the discount on the dog food is $0.27, and the discounted price is $1.08.
What is the percentage?
A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.
If the original price of the dog food is $1.35 and it is on sale for 20% off, the discount would be:
Discount = 20% of $1.35
Discount = 0.20 x $1.35
Discount = $0.27
Therefore, the discounted price of the dog food would be:
Discounted price = Original price - Discount
Discounted price = $1.35 - $0.27
Discounted price = $1.08
So the discount on the dog food is $0.27, and the discounted price is $1.08.
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Are all intersecting lines perpendicular?
Answer:
no
Step-by-step explanation:
Need help quick please!
Answer:
cosΘ = [tex]\frac{\sqrt{7} }{4}[/tex]
Step-by-step explanation:
using the identity
sin²x + cos²x = 1 ( subtract sin²x from both sides )
cos²x = 1 - sin²x ( take square root of both sides )
cosx = ± [tex]\sqrt{1-sin^2x}[/tex]
given
sinΘ = [tex]\frac{3}{4}[/tex] , then
cosΘ = ± [tex]\sqrt{1-(\frac{3}{4})^2 }[/tex]
= ± [tex]\sqrt{1-\frac{9}{16} }[/tex]
= ± [tex]\sqrt{\frac{16}{16}-\frac{9}{16} }[/tex]
= ± [tex]\sqrt{\frac{7}{16} }[/tex]
= ± [tex]\frac{\sqrt{7} }{\sqrt{16} }[/tex]
since Θ is in quadrant 1 , then cosΘ > 0
cosΘ = [tex]\frac{\sqrt{7} }{4}[/tex]
Simplify as much as possible:
Answer:
-3
Step-by-step explanation:
First, -7 minus 8 is -15.
-15 divided by 5 is -3.
therefore, the simplified answer is -3.
the width of a block of wood with rectangular cross-section is x cm. it's height is two- thirds its width and length is 4 times its height what is its volume in cm3?
Answer:
The height of the block is two-thirds of its width, so we have h = (2/3)x.
The length of the block is 4 times its height, so we have l = 4h = 4(2/3)x = (8/3)x.
The volume of the block is given by V = lwh, so substituting the values we have:
V = (8/3)x * x * (2/3)x = (16/81)x³
Therefore, the volume of the block is (16/81)x³ cubic cm.
. Teachers' Federal Credit Union offers a 3.25%, 10-year mortgage. Moira wants to borrow'
$380,000 and "purchase" enough negative points to eliminate her $14,000 closing costs. Each
negative point reduces the closing costs by 1% of the principal and increases the APR by 0.135%.
a. How many points will she need?
b. What will her new APR be?
C.
What is the breakeven time for Moira's loan?
a)she need 3.68 negative point , The new APR for Moira will be 3.25% + (3.68 x 0.135%) = 3.7452% because each negative point raises the APR by 0.135%.and the breakeven time for Moira's loan is 10 months
What is Breakeven time?Breakeven time refers to the amount of time it takes for the savings from a particular action to equal the costs associated with that action. It is the point at which the benefits and costs are equal, and after which the benefits will begin to exceed the costs.
According to given informationa. Moira has to buy 14,000/380,000 = 0.0368 or 3.68% in negative points to offset $14,000 in closing fees. The closing expenses are reduced by 1% of the principle for every negative point, therefore Moira has to buy 3.68/1 = 3.68 negative points.
b. The new APR for Moira will be 3.25% + (3.68 x 0.135%) = 3.7452% because each negative point raises the APR by 0.135%.
c.When the savings from buying the negative points equal the additional interest paid because of the higher APR, that is the breakeven point for Moira's loan. 3.68 x 380,000 x 1% = $14,040 is the savings from buying 3.68 negative points. The difference between the interest paid at the original APR of 3.25% and the interest paid at the new APR of 3.7452% represents the additional interest paid as a result of the higher APR. A 10-year, $380,000 mortgage at 3.25% would have a monthly payment of $3,680.97 according to an online mortgage calculator. During a period of ten years, interest payments total $73,276.23. A 10-year, $380,000 mortgage at 3.7452% has a $3,918.23 monthly payment. Throughout a ten-year period, interest was paid a total of $88,668.83. The additional interest paid as a result of the higher APR equals $15,392.60 ($88,668.83 x $73,276.23). The breakeven point is therefore $14,040/$15,392.60 = 0.910 or roughly 10 months.
