Answer:
Step-by-step explanation:
The point estimate is the sample proportion.
Considering the sample,
Sample proportion, p = x/n
Where
x = number of success = 137
n = number of samples = 200
p = 137/200 = 0.685
From the information given,
Population proportion = 62% = 62/100 = 0.62
The correct options are
A) Yes, the sample size is greater than 30.
B) Yes, there are at least 10 adults saying they get their news from social media and at least 10 that do not.
Which point is an x-intercept of the quadratic function f(x) = (x + 6)(x – 3)? (0,6) (0,–6) (6,0) (–6,0)
Answer: (-6, 0)
Step-by-step explanation:
X-intercepts of equations are any points on the equation that lie on the x-axis, or the horizontal line "y = 0".
In order to find the x-intercept of an equation, find the points that will satisfy the equation "y = 0":
y = (x + 6)(x - 3)
y = 0
(x + 6)(x - 3) = 0
With this equation, you can find which points lie on the x-axis.
When x = -6, the equation is: 0 * -9 = 0, which is correct.
When x = 3, the equation is 9 * 0 = 0, which is correct.
Make sure you're picking the correct coordinate out of the answer choices.
The x-coordinates are -6 and 3, and the y-coordinates are 0, because the points lie on the x-axis.
The correct answer is (-6, 0).
(3, 0) is also correct, but the question does not require it.
Answer:
D
Step-by-step explanation:
an amount was invested at r% per quarter. what value of r will ensure that accumulated amount at the end of one year is 1.5 times more than amount invested
Answer:
[tex]r=25.7\%[/tex] will ensure that accumulated amount at the end of one year is 1.5 times more than amount invested
Step-by-step explanation:
Given: An amount was invested at r% per quarter.
To find: value of r such that accumulated amount at the end of one year is 1.5 times more than amount invested
Solution:
Let P denotes amount invested and n denotes time
As an amount (A) was invested at r% per quarter,
[tex]A=P\left ( 1+\frac{r}{400} \right )^{4n}[/tex]
According to question, accumulated amount at the end of one year is 1.5 times more than amount invested.
So,
[tex]A=1.5P+P=2.5P\\A=2.5P\\P\left ( 1+\frac{r}{400} \right )^{4n}=2.5P[/tex]
Put n = 1
[tex]P\left ( 1+\frac{r}{400} \right )^{4}=2.5P\\\left ( 1+\frac{r}{400} \right )^{4}=2.5\\1+\frac{r}{400} =(2.5)^{\frac{1}{4}}\\\frac{r}{100}=(2.5)^{\frac{1}{4}}-1\\r=100\left [ (2.5)^{\frac{1}{4}}-1 \right ]\\=25.7\%[/tex]
Sean tossed a coin off a bridge into the stream below. The path of the coin can be represented by the equation h = -16t2 + 72t + 100. what is the height of the bridge
Answer:
100
Step-by-step explanation:
When t=0 (no time has passed), the coin is at height 100. This means the bridge must be 100 units high for this to be possible.
Answer:
100
Step-by-step explanation:
:3
Noah has a t-shirt collection. Three-eighths of the t-shirts are blue. Of the blue t-shirts,two-ninths of them have a pocket. What fraction represents the numbers of t-shirts that are blue and have a pocket?
Answer:
1/12
Step-by-step explanation:
blue = (3/8)collection
blue&pocket = (2/9)blue = (2/9)(3/8)collection
blue&pocket = (6/72)collection = (1/12)collection
1/12 of Noah's collection is blue and has a pocket.
Find the area of a circle with radius, r = 9cm.
Give your answer in terms of π .
Answer:
[tex]81\pi[/tex]
Step-by-step explanation:
[tex]Area = \pi * r^{2} \\\pi *9^{2} =81\pi[/tex]
Answer:
81 π
Step-by-step explanation:
formula is radius squared times pi or π so the answer would be 9x9=81 and you said to leave in terms of π so the answer is 81 π.
Which is greater between |5| amd |2|
Answer:
|5| = 5 and |2| = 2 and because 5 > 2, our answer is |5| > |2|.
Answer:
|5|
Step-by-step explanation:
5 is greater than 2
HELPPPPPPWhich is the simplified form of -7 +5-12?
