Answer:
y=10x-15
Step-by-step explanation:
Use slope-intercept form: y=mx+b
M is your slope and B is your Y intercept
since your Y-intercept is negative, and adding a negative is just subtracting, you can just put -15 instead of +-15
A statistics student is interested in the relationship
between the number of aunts and uncles a person has
and the number of cousins. She surveys a simple
random sample of 12 people and asks them how many
of each they have. She calculates the least-squares
regression line and finds the equation is ý = 2.6 +
1.64x, where y is the number of cousins and x is the
number of aunts and uncles. The residual plot is
shown.
Based on the residual plot, is the linear model
appropriate?
No, the residuals are relatively large.
No, there is a clear pattern in the residual plot.
Yes, there is no clear pattern in the residual plot.
Yes, about half of the residuals are positive and half
are negative.
The answer is,
Yes, the residual plot lacks a recognizable pattern.
So, the correct option is c
What is a simple random sampling?A simple random sample, in which each participant has an equal chance of being chosen, chooses a small, random portion of the whole population to represent the entire data set.
Researchers may produce an uncomplicated random sample by using methods like lotteries or random draws.
A sampling error may have occurred if the sample does not accurately reflect the population it is supposed to represent.
By selecting values at random from a population and giving each item a series of values, simple random samples are produced.
Simple random sampling is a sample design option to systematic, stratified, or cluster sampling.
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Please help me answer this question
The double angle results are;
sin 2x = 62/64
cos 2x = 14/64
tan 2x = 384/83
What is double angle?We can see that it is possible for an angle to be given in the double angle format and we need to obtain the angles from it.
We know that sin x = 5/8
Using the Pythagoras theorem;
c^2 = a^2 + b^2
c = 8
a= 5
b= √c^2 - a^2
b = √ 8^2 - 5^2
b = √ 64 -25
b= 6.2
cos x = 6.2/8
Tan x = 5/6.2
Then;
sin2x = 2 sinxcosx
sin 2x = 2(5/8 × 6.2/8)
sin2x = 2(31/64)
sin2x = 62/64
cos 2x = 1 - 2sin^2x
cos 2x = 1 - 2(5/8)^2
cos 2x = 1 - 2(25/64)
cos 2x = 1 - 50/64
cos 2x = 14/64
Tan 2x = 2tan x/1 - tan^2 x
tan 2x = 2 (5/6.2)/1 - (5/6.2)^2
tan 2x = 10/6.2/1 - 25/38.4
tan2x = 10/6.2/13.4/38.4
tan2x = 10/6.2 * 38.4/13.4
tan 2x = 384/83
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A farmer has 70 acres of land available for planting either soybeans or wheat. The
preparation cost per acre of land is $60 for soybeans and $30 for wheat. Soybeans
require 3 workdays per acre, while wheat requires 4 days. The farmer can make a
profit of $180 per acre of soybeans and $100 per acre of wheat. He cannot spend more
than $1800 in preparation costs and cannot use a total of more than 120 workdays.
How many acres of each crop should be planted to maximize the profit? What is the
maximum profit he can make off of these 70 acres?
The maximum profit for soybeans is 30 acres and the maximum profit for wheat is 60 acres.
The maximum profit from these 70 acres is $12600
What is profit?Mathematically profit is considered the amount of gain from any business activity. Whenever a shopkeeper sells a product, his motive is to take advantage of the buyer in the name of profit. .
Given,
Total land = 70 acres
For soyabeans,
1 acre = $60 for 3days
⇒Profit=$180
Foe wheat,
1 acre = $30 for 4days
⇒Profit=$100
Working days must ≤ 120
Preparation cost ≤ 1800
For soyabeans,
60$ for 3 days
1800$ for ?
x = (1800×3)/60
x = 90 days
1 acre = 3 days
? = 90 days
x = 90/3
x = 30 acres
For wheat,
30$ for 4 days
1800$ for ?
x = (4×1800)/30
x = 240 days
1 acre for 4 days
? for 240 days
x = 240/4
x = 60 acres
The maximum profit for soybeans is 30 acres and the maximum profit for wheat is 60 acres.
Maximum profit is:
1 acre for 180$
70 acres for ?
x = (180×70)/1
x = $12600
The maximum profit from these 70 acres is $12600
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A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 40 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16t²+40t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at 1.25 second(s) after launch. (Simplify your answer.)
The maximum height reached by the object is _____ feet. (Simplify your answer.)
The rocket reaches its maximum height at 1.25 second(s) after launch
The maximum height reached by the object is 32 feet.
Time to reach the maximum heightThe function is given as
h(t) = -16t² + 40t + 7
Differentiate the above function
So, we have the following representation
h'(t) = -32t + 40
Set to 0
-32t + 40 = 0
So, we have
32t = 40
Divide by 32
t = 1.25
Hence, the time is 1.25 seconds
The maximum heightIn (a), we have
t = 1.25
Substitute t = 1.25 in h(t) = -16t² + 40t + 7
h(1.25) = -16(1.25)² + 40(1.25) + 7
Evaluate
h(1.25) = 32
Hence, the maximum height is 32 feet
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If you have 6 eggs and 2 bananas for 4 people, how many eggs and bananas would you need for 10 people?
Answer:
15 eggs
5 bananas
Step-by-step explanation:
6/4=x/10
6(10)=4x
60=4x
/4. /4
15=x
We need 15 eggs
2/4=x/10
2(10)=4x
20=4x
5=x
We need 5 bananas
Or
6/4=1 1/2
Now we make 1 and 1/2 have a denominator of 10
1 5/10=15/10
Meaning 15 eggs
2/4=1/2=5/10
Meaning 5 bananas
Hopes this helps please mark brainliest
Answer:you would need 15 eggs and 5 bananas for 10 people
Step-by-step explanation:multiply the 6 eggs and 2 bannanas by 2 then add half more of each
sorry if this confuses you im not a good explainer
4\5 of a liter of water filled 4\7 of a bucket. how many liters of water can the bucket hold?
The liters of water that the bucket hold is 5/7 liters of water.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, 4/5 of a liter of water filled 4/7 of a bucket. The liters that it can hold will be:
= 4/7 ÷ 4/5
= 4/7 × 5/4
= 20 / 28
= 5/7
It can hold 5/7 liters.
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IXL Help fast please and thank you
Answer:
y = 4/3 x + 4/3
Step-by-step explanation:
y - (-4) = 4/3(x-(-4)
y+4 = 4/3 (x +4)
y + 4 = 4/3 x + 16/3
y = 4/3 x +16/3 -4
y = 4/3 x + (16- 12)/3
y = 4/3 x + 4/3
y = 4/3 x + 4/3
Answer:
y=4/3x+4/3
Step-by-step explanation:
-4=4/3(-4)+9
-4=-16/3+9
-4=-5 1/3+9
-4= 4 1/3
4+4 1/3=8 1/3
9-8 1/3=2/3
-4=4/3(-4)+2/3
-4=-16/3+2/3
-4=-14/3
-4=-4 2/3
2/3+2/3=4/3
-4=4/3(-4)+4/3
-4=-16/3+4/3
-4=-12/3
-4=-4
Pleaseeee helppp fastest and accurate answer will get the most points
The difference of the cubes of two consecutive positive even integers is 56. Find the integers.
Step-by-step explanation:
(x+2)³ - (x)³ = 56
(x²+4x+4) (x+2) - (x)³ = 56
x³ + 2x² +4x²+ 8x + 4x + 8 -x³ = 56
6x² + 12x + 8 = 56
6x² + 12x - 48 = 0
x² + 2x - 8 = 0
(x+4) (x-2) = 0
x = -4
x = 2
the integers are 2 and 4
The required two consecutive positive even integers are 2, and 4.
What is an integer?A number which is not a fraction, and it is a whole number.
For example -1,-2,-3,0,1,2 etc. are integers.
Let two consecutive even numbers are x and x+2,
According to given condition, the difference of cube of x and x+2 is 56,
Implies that,
(x+2)³ - (x)³ = 56
x³ + 8 + 3.x².2+ 3.x.2² -x³ = 56
6x² + 12x - 48 = 0
x² + 2x - 8 = 0
x² + 4x - 2x - 8 = 0
x = -4, 2
Both the integers are positive, so the value of x can't be negative.
Therefore, x=2 and x+2 = 4
So the integers are 2 and 4.
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What is the factored form of 16x^2 - 16x - 12?
Answer:
4(2x +1)(2x-3)
Step-by-step explanation:
8:24=26:X
Help me find the missing term.
Answer:
x = 78
Step-by-step explanation:
[tex]\frac{8}{24} =\frac{26}{x}[/tex]
==> cross multiply
26 x 24 = 8 x "x"
==> simplify
624 = 8x
==> divide both sides by 8
78 = x
Answer: x = 78
Step-by-step explanation:
It is 78 because if you cross-multiply, you get 624 = 8x. Then if you divide by 8 on both sides, you get x = 78.
Select the correct answer. Which statement best describes the solution set to this inequality? 0 < 8 + x < 17 A. The solution set includes all values of x greater than 8 and less than 25. B. The solution set includes all values of x less than -8 or more than 9. C. The solution set includes all values of x greater than -8 and less than 9. D. The solution set includes all values of x less than 8 or more than 25.
The correct option is C.
The statement best describes the solution set to the inequality as the solution set includes all values of x greater than -8 and less than 9.
Inequality: An inequality is an expression that shows an unequal comparison of two or more numbers and variables.
Given that:
Inequality
0 < 8 + x < 17
Adding on both sides by -8.
=> 0 - 8 < 8 + x - 8 < 17 - 8
=> -8 < x < 9
The solution set is (-8,9).
Therefore, the solution set includes the value of x greater than -8 and less than 9.
Hence, the correct statement that best describes the solution is option C.
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PLEASE HELP will give brainly and 10 points Which inequality is represented by the number line graph?
Answer: A
Step-by-step explanation: The dot is a filled-in circle, meaning it has to be A, B, or E. Then, B is saying that the arrow is going left, so that's wrong. E is saying that it is just 6 instead of -6, which leaves us with A.
hope this helps!
please give brainliest!
Does this have 1 solution, infinite, or none at all?? 36-7p = -7p-35
The equation 36-7p=-7p-35 has no solution.
What is equation?
Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. Since we can balance this by deducting the expression on the right from the expressions on both sides, this won't reduce the generality.
Here the given equation is
=> 36-7p=-7p-35
=>-7p+7p=-35-36
=>0=71
Then the statement is false for any value of p.
Hence the given equation has no solution.
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b) If a-b=5 and a² + b² = 37, find the value of ab
The value of ab=6.
What is [tex](a-b)^2[/tex] formula ?
To find the square of a binomial, use the [tex](a-b)^2[/tex] formula. One of the most common algebraic identities is the a minus b Whole Square Formula. This formula is also known as the difference between two terms squared formula. To factorise some special types of trinomials, the [tex](a-b)^2[/tex] formula is used.
Here [tex](a-b)^2 = a^2+b^2-2ab[/tex] then,
=> [tex](a-b)^2 = a^2+b^2-2ab[/tex]
Here a-b=5 and [tex]a^2+b^2[/tex] = 37.
=> [tex]5^2[/tex] = 37-2ab
=> 25 = 37-2ab
=> 2ab=37-25
=> 2ab = 12
=> ab=6.
Hence the value of ab=6.
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Write a slope-intercept equation for a line that passes through (-3,1) and (4, -13).
Answer:
[tex] \huge{ \bold{y = - 2x - 5}}[/tex]
Step-by-step explanation:
The equation of a line in slope-intercept form is represented by
y = mx + c
where
m is the slope
c is the y-intercept
First of all we have to find the slope from the two points given by using the formula
[tex]m = \frac{y_2 -y_ 1}{x_2 -x_1 } \\ [/tex]
where
(x1, y1) and (x2, y2) are the points
From the question the points are (-3,1) and (4, -13)
We have
[tex]m = \frac{ - 13 - 1}{4 - - 3} = \frac{ - 13 - 1}{4 + 3} = - \frac{14}{7} = - 2 \\ [/tex]
Next we find the y-intercept 'c' by placing one of the points and the slope into the slope-intercept form equation
Using point (-3,1) and m = -2
We have
[tex]1 = ( - 2)( - 3) + c \\ 1 = 6 +c \\ c = 1 - 6 = - 5[/tex]
Since we have both m and c we can place it into the main equation to find the equation
Using point and m = -2 c= -5
We have the final answer as
[tex] \bold{y = - 2x - 5}[/tex]
Hope this helps you
Which of the following shows the extraneous solution to the logarithmic equation log7 (3x³ + x)-log7(x)=2?
O x=-16
Ox=-4
Ox=4
O x-16
Answer: x=16
Step-by-step explanation:
log₇(3x²+x)-log₇x=2
Domian:
1)
3x²+x>0
x(3x+1)>0
-∞__+__-1/3__-__0__+__∞
x∈(-∞,-1/3)U(0,∞)
2)
x>0
Hence, x∈(0,∞)
Thus x∈(0,∞)
In this problem we use the following formula:
[tex]\boxed {log_ax-log_ay=log_a\frac{x}{y}}[/tex]
[tex]\displaystyle\\log_7(3x^2+x)-log_7x=2\\\\log_7(x(3x+1))-log_7x=2(1)\\\\log\frac{x(3x+1)}{x} =2(log_77)\\\\log(3x+1)=log_77^2\\\\log_7(3x+1)=log_749\\\\Hence,\\\\3x+1=49\\\\3x+1-1=49-1\\\\3x=48\\\\ Divide\ both\ parts \ of\ the \ equation\ by\ 3:\\\\x=16[/tex]
The extraneous solution to the logarithmic equation log7 (3x³ + x)-log7(x)=2 is x= 4.
What is Logarithm?A base must be raised to a certain exponent or power, or logarithm, in order to produce a specific number.
We have Logarithmic expression as
log7 (3x³ + x)-log7(x)=2
we know, [tex]log_ax - log_a y= log_a (x/y)[/tex]
Using the above property as
log7 (3x³ + x)-log7(x)=2
[tex]log_7[/tex] (3x³ + x) - [tex]log_7[/tex] x =2
[tex]log_7[/tex] x(3x² +1) / x = 2
[tex]log_7[/tex] (3x²+1) = 2(1)
[tex]log_7[/tex] (3x²+1) = 2(1)[tex]log_7 (7)[/tex]
[tex]log_7[/tex] (3x²+1) = [tex]log_7[/tex]7²
Now, comparing we get
3x² +1 = 7²
3x² = 48
x² = 16
x = 4
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The front of a brush fire is moving through some dead grass at a rate of 3 miles per hour. Luckily, it is moving directly toward the fire station, which can dispatch a fire truck to fight the blaze. If the fire station is 1 mile away and the truck can travel straight to the fire's front at 44 miles per hour, how long will it be before the fire truck reaches the fire's front?
The fire truck, a mile away, traveling at 44 miles per hour towards the the bush fire, which is also traveling towards at 3 miles per hour towards it, reaches the fire's front in 1/47 hours or approximately 76.6 seconds
How many minutes are there in one hour?There are 60 seconds in a minute and 60 minutes in an hour, which makes 60 × 60 = 3600 seconds in one hour.
The rate at which the bush fire is moving, v₁ = 3 miles per hour
The direction the bush fire moves = Towards the fire station
Distance of the bush fire from the fire station, d = 1 mile
Speed of the fire truck, v₂ = 44 miles per hour
The equation that gives the time, t, the fire truck reaches the fire front is presented as follows;
v₁·t + v₂·t = d
Which gives; 3 × t + 44 × t = 1
47 × t = 1
[tex]t = \dfrac{1}{47}[/tex]
The time it takes the fire truck to reach the bush fire is 1/47 of an hour, which is approximately 76.6 seconds
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AP STATISTICS MATH
(Image above) PLEASE HELP THANK YOU (brainlist answer)
The probabilities are given as follows:
3. P(rides bus|owns a car) = 1/3.
4. P(red|organic) = 3/5.
How to calculate a probability?The probability of an event in an experiment is obtained as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.
For item 3, the outcomes are given as follows:
Desired outcomes: rides bus and owns a car -> 8 people.Total outcomes: owns a car -> 24 people.Hence the probability is:
P(rides bus|owns a car) = 8/24 = 1/3.
For item 4, the outcomes are given as follows:
Desired outcomes: red and organic -> 18%Total outcomes: organic -> 30%.The error was in identifying the total outcomes, and the probability is:
P(red|organic) = 18/30 = 3/5.
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How do you find the margin of error for the difference between means?
The margin of error can be calculated in two ways, depending on whether you have population parameters or sample statistics:
Margin of error (parameter) = critical value x population standard deviation Margin of error (statistic) = Critical value x Sample standard error
What is a margin of error?A margin of error is a statistical metric that accounts for the difference between actual and projected survey results in a random sample.
In layman's terms, the margin of error measures the degree of unpredictability in data and research results. The margin of error formula is calculated by multiplying a critical factor. The result is then divided by the square root of the sample's number of observations.
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30. A big candle is made up of a pyramid with a slant height of attached to a cuboid with a square base of sides and a height of . (i) Calculate the volume of the candle. Another candle is made in the shape of a sphere. The volume of this candle is one-tenth the volume of the big candle. (ii) Show that the radius of the spherical candle is , correct to 3 significant figures. The diagram shows the plan view of a box holding two of the spherical candles. The candles just fit into the box in the shape of a cuboid. (iii) Calculate the volume of empty space in the box.30. A big candle is made up of a pyramid with a slant height of attached to a cuboid with a square base of sides and a height of . (i) Calculate the volume of the candle. Another candle is made in the shape of a sphere. The volume of this candle is one-tenth the volume of the big candle. (ii) Show that the radius of the spherical candle is , correct to 3 significant figures. The diagram shows the plan view of a box holding two of the spherical candles. The candles just fit into the box in the shape of a cuboid. (iii) Calculate the volume of empty space in the box.
i) The volume of the candle is 48047.96 cubic cm. ii)the radius of the candle is 10.468 cm and iii)Volume of empty spaces in the box is 8749.73 cubic cm.
i) Slant height of the Pyramid = 39cm
Base length = 30 cm
Height of the pyramid part = √(39²-30²) = 24.92 cm
Volume of the pyramid part = 30 × 30 × 24.92 ÷ 3 = 7475.96 cm³
Height of the candle = 70 cm
Height of the cuboid= 70 - 24.92 = 45.08cm
Volume of the cuboid = 30 × 30 × 45.08 = 40572 cubic cm
Total volume of the candle = 7475.96 cm³ + 40572 cm³ = 48047.96 cm³
ii) Volume of the spherical candle = 0.1 × 48047.96 cm³ = 4804.79 cm ³
Now let the radius be r.
Hence 4/3 πr³ = 4804.79
or, r = 10.4679.. cm
or, r ≈ 10.468 cm
iii) Dimensions of the box = 10.468 × 2 = 20.94 cm
Height = 20.94cm
Width = 10.468 × 4 = 41.87 cm
Volume of the box = 41.87 × 20.94 × 20.94 = 18359.31 cubic cm
Volume of the candles = 4804.79 cm ³× 2 = 9609.58 cm³
Empty space in the box = 8749.73 cm³
Hence the empty spaces is 8749.73 cm³
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In a two digit number, the ones digit is
twice the tens digit. If the gits are reversed, the new number is 36 more than the original What is the number
Answer:
I think 48!
Step-by-step explanation:
I’m just really confused
Answer:
27
Step-by-step explanation:
cancel out the dilation by multiplying it by the reciprocal
18 x 3/2
27
I'm 80% sure
Answer:
12 is the answer
Step-by-step explanation:
you need to multiply the pre-image (the letters without an apostrophe beside it) with the dilation number (2/30)
Translate the sentence into an equation.
The product of 5 and w is the same as w to the
third power.
