=====================================================
Explanation:
The domain is the set of all real numbers. This is because the graph goes on forever to the left and right. We can use any x value we want as an input. There are no restrictions to worry about such as to prevent dividing by zero errors.
To say "all real numbers" in interval notation, we write [tex](-\infty, \infty)[/tex] which is another way of saying [tex]-\infty < x < \infty[/tex]
-------------------
The range in interval notation is [tex][3, \infty)[/tex] since y = 3 is the smallest y output possible, and we could have larger y values as well. So basically [tex]y \ge 3[/tex] can be used to describe the range without saying much else.
Note the use of a square bracket to include 3 as part of the interval.
-------------------
There are no x intercepts because this graph does not cross the x axis. The lowest point is at (-2,3) so there's no way we could reach y = 0. Put another way, y = 0 is not part of the range so we cannot have any x intercepts.
There is one y intercept and it is at (0,7) where the graph crosses the y axis. For any function, the max number of y intercepts is 1.
-------------------
When it says "interval positive", its asking "which part(s) of the graph are above the x axis?". That would be the entire graph meaning we have the interval [tex](-\infty, \infty)[/tex]. Every point on this V shaped curve is of the form (x,y) where y is positive.
So this means that we do not have any points with a negative y value, and therefore the answer to "interval negative" is none.
-------------------
Now onto the "interval increasing". This is similar to the previous section, but now we're looking when the graph is going uphill as we read from left to right. This happens on the interval [tex](-2, \infty)[/tex] or put another way when x > -2.
The graph goes downhill whenever x < -2. So that's why the answer for the "interval decreasing" is [tex](-\infty, -2)[/tex]
-------------------
Note the points (-2,3) and (0,7) are on the V shaped graph. These points have x coordinates of x = -2 and x = 0, which are the endpoints of the interval we're focusing on.
Compute the slope of the line through those two points
m = (y2-y1)/(x2-x1)
m = (7-3)/(0-(-2))
m = (7-3)/(0+2)
m = 4/2
m = 2
The positive slope means the line goes uphill as we read from left to right
The average rate of change on the interval [-2, 0] is the value 2
In other words, we go up 2 units each time we move to the right 1 unit.
Prove: (AUB) \ (AnB) =(A\B) u (B\A)
Answer:
Prove that (A-B) U (B-A) =(A U B) - (A intersection B). 2. See answers ... izvoru47 and 170 more users found this answer helpful
Which of the following is most likely the next step in the series
Answer:
C
Step-by-step explanation:
In the pattern, there are some similarities with the first three circles.
1. The number is on the blue half.
2. The halves switch spots, red-blue, blue-red, red-blue.
So, the next one should have the number on the blue half and the next pattern should be red-blue, blue-red, red-blue, and blue-red.
Which one has both the number on the blue half and the pattern blue-red?
C
Hoped this helped.
A study of 200 computer service firms revealed these incomes after taxes: Income After Taxes Number of Firms Under $1 million 102 $1 million up to $20 million 61 $20 million or more 37 What is the probability that a particular firm selected has $1 million or more in income after taxes
Answer: 0.49
Step-by-step explanation:
given data:
no of computer services firms =200
no of firms under $1million = 102
no of firms between $1million to $20million = 61
no of firms $20million and above = 37
solution:
probability that a firm selected has 1$million or above.
P ( x ≥ $1million )
= 61/200 + 37/200
= 49/100
= 0.49
the probability of selecting with $1million or more in income taxes is 0.49%
A 20-person fraternity is making their weekend plans around 5 different parties in IV. Each brother will attend exactly one of the parties. Fraternity rules state that the fraternity must have a representative at each party. Assume that only the number of brothers that show up at a party is important, i.e. the brothers are indistinguishable. (a) How many different arrangements of plans are possible
Answer:
3876
Step-by-step explanation:
Given the following :
Fraternity members = 20
They are to attend 5 different parties in groups of 4
Meaning a group = 4 persons
Atleast one brother will attend exactly one of the parties. (the brothers are indistinguishable).
Then, exactly one brother at a party (20 - 1) = 19, since they are indistinguishable.
Group members are in 4's
19C4
From: nCr = n! /(n-r)! r!
19C4 = 19! / (19 - 4)! 4!
= 19! / 15! 4!
= (19 * 18 * 17 * 16) / (4 * 3 * 2)
= 93024 / 24
= 3876
cells splits into 2 cells every hour. Write expression to find number of cells in 6 hours
Answer:
12 cells every hour.
Step-by-step explanation:
You would do 2 x 6
(the 2 is the cells per hour, and the 6 is the amount of hours)
Find the value of x that makes AFGH~AJKL.
(Lesson 11.3) (1 point)
X+3.5
20
Answer: The answer is: " x = 2.833333333333...." .
___________________________
or: write as: " 2 [tex]\frac{5}{6}[/tex] " .
___________________________
Step-by-step explanation:
___________________________
Set up a ratio:
Note: Segment FH = (x + 35)
Segment JL = 20 ;
Segment FH ~ Segment JL ;
___________________________
Note: Segment GH = (x - 4) ;
Segment KL = 5 ;
Segment GH ~ Segment KL .
___________________________
So, ( x + 3.5) : 20 :: (x-4) : 5 ;
Write this ratio in fraction format:
___________________________
→ [tex]\frac{(x+3.5) }{20 } = \frac{(x-4) }{5}[/tex] ;
Now; "cross-factor multiply" :
→ [tex]\frac{a}{b} = \frac{c}{d }[/tex] ; → [tex]ad = bc[/tex] ; { [tex]{ a\neq0 ; b\neq0 ; c\neq0 ; d\neq0[/tex] .}.
___________________________
So:
5(x + 3.5) = 20(x - 4) ;
___________________________
→ To simplify, start by divide each side of the equation by "5" ;
___________________________
→ {5(x + 3.5) } / 5 = { 20(x - 4) } / 5 ;
to get:
→ (x + 3.5) = 4(x - 4) ;
___________________________
Now, on the right-hand side of the equation;
let us expand the expression;
___________________________
We have the expression: " 4(x - 4) " ;
To expand:
Note the "distributive property of multiplication:
→ a(b + c) = ab + ac ;
Likewise:
→ 4(x - 4) = 4x - 16 ;
___________________________
Now, we can rewrite our equation:
___________________________
→ " x + 3.5 = 4x - 15 " ;
Now, we can subtract "x" from each side of the question;
& add "15" to each side of the equation; as folllows:
___________________________
→ x + 3.5 = 4x - 15 ;
- x + 15 = - x +15
___________________________
to get: 8.5 = 3x ;
↔ 3x = 8.5 ;
Now, divide each side of the equation by "3" ;
to isolate "x" on one side of the equation;
& to solve for "x" ; as follows:
→ 3x / 3 = 8.5 / 3 ;
to get: x = 8.5 /3
= 2.83333333333 ;
or; write as: " 2 [tex]\frac{5}{6}[/tex] ."
___________________________
Hope this is helpful to you! Best wishes!
___________________________
What number should be placed in the box to help complete the division calculation? long division setup showing an incomplete calculation. 12 is in the divisor, 8587 is in the dividend, and 7 hundreds and 1 tens is written in the quotient. 8400 is subtracted from 8587 to give 187. An unknown value represented by a box is being subtracted from 187.
Answer:
120
Step-by-step explanation:
Your description is a little different from below picture, but the logic is the same. The 1 in the tens position represents 10x12 = 120, hence 120 should be subtracted and leaves you with 67 to continue.
Answer:
187
Step-by-step explanation:
12 in not the divisor of 8587 in the dividend with 7 hundreds and 1 tens. 8400 you subtracted from 8587 to give 187.
Sam missed a question on his Algebra Test. He wrote his work down. Where is his error in solving 3x + 2 = 14?
Answer:
10/3
Step-by-step explanation:
Step 1: Subtract 4 from both sides.
3
x
+
4
−
4
=
14
−
4
3
x
=
10
Step 2: Divide both sides by 3.
3
x
3
=
10
3
Which figure shows △MNP reflected over the y-axis to form △M`N`P`?
Answer:
The answer is in the picture below
Step-by-step explanation:
Hope this helps!
Figure number four in the image shows △MNP reflected over the y-axis to form △M`N`P`. The correct option is D.
What is the reflection of an image?The reflection operator geometrically repositions image elements, or pixel values, in such a way that they are reflected about a user-specified image axis or image point and placed in a new position in a matching output image.
In the given image option fourth is showing the correct reflection of the triangle △MNP over the y-axis to the form △M`N`P'.
It is observed that every point of the triangle MNP is at the same distance from the y-axis as every point of the triangle M'N'P'.
Therefore, figure number four in the image shows △MNP reflected over the y-axis to form △M`N`P`. The correct option is D.
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5. ACT scores for a group of six students from a local high school is 21, 22, 23, 25, 26, 33. What is the range for this distribution of scores?
Answer:
12
Step-by-step explanation:
The formula for RANGE of a given set if data = Maximum value - Minimum value.
In the above question, we are given a group of ACT scores
21, 22, 23, 25, 26, 33.
Maximum value = 33
Minimum value = 21
Range = 33 - 21
= 12
Therefore, the range for this distribution of scores is 12
I will Mark you as brainliest if you show your work
Answer:
16 miles long to work it would be 0 miles shorter
Step-by-step explanation:
8+8 is 16
if the road was just one street it would still be the same distance
I hope this helps. THIS MIGHT BE WRONG though if someone say something else, take a good look at their answer too because the way I did it, seems like it's a little too simple.
Answer: The distance will be about 11 miles . 2) The man's one way-trip will be 5 miles shorter.
Step-by-step explanation:
If the man drove east by 8 miles and North by 8 miles and we want to determine the distance that is directly from east to north then we will use the Pythagorean Theorem solve for that distance.
Now since we are solving for the distance directly from his home to work we will be looking for the hypotenuse in this case.
a^2 + b^2 =c^2 where c is the hypotenuse
8^2 + 8^2 =c^2
64 +64 = c^2
c= [tex]\sqrt{128}[/tex]
c = 11.31
In this case the distance from his home directly to his work will be about 11 miles.
2. To find out how much shorter the man will travel ,add the east and north distance and subtract 11.31 from it.
8 + 8 = 16
16 - 11.31 = 4.69
if 6x is 6, then what is the square root of 4761 x
Answer:
the answer is 69
Step-by-step explanation:
you find the square root of 4761
Answer:
its 69
Step-by-step explanation:
Write -5 less than p as an expression
Answer:
the answer is -5 -p
Step-by-step explanation:
the reason why this is, because negative 5 is less than (-) the variable p.
2(3w+9z) simplify it please .
Answer:
6w + 18z
Step-by-step explanation:
distribute the 2
2 x 3w = 6w
2 x 9z = 18 z
6w + 18z
Answer:
6w+18z
Step-by-step explanation:
The number of foxes in a national forest had grown by 1160 in the past year If the number of foxes at the beginning of the year was 5800 by what percent did it increase
Answer:
5800-1160=4640
1160×100÷4640=25
=25%
Are these ratios equivalent 4:5 and 16:20 yes or no
Answer:
yes
Step-by-step explanation:
this is correct because if you multipy them both by 4 you get those answers .
4 x 4 = 16
5 x 4 = 20
The ratios 4:5 and 16:20 are equivalent to each other. Yes, the ratios are equal to 4: 5.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
The equivalent is the expression that is in different forms but is equal to the same value.
The two ratios are given below.
4:5 and 16:20
Convert the ratios into their simplified form. Then the ratios are given as,
4:5 and 16:20
4:5 and 4:5
The ratios 4:5 and 16:20 are equivalent to each other. Yes, the ratios are equal to 4: 5.
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From 12:00 midnight to 6:00am
Answer:
6 hours?
Step-by-step explanation:
12:00 0 hour(s)
1:00 1 hour(s)
2:00 2 hour(s)
3:00 3 hour(s)
4:00 4 hour(s)
5:00 5 hour(s)
6:00 6 hour(s)
Which Greek geometer founded a philosophical society that devoted itself to the study of mathematics?'
Answer:
Pythagoras
Step-by-step explanation:
Pythagoras
Solve each equation.
1. 6k – 3 = 2k + 13
Answer:
4k=16
k=4
Step-by-step explanation:
please give 5 star i need it
A rectangular tank that is 2048 ft cubed with a square base and open top is to be constructed of sheet steel of a given thickness. Find the dimensions of the tank with minimum weight.
Answer:
The box should have base 16ft by 16ft and height 8ft Therefore,dimensions are 16 ft by 16 ft by 8 ft
Step-by-step explanation:
We were given the volume of the tank as, 2048 cubic feet.
Form minimum weight, the surface area must be minimum.
Let the height be h and the lengths be x
the volume will be: V=x²h then substitute the value of volume, we have
2048=hx²
hence
h=2048/x²
Since the amount of material used is directly proportional to the surface area, then the material needs to be minimized by minimizing the surface area.
The surface area of the box described is
A=x²+4xh
Then substitute h into the Area equation we have
A= x² + 4x(2048/x²)
A= x² + 8192/x
We want to minimize
A
dA/dx = -8192/x² + 2 x= 0 for max or min
when dA/dx=0
dA/dx= 2x-8192/x²=0
2x=8192/x²
Hence
2x³=8192
x³=4096
x=₃√(4096)
X=16ft
Then h=2048/x²
h=2048/16²
h=8ft
The box should have base 16ft by 16ft and height 8ft
Hence the dimensions are 16 ft by 16 ft by 8 ft
Data for price and thickness of soap is entered into a statistics software package and results in a regression equation of ŷ = 0.4 + 0.2x.
What is the correct interpretation of the slope if the price is the response variable and the thickness is an explanatory variable?
A. The price of the soap increases by $0.20, on average, when the thickness increases by 1 cm.
B. The price of the soap decreases by $0.40, on average, when the thickness increases by 1 cm.
C. The price of the soap increases by $0.40, on average, when the thickness increases by 1 cm.
D. The price of the soap decreases by $0.20, on average, when the thickness increases by 1 cm.
Answer: A. The price of the soap increases by $0.20, on average, when the thickness increases by 1 cm
Step-by-step explanation:
Given the following :
Regression equation : ŷ = 0.4 + 0.2x
Price is the response variable (ŷ)
Thickness is the explanatory variable (x)
Relating the equation given to the regression model:
ŷ = c + mx
Here c = intercept ; y = response variable ;x = explanatory variable and m = slope or gradient.
Hence, mx = 0.2x
Where m = 0.2
The slope means :
Change in y / change in x
Changes in the response variable with respect to change in the explanatory variable.
The slope is positive meaning an increase in the thickness will result in a corresponding increase in price.
With a 0.2 gradient value, that means there is an $0.2 average increase in price of soap as the thickness increases by 1 cm.
Answer:
The price of the soap increases by $0.20, on average, when the thickness increases by 1 cm.
Step-by-step explanation:
**WILL GIVE BRAINLIEST** Absolute Value Question. PLEASE HELP QUICK.
Cross multiply the numbers in the matrix:
1 *2 + 5*x = -13
Simplify:
2 + 5x = -13
Subtract 2 from both sides:
5x = -15
Divide both sides by 5
X = -15/5
X = -3
Because it’s absolute value it needs to be positive so x = 3
The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, μ, of 42°F, ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the true mean temperature is incorrect. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.There is not sufficient evidence to support the claim that the mean temperature is different from 42 deg There is not sufficient evidence to support the claim that the mean temperature is equal to 42 deg There is sufficient evidence to support the claim that the mean temperature is different from 42 deg There is sufficient evidence to support the claim that the mean temperature is equal to 42deg
Answer:
There is sufficient evidence to support the claim that the mean temperature is different from 42 deg
Step-by-step explanation:
From the given information, we are being told that:
The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, μ, of 42°F
i. e mean μ = 42
The owner of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the true mean temperature is incorrect.
Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.
From above;
The null and the alternative hypothesis can be computed as:
[tex]\mathbf{H_o : \mu = 42} \\ \\ \mathbf {H_1 : \mu \neq 42}[/tex]
Here , the hypothesis test of the claim is the alternative hypothesis.
The conclusion based on the decision rule: is to reject the null hypothesis
∴
The conclusion in non technical terms is that :
There is sufficient evidence to support the claim that the mean temperature is different from 42 deg
2y + 18 y + 39 Find y
Answer:
Step-by-step explanation: 2y+18 = y+39
y=21
Answer:
y = 21
Step-by-step explanation:
In the figure , 2y + 18 and y + 39 are opposite interior angles . We know that opposite interior angles are equal , so
2y + 18 = y + 39
=> 2y - y = 39 - 18
=> y = 21
1 meter is equivalent to how many feet
The profit that a business made during a year is $536,897,000. If the business divides the profit evenly for each share, estimate how much each share made if there are 10,995,000 shares.
48% of their readers own a particular make of car. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 300 found that 45% of the readers owned a particular make of car. Is there sufficient evidence at the 0.02 level to support the executive's claim?
Answer:
There is no sufficient evidence to support the executive claim
Step-by-step explanation:
From the question we are told that
The population proportion is [tex]p = 0.48[/tex]
The sample proportion is [tex]\r p = 0.45[/tex]
The sample size is [tex]n = 300[/tex]
The level of significance is [tex]\alpha = 0.02[/tex]
The null hypothesis is [tex]H_o : p= 0.48[/tex]
The alternative hypothesis is [tex]H_a : p \ne 0.48[/tex]
Generally the test statistics is mathematically evaluated as
[tex]t = \frac{\r p - p }{ \sqrt{ \frac{p(1 - p )}{n} } }[/tex]
=> [tex]t = \frac{0.45 - 0.48 }{ \sqrt{ \frac{0.48 (1 - 0.48 )}{300} } }[/tex]
=> [tex]t = -1.04[/tex]
The p-value is mathematically represented as
[tex]p-value = 2P(z > |-1.04|)[/tex]
Form the z-table
[tex]P(z > |-1.04|) = 0.15[/tex]
=> [tex]p-value = 2 * 0.15[/tex]
=> [tex]p-value = 0.3[/tex]
Given that [tex]p-value > \alpha[/tex] we fail to reject the null hypothesis
Hence we can conclude that there is no sufficient evidence to support the executive claim
What is the slope of the function y= 4x+ 6
Answer:
The answer is 4Step-by-step explanation:
Since the function is a linear function
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
From the question the equation is
y = 4x + 6
Comparing with the general form of equation above the slope of the function is
4Hope this helps you
Simplify: (x-3) (x-3)
Answer:
x^2 -6x +6
Step-by-step explanation:
Square of a difference (can be found in IM2)
Formula: a^2 -2ab +b^2
x= a; 3= b
(x -3)(x -3)
Plug in to formula.
x^2 -2(x)(3) +3^2
Simplify.
x^2 -6x +6
Answer:
[tex](x - 3)^{2}[/tex]
Help Please!!!!! What is the absolute value of ∣∣2 1/3 ∣∣? Use this number line to determine the absolute value. Enter your answer in the box as a mixed number in simplest form.
Answer:
2 1/3
Step-by-step explanation:
i know because i did the test in k 12
An absolute value of |x| {modulus of x} is the value of a real number x. The absolute value of ||2 1/3|| is 2 1/3.
What is Absolute Value?An absolute value of |x| {modulus of x} is the value of a real number x, the value we get is always a non-negative number, for example, |-5| will give 5, and also, |5| will give 5 as well.
The absolute value of ||2 1/3|| is,
||2 1/3||
= |2 1/3|
= 2 1/3
Hence, The absolute value of ||2 1/3|| is 2 1/3.
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