Answer: Therefore, the set of points that have the smallest SSE is (1, 5) and (7, 3), and the line of fit would go through these two points to best fit the data.
Step-by-step explanation:
To determine the line of best fit, we need to find the equation of the line that passes through the given points. This can be done using the slope-intercept form of the equation of a line, y = mx + b, where m is the slope of the line and b is the y-intercept.
For each set of points, we can find the slope using the formula:
m = (y2 - y1) / (x2 - x1)
and then use one of the points to solve for b.
(6, 4) and (9, 1):
m = (1 - 4) / (9 - 6) = -3/3 = -1
Using point (6, 4):
4 = -1(6) + b
b = 10
So the equation of the line is y = -x + 10.
(3, 5) and (10, 1):
m = (1 - 5) / (10 - 3) = -4/7
Using point (3, 5):
5 = (-4/7)(3) + b
b = 41/7
So the equation of the line is y = (-4/7)x + 41/7.
(1, 8) and (10, 1):
m = (1 - 8) / (10 - 1) = -7/9
Using point (1, 8):
8 = (-7/9)(1) + b
b = 71/9
So the equation of the line is y = (-7/9)x + 71/9.
(1, 5) and (7, 3):
m = (3 - 5) / (7 - 1) = -1/3
Using point (1, 5):
5 = (-1/3)(1) + b
b = 16/3
So the equation of the line is y = (-1/3)x + 16/3.
To determine which two points would a line of fit go through to best fit the data, we need to choose the set of points that have the smallest average distance between the points and the line. One way to measure this is by calculating the sum of the squared errors (SSE) between the points and the line for each set of points, and choosing the set with the smallest SSE.
Using the equations we found for each set of points, we can calculate the SSE:
(6, 4) and (9, 1):
SSE = (4 - (-1(6) + 10))^2 + (1 - (-1(9) + 10))^2 = 29
(3, 5) and (10, 1):
SSE = (5 - (-4/7)(3) + 41/7)^2 + (1 - (-4/7)(10) + 41/7)^2 = 16.9
(1, 8) and (10, 1):
SSE = (8 - (-7/9)(1) + 71/9)^2 + (1 - (-7/9)(10) + 71/9)^2 = 28.7
(1, 5) and (7, 3):
SSE = (5 - (-1/3)(1) + 16/3)^2 + (3 - (-1/3)(7) + 16/3)^2 = 7.6
The ratio of the birth weight to the adult weight of a male black bear is 3:1000. The average birth weight is 12 ounces. Find the average adult weight. Your answer is probably in ounces. If there are 16 ounces in 1 pound, how many pounds does the adult bear weigh?
In response to the stated question, we may state that As a result, an expressions adult black bear weighs 250 pounds.
what is expression ?An expression in mathematics is a collection of numbers, variables, and mathematical (such as addition, reduction, multiplication, division, exponentiation, etc.) that express a quantity or value. Expressions might be as basic as "3 + 4" or as complicated as "(3x2 - 2) / (x + 1)". They may also contain functions like "sin(x)" or "log(y)". Expressions can also be evaluated by substituting values for the variables and performing the mathematical operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.
Let B represent the birth weight of a male black bear and A represent the mature weight. The ratio of B to A is supplied to us as 3:1000. As a result, we may write:
B/A = 3/1000
The average birth weight (B) is also reported as 12 ounces. We may use these data to get the average adult weight (A):
[tex]B/A = 3/1000\\12/A = 3/1000\\A = 12/(3/1000)\\A = 4000[/tex]
A male black bear's typical mature weight is 4000 ounces.
To convert ounces to pounds, divide by 16 (since one pound contains 16 ounces):
[tex]4000/16 = 250[/tex]
As a result, an adult black bear weighs 250 pounds.
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Which of the following are true of
all linear functions?
A. The rate of change is
non-zero.
B. The domain is all real
numbers.
C. The range is all real
numbers.
D. There is one x-intercept.
E. There is one y-intercept.
The domain is all real numbers, The range is all real numbers and There is one y-intercept is true from the given option in context of all linear functions. option B. The domain is all real numbers, C. The range is all real numbers , and E. There is one y-intercept is right choice.
