Use the graph to answer the question. Graph of a polygon ABCD with vertices at 4 comma 4, 12 comma 4, 12 comma 8, 4 comma 8 and a second polygon A prime B prime C prime D prime with vertices at 1 comma 1, 3 comma 1, 3 comma 2, 1 comma 2. Determine the scale factor used to create the image. one half 2 one fourth 2.5
Answers
Given polygons ABCD and A'B'C'D' have scale factors of 1/4 since their respective side ratios are the same.
What is scale-factor?The amount by which a shape is made smaller or larger is referred to as its scale factor. This method is employed when a 2D polygon, irregular or regular shape, such as a circle, triangle, square, or rectangle, needs to be enlarged larger. In the equation y = px, p is the scale factor for x. One may identify the scale factor between any two shapes or figures by comparing the measurements of the new shape to those of the prior shape.
Scale factor = Dimensions of new shape/Dimensions of original shape
given the original polygon's coordinates:
A(4,4) ; B(12,4) ; C(12,8) ; D(4,8)
Distance AB = X₂ - X₁
= 12 - 4
= 8 units
Distance BC = Y₂ - Y₁
= 8 - 4
= 4 units
Distance CD = X₂ - X₁
= 12 - 4
= 8 units
Distance DA = Y₂ - Y₁
= 8 - 4
= 4 units
Added coordinates for the new polygon:
A'(1,1) ; B(3,1) ; C(3,2) ; D(1,2)
Distance A'B' = X₂ - X₁
= 3 - 1
= 2 units
Distance B'C' = Y₂ - Y₁
= 2 - 1
= 1 units
Distance C'D' = X₂ - X₁
= 3 - 1
= 2 units
Distance D'A' = Y₂ - Y₁
= 2 - 1
= 1 units
Scale factor = [tex]\frac{A^{\prime} B^{\prime}}{A B}=\frac{B^{\prime} C^{\prime}}{B C}=\frac{C^{\prime} D^{\prime}}{C D}=\frac{D^{\prime} A^{\prime}}{D A}[/tex]
[tex]\frac{A B}{A^{\prime} B^{\prime}}=\frac{2}{8}=\frac{1}{4}\\\\\frac{B^{\prime} C^{\prime}}{B C}=\frac{1}{4}\\\\\frac{C^{\prime} D^{\prime}}{C D}=\frac{2}{8}=\frac{1}{4}\\\\\frac{D^{\prime} A^{\prime}}{D A}=\frac{1}{4}[/tex]
Scale factor = [tex]\frac{A^{\prime} B^{\prime}}{A B}=\frac{B^{\prime} C^{\prime}}{B C}=\frac{C^{\prime} D^{\prime}}{C D}=\frac{D^{\prime} A^{\prime}}{D A}=\frac{1}{4}[/tex]
The image was reduced using a one-fourth scale factor.
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Refer to the attachment for the graph.
Related Questions
What is the longest line segment that can be drawn in a right rectangular prism that is 14 cm long, 13 cm wide, and 8 cm tall?
NEED ANSWERED ASAP!
Answers
To find the length of the space diagonal, we can use the Pythagorean theorem in three dimensions:
d^2 = l^2 + w^2 + h^2
where d is the length of the space diagonal, l is the length of the prism, w is the width of the prism, and h is the height of the prism.
Substituting the given values, we get:
d^2 = 14^2 + 13^2 + 8^2
d^2 = 196 + 169 + 64
d^2 = 429
d = sqrt(429)
d ≈ 20.7 cm
Therefore, the longest line segment that can be drawn in the right rectangular prism is approximately 20.7 cm long.
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Give the equation of a rational function which has all of the properties above.
Answers
To find the equation of a rational function that satisfies the given properties, we can use the fact that a rational function can be written as the quotient of two polynomials. We know that the function has x-intercepts at (2,0) and (6,0), which means that the denominator must contain factors of (x-2) and (x-6):
r(x) = A(x-2)(x-6)/...
where A is a constant coefficient that we need to determine and the ellipsis (...) represents the remaining factors of the denominator.
