Using the normal distribution and the central limit theorem, we have that:
a) The sampling distribution is approximately normal, with mean 0.22 and standard error 0.0338.
b) There is a 0.1867 = 18.67% probability that in a random sample of 150 couples more than 25% met online.
c) There is a 0.2584 = 25.84% probability that in a random sample of 150 couples between 15% and 20% met online.
Normal Probability DistributionIn a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].In this problem:
22% of couples meet online, hence p = 0.22.A sample of 150 couples is taken, hence n = 150.Item a:
The mean and the standard error are given by:
[tex]\mu = p = 0.22[/tex]
[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.22(0.78)}{150}} = 0.0338[/tex]
The sampling distribution is approximately normal, with mean 0.22 and standard error 0.0338.
Item b:
The probability is one subtracted by the p-value of Z when X = 0.25, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.25 - 0.22}{0.0338}[/tex]
Z = 0.89
Z = 0.89 has a p-value of 0.8133.
1 - 0.8133 = 0.1867.
There is a 0.1867 = 18.67% probability that in a random sample of 150 couples more than 25% met online.
Item c:
The probability is the p-value of Z when X = 0.2 subtracted by the p-value of Z when X = 0.15, hence:
X = 0.2:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.2 - 0.22}{0.0338}[/tex]
Z = -0.59
Z = -0.59 has a p-value of 0.2776.
X = 0.15:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.15 - 0.22}{0.0338}[/tex]
Z = -2.07
Z = -2.07 has a p-value of 0.0192.
0.2776 - 0.0192 = 0.2584.
There is a 0.2584 = 25.84% probability that in a random sample of 150 couples between 15% and 20% met online.
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Solve by completing the square
[tex]4x^2+12x=32\\\\\implies x^2+3x=8\\\\\implies x^2 +2 \cdot \dfrac 32 \cdot x+\left(\dfrac 32 \right)^2 - \left(\dfrac 32\right)^2 =8\\ \\\implies \left(x+\dfrac 32 \right)^2 = 8 + \dfrac 94 = \dfrac{41}4\\\\\implies x+\dfrac 32 = \pm\dfrac{\sqrt{41}}2\\\\\implies x = \pm \dfrac{\sqrt {41}}2 - \dfrac 32\\\\\text{The roots are}~ x = -\dfrac 32-\dfrac{\sqrt{41}}2~ \text{and}~~ x = -\dfrac 32+\dfrac{\sqrt{41}}2[/tex]
A rectangular prism has a length of 20 meters, a height of 12 meters,
and a width of 12 meters. What is its volume, in cubic meters?
Answer:
2880 cubic meters.
Step-by-step explanation:
To find the area of a rectangular prism, multiply the length width and height.
20*12*12=144*20=2880
The volume of the Rectangular Prism is 2880 cubic meters.
What is Rectangular Prism?Rectangular prism can be defined as a" 3-dimensional solid shape which has six faces that are rectangles. A rectangular prism is also a cuboid".
According to the question,
Length of the rectangular prism = 20 meters
Height of the rectangular prism = 12 meters
Width of the rectangular prism = 12 meters
Formula for Rectangular Prism = length × breadth × height
= 20 × 12 × 12
= 2880 cubic meters.
Hence, the volume of the Rectangular Prism is 2880 cubic meters.
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Find the domain of the function f(x) 4 x - 7.
Answer: The domain of this function is any real number. More mathematically it is put as
-∞ < x <+∞
Answer:
The domain of this function is any real number. More mathematically it is put as
-∞ < x <+∞
Step-by-step explanation:
LOOK AT PICTURE!!! DO THE QUESTION THAT IS CIRCLED. IF CORRECT 50 POINTS!
Answer:
v = length x width x hight
This question is worth 100 points if you get this right.
Answer:
7 nights
Step-by-step explanation:
If he does 1/3 every night then you must turn 2 1/3 into a mixed fraction.
7/3
Then divide.
7/3 by 1/3
your answer is 7/1 or just 7 nights
Just divide
No of nights
2-1/3 ÷1/37/3÷1/37/3×37nightsHe need 7 nights
Please help cannot figure out how to get the answers
Answer:
Step-by-step explanation:
Sandra makes and sells bracelets. It costs her $2 to make each bracelet, plus a one-time cost of $15 for supplies. She plans to sell each bracelet for $5. Let x represent the number of bracelets. Which equation can be used to find the number of bracelets she needs to sell to break even?
2 x minus 5 x = 15
2 x + 5 x = 15
2 x + 15 = 5 x
5 x + 15 = 2 x
Luka and Gabby rent a tandem bike for $25/hr.Which value is the dependent variable? Which is the independent variable? Write an equation to represent the relationship between the number of hours, h, and the total cost of c.
c = 25(h)
dependent variable : They must give $25 per hour.
independent variable: time is independent as no specific time given.
total cost = $25 * hours taken
c = 25 * h
c = 25(h)
Answer:
See below ↓
Step-by-step explanation:
Given
rate of renting a tandem bike = $25/hh = number of hoursc = total costSolving
Clearly, as the number of hours does not depend on another variable, h is the independent variableTherefore, c is the dependent variableThe equation is :⇒ c = 25hI really need this answer plss
Answer:
No No No No No No No No No No No No No
can someone solve what is n/n^3
Answer:
Alex = No B.
Step-by-step explanation:
1) Use Quotient Rule: [tex]\frac{x^{a} }{x^{b} } =x^{a-b}[/tex]
[tex]n^{1-3}[/tex]
2) Simplify 1 - 3 = 2
[tex]n^{-2}[/tex]
3) Use Negative Power Rule: [tex]x^{-a} =\frac{1}{x^{a} }[/tex]
[tex]\frac{1}{n^{2} }[/tex]
Help help help help help
Answer:
x = 12
Step-by-step explanation:
Becuase 6/12 = 2 and 9 + 2 = 11
12
Mt. Everest, the tallest mountain in the world, is 29,029 ft tall. K2, the world’s second tallest mountain is 28,251 ft tall. How much taller is Mt. Everest than K2?
Answer:
778ft
Step-by-step explanation:
I need help solving this pls
Answer:
x = 44.5 due to the Triangle Angle Sum Theorem
Step-by-step explanation:
This is the Triangular Angle Sum Theorem.
This rule states that every angle inside the triangle has to equal 180.
This is a solve for x situation
2x + x + x + 2 = 180
Add all the x's first
3x + x + 2 = 180
4x + 2 = 180
Now subtract 2 both sides
4x = 180 -2
4x = 178
Divide 178 by 4
x = 44.5
You could verify by plugging 44.5 into the x's
2(44.5) + 44.5 + 44.5 + 2 = 180
89 + 44.5 + 46.5 = 180
Answer:
x = 44.5
Step-by-step explanation:
2x + x + (x+2) = 180
4x + 2 = 180
4x = 178
x = 44.5
Just saw your last comment :)
Let me know if you have any questions!
Solve for x 5x + 14 >54
Answer:
x > 8
Step-by-step explanation:
5x > 40
40/5 = 8
x> 8
subtract 14
divide by 5
Simplify expression:
2(4x + 3) - 3(x + 1)
Answer:
5x+3
Step-by-step explanation:
[tex]\left[Thank\;you\;for\;Joining\;Brainly!][/tex]
Answer:
5x + 3
Step-by-step explanation:
[tex]2\left(4x+3\right)-3\left(x+1\right)[/tex]
[tex]\mathrm{Expand\;2(4x+3)}:8x+6[/tex]
[tex]=8x+6-3\left(x+1\right)[/tex]
[tex]\mathrm{Expand\;-3(x+1)}:-3x-3[/tex]
[tex]=8x+6-3x-3[/tex]
[tex]\mathrm{Group\:like\:terms}[/tex]
[tex]=8x-3x+6-3[/tex]
[tex]\mathrm{Subtract\:the\:numbers:}\:6-3=3[/tex]
[tex]=8x-3x+3[/tex]
[tex]\mathrm{Add\:similar\:elements:}\:8x-3x=5x[/tex]
[tex]=5x+3[/tex]
Hence, your answer is 5x + 3
[RevyBreeze]
What is the slope-intercept equation for this line?
y = [?]x +[?]
Answer:
y = -3x + 1
Step-by-step explanation:
as we can see the y intercept is 1 because on the y- axis (0,1)
for slope it is 3 because rise over run. We rise 3 and run 1 = 3/1 = 3
the slope is negative because of the line
Hope this helps!!
Answer:
y=-3x+1
Step-by-step explanation:
50 points
Maya puts groceries into bags. The terms and their weights in kilograms are given below.
Bread 0.27
Bananas 49/100
Cheese 75/100
Carrots 0.49
Grapes 27/100
Eggs 0.75
Plot the weight in kilograms of each item on the number line below
⬇️⬇️⬇️⬇️⬇️⬇️⬇️⬇️⬇️⬇️⬇️⬇️⬇️⬇️⬇️⬇️⬇️
➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖
Answer:
see attached
Step-by-step explanation:
The values are plotted on the number line attached.
__
Each value is represented on the list both as a fraction and as a decimal. Equal values map to the same point on the number line.
0.27 = 27/100
0.49 = 49/100
0.75 = 75/100
The location on the number line is found by effectively dividing the distance between 0 and 1 into 100 parts, then locating the point on the corresponding division. The attached number line shows the interval divided into 50 parts, so the given values will lie halfway between the grid marks on this number line.
Prove that:-
[tex] \sqrt{ \frac{1 + cos30 {}^{ \circ} }{1 - cos {30}^{ \circ} } } = sec \: {60}^{ \circ} + tan \: {60}^{ \circ} [/tex]
Answer:
[tex] \displaystyle{ \sqrt{ \frac{1 + cos \: {30}^{ \circ} }{1 - cos \: {30}^{ \circ} } } = sec \: {60}^{ \circ} + tan \: {60}^{ \circ} }[/tex]
[tex]LHS = \displaystyle{ \sqrt{ \frac{1 + cos \: {30}^{ \circ} }{1 - cos \: {30}^{ \circ} } } }[/tex]
[tex] \displaystyle{ \sqrt{ \frac{1 + \frac{ \sqrt{3} }{2} }{1 - \frac{ \sqrt{3} }{2} } } }[/tex]
[tex] \displaystyle{ \sqrt{ \frac{ \frac{2 + \sqrt{3} }{2} }{ \frac{2 - \sqrt{3} }{2} } } }[/tex]
[tex] \displaystyle{ \sqrt{ \frac{2 + \sqrt{3} }{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } } }[/tex]
[tex] \displaystyle{ \sqrt{ \frac{(2 + \sqrt{3} {)}^{2} }{4 - 3} } }[/tex]
[tex] \displaystyle{2 + \sqrt{3} }[/tex]
[tex]RHS = sec \: {60}^{ \circ} + tan \: {60}^{ \circ} [/tex]
[tex] = 2 + \sqrt{3} [/tex]
[tex] \rm\therefore{LHS=RHS,proved. }[/tex]
No Calculator Let gbe a twice-differentiable function. The function g and its derivatives have the properties indicated in the table above. 0 0
Hi there!
Part D:
We can use the Taylor Polynomial expansion for a second-degree polynomial:
[tex]P_3(x) = g(c) + \frac{g'(c)}{1!}(x - c) + \frac{g''(c)}{2!}(x - c)^2[/tex]
Where c is the value that the polynomial is centered about.
We are given that:
[tex]g(c) = 1\\\\g'(c) = 0\\\\g''(x) = 2[/tex]
Therefore:
[tex]P_3(x) = 1 + \frac{0}{1}(x - 2) + \frac{2}{2!}(x - 2)^2\\\\\boxed{P_3(x) = 1 + (x - 2)^2}[/tex]
What is the slope-intercept equation for this line?
y = [?]x+ [ ]
Answer:
y = -2x - 2
Step-by-step explanation:
what is the value of x if x over 5=3
Answer:
x = 15
Step-by-step explanation:
the easiest way to do this is 5 times 3 and with that we get 15 :)
Have an amazing day!!
Please rate and mark brainliest!!
Answer:
Step-by-step explanation:
answer: x = 15
explanation in picture
PLEASE EXPLAIN SO I CAN UNDERSTAND
Which of the following numbers
could be the absolute value of
another number?
A -425
B 1,200
C -1,300
D-2,525
Answer:
Step-by-step explanation:
Essentially, recall what an absolute value function is.
When you plug number into an absolute value function, or make it an absolute value, you will ALWAYS get a positive version of that number.
When the question asks, what number could be the absolute value of another number, it's asking you what is a possible outcome of making a number an absolute value.
Since we know that making any number an absolute value, makes that number positive. We can get rid of all of the negative answers.
You are left with B.
Answer:
B. 1200
Step-by-step explanation:
Absolute value is the non-negative version of a number/variable. Whether the sign is negative or positive, the absolute value is always positive.
Example:
|-4|=4
|2|=2
PLEASE HELP I WILL GIVE BRAINLIEST
Answer:
65 degrees
Step-by-step explanation:
The angles will sum up to 360, just do 360 - all known angles
360 - 90 - 128 - 77 = 65
Answer:
Step-by-step explanation:
Sum of all angles is 360 degrees
Let the measure of angle M equal x.
x+90+77+128=360
x=65
Measure of angle M is 65 degrees
Use the drop-down menus to label the points on the number line.
Point A is at
.
Point B is at
.
Point C is at
.
Point D is at
.
Answer: B,D,C,A
Step-by-step explanation:
I hope that helps
Please mark me the brainiest !
Type the correct answer in each box, Spell all the words correctly, and use numerals instead of words for numbers. If necessary, use / for the
fraction bar(s).
y +10
А
18
6
B
X
+
- 10
-8
-6
-4
-2
2
4
6
8
10
-2
B
-4
C
-8
-10
units)
and a
across the
-axis
We can show that ABC is congruent to AABC by a translation of
Step-by-step explanation:
We can Show that ∆ABC is congruent to∆A'B'C' by a translation of 1 units(s) to the left and a reflection across the X -axis.
We can show that ΔABC is congruent to ΔA'B'C' by a translation of 2 units to the left and reflection across the x-axis.
What is a reflection?A reflection is a type of transformation that involves flipping a shape, known as the preimage, over a line, known as the line of reflection, to produce a new shape (called the image). You can picture what would happen if you flipped the form over the line in order to graph a reflection.
Given that the two triangles ABC and A'B'C'.
The points are A(8, 8), B(10, 4) and C(2, 6).
And A'(6, -8), B'(8, -4), and C'(0, -6).
The translation rule 2 units to the left and reflection across the x-axis.
We can show that ΔABC is congruent to ΔA'B'C' by a translation of 2 units to the left and reflection across the x-axis.
Therefore, the required translation rule is given above.
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Evaluate the expression (3-2i)(3-2i) and write the result in the form a+bi ,where a is the real part of your answer and bis the coefficient in front of the imaginary part
Answer:
a = 5, b = -12
Step-by-step explanation:
By basic factoring, you get 9 - 12i + [tex]4i^2[/tex]. Since [tex]i^2[/tex] is simply -1, the expression evaluates to 9 - 12i - 4, which is 5 - 12i.
-2x > 12
A. X>-6
B.x>14
C. X<14
D. X<-6
Answer:
D. x< -6
Step-by-step explanation:
Divide both sides by −2. Since −2 is negative, the inequality direction is changed.
x < 12/-2
Divide 12 by −2 to get −6.
x < -6
Write in 0.85 as a common fractionin its simplest form
[tex]\mathsf\pink{♧ANSWER♧}[/tex]
[tex] \mathsf \purple{0.85 = \frac{85}{100} = \frac{17}{20} }[/tex]
85/100 = 17/20
first we write the fraction from of 0.85 which is 85/100
then for simplifying it, we divide both 85 and 100 by 5
then we get to 17/20 which is our final answer
find the equation (in the terms of x) of the line through the points (-2,-5) and (5,0)
Answer:
-5x+7y+25=0
Step-by-step explanation:
vecto AB= (7;5)
vecto n = (-5;7)
line through the points (-2;5) and (5;0) :
-5*(x+2)+7*(y+5)=0
-5x+7y+25=0
Find the measure of x
Answer:
x=23
Step-by-step explanation:
An inscribed angle is half of the intercepted arc.