To find the simple interest rate, you can use the following formula:
Simple interest rate = (ending balance - starting balance) / (starting balance * number of years)
In this case, the starting balance is $7,590, the ending balance is $11,916.30, and the number of years is 10. Plugging in these values, we have:
Simple interest rate = ($11,916.30 - $7,590) / ($7,590 * 10)
= ($4,326.30) / ($7,590 * 10)
= $4,326.30 / $75,900
= 0.057 or 5.7%.
Therefore, the simple interest rate is 5.7%.
Answer:
Suppose an investor invested $7,590 in a savings account with basic yearly interest 10 years ago. The account currently has a balance of $11,916.30. 5.7% is the basic interest rate.
Why do we call something "interesting"?
You must pay interest on money you borrow, and you must add interest to money you lend. The most typical approach to display interest is as a percentage of the annualized principal amount of a loan. This ratio represents the interest rate on the loan.
What is meant by an interest example?
By examining the rate, a person can figure out exactly how much interest they will accrue or pay on a loan. For example, if a $100 loan had a nominal interest rate, there would be a $6 interest fee.of 6% ($100 X 0.06). Despite an increase in loan size, the rate doesn't change. Even if the loan amount were increased to$1,000, the borrower would still be expected to pay 6% of the total.
Step-by-step explanation:
Type the correct answer in each box. Use numerals instead of words.
Consider function g.
6,
-8<-2
= 0,
-2 ≤ x ≤ 4
-4,
4x10
What are the values of the function when x = -2 and when = 4?
g(x)
g (-2)
g (4)
=
The values of the function when x = -2 and when = 4 are,
⇒ g (-2) = 0
⇒ g (4) = - 4
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
We have to given that;
The function is,
⇒ g (x) = 6 ; - 8 ≤ x < - 2
= 0 ; - 2 ≤ x ≤ 4
= - 4 ; 4 ≤ x ≤ 10
Now, The value of function are,
At x = - 2;
⇒ g (x) = 6 ; - 8 ≤ x < - 2
= 0 ; - 2 ≤ x ≤ 4
= - 4 ; 4 ≤ x ≤ 10
⇒ g (- 2) = 0
At x = 4;
⇒ g (x) = 6 ; - 8 ≤ x < - 2
= 0 ; - 2 ≤ x < 4
= - 4 ; 4 ≤ x ≤ 10
⇒ g (4) = - 4
Thus, The values of the function when x = -2 and when = 4 are,
⇒ g (-2) = 0
⇒ g (4) = - 4
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A cake has circumference of 2517
inches. What is the area of the cake? Use 227
to approximate π. Round to the nearest hundredth. Enter your answer in the box.
Answer:
Below
Step-by-step explanation:
Circumference = pi * d = 22/7 * d
2517 = 22/7 * d ( are you sure 2517 is correct??)
d = 2517 * 7/22 = 800.86 inches ( a VERY large pie)
radius = 1/2 * d = 400.43 inches
Area = pi r^2
= 22/7 * (400.43)^2 = 503 943 in^2
Solve for x: −12x−7=18
Answer:
x=-2.083
or x=-25/12
Step-by-step explanation:
Answer:
x = -25/12
Step-by-step explanation:
We can solve for x by isolating x:
[tex]((-12x-7)=18)+7\\((-12x=25)/12\\x=-25/12[/tex]
what value of the correlation coefficient implies that there is no relationship between the two variables of a linear regression model?
The correlation coefficient is 0, implying that there is no linear relationship between the two variables.
The correlation coefficient is a measure of how strongly two variables are linearly related. The value of the correlation coefficient is between -1 and +1. A correlation coefficient of zero (0) implies that there is no linear relationship between the two variables. This means that the variables do not change in relation to each other; that is, if one variable goes up, the other variable does not necessarily go up or down.
The formula of correlation coefficient is given by:
r = ∑(x - X)(y - Y)/√[∑(x - X)2∑(y - Y)2]
where,
r = correlation coefficient
x = independent variable
X = mean of independent variable
y = dependent variable
Y = mean of dependent variable
When the correlation coefficient (r) is 0, this means that the two variables have no linear relationship. This can be calculated by substituting the values of x,X, y, and Y in the formula for the correlation coefficient.
For example, if x = 4, X = 3, y = 5 and Y = 4, then the correlation coefficient (r) can be calculated as follows:
[tex]r = [4 - 3)(5 - 4)]/√[(4 - 3)2 (5 - 4)2] r = (1)(1)/√[12] r = 1/√12 r = 1/3.464[/tex]
Thus, the correlation coefficient is 0, implying that there is no linear relationship between the two variables.
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what would this normal probability plot lead you to believe about the normality of the population from which the data were taken?
The normal probability plot can reveal information about the population from which the data were drawn. A straight line pattern indicates normality, whereas deviations from the straight line indicate non-normality.
A normal probability plot is a graphical method for determining whether a set of data values is normally distributed. The plot depicts sample data values on the y-axis and theoretical normal deviate values on the x-axis.
If the plotted points follow a roughly straight line, the population is likely to be normally distributed. If the points plotted deviate significantly from a straight line, the population is not normally distributed.
As a result, the shape of the normal probability plot can provide insight into the normality of the population from which the data were drawn. A straight line pattern indicates that the distribution is normal, whereas deviations from the straight line indicate non-normality.
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identify the coefficient in the expression 3y plus 5
Answer:The coefficient in this expression is 3.
Step-by-step explanation:
What is a Coefficient?
By definition, a coefficient is a numerical or constant quantity placed before and multiplying the variable in an algebraic.
What is a variable?
A variable is a symbol that represents a mathematical object. So for example, 9p + 2. In this equation, the variable would be the letter "p."
sam can jump 4 steps at a time and nina can jump 5 steps at a time. on which of the steps will both meet if both start jumping together?
Sam can jump 4 steps at a time and Nina can jump 5 steps at a time. on 20th of the steps will both meet if both start jumping together. we can find it out with the help of HCM and LCM
GIVEN
Sam can jump four steps at a time and Nina can jump five steps at a time.
TO DETERMINE
On which of the steps will both meet if both start jumping together
EVALUATION
Here it is given that Sam can jump 4 steps at a time and Nina can jump 5 steps at a time.
Now we find the LCM of 4 and 5
Since 4 and 5 are prime to each other
So LCM of 4 and 5 = 4 × 5 = 20
Hence after 20 steps both meet if both start jumping together
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in a study, the sample is chosen by grouping the class by gender, then selecting 10 males and 10 femaleswhat is the sampling method?
The correct answer is Stratified Random Sampling
Given that,
In a study, the sample is selected by dividing the class into gender-based groups, then choosing 10 men and 10 women.
Researchers split a population into homogeneous subpopulations called strata (plural of stratum) depending on particular traits in a stratified sample (e.g., race, gender identity, location, etc.).
In order to estimate statistical measures for each subpopulation, each stratum is then sampled using a different probability sampling technique, such as cluster sampling or simple random sampling.
When a population's traits are varied and researchers want to make sure that each characteristic is accurately represented in the sample, they rely on stratified sampling. This aids in the study's validity and generalizability while preventing biases in the research process like undercoverage bias.
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suppose that x is the number of cars per minute that pass through a certain intersection, and that x has the poisson distribution. if the mean of x is equal to 9 cars, what is the standard deviation of x? 3 cars2 3 cars per minute 3 cars 32 cars
The standard deviation of x is 3 cars. So the option A is correct.
Suppose that x is the number of cars per minute that pass through a certain intersection, and that x has the Poisson distribution.
If the mean of x is equal to 9 cars, then we have to determine the standard deviation of x.
An indicator of how much variance from the mean there is is the standard deviation, which can be expressed as spread, dispersion, or spread. A "typical" departure from the mean is represented by the standard deviation. As a result of returning to the data set's original units of measure, it is a well-liked measure of variability.
The Mean = 9 cars
Standard Deviation = Square Root of Mean
Standard Deviation = √9
Standard Deviation = 3 cars
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In the diagram, the measurements that are labeled are known, while the other measurements are unknown. Which measurement of acute triangle ABC can you find by direct substitution of the labeled measures in the Law of Sines?
The measurement of acute triangle ABC we can find by direct substitution of the labeled measures in the Law of Sines is,
a/ sin a = b/sin b
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know the sine rule for a triangle ABC is, a/sinA = b/sinB = c/sinC .
In the diagram, there are two identified sides and if you use the sine rule, you can find the opposed angles easily.
Side a, with angle A.
Side b, with angle B.
