The new yield strength of the 1040 steel will be the intercept on the curve for 30.56 %of cold work which is between700 to 800 MPA
Given original diameter do = 12 mm
Ao = [tex]\pi[/tex]/4 x 12² = 113.097 mm²
Deformed diameter d =10mm
Ad = [tex]\pi[/tex]/4 x 10² = 78.54 mm²
Degree of cold work %CW = (Ao - Ad/Ao)X 100
=(113. 097 - 78. 54/113.097) x 100
= 30.56%
% CW is 30.56 %
Therefore, the intercept on the curve for 30.56% of cold work, which is between 700 and 800 MPA, will represent the new yield strength of the 1040 steel.
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Solve the inequality 2m - 125 or 5m> -25.
Answer:
m = -5
Step-by-step explanation:
I'm not sure of the first part, but this is how to solve the second:
5m > -25
5m/5 > -25/5
m = -5
a school has 400 grade 9's, 375 grade 10's, 300 grade 11's and 325 grade 12's. twenty students from each grade are surveyed
The type of bias that can be present in stratified sampling is that the students cannot be selected to accurately reflect the population.
How are samples classified?Samples may be classified according to the five options as follows:
A convenient sample is drawn from a conveniently available pool of options.A random sample is equivalent to placing all options into a hat and taking some of them.In a systematic sample, every kth element of the sample is taken.Cluster sampling divides population into groups, called clusters, and each element of the group is surveyed.Stratified sampling also divides the population into groups. However, an equal proportion of each group is surveyed.In this problem, an equal amount of students from each class was surveyed, hence a stratified sample was used.
The type of bias present in stratified sampling is that the students cannot be selected to accurately reflect the population.
Missing InformationThe problem asks for which type of bias is present in this sample.
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What is the correct way to write 0.0000250 m in scientific notation? 2.50 times. 10â€""5 m 2.5 times. 10â€""5 m 2.50 times. 10â€""4 m 2.5 times. 10â€""4 m
The correct way to write 0.0000250 m in scientific notation is 2.5 · 10⁻⁵ m.
What is scientific notation?Scientific notation is a convenient way to write numbers that are very large or very small. A number written in scientific notation consists of a number greater than or equal to 1 but less than 10 multiplied by a power of 10. Here are some examples of numbers written in scientific notation:
1.23 × 10⁻⁴9.9 · 10¹⁰⁰5 · 10²Since you're given a number less than 1, move the decimal point to the right until you have a number between 1 and 10. Then, count the number of times you moved the decimal and write that as negative exponent over a base of 10. Finally, write out number multiplied by the power. You'll get 2.5 · 10⁻⁵ if you do those things correctly.
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Answer:
A. 2.50 Times. 10–5 m
Step-by-step explanation:
other one is wrong
Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot 8(x2 + 2x + 1) = 3 + 1 8(x2 + 2x) = –3
The quadratic equation 8x² + 16x + 3 = 0 can be solved by using the quadratic formula.
The given quadratic equation is : 8x² + 16x + 3 = 0
Comparing this equation with ax² + bx + c = 0 we get :
a = 8 , b = 16 and c = 3
Now we will use the quadratic formula:
[tex]{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}[/tex]
Now we will substitute the values in this formula to find the values of x that satisfy the quadratic equation.
[tex]{\displaystyle x={\frac {-16\pm {\sqrt {16^{2}-4\times8\times3}}}{2\times8}}}\\\\{\displaystyle x={\frac {-16\pm {\sqrt {160}}}{16}}}\\\\[/tex]
The values for x that satisfy the equation are the roots or zeros of both expressions on the left-hand side of the equation. In a quadratic problem, there can only be two possible solutions.
A problem is said to have a double root if there is only one solution. One real double root, two complex solutions that appear to be complex conjugates of one another, two real solutions, or two real solutions if all the coefficients have real values are the only options.
Hence the values of x are : [tex]-\frac{4-\sqrt{10}}{4}[/tex] and [tex]-\frac{4+\sqrt{10}}{4}[/tex].
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An order of brown rice and quinoa weighs 17 pounds and costs $54.
Brown rice: $2.00 per pound
Quinoa: $4.50 per pound
How many pounds of brown rice and quinoa are in this order?
