[489.68, 510.32] is the confidence interval for the average amount spent on textbooks in a year if the desired level of confidence is 99%.
n=400
sample mean (x)=500
sample standard deviation (s)=80
99% confidence interval for mean
α=0.01
critical value [tex]Z_{\frac{a}{z} }[/tex] =2.58
Standard error of sample mean Sx = [tex]\frac{s}{\sqrt[]{n} }[/tex] = [tex]\frac{80}{\sqrt[]{400} }[/tex] = [tex]\frac{80}{20}[/tex] = [tex]4[/tex]
∴ Sx = 4
Confidence interval (μ)
μ= [tex]x[/tex] ± [tex]Z_{\frac{a}{z} }[/tex] [tex]\frac{s}{\sqrt[]{n} }\\[/tex]
μ= [tex]x[/tex] ± [tex]Z_{\frac{a}{z} }[/tex] (Sx)
=500 ± 2.58(4)
=500 ± 10.32
lower limit = 500 - 10.32 = 489.68
upper limit= 500 + 10.32= 510.32
Hence, [489.68, 510.32] is the confidence interval for the average amount spent on textbooks in a year if the desired level of confidence is 99%.
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Which expression is equivalent to
-[tex](-\sqrt{8-2)[/tex] +[tex]\sqrt{36[/tex]
Select one:
a. 2i
b. −10i
c. −4+6i
d. −4−6i
calculate f (x) = 3 - | 2 - 3x| when x = - 5
Answer: fx=−14
Step-by-step explanation:
translate triangle P by the vector (2 -7)
The transformation rule for triangle P by translating using the vector [tex](^{\ 2}_{-7})[/tex] is (x, y) ⇒ (x + 2, y - 7)
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, reflection, rotation and dilation.
The transformation rule for triangle P by translating using the vector [tex](^{\ 2}_{-7})[/tex] is (x, y) ⇒ (x + 2, y - 7)
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If f(x)=x²-1, and
g(x)=x+2, then
Answer:
f(g(x) = 1x² + 4x + 3
Explanation:
Question: f(g(x))
Given following:
f(x) = x² - 1g(x) = x + 2While solving such function questions, solve from right to left.
⇒ f(x + 2)
⇒ (x + 2)² - 1
⇒ x² + 4x + 4 - 1
⇒ x² + 4x + 3
10-2 area about the x axis. 6. Determine the moment of inertia of the composite 150 mm 1150 mm 1 100 mm 100 mm 75 mm 300 mm.
Answer:21
Step-by-step explanation:
add 3x to 4
a. 7x
b. 7
c. 34x
d. 4+3x
Area= cm2
Help me please thank you so much :)
Answer:
153
Step-by-step explanation:
The formula for a triangle is 1/2 x base x height
17 x 18 = 306
306 x 1/2 = 153
So therefore your answer would be 153.
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0.285714 as a fraction
Answer:
See below
Step-by-step explanation:
285714 / 1000 000 which simplifies to 142,857 / 500,000
Calculate the slope of the line passing through the given points. If the slope is undefined, so state. Then indicate whether the line rises, falls, is horizontal, or is vertical.
(-5, 2), (-3, 6)
Answer:
Step-by-step explanation:
PLS HELP ASAP!!! im struggling
The correct options, in order, are:
[tex]f(n) = 3*(2)^{n-1}[/tex]
[tex]f(n) = 2*(6)^{n - 1}[/tex]
[tex]f(n) = 2*(4)^{n - 1}[/tex]
How to match the equations and the tables?The first table is:
n f(n)
1 3
2 6
3 12
Notice that when n = 1, all the exponents are 0, then the initial value is 3.
When n = 2, all the exponents are 1. Then we need to find the exponential equation with a base equal to 2.
So the exponential equation is:
[tex]f(n) = 3*(2)^{n-1}[/tex]
The second table is:
n f(n)
1 2
2 12
3 72
By looking at the first pair, we conclude that the initial value is 2, and by looking at the second pair, we conclude that:
2*b = 12
b = 12/2 = 6
The base is 6.
So the exponential equation now is:
[tex]f(n) = 2*(6)^{n - 1}[/tex]
The last table is:
n f(n)
1 2
2 8
3 32
Here we again have an initial value of 2, and the base is:
2*b = 8
b = 8/2 = 4
Then the correct option now is:
[tex]f(n) = 2*(4)^{n - 1}[/tex]
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is 30x^2 - 26x -12 a polynomial
Answer:
Yes.
Step-by-step explanation:
It is a polynomial with degree 2 ( as it has x^2 as its highest power)
The diagram shows the length and width of a cell phone, and the length of a larger version of the same brand cell phone.
The lengths and widths of the two cell phones are proportional. What is the width, in inches?
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
missing length = 2.99 in[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
Both the figures are similar to each other, so ratio of their corresponding sides will be equal to one another.
[tex] \qquad❖ \: \sf \: \dfrac{2.6}{5.4} = \dfrac{x}{6.21} [/tex]
( taking missing width be x )
[tex] \qquad❖ \: \sf \: x = \dfrac{1.3}{2.7} \sdot6.21[/tex]
[tex] \qquad❖ \: \sf \: x = {(1.3)}{} \sdot(2.3)[/tex]
[tex] \qquad❖ \: \sf \:x = 2.99 \: \: in[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
Missing side measures : 2.99 inches
What kinds of ""failures"" occur when you experiment in order to learn under conditions of high uncertainty?.
Intelligent failure occur when you experiment in order to learn under conditions of high uncertainty
It's always possible to move forward from failure stronger and wiser. To do this, we must
a) descry and accept our failures snappily,
b)Dissect what happed and how it happed effectively to maximize what we can learn,
c)Apply our literacy to change our mindsets, behaviours, and the way we do our work, and
d)Continue to take smart pitfalls and introduce, icing we make better miscalculations on our coming bold attempt.
Unfortunately, our instinct tends to be to exit the circle at every step.
That’s why the skill of Intelligent Failure takes practice.
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I need help with question 3, I chose the answers that made the most sense but it keeps telling me I'm wrong?
Answer: DL, PS, SL
Step-by-step explanation:
All sides of a square are congruent.
A high school senior applies for admission to college A and to college B. He estimates that the probability of his being admitted to A is .7, that his application will be rejected at B with probability .5, and that the probability of at least one of his applications being rejected is .6. What is the probability that he will be rejected to at least one of the colleges
The probability that he will be rejected to at least one of the colleges is 0.51.
Given probability that he will admit in A is 0.7, probability that he will not be admit in B is 0.5, probability that atleast one of his applications got rejected is 0.6.
We have to find the probability that he will be rejected to at least one of the colleges.
Probability that he will admit in A =0.7
Probability that he will not admit in A=1-0.7=0.3
Probability that he will not admit in B =0.5
Probability that he will admit in B=1-0.5=0.5
Probability that he will be rejected to at least one of the colleges=probability that he will admit in A* probability that he will not admit in B+ probability that he will admit in B* probability that he will not admit in A+ probability that he will not admit in A* probability that he will not admit in B
=0.7*0.5+0.5*0.3+0.5*0.3
=0.35+0.15+0.15
=0.51
Hence the probability that he will be rejected to at least one of the colleges is 0.51.
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hi, I need help I don't understand
Answer: [tex]60cm^2[/tex]
Step-by-step explanation:
Looking at the figure, you can see that the length is 5cm + 3cm = 8cm and the width is 2cm + 5cm + 2cm = 9cm.
The formula for area is length x width, therefore you do 8x9 which is 72.
Next, we solve for the two "dips" in the rectangle. We can do that by subtracting the area of the "mini-rectangles" from the