Solution :
Given data :
x = 65, n = 300
[tex]$\hat p = \frac{x}{n}[/tex]
[tex]$=\frac{65}{300}$[/tex]
= 0.2167
The hypothesis are :
[tex]$H_0: p \leq 0.3$[/tex]
[tex]$H_0: p> 0.3$[/tex]
The [tex]\text{level of significance}[/tex], α = 0.05
The test is right tailed.
The standard deviation is :
[tex]$\sigma = \sqrt{\frac{0.3(1-0.3)}{300}}$[/tex]
σ = 0.0265
The test statistics is :
[tex]$z=\frac{\hat p - p}{\sigma}$[/tex]
[tex]$z=\frac{0.2167 - 0.3}{0.0265}$[/tex]
= -3.14
The critical value is 1.645
The rejection region is : If z > 1.645, then we reject [tex]H_0[/tex]
Decision :
Since the test statistics does not lie in the rejection, so we fail to . [tex]\text{reject the null hypothesis}[/tex].
P-value : [tex]$P(z > - 3.14)$[/tex] = 0.9992
Therefore, the p-value is not less than the level of significance so we fail to [tex]\text{reject the null hypothesis}[/tex].
Last year, Mary opened an investment account with $5400. At the end of the year, the amount in the account
had decreased by 6%.
here is another question i need help
The population of valleytown is also 5,000 with an annual increase of 1,000. Can the expected population for Valleytown be modeled with an exponential growth fu nction ? Explan
Answer:
An annual increase of 1000 means that the number by which the population increases is constant, which means that the population cannot be modeled with an exponential growth function, it is modeled by a linear growth function.
Step-by-step explanation:
Linear growth:
The number by which it increases is constant.
Exponential growth:
The rate which it increases is constant, that is, a proportion of population.
Annual increase of 1,000.
An annual increase of 1000 means that the number by which the population increases is constant, which means that the population cannot be modeled with an exponential growth function, it is modeled by a linear growth function.
A basketball team won 8 games and lost 7 games. Based on these results what is the probability of winning a game
the probability is made of the desired outcome divided by the total outcome.
desired = wins = 8
total = wins and losses = 15
8/15 is the probability (approx. 53%)
hope it helps :)
Writing equations in standard form:
(1,-6) and (-7,2)
How would I write this in standard form? I already tried but I keep getting x+y=7 and it says it’s wrong so could someone help?
Answer:
[tex]x + y = - 5[/tex]
Step-by-step explanation:
hopefully it is clear and makes sense
:)
What is the area of the circle?
Diameter = radius x 2
So, the radius is half of the denominator.
10 / 2 = 5
A = pi x r^2
A = pi x 5^2
A = 3 x 25
A = 75 ft^2
Hope this helps!
Find the missing length the triangles are similar.
Answer:
Step-by-step explanation:
The missing length is 13 because,
Lets say the top triangle is A and the bottom triangle is B.
Triangle A gives us the side GF, and Triangle B gives us the sides TU and ST. Since the triangles are similar(as stated in the problem), we can pair 2 sides GF(A) and TU(B) which is 11:22.(one way I usually figure which sides are similar is by first- matching the hypotenuse, then checking which of the remaining two is longer.. if that made any sense). You can see that their relationship is x2 or /2 (In another word, from A to B is multiplication- ex: 11 * 2 is 22, and from B to A is division- ex 22/2 is 11.) Since the missing number is the hypotenuse of triangle A and you know the Hypotenuse of triangle B all you have to do is divide side TS by 2 to get side SF. So the missing side is 13.
Answer: 13
Plz help me out with this ;)
The population of a large U.S. city is 2,707,210. Which of the following best expresses this population?
A 2.7 × 106 C 2.707 × 106
B 2.7 × 107 D 27.07 × 106
Answer:
2.707 * 10^6
i think it is the best expression
Amy bakes and sells cupcakes out of her home. She uses baking pans that hold 12 cupcakes and 36 cupcakes to fill her orders. Amy needs to fill her biggest order of 504 cupcakes for a special event.
a. Write an equation to represent the number of 12-cup and 36-cup baking pans for her
order.
b. Amy needs to use a combination of the 12-cup and 36-cup baking pans to fill the order. With only eighteen 12-cup baking pans in her shop, how many of the 36-cup baking pans does she need to complete the order?
Answer:
Below
Step-by-step explanation:
a) let's say that x represents the number of 12 pan cupcakes and y represent the number of 36 pan cupcakes. For her larger order she needs 504 cupcakes so that is the total. This can be demonstrated by the equation below!
12x + 36y = 504
b) here we know that x = 18, so...
12(18) + 36y = 504
216 + 36y = 504
36y = 288
Divide both sides by 36
y = 8
Amy needs 8 of the 36 cup baking pans in order to complete her order.
Hope this helps! Best of luck <3
[tex]\sqrt{\\\frac{9+\sqrt{17} }{2}[/tex]
[tex]\huge\underline\pink{✏ANSWER}[/tex]
Hello and sorry but it's a Gatheted Question Can you fix it Can you?Sorry for answering a nonsense
#BrainliestBunch
Write an equation of the graph (shown below) in slope intercept form.
Answer:
Step-by-step explanation:
Okay! so first, let's specify the components of a slope intercept form equation.
We got y=mx+b as a general formula, where m is slope and b is the y intercept.
The graph gives us two points on the line at (0, 5) and (-6, 7)
To find slope, we can use this slope equation. I suggest you memorize it-it helps a lot with future problems!
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1} }[/tex]
Plugging in the points into the equation, we get 2/-6, or -1/3
we really don't need to do much work anymore, since the choices are given. There is only one choice left with -1/3 as slope m, which is D.
The y intercept can be found at wherever the line intersects the y axis. In this line, it crosses 5, which means b=5.
y=mx+b
y=-1/3x+5
Evelyn earned a score of 86 on Exam A that had a mean of 71 and a standard deviation of 20. She is about to take Exam B that has a mean of 550 and a standard deviation of 40. How well must Evelyn score on Exam B in order to do equivalently well as she did on Exam A? Assume that scores on each exam are normally distributed.
Answer:
580
Step-by-step explanation:
Assuming that the answer should be in terms of z scores, we can calculate the z score as
z = (observed value - mean)/(standard deviation)
For the first exam, the observed value is 86, the mean is 71, and the standard deviation is 20. The z score fot that exam is
z = (86-71)/20 = 0.75
Then, for the second exam, Evelyn has to do equivalently well, so the z score must be the same. Therefore, we have
0.75 = (observed score - 550)/40
multiply both sides by 40 to remove a denominator
0.75 * 40 = observed score - 550
add 550 to both sides to isolate the observed score
0.75 * 40 + 550 = observed score = 580
**URGENT PLEASE HELP**
Find g(x), where g(x) is the translation 2 units right and 13 units down of f(x) = -2x + 5.
Answer:
g(x)=x+9
Step-by-step explanation:
When translating a graph, adding the number of units shifts the graph to the left and subtracting the number of units shifts it to the right. Since you need the graph translated 9 units to the left, you will need to add that many units to x
therefore, g(x)=x+9
Answer:
g(x)=x-8
Step-by-step explanation:
-2+2 = 0, so g(x) = x
5-13 = -8
A rectangular box contain 782 apples. If there are 23 rows in a box, how many columns are there?
Answer:
34
Step-by-step explanation:
This is because you will have to simply divide 782 by 23.
782 / 23 =
34 :D
What is 3x^2-5x-13=0
Answer:
D. 58
Step-by-step explanation:
Given, 3x+8x+4x=6x+63
⇒15x=6x+63
⇒9x=63
⇒x=7
Then 5x+23=5(7)+23
=35+23
=58
The perimeter of a rectangle is given by the formula P=2w+2l,where w is the width and l is the length.Rearrange the formula for the length ( ).
Answer:
l = (p - 2w)/2
Step-by-step explanation:
Two sides of a right triangle measure 5 inches and 6 nches, and the third side measures 61 inches.
The length of the third side is about
inches _ . The perimeter of the triangle is about
inches. __
Answer:
The length of the third side is 7.81 inches and the perimeter of the triangle is about 18.81 inches
Step-by-step explanation:
[tex]\frac{3}{2x}[/tex]-[tex]\frac{11}{5}[/tex]=[tex]\frac{7}{8}[/tex].[tex]\frac{64}{49}[/tex]
Answer:
x=35/78
Step-by-step explanation:
3/2x-11/5=(7/8)*(64/49)
3/2x-11/5=8/7
3/2x=8/7+11/5
3/2x=117/35
x=(35*3)/(2*117)
x=35/78
Inverse proportion
it takes 3 hrs for two people to clean six identical rooms.
how long would it take 5 people to clean 20 of the same rooms at the same k rate
i know answer need explan.
Answer:
Hello,
4 hours
Step-by-step explanation:
Let say w the work clean one room.
h the number of hours worked
p the number of people who works
k is a constant
6w=k*h*p
3 h, 2 p==> 6w
6w=k*3*2 ==> k=w
5 p, 20 w ==>
20w=k*h*p
20w=w*h*5
20=h*5
h=20/5
h=4
It will take 4 hours.
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
Data should be analyzed using each of the following except:
A. measures of central tendency
B. shape
C. population size
D. spread
Use the quadratic formula to find the solutions to the quadratic equation below. Check all that apply. 5x2-X-4 = 0 A. -4/5 B. 5/4C. 2/3 D. 1 E. -1 F.3/2
Hi
5x²-x-4 = 0
Δ= (-1)² - 4*5*(-4)
Δ = 1 -4*-20
Δ = 1 +80
Δ = 81
√Δ= 9
as Δ ≥ 0 , so 2 solutions exist in R
S1 is : ( 1+9) /2*5 = 10/10 = 1
s2 = (1 -9)/2*5 = -8/10 = -4*2 /2*5 = -4/5
Corrects answers are A and D
Answer:
A. -4/5 And D. 1
Step-by-step explanation:
i just got it right
a(b^2+c^2+bc) + b(c^2+a^2+ca) + c(a^2+b^2+ab)
Answer:
(a-b)(b-c)(a-c)
Step-by-step explanation:
a^2(b - c) + b^2(c-a) + c^2(a - b)
= a^2b - a^2c + b^2c - b^2a + c^2a-c^2b
=a^2b - b^2a - a^2c + b^2c + c^2a -c^2b
= ab(a - b) - c(a^2 - b^2) +c^2(a - b)
=ab(a - b) -c(a - b)(a + b) +c^2(a - b)
=(a - b)(ab - c(a + b) +c^2)
=(a - b)(ab - cb -ca + c^2)
= (a - b)(b(a-c) -c(a-c))
=(a-b)(b-c)(a-c)
One model of Earth's population growth is P(t)= 64/(1+11e^0.8t)
where t is
measured in years since 1990, and P is measured in years since 1990, and Pis measured in billions of people. Which of the following statements are true? Check all that apply.
Answer: C and D
Step-by-step explanation:
Using the logistic equation, it is found that options C and D are correct.
The logistic equation for population growth is given by:
[tex]P(t) = \frac{K}{1 + Ae^{-kt}}[/tex]
[tex]A = \frac{K - P(0)}{P(0)}[/tex]
In which:
K is the carrying capacity. P(0) is the initial value. k is the growth rate, as a decimal. The population grows exponentially for a while, but as it gets closer to the carrying capacity, the growth slows down.For this problem, the equation is:
[tex]P(t) = \frac{64}{1 + 11e^{-0.08t}}[/tex]
Which means that:
The carrying capacity is of 64 billion people, as [tex]K = 64[/tex].The growth rate is of 8% per year, but it is not steady.The initial population, in millions of people, is of [tex]P(0) = \frac{64}{1 + 11} = 5.3[/tex].Hence, options C and D are correct.
To learn more about the logistic equation, you can check https://brainly.com/question/25697660
convert 123000000 milligram into gram
Answer:
123,000 grams
Step-by-step explanation:
1000 mg is equivalent to 1 gram.
Answer:
123000g
Step-by-step explanation:
1000mg=1g
123000000mg= xgrams
cross multiplying,
you'll have
[tex] \frac{123000000}{1000} = 123000[/tex]
Melissa will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of 59 and costs an additional 0.15 per mile driven. The second plan has an initial fee of 50 and costs an additional 0.20 per mile driven. For what amount of driving do the two plans cost the same? What is the cost when the two plans cost the same?
Answer:
Step-by-step explanation:
Let
x = cost per mile
y = Total cost
Plan 1:
y = 59 + 0.15x
Plan 2:
y = 50 + 0.20x
Equate the total cost of the two plans
59 + 0.15x = 50 + 0.20x
59 - 50 = 0.20x - 0.15x
9 = 0.05x
x = 9/0.05
= 180
x = 180 miles
y = 50 + 0.20x
= 50 + 0.20(180)
= 50 + 36
= 86
y = 86
I need help to find x=
Answer:
x=12
Step-by-step explanation:
Since the polygons are similar, we can write a ratio to solve
red side / yellow side
4 2
--- = ---
x 6
Using cross products
4*6 = 2x
24 = 2x
Divide by 2
24/2 =2x/2
12=x
Answer:
12
Step-by-step explanation:
When two shapes are similar, you need to find the scale factor of two existing corresponding sides.
For example, you can do 6 and 2.
Divide:
6/2 = 3
The scale factor: 3
Now multiply 4 and the scale factor (3):
4 × 3 = 12
So, x = 12.
Hope this helped.
Solve the system of equations and choose the correct ordered pair.
4x - 2y = -2
6x + 3y = 27
A. (2,5)
B. (3,7)
C. (0, -1)
D. (0,9)
Answer:
(2,5)
Step-by-step explanation:
4x - 2y = -2
6x + 3y = 27
Divide the first equation by 2 and the second equation by 3
2x - y = -1
2x + y = 9
Add the equations together
2x - y = -1
2x + y = 9
-------------------
4x = 8
Divide by 4
4x/4 = 8/2
x =2
2x+y = 9
2(2) +y = 9
4+u = 9
y = 9-4
y=5
(2,5)
Find a recursive rule for the nth term of the sequence.
-8, 3, 14, 25, ...
Answer:
Step-by-step explanation:
a1=-8
a2=3
D=11
n=-8+11(n-1)
Can somebody help me please.
