The predicted fuel efficiency for a speed of 30 mph will be 26.50 mpg when the least-squares regression line is given.
What is the least-squares regression line?If the data demonstrates a stronger link between two variables, the line that best matches this linear relationship is known as a least-squares regression line, and it minimizes the vertical distance between the data points and the regression line. A regression line is a straight line that illustrates how a response variable y varies when an explanatory variable x changes. The line is a mathematical model that predicts the value of y given a value of x. A regression line predicts the value of y for a given value of x. A regression line is discovered through regression analysis. When the explanatory variable changes, the regression line shows how much and in which direction the response variable changes.
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What is the answer to x - 5 > 12?
Answer:
x > 17
Step-by-step explanation:
x - 5 > 12 ( isolate x by adding 5 to both sides )
x > 17
-------------- from your comment
x - (- 5) > 12 , that is
x + 5 > 12 ( subtract 5 from both sides )
x > 7
Consider the infinite geometric sequence 4480, -3360, 2520, -1890…
a. Find the common ratio, r.
b. Find the 20th term.
c. Find the exact sum of the infinite sequence.
The common ratio, r = -0.75, 20th term = -18.9056, exact sum of the infinite sequence = 1750.
a.
common ratio r = a2/a1
= -3360/4480
= -0.75.
r = a3/a2
= 2520/-3360
= -0.75
b.
[tex]a_{n}[/tex] = a*r^(n-1)
here a = 4480 and r = -0.75.
= 4480(-0.75)^(20-1)
= 4480(-0.75)^19
= 4480*(-0.00422)
[tex]a_{20}[/tex] = -18.9056.
c.
[tex]s_{n}[/tex] = a*((1-r^n)/(1-r))
= 4480*((1--0.75^4)/(1--0.75))
= 4480*((1-0.31640625)/(1--0.75))
= 4480*(0.68359375/1.75)
= 4480*0.390625
= 1750
Therefore the common ratio, r = -0.75, 20th term = -18.9056, exact sum of the infinite sequence = 1750.
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A single bathc of your mother resipe for slalsa call for 3 tomatos. 1/4 cup cilantro,1/2 onion, and spices. you are having a party and need 5 batches of salsa how many cups of onions do you need?
To produce five constructive batches of salsa, 2.5 cups of onion will be needed.
What is unitary method of problem solving?
The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. The unitary approach involves calculating the value of a single unit, from which we can calculate the values of the necessary number of units.
Given, the number of onions required to produce one batch = 0.5 cup(s)
∴ The number of onions required to produce five batches = 0.5×5
= 2.5 cup(s)
Thus, to produce five constructive batches of salsa, 2.5 cups of onion will be needed.
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Gabriel Harris earns an annual salary of $156,000 as CFO of
TechMedia, Inc. He is married and claims three dependents. TechMedia
recently converted from a weekly pay plan to a monthly pay plan.
How much more will Gabriel have deducted from his monthly pay
than from his weekly pay for state income tax?
Answer:
Step-by-step explanation:
Gabriel Harris earns an annual salary of $156,000 as CFO ofTechMedia, Inc. He is married and claims three dependents. TechMediarecently converted from a weekly pay plan to a monthly pay plan.How much more will Gabriel have deducted from his monthly paythan from his weekly pay for state income tax?
you are going to paint the 6-sector spinner shown. there are 4 colors to choose from. 0 how many different ways can you paint the spinner, if each color can be used more than once, and: there are no other restrictions?
The different ways can paint the spinner is [tex]4^{6}[/tex].
Permutation and Combination:
A permutation is an act of arranging objects or numbers in order. Combinations are the way of selecting objects or numbers from a group of objects or collections, in such a way that the order of the objects does not matter.
Here it is given that to paint the 6-sector spinner shown there are 4 colors to choose from.
The total number of ways to color this spinner with 6 different parts and 4 different colors is 4 × 4 × 4 × 4 × 4×4 = [tex]4^{6}[/tex] ways
Therefore the ways is [tex]4^{6}[/tex].
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The rectangular floor of a classroom is 36 feet in length and 28 feet in width. a scale drawing of the floor has a length of 9 inches. what is the perimeter, in inches, of the floor in the scale drawing?
The perimeter of the floor in the scale drawing is 32 inches.