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A rectangular garden is to be constructed using a rock wall as one side of the garden and wire fencing for the other three sides. Given that there are 30 meters of fencing available, determine the dimensions that would create the garden of maximum area. What is the maximum possible area?
The dimensions of the garden that create the maximum area are 5 meters by 15 meters, and the maximum possible area is 75 square meters
What is measurement?
Measurement is the process of assigning numerical values to physical quantities, such as length, mass, time, temperature, and volume, in order to describe and quantify the properties of objects and phenomena.
Let's assume that the rock wall is the width of the garden and the wire fencing is used for the length and the other two sides. Let's denote the length of the garden as L and the width as W.
Since we have 30 meters of fencing available, the total length of wire fencing used is:
L + 2W = 30 - W
Simplifying this equation, we get:
L = 30 - 3W
The area of the garden is:
A = LW
Substituting the expression for L from the previous equation, we get:
A = W(30 - 3W)
Expanding the expression, we get:
A = 30W - 3W²
To find the maximum area, we need to take the derivative of A with respect to W and set it equal to zero:
dA/dW = 30 - 6W = 0
Solving for W, we get:
W = 5
Substituting this value back into the expression for L, we get:
L = 15
Therefore, the dimensions of the garden that create the maximum area are 5 meters by 15 meters, and the maximum possible area is:
A = 5(15) = 75 square meters
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228 in base three is
228 in base 10 to base three is determined as 22110₃.
What is 228 in base 10 to base 3?
Converting a number from one base to another involves representing the same value in a different positional numeral system.
To convert the number 228 from base 10 to base 3, we can follow these steps:
3 | 228
= 76 R 0 (so the remainder here 0)
= 25 R 1 (the remainder here 1)
= 8 R 1 (the remainder here 1)
= 2 R 2 (the remainder here 2)
= 0 R 2 (the remainder here 2)
write the remainders from bottom to top = 22110₃
228 in base 10 to base 3 = 22110₃
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How do solve this question? I don't understand the part where they say to change the equation to 4
Answer:
Step-by-step explanation:
A survey of 2,000 doctors showed that an average of 3 out of 5 doctors use brand A aspirin how many docs use brand A aspein
Help solve this problem
The equivalent expression to the given expression; - √-7 as required to be written in terms of i is; -i√7.
What is the equivalent expression?It follows from the task content that the equivalent expression to the given; -√-7 is to be determined.
Since the given expression is; - √-7; we have;
- (√-1 × √7) where √-1 = i, so that we have;
= -i√7.
Ultimately, the expression in terms of i is; -i√7.
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How many liters each of a 35% acid solution and a 70% acid solution must be used to produce 70 liters of a 55% acid solution
We need 30 liters of the 35% acid solution and 40 liters of the 70% acid solution.
What is the volume of each solution?The volume of each solution is calculated as follows;
Let x be the number of liters of the 35% acid solution
Let y be the number of liters of the 70% acid solution
x + y = 70 ----- (1)
0.35x + 0.70y = 0.55(70) ----- (2)
The equation is simplified as;
0.35x + 0.70y = 38.5
from (1) x = 70 - y
Substitute x = 70 - y into equation 2:
0.35(70 - y) + 0.70y = 38.5
24.5 - 0.35y + 0.70y = 38.5
0.35y = 14
y = 40
Substitute y = 40 into equation 1 to solve for x:
x + 40 = 70
x = 30
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Y-4=-3x+6 in standard form with explanation.