1
12
S
O M - 512
12
S
o
1
12
S
Answer:
Step-by-step explanation:
[tex]r^{-7} +s^{-12} \\Use Negative Power Rule: x^{-a} =\frac{1}{x^{a} } \\r^{\frac{1}{7} } +s^{\frac{1}{12} } \\[/tex]
I hope i am correct
:4. In the Department of Natural Sciences, 14 faculty members have a PhD, and 30 faculty members do not have a PhD. In the Department, the number of female faculty who do not have a PhD is 10 more than the number of females who have a PhD. If a third of the male faculty in the Department have a PhD, then what is the number of female faculty in the Department with a PhD?
Answer:
The number of female faculty in the Department with a PhD is 8.
Step-by-step explanation:
There are 14 + 30 = 44 faculty members.
Of those, x are male and y are female.
Then
x + y = 44.
The number of female faculty who do not have a PhD is 10 more than the number of females who have a PhD.
y = z + w
z is the number of females with PhD.
w is the number of females without PhD.
w = z + 10
If a third of the male faculty in the Department have a PhD
[tex]\frac{x}{3} + z = 14[/tex]
Now, we can write all variables as functions of z, which is the number of female faculty in the Department with PhD.
The objective is:
To find z from the first equation, that is:
[tex]x + y = 44[/tex]
To do this, we have to write x and y as functions of z.
Writing x and y as functions z.
[tex]\frac{x}{3} + z = 14[/tex]
[tex]\frac{x}{3} = 14 - x[/tex]
[tex]x = 3(14 - z)[/tex]
[tex]x = 42 - 3z[/tex]
And
[tex]y = z + w[/tex]
In which
[tex]w = 10 + z[/tex]
So
[tex]y = z + 10 + z[/tex]
[tex]y = 2z + 10[/tex]
Replacing:
[tex]x + y = 44[/tex]
[tex]42 - 3z + 2z + 10 = 44[/tex]
[tex]-z + 52 = 44[/tex]
[tex]z = 52 - 44[/tex]
[tex]z = 8[/tex]
The number of female faculty in the Department with a PhD is 8.
What’s the correct answer for this question?
Answer:
B
Step-by-step explanation:
The triangular prism must have a larger base than the cylinder
• Write the number that is 10 more than 178.25:
Step-by-step explanation:
10 more than 178.25 is add so
178.25 + 10 = 188.25
find the LCM
of
75, 5,3
Answer:
LCM = 75
Step-by-step explanation:
1: Multiply the factor by the greatest number
Description:
The least common multiple for 75,5,3 is 75.
LCM= Least common Multiple
Please mark brainliest
Hope this helps.
Answer:
75
Step-by-step explanation:
Break each number into prime factors
75 = 25*3 = 5*5*3
5 = 5*1
3 = 3*1
Multiply by the greatest number of each factor
3 = 1 time
5 = =2 times
The least common multiple = 3 * 5*5 = 75
The amount of pollutants that are found in waterways near large cities is normally distributed with mean 9 ppm and standard deviation 1.5 ppm. 38 randomly selected large cities are studied. Round all answers to 4 decimal places where possible.
1. What is the distribution of XX? XX ~ N(,)
2. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
3. What is the probability that one randomly selected city's waterway will have more than 9.6 ppm pollutants?
4. For the 37 cities, find the probability that the average amount of pollutants is more than 9.6 ppm.
5. For part d), is the assumption that the distribution is normal necessary? YesNo
6. Find the IQR for the average of 37 cities.
Q1 = ppm
Q3 = ppm
IQR: ppm
Answer:
Step-by-step explanation:
Hello!
There are two values of n in the text, I'll use the one that appears in all the questions.
The variable of interest is
X: pollutants found in waterways near large cities. (ppm)
This variable has a normal distribution with parameters μ= 9ppm and σ= 1.5ppm
1) X~N(μ;σ²)
X~N(9;2.25)
2) The distribution of the sample mean is X~N(μ;σ²/n)
σ²/n= 2.25/37= 0.06
X~N(9;0.06)
3) P(X>9.6)
To calculate this probability you have to use the standard normal distribution. Using the population parameters, you can calculate the corresponding Z value:
Z= (X-μ)/σ= (9.6-9)/1.5= 0.4
P(Z>0.4)= 1-P(Z≤0.4)= 1 - 0.65542= 0.34458
The probability of selecting a city at random and finding 9.6ppm pollutants.
4) In this item, instead of calculating the probability of one value of the variable you have to calculate the probability of the sample average taking a determined value. Because of this, you have to work using the distribution of the sample mean, instead of the distribution of the variable.