Using ratio and proportion, determine the width of the scale drawing of the floor.
actual length / scale length = actual width / scale width
36 feet / 9 inches = 28 feet / scale width
scale width = 28 feet (9 inches / 36 feet)
scale width = 7 inches
Perimeter is defined as distance around a two-dimensional shape.
The perimeter of a rectangle can be calculated using the formula below.
P = 2(l + w)
where P = perimeter
l = length
w =width
Plug in the values of the dimension of the scale drawing and determine its perimeter.
P = 2(l + w)
P = 2(9 inches + 7 inches)
P = 32 inches
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in the construction of confidence intervals, if all other quantities are unchanged, an increase in the sample size will lead to a
If all other values remain constant, an increase in sample size will result in a broader confidence interval when constructing one.
The definition of the MoE, or margin of error, is
MoE = sigma ÷ sqrt(n)
The population standard deviation is represented by sigma. If you don't know sigma, utilize s to get a rough idea of it. The sample standard deviation is denoted by the variable s.
The MoE increases along with the sigma. The width or narrowness of the confidence interval is directly determined by the MoE. A smaller MoE indicates greater confidence with less error, whereas a larger MoE indicates greater net casting but increased error.
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whats the quotient for 2.0 and 4.0
The solution to the quotient for 2.0 and 4.0 is 0.50
How to determine the quotient of the numbers?From the question, the mathematical statement is given as
The quotient for 2.0 and 4.0
The quotient of numbers is their division
This in other words mean that:
The quotient for a and b is a/b
Using the above highlights as a guide, we have
The quotient for 2.0 and 4.0 to be 2.0/4.0
Evaluate the quotients
So, we have the following representation
The quotient for 2.0 and 4.0 to be 0.50
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GEOMETRY A triangle has vertices at (a,0), (b,4), and (c,0), where a
The expression that represents the area of the triangle is given as follows:
A = (c - a)[8 - (c - a)]/4.
How to obtain the area of a triangle?The area of a triangle is obtained as half the multiplication between the base b and the height h, that is:
A = 1/2 x b x h.
For the triangle in this problem, the base is composed by these following vertices:
(a, 0).(c, 0).Hence the length of the base is of:
b = c - a.
The height is given by the difference between the y-coordinate of the vertex (b,4) and the midpoint of the base ac, hence:
h = 4 - (c - a)/2 = [8 - (c - a)]/2
Hence the area is given as follows:
A = 1/2 x (c - a) x [8 - (c - a)]/2
A = (c - a)[8 - (c - a)]/4.
Missing InformationThe problem asks for which expression gives the area of the triangle with these vertices.
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4. A farmer is taking a break
to watch a movie that is 25
minutes long. He doesn't have
time to watch the whole thing
in one day. So he watched 20
minutes the first day and 12
minutes the next day. How
much more of the movie does
he have left to watch?
A cake is made of 300 grams of flour,150 grams of sugar powder, and 0.75 liters of
water. Find the ratio of the floor to the total mass of the mixture.
Answer: 1/4
Step-by-step explanation:
0.75 liters is the same as 750 grams.
So, the total mass of the mixture is [tex]300+150+750=1200[/tex] g.
This means the ratio is [tex]\frac{300}{1200}=\frac{1}{4}[/tex].
Answer:
Flour : total mass = 1 : 4
Step-by-step explanation:
Given ingredients for the cake:
Flour = 300 gSugar = 150 gWater = 0.75 LFirst convert the mass of the water to the same SI units as the other ingredients.
1 liter = 1000 g
⇒ Water = 0.75 liters = 750 g
Total mass of the mixture:
= flour + sugar + water
= 300 g + 150 g + 750 g
= 1200 g
Therefore, the flour to total mass ratio is:
⇒ Flour : total mass = 300 : 1200 = 1 : 4
kara categorized her spending for this month into four categories: rent, food, fun, and other. the amounts she spent in each category are pictured here. rent $500 food $400 fun $300 other $600 [graphs generated by this script: initpicture(-5.5,5.5,-5.5,5.5);circle([0,0],5);line([0,0],[5,0]);line([0,0],[-.868,4.924]);text([1,2],'rent','right');text([1,1],'$500','right');line([0,0],[-5,0]);text([-1,2],'food','left');text([-1,1],'$400','left');line([0,0],[2.5,-4.33]);text([1,-1],'fun','right');text([1,-2],'$300','right');text([-1,-1],'other','left');text([-1,-2],'$600','left');] what percent of her total spending did she spend on fun? answer to the nearest whole percent. %
Answer: is 16.6%
Step-by-step explanation: Use the rule of three (mathematic).