If you input these into the sine rule, it would be, a/ sin a = b/sin b
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My friend Rew has either no more than 5 totts or more than 10 totts. Graph the compound inequality
The compound inequality would be: 0 <= x <= 5 or x >= 10
How to graph the compound inequalityFrom the question, we have the following parameters that can be used in our computation:
no more than 5 totts or more than 10 totts
Represent the variable with s
So, we have the following representation
x no more than 5 totts or x more than 10 totts
As an inequality, we have
0 <= x <= 5 or x >= 10
See attachment for the graph
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90. Last week we drove to Detroit. At an
average speed of 50 miles per hour, the
trip took 4 1/2 hours. How far was it?
The distance travelled was 225 miles.
What is Speed?Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.
Speed is a scalar quantity as it only has magnitude and no direction.
Given that,
Average speed = 50 miles per hour
Time taken = 4 1/2 hours = 4.5 hours
Speed can be calculated using the formula,
Speed = Distance / Time
Distance = Speed × Time
= 50 × 4.5
= 225 miles
Detroit was 225 miles away.
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leonard wants to cut identical square as big as he can from a piece of paper 168 mm by 196 mm. what is the length of each square?
The length Thebe the HCF (highest common factor) of the given dimensions that are 168mm and 196 mm. Hence, the length of each square will be equal to 28mm.
The greatest of all their common factors is the Highest Common Factor (HCF) of two or more numbers. As a result, it is also known as the greatest common factor (GCF). If M is the greatest common factor of N, then M is the greatest possible number that divides N.
The length of the each square will be given by the HCF of the dimensions that are 168mm and 196mm.
[tex]168=2*2*2*3*7\\196=2*2*7*7[/tex]
So, the length of the each square paper=[tex]2*2*7=28mm.[/tex]
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he owner of a used tire store wants to construct a fence to enclose a rectangular outdoor storage area by using part of one side of the store, which is 240 feet long, as one of the sides of the enclosed area. there are 460 feet of fencing available for the other three sides of the enclosure. find the dimensions of the outdoor enclosure with the most area.
The length and width each need to be 230 feet, and the area of the outdoor enclosure will be A=(230)(230)=52900 sq. ft.
The owner of the used tire store wants to construct a fence to enclose a rectangular outdoor storage area. The side of the store is 240 feet long and there are 460 feet of fencing available for the other three sides. The formula for the area of a rectangle is A=LxW, where A is the area, L is the length, and W is the width. To find the dimensions of the outdoor enclosure with the most area, the length and width must be equal so that all of the fencing is used. Therefore, the length and width each need to be 230 feet, and the area of the outdoor enclosure will be A=(230)(230)=52900 sq. ft.
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Given the km represents an angle bisector, find the value of x.
In ΔJKL using the angle bisector theorem the value for x is obatined as 48.6 units.
What is angle bisector theorem?
The opposite side of a triangle is divided into two pieces by the angle bisector in proportion to the other two sides. If the interior point of a triangle is equally spaced from its two sides, that point will be on the angle bisector of the angle created by the two line segments.
The measurement for line segment JK = 54 units.
The measurement for line segment LK = x units.
The measurement for line segment LM = 36 units.
The measurement for line segment JM = 40 units.
In ΔJKL line segment KM is an angle bisector.
So, according to the angle bisector theorem -
JM / LM = JK / LK
Substitute the values in the equation -
40 / 36 = 54 / x
Simplify to find the value of x -
x = (54 × 36) / 40
x = (27 × 9) / 5
x = 48.6 units
Therefore, the value of x is 48.6 units.
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Write the linear equation for the graph of line q.
y = x+
Using the graph we will see that line q can be written as:
y = (-1/2)*x + 3
How to write the linear equation q?Remember that the general linear equation is written as:
y = a*x +b
Where a is the slope and b is the y-intercept.
We know that if the line passes through two points (x₁, y₁) and (x₂, y₂) then the slope is:
a = (y₂ - y₁)/(x₂ - x₁)
Using the graph we can identify the two points (0, 3) and (2, 2), then the slope is:
a = (2 - 3)/(2 - 0) = -1/2
And the y-intercept is y = 3, then the linear equation is:
y = (-1/2)*x + 3
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CAN ANYONE PLSS HELP ME
Answer:
a = 5.76b = 8.69C = 85°Step-by-step explanation:
You want to solve the triangle with A=35°, B=60°, and c=10.
Law of SinesWhen two angles and a side are given, the Law of Sines is useful for providing a solution. In order to use it, we need to know an angle and its opposite side. That is, we need angle C.
Using the sum of angles of a triangle, we have ...