All linear functions have a domain that includes all real numbers, a range that includes all real numbers, and exactly
one y-intercept.
The rate of change of a linear function is non-zero only if the function is not constant (i.e. its slope is not zero).
However, there are linear functions that have a slope of zero, such as the function f(x) = 2, which is a horizontal line.
This means that statement A is not true of all linear functions.
Furthermore, there are linear functions that have no x-intercept (if the line is parallel to the x-axis) or that have more
than one x-intercept (if the line intersects the x-axis more than once).
Therefore, statement D is also not true of all linear functions.
The correct answers to this question are B. The domain is all real numbers, C. The range is all real numbers , and E. There is one y-intercept.
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Find the simplified form of the expression. Give your answer in scientific notation.
(8 × 10^4)(9 × 10^–8)
Answer:
7.2×10^-3
Step-by-step explanation:
8 × 10^4×9 × 10^–8
=8×9×10^(4-8)
=72×10^-4
=7.2×10^-3
Tauri is 3 years older than Treasure. In 5 years the sum of their ages will be 63. How old is Tauri now?
Answer:
Tauri is currently 28 years old
Step-by-step explanation:
Three siblings, Peyton, Cameron, and Dakota, all ask their parents to borrow the family car for different events
around town. Since they cannot all borrow the car at the same time, the parents decide to use randomness to
decide who gets the car. They will roll a single, fair, six-sided number cube. Peyton gets the car if a 1 or 2 is
rolled. Cameron gets the car if a 3 or 4 is rolled, and Dakota gets the car if a 5 or 6 is rolled. Which of the
following is the probability distribution for who gets the car?
Well for each person, the probability is 1/3. This is because they all have 2 out of 6 possible outcomes.
(PLEASE HELP MY GRADES WRE DUE TMRO)Scientists are preparing two satellites to be launched. The graph below represents the
number of miles, y, that the satellite, Space Explorer A, flies in a hours.
Miles
The rate of change is equal to 6,800 miles per hour.
What is the rate of change?In Mathematics and Geometry, the rate of change can be determined by using the following mathematical equation (formula);
Rate of change, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Rate of change, m = (y₂ - y₁)/(x₂ - x₁)
Next, we would determine the rate of change of the value of y with respect to the value of x for Space Explorer A;
Rate of change, m = (68,000 - 34,000)/(10 - 5)
Rate of change, m = 34,000/5
Rate of change, m = 6,800 miles per hour.
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Complete Question:
Scientists are preparing two satellites to be launched. The graph below represents the number of miles, y, that the satellite, Space Explorer A, flies in a hours. Find the rate of change.
What is the answer to this?
Answer:
B
Step-by-step explanation:
x + 3y = 2 → (1)
4x - 3y = 23 → (2)
adding (1) and (2) term by term will eliminate y
(x + 4x) + (3y - 3y) = 2 + 23
5x + 0 = 25
5x = 25 ( divide both sides by 5 )
x = 5
How many solutions does this equation have? –8 + 3s + 17s = 20s + 8
Answer: There are no solutions
Step-by-step explanation:
Step 1: simplify both sides of the equation
-8 + 3s + 17s = 20s + 8
(3s+17s) + (-8) = 20s + 8 (combine like terms)
20s + -8 = 20s + 8
20s - 8 = 20s + 8
Step 2: Subtract 20s from both sides
20s - 8 - 20s = 20s + 8 - 20s
-8 = 8
Step 3: Add 8 to both sides
-8 + 8 = 8 + 8
0 = 16
Thus, there are no solutions
A business analyst wants to determine if the prices of goods at a supermarket have changed significantly since the new owner of the company took over. She looks at the prices of ten items before the new owner took over compared to after the new owner started.
(Chart in photo below)
Based on the data in the table and using a significance level of 0.05, what is the correct P-value and conclusion?
A. With a t statistic of 1.4789 and a P-value of 0.173292, reject the no hypothesis that prices have not changed
B. With a T statistic of 1.4789 and a P value of 0.173292, fail to reject the null hypothesis. The prices have not changed.