P(X[bar]>9.6)
Z= (X[bar]-μ)/(σ/√n)= (9.6-9)/√0.06= 2.45
P(Z>2.45)= 1 - P(Z≤2.45)= 1 - 0.99286= 0.00714
5) The assumption of a normal distribution is not necessary for item 4. Since the sample size is large enough (greater than 30) you can apply the central limit theorem and approximate the distribution of the sample mean to normal, regarding the distribution of the original variable.
6)
In this case, you have to work starting with the standard normal distribution and then "translate" the Z values into values of the average amount of pollutants.
The first quartile divides the bottom 25% of the distribution from the top 75%, symbolically:
P(Z≤z₁)= 0.25
z₁= -0.674
z₁= (X[bar]-μ)/(σ/√n)
z₁*(√n/σ)=X[bar]-μ
X[bar]=z₁*(√n/σ)+μ
X[bar]=(-0.674)*(√37/1.5)+9= 6.27ppm
The third quartile divides the bottom 75% of the distribution from the top 25%, symbolically:
P(Z≤z₂)= 0.75
z₂= 0.674
z₂= (X[bar]-μ)/(σ/√n)
z₂*(√n/σ)=X[bar]-μ
X[bar]=z₂*(√n/σ)+μ
X[bar]=(0.674)*(√37/1.5)+9= 11.7.3ppm
IQR= Q₃-Q₁= 11.73-6.27= 5.46ppm
I hope this helps!
The altitude drawn to the hypotenuse of a right triangle divides the hypotenuse into segments of lengths 4 and 12. Find the length of the shorter leg of the right triangle.
Answer:
8 units.
Step-by-step explanation:
The smaller of the right triangles formed is similar to the whole triangle so
4/x = x/16 where x = the shorter leg
x^2 = 64
x = 8.
The length of the shorter leg of the right triangle is 3 units.
Let's denote the length of the shorter leg of the right triangle as "x." Since the altitude drawn to the hypotenuse divides it into segments of lengths 4 and 12, we can set up a proportion between the two triangles formed.
According to the similarity of triangles, the length of the shorter leg to the length of the segment of the hypotenuse it divides is the same as the length of the longer leg to the length of the other segment of the hypotenuse.
So, we can set up the proportion:
x / 4 = 12 / (hypotenuse length).
Now, we know that the hypotenuse length is equal to the sum of the two segments (4 + 12 = 16). We can substitute it into the proportion:
x / 4 = 12 / 16.
Now, cross-multiply and solve for x:
16x = 4 * 12,
16x = 48,
x = 48 / 16,
x = 3.
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Determine whether the numerical value in braces is a parameter or a statistic. Explain your reasoning. In a certain soccer league (43%) of the 14 teams had won more games than they had lost.
Choose the correct answer below.
a. Statistic, because the data set of a sample of teams in a league is a sample.
b. Statistic, because the data set of a sample of teams in a league is a population.
c. Parameter, because the data set of all 14 teams is a population.
d. Statistic, because the data set of all 14 teams is a sample.
e. Parameter, because the data set of all 14 teams is a sample.
f. Parameter, because the data set of a sample of teams in a league is a population.
g. Parameter, because the data set of a sample of teams in a league is a sample.
h. Statistic, because the data set of all 14 teams is a population.
Answer:
C. Parameter since the data set of all 14 teams is a population.
Explanation:
Find the attachment
Solve the inequality for x
Answer:
see below
Step-by-step explanation:
[tex]\frac{x-c}{d} > y[/tex]
x - c > dy
x > dy + c
The total mass of the Sun is about 2×10^30 kg, of which about 76 % was hydrogen when the Sun formed. However, only about 12 % of this hydrogen ever becomes available for fusion in the core. The rest remains in layers of the Sun where the temperature is too low for fusion.
Part A
Use the given data to calculate the total mass of hydrogen available for fusion over the lifetime of the Sun.
Express your answer using two significant figures.
Part B
The Sun fuses about 600 billion kilograms of hydrogen each second. Based on your result from part A, calculate how long the Sun’s initial supply of hydrogen can last. Give your answer in both seconds and years.
Express your answer using two significant figures.
Part D
Given that our solar system is now about 4.6 billion years old, when will we need to worry about the Sun running out of hydrogen for fusion?
Express your answer using two significant figures.
Answer:
A. 1.8 ×[tex]10^{30}[/tex] Kg
B i. 3.0 × [tex]10^{17}[/tex] seconds
ii. 9.6 × [tex]10^{9}[/tex] years
C. After 9.2 × [tex]10^{9}[/tex] (9.2 billion) years
Step-by-step explanation:
Given that the mass of the Sun = 2× [tex]10^{30}[/tex] Kg.