We also know that there is a hole at x=1, which means that both the numerator and denominator have a factor of (x-1). To ensure that the hole cancels out, we can simplify the expression by dividing both the numerator and denominator by (x-1):
r(x) = A(x-2)(x-6)/(x-1)(x-1)... (1)
Now, we need to include the vertical asymptotes at x=5 and x=3. This means that the denominator must contain factors of (x-5) and (x-3). However, we also need to ensure that the end-behavior of the function is given by f(x) -> 1 as x -> ± infinity. This can be achieved by making the degree of the numerator equal to the degree of the denominator, and ensuring that the leading coefficient of the numerator is equal to the leading coefficient of the denominator.
To achieve this, we can set the denominator to be (x-5)(x-3)^2, and choose the numerator to be a constant multiple of (x-1)(x-1):
r(x) = A(x-2)(x-6)/(x-1)(x-1)(x-5)(x-3)^2
Now, we need to determine the value of the constant A. Since we know that r(x) has a hole at x=1, we can use the fact that the limit of r(x) as x approaches 1 must exist and be finite. This means that the factors of (x-1) must cancel out in the numerator and denominator, and we can use this to solve for A:
lim(x->1) r(x) = lim(x->1) A(x-2)(x-6)/(x-1)(x-1)(x-5)(x-3)^2
= A(-1)(-5)/(-4)^3
= 5A/64
We know that the limit must exist and be finite, and we also know that it must equal some number k, since r(x) has a hole at x=1. Therefore, we can set 5A/64 = k, and solve for A:
A = 64k/5
Substituting this value of A into equation (1), we get the final equation for r(x):
r(x) = (64k/5)(x-2)(x-6)/(x-1)(x-1)(x-5)(x-3)^2
where k is any non-zero constant.
Answer:
One possible rational function that satisfies the given properties is:
r(x) = (x-2)(x-6) / [(x-3)(x-5)]
Step-by-step explanation:
x-intercepts at (2,0) and (6,0)
The x-intercepts are the points where the function crosses the x-axis, i.e., where the function value is zero. Since we are given that the function has x-intercepts at (2,0) and (6,0), we know that the function can be factored as:
r(x) = A(x-2)(x-6)
where A is a constant that we need to determine.
A hole at x=1 and vertical asymptotes at x=5 and x=3
A hole in a rational function occurs when there are factors in the numerator and denominator that cancel out, leaving a "hole" in the graph. In this case, we are given that there is a hole at x=1, which means that there must be a common factor of (x-1) in both the numerator and denominator. So, we can write:
r(x) = A(x-2)(x-6) / (B(x-1)(x-3)(x-5))
where B is another constant that we need to determine.
We are also given that there are vertical asymptotes at x=5 and x=3, which means that the denominator must have factors of (x-5) and (x-3) that do not cancel out with any factors in the numerator. So, we can write:
r(x) = A(x-2)(x-6) / (B(x-1)(x-3)(x-5)) = [A(x-2)(x-6)] / [(B(x-1))(x-3)(x-5)]
End behavior given by x → ∞ ,f(x) → 1 and x → -∞ ,f(x) → 1
The end behavior of a rational function is determined by the degree of the numerator and denominator. Since the numerator and denominator in this case have the same degree (3), we know that the end behavior is given by the ratio of the leading coefficients, which is A/B. We are told that the end behavior approaches 1 as x approaches infinity or negative infinity, so we can set A/B = 1 and solve for A in terms of B:
A/B = 1, so A = B
Putting it all together
We now have enough information to write the equation for the rational function with the given properties:
r(x) = A(x-2)(x-6) / (B(x-1)(x-3)(x-5))
Using A = B, we get:
r(x) = A(x-2)(x-6) / [A(x-1)(x-3)(x-5)]
Canceling out the common factor of (x-1) in the numerator and denominator, we get:
r(x) = (x-2)(x-6) / [(x-3)(x-5)]
which is the equation for the desired rational function.
2, 8, 18, 32, …
This sequence can be represented by the explicit function f(x) = 2x^2
True or False?
Answers
Answer:
False.
To determine if the sequence 2, 8, 18, 32, ... can be represented by the explicit function f(x) = 2x^2, we can test whether this formula generates the terms of the sequence.
When x = 1, we have f(1) = 2(1)^2 = 2, which is the first term of the sequence.
When x = 2, we have f(2) = 2(2)^2 = 8, which is the second term of the sequence.
However, when x = 3, we have f(3) = 2(3)^2 = 18, which is the third term of the sequence. But the fourth term of the sequence is 32, which is not generated by the formula f(x) = 2x^2 when x = 4.
Therefore, the sequences 2, 8, 18, 32, ... cannot be represented by the explicit function f(x) = 2x^2.
what is the quotient of 837 and 26
Answers
Answer:
The quotient of 837 divided by 26 is approximately 32.2692 (rounded to four decimal places).
What is the value of u?
Answers
since its on a straight line we instantly know that u+100=180 since a straight line is 180 degrees. From thay we can easily find out that u=180-100=80. So u is 80 degrees. Also pls mark as brainliest answer thx.
Answer:
u=180
Step-by-step explanation:
The two angles add together to form a straight line, so they add to 180
100+u = 180
u = 180-100
u= 80
A bag contains 2 gold marbles, 10 silver marbles, and 29 black marbles. The rules of the game are as follows: You randomly select one marble from the bag. If it is gold, you win $6, if it is silver, you win $4. If it costs $1 to play, what is your expected profit or loss if you play this game?
Answers
Answer:
33 thats with the 1 dollar subtracted for the entry fee
Step-by-step explanation:
first you add all the number of marbles you have then you get 41 then divide it by 12 because you have 2 gold and 10 silver and you get 3.4 and multiply that by 10 because its 6 and 4 and you get 34 subtract the entry fee
To be able to buy a new computer, Lisa decides to save for 5 years. She opens a savings account with $600. The account pays simple interest at an annual rate of 4%. She doesn't make any more deposits. Answer the following questions. If necessary, refer to the list of financial formulas. (a) How much total interest will Lisa earn? ${ (b) What will the total amount in the account be (including interest)? $ X
Answers
Okay, here are the step-by-step solutions:
(a) To find the total interest earned:
* Lisa opened the account with $600.
* The interest rate is 4% annually.
* The account earns simple interest for 5 years.
So:
Interest rate = 4%
Principal amount = $600
Time = 5 years
Interest = (Interest rate) x (Principal amount) x (Time)
= (0.04) x ($600) x (5 years)
= $200
Therefore, the total interest earned is $200
(b) To find the total amount in the account (principal + interest):
Principal amount = $600
Interest earned = $200
Total amount = Principal amount + Interest earned
= $600 + $200
= $800
So the total amount in the account including interest is $800
Does this make sense? Let me know if you have any other questions!
What is the equivalent to this
Answers
None of the given options A, B, C, or D is correct as they all provide different answers.
what is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.
The question asks for the equivalent of 6 × 2. This means that we need to find a number that is equal to the result of multiplying 6 and 2 together.
When we multiply 6 and 2, we get:
6 × 2 = 12
So, the equivalent of 6 × 2 is 12.
However, none of the answer options provided matches this answer.
Option A suggests that the equivalent of 6 × 2 is 2 × 1, which is equal to 2, not 12.
Option B suggests that the equivalent of 6 × 2 is 3 × 2, which is equal to 6, not 12.
Option C suggests that the equivalent of 6 × 2 is 9 × 3, which is equal to 27, not 12.
Option D suggests that the equivalent of 6 × 2 is 18 × 1/2, which is equal to 9, not 12.
Therefore, none of the options provided is correct.
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How do I solve this problem?
Answers
The measure of angle CFE is determined as 29⁰.
What is the measure of angle CFE?The measure of angle CFE is calculated by applying the following formula.
The intersecting chord theorem, also known as the intersecting chords inside and outside theorem, is a geometric property that applies to chords (line segments that connect two points on the circumference of a circle) that intersect inside or outside a circle.
Based on the angle of intersecting chord theorem, we will have the following equation.
m∠CFE = ¹/₂( arc angle CE )
arc CE = 360 - 302 (sum of angles in a circle)
arc CE = 58⁰
m∠CFE = ¹/₂ x 58
m∠CFE = 29⁰
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Show that by the uniqueness theorem the linear transformation,
Y = aX + b, is also a normal random variable.