A +B +C = 180°
C = 180° -A -B = 180° -35° -60° = 85°
Now, we can use ...
a/sin(A) = b/sin(B) = c/sin(C)
b = c·sin(B)/sin(C) = 10·sin(60°)/sin(85°) ≈ 8.69
a = c·sin(A)/sin(C) = 10·sin(35°)/sin(85°) ≈ 5.76
a frozen yogurt factory makes 100 quarts of frozen yogurt in 5 hours. how many quarts could be made in 36 hours
The required quarts of frozen yogurt made in 36 hours as per the given information is equal to 720 quarts.
Quarts of frozen yogurt made by factory is equal to 100 quarts
Time required to make 100 quarts of frozen yogurt is equal to 5 hours
Let 'x' quarts of frozen yogurt made in 36 hours
5 hours = 100 quarts of frozen yogurt
⇒ 1hour = ( 100 / 5 ) quarts of frozen yogurt
⇒ 36 hours = ( 100 / 5 ) × ( 36 ) quarts of frozen yogurt
⇒ 36 hours = ( 20 ) × ( 36 ) quarts of frozen yogurt
⇒ 36 hours = ( 720 ) quarts of frozen yogurt
Therefore, the quarts of frozen yogurt made in 36 hours is equal to 720 quarts.
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suppose we want to estimate family size, where family is defined as one or more parents living with children. if we select students at random at an elementary school and ask them what their family size is, will our average be biased? if so, will it overestimate or underestimate the true value?
Yes, the average family size obtained from asking students at an elementary school would likely be biased. The average is likely to underestimate the true value of the family size for the population.
This is because a student’s family size only includes individuals who are living in the same household as the student and not everyone in the family.
For example, the student's siblings who have left the household to attend college or have moved out for other reasons would not be included in the student's family size estimate. Additionally, grandparents, uncles, aunts, and cousins who may also be part of the family are not included. Thus, the average family size obtained from asking students would be lower than the true average family size for the population.
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On Monday, Florencia's hair was H centimeters long. She got a haircut on Tuesday, so her hair was only 75% percent of the length it was on Monday.
Which of the following expressions could represent how many centimeters long Florencia's hair was after the haircut?
Choose 2 answers
The two forms of representing her hair length are (3/4)H cm and 0.75H cm.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, On Monday, Florencia's hair was H centimeters long.
Therefore, After the hair cut her hair length will be,
= (75/100)×H.
= (3/4)H cm.
Now, We can also write it in terms of decimals which is,
= (75/100)×H.
= 0.75H cm.
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35 is 70% of what number? 50 55 60 75
Answer: 35 is 70% of 50
Step-by-step explanation:
Steps to solve "35 is 70 percent of what number?"
We have, 70% × x = 35
or,
70
100
× x = 35
Multiplying both sides by 100 and dividing both sides by 70,
we have x = 35 ×
100
70
x = 50
If you are using a calculator, simply enter 35×100÷70, which will give you the answer.
Answer:
50
Step-by-step explanation:
35 + 15 = 50
---------------------------
15 is 30% of 50 There fore 50 is the correct answer
I took this exam, its the 5.08 Ratios and rates practice exam right?
Have an amazing Day and good luck (:
Graph the inequality.
The graph of the inequality -3x + y ≥ 1 is given below.
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Given:
An inequality:
-3x + y ≥ 1.
The intercepts are (0, 1) and (-0.33, 0)
The graph of the inequality is given in the attached image.
Therefore, the graph is given.
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PLEASE HELP ASAP!!!!
A music store sells CD's with a 50% markup. If the store buys the CD for $7.80, what is the markup? What is the selling price?
(a) The markup is $3.9.
(b) The selling price of the CD is $11.70.
What is the markup?
The markup of the CD is calculated by applying the following formula.
The markup = 50% x $7.80
The markup = ( 50 / 100 ) x $7.80
The markup = 0.5 x $7.80
The markup = $3.9
The selling price of the CD is calculated as follows;
selling price = $7.80 + $3.9
selling price = $11.7
Thus, the selling price of the CD is a function of the cost price, and mark up price. So the final selling price of the CD is $11.7 while the mark up is $3.9
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Nathan and Jackson are each saving money.
• Nathan has $15 saved and plans to save $5 more each week.
• Jackson has $25 saved and plans to save $4 more each week.
How many weeks will it be before both boys have saved the same amount of money?
Answer:
Nathan will make $20
Jackson will make $29
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The total cost (in dollars) of producing x food processors is C(x) = 2300 +20x−0.1x².
(A) Find the exact cost of producing the 41st food processor.
(B) Use the marginal cost to approximate the cost of producing the 41st food processor.
How do I simplify this expression?:
15x - 7x
-----------
2x
i need help question is below
The correct proportion to represent the triangle ABC is similar to triangle PQR is,
⇒ 4 / 9 = 12 / n
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
We have to given that;
Triangle ABC is similar to triangle PQR.
Hence, Corresponding sides of both triangles are equal to each other.
So, We ca formulate;
⇒ Base / Hypotenuse
⇒ 4 / 9 = 12 / n
Thus, Correct proportion to represent the triangle ABC is similar to triangle PQR is,
⇒ 4 / 9 = 12 / n
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jesse engages in self-injurious behavior every time he is denied access to the ipad. each time this occurs, you tally one mark on your data sheet which represents this type continuous measurement?
Jesse engage in self injuries behavior every time he is denied access to the ipad and when it occurs we tally one mark on the data sheet it represents the Frequency
The frequency (f) of a specific fee is the variety of times the value takes place in the facts. The distribution of a variable is the pattern of frequencies, that means the set of all viable values and the frequencies associated with those values. Frequency distributions are portrayed as frequency tables or charts.
As a statistical device, a frequency distribution affords a visible illustration of the distribution of observations within a particular check. Analysts often use a frequency distribution to visualise or illustrate the facts accrued in a pattern
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What is the 5th term in the expansion of (1/2x³y² - 4y)^9?
Drag a value into each box to correctly express the term. Apply the convention of a leading numerical coefficient and variables listed
in alphabetical order.
The fifth term of the expansion by using Binomial Expansion is +1008x¹⁵y¹⁴.
What is Binomial Expansion?When algebraic identities cannot be employed to extend a binomial, the binomial expansion formulae are used to determine the powers of the binomials.
The expansion of (x + y)^n is given by this binomial expansion formula, where n is a natural number. There are (n + 1) terms in the expansion of (x + y)^n.
Given that:
[tex]=(\dfrac{1}{2}x^3y^2-4y)^9[/tex]
Use the binomial expansion theorem to find each term. The binomial theorem states [tex](a+b)^n = \sum \limits^n_{k=0}nCk*(a^{n-k}b^k)[/tex]
[tex]\sum \limits^9_{k=0} \dfrac{9!}{(9-k)!k!}* (\dfrac{1}{2}*(x^3y^2))^{9-k}*(-4y)^k[/tex]
Expand the summation.
[tex]=\dfrac{9!}{(9-0)!0!}*(\dfrac{1}{2}*(x^3y^2)^{9-0}*(-4y)^0+ \dfrac{9!}{(9-1)!1!}*(\dfrac{1}{2}*(x^3y^2)^{9-1}*(-4y)^1+...+\dfrac{9!}{(9-9)!9!}*(\dfrac{1}{2}*(x^3y^2)^{9-9}*(-4y)^9[/tex]
Simplify the exponents for each term of the expansion.
[tex]=1*(\dfrac{1}{2}*(x^3y^2)^{9}*(-4y)^0+ 9*(\dfrac{1}{2}*(x^3y^2)^{8}*(-4y)^1+...+1*(\dfrac{1}{2}*(x^3y^2)^{0}*(-4y)^9[/tex]
Simplify the polynomial result.
[tex]=\dfrac{x^{27}y^{18}}{512}-\dfrac{9x^{24}y^{17}}{64}+\dfrac{9x^{21}y^{16}}{2}-84x^{18}y^{15}+1008x^{15}y^{14}-8064x^{12}y^{13}+43008x^9y^{12}-147456x^6y^{11}+294912x^3y^{10}-262144y^9[/tex]
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The sum of one-third of a number and one-quarter of the same number is 28.
Find the number.
Answer: 90
Step-by-step explanation:
The number that you need to find because it is missing in the equation is 48.
How do I find the number?Let's assume the number we're trying to find is "x."
According to the problem, one-third of the number is (1/3)x, and one-fourth of the number is (1/4)x.
We're told that the sum of one-third of the number and one-fourth of the number is 28, so we can write the equation as follows:
(1/3)x + (1/4)x = 28
To solve this equation, we need to find a common denominator. The least common multiple of 3 and 4 is 12, so we can rewrite the equation as:
(4/12)x + (3/12)x = 28
Combining the fractions, we get:
(7/12)x = 28
To isolate x, we multiply both sides of the equation by the reciprocal of (7/12), which is (12/7):
x = 28(12/7)
Simplifying the right side of the equation, we have:
x = 48
Therefore, the number we're looking for is 48.
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