Answer:
The 95% confidence interval is [tex]10.5 < \mu <13.3[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 41[/tex]
The sample mean is [tex]\= x = 11.9 \ hr[/tex]
The standard deviation is [tex]\sigma = 4.5[/tex]
For a 95% confidence interval the confidence level is 95%
Given that the confidence level is 95% then the level of significance can be mathematically represented as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5 \%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical values of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table
The values is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{ \sqrt{n} }[/tex]
substituting values
[tex]E = 1.96 * \frac{ 4.5 }{ \sqrt{41} }[/tex]
[tex]E = 1.377[/tex]
The 95% confidence interval is mathematically represented as
[tex]\= x - E < \mu < \= x - E[/tex]
substituting values
[tex]11.9 - 1.377 < \mu <11.9 + 1.377[/tex]
[tex]10.5 < \mu <13.3[/tex]
graph the linear equation. Find three points that solve the equation, the plot them on the graph. -2y= 5x +11
Answer:
Three points are (0,-5.5), (-1,-3), (-2.2,0) and graph is shown below.
Step-by-step explanation:
The given equation is
[tex]-2y=5x+11[/tex]
We need to find three points that solve the equation.
Put x=0,
[tex]-2y=5(0)+11[/tex]
[tex]-2y=11[/tex]
[tex]y=-5.5[/tex]
Put x=-1,
[tex]-2y=5(-1)+11[/tex]
[tex]-2y=6[/tex]
[tex]y=-3[/tex]
Put y=0,
[tex]-2(0)=5x+11[/tex]
[tex]5x=-11[/tex]
[tex]x=-2.2[/tex]
So, three points (0,-5.5), (-1,-3) and (-2.2,0) are the solutions of the given equation.
Plot these points on a coordinate plane and connect them by a straight line as shown below.
602/100 into a decimal describe plz
Answer:
6.02
six point zero two
Step-by-step explanation:
Answer:
602 / 100= 6,02
Step-by-step explanation:
602 to divide 100 = 6,02
Help and show work plz
Answer:
30
Step-by-step explanation:
If we have 4 integers that have an average of 9, then all the numbers will add up to [tex]9\cdot4=36[/tex].
If we want the greatest number possible, the other 3 need to be the lowest possible.
Since they are all different, the lowest possible values of the first 3 numbers are 1, 2, and 3.
[tex]1 + 2 + 3 = 6[/tex]
[tex]36 - 6 = 30[/tex]
So 30 is the greatest value of one of the integers.
Hope this helped!
Please answer this correctly without making mistakes
Answer:
17/16 OR [tex]1\frac{1}{16}[/tex] minutes
Step-by-step explanation:
Since Jayla spent 1/16 of a minute AND one whole minute watching a millipede crawl, we'd need to first add the two numbers.
Since the given minute is out of 16, we can convert the one minute to 16/16. This means we can add the other 1/16 of a minute.
This leaves us with Jayla watching the millipede for 17/16 OR [tex]1\frac{1}{16}[/tex] minutes.
Hope this helps!! <3 :)
you pick a card at random from an ordinary deck of 52 cards. If the card is an ace, you get 9 points; if not, you lose a point
Answer: a = 9, b = 48, c = -1
Step-by-step explanation:
"a" represents the points you receive if an Ace is picked. It is given that you get 9 points ----> a = 9
"b" represents the number of cards that are Not an Ace. 4 cards in the deck are Aces so 52 - 4 = 48 cards are Not an Ace -----> b = 48
"c" represents the points you receive if Not an Ace is picked. It is given that you lose 1 point ----> c = -1
Answer:
Here is the rest of the page
Step-by-step explanation:
Which best describes the relationship between the lines with equations -36x + 8y = 16 and
-9x + 2y = 4?
Hi there! :)
Answer:
The lines are the same.
Step-by-step explanation:
Begin by converting each equation into its simplest form in slope-intercept form:
-36x + 8y = 16
Move the "x" variable to the right side of the equation:
8y = 36x + 16
Divide all terms by 8:
y = 36/8x + 16/8
y = 9/2x + 2
-------------------------------
-9x + 2y = 4
Move "x" variable:
2y = 9x + 4
Divide both sides by 2:
y = 9/2x + 2
Both of the equations are equivalent, meaning both of the lines are the same.
Which of the following expression is equal to X^2+9
Answer:
(x + 3i) * (x - 3i) = x^2 + 3xi - 3xi - 9(i^2) = x^2 + 9
Step-by-step explanation:
After setting up the width of the compass using the original line segment, why is it important to keep the compass the same
width before drawing an arc? (1 point)
If the width of the compass changed, it would make the arc smaller or larger. This would then make the line segment to be drawn
smaller or larger, so it would not match the original.
of the width of the compass changed, it would make the arc smaller or larger. This would change the angle the new line segment is
drawn at, so it would not match the original.
O if the width of the compass changed, it would be possible for the arc to intersect the original line segment, which is not allowed.
The width of the compass does not matter. All that matters is that a straightedge is used to draw the line segment
Answer:
If the width of the compass changed, it would make the arc smaller or larger. This would then make the line segment to be drawn smaller or larger, so it would not match the original.
Step-by-step explanation:
We assume your construction is trying to copy the length of a line segment. That length is "measured" by the width of the compass. If it is changed, it no longer matches the length of the segment you're trying to copy, so you will not get the copy you want.
Eliminate the parameter for the following set of parametric equations: x= t + 6 y= 3t – 1
Answer:
Solution : Option A
Step-by-step explanation:
What we want to do here is eliminate the parameter t. In order to do that, we can isolate t in our first equation x = t + 6 ----- ( 1 ) and then plug that value for t in the second equation y = 3t - 1. Our solution will be an equation that is not present with t.
( 1 ) x = t + 6, t = x - 6
( 2 ) y = 3( x - 6 ) - 1 ( Distribute the " 3 " in 3( x - 6 ) )
y = 3x - 18 - 1 ( Combine like terms )
y = 3x - 19
As you can see our result will be option a, y = 3x - 19.
Find the first six partial sums S1, S2, S3, S4, S5, S6 of the sequence whose nth term is given. 1 2 , 1 22 , 1 23 , 1 24 , . .
Answer:
the first partial sum [tex]\mathbf{S_1= \dfrac{1}{2}}[/tex]
the second partial sum [tex]\mathbf{S_2= \dfrac{3}{4} }[/tex]
the third partial sum [tex]\mathbf{S_3= \dfrac{7}{8}}[/tex]
the fourth partial sum [tex]\mathbf{S_4= \dfrac{15}{16}}[/tex]
the fifth partial sum [tex]\mathbf{S_5= \dfrac{31}{32}}[/tex]
the sixth partial sum [tex]\mathbf{S_6= \dfrac{63}{64}}[/tex]
Step-by-step explanation:
The term of the sequence are given as : [tex]\dfrac{1}{2}[/tex], [tex]\dfrac{1}{2^2}[/tex], [tex]\dfrac{1}{2^3}[/tex], [tex]\dfrac{1}{2^4 }[/tex] , . . .
The nth term for this sequence is , [tex]\mathtt{a_n =( \dfrac{1}{2})^n}[/tex]
The nth partial sum of the sequence for [tex]\mathtt{a_1,a_2,a_3.... a_n}[/tex] is [tex]\mathtt{S_n}[/tex]
where;
[tex]\mathtt{S_n = a_1 +a_2+a_3+ ...+a_n}[/tex]
The first partial sum is: [tex]\mathtt{S_1= a_1}[/tex]
[tex]\mathtt{S_1= (\dfrac{1}{2})^1}[/tex]
[tex]\mathbf{S_1= \dfrac{1}{2}}[/tex]
Therefore, the first partial sum [tex]\mathbf{S_1= \dfrac{1}{2}}[/tex]
The second partial sum is: [tex]\mathtt{S_2= a_1+a_2}[/tex]
[tex]\mathtt{S_2= (\dfrac{1}{2})^1 + (\dfrac{1}{2})^2}[/tex]
[tex]\mathtt{S_2= \dfrac{1}{2} + \dfrac{1}{4}}[/tex]
[tex]\mathtt{S_2= \dfrac{2+1}{4} }[/tex]
[tex]\mathbf{S_2= \dfrac{3}{4} }[/tex]
Therefore, the second partial sum [tex]\mathbf{S_2= \dfrac{3}{4} }[/tex]
The third partial sum is : [tex]\mathtt{S_3= a_1+a_2+a_3}[/tex]
[tex]\mathtt{S_3= (\dfrac{1}{2})^1 + (\dfrac{1}{2})^2+(\dfrac{1}{2})^3 }[/tex]
[tex]\mathtt{S_3= \dfrac{1}{2} + \dfrac{1}{4}+\dfrac{1}{8}}[/tex]
[tex]\mathtt{S_3= \dfrac{4+2+1}{8}}[/tex]
[tex]\mathbf{S_3= \dfrac{7}{8}}[/tex]
Therefore, the third partial sum [tex]\mathbf{S_3= \dfrac{7}{8}}[/tex]
The fourth partial sum : [tex]\mathtt{S_4= a_1+a_2+a_3+a_4}[/tex]
[tex]\mathtt{S_4= (\dfrac{1}{2})^1 + (\dfrac{1}{2})^2+(\dfrac{1}{2})^3+(\dfrac{1}{2})^4 }[/tex]
[tex]\mathtt{S_4= \dfrac{1}{2} + \dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}}[/tex]
[tex]\mathtt{S_4= \dfrac{8+4+2+1}{16}}[/tex]
[tex]\mathbf{S_4= \dfrac{15}{16}}[/tex]
Therefore, the fourth partial sum [tex]\mathbf{S_4= \dfrac{15}{16}}[/tex]
The fifth partial sum : [tex]\mathtt{S_5= a_1+a_2+a_3+a_4+a_5}[/tex]
[tex]\mathtt{S_5= (\dfrac{1}{2})^1 + (\dfrac{1}{2})^2+(\dfrac{1}{2})^3+(\dfrac{1}{2})^4 +(\dfrac{1}{2})^5 }[/tex]
[tex]\mathtt{S_5= \dfrac{1}{2} + \dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}}[/tex]
[tex]\mathtt{S_5= \dfrac{16+8+4+2+1}{32}}[/tex]
[tex]\mathbf{S_5= \dfrac{31}{32}}[/tex]
Therefore, the fifth partial sum [tex]\mathbf{S_5= \dfrac{31}{32}}[/tex]
The sixth partial sum: [tex]\mathtt{S_5= a_1+a_2+a_3+a_4+a_5+a_6}[/tex]
[tex]\mathtt{S_6= (\dfrac{1}{2})^1 + (\dfrac{1}{2})^2+(\dfrac{1}{2})^3+(\dfrac{1}{2})^4 +(\dfrac{1}{2})^5 +(\dfrac{1}{2})^6 }[/tex]
[tex]\mathtt{S_6= \dfrac{1}{2} + \dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64} }[/tex]
[tex]\mathtt{S_6= \dfrac{32+16+8+4+2+1}{64}}[/tex]
[tex]\mathbf{S_6= \dfrac{63}{64}}[/tex]
Therefore, the sixth partial sum [tex]\mathbf{S_6= \dfrac{63}{64}}[/tex]
Question (1)
(i) Explain Pythagorean theorem in detail.
(ii) What is "Hippacus of Croton"?
Answer:
● The pythagorian theorem
The pythagorian theorem is used to find a missing side of a right triangle.
It states that the square of the hypotenus of a right triangle is equal to the sum of the squares of the two other sides.
Let a be the hypotenus, b and c are the othet sides:
☆☆☆☆☆ a^2 = b^2 + c^2☆☆☆☆☆
There are more than 350 way to prove this theorem.
■■■■■■■■■■■■■■■■■■■■■■■■■■
● Hippasus of Croton was a member of the highly-secretive school og Pythagoras in Croton. He is credited in history as the first person to prove the existence of irrational numbers.
a milha eh uma unidade usada para medir distancias. ela equivale a cerca de 1,6 quilometros. se cada carro percorrer 240 quilometros, quantas milhas tera percorrido? urgente
Classica aplicação de regra de 3:
é dito que: 1 milha = 1,6km
Logo, eis a regra de 3:
milha km
1 -------- 1,6
X -------- 240
1,6X = 240.1
X = 240/1,6
X = 150milhasLogo 240km equivalem a 150milhas
For the following graph, state the polar coordinate with a positive r and positive q (in radians). Explain your steps as to how you determined the coordinate (in your own words). I'm looking for answers that involve π, not degrees for your angles. State the polar coordinate with (r, -q). Explain how you found the new angle. State the polar coordinate with (-r, q). Explain how you found the new angle. State the polar coordinate with (-r, -q). Explain how you found the new angle.
the graph has 12 segments so angle enclosed by each segment is [tex] {2\pi\over 12}=\frac{\pi}6[/tex]
anti-clockwise is taken as positive, so if you want positive q, you need to rotate 8 segments [tex] q=8\frac,{\pi}6=\frac{4\pi}3 [/tex] , and and 8 circles or units so r=8
and for a negative angle, you need to rotate clockwise
Which is 4 segments from the horizontal line. so [tex]q=-\frac{2\pi}3[/tex] and r will be same, 8 units.
[not sure about -r so I won't include it in answer]
Answer:
Points : ( 8, - 2π/3 ), ( - 8, π/3 ), ( - 8, - 5π/3 )
Step-by-step explanation:
For the first two cases, ( r, θ ) r would be > 0, where r is the directed distance from the pole, and theta is the directed angle from the positive x - axis.
So when r is positive, we can tell that this point is 8 units from the pole, so r is going to be 8 in either case,
( 8, 240° ) - because r is positive, theta would have to be an angle with which it's terminal side passes through this point. As you can see that would be 2 / 3rd of 90 degrees more than a 180 degree angle,or 60 + 180 = 240 degrees.
( 8, - 120° ) - now theta will be the negative side of 360 - 240, or in other words - 120
Now let's consider the second two cases, where r is < 0. Of course the point will still be 8 units from the pole. Again for r < 0 the point will lay on the ray pointing in the opposite direction of the terminal side of theta.
( - 8, 60° ) - theta will now be 2 / 3rd of 90 degrees, or 60 degrees, for - r. Respectively the remaining degrees will be negative, 360 - 60 = 300, - 300. Thus our second point for - r will be ( - 8, - 300° )
_________________________________
So we have the points ( 8, 240° ), ( 8, - 120° ), ( - 8, 60° ), and ( - 8, - 300° ). However we only want 3 cases, so we have points ( 8, - 120° ), ( - 8, 60° ), and ( - 8, - 300° ). Let's convert the degrees into radians,
Points : ( 8, - 2π/3 ), ( - 8, π/3 ), ( - 8, - 5π/3 )
Evaluate the expression 8p6
Answer:
Evaluate 8P6 P 6 8 using the formula nPr=n!(n−r)! P r n = n ! ( n - r ) ! . 8!(8−6)! 8 ! ( 8 - 6 ) ! Subtract 6 6 from 8 8 . 8!(2)! 8 ! ( 2 ) ! Simplify 8!(2)! 8 !
Step-by-step explanation:
evaluate" usually means to put a value in for the variable, but you don't give us a value for p. also, it is unclear if you ...
The value of the expression [tex]^8P_6[/tex] is 20160.
What is permutation?A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order.
The value of the expression is calculated as:-
[tex]^8P_6=\dfrac{8!}{8!-6!}=\dfrac{8!}{2!}[/tex]
[tex]^8P_6 =\dfrac{8\times 7\times 6\times 5\times 4\times 3\times 2}{2}[/tex]
[tex]^8P_6[/tex] = 20160
Hence, the value is 20160.
To know more about permutations follow
https://brainly.com/question/4658834
#SPJ5
Simplify the expression. Write the answer using scientific notation.
(5x107)(6x104)
A) 1.1 x 1012
B) 3.0x 1029
C) 3.0 x 1012
D) 1.1 x 1029
Answer:
3* 10 ^12
Step-by-step explanation:
(5x10^7)(6x10^4)
Multiply the numbers together
5*6 =30
Add the exponents
10^7 * 10 ^ 4 = 10 ^(7+4) = 10 ^11
30 * 10 ^11
But this is not scientific notation since 30 >10
Move the decimal one place to the left and add 1 to the exponent
3* 10 ^12
Answer:
3* 10 ^12
Step-by-step explanation:
what's the equation that represents the new path
Answer:
A: y= 1/4x - 7
if it is perpendicular, then it creates 4 right angles. so that new line would pass through (0,-7) and something else that isnt important. but the slope, or m, would be 1/4, and the y intercept would be -7. so the new equation is y=1/4x-7
Adam’s house is 2 centimeters from Juan’s house on a map. If each centimeter on the map represents 6 kilometers, how far apart are the two houses?
Answer:
Since 1 cm represents 6 km
2 cm will represent 12 km
Hence Adam's house is 12 km away
Answer:
The answer is C. 3
Step-by-step explanation:
If u divide 6 divided by 2 it will get you 3
i also got it right bc i took the quiz.
MY
A circle with radius of 5 cm sits inside a 11 cm x 11 cm rectangle.
Col
What is the area of the shaded region?
Round your final answer to the nearest hundredth.
MY
11 cm
Pro
Pro
Теа
5 cm
11 cm
cm2
2 of 4 OOO
Help
Step-by-step explanation:
Hi, there!!!
According to the question we must find the area of shaded region, but we must find area of circle and rectangle to find area of shaded region,
So, let's simply work with it,
Firstly, finding the area of rectangle,
length = 11cm.
breadth = 11cm.
now, area= length× breadth.
or, a = 11cm× 11cm.
a= 121cm^2
Now, let's work out the area of circle.
radius= 5cm
and pi. = 3.14 {using pi value as 3.14}
now,
area of a circle = pi× r^2
or, a= 3.14×5^2
or, a = 78.5 cm^2.
Therefore, The area of a circle is 78.5cm^2.
Now lastly finding the area of shadedregion,
area of shaded region = area of rectangle - area of circle.
or, area of shaded region = 121cm^2 - 78.5cm^2
Therefore, the area of shaded region is 42.5 cm^2.
Hope it helps...
How would you find the coefficient of the third term in (x+5)^7?
Answer:
The answer is option B
Step-by-step explanation:
To find the coefficient of the third term in
[tex](x + 5)^{7} [/tex]
Rewrite the expansion in the form
[tex](a + x)^{n} [/tex]
where n is the index
So we have
[tex] ({5 + x})^{7} [/tex]
After that we use the formula
[tex]nCr( {a}^{n - r} ) {x}^{r} [/tex]
where r is the term we are looking for
For the third term we are looking for the term containing x²
that's
r + 1 = 3
r = 2
So to find the coefficient of the third term
We have
[tex]7C2[/tex]
Hope this helps you
first of all, the notation is wrong it should be [tex] {}^nC_r \text{ and more usual notation is } {n \choose k} [/tex]
second, the
[tex](r+1)^{\text{th}} \text{ term } T_{r+1} \text{ in the expansion of } (x+a)^n \text{ is } {n \choose r}x^{(n-r)}a^r[/tex]
here [tex] a=5 \text{ and } n=7 \text{ and for } 3^{\text{rd}} \text{ term } T_3, \quad r+1=3 \implies r=2 [/tex]
so the coefficient of third term is, [tex]{7 \choose 2}={7\choose 5}[/tex]
an important property of binomial coefficient you should know:
[tex] {n \choose k}={n \choose {n-k}}[/tex]
and if you interchange [tex] x \text{ and } a[/tex]
only the "order" will get reversed. i.e. the series will start from back.
another thing, the [tex] k^{\text{th}} \text{ term from beginning, is the } (n-k+2)^{\text{th}} \text{ term from behind}[/tex]
Why is 12 * 10-8 is NOT a correct representation of scientific notation?
Answer:
see below
Step-by-step explanation:
Scientific notation is a * 10 ^b
a must be a number between 1 ( including 1 ) and less than 10
12 is greater than 10 so it is not scientific notation
Diane has a rectangular poster that is 20 centimeters long and 15 centimeters wide. What is the area of the poster in square meters? Do not round your answer. Be sure to include the correct unit in your answer.
Answer:
0.03 square meters
Step-by-step explanation:
1. convert 20 cm, 15 cm into m by dividing the number by 100 then you got 0.2 m and 0.15 m respectively
2. calculate the area by multiply 2 numbers together
0.2 × 0.15 = 0.03 square meter
What's the solution of the following linear system? 5x + 2y = 9 –5x – 2y = 3
━━━━━━━☆☆━━━━━━━
▹ Answer
(-39/35, 9/7)
▹ Step-by-Step Explanation
5y + 2y = 9
-5x - 2y = 3
Solve the equation:
y = 9/7
-5x - 2y = 3
Substitute the value of y:
-5x - 2 * 9/7 = 3
x = -39/35
(x, y) = (-39/35, 9/7)
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
To solve this system by addition, we start by adding both of our equations together but notice that the x terms and the y terms cancel out.
This leaves us with 0 on the left side and on the right side,
9 + 13 = 12 so we are left with the equation 0 = 12.
Since 0 = 12 is a false statement, this means that
there is no solution to our system of equations.
Please help! Find the equation of the line (graph provided in attached picture) Use exact numbers. y =_ x+_ ( _ represent blanks in the equation)
Answer:
[tex] y = \frac{3}{4}x - 2 [/tex]
Step-by-step explanation:
Equation of a line is given as [tex] y = mx + b [/tex]
Where,
m = slope of the line = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]
b = y-intercept, which is the value at the point where the line intercepts the y-axis. At this point, x = 0.
Let's find m and b to derive the equation for the line.
[tex] m = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Use the coordinate pair of any two points on the line. Let's use the following,
[tex] (0, -2) = (x_1, y_1) [/tex] => on the line, when x = 0, y = -2
[tex] (4, 1) = (x_2, y_2) [/tex] => on the line, when x = 4, y = 1
Plug in the values and solve for m
[tex] m = \frac{1 - (-2)}{4 - 0} [/tex]
[tex] m = \frac{1 + 2}{4} [/tex]
[tex] m = \frac{3}{4} [/tex]
b = -2 (the line intercepts the y-axis at this point)
Our equation would be =>
[tex] y = mx + b [/tex]
[tex] y = \frac{3}{4}x + (-2) [/tex]
[tex] y = \frac{3}{4}x - 2 [/tex]
Problem 1. (1 point) A steel ball weighing 128 pounds is suspended from a spring. This stretches the spring 128101 feet. The ball is started in motion from the equilibrium position with a downward velocity of 2 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second) . Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t. (Note that this means that the positive direction for y is down.)
Answer:
seeed
Step-by-step] explanation:
ddd~!`
The parallelogram to be a square,x=?
Answer:
7°
Step-by-step explanation:
for this paralellogram to be a square, the sides should be perpendicular.
Woch means that 4x+17° = 45°
● 4x +17° = 45°
Substract 17 from both sides.
● 4x +17°-17° = 45°-17°
● 4x = 28°
Divide both sides by 4
● 4x/4 = 28°/ 4
● x = 7°
Please help. I’ll mark you as brainliest if correct!
Answer:
x and y can have many values
Step-by-step explanation:
-24x - 12y = -16
Then: 24x + 12y = 16
We know: 6x + 3y = 4
X and Y can have a lot of valoues.
6x + 3y = 4
3 ( 2x + y) = 4
2x + y= 4/3
2x+y= 1.333...
solve the equation: 14<2x−1≤20
Answer:
7.5 < x≤10.5
Step-by-step explanation:
14<2x−1≤20
Add 1 to all sides
14+1<2x−1+1≤20+1
15<2x≤21
Divide each side by 2
15/2 <2x/2 ≤21/2
7.5 < x≤10.5
Steps to solve:
14 < 2x - 1 <= 20
~Add 1 to everything
15 < 2x <= 21
~Divide 2 to everything
7.5 < x <= 10.5
Best of Luck!
A shopping centre wants to examine the amount of space required for parking. Studies indicated that 50% of staff and shoppers use public transportation. A survey of 1002 was taken, and 483 responded that they used public transportation. At 5% level of significance, is it reasonable to conclude that the survey results indicate a change?
Answer:
We accept H₀ data from the survey is not enough to claim that 50% of the proportion indicated in previous studies have change
Step-by-step explanation:
To get conclusions about the survey we need to develop a hypothesis test of proportion
According to previous studies, (p₀ ) 50 % of staff and customers use public transportation, and we got from a survey 0f 1002 people 483 responded they also use then p = 483/1002 then
n sample size is 1002 and p = 0,482 (48,2 % )
Test Hypothesis
Null hypothesis H₀ p = p₀
Alternative hypothesis Hₐ p < p₀
CI = 95 % α = 5 % α = 0,05 and from z-table we find z score for that value z(c) = - 1,64
z(s) = ( p - p₀ ) / √ (p₀*q₀)/ n p₀ = q₀ = 0,5
z(s) = - 0,018* 31,65 / 0,5
z(s) = - 1,1394
To compare
z(s) and z(c) -1,1394 > 1,64
Then z(s) is inside the acceptance region. We accept H₀ , because we don´t have enough evidence to claim that the survey results indicate a change in
the original proportion
Given there are 26 alphabets in the English language, how many possible three-letter words are there?
We have 26 letters and 3 slots to fill. We can reuse a letter if it has been picked, so we have 26^3 = 26*26*26 = 17,576 different three letter "words". I put that in quotes because a lot of the words aren't actual words, but more just a sequence of letters.
Find the missing side or angle.
Round to the nearest tenth.
Answer:
a = 4.1Step-by-step explanation:
To find the missing side in the question, we use the cosine rule
That's
Since we are finding a we use the formula
a² = b² + c² - 2(b)(c) cos AFrom the question
b = 2
c = 4
A = 78°
Substitute the values into the above formula
We have
a² = 2² + 4² - 2(2)(4) cos 78
a² = 4 + 16 - 16 cos 78
a² = 20 - 16cos 78
a² = 16.67341
Find the square root of both sides
a = 4.0833
We have the final answer as
a = 4.1 to the nearest tenthHope this helps you