Mass of hydrogen when Sun was formed = 76% of 2× [tex]10^{30}[/tex] Kg
= [tex]\frac{76}{100}[/tex] ×2× [tex]10^{30}[/tex] Kg
= 1.52 × [tex]10^{30}[/tex] Kg
Mass of hydrogen available for fusion = 12% of 1.52 × [tex]10^{30}[/tex] Kg
= [tex]\frac{12}{100}[/tex] × 1.52 × [tex]10^{30}[/tex] Kg
= 1.824 ×[tex]10^{30}[/tex] Kg
A. Total mass of hydrogen available for fusion over the lifetime of the sun is 1.8 ×[tex]10^{30}[/tex] Kg.
B. Given that the Sun fuses 6 × [tex]10^{11}[/tex] Kg of hydrogen each second.
i. The Sun's initial hydrogen would last;
[tex]\frac{1.8*10^{30} }{6*10^{11} }[/tex]
= 3.04 × [tex]10^{17}[/tex] seconds
The Sun's hydrogen would last 3.0 × [tex]10^{17}[/tex] seconds
ii. Since there are 31536000 seconds in a year, then;
The Sun's initial hydrogen would last;
[tex]\frac{3.04*10^{17} }{31536000}[/tex]
= 9.640 × [tex]10^{9}[/tex] years
The Sun's hydrogen would last 9.6 × [tex]10^{9}[/tex] years.
C. Given that our solar system is now about 4.6 × [tex]10^{9}[/tex] years, then;
[tex]\frac{9.6*10^{9} }{4.6*10^{9} }[/tex]
= 2.09
So that; 2 × 4.6 × [tex]10^{9}[/tex] = 9.2 × [tex]10^{9}[/tex] years
Therefore, we need to worry about the Sun running out of hydrogen for fusion after 9.2 × [tex]10^{9}[/tex] years.
Part(A): The total mass of hydrogen available 9.6 billion years.
Part(B): The total time is 5.10 billion years.
Part(D): The hydrogen will last [tex]5.04\times 10^9 \ years[/tex]
Mass of the sun:Our sun is the largest object in our solar system. The mass of the sun is approximately [tex]1.988\times 1030[/tex] kilograms
Part(A):
Given that,
The total mass of the Sun =[tex]2\times10^{30} kg[/tex]
Mass of hydrogen in Sun = [tex]2\times10^{30} \times0.76\ kg[/tex]
The mass of hydrogen ever available for fusion is,
[tex]2\times10^{30} \times 0.76 \times 0.12 kg = 1.824\times 10^{29}[/tex]
Mass of hydrogen fuses each second = 600 billion kg/second.
Time hydrogen will last in seconds=[tex]1.824\times 10^{29}seconds.[/tex]
[tex]= 0.00304\times 10^{29 }= 3.04\times 10^{17}.[/tex]
Time hydrogen will last in seconds =[tex]1 year = 31,536,000 seconds.[/tex]
[tex]31,536,000 x = 3.04\times 10^{17} = 9.6 \ billion \ years.[/tex]
(B) Present age of sun = [tex]9.6-4.5 \ billion \ years[/tex]
The time when we need to worry about Sun running out of hydrogen for fusion = 5.10 billion years.
(D) The solar system is 4.6 billion years old that is [tex]4.6\times 10^9\ years[/tex]
And in part (B) we have calculated that hydrogen will last [tex]9.64\times 10^9[/tex] then,
[tex]9.64\times 10^9-4.6\times 10^9=5.04\times 10^9[/tex]
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what is the solution? X - 7 > -6
Answer:
x > 1
Step-by-step explanation:
Add 7 to both sides
x > 1
A rectangular deck is 12 ft by 14 ft. When the length and width are increased by the same amount, the area becomes 288 sq. Ft. How much were the dimensions increased?
Answer:
4 ft
Step-by-step explanation:
288=16 * 18
12+4=16
14+4=18
The dimensions increased by 4 feet.
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
Given;
Dimensions of rectangle = 12 + x and 14 + x
The area of the rectangle= (12 + x) (14 + x) = 288
x² + 26x + 168 = 288
x² + 26x - 120 = 0
(x + 30) (x - 4) = 0
x=-30, x =4
Hence, The dimensions increased by 4 feet.
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help!! Algebra 1!!
sorry if the picture is bad
Answer:
The first one matches with f(x)√x because a square root cannot be negative
The second one matches with f(x)=√(x-5) because the square root would be negative if it were less than five.
The third one matches with f(x)=8x because there is nothing that makes it a not possible answer
The last one matches with 7/(x-8) because there cannot be a denominator of zero.
What are the zeroes of the polynomial x(x²+4x-12)
Answer:
x= 0, 2, -6
Hope this helps!
5+7.(9-4)
5+7=11
11×5=55
Answer: itz 605
Step-by-step explanation:
Help help , Please help! Brainliest if correct! What was the equation of the graph below before it was shifted to the left 1.5 units? A. G(x)=(x3)^3-(x-3) B. G(x)=(x-1.5)^3 C. G(x)=(x)^3 D.G(x)=x^3-x
Answer:
A. G(x) = (x -3)^3 -(x -3)
Step-by-step explanation:
The graph before it was shifted left will be a right-shift of the equation shown. That is accomplished by replacing x with (x-1.5). Then the right-shifted equation is ...
G(x) = ((x-1.5) -1.5)^3 -((x -1.5) -1.5)
G(x) = (x -3)^3 -(x -3) . . . . matches choice A
What is the value of k?
k=
8
m
o
4
k
N
M
Answer: It’s 2
Step-by-step explanation:
look at picture
A sample of carbon-12 has a mass of 6.00 g. How many atoms of carbon-12 are in the sample?
3.01 x 10^23
6.02 x 10^23
1.20 x 10^24
3.60 x 10^24
Answer:
The answer is 3.01 x 10’23
Step-by-step explanation:
I got the answer to wrong and guessed the first one and it was correct
Which is the correct classification of StartFraction 3 Over 8 EndFraction?
Answer:
Classifications would include
Rational; Fraction; Can be turned into Decimal; Positive
Those would be classifications
Answer: rational number, 0.375
Step-by-step explanation:
Mr Chan flies from London to Los Angeles, a distance of 8800 km.
The flight takes 11 hours and 10 minutes.
His plane leaves London at 09 35 local time.
The local time in Los Angeles is 8 hours behind the time in London.
Calculate the local time when the plane arrives in Los Angeles.
Answer:
12 45
Step-by-step explanation:
plane leaves London at 09 35
plane arrives in Los Angeles after 11 hrs and 10 min
considering time difference:
11 10 - 8 00= 03 10local arrival time:
09 35 + 03 10= 12 45 local timeThis table gives a few (x,y) pairs of a line in the coordinate plane. What is the y-intercept of the line? (full problem attached)
Answer:
(0,34)
Step-by-step explanation:
For each rise of 14 in the x direction, this graph rises by -8 in the y direction. This means that, when x is 0, and the graph intersects the y axis, the y value will be 50-8-8=34. Therefore, the y intercept of this line is (0,34). Hope this helps!
Answer:
The answer is (0,34)
The Sunshine Droogs are unhappy as they have not yet been paid for their concert. It was agreed they would be paid eleven thousand, four hundred and fifty three pounds for the concert. What is this amount in numbers?
Answer:
11453
Step-by-step explanation:
A gas company president for a particular city is interested in the proportion of homes heated by gas. Historically, the proportion of homes heated by gas has been 0.72. A sample of 75 homes was selected and it was found that 45 of them heat with gas. Perform the appropriate test of hypothesis, at level .05, to determine whether the proportion of home heated by gas has changed. Group of answer choices
Answer:
p-value (0.0208) is less than alpha = 0.05 reject H0.
Step-by-step explanation:
we have the following data:
sample size = n = 75
x, the number to evaluate is 45
the sample proportion would be: x / n = 45/75
p * = 0.6
Now, the null and alternative hypotheses are:
H0: P = 0.72
Ha: P no 72
two tailed test
statistic tes = z = (p * - p) / [(p * (1-p) / n)] ^ (1/2)
replacing we have:
z = (0.6 - 0.72) / [(0.72 * (1-0.72) / 75)] ^ (1/2)
z = -2.31
p-vaule = 2 * p (z <-2.31)
using z table, we get:
p-vaule = 2 * (0.0104)
p-vaule = 0.0208
Therefore, p-value (0.0208) is less than alpha = 0.05 reject H0.
(TEKS 2A.) EF has endpoints E (8,3) and F(-4,9). What is the distance of the given segment?
A 8.544
C 11.250
B 10.345
D 13.416