Answer: 5w=w^3
Step-by-step explanation:
This is because the product means multiplication and so it would be 5w and then is in math is the same as equals so you have an equal sign and then it would w to the third power.
i need help asap with this question
Answer:
C
Step-by-step explanation:
to find the unit rate divide miles travelled by petrol used , that is
60 [tex]\frac{2}{3}[/tex] ÷ 4 [tex]\frac{2}{3}[/tex] ← change mixed numbers to improper fractions
= [tex]\frac{182}{3}[/tex] ÷ [tex]\frac{14}{3}[/tex]
• leave first fraction, change ÷ to × , turn second fraction ' upside down'
= [tex]\frac{182}{3}[/tex] × [tex]\frac{3}{14}[/tex] ( cancel 3 on numerator/ denominator )
= 182 × [tex]\frac{1}{14}[/tex]
= [tex]\frac{182}{14}[/tex]
= 13
the car travels 13 miles per gallon of petrol
help me out thank you so much
The pairs of equations and their responses are below
(1/5)^2 + 1 and 2 12/25 No
(1 + 1/4)^2 and 2 - 7/16 Yes
How to know if the expressions will form equationsThis is done by solve both sides of the equation. If they have same answer then they can form equation. If otherwise they they cannot form equation
solving the first expressions
left hand side
(1/5)^2 + 1
= 1/25 + 1
= 26/25
right hand side
2 * 12/25
= 24/25
comparing the two sides shows that the 26/25 ≠ 24/25
solving the second expressions
left hand side
(1 + 1/4)^2
= (5/16)^2
= 25/16
right hand side
2 - 7/16
= 25/16
comparing the two sides shows that the 25/16 = 25/16solving the first part
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Choose ALL answers that describe the quadrilateral VWXYVWXY if VW = 15VW=15, WX = 15WX=15, XY = 15XY=15, YV = 15YV=15, and diagonals have equal length: VX = WYVX=WY.
A description of the quadrilateral VWXY that has equal length sides and equal length diagonals is that the quadrilateral is a square
What is a quadrilateral?A quadrilateral is a polygon that has four sides and four vertices or corners, such that a quadrilateral ABCD has sides AB, BC, CD, and AD, and interior angles ∠A, ∠B, ∠C, and ∠D
The given description of the quadrilateral VWXY are;
VW = 15, WX = 15, XY = 15, YV = 15
The lengths of the sides of the quadrilateral VWXY are the same
The length the diagonals are the same;
VX = WY = VX = WY
The properties of a square are;
The interior angles are congruent and equal to 90°
The four sides have equal length
Opposite sides of a square are congruent
The length of the diagonals are the same
The the same length diagonals of quadrilateral indicates that the quadrilateral can be either a square or a rectangle
The property of the quadrilateral of equal length sides indicate that the quadrilateral is a square.
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What number is the abscissa of the point ( 8,7 )
In coordinate system, the number that is the abscissa of the point ( 8,7 ) is 8.
coordinate geometry:
It establishes a connection between geometry and algebra using curves and line graphs.
A point's x and y coordinates are also referred to as abscissa and ordinate, respectively.
The abscissa and ordinate all together are called coordinates.It is for a point in the Cartesian plane, an ordered pair is used as the symbol.the abscissa is the x–coordinate of any point A(x, y).
so,
abscissa of the point ( 8,7 ) is 8.
In coordinate system, the number that is the abscissa of the point ( 8,7 ) is 8.
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Solve: 12x² +5x-4_122x+6
Ox=2
O x = -5
O x = 2, x = -5
Ono solution
Solution of the expression are,
⇒ x = - 5, x = 2
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ [tex]12^{x^{2} + 5x - 4} = 12^{2x + 6}[/tex]
Now, We can compare as;
⇒ x² + 5x - 4 = 2x + 6
Solve for x as;
⇒ x² + 3x - 10 = 0
⇒ x² + 5x - 2x - 10= 0
⇒ x (x + 5) - 2 (x + 5) = 0
⇒ (x + 5) (x - 2) = 0
⇒ x = - 5, x = 2
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A phone company offers two monthly plans. Plan A costs $28 plus an additional $.0.10 for each minute of calls. Plan B has no initial fee but costs $.0.15 for each minute of calls. What amount of calling do the two plans cost the same
The amount of calling for which the two plans cost the same will be 525 minutes.
The cost when two plans cost the same amount is $68.25.