Answer:
Y + 3x = 10
Step-by-step explanation:
You need to know that Standard Form is: Ax + By = C
Y-4=-3x+6 Add 3x to both sides
Y - 4 + 3x = 6 Add 4 to both sides
Y + 3x = 10
Customers of a phone company can choose between two service plans for long distance calls. The first plan has an $18 monthly fee and charges an additional $0.15 for each minute of calls. The second plan has a $12 monthly fee and charges an additional $0.20 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?
Let's call the number of minutes of calls "x".
For the first plan, the cost will be:
Cost = $18 + $0.15x
For the second plan, the cost will be:
Cost = $12 + $0.20x
To find the point at which the costs of the two plans are equal, we can set the two equations equal to each other and solve for x:
$18 + $0.15x = $12 + $0.20x
Subtracting $12 from both sides, we get:
$6 + $0.15x = $0.20x
Subtracting $0.15x from both sides, we get:
$6 = $0.05x
Dividing both sides by $0.05, we get:
x = 120
Therefore, if a customer makes more than 120 minutes of calls per month, the first plan with the $18 monthly fee and $0.15 per minute charge will be more cost-effective. If a customer makes less than 120 minutes of calls per month, the second plan with the $12 monthly fee and $0.20 per minute charge will be more cost-effective.
Answer:
120 minutes
Step-by-step explanation:
Let x be the number of minutes of calls made in a month.
For the first plan, the monthly cost is $18 + $0.15x.
For the second plan, the monthly cost is $12 + $0.20x.
To find the point where the costs are equal, we need to solve the equation:
18 + 0.15x = 12 + 0.20x
Subtracting 0.15x from both sides gives:
18 = 12 + 0.05x
Subtracting 12 from both sides gives:
6 = 0.05xDividing both sides by 0.05 gives:
x = 120
Therefore, the costs of the two plans will be equal for 120 minutes of calls.
Desmond is saving for a bicyle tha cost $125. So far he has saved $82. Write and solve an equation that can be used to find the amount of money he still has to save to buy the bicycle
Required equation is $125 = $82 + x and the amount of money he still has to save to buy the bicycle is $43.
What is equation?
A statement that two expressions are equal. It typically contains one or more variables is called equation which are usually represented by letters, and it may also contain numbers and mathematical operations such as addition, subtraction, multiplication, and division.
Let x be the amount of money that Desmond still needs to save to buy the bicycle.
Since he has already saved $82, the total amount of money he needs to save,
Total cost of bicycle = Cost he has saved + Amount he still needs to save
$125 = $82 + x
We can solve for x by subtracting $82 from both sides:
$125 - $82 = x
Simplifying, we get:
$x = $43
Therefore, Desmond still needs to save $43 to buy the bicycle.
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Answer: 24 i am a expect
A bank loaned out $36,000, part of it at the rate of 5% annual interest, and the rest at 4% annual
interest. The total interest earned for both loans was $1,625.00. How much was loaned at each rate?
SA
SA
was loaned at 5% and
was loaned at 4%.
I’ll give all 30 points for just the back of this, maybe show some work
The Savings budget is $150 per month
Utility budget is $225,000
Auto budget is $823 per month
How to calculate the valueSaving behavior, they want to save 15% of their income, so their savings budget would be:
a. Savings budget = 15% of $1,000 = $150 per month
b. Tri-County Supply budgets 5% of the previous year's total revenue for utilities, so their utility budget would be:
Utility budget = 5% of $4,500,000 = $225,000
c. Mr. Jones needs to increase his auto budget to 15% of his monthly income, which is $5,488 per month. So his monthly auto budget would be:
Auto budget = 15% of $5,488 ≈ $823 per month
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For the right triangles below, find the exact values of the side lengths c and h. If necessary, write your answers in simplified radical form.
the value of the side c is √3 and h is 7.
What is Trigonometric Functions?