Question:
simplify 5√18
Answer template:
___ √ ___
The simplification of the number by solving square root 5√18 is 15√2.
What is meant by the term square root?A number's square root is a value that, if multiplied by itself, yields the original number. The other procedure to square an integer is to find its square root. Squares as well as square roots are hence related ideas.Providing that x is just the square root of y, the equation would be written as x=y or as x² = y. The radical symbol for the number's root is "√" in this instance. The square of the positive number is shown by multiplying it by itself. The original number is obtained by taking the square root of a square of such a positive number.For the given number
= 5√18
Find the factors of 18 by prime factorization.
18 = 2 ×3 ×3
Put in the number.
= 5√2 ×3 ×3
Taking 3 out of root.
= 5×3√2
Further solving.
= 15√2
Thus, the simplification of the number by solving square root 5√18 is 15√2.
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Please help me with my math
The product of a number minus 17 and 5 are equivalent to: 5 (n - 17) .
How do you find the equivalent expressions?X-terms and constants should be combined with any other like terms on either side of the equation. Put the terms in the same order, with the x-term usually coming before the constants. The two phrases are equal if and only if each of their terms is the same.
the sum of a number less than 17 and five
If x is an ambiguous number,
The sign for minus is -
A number less than 17 is denoted by x-17.
The multiplication is the product.
Add x-17 and (x-17)5 to get the answer.
In this case, the expression is 5 (n - 17).
When two numbers are multiplied together, the outcome is known as the product.
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From the diagram below, choose the correct letter for each of the
following parts of a circle:
a) a major arc
b) a minor sector
c) a major segment
A
B
D
✓ Scroll down
E
From the diagram, A is the major arc
B is the minor sector
C is the major segment.
What do you mean by major arc, minor sector, and a major segment of a circle?
1. Major arc: A significant arc is one that is larger than 180 degrees in measure.
2. Minor sector: A circle's intercepted arc and two of its radii define a region known as a sector. The center angle is the intersection of the two radii. A minor sector is defined as having a center angle of less than 180°.
The major arc is A significant arc is one that is larger than 180 degrees in measure. So, A is the major arc. The minor sector is defined as having a center angle of less than 180°. So, B is the minor sector. And C has the maximum portion of length so C is a major segment.
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EASY POINTS WILL GIVE BRAINLIST TO BEST ASWER!!
write the point slope form of the equation of the line through the given point with the given slope
through: (-1, -2) slope =3
Answer:
y=3x+1
Step-by-step explanation:
we know slope so just fill in the rest
y=3x
-2=3(-1)
-2=-3
We add 1 to make the equation true so the y intercept is 1
Hopes this helps please mark brainliest
Use the properties of exponents to rewrite this expression.
(204)
a0a5
What is the value of the rewritten expression when a = -5?
The rewritten expression will be 4a³ and the value of this expression is -500.
Given in the question:
(2a⁴)² / a⁰a⁵
We know that
(xy)ⁿ = xⁿ × yⁿ ... (i)
We can use equation (i) for the next step of our given expression.
In the case of the numerator:
(2a⁴)² = 2² × a⁸ = 4a⁸
Now, we know, any number to the power of zero is 1.
So, for the denominator, we get:
a⁰a⁵ = 1 × a⁵ = a⁵
We know,
pˣ / pʸ = y ⁽ˣ⁻ʸ⁾ ... (ii)
Using this equation, we can further simplify the given expression:
⇒ 4a⁸ / a⁵
⇒ 4 a⁽⁸ ⁻ ⁵⁾
⇒ 4 a ³ ... (iii)
Now, in the second part of the question, we need to find the value of the expression.
Given a = -5
Putting this value in equation (iii) we get:
4 a ³
⇒ 4 (-5) ³
⇒ 4 × (-125)
⇒ -500
Hence, the simplified expression is 4 a ³ and the value of the simplified equation is -500.
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What are some Mathematical Concepts for Slopes and equations? Any kind of help would be much appreciated.
Answer:25256
Step-by-step explanation:
which expressions are equivalet to the one below check all that apply (7^3) * (7^x)
A. 49^3x
B. (7 * x)^3
C. 343 * 7^x
D. 7^(3+x)
E. 7^(3x)
F. 7^(3-x)
For given expression (7^3) * (7^x) equivalent expressions are:
343 * 7^x and 7^(3+x)
The correct options are option (C) and option (D)
In this question, we have been given an expression (7^3) * (7^x)
We need to find expressions that are equivalent to given expression.