C. With a T statistic of 0.7394 and a P value of 0.478505, reject the no hypothesis that prices have not changed.
D. With a T statistic of 0.7394 anda P value of 0.478505, fail to reject the no hypothesis that prices have not changed.
Please answer quickly, 100 points thank you !
Answer: Option A
Step-by-step explanation:
The t-statistic and P-value can be calculated using statistical software or a t-test calculator. Using a two-tailed t-test with a significance level of 0.05 and 8 degrees of freedom (n1 + n2 - 2), we obtain:
t = -1.4789
P-value = 0.173292
Therefore, the correct answer is A. With a t statistic of -1.4789 and a P-value of 0.173292, we fail to reject the null hypothesis that the prices have not changed significantly since the new owner took over. We cannot conclude that the prices have changed significantly.
With a T statistic of 0.7394 and a P value of 0.478505, fail to reject the no hypothesis that prices have not changed. The correct option is D.
What is null hypothesis?A null hypothesis is a type of statistical hypothesis that asserts that there is no statistical significance in a given set of observations.
Using sample data, hypothesis testing is used to assess the credibility of a hypothesis.
To determine if the prices of goods at a supermarket have significantly changed since the new owner took over, we can perform a two-sample t-test with the null hypothesis being that the mean difference in prices before and after the new owner took over is zero.
Using a significance level of 0.05, the critical t-value for a two-tailed test with 9 degrees of freedom is approximately 2.306.
To calculate the t-statistic, we first need to calculate the mean and standard deviation of the differences in prices:
Mean difference = (0.30 - 0.07) / 10 = 0.023
Standard deviation = 2.967
t-statistic = (0.023 - 0) / (2.967 / sqrt(10)) = 0.7394
The calculated t-value of 0.7394 is less than the critical t-value of 2.306, and the corresponding p-value is 0.4785. This means we fail to reject the null hypothesis that the mean difference in prices is zero.
Therefore, based on the given data and using a significance level of 0.05, the correct P-value and conclusion are:
Thus, the correct option is D.
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How will the product change if one number is decreased by a factor of 2 and the other is decreased by a factor of 8 ?
The product is decreased by a factor of 16.
What is a factor?
In mathematics, a factor is a number or quantity that, when multiplied with another number or quantity, produces a given result. For example, in the expression 3 x 4 = 12, 3 and 4 are factors of 12. Factors can also refer to algebraic expressions, where they are the expressions that are multiplied together to obtain a larger expression.
Let's say we have two numbers, A and B, and we want to find the product of A and B.
The product of A and B is AB.
If we decrease A by a factor of 2, the new value of A becomes A/2. If we decrease B by a factor of 8, the new value of B becomes B/8.
So the new product of A/2 and B/8 is:
(A/2)(B/8) = AB/16
Therefore, the product is decreased by a factor of 16.
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Mrs. Brown has constructed a pool that has a capacity of 800cm3 and a depth of 8cm what is the area of the upper surface?
Answer:
Step-by-step explanation:
To find the area of the upper surface of the pool, we need to know the dimensions of the pool. If we assume the pool has a rectangular shape, we can use the formula:
Area = length x width
We can find the length and width by using the given volume and depth. Since the volume of the pool is 800 cubic cm and the depth is 8cm, we can find the length and width using the formula:
Volume = length x width x depth
800 = length x width x 8
length x width = 800/8
length x width = 100
Now, we do not have enough information to determine the exact dimensions of the pool. However, we do know that the area of the upper surface of the pool is equal to the length times the width. Therefore, the area of the upper surface is 100 square cm.
I need help on question 30 and 32.
Refer to the attached images.
Simplify 1/cos x + 1/cos x -1
Answer:
-2cotxcscx
Step-by-step explanation:
Step 1: Find a common denominator
Step 2: Simplify
The proof shows that ABCD is a rhombus. Which of the following is the
missing reason?
A. Reflective property
B. Symmetric property
C. Transitive property
D. Addition property
The correct answer is B. Symmetric property.