Answers
We can show by the uniqueness theorem that the linear transformation, Y = aX + b, is also a normal random variable because the resultant probaility density fnction of Y equals: f(y) = (1/√(2πa^2σX^2)) * exp(-(y-aμX-b)^2/(2a^2σX^2)).
How to prove a normal random variableTo show that the linear transformation, Y = aX + b is a normal random variable, we need to demonstrate that it satisfies the properties of a normal distribution. This means that it should have a bell-shaped probability density function, mean, and variance.
We can prove that it meets the mean condition this way:
E(Y) = E(aX + b) = aE(X) + b = aμX + b
Next, we can prove that it meets the variance condition thus:
Var(Y) = Var(aX + b) = a^2Var(X) = a^2σX^2
Lastly, the probability density function is given as f(y) = (1/√(2πa^2σX^2)) * exp(-(y-aμX-b)^2/(2a^2σX^2)). This proves that the conditions for a normal random variable is met.
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2. Mrs. Cooper created a triangular shaped vegetable garden and needs to put down fertilizer to cover the space. If the garden has a base of 8m and a height of 10m, how much fertilizer will she need?
Answers
Answer:
40 m²
Step-by-step explanation:
Area of triangle:
To find the area of triangle, multiply the base and area and then divide it by 2.
base = b = 8 m
height = h = 10m
[tex]\boxed{\bf Area \ of \ triangle = \dfrac{1}{2}*b*h}[/tex]
[tex]= \dfrac{1}{2}*8 * 10\\\\= 4 * 10\\\\= 40 \ m^2[/tex]
6. WRITING IN MATH Describe why the
difference of squares pattern has no middle term
with a variable. Example w-121
Answers
The two middle terms, -11w and +11w, cancel each other out, leaving only the first and last terms. This is why there is no middle term with a variable in the factorization of the difference of squares pattern.
How do you find a middle term?When expanding a binomial expression in the form of (a + b)ⁿ, the middle term can be found using the following formula:
Middle term coefficient = nC(k), where k = (n+1)/2 if n is odd, and k = n/2 or (n/2 + 1) if n is even. The middle term coefficient is then multiplied by the product of a raised to the power of (n-k) and b raised to the power of k.
The difference of squares pattern is a special algebraic pattern that arises when we factor a polynomial that is the difference between two perfect squares. For example,
x² - y² = (x+y)(x-y)
When we apply this pattern to the expression w - 121, we can rewrite it as:
w² - 11²
And, we can use the difference of squares pattern to factor it as:
(w + 11)(w - 11)
Notice that there is no middle term with a variable in this factorization. This is because when we multiply (w + 11)(w - 11), the middle term cancels out.
To see why this happens, let's expand the product:
(w + 11)(w - 11) = w² - 11w + 11w - 121
The two middle terms, -11w and +11w, cancel each other out, leaving only the first and last terms. This is why there is no middle term with a variable in the factorization of the difference of squares pattern.
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Sam has a goal of walking 3 1/2 miles by the end of the day. He walks 1 1/8 miles before lunch and 3/4 mile after resting. What is the remaining distance, in miles, that Sam needs to walk to reach his goal?
Answers
Remaining distance left to cover his goal = 13/8 miles
What is Distance?Distance is an object's overall motion in a directionless fashion. Regardless of the starting or ending point, distance can be defined as the amount of space an object has covered.
What is Fraction?In mathematics, a fraction is used to represent a portion or component of the whole. It stands for the equally important components of the whole. The numerator and denominator are the two components of a fraction. The numerator is the number at the top, while the denominator is the number at the bottom. The denominator specifies the total number of equal parts in the whole, whereas the numerator specifies the number of equal parts taken.For example, 5/10 is a fraction.
Here, 5 is a numerator and 10 is a denominator.
According to question,
Total distance by sam = 7/2 miles
Distance walked before lunch = 9/8 miles
Distance walked after resting = 3/4 miles
Remaining distance needed to cover = 7/2-(9/8+3/4)
=7/2-15/8
=13/8 miles
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Given: The radius of circle Q is 6.
Segments XY, YZ, and XZ are tangent to circle Q.
XY = 18
.e
What is the area of AXYZ?