8 ounce of brown rice and 9 ounce quinoa sold.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Brown rice: $2.00 per pound
Quinoa: $4.50 per pound
let the brown rice sold x ounces
and, let the Quinoa sold be y ounces
So, the equations are:
x + y= 17
2x+ 4.5y= 54
2( 17- y) + 4.5y= 54
34 - 2y + 4.5y= 54
2.5y= 20
y= 20/2.5
y= 8 ounce
and, x= 17-8= 9 ounce
Hence, 8 ounce of brown rice and 9 ounce quinoa sold.
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The largest U.S. flag in the world is 225 feet by 505 feet.
------------------------
If a square yard of the flag weighs about 3.8 ounces, how much does the entire flag weigh in pounds?
The weight of the U.S. flag in pounds is 2,998.44 pounds.
What is the weight of the flag?The dimension of the U.S. flag is in feet. The dimensions have to be converted to yards.
1 foot = 1/3 yards
225 / 3 = 75 yards
505 / 3= 168.33 yards
The next step is to determine the area of the U.S. flag.
Area = length x width
75 x 168.33 = 12,625 yards²
Weight of the U.S. flag in ounces = 12,625 yards² x 3.8 = 47,975 ounces
1 ounce = 1/16 pounds
Weight of the U.S. flag in pounds = 47,975 / 16 = 2,998.44 pounds
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Complete the table. Round percent change to the nearest tenth of a percent.
Please find attached the completed table of the percentage changes on the amounts drawn with MS Word.
What is the percentage change on an amount?The percentage change on an amount is found by finding ratio of the change in the amount to the original amount then multiplying the obtained ratio by 100.
The percentage change formula is presented as follows;
[tex]\%C = \dfrac{x_2-x_1}{x_1} \times 100[/tex]Where;
%C = The percentage changex₂ = The new amountx₁ = the initial amountMaking each of the variables the subject, indicates;
The new amount, [tex]x_2 = \dfrac{\%C \times x_1}{100} + x_1[/tex]
[tex]\%C \times x_1+100\cdot x_1 = 100\cdot x_2[/tex]
[tex]x_1\cdot (\%C+100) = 100\cdot x_2[/tex]
The original amount, [tex]x_1 = \dfrac{100\cdot x_2}{(\%C+100)}[/tex]
The percentage change, [tex]\%C = \dfrac{c}{x_1} \times 100[/tex]
The original amount, [tex]x_1 = \dfrac{c}{\%C} \times 100[/tex]
Using the above formulas, the completed table is created with MS Excel and is presented as follows;
Original amount Change Percent Change New Amount
68 [tex]{}[/tex] 15 22.1 83
590 [tex]{}[/tex] -40 -6.8 550
115 [tex]{}[/tex] 20 17.4 135
120[tex]{}[/tex] -33 -27.5 87
125[tex]{}[/tex] -39 -31.2 86
163 [tex]{}[/tex] 47 28.8 210
274[tex]{}[/tex] 145.22 17.4 419.22
70 [tex]{}[/tex] -15.4 -27.5 54.6
1400[tex]{}[/tex] -1050 22.1 350
1250[tex]{}[/tex] -25 -2.0 1225
0.24[tex]{}[/tex] 0.3 125.0 0.54
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De la comida que hay en la nevera, un tercio son alimentos sólidos. De estos un medio son vegetales, de los cuales tres quintos son frutas, de las que dos quintos son manzanas.
¿Qué fracción del total son manzanas?
Si X es la cantidad total de alimento en la heladera, (1/10)*X es la cantidad de manzanas, entoces vemos que la fraccion es 1/10.
¿Qué fracción del total son manzanas?Digamos que la variable X representa la cantidad total de comida en la heladera.
Sabemos que un tercio del total de los alimentos son solidos, entonces la cantidad de alimentos solidos es:
(1/3)*X
Luego 1/2 de estos son verduras, entonces la cantidad de verduras que tenemos es:
(1/2)*(1/3)*X
Finalmente, 3/5 de las verduras son manzanas, entonces la cantidad de manzanas es:
(3/5)*(1/2)*(1/3)*x = (1/10)*x
Asi hemos encontrado la fraccion.
