conclude that he needs 81 hooks to catch 189 fish.
How many hooks can he expect to use if he needs to catch 189 fish?We assume there is a proportional relationship of the form:
F = k*H
where:
F = number of fish.k = constant of proportionality.H = number of hooks.We know that with 3 hooks he catches 7 fish, then we can replace that:
7= k*3
7/3 = k
So the proportional relation is:
y = (7/3)*x
Then if he wants to get 189 fish we can write:
189 = (7/3)*x
And solve this for x:
189*(3/7) = x =81
He will need 81 hooks.
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Determine whether the
quadratic function
y=x² + 4x + 6 has
a maximum or minimum value.
Then find the value.
O maximum
minimum
The value is
Answer:
(a) The function has a minimum value
(b) The minimum value is 2
Step-by-step explanation:
(a)Currently y = x^2 + 4x + 6 is in standard form, whose general equation is
y = ax^2 + bx + c.
We know that for our function a = 1.
When a > 0, the parabola opens upward and the vertex is a minimumWhen a < 0, the parabola opens downward and the vertex is a maximumThus, y = x^2 + 4x + 6 must have a minimum value.
(b) Whenever a problem asks for the minimum value, it's asking for the y-coordinate of the minimum.
Step 1: First we can find the x-coordinate of the minimum using the equation -b/2a from the quadratic formula.
Plugging in 4 for b and 1 for a, we get:
x-coordinate of minimum = -4 / 2(1)
x-coordinate of minimum = -4 / 2
x-coordinate of minimum = -2
Step 2: Now we can plug in -2 for x in the quadratic function. The result will be our minimum value:
f(-2) = (-2)^2 + 4(-2) + 6
f(-2) = 4 - 8 + 6
f(-2) = -4 + 6
f(-2) = 2
Thus, the minimum value of the quadratic function is 2.
REIVIAINING
29:07
LS
Charissa is eating out with friends, and it is her turn to pay the gratuity. The bill for the food is $26.50. If she plans to
tip at 20%, what should she pay if she doesn't want to leave pennies on the table?
O $0.55
Answer:
$5.30 :DDD
Step-by-step explanation:
SO WHAT YOU DO IS 26.50 X 0.20 AND YOU WILL GET 5.30 SO BAM
Please solve the equation for z
Answer:
z = 2y - 4x
Step-by-step explanation:
\({ \sf{x = \frac{2y - z}{4} }} \)
multiply both sides by 4:
\({ \sf{(4 \times x) = ( \frac{2y - z}{4}) \times 4 }} \\ \\ { \sf{4x = 2y - z}} \\{ \sf{z = 2y - 4x}}\)
How many Squares are there ?
Answer:
6
Step-by-step explanation:
most of them are rectangles
which of the following statements is true?
Answer:
i think its b
Step-by-step explanation:
Answer:
jjjjjk
Step-by-step explanation:
What is bigger 8,000g or 5kg
Answer:
8,000g is bigger than 5kg.
Step-by-step explanation:
To compare these two quantities, we need to convert them to the same unit of measurement. We can convert 5 kg to grams by multiplying by 1000:
5 kg = 5,000 g
Now we can compare:
8,000 g > 5,000 g
Therefore, 8,000 g is bigger than 5 kg.
3. What is the coefficient in the expression: 94a+2?
Answer:
The coefficient would be 94
Step-by-step explanation:
A coefficient is the number used to multiply the variable! Hope this helps!
find the exact value of cos A in simplest radical form?
Answer:
cosA = 7/8
Step-by-step explanation:
cos∅ = adjacent over hypotenuse
cosA = 14/16
cosA = 7/8
a one sided confidence interval bounding the high side is desired for the true average stray-load loss (in watts) for a certain induction motor when the line current is held at 10 amps for a speed of 1500 rpm. assume that the stray-load loss population is normally distributed with standard deviation = 2. Compute a one-sided 99% Confidence Interval for mu when n = 86, and X_Bar =71. Give your answer accurate to three decimal pointsPlease show steps with out excel or calculators I use tables only
using the formula Upper Bound = X_Bar + (critical value * standard deviation/sqrt(n)) to calculate the upper bound of the interval. The result is an upper bound of 72.41.
The standard normal distribution table is used to calculate the critical value for this problem.
The critical value at 99% confidence level is 2.576.
The formula for the one-sided confidence interval is given by:
Upper Bound = X_Bar + (critical value * standard deviation/sqrt(n))Therefore, the one-sided 99% Confidence Interval for mu when n = 86, and X_Bar =71 is:
Upper Bound = 71 + (2.576 * 2/sqrt(86))
Upper Bound = 71 + (1.41)
Upper Bound = 72.41
The one-sided 99% Confidence Interval for mu when n = 86 and X_Bar =71 is calculated by using the standard normal distribution table to find the critical value of 2.576, and then using the formula Upper Bound = X_Bar + (critical value * standard deviation/sqrt(n)) to calculate the upper bound of the interval. The result is an upper bound of 72.41.
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