O 162 square units
O432 square units
O 270 square units
O 216 square units
Answers
The answer to the question is O 216 square units
Convert: 83.36m= cm
pls help
Answers
Answer: 8,336
Step-by-step explanation:
So 1 meter is equal to 100 centimeters. All you have to do is multiply 83.36 by 100.
83.36 * 100 = 8,336
Hope this helps!!! :)
Triangle ABC with vertices at A(−4, −4), B(8, 8), C(2, 6) is dilated to create triangle A′B′C′ with vertices at A′(−2, −2), B′(4, 4), C′(1, 3). Determine the scale factor used. 2 one half 4 one fourth
Answers
Answer: It is similar to triangle ABC and has coordinates A′(8, −12), B′(4, −16), and C′(−20, 8)
Step-by-step explanation: Dilated triangles are never congruent, only similar (unless the dilation factor is exactly 1).
The coordinates of an image dilated about the origin are those of the pre-image multiplied by the dilation factor. For example,
A' = 2A
A'(8, -12) = 2×A(4, -6)
These facts are all you need to know to choose the correct answer (shown above).
Answer: 1/2
Step-by-step explanation:
I took the quiz!
A farmer counted the number of apples on each tree in his orchard. How many trees have at least 21 apples but fewer than 80 apples?
Answers
Answer: We can solve this problem by counting the number of trees that have at least 21 apples and subtracting the number of trees that have at least 80 apples.
Let T be the total number of trees in the orchard, and let n1 be the number of trees that have at least 21 apples, and n2 be the number of trees that have at least 80 apples. Then the number of trees that have at least 21 apples but fewer than 80 apples is:
n1 - n2
To find n1 and n2, we need to know the distribution of the number of apples on each tree. Without this information, we can't find an exact answer. However, we can make some reasonable assumptions and estimate the answer.
Assuming that the number of apples on each tree follows a normal distribution with mean μ and standard deviation σ, we can use the empirical rule (also known as the 68-95-99.7 rule) to estimate the proportion of trees that have at least 21 apples and at least 80 apples. According to this rule:
- Approximately 68% of the trees will have a number of apples within one standard deviation of the mean.
- Approximately 95% of the trees will have a number of apples within two standard deviations of the mean.
- Approximately 99.7% of the trees will have a number of apples within three standard deviations of the mean.
Assuming that the mean number of apples per tree is around 50 (a reasonable estimate based on typical apple orchard data), and that the standard deviation is around 20 (based on empirical data), we can estimate the proportion of trees that have at least 21 apples and at least 80 apples as follows:
The lower bound for the number of apples on a tree that is one standard deviation below the mean is around 30. Therefore, approximately 16% of the trees will have at least 21 apples.
The upper bound for the number of apples on a tree that is two standard deviations above the mean is around 90. Therefore, approximately 2.5% of the trees will have at least 80 apples.
Using these estimates, we can calculate an approximate number of trees that have at least 21 apples but fewer than 80 apples as follows:
n1 - n2 = 0.16T - 0.025T = 0.135T
Therefore, approximately 13.5% of the trees in the orchard have at least 21 apples but fewer than 80 apples. If we know the exact distribution of the number of apples on each tree, we could calculate a more precise answer.
Step-by-step explanation:
April buys soil for her flowerpots. she uses 9 kilograms of soil for her violets and 4 kilograms of soil for her tulips. she has 3,000 grams of soil left for some daisies (1 kilogram = 1,000 grams) use the drop down menus to show how much soil she bought
Answers
April bought 16 kilograms of soil in total.
To show how much soil April bought
We need to add the amounts of soil she used for her violets and tulips. Since April used kilograms for violets and tulips, we need to convert the 3,000 grams to kilograms before we can add them up.
April bought:
9 kilograms of soil for violets
4 kilograms of soil for tulips
3 kilograms of soil for daisies (since 3,000 grams is 3 kilograms)
Therefore, April bought 16 kilograms of soil in total.
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Select all of the following indicators which would cause you to reject normality for a sample of data
Answers
The indicators which would cause you to reject normality for a sample of data are:
A histogram of the data shows bar heights decreasing from left to right.
A histogram of the data shows bar heights decreasing from right to left.