Consider given expression (7^3) * (7^x)
We know that 7^3 = 343
So given expression becomes, (7^3) * (7^x) = 343 * (7^x)
For given expression, the bases of the exponents are equal.
so, by the properties of exponents
(7^3) * (7^x) = 7^(3 + x)
Therefore, for given expression (7^3) * (7^x) equivalent expressions are:
343 * 7^x and 7^(3+x)
The correct options are option (C) and option (D)
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Please answer part d
Answer:
∆JGF ≅ ∆GJH by the SAA Postulate
Step-by-step explanation:
Given a figure showing two triangles with a common side, and two marked angles not at either end of that side, you want to know the applicable congruence postulate.
SAAThe letters S and A in the congruence postulate references refer to "Side" and "Angle". The sequence of the letters corresponds to the sequence of corresponding parts in the triangles.
In the given figure, two angles in each triangle are marked with a single arc and a double arc. The triangles share a side that has the double-arc angle at one end. Hence, the sequence of corresponding parts can be seen to be (common) Side - (double-arc) Angle - (single-arc) Angle. The SAA congruence postulate applies.
∆JGF ≅ ∆GJH by the SAA Postulate
Andy needs to solve
3/5
A. No, because and are not equivalent.
3
OD. Yes, because
3. In order to do this, he multiplies. Will Andy's method work?
OB. Yes, because dividing by a fraction is the same as multiplying by the reciprocal of the fraction.
OC. No, because one strategy involves division and the other involves multiplication.
3/6
and are equivalent
if a 5-card poker hand is dealt from a well-shuffled deck of 52 cards, what is the probability of being dealt a two pair (2 cards of the same rank and 2 cards of any other rank with an unmatched card)?
Answer: 0.4754
A poker hand is a combination of 5 cards from the pack of 52 cards.
One hand full is said when we have 2 cards of the same rank.
In this question, we have to find the probability of 2 hands full of different ranks.
So,
We use the formula : C(n,k)=\frac{n!}{k!(n-k)!}
From permutations and combinations, since order doesn't exist.
From a suit of 13 cards any two cards are chosen:
C(13,2)=\frac{13!}{2!(13-2)!}
C(13,2)=\frac{13×12×11!}{2!11!}
C(13,2)=\frac{13×12!}{2!}
C(13,2)=156/2
C(13,2)=78
78 ways are there to choose for each of the pairs .
Now,
If one of the ranks is of any particular suit or maybe a face card out of which two of them are chosen.
C(4,2)=\frac{4!}{2!(4-2)!}
C(4,2)=6
And same for the other sets of cards of another pair.
We have 78×6×6= 2808 ways to pick the first 4 cards.
Now,
For the fifth card which can be any card except for the paired suit i.e, 13-2=11
There are 4 suits to pick from, 4×11= 44 cards to pick for the final card.
For the first card = 2080
For the fifth card= 44
Total number of two pair hands possible= 2080×44= 123,552
Out of:
C(52,5)=\frac{53!}{5!(52-5)!}
C(52,5)= 2,598,960
Probability of event= 123,552/2,598,960
= 0.4753901560624
Final answer= 0.4754
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The probability of being dealt a two-pair is 0.4754.
Given;
What is the likelihood of receiving a two-pair when dealing a five-card poker hand from a 52-card deck that has been properly shuffled?
We use combinations to solve the given case;
From each suit, any two cards are chosen,
C(13,2) = [tex]\frac{13!}{2!(13-2)!}[/tex]
= [tex]\frac{13*12*11!}{2!11!}[/tex]
= 156/2
= 78
Hence, there are 78 ways to choose for each of the pairs.
Now,
If one of the ranks is a face card, two of them are chosen, or if one of the ranks is a certain suit.
C(4,2) = [tex]\frac{4!}{2!(4-2)!}[/tex]
=6
Similar to the other sets of cards of another pair.
We have 78×6×6= 2808 ways to pick the first 4 cards.
Now,
The fifth card, which can be any card other than the paired suit, is dealt as follows: 13 - 2 = 11.
There are 44 cards total to choose from among the 4 suits, or 4 x 11.
2080 for the primary card.
44 for the fifth card.