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c) √6 x √6 x√6 can someone help
Answer:
14.7
Step-by-step explanation:
Answer:
6[tex]\sqrt{6}[/tex]
or
≈14.7
Step-by-step explanation:
√6 x √6 x√6 can someone help
√6 x √6 x√6 =
6[tex]\sqrt{6}[/tex]
or
≈14.7
please answer this "3y=2x
Answer:
y=2/3x
Or
X=3/2y
Step-by-step explanation:
3y=2x
/3. /3
y=2/3x
3y=2x
/2. /2
3/2y=x
Hopes this helps please mark brainliest
Answer:
x=3/2y
y=2/3x
Step-by-step explanation:
for x - first screen shot
for y - second screen shot
Hope that helps!
PLS HELP ME ANSWER THIS QUESTIONNAIRE
The correct value of the simplified expressions found using the laws of indices gives;
d. [tex]\sqrt[4]{4}[/tex]a. [tex]\sqrt{\frac{5}{6} }[/tex]d. 3a. [tex]x\cdot \sqrt{y}[/tex]b. x²·yb. 1a. 1/315·x²·y⁴e. 6·x³·y⁵c. [tex]\frac{5}{9}[/tex]What are the laws of indices?The laws of indices state rules that enable the simplification of the combination of expressions of numbers and variables that are given in index form or involve powers of other numbers or variables
1. [tex]3^{\frac{1}{4} } = \sqrt[4]{4}[/tex]
The radical sign is used for expressing fractional indices.
The correct option is d. [tex]\sqrt[4]{4}[/tex]
2. The radical is in its simplest form when it cannot be further simplified, which gives the radical in its simplest form as option a. [tex]\sqrt{\dfrac{5}{6} }[/tex]
3. The index of a number is the number to which the variable or number is raised
The index of x³ in [tex]\sqrt{x^3}[/tex] is d. 3
4. The given expression has y raised to the power of [tex]\frac{1}{2}[/tex], which gives;
[tex]x\cdot y^\frac{1}{2} = x\cdot \sqrt{y}[/tex]
The correct option is a. [tex]x\cdot \sqrt{y}[/tex]
5. The common index of the expression within the parenthesis is [tex]\frac{1}{2}[/tex], which gives;
[tex](x^4\cdot y^2)^\frac{1}{2} = (x^{4\times \frac{1}{2} }\cdot y^{2 \times \frac{1}{2} })=x^2\cdot y[/tex]
The correct option is b. x²·y
6. The value of all numbers raised the power of zero is 1, therefore;
[tex](2^{1/3}\cdot 3^{1/4})^0\cdot (2^{1/5}\cdot 3)^0 = 1 \times 1=1[/tex]
The correct option is b. 1
7. The given expression can be simplified as follows;
[tex]\sqrt[5]{\dfrac{1}{243} } = \sqrt[5]{\dfrac{1}{3^5} } = \sqrt[5]{\left(\dfrac{1}{3} \right)^5} = \dfrac{1}{3}[/tex]
The correct option is therefore; a. 1/3
8. The given expression [tex]\sqrt{225\cdot x^4\cdot y^8} = \sqrt{15^2\cdot x^4\cdot y^8} = 15\cdot x^2\cdot y^4[/tex]
The correct option is [tex]15\cdot x^2\cdot y^4[/tex]
9. The given expression is [tex]\sqrt[3]{216\cdot x^9\cdot y^{15}}[/tex]
[tex]\sqrt[3]{216\cdot x^9\cdot y^{15}} = \sqrt[3]{6^3\cdot x^9\cdot y^{15}} = 6\cdot x^3\cdot y^5[/tex]
The correct option is e. [tex]6\cdot x^3\cdot y^5[/tex]
10. [tex]\sqrt{\dfrac{50}{162} } = \sqrt{\dfrac{25\times 2}{81\times 2} } = \sqrt{\dfrac{25}{81} } = \dfrac{5}{9}[/tex]
The correct option is c. [tex]\frac{5}{9}[/tex]
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Find the measurement of X.
Answer:333
Step-by-step explanation:
Since this is a scalene triangle, two sides will equal the same, meaning two angles will equal the same. So 70 has an equal on the other side, meaning 70+70=140, and x will equal the remainder, meaning x=40.
Hope that helps.
decide whether inductive reasoning or deductive reasoning is used to reach the conclusion: "what goes up must come down. the ball went up. it will come down."
The statement ""what goes up must come down. the ball went up. it will come down." can be reached through a deductive reasoning.