What is sample?In statistics, a sample refers to a group of individuals, objects, or observations selected from a larger population. The sample is chosen to represent the population and to provide information about the characteristics, behavior, or preferences of the population. Sampling is a common method used in statistical analysis to estimate population parameters, such as the mean or standard deviation. By analyzing the sample data, researchers can draw inferences about the population from which the sample was drawn.
Here,
Both of these indicators suggest that the data is not symmetric and may have a skewed distribution. The following indicators suggest that the data is likely normally distributed:
A normal probability plot of the data follows a linear pattern.
A histogram of the data shows that all bars have similar heights.
A normal probability plot is a graphical tool used to assess the normality of a data set. If the plot follows a straight line, it suggests that the data is normally distributed. Similarly, a histogram with bars of similar heights suggests that the data is symmetric and may be normally distributed.
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PROBABILITY:
b) A Jar contains four green tickets numbered one to four,
Six blue tickets numbered one to six, and two red tickets
numbered one to two. You randomly pick a ticket.
Answers
The probability of picking a blue marble or a marble with an odd number is 7/9.
How to solve the probabilityWe can use set theory to calculate the probability of picking a blue marble or a marble with an odd number. Let B be the set of blue marbles and O be the set of marbles with odd numbers. Then, we need to calculate the probability of the union of B and O.
P(B or O) = P(B U O) = P(B) + P(O) - P(B and O)
We know that P(B) = 4/9 and P(O) = 5/9. To calculate P(B and O), we need to count the number of marbles that satisfy both conditions, i.e., they are blue and have an odd number. There are two such marbles: B1 and B3.
Therefore, P(B and O) = 2/9, and the probability of picking a blue marble or a marble with an odd number is:
P(B or O) = P(B U O) = P(B) + P(O) - P(B and O) = 4/9 + 5/9 - 2/9 = 7/9
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during the winter months, Starbucks has a sale every 4 days and a McCafe has a sale every 5 days. If stores had a sale today, when is the next time both stores will have sales on the same day
Answers
Check the picture below.
so we can just look at it as the LCD and 4 and 5 is 20, so they'll have a simultaneous sale every 20 days or every LCD time.
An equipment was purchased from China and arrived at Kampala at a value of shs.5,000,000 shs with transport cost of 800,000 shs. and total taxes amounted to 1,500,000 the equipment is expected to be useful for 6 years and an estimated salvage value of 1,300,000 shs. calculate the depreciation expense for each year and accumulated depreciation upto year 6. Using the straight line method.
Answers
The depreciation expense for each year is 1,000,000 shs.
Accumulated depreciation up to year 6 is 6,000,000 shs.
How to calculate depreciation using the straight line method?The depreciation using the straight line method is given by the formula:
Depreciation expense per year = (Initial cost - Salvage value) / Useful life
Initial cost = 5,000,000 + 800,000 + 1,500,000 = 7,300,000 shs.
Salvage value = 1,300,000 shs.
Depreciation expense per year = (7,300,000 - 1,300,000) / 6
= 6,000,000 / 6
= 1,000,000 shs.
Thus, the depreciation expense for each year is 1,000,000 shs.
Accumulated depreciation up to year 6 = Depreciation expense per year * Number of years
Accumulated depreciation up to year 6 = 1,000,000 * 6 = 6,000,000 shs.
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You and your friend are comparing finance charges on a 5 year $5000. Due to your low credit score, you locked in a 15% APR, while your friend got a 5% APR. How much more did you pay for this loan due to your bad credit score? Use the payment formula to find the monthly payment and the total amount paid over 5 years.
Answers
With the given compound interest, Total amount paid is $5,593.20 and you paid $1,379.40 more for the loan due to your bad credit score.
What is Compound interest?
Compound interest is the interest calculated on the initial principal as well as on the accumulated interest from previous periods. In other words, it is the interest earned not only on the principal amount but also on the interest previously earned.
Now,
To find the monthly payment, we can use the loan payment formula:
P = (Pv*r)/(1-(1+r)⁻ⁿ)
where P is the monthly payment, Pv is the present value of the loan, r is the monthly interest rate, and n is the total number of payments.
For your loan with a 15% APR, the monthly interest rate is 15%/12 = 1.25%.
For a 5-year loan with monthly payments, the total number of payments is 5 x 12 = 60.
So, plugging in the values, we get:
P = (5000*0.0125)/(1-(1+0.0125)⁻⁶⁰)) = $116.21
Your total amount paid over 5 years is:
Total amount paid = P x n = $116.21 x 60 = $6,972.60
For your friend's loan with a 5% APR, the monthly interest rate is 5%/12 = 0.42%.
Using the same formula as above, we get:
P = (5000*0.0042)/(1-(1+0.0042)⁻⁶⁰) = $93.22
Your friend's total amount paid over 5 years is:
Total amount paid = P x n = $93.22 x 60 = $5,593.20
The difference in the total amount paid is:
$6,972.60 - $5,593.20 = $1,379.40
Therefore, you paid $1,379.40 more for the loan due to your bad credit score.
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Identify the interquartile range from the box and whisker plot above
Answers
Answer:
interquartile range = 6
Step-by-step explanation:
the interquartile range is the difference between the upper quartile Q₃ and the lower quartile Q₁
Q₃ is the value at the right side of the box, that is 86
Q₁ is the value at the left side of the box, that is 80
interquartile range = Q₃ - Q₁ = 86 - 80 = 6
What number increased by 3.5% of itself equals 621?
Answers
Answer:
Step-by-step explanation:
We need to find a number which increased by 3.5 of itself equals 621.
Let that number be x.
x increased by 3.5 of itself equals 621 implies x+ 3.5x = 621.
x(1+3.5) = 621
x(4.5) = 621
x = 621/4.5
x = 138
Therefore the required number is 138.
Answer: 138
Step-by-step explanation:
We need to find a number which increased by 3.5 of itself equals 621.
Let that number be x.
x increased by 3.5 of itself equals 621 implies x+ 3.5x = 621.
x(1+3.5) = 621
x(4.5) = 621
x = 621/4.5
x = 138
Therefore the required number is 138.
Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find P32, the 82-percentile (using GeoGebra). This is the temperature reading separating the bottom 82% from the top 18%. Round your answer to the nearest 1000th if necessary.
Answers
Answer: To find the temperature reading separating the bottom 82% from the top 18%, we need to find the z-score that corresponds to the 82nd percentile, and then use it to find the temperature value. We can use GeoGebra to find the z-score and the corresponding temperature value as follows:
Click on the "Functions" icon and select "InvNorm" function.
Enter the percentile value, which is 0.82 for the 82nd percentile.
Enter the mean and standard deviation values, which are 0 and 1 for this problem.
Click on the "Evaluate" button to find the z-score.
The resulting z-score is 0.934, rounded to 3 decimal places.
This means that the temperature reading separating the bottom 82% from the top 18% is 0 + (0.934)(1.00) = 0.934°C above freezing.
Rounded to the nearest 1000th, this value is 0.934°C.
Therefore, P32, the temperature reading separating the bottom 82% from the top 18%, is approximately 0.934°C.
Step-by-step explanation:
28) The number of hours per week that high school students spend on computers is normally distributed, with a mean
of 5 hours and a standard deviation of 2 hours. 70 students are chosen at random. Let y represent the mean number
of hours spent on the computer for this group. Find the probability that y is between 5.1 and 5.7.
Answers
The probability that y is between 5.1 and 5.7 is approximately 0.4292.
What is probability?Probability is a way to gauge how likely or unlikely something is to happen. It is a number between 0 and 1, where 0 denotes an improbable event and 1 denotes an inevitable one.
According to question:Since the sample size is large (n = 70), we can use the Central Limit Theorem to approximate the sampling distribution of the sample mean as normal with mean μ = 5 and standard deviation σ/sqrt(n) = 2/sqrt(70) ≈ 0.24.
Now we want to find the probability that y, the sample mean, is between 5.1 and 5.7. We can use the standard normal distribution to do this by standardizing y:
z = (y - μ) / (σ / sqrt(n)) = (y - 5) / 0.24
The probability that y is between 5.1 and 5.7 is equivalent to the probability that z is between:
z1 = (5.1 - 5) / 0.24 ≈ 0.42
and
z2 = (5.7 - 5) / 0.24 ≈ 2.92
Using a standard normal distribution table or calculator, we can find that the probability of z being between z1 and z2 is approximately 0.4292.
Therefore, the probability that y is between 5.1 and 5.7 is approximately 0.4292.
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Part A Select the location of -2 and -9 on the number line. Select the places on the number line to plot the points. -10 20 10 Part B Use mathematical symbols to write an inequality that compares -2 and -9. Explain how the number line can be used to show that your inequality is correct. Enter your inequality and your explanation in the space provided. 109 10 - Math symbols + px C 1 1 0 ▷ Relations ▸ Geometry X . 00 1.1 0.8
Answers
It should be noted that to select the location of -2 and -9 on the number line, the steps are given below.
What are the steps?Draw a number line with zero in the center and a positive direction to the right and a negative direction to the left.
Find the position of -9 by counting 9 units to the left of zero on the number line. Mark this point with a dot or a cross.
Find the position of -2 by counting 2 units to the left of zero on the number line. Mark this point with a dot or a cross.
Label the points as -9 and -2 to indicate their values.
Your number line should now have two marked points at positions -9 and -2.
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In a country club of 141 people, 61 play football, 65 play base ball and 72 play hockey hockey.
22. play all the games while 11 play none of the games. An equal number play only two games (How many play only two games (i) How many play only football?
Answers
The number of people who play only football is |A' ∩ B' ∩ C'| = 25. So, 25 people play only football.
Describe Statistics?Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves the use of various methods and techniques to draw conclusions from data and make informed decisions.
The main goal of statistics is to provide a systematic approach to understanding and interpreting data, which can be used in a wide variety of fields, including business, social sciences, engineering, medicine, and many others. Statistics is used to study and analyze various types of data, including numerical, categorical, and ordinal data, as well as time series and spatial data.
Let A, B, and C be the sets of people who play football, baseball, and hockey, respectively. We know that:
|A| = 61, |B| = 65, |C| = 72
We also know that:
|A ∩ B ∩ C| = 22, |A ∪ B ∪ C| = 141, |A' ∩ B' ∩ C'| = 11
where A', B', and C' denote the complements of A, B, and C, respectively.
We can use the principle of inclusion-exclusion to find the number of people who play only two games. This principle states that:
|A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C|
Using the given values, we can substitute and simplify to get:
141 = 61 + 65 + 72 - |A ∩ B| - |A ∩ C| - |B ∩ C| + 22
|A ∩ B| + |A ∩ C| + |B ∩ C| = 75
We also know that an equal number of people play only two games, so let x be that number. Then:
|A ∩ B| = |A ∩ C| = |B ∩ C| = x
Substituting into the previous equation, we get:
3x = 75
x = 25
Therefore, 25 people play only two games. To find the number of people who play only football, we need to subtract the number of people who play baseball and hockey from the number of people who play only two games:
|A' ∩ B ∩ C| = x = 25
|A' ∩ B ∩ C'| = 11
|A' ∩ C ∩ B'| = x = 25
|A ∩ B' ∩ C'| = x = 25
|A' ∩ B| = 65 - (25 + 11) = 29
|A' ∩ C| = 72 - (25 + 11) = 36
|A' ∩ B' ∩ C| = 61 - (25 + 11) = 25
|A ∩ B' ∩ C| = 141 - (29 + 25 + 36 + 11) = 40
Therefore, the number of people who play only football is:
|A' ∩ B' ∩ C'| = 25
So, 25 people play only football.
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How many years will it take $6,000 invested at 8% interest to earn $1,680?
Answers
Answer:
We can use the formula for simple interest to solve this problem:
I = Prt
where I is the amount of interest earned, P is the principal (the initial amount invested), r is the annual interest rate (as a decimal), and t is the time (in years).
In this problem, we know that P = $6,000, r = 0.08, and I = $1,680. We want to find t, the time required to earn $1,680 in interest.
Substituting these values into the formula, we get:
$1,680 = $6,000 x 0.08 x t
Simplifying and solving for t, we get:
t = $1,680 / ($6,000 x 0.08) = 3.5 years
Therefore, it will take 3.5 years for $6,000 invested at 8% interest to earn $1,680 in interest.