The symmetric property states that if a = b, then b = a. In the context of geometry, this property can be used to show that if one side of a figure is congruent to another side, then the second side is also congruent to the first. In the case of the given proof, it is possible that the symmetry of the figure is used to show that opposite sides of the rhombus are congruent.
The reflective property (A) is not typically used to prove that a figure is a rhombus, as it relates to the reflection of a figure across a line. The transitive property (C) and the addition property (D) are also unlikely to be used in this context, as they relate to the properties of equality and addition, respectively, rather than geometric properties of figures.
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100 POINTS PLEASEE HELPPP BRAINLIEST
Answer:
C
.........................
Answer: the answer is A
Step-by-step explanation: The process of nuclear fusion is the union of two light atomic nuclei into one heavier one while releasing enormous quantities of energy.
Find the missing length indicated. * A) 12 C) 8 A OB D 16 24 36 B) 18 D) 15
Answer:
Is D
Step-by-step explanation:
Taylor wants to take out a mortgage of $380,000 with interest that compounds monthly. Use the formula A = P(1 +)*t to find which of these loans will have the lowest total cost. A) 20 years at 10% interest B) 25 years at 6.5% interest C) 30 years at 5% interest D) 35 years at 4% interest
Using the compound interest formula it is obtained that the loans which will have the lowest total cost is option C) - 30 years at 5% interest.
What is Compound Interest?
The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.
We can use the formula of compound interest [tex]A = P\big(1 + \frac{r}{n} \big)^{(nt)}[/tex] to calculate the total cost (A) of each loan, where P is the principal (the initial amount borrowed), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the total number of years.
For all loans, the principal P is $380,000.
For Loan A, the annual interest rate is 10%, and the interest is compounded 12 times per year (monthly), so r = 0.1/12 and n = 12.
The total time is 20 years, so t = 20.
Plugging in the values, we get -
[tex]A = $380,000(1 +0.1/12)^{(12 \times20)} = $1,245,956.70[/tex]
For Loan B, the annual interest rate is 6.5%, and the interest is compounded 12 times per year (monthly), so r = 0.065/12 and n = 12.
The total time is 25 years, so t = 25.
Plugging in the values, we get -
[tex]A = $380,000(1 +0.065/12)^{(12 \times25)} = $844,275.92[/tex]
For Loan C, the annual interest rate is 5%, and the interest is compounded 12 times per year (monthly), so r = 0.05/12 and n = 12.
The total time is 30 years, so t = 30.
Plugging in the values, we get -
[tex]A = $380,000(1 +0.05/12)^{(12 \times30)} = $766,726.73[/tex]
For Loan D, the annual interest rate is 4%, and the interest is compounded 12 times per year (monthly), so r = 0.04/12 and n = 12.
The total time is 35 years, so t = 35.
Plugging in the values, we get -
[tex]A = $380,000(1 +0.04/12)^{(12 \times35)} = $810,780.25[/tex]
Therefore, Loan C with 30 years at 5% interest has the lowest total cost, with a total cost of $766,726.73.
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9. The price of a Delta Air Lines ticket from New York to Orlando increased to $450. This is an 8% increase. What was the old fare to nearest cent?
Answer:
$416.66
Step-by-step explanation:
We take
450 divided by 108, then time 100 = $416.66
So, the old fare is $416.66
The diagram shows two circles with center O.
The radius of the outer circle is 3 units and the radius of the inner circle is 2 units.
What is the area of the shaded ring (annulus)?
Look at the picture below please answer quick because of my appointment?