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used in various fields such as engineering, physics, and navigation. The six fundamental trigonometric functions are sine, cosine, tangent, secant, cosecant, and cotangent. These functions are based on the ratios of the sides of a right-angled triangle. By using trigonometric formulas and identities, we can calculate the values of these functions for the perpendicular side, hypotenuse, and base of a right triangle.
tan(60)= 3/c
c = 3/tan(60)
c = 3/√3
c = √3
for 2nd
tan(45)= h/7
h = 7*1
h=7
Hence the value of the side c is √3 and h is 7.
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give the statement missing for number 3 and the reason missing for number 5 in the column proof below.
Answer:
3 = equal
5 = equal
Step-by-step explanation:
3. both angles are alternate angles
5. both triangles are equal
What is the value of x to the nearest tenth?
In a triangle, the acute angle is 28 degrees and the obtuse angle is 126 degrees. The adjacent side of 28-degree angle is 8.2 and the opposite side is x.
The value of the side x is 4. 36
How to determine the valueTo determine the value, we need to know that there are six different trigonometric identities. They are;
tangentcotangentcosecantsecantsinecosineFrom the information given, we have that;
the acute angle is 28 degrees and the obtuse angle is 126 degrees. The adjacent side of 28-degree angle is 8.2 and the opposite side is x.
Opposite side = x
Adjacent side = 8.2
Now, using the tangent identity;
tan 28 = x/8.2
multiply the values
x = 0. 5317(8.2)
multiply
x = 4. 36
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HELP
Draw any length line segment that will fit in the space shown. The line segment can go in any direction, but it must be straight. Draw another line segment of any length that is parallel to the first one. Connect the ends of each line segment with line segments to make a closed four-sided figure. What does your shape look like? Can you classify it?
Note that the shape with with two parallel sides is called an irregular parallelogram. See the attached image.
What is an irregular parallelogram?The polygon is an irregular quadrilateral because two sides are parallel lines and the other two sides are not.
Irregular polygons have infinitely many sides because their lengths are not equal. Shapes such as parallelograms, trapeziums, and quadrilaterals are irregular polygons because their neighboring sides and angles are not equal.
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Darrel loaned his friend $2,500 to help him with his business. If his friend pays Darrel back in 1 year with 15% simple interest, how much will he owe Darrel altogether
Based on simple interest, the solution to the question is that his friend will ultimately owe Darrel $2,875.
What is Simple interest?A loan or investment's interest can be calculated using simple interest using the principal, interest rate, and duration of the transaction. Because it just considers the original principal and does not account for any compounded interest, it is known as "simple" interest.
Darrel will be indebted to his friend for the following sum if he lends him $2,500 and receives repayment with 15% simple interest after a year:
Interest = Principal x Rate x Time
Interest = $2,500 x 0.15 x 1
Interest = $375
Thus, the total sum his friend will be required to pay Darrel is:
Total amount = Principal + Interest
Total amount = $2,500 + $375
Total amount = $2,875
Thus, the total amount his friend owes Darrel is $2,875.
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You ride an express bus from the center of town to your street. You have two payment options. Option A is to buy a monthly pass for $50 and pay $2 per ride.
Option B is to pay $4.50 per ride. After how many rides will the total costs of the two options be the same? Write a system of equations in order to solve this problem.
Answer the following questions in order making sure you number your answers:
1. What does × represent in the equation?
2.) What does y represent in the equation?
3.) What is the equation for Option A?
You will need to type the equation
4.) What is the equation for Option B?
You will need to type the equation
5.) What is the solution? Remember I need your solution (answer) in an ordered pair (x,y)
Which of these would most likely weigh 2 kilograms
Answer:
The following objects would most likely weigh 2 kilograms:
A large pineappleA liter of waterA bag of sugarA small catA laptop computerA large bookThe actual weight of each object may vary, but based on typical weights, any of these objects could weigh around 2 kilograms.