What is a deductive reasoning?The mental process of forming deductive deductions is known as deductive reasoning. An inference is deductively valid if its conclusion follows logically from its premises, i.e. if the premises cannot be true while the conclusion is false.
The primary distinction between inductive and deductive thinking is that inductive reasoning seeks to develop a hypothesis, whereas deductive reasoning seeks to test an existing theory. Inductive thinking proceeds from individual observations to broad generalizations, whereas deductive reasoning proceeds in the other direction.
In conclusion, the correct option based on the information is a deductive reasoning.
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Need help quick look at photo
Answer: the slope is unidentified
Step-by-step explanation:
Solve for X:
1/2x + 1/3x = 10
Answer:
Step-by-step explanation:
weknr f not sure
Answer:
12
Step-by-step explanation:
1/2x+1/3x=10
We simplify by making common denominator and adding them (if you don’t know how to do that please tell me)
3/6x+2/6x=10
5/6x=10
Now divide 5/6 on both sides
5/6x=10
/5/6. /5/6
x=10*6/5
x=60/5
x=12
Hopes this helps please mark brainliest
What is the perimeter of the figure?
32.0cm
51.0cm
19.0cm
63.0cm
The perimeter of the figure is 32 cm
How to determine the perimeter of the shape?The figure represents the given parameters
On the figure, we have the lengths of the side lengths to be:
Lengths = 7 cm, 5 cm, 3 cm, 4 cm, 4 cm, 9 cm
To determine the perimeter of the shape, we simply add the side lengths
Mathematically, this can be represented as
Perimeter = Sum of side lengths
Substitute the known values in the above equation So, we have the following equation
Perimeter = 7 cm + 5 cm + 3 cm + 4 cm + 4 cm + 9 cm
Evaluate the sum
Perimeter = 32 cm
Hence, the perimeter is 32 cm
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The radius of a circle is 15 inches. What is
the circumference of the circle? Write
your answer using T.
Answer:
C = 30pi inches
Step-by-step explanation:
The radius is 15 inches (said so in the question)
The diameter is 30 inches (The diameter is twice the radius)
The circumference is
C = pi•d
C = pi•30
C = 30pi
The circumference is 30pi inches.
The price of a movie ticket at the theater is $7 for students.
The price is higher for adults.
A group of 4 students and 3 adults paid $64 in all for movie tickets.
How much does each adult ticket cost?
Each adult tickets costs
The cost of each adult ticket for watching movie at the theatre equals to $12.
How do we derive the cost of each adult ticket?Given data:
Student ticket price = $7
Group of 4 students and 3 adults paid $64 in all for movie tickets.
The computation of each of the adult ticket cost is as follows:
Let x be the cost of each adult ticket.
Then, cost of 3 adult tickets = 3x.
Now:
The cost of 1 student ticket = $7
The cost of 4 student ticket = $7(4)
Then, we get the following equation:
7(4) + 3x = 64
18 + 3x = 64
3x = 64 - 18
3x = 36
x = 12
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Each of PQ and RS represents a 2-digit number. Different letter represent different digits, chosen from 6, 7, 8 and 9. What is the greatest product that PQx RS can have?
The greatest product that PQ x RS can have: 96 * 87 = 8352
In this question, we have been given PQ and RS represents a 2-digit numbers. Different letter represent different digits, chosen from 6, 7, 8 and 9
We need to find the greatest product that PQ x RS can have.
Consider P = 9, Q = 6, R = 8 and S = 7
So the two digit numbers would be,
PQ = 96 and RS = 87
PQ x RS
= 96 * 87
= 8352
Therefore, the greatest product that PQ x RS can have: 96 * 87 = 8352
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What is the image of (5,8) after the reflection over the line y=-x?
The image of (5, 8) after a reflection over the line y = - x is (-5, -8 ).
To see the graph.
Given,
In the question:
What is the image of (5,8) after the reflection over the line y= -x?
Now, According to the question:
The image of (-5,8) after a reflection over the y-axis
When a point is reflected over y axis, then the value of x changes to -x.
the value of y remains the same.
But, It is given that the reflection over the line y= -x
Hence, The image of (5, 8) after a reflection over the line y = - x is
(-5, -8 ).
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brian borrowed a 20-foot extension ladder to use to paint his house. If he sets the base of the ladder six feet from the house how far up will the top of the ladder reach?