Answer:
5
Step-by-step explanation:
S1=R1²=*3²=9 (the outer circle)
S2=R2²=*2²=4 (the inner circle)
S=S1-S2=9-4=5 (the shaded ring)
Write the ratio of corresponding sides for the similar triangles and reduce the ratio to lowest terms. 2 similar right triangles. Triangle 1 has side length 12, hypotenuse 15, and blank side. Triangle 2 has side length 4, hypotenuse 5, and blank side. a. StartFraction 4 Over 15 EndFraction = StartFraction 5 Over 12 EndFraction = StartFraction 4 Over 15 EndFraction b. StartFraction 4 Over 5 EndFraction = StartFraction 12 Over 15 EndFraction = StartFraction 4 Over 5 EndFraction c. StartFraction 4 Over 12 EndFraction = StartFraction 5 Over 15 EndFraction = StartFraction 1 Over 3 EndFraction d. StartFraction 5 Over 4 EndFraction = StartFraction 15 Over 12 EndFraction = StartFraction 5 Over 4 EndFraction
Answer:
Step-by-step explanation: To find the ratio of corresponding sides for the two similar triangles, we need to match up the corresponding sides of the triangles and write the ratios of their lengths.
For Triangle 1, we have:
Side length = 12
Hypotenuse = 15
We can use the Pythagorean theorem to find the length of the blank side:
(Blank side)^2 = (Hypotenuse)^2 - (Side length)^2
(Blank side)^2 = 15^2 - 12^2
(Blank side)^2 = 225 - 144
(Blank side)^2 = 81
Blank side = 9
So, for Triangle 1, we have the following ratios:
Side length : Hypotenuse = 12 : 15
Side length : Blank side = 12 : 9
Hypotenuse : Blank side = 15 : 9
For Triangle 2, we have:
Side length = 4
Hypotenuse = 5
We can use the Pythagorean theorem to find the length of the blank side:
(Blank side)^2 = (Hypotenuse)^2 - (Side length)^2
(Blank side)^2 = 5^2 - 4^2
(Blank side)^2 = 25 - 16
(Blank side)^2 = 9
Blank side = 3
So, for Triangle 2, we have the following ratios:
Side length : Hypotenuse = 4 : 5
Side length : Blank side = 4 : 3
Hypotenuse : Blank side = 5 : 3
Therefore, the ratio of corresponding sides for the two similar triangles is:
Side length : Side length = 12 : 4 = 3 : 1
Hypotenuse : Hypotenuse = 15 : 5 = 3 : 1
Blank side : Blank side = 9 : 3 = 3 : 1
Reducing each ratio to lowest terms, we get:
Side length : Side length = 3 : 1
Hypotenuse : Hypotenuse = 3 : 1
Blank side : Blank side = 3 : 1
So the correct answer is (b) StartFraction 4 Over 5 EndFraction = StartFraction 12 Over 15 EndFraction = StartFraction 4 Over 5 EndFraction.
Solid metal support poles in the form of right cylinders are made out of metal with a
density of 6.6 g/cm³. This metal can be purchased for $0.38 per kilogram. Calculate
the cost of a utility pole with a diameter of 17.6 cm and a height of 790 cm. Round
your answer to the nearest cent.
The cost of the utility pole is $127.36.
Marcus gives 25% of his income to his parents to help cover expenses. He earns $340 per week. How much money does he gives his parents?
Answer:
$85
Step-by-step explanation:
340*0.25
Need help due soon.
Answer:
The correct equation that represents the relationship between b and f is:
Ob = (3/2)f
Explanation:
We know that Priya uses 4 cups of flour to make 3 loaves of banana bread.
So, the amount of flour required per loaf of bread is 4/3 cups.
Now, if Andre makes b loaves of bread using f cups of flour, then the amount of flour required per loaf of bread is f/b cups.
We can set up a proportion as follows:
4/3 = f/b
Cross multiplying, we get:
4b = 3f
Dividing both sides by 3, we get:
b = (3/4)f
This means that Andre can make (3/4) loaves of bread per cup of flour.
But the question asks for the relationship between b and f, so we need to rearrange the equation:
b = (3/4)f
Multiplying both sides by (2/3), we get:
(2/3)b = (1/2)f
Simplifying, we get:
Ob = (3/2)f
Therefore, the correct equation that represents the relationship between b and f is Ob = (3/2)f.
Allison cut 4 pieces of ribbon to make bookmarks. Each piece of ribbon was 50 cm long. How many meters of ribbon did Allison use to make the bookmarks?