Find the equation of a line passing through the point (-3, -7) that is perpendicular to the line 5x-3y=10. Show detailed steps.
To find the equation of a line passing through a given point that is perpendicular to a given line, we need to follow these steps:
Find the slope of the given line by rearranging the equation into slope-intercept form y = mx + b, where m is the slope.
Find the slope of a line perpendicular to the given line by taking the negative reciprocal of the slope found in step 1.
Use the point-slope form y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope found in step 2, to write the equation of the perpendicular line.
Step 1: Find the slope of the given line 5x - 3y = 10
We can rearrange the equation into slope-intercept form by solving for y:
5x - 3y = 10
-3y = -5x + 10
y = (5/3)x - (10/3)
The slope of this line is 5/3.
Step 2: Find the slope of a line perpendicular to the given line
The slope of a line perpendicular to the given line is the negative reciprocal of 5/3:
m_perp = -3/5
Step 3: Use the point-slope form to write the equation of the perpendicular line passing through (-3, -7).
We plug in the values we found for the slope and the given point into the point-slope form:
y - y1 = m_perp(x - x1)
y - (-7) = (-3/5)(x - (-3))
Simplifying this equation, we get:
y + 7 = (-3/5)x - 9/5
Now we can rearrange this equation into slope-intercept form y = mx + b, where m is the slope and b is the y-intercept:
y = (-3/5)x - 44/5
Therefore, the equation of the line passing through the point (-3, -7) and perpendicular to the line 5x - 3y = 10 is y = (-3/5)x - 44/5.
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Answer: -4
Step-by-step explanation:
Find the volume of the following regular pentagonal prism, if the apothem is 6.9 cm and the height of the prism is 8 cm. Round your final answer to the nearest tenth if necessary.
The volume of the following regular pentagonal prism rounded to the nearest tenth is: 1384.1 cm³.
How to calculate the volume of a pentagonal prismTo calculate the volume of a pentagonal prism, we should apply the formula:
V = 5/2 × apothem × base × height
In the given question, the height is 8 cm and the apothem is 6.9 cm. This apothem can be applied in solving for side length as follows:
2 × 6.9cm × tan 36°
= 10.03
Next, we find the area of the Pentagon as follows:
5/2 × 10.03 × 6.9 cm
= 173.02
The volume now equals:
173.02 × 10.03
= 1384.1 cm³.
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What is the equation in slope intercept form of the line that passes through the point (-13,-2)and (26,25)
Answer:
y =27/39x + 7
Step-by-step explanation:
Step 1: Calculating Slope (m).
m = y2-y1/x2-x1
m = (25)-(-2)/(26)-(-13)
m = 25+2/26+13
m = 27/39
m = 0.692
Now putting value of m in equation (i)
y = 0.692x + b -----(ii)
Step 2: Calculating Y-intercept (b).
Lets choose the first point, (-13,-2) for calculating y-intercept:
y = mx + b
-2 = 0.692(-13) + b
-2 = -9.00 + b
7 = b
b = 7
Now putting value of b in equation (ii)
y = 0.692x + 7
What is the quotient of 2 and 1 over 3 divided by 3 over 5
let's firstly convert the mixed fraction to improper fraction and then divide.
[tex]\stackrel{mixed}{2\frac{1}{3}}\implies \cfrac{2\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{7}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{7}{3}\div \cfrac{3}{5}\implies \cfrac{7}{3}\cdot \cfrac{5}{3}\implies \cfrac{35}{9}\implies {\Large \begin{array}{llll} 3\frac{8}{9} \end{array}}[/tex]
Rewrite each of these mixed numbers 9 2/5
Answer:
To rewrite the mixed number 9 2/5 as an improper fraction, we can multiply the whole number (9) by the denominator of the fraction (5) and add the numerator of the fraction (2), then write the result over the denominator:
9 2/5 = (9 × 5 + 2)/5 = 47/5
Therefore, 9 2/5 can be written as the improper fraction 47/5.
