a. The probability that the sample proportion will be within ±0.02 of the population proportion - 0.5223
b. The probability that the sample proportion will be within 0.05 of the population proportion - 0.9232
[tex]Given, \\$P=0.2 a$ \\$n=200$ \\mean, \ $\mu \hat{p}=p$ \\$=0.20$ \\Standard deviation, $\sigma_p=\sqrt{\frac{p(1-p)}{n}}$ \\$=\sqrt{\frac{0.20(1-0.20)}{208}}$ \\$=\sqrt{\frac{0,20(0,80)}{200}}$ \\$=\sqrt{\frac{0.16}{200}}$. \\$=0.0283$ \\a) $p(|x-\mu|=\pm 0.02)=f\left(\frac{-|x-\mu|}{\sigma \hat{p}} < z < \frac{|x-\mu|}{\sigma_{\hat{p}}}\right)$ \\$=1\left(\frac{-0.02}{0.0283} < = < \frac{0.02}{0.0283}\right)$ \\$=P(-0,71 < z < 0,71)$[/tex]
[tex]$$\begin{gathered}=p(z < 0,71)-p(z < -0,71) \\=0,7612-0.2389 \\=0,5223 } \\\therefore P(|x-\mu|=\pm 0.021=0,5223)\end{gathered}$$[/tex]
[tex]b)\\$$\begin{aligned}p(|x-\mu|=\pm 0.05)=p\left(\frac{|x-\mu|}{\sigma \hat{p}} < z < \frac{|x-\mu|}{\sigma \hat{p}}\right) \\=p\left(\frac{-0.05}{0.0283}-z < \frac{0.05}{0.0283}\right) \\=& p(-1.77 < z < 1.77) \\=& P(z < 1.77)-p(z < -1.77) \\\therefore p(i x-\mu \mid&=\pm 0.05)=0.9232\end{aligned}$$[/tex]
What is the population ?A population is a complete group of individuals, regardless of whether that group consists of a nation or a group of people with a common characteristic.
In statistics, a population is a group of individuals from which a statistical sample is taken for research. Thus, any selection of individuals grouped together on the basis of some common characteristic can be called a population. A sample may also refer to a statistically significant portion of the population rather than the entire population. Therefore, statistical analysis of a sample must report the approximate standard deviation or standard error of the results for the entire population. Only the whole population analysis has no standard error
To learn more about population , visit;
https://brainly.com/question/27779235
#SPJ13
11. The list price of an orange dial Luminox watch is $450. Katz Jewelers receives a tradediscount of 25%. Find the trade discount amount and the net price.
In order to find the trade discount amount and the net price, you first calculate the 25% of $450. You proceed as follow:
(25/100) x 450 = 112.5
the percentage is divided by 100, an
Then, $112.5 is the 25% of $450. And $112.5 is the discount amount
Next, to calculate the net price, you simply calculate the difference between the intial price ($450) and the price after the discount ($112.5), just as follow:
net price = $450 - $112.5 = $337.5
Hence, the discount amount is $112.5 and the net price is $337.5
Select the equations below that are equivalent to -6 = -20 - v
Given
[tex]-6=-20-v[/tex]- For -72 = 9(-20 - v):
[tex]\begin{gathered} -\frac{72}{9}=\frac{9(-20-v)}{9} \\ -8=-20-v \end{gathered}[/tex]The equation is not equivalent
- For -90 = 15(-20 - v):
[tex]\begin{gathered} \frac{-90}{15}=\frac{15(-20-v)}{15} \\ -6=-20-v \end{gathered}[/tex]The equation is equivalent
- For 5 * -6 = -100 - 5v:
Common factor 5
[tex]\begin{gathered} -30=5(-20-v) \\ \frac{-30}{5}=\frac{5(-20-v)}{5} \\ -6=-20-v \end{gathered}[/tex]The equation is equivalent
- For 3 * -6 = -60 - 3v:
Common factor 3
[tex]\begin{gathered} -18=3(-20-v) \\ \frac{-18}{3}=\frac{3(-20-v)}{3} \\ -6=-20-v \end{gathered}[/tex]The equation is equivalent
Answer:
-90 = 15(-20 - v)
5 * -6 = -100 - 5v
3 * -6 = -60 - 3v
Find the radius of the circle and the coordinates of its center
Hence, the radius of the circle is 10, and the coordinates of its centre is (6,-2)
Plot the point given in polar coordinates.Find three additional polar representations of the point, using −2 < < 2. (Enter your answers in order from smallest to largest first by r-value, then by -value.)
Correct graph: C
[tex]\begin{gathered} 1st\text{ alternative form:} \\ (-9,\frac{2}{3}\pi)\frac{}{} \\ 2nd\text{ alternative form:} \\ (9,\frac{5}{3}\pi) \\ 3rd\text{ alternative form:} \\ (-9,\frac{8}{3}\pi) \end{gathered}[/tex]
The box plots below show the number of goals that two hockey players, Sam and Barry, Scored each season during their careers.Select all that are TRUE1) Barrys data is nearly symmetrical2) the median is Sams data is more than Barrys data3) Sam scored more goals in one season than berry did.4) Barrys chart shows more variable than Sams5) Sams distribution is skewed left
From the given distribution, it is clear that
Sam scored more goals in one season than berry did.
and
Barrys data is nearly symmetrical
j
knjfjfjfjfjfjf help me solve this thanks !!
Answer:
132 degrees
Step-by-step explanation:
102+30 = 132
A jeweler has found that the monthly revenue received from selling a pair of earrings at a cost of d dollars each is given by the polynomial −7d2+180d. Find the monthly revenue received when d=17 dollars.
The monthly revenue is $1037
What is a linear equation in one variable?
A linear equation in one variable is equation whose degree is one and there is only one variable present.
We are given the monthly revenue received from selling a pair of earrings at a cost of d dollars is given by equation [tex]-7d^{2}+180d[/tex]
We have to find the monthly revenue received when the cost is $17
That is d=17
Now we substitute d=17 in the given equation to find the monthly revenue
We get,
[tex]-7d^{2}+180d\\[/tex]
⇒[tex]-7(17^{2})+180(17)\\[/tex]
⇒ -2023+3060
⇒1037
Hence the monthly revenue earned is $1037
To learn more about linear equation please refer
https://brainly.com/question/26310043
#SPJ9
Use the long division method to find the result when 8x3 + 14x2 11x - 8 is divided by 2x + 1. If there is a remainder, express the result in the form q(a) +
Let's develop a synthetic division
As you can observe, the division is exact because its reminder is zero.
Hence, the answer is-
[tex]\frac{8x^3+14x^2-11x-8}{2x+1}=4x^2+5x-8[/tex]need answer asap ty
multiplying integers
1. 13 + (-20) =
2.29 + (-12) =
3.21 + (-13) =
4.-19 + (-26) =
answer 1=-7
2=17
3=8
4=-45
see imageThere were 400 people that tooka survey about quality ofrestaurants. 240 people said thatOutback was the beststeakhouse. What percent ofpeople said Outback was the beststeakhouse?
total people(TOTAL) : 400
People that said that the outback was the best ( BEST) : 240
percent of people said Outback was the best steakhouse : BEST / TOTAL : 240/400 = 0.6
Percent = 0
Which letrero Best represents √27 on the number line.
You have the following number
√27
In order to determine which letter best represent the previous number, you take into account the following square roots:
√25 = 5
√36 = 6
Then, you can consider that √27 is a number in between 5 and 6, because √27 in anumber in between √25 and √36.
The only letter that is in between 5 and 6 on the number line, is the letter C.
Hence, letter C best represents √27
Multiply. Simplify, you may leave the numerator and denominator in answer in factored form.
Step 1
Given;
Step 2
Multiply
[tex]\frac{x^3+1}{x^3-x^2+x}\times\frac{3x}{-15x-15}=\frac{3x^4+3x}{-15x^4-15x}[/tex]Simplify
[tex]\frac{3x\left(x+1\right)\left(x^2-x+1\right)}{-15x\left(x+1\right)\left(x^2-x+1\right)}=-\frac{1}{5}[/tex]Answer;
[tex][/tex]The probability of rolling an odd number with a six-sided number cube is 1/2 Choose the tikelihood that best describes the probability of this event.O A. Certain O B. Likely O C. Neither likeiy nor unlikety O D. Unlikely
In a dice, obtain odd number
Its A CERTAIN probability, because can be calculated
P = (1,3,5) /(1,2,3,4,5,6) = 3/6 = 1/2
Then ANSWER IS OPTION A)
data collected for a study involving IQ scores of four year old girls produced a mean of 100 and a standard deviation of 10 what IQ score does a z-score of -1.5 represent
Answer:
85
Explanation:
First, recall the formula for Z-Score.
[tex]Z-\text{Score}=\frac{X-\mu}{\sigma}\text{ where }\begin{cases}X=\text{raw score} \\ \mu=\operatorname{mean} \\ \sigma=\text{standard deviation}\end{cases}[/tex]Substitute the given values:
[tex]\begin{gathered} -1.5=\frac{X-100}{10}\text{ } \\ X-100=-1.5\times10 \\ X-100=-15 \\ X=100-15 \\ X=85 \end{gathered}[/tex]A z-score of -1.5 represents an IQ score of 85.
0.149 divided 8,712
A vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. If x cars are made, then theunit cost is given by the function C (x) = 0,3x2 -96x+14,848. How many cars must be made to minimize the unit cost?Do not round your answer
Answer:
[tex]160\text{ cars}[/tex]Explanation:
Here, we want to get the number of cars to be made so as to minimize the unit cost
What we have to do here is to find the first derivative of the given cost function
Mathematically, we have that as:
[tex]C^{\prime}(x)\text{ = 0.6x -96}[/tex]To get the minimum x value, we simply set the first derivative to zero and solve for x
Mathematically, that would be:
[tex]\begin{gathered} 0\text{ = 0.6x-96} \\ 0.6x\text{ = 96} \\ x\text{ = }\frac{96}{0.6} \\ x\text{ = 160 } \end{gathered}[/tex]Robin and Dovey have four pet pigeons that they train to race. They release the birds at Robin's house and then drive to Dovey's to collect them. To drive from Robin's to Dovey's, because of one-way streets, they go 3.1 km north, turn right and go 1.7 km east, turn left and go 2.3 km north, turn right and go 0.9 km east, turn left and go 1.2 km north, turn left and go 4.1 km west, and finally turn left and go 0.4 km south. How far do the pigeons have to fly to go directly from Robin's house to Dovey's house? Round your answer to the nearest tenth. (HINT: draw a picture!) *
Let the north and east with a positive sign, so, the south and west are negative signs
Because of one-way streets, they go 3.1 km north, turn right and go 1.7 km east, turn left and go 2.3 km north, turn right and go 0.9 km east, turn left and go 1.2 km north, turn left and go 4.1 km west, and finally turn left and go 0.4 km south.
So, the resultant horizontal distance = 1.7 + 0.9 - 4.1 = -1.5 km
The resultant vertical distance = 3.1 + 2.3 + 1.2 - 0.4 = 6.2 km
So, the direct distance will be calculated using Pythagorean theorem :
So, the distance d =
[tex]\begin{gathered} d=\sqrt[]{(-1.5)^2+(6.2)^2}=\sqrt[]{2.25+38.44} \\ \\ d=\sqrt[]{40.69}=6.37887 \end{gathered}[/tex]Rounding the answer to the nearest tenth
so, the answer is : 6.4 km
helpppppppp ur gurlll out
Answer:
Step-by-step explanation:
2(x-3) + 21 = -3
So:
My first step is to open the brackets
2x - 6 + 21 = -3
Then I plus two numbers in the equation:
2x + 15 = -3
Third step is: 2x = -3 - 15
2x = -18
The value of x that makes the equation true is:
x = -18/2
x = -9
you invest 1,000 in an account that pays simple interest of 3% for 10 years. what is the amount of money you'll have at the end of the 10 years?
Given data:
The given principal is P=1,000.
The given rate of interest is r=3%.
The given time is t=10 years.