Answer:
2 meters
Step-by-step explanation:
If she cut 4 pieces and each was 50 cm, we know that she used 200 cm of ribbon.
Cm to M conversion is that 100 cm = 1 meter, so 200 cm would be 2 meters
The figure below shows a circle with Center A, diameter IP, and tangents SL, PL, and IC. Which of the angles must be right angles?
Let S = {r, e, l, a, x} and T = {i, t, s, o, k, a, y}. Find n(S), n(T), n( ∪ ), and n( ∩ ).
The value of n (S) is 5, n (T) is 7, n (∪) is 11 and n (∩) is 1. The solution has been obtained by using the given sets.
What is a set?
Sets are represented as a collection of well-defined objects or elements and it does not change from person to person. A set is symbolised by a capital letter. The number of items in the finite set is known as the cardinal number of a set.
We are given two sets as S = {r, e, l, a, x} and T = {i, t, s, o, k, a, y}.
Now,
n (S) = 5
This is because there are 5 elements in this set.
n (T) = 7
This is because there are 7 elements in this set.
S ∪ T = {r, e, l, a, x, i, t, s, o, k, y}
n (∪) = 11
This is because there are 11 distinct elements in the sets.
S ∩ T = {a}
n (∩) = 1
This is because there is only 1 element common in the sets.
Hence, the required solution has been obtained.
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Matt increased his typing speed from 32 to 38 words per minute. What is the percent of increase
Answer:
Matt's typing speed increased by 18.75%.
Step-by-step explanation:
To find the percent increase, we can use the following formula:
percent increase = (new value - old value) / old value x 100%
Using this formula, we can calculate the percent increase in Matt's typing speed as follows:
percent increase = (38 - 32) / 32 x 100%
percent increase = 6 / 32 x 100%
percent increase = 0.1875 x 100%
percent increase = 18.75%
PLEASE HELP PICTURE BELOW
Joseph is 1.75 meters tall. At 11 a.m., he measures the length of a tree's shadow to be
34.05 meters. He stands 29.7 meters away from the tree, so that the tip of his shadow
meets the tip of the tree's shadow. Find the height of the tree to the nearest
hundredth of a meter.
(Diagram is not to scale.)
Answer:
34.05 m-
2T
1.75 m
29.7 m
Answer:
Step-by-step explanation:
34,05m my love
Answer:
The height of the tree is approximately 15.14 meters, rounded to the nearest hundredth of a meter.
Step-by-step explanation:
Let's call the height of the tree "h". We can use similar triangles to set up an equation involving Joseph's height, the length of his shadow, the height of the tree, and the length of the tree's shadow.
The two triangles we're interested in are:
Joseph's triangle: This triangle has a height of 1.75 meters (Joseph's height) and a base of x meters (the length of Joseph's shadow).
Tree's triangle: This triangle has a height of h meters (the height of the tree) and a base of 29.7 - x meters (the length of the tree's shadow).
Since the two triangles are similar, we can set up the following proportion:
h / (29.7 - x) = 1.75 / x
To solve for h, we can cross-multiply and simplify:
h * x = 1.75 * (29.7 - x)
h * x = 52.075 - 1.75x
h = (52.075 - 1.75x) / x
Now we need to find the value of x that makes the tips of the two shadows meet. From the problem statement, we know that x + 34.05 = 29.7, so:
x = 29.7 - 34.05
x = -4.35
This means that the tips of the shadows don't actually meet, but the problem is likely assuming that the tips of the shadows are very close together, so we can use the value x = -4.35 to approximate the height of the tree.
Substituting x = -4.35 into our equation for h, we get:
h = (52.075 - 1.75(-4.35)) / (-4.35)
h = 15.14
At Christmas, Ben, Sam and Tom received cards in the ration 2 : 3 : 12.
If Tom received 60 cards.
(a) What fraction of the cards did Ben receive?
(b) What fraction did Ben and Sam receive between them?
(c) How many cards did Sam receive?
(d) How many cards did they receive altogether?
Find x
Given: x=AC, m
Answer:
x = 15.733
Step-by-step explanation: