Answer:
Step-by-step explanation:
From the given information:
the null hypothesis and the alternative hypothesis can be computed as follows:
[tex]\mathbf{H_o:}[/tex] The sample have a distribution that agrees with the distribution of state populations.
[tex]\mathbf{H_1:}[/tex] The sample have a distribution that does not agrees with the distribution of state populations.
The Chi-Square test statistics [tex]\mathbf{X^2 = \dfrac{(Observed \ value - Expected \ value )}{(Expected \ value ) ^2 }}[/tex]
Among the four northwestern states, Washington has 51% of the total population, Oregon has 30%, Idaho has 11%, and Montana has 8%. A market researcher selects a sample of 1000 subjects, with 450 in Washington, 340 in Oregon, 150 in Idaho, and 60 in Montana.
The observed and the expected value can be computed as follows:
States Observed Expected [tex]X^2 = \dfrac{(O- E)^2}{E}[/tex]
Washington 450 0.51 × 1000 = 510
Oregon 340 0.30 × 1000 = 300
Idaho 150 0.11 × 1000 = 110
Montana 60 0.08 × 1000 = 80
Total 1000 1000
For washington :
[tex]X^2 = \dfrac{(O- E)^2}{E}[/tex]
[tex]X^2 = \dfrac{(450 -510)^2}{510}[/tex]
[tex]X^2 = \dfrac{3600}{510}[/tex]
[tex]X^{2}=[/tex] 7.06
For Oregon
[tex]X^2 = \dfrac{(O- E)^2}{E}[/tex]
[tex]X^2 = \dfrac{(340- 300)^2}{300}[/tex]
[tex]X^2 = \dfrac{1600}{300}[/tex]
[tex]X^{2}=[/tex] 5.33
For Idaho
[tex]X^2 = \dfrac{(O- E)^2}{E}[/tex]
[tex]X^2 = \dfrac{(150- 110)^2}{110}[/tex]
[tex]X^2 = \dfrac{1600}{110}[/tex]
[tex]X^2 =14.55[/tex]
For Montana
[tex]X^2 = \dfrac{(O- E)^2}{E}[/tex]
[tex]X^2 = \dfrac{(60- 80)^2}{80}[/tex]
[tex]X^2 = \dfrac{400}{80}[/tex]
[tex]X^2 = 5[/tex].00
The Chi-square test statistics for the observed and the expected value can be computed as follows:
States Observed Expected [tex]X^2 = \dfrac{(O- E)^2}{E}[/tex]
Washington 450 0.51 × 1000 = 510 7.06
Oregon 340 0.30 × 1000 = 300 5.33
Idaho 150 0.11 × 1000 = 110 14.55
Montana 60 0.08 × 1000 = 80 5.00
Total 1000 1000 31.94
The Chi-square Statistics Test [tex]\mathbf{X^2 = 31.94}[/tex]
Degree of freedom = n - 1
Degree of freedom = 4 - 1
Degree of freedom = 3
At 0.05 level of significance, the critical value of :
[tex]X^2_{(df, \alpha) }=X^2_{(3, 0.05)[/tex] = 7.815
Decision Rule: To reject null hypothesis if the test statistics is greater than the critical value
Conclusion: We reject the null hypothesis since test statistics is greater than critical value, therefore, we conclude that there is sufficient information to say that the sample has a distribution that does not agrees with the distribution of state populations.
If 7x + 4 = -19 + 5x, then 2x – 14 equals
A-23
B 23
C-37
D-14
Answer:
C
Step-by-step explanation:
Here we have the question,
7x+4 = -19 + 5x
Now we add 19 to both sides,
7x + 4 + 19 = -19 + 19 + 5x
7x + 23 = 5x
Now we subtract 7x from both sides,
23 = -2x
We divide -2 from both sides,
x = -23/2
Now we plug this in into 2x - 14,
2(-23/2) - 14 = -23-14 = -37
Our answer is C
Lori is picking up lunch for herself and her coworkers. Some of her coworkers ordered the salad which costs $7.50, and some of her coworkers ordered the soup which costs $6.25. When Lori gets to the restaurant, she had lost the paper where she had written down who ordered which. She recalls that twice as many people ordered the salad than the soup, and she has a total of $63.75 to pay for the orders. How many people must have ordered the soup?
Answer: 3 people ordered soup.
Step-by-step explanation:
Let x be the number of people ordered salad and y be the number of people ordered soup.
As per given,
x=2y (i)
7.50x+6.25y= 63.75 (ii)
Substitute value of c =2y in (ii) , we get
7.50(2y)+6.25y= 63.75
⇒ 15y+6.25y = 63.75
⇒21.25y = 63.75
⇒ y= 3 [divide both sides by 21.25]
Then, x= 2(3) =6
So 6 people ordered salad and 3 people ordered soup.
Help me please thank you
Answer: 62°
Step-by-step explanation:
apply concept: the interior angle sum of triangle is = 180°
a+b+c=180
a+68.5+49.5=180
a+118=180
a=62
Answer:
x = 62°Step-by-step explanation:
Since it's a triangle it's interior angles sum up to 180° .
In order to find x add up all it's known interior angles and subtract it from 180° to find x.
That's
x + 68.5 + 49.5 = 180
x + 118 = 180
x = 180 - 118
We have the final answer as
x = 62°Hope this helps you
Beth is considering two job offers. One has an annual salary of $61.1K and the other has an annual salary of $63.4K. What is the difference in the weekly pay for these two job? (K means $1,000, so $61.1K is $61,100 for example) *
Answer: The difference is approximately $44. Remember that is not an exact amount because the weeks are approximated and the second offer was also approximated.
Step-by-step explanation:
If one has $61,100 and the other has 63,400 annually which means that is the amount they will be offered a year. So first we need to determine how many weeks are in a year.There are approximately 52 weeks in one year so we will divide the salaries by 52 to find how much they each offer in one week.
First Offer: 61,100 / 52 = 1175
Second Offer: 63,400/52= approximately 1219
Now find the difference between the numbers
1219. - 1175 = $44
The difference in weekly pay for these two job will be around $0.04k.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Summation = addition of two or more numbers or variable
For example = 2 + 8 + 9
Subtraction = Minus of any two or more numbers with each other called subtraction.
For example = 4 - 8
Division = divide any two numbers or variable called division.
For example 4/8
Multiplication = to multiply any two or more numbers or variables called multiplication.
For example 5 × 7.
Number of weeks in 1 year = number of weeks in 1 month × 12
Number of weeks in 1 year = 4 × 12 = 48
Annual salary in the first job = $61.1k
So weekly salary of first job =$1.28k
Annual salary in the second job = $63.4k
So weekly salary of second job = $1.32k per week
Difference between weekly pay = 1.32 - 1.28 = 0.04k
Hence "The difference in weekly pay for these two job will be around $0.04k".
To learn more about the arithmetic operators,
brainly.com/question/25834626
#SPJ2
To mix a particular shade of purple paint, red paint and blue paint are mixed in the ratio 5:3. To make 20 gallons of this shade of purple paint, how many gallons of red and blue paint should be used?
Answer:
quantity of red paint = 12.5 gallons
quantity of blue paint = 7.5 gallons
Step-by-step explanation:
Ratio of red and blue paint : 5:3
in ratio
a:b = ax:bx
let the
quantity of red paint be 5x
quantity of blue paint be 3x
then quantity of purple paint = quantity of red paint + quantity of blue paint
= 8x
given quantity of purple paint is 20 gallons
thus,
8x = 20
x = 20/8 = 2.5
thus,
quantity of red paint = 5x = 5*2.5 = 12.5 gallons
quantity of blue paint = 3x = 3x*2.5 = 7.5 gallons
Answer:
7 and 12.5
Step-by-step explanation:
The length of the shadow of a pole on level ground increases by 90m when the angle of elevation of the sun changes from 58° to 36° find the height of the pole
Answer:
119.45 m
Step-by-step explanation:
Given:
When angle of elevation of the sun changes from 58° to 36° the length of shadow of a pole increases by 90 m.
To find:
Length of pole = ?
Solution:
Kindly refer to the attached image.
[tex]\triangle ABC[/tex] represents the 1st angle of elevation of sun i.e. 58°
[tex]\triangle ABD[/tex] represents the 2nd angle of elevation of sun i.e. 36°
Change in shadow is represented by CD = 90 m
Let height of pole, AB = [tex]h[/tex] m
Let side BC = [tex]x[/tex] m
Now, let us apply tangent rules in [tex]\triangle ABC, \triangle ABD[/tex] one by one:
[tex]tan\theta = \dfrac{Perpendicular}{Base}\\\Rightarrow tan58^\circ=\dfrac{AB}{BC}\\\Rightarrow tan58^\circ=\dfrac{h}{x}\\\Rightarrow x = 0.624h ..... (1)[/tex]
[tex]tan36^\circ = \dfrac{h}{x+90}[/tex]
Putting value of [tex]x[/tex] using equation (1):
[tex]tan36^\circ = \dfrac{h}{0.624h+90}\\\Rightarrow 0.726\times 0.624h+0.726\times 90 = h\\\Rightarrow h-0.453h =65.34\\\Rightarrow \bold{h = 119.45\ m}[/tex]
119.45 m is the height of pole.
Classify the number 0 by listing all the sets of numbers to which it belongs
Answer:
0 belongs to the set of whole number,set of rational numbers,set of real numbers and integers
Step-by-step explanation:
Find a such that the line x = a divides the region bounded by the graphs of the equations into two regions of equal area. (Round your answer to two decimal places.) y2 = 16 − x, x = 0
Answer:
y2=16-x
x=0
y2=16-0
y2=16
y2/2=16/2
y=8
Solve the equation 3(x + 1) − 2 = x + 5.
Answer:
X=2
Step-by-step explanation:
First, distribute the 3 to get
3x+3-2=x+5
Solve for 3-2 to get
3x+1=x+5
subtract 1 from both sides to get
3x=x+4
subtract x from both sides to get
2x=4
divide both sides by 2 to finalily get
x=2
Enter the number in two other forms. six million, ninety thousand, thirty-six
Standard form and expanded form
Answer:
Standard form:
Simplify the words.
6,090,036
Expanded form:
Take the standard number and expand it.
6000000 + 90000 + 30 + 6
I'm sorry if I misunderstood.
Good luck though! :)
Please add Brainliest if you'd like, not that it matters.
A cement walk 3 ft wide is placed around the outside of a circular pond with radius 17 ft. What is the total cost of the walk if the cost per square foot is $1.66 ? A. $582.73 B. $581.15 C. $579.90 D. $583.38 E. $578.87
Answer:
$578.87
Step-by-step explanation:
Find the area made by the circle made by the 3 ft. walk:
Radius = 17 + 3 = 20
Area = 22/7 x 20 x20 = 1257.14
Find the area made by the pond:
Area = 22/7 x 17 x 17 = 908.29
Subtract area 2 from area 1:
1257.14 - 908.29 = 348.85
Muliply this area by the cost er squar foot:
348.85 x $1.66 = 579.09
It depends on the value of pi used
In an election between two candidates,a candidate secured 47% of the votes polled and the lost the election by 8700 votes . Find the total number of votes polled and the votes secured by winning candidate
Answer:
Total number of votes- 145,000
Votes secured by winning candidate- 76,850
Step-by-step explanation:
Candidate A- 47%
Candidate B- 53%
6% difference or 8700 votes so
6%=8700
1%=1450
100%=145,000
53%= 76,850
14+-6 what is the answer answer
Answer:
the answer is 8. just think of it as subtraction. subtract +6 from +14. then you get the answer for +14+-6.
my last question please help
Step-by-step explanation:
(2) (x+2)^2 + (-15x -3)
I hope this will be helpful for you.
Answer:
[tex]2(x + 2)^{2} + (-15x - 3)[/tex]
The guy above is correct
Proof :
[tex]2(x + 2)^{2} - 15x - 3 \\ 2((x + 2)(x + 2) - 15x - 3 \\ 2( {x}^{2} + 4x + 4) - 15x - 3[/tex]
[tex]2 {x}^{2} + 8x - 15x + 8 - 3 \\ 2 {x}^{2} - 7x + 5[/tex]
My workings are in the picture
My asnwer was 5/2 and -1
3.87 m to kilometers
Answer:
0.00387
To convert from meters to kilometers, you must divide the number pf meters by 1000.
3.87 ÷ 1000 = 0.00387.
So, that is the answer. Hope it helps!
I WILL GIVE BRAINLIEIST!!
Answer:
y= -7
Step-by-step explanation:
This line is a horizontal line.
Horizontal lines all have the same form of y=k (where k is the y-intercept of the horizontal line).
The y-intercept is the point where the line meets the y-axis (the vertical axis). For this line, the y-intercept is in between -6 and -8, making it: (0,-7) or just -7.
Let's return to the form for horizontal lines.
y= k
The y-intercept is -7. Substitute -7 in for k.
y= -7
The equation of the line is y= -7
which of the following sounds like a bisector?
1.A segment is intersected by a line
2.A segment is intersected by another segment
3.A segment is intersected by a line through the segments midpoint
4.A segment is a parallel to another segment
Answer:
3
Step-by-step explanation:
because it's being intersected
hope I helped?
PLease help i dont know how to do this please explain too!!
Answer:
6.25
Step-by-step explanation:
The perimeter is the sum of the lengths of the sides.
For a rectangle, it's the two widths plus the two heights.
P = 2W + 2H
Plugging in values:
52 = 2(3x − 1) + 2(x + 2)
52 = 6x − 2 + 2x + 4
52 = 8x + 2
50 = 8x
x = 6.25
Find the value of x.
Formula used:-Perimeter of rectangle = 2 ( l + b )
Solution:-We know that,
Perimeter of rectangle = 52 [ Given ]
⇒ 2 ( l + b ) = 52
⇒ 2 ( 3x - 1 + x + 2 ) = 52
⇒ 2 ( 4x + 1 ) = 52
⇒ 8x + 2 = 52
⇒8x = 52 - 2
⇒ 8x = 50
⇒ x = 50/8
⇒ x = 6.25 inches
A student measures the mass of an 8 cm 3 block of brown sugar to be 12.9 g. What is the density of the brown sugar?
Answer:
[tex]\huge\boxed{\rho=1.6125\dfrac{g}{cm^3}}[/tex]
Step-by-step explanation:
The formula of a density:
[tex]\text{density}=\dfrac{mass}{volume}\Rightarrow\rho=\dfrac{m}{V}[/tex]
We have
[tex]\text{mass}\ m=12.9g\\\\\text{volume}\ V=8cm^3[/tex]
Substitute:
[tex]\rho=\dfrac{12.9g}{8cm^3}=\dfrac{12.9\cdot10}{8\cdot10}\dfrac{g}{cm^3}=\dfrac{129}{80}\dfrac{g}{cm^3}=1.6125\dfrac{g}{cm^3}[/tex]
The the density of the brown sugar is equal to [tex]1.6125 \;g/cm^3[/tex]
Given the following data:
Volume = 8 [tex]cm^3[/tex]Mass = 12.9 gramsTo find the density of the brown sugar;
Density can be defined as mass all over the volume of an object.
Simply stated, density is mass per unit volume of an object.
Mathematically, the density of a substance is given by the formula;
[tex]Density = \frac{Mass}{Volume}[/tex]
Substituting the values into the formula, we have;
[tex]Density = \frac{12.9}{8}[/tex]
Density = [tex]1.6125 \;g/cm^3[/tex]
Therefore, the the density of the brown sugar is equal to [tex]1.6125 \;g/cm^3[/tex]
Find more information: brainly.com/question/5995838
A particular fruit's weights are normally distributed, with a mean of 733 grams and a standard deviation of 9 grams. The heaviest 5% of fruits weigh more than how many grams?
Answer:
The heaviest 5% of fruits weigh more than 747.81 grams.
Step-by-step explanation:
We are given that a particular fruit's weights are normally distributed, with a mean of 733 grams and a standard deviation of 9 grams.
Let X = weights of the fruits
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean weight = 733 grams
[tex]\sigma[/tex] = standard deviation = 9 grams
Now, we have to find that heaviest 5% of fruits weigh more than how many grams, that means;
P(X > x) = 0.05 {where x is the required weight}
P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{x-733}{9}[/tex] ) = 0.05
P(Z > [tex]\frac{x-733}{9}[/tex] ) = 0.05
In the z table the critical value of z that represents the top 5% of the area is given as 1.645, that means;
[tex]\frac{x-733}{9}=1.645[/tex]
[tex]{x-733}}=1.645\times 9[/tex]
[tex]x = 733 + 14.81[/tex]
x = 747.81 grams
Hence, the heaviest 5% of fruits weigh more than 747.81 grams.
HELP PLEASE I will appreciate it and reward
Johnny already has 3 plants in his backyard, and he can also grow 4 plants with every seed packet he uses. Write an equation that shows the relationship between the number of seed packets x and the total number of plants y.
- Write your answer as an equation with y first, followed by an equals sign
Answer:
y = 4x + 3
Step-by-step explanation:
If he has x seed packets, Johnny can grow 4 * x = 4x plants. The 3 is a constant because he already has 3 so the equation is y = 4x + 3.
Rhonda is building a rectangular patio. The perimeter of the patio is to be 96 feet. Determine the dimension of the patio if the length is to be 6 feet less than twice the width
Answer:
Length= 30 ft
Width= 18ft
Step-by-step explanation:
The perimeter of the rectangular patio is to be 96 feet.
the length is to be 6 feet less than twice the width
Perimeter=2(length+width)
But
Length= 2(width)-6
Substituting in perimeter equation
Perimeter=2(length+width)
Perimeter=2((2(width)-6)+width)
Perimeter= 96 feet
Let width= x
Perimeter=2((2(width)-6)+width
96=2((2(x)-6)+x)
96= 4x-12+2x
108= 6x
18= x
Width= 18ft
Length= 2(width)-6
Length= 2(18)-6
Length= 36-6
Length= 30 ft
Complete the following table using the equation:
y = 2x^2
Plot the points on a graph and determine which graph best represents the equation.
Graph A
Answer:8,2,0,2,8; Graph A
Step-by-step explanation:
The graph of the given equation best represents a parabola.
What is the graph of an equation?A graph represents the nature of the equation graphically by plotting the points of it.
Given, y = 2x²
For x = - 2, y = 2(- 2)² = 8
For x = - 1, y = 2(- 1)² = 2
For x = 0, y = 2(0)² = 0
For x = 1, y = 2(1)² = 2
For x = 2, y = 2(2)² = 8
Therefore, the given table will be:
x - 2 - 1 0 1 2
y 8 2 0 2 8
By plotting the graph, it is clear that, the graph best represents a parabola.
Learn more about the graph of an equation here: https://brainly.com/question/4047677
#SPJ2
PLEASE HELP MEEEEE!!!!
Answer:
5
Step-by-step explanation:
The leading coefficient is the coefficient with a variable with the greatest exponent.The exponent is the number you would say "the power to". What I mean is let's say you have this number: [tex]3^{2}[/tex] . The exponent would be 2 in this equation because it's saying what power 3 is too. Therefore, 5 is the leading coefficient.
A square pyramid has a height of 12 units and a volume of 256 units3. If a square prism has the same the base area and volume as the square pyramid, what is its height?
Answer:
4 units
Step-by-step explanation:
The volume of a square pyramid is (a²)*h/3
256=a²*12/3
256=a²*4
256/4=a²
64=a²
a=8
Now we know that the square is 8 by 8.
The volume of a square prism is a²h
256=64h
256/64=h
h=4
Also, a square pyramid is 1/3 the volume of a square prism.
12÷3=4
Answer:
the answer is C 4 units
Step-by-step explanation:
Translate the figure 1 unit left and 2 units up.
Draw a vector from the origin 1 unit left and 2 units up.
I need help asap
Answer:
Hey there!
The correct answer would be a line from (0, 0) to (-1, 2)
Let me know if this helps :)
Let u,v,wu,v,w be three linearly independent vectors in R7R7. Determine a value of kk, k=k= , so that the set S={u−3v,v−2w,w−ku}S={u−3v,v−2w,w−ku} is linearly dependent.
Answer:
1/6
Step-by-step explanation:
For a set of vectors a, b and c to be linearly dependent, the linear combination of the set of vectors must be zero.
C1a + C2b + C3c = 0
From the question, we are given the set S={u−3v,v−2w,w−ku}, the corresponding vectors are a(0, -3, 1), b(-2,1,0) and c(1,0,-k)
The values in parenthesis are the ccoefficients of w, v and u respectively.
On writing this vector as a linear combination, we will have;
C1(0, -3, 1) + C2(-2,1,0) + C3(1,0,-k) = (0,0,0)
0-2C2+C3 = 0........ 1
-3C1+C2 = 0 ........... 2
C1-kC3 = 0 ….......... 3
From equation 2, 3C1 = C2
Substituting into 1, -2(3C1)+C3 = 0
-6C1+C3 = 0
-6C1 = -C3
6C1 = C3.…..4
Substitute 4 into 3 to have
C1-k(6C1) = 0
C1 = k6C1
6k = 1
k = 1/6
Hence the value of k for the set of vectors to be linearly dependent is 1/6
A jar contains 6 aqua beads and 4 black beads. If two beads are selected at random, what is the probability that both beads will be aqua? Round to the nearest hundredth if needed.
Answer:
0.33
Step-by-step explanation:
We would like to find the probability that both beads are aqua.
There are 6 aqua beads. Let's calculate the number of ways we can select 2 aqua beads from these 6. We use combinations, which is [tex]_6C_2=\frac{6!}{(6-2)!*2!}[/tex], where the n! means n * (n - 1) * (n - 2) * ... * 2 * 1.
The value of the expression is:
[tex]_6C_2=\frac{6!}{(6-2)!*2!}=\frac{720}{24*2} =15[/tex]
So there are 15 ways to choose 2 aqua beads.
Now let's calculate the number of ways we can select any 2 beads. There are 6 + 4 = 10 beads in total, so we do the same thing as before using combinations:
[tex]_{10}C_2=\frac{10!}{(10-2)!*2!} =\frac{3628800}{40320*2} =45[/tex]
Our fraction is thus:
15 / 45 = 1/3 ≈ 0.33
The answer is thus 0.33.
~ an aesthetics lover
What are the odds against choosing a green or red marble from a bag that contains two blue marbles, one green marble, seven white marbles, and four red marbles?
Answer:
5/14
Step-by-step explanation:
you would just add the number of marbles which is 14 and add the green and red marbles which is 5 and your answer is 5/14
Probability helps us to know the chances of an event occurring. The probability of choosing a green or red marble from the bag is 5/14.
What is Probability?Probability helps us to know the chances of an event occurring. It is always the ratio of desired outcomes or the sample that is needed to the total number of outcomes.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Given that the bag that contains two blue marbles, one green marble, seven white marbles, and four red marbles.
Now, the total number of marbles in the bag is 14.
Therefore, the probability of choosing a green or red marble from the bag is,
Probability = (Number of green and red marbles)/(Total number of marbles)
= (1+4)/(2+1+7+4)
= 5/14
Hence, the probability of choosing a green or red marble from the bag is 5/14.
Learn more about Probability:
https://brainly.com/question/795909
#SPJ5
Find the missing length. The triangles are similar.
Answer:
RK= 13 SK= 12
Step-by-step explanation
First, we find the missing length of RK using the given information: 65-52=13
Then we divide 65 by 13 to get a scale factor: 65/13=5
(To check, we multipuly: 13*5=65)
We then apply the scale factor to MK to find SK: 60/5=12
(To check we multipuly: 5*12=60)
We now have our answers: RK:13, SK:12