The expression for the final amount after 10 years is,
[tex]A=P+\frac{P\times r\times t}{100}[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} A=1,000+\frac{1,000\times3\times10}{100} \\ =1,300 \end{gathered}[/tex]Thus, the final amount after 10 years is 1,300.
PLSSS!! Help me with this question I’ve been on it for hours!! Pls show decimal form or fraction form
Answer:
(6, 4)
Step-by-step explanation:
(x, y) = ((x1 + x2)/2, (y1 + y2)/2)
= ((10 + 2)/2, (7 + 1)/2)
= (12/2, 8/2)
= (6, 4)
Answer:8.5 and 2.5
Step-by-step explanation:7, 8, MD 9, 10 There are four numbers in this sequence and MD is the midpoint. To find MD we have to find what is in the middle of 8 and 9. The number between them is 8.5 or
8 1/2(which is also 8 and one half)
For 2 and 1 same thing, what is between 2 and 1? To find that the number line goes 2, 2.9, 2.8, 2.7, 2.6, 2.5, 2.4, 2.3, 2.2, 2.1, and 1.
What is the midpoint in all of this? 2.5!Find the approximate area between the curve and the x-axis on the interval using 4 rectangles. Use the left endpoint of each rectangle to determine the height.
We have to approximate the area under the curve using the given rectangles.
Each rectangle will have an area that is equal to the width (the interval Δx) times the height (that is f(xi)).
We can express the formula for the approximation as:
[tex]A=\sum_{i=1}^4f(x_i)\cdot\Delta x=\sum_{i\mathop{=}1}^4f(x_i)(x_{i+1}-x_i)[/tex]We will have to calculate f(x) for x = 0, 4, 8 and 12, which are the left endpoints of the interval for each rectangle.
Given that f(x) is defined as:
[tex]f(x)=-2x^2+32x+5[/tex]we can calculate each value as:
[tex]f(0)=-2(0)^2+32(0)+5=5[/tex][tex]\begin{gathered} f(4)=-2(4)^2+32(4)+5 \\ f(4)=-2(16)+128+5 \\ f(4)=-32+128+5 \\ f(4)=101 \end{gathered}[/tex][tex]\begin{gathered} f(8)=-2(8)^2+32(8)+5 \\ f(8)=-128+256+5 \\ f(8)=133 \end{gathered}[/tex][tex]\begin{gathered} f(12)=-2(12)^2+32(12)+5 \\ f(12)=-288+384+5 \\ f(12)=101 \end{gathered}[/tex]We can now calculate the approximation as:
[tex]\begin{gathered} A=f(0)(4-0)+f(4)(8-4)+f(8)(12-8)+f(12)(16-12) \\ A=5(4)+101(4)+133(4)+101(4) \\ A=20+404+532+404 \\ A=1360 \end{gathered}[/tex]Answer: the approximation is equal to 1360 square units [Fourth option].
od 2 - 7th Grade Math) Simplify the following expressions: (9x + 3) - (5x - 7) (1 Point) Enter your answer
Simplifying the expression, we have:
[tex]\begin{gathered} (9x+3)-(5x-7) \\ =9x+3-5x+7 \\ =(9x-5x)+(3+7) \\ =4x+10 \end{gathered}[/tex]So the simplified expression is 4x + 10.
Which shape is the most general of the quadrilaterals below?
Given:
There are four shapes square, parallelogram, isosceles trapezoid and rectangle.
To find:
The shape is the most general of the quadrilaterals.
Explanation:
As we know,
If the quadrilateral has equal opposite sides and equal opposite angles, then it is a parallelogram.
So,
All squares are parallelograms.
All rectangles are parallelograms.
All rhombus is a parallelogram.
Therefore, the most general of the quadrilaterals is a parallelogram.
Final answer:
A parallelogram is the most general of the quadrilaterals.