Possible two-pair hands total 2080 x 44 = 123,552.
Then,
C(52,5) = [tex]\frac{53!}{5!(52-5)!}[/tex]
= 2,598,960
Probability of event = Possible two-pair hands / Total outcome
= 123,552 / 2,598,960
= 0.47539
Hence, the probability of being dealt a two-pair is 0.4754.
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What is 36.9 rounded to the nearest percent
Answer: 37%
Step-by-step explanation:
36.9 rounds up into 37%
Find the slope of the line(4,9) and (4,13)
Answer:
the slope of the line is undefined
Expand and simplify (x + 3)(x + 5)
Answer:
expanded: x^2+8x+15
Step-by-step explanation:
(x+3)(x+5)
x^2+5x+3x+15
What’s is the equation of this line in slope intercept form? 2x+3y=-6
Answer:
[tex]y=-\frac{2}{3}x-2[/tex]
Step-by-step explanation:
To find the equation in slope-intercept form, isolate [tex]y[/tex].
[tex]2x+3y=-6 \\ \\ 3y=-2x-6 \\ \\ y=-\frac{2}{3}x-2[/tex]
a restaurant manager collected data to predict monthly sales for the restaurant from monthly advertising expenses. the model created from the data showed that 36 percent of the variation in monthly sales could be explained by monthly advertising expenses. what was the value of the correlation coefficient? responses 0.64 0.64 0.60 0.60 0.40 0.40 0.36 0.36 0.13
The value of the correlation coefficient is 0.60.
There is a 0.6 correlation coefficient between two variables, which measures the strength of the relationship.
R² is the coefficient of determination, which measures how much variation can be explained by the regression line.
This means that, the R² value of the data is 36%
R² = 36% = 0.36
Correlation coefficients measure the strength of relationships between variables in the form of square roots.
That is ; R = √R²
R = √0.36
Hence, the correlation Coefficient, R is 0.60
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Two fire towers are 21 miles apart. Tower B is due East of Tower A. The rangers at Tower A spot a fire at 43°north of east. The rangers at Tower B spot the same fire 31° north of west.
How far is Tower B from the fire? Round to the nearest tenth.
Tower B is 14.9 miles away from the fire.
What is the law of sines?
According to the law of sine, or sine law, the ratio of a triangle's side length to the sine of the opposing angle remains constant for all three sides. The sine rule is another name for it.
Here,
According to the law of sines
BC/sin A = AC/sin B = AB/sin C
∠A = 43°, ∠B = 31°, ∠C = 180° - ∠A - ∠B = 106°
AB = 21 miles
So, BC = (AB/SinC)×SinA
BC = 14.9 miles
Hence, Tower B is 14.9 miles away from the fire.
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In how many ways can a committee of five be selected from eight students if two particular students are to be included
There are 56 ways to choose a committee of students.
What is Combination?
A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
Given that;
A committee of five be selected from eight students if two particular students are to be included.
Now,
Since, 2 members are must be included.
So, We have to choose 3 student from 8 student to form a committee.
Hence, The number of ways to choose 3 students from 8 students is,
= [tex]^{8} C_{3}[/tex]
= 8! / (8-3)! 3!
= 8! / 5! 3!
= 8 x 7 x 6 / 3 x 2
= 56
Thus, There are 56 ways to choose a committee of students.
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pls solve all the question as er the questions given below
1a) The additional information required using SAS Congruency postulate is; ∠AOB ≅ ∠BOD
1b) The additional information required using ASA Congruency postulate is BC ≅ QR
2a) The symbolic form of the congruent triangles is written as;
ΔABC ≅ ΔADC
2b) The congruence Postulate that is used is SAS Congruency postulate.
How to use congruency postulates?1a) We want to prove that the triangles are congruent by SAS Congruency postulate. SAS congruency postulate denotes Side - Angle - Side. That is 2 congruent sides and the included angle. This means we have our additional information as;
∠AOB ≅ ∠BOD
1b) We want to prove that the given triangle ABC is congruent to the other triangle PQR by the ASA Congruency. ASA Congruency means 2 congruent angles and the included side. We are given;
∠Q = ∠B
∠R = ∠C.
Therefore, the additional information is BC ≅ QR
2a) The symbolic form of the given congruent triangles is expressed as;
ΔABC ≅ ΔADC
2b) The congruence postulate that was used here is SAS Congruency postulate.
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