The ladder Brian borrowed for painting should go 19.08 feet up the house if Brian sets the base 6 feet from the house
How to find the distance up the house the ladder will goinformation given in the question
hypotenuse = 20-foot ladder
adjacent = 6 feet from the house
opposite = how far up the house = ?
The problem is solved using the Pythagoras theorem is applicable to right angle triangle. the formula of the theorem is
hypotenuse² = opposite² + adjacent²
plugging the values as in the problem
let x be the required distance
20² = 6² + x²
400 = 36 + x²
400 - 36 = x²
x² = 364
x = √364
x = 19.08
The ladder Brain borrowed will go 19 feet high
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A. Your bed is a rectangle that is 4 feet by 6 feet wide. Draw a model of it below and label the dimensions. Find the perimeter and area of the bed. B. Dad reminds you that you keep you suitcase, a box of legos, your memory box, and your stash of snacks underneath your bed. They are all rectangle. The suitcase has a perimeter of 14 feet. The Lego box has a perimeter of 10 feet. The stash has a perimeter of 10 feet. The stash has a perimeter of 6 feet. C. Find the area and dimensions of each item under your bed
The model which model the dimensions of the bed has been attached.
The perimeter and area of the bed is 10 feet and 24 square feet respectively.The perimeter of your bed is less than the perimeter of the items, so not all items can be underneath your bed.What is the perimeter and area of the bed?Length of the rectangle = 6 feetWidth of the rectangle = 4 feetPerimeter of the bed = 2(length + width)
= 2(6 + 4)
= 2(10)
= 20 feet
Area of the bed = Length × width
= 6 feet × 4 feet
= 24 square feet
Perimeter of the suitcase = 14 feetPerimeter of Lego box = 10 feetPerimeter of memory box = 10 feetPerimeter of stash = 6 feetTotal perimeter = 14 + 10 + 10 + 6
= 40 feet
Therefore, the items listed can not all be underneath your bed because the total perimeter of the items is greater than the perimeter of your bed.
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Convert 37/2 to a mixed fraction
For each sequence, decide whether it could be arithmetic, geometric, or
neither.
1. 27, 9, 3, ...
2. 4, 8, 12,...
3. 50, 56, 60, ...
4. 36, 12, 4, ...
5. 4, 24,...
1. Therefore, the sequence is geometric.
2. Therefore, the sequence is arithmetic.
3. Therefore, the sequence is neither arithmetic nor geometric.
4. Therefore, the sequence is geometric.
5. Therefore, the sequence is neither arithmetic nor geometric.
Explain sequences and seriesFor the arithmetic, geometric, and harmonic sequences, a collection of sequences and series formulas is provided below. The sequence and series formulas presented here contain formulas for determining the sum of the n terms in a series as well as the nth term of the sequence.
A common difference exists between two succeeding terms in an arithmetic series. There is a typical ratio between succeeding terms in a geometric series.
1. Given sequence is 27, 9, 3, ...
As the difference between the number is large.
So, we will check for geometric sequence.
[tex]r = \frac{27}{9} = \frac{3}{3} = \frac{1}{3}[/tex]
Therefore, the sequence is geometric.
2. Given sequence is 4, 8, 12, ...
As we can see there is uniform difference of 4
Therefore, the sequence is arithmetic.
3. Given sequence is 50, 56, 60, ...
As the difference between the number is not uniform.
So, we will check for geometric sequence.
[tex]r = \frac{50}{56} \neq \frac{56}{60}[/tex]
There, the sequence is neither arithmetic nor geometric.
4. Given sequence is 36, 12, 4, ...
As the difference between the number is large.
So, we will check for geometric sequence.
[tex]r = \frac{36}{12} = \frac{12}{4} = 3[/tex]
Therefore, the sequence is geometric.
5. Given sequence is 4, 24, ...
The number of terms is very less and hence we can't decide.
There, the sequence is neither arithmetic nor geometric.
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rewrite the function g(x)=2x^2+16x+6 in vertex form by completing the square
The vertex form of the function g(x)= 2[tex]x^2[/tex]+16x+6 is g(x)= 2[tex](x+4)^2[/tex]-26.
What is vertex form of the function?
The function's maximum or lowest possible output is represented by the vertex of the quadratic function's graph. When viewing a graph, the vertex is the highest or lowest point on the parabola. Utilizing the vertex formula is the simplest technique to discover the vertex. It is simple to locate the vertex of the parabola using the vertex form of a quadratic equation. Y=a(xh)2+k is the definition of the generic vertex form, where h is the x-coordinate and k is the y-coordinate of the vertex.
Here the given function is ,
=> g(x) = 2[tex]x^2[/tex]+16x+6
=> g(x) = 2([tex]x^2+[/tex]8x+3)
=> g(x) = 2([tex]x^2+[/tex]8x+16-16+3)
=>g(x) = 2 [[tex](x+4)^2[/tex]-13]
=> g(x)= 2[tex](x+4)^2[/tex]-26
Therefore vertex form of the function is g(x)= 2[tex](x+4)^2[/tex]-26 and vertex is (-4,-26).
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Answer:
g(x)=2(x+4)^2-26
Has a minimum value of -26
Step-by-step explanation:
i got it right!
HELP MEEEE PLEASEEEE
Answer:
24.4 km
Step-by-step explanation:
The Pythagorean theorem states that a^2 + b^2 = c^2, where c is the hypotenuse of the triangle, and a and b are the legs. Plugging in your values, we get:
20^2 + 14^2 = c^2
Simplify: 400 + 196 = c^2
Simplify again: 596 = c^2
Square root both sides to cancel out the exponent on the right: 24.4131=c
Round: 24.4
Suzanne's average daily balance for last month was x dollars. The finance
charge was y dollars.
a. What was the monthly percentage rate?
b. What was the APR?
Part a: Monthly percent rate = y/x
Part b: APR = y/x × 12.
What is meant by the term APR?The annual interest produced by a sum that is paid to investors or charged to borrowers is referred to as the annual percentage rate (APR). APR is a percentage that expresses the actual annual cost of borrowing money over the course of a loan or the income from an investment. An APR might not accurately represent the cost of borrowing but since lenders have some latitude in determining it, excluding some fees.APR and APY (annual percentage yield), a computation that takes interest compounding into account, should not be confused.For the given question;
Average daily balance sheet of Suzanne's is x dollars.
Finance charges = y
Part a: monthly percentage rate
Finance charge = Monthly percent rate × Average daily balance
Monthly percent rate = Finance charge/Average daily balance
Monthly percent rate = y/x
Part b: APR
The annual percentage rate (APR) is calculated by dividing the periodic interest rate even by number of periods in the year that it was in effect. The number of times the rate is applied to a balance is not stated.Thus,
For 12 months.
APR = y/x × 12
Thus, the value of APR for the period of 12 months is APR = y/x × 12 .
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Karama can paint a staircase banister in 50 minutes. Find the rate per minute at which Karama can paint banisters
The rate per minute at which Karama can paint banisters is 0.02.
In the given question,
Karama can paint a staircase banister in 50 minutes.
We have to find the rate per minute at which Karama can paint banisters.
Since we have to find the rate per unit. Rate per unit means how much Karama can paint in one minute.
To find the rate per unit we divide 1 by 50.
As we know that Karama can paint one staircase banister in 50 minute.
So we can write it as
50 minute = 1 staircase banister paint
Now in 1 minute.
1 minute = 1/50 staircase banister paint
Simplifying
1 minute = 0.02 staircase banister paint
Hence, the rate per minute at which Karama can paint banisters is 0.02.
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Pls help ASAP the question is in the picture
Find the equation of the straight line passing through the point (3, 5)
which is perpendicular to the line
y = 3x + 2
Answer:
y = -1/3x +6
Step-by-step explanation:
You want the equation of the line through (3, 5) perpendicular to the line y = 3x +2.
Perpendicular lineThe given equation is in slope-intercept form. This lets us identify its slope as 3.
y = mx + b . . . . . . line with slope m and y-intercept b
y = 3x +2 . . . . . . . line with slope 3 and y-intercept 2
The perpendicular line will have a slope that is the opposite reciprocal of this:
m = -1/3 . . . . slope of the perpendicular line
Point-slope formThe equation for a line with slope m through point (h, k) is ...
y -k = m(x -h)
The equation for a line with slope -1/3 through point (3, 5) is ...
y -5 = -1/3(x -3)
Slope-intercept formSolving for y gives us ...
y = -1/3x +1 +5 . . . . . eliminate parentheses, add 5
y = -1/3x +6 . . . . . equation of the desired line
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