Find the equation of the line with the following:slope = 2/5; passes through (-3, 1)
Answer:
[tex]y=\frac{2}{5}x+\frac{11}{5}[/tex]Explanation:
Given the slope and a point on the line, we use the point-slope form to find the equation of the line:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ m=\frac{2}{5} \\ (x_1,y_1)=(-3,1) \end{gathered}[/tex]Substitute the given values:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-1=\frac{2}{5}(x-(-3)) \\ y-1=\frac{2}{5}(x+3) \\ y=\frac{2}{5}(x+3)+1 \\ y=\frac{2}{5}x+\frac{6}{5}+1 \\ y=\frac{2}{5}x+\frac{11}{5} \end{gathered}[/tex]The equation of the line in slope-intercept form is:
[tex]y=\frac{2}{5}x+\frac{11}{5}[/tex]A rocket is launched straight up with a velocity of 8.36. What would be the velocity when it lands?
If the rocket is launched straight up with a velocity of 8.36 then at the velocity of landing the speed of the rocket will also be 8.36.
Given that the rocket is launched straight up with a velocity of 8.36.
We are required to find the velocity when the rocket lands.
Velocity is basically the directional speed of a object in motion as an indication of its rate of change in position as observed from a particular frame of reference.
When the velocity of rocket while it goes up is 8.36 then the velocity when it lands is also 8.36 because if the velocity will increase then the rocket will crash also.
Hence if the rocket is launched straight up with a velocity of 8.36 then at the velocity of landing the speed of the rocket will also be 8.36.
Learn more about velocity at https://brainly.com/question/25749514
#SPJ1
Nick bakes 3 dozen cookies for the bake sale. Each cookie requires 12 milliliters of water. How
many milliliters of water does he use?
In linear equation, 432 milliliters of water does he use .
What are a definition and an example of a linear equation?
An equation with only one variable is referred to as a linear equation in one variable. It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value. A linear equation in one variable would be 9x + 78 = 18, for instance.With only a constant and a first-order (linear) term, a linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept.Nick bakes 3 dozen cookies for the bake sale.
1 cookie requires 12 milliliters of water.
water does he use = 3 × 12 × 12
= 432 milliliters of water
Learn more about linear equation
brainly.com/question/11897796
#SPJ10
The point (a,b) is reflected across the line y=x and then across the x-axis. Which of the following are the coordinates of its final image point in terms of a and b?(1) (-b,-a)(2) (-b,a)(3) (b,-a)(4) (-a,-b)
When a point is reflected across the line, y = x, the x and y coordinates changes places. Given that the coordinates of the original point is (a, b), the coordinate of the new point would be (b, a)
Again, this new point was reflected across the x axis. Recall, if reflection is done across the x axis, the sign of the x coordinate remains the same while the sign of the y coordinate is reversed,
Therefore, the coordinates of its final image point in terms of a and b is (b, - a)
The correct option is number 3
Amrita wants to raise more than $200 for a charity by walking dogs in her neighborhood. She charges $7 per walk.What is an inequality that can be used to find the number of walks, w, that Amrita needs to complete?
Given:
Amrita wants to raise more than $200 for a charity.
She charges $7 per walk.
[tex]\begin{gathered} 7w>200 \\ \end{gathered}[/tex]if you roll a dice twice, what is the possibility of getting a number less than 5 on both rolls?
Solution
Step 1
Write an expression for the probability of an event
[tex]\begin{gathered} \text{If an event is A} \\ P(A)\text{ = }\frac{No\text{ of required events}}{No\text{ of total possible events}} \end{gathered}[/tex]
No of the required events can be found with the following table
The numbers(1,2,3,4,5,6) on the vertical are for one dice and the others on the horizontal are for the second dice
No of required of numbers on both dices less than 5 are : 1,1 1,2 1,3 1,4 2,1 2,2 2,3 2,4 3,1 3,2 3,3 3,3 3,4 4,1 4,2 4,3 4,4. The number of the events are therefore, = 16
No of total events = 36
Step 2
Substitute the values and find the required probability
[tex]\text{Probability of getting numbers less than 5 on both dice = }\frac{16}{36}=\text{ }\frac{4}{9}[/tex]Solve -4x + 3 > 23 or 7x - 6 > 22
Answer:
-4x + 3 > 23 Answer is x<-5
Step-by-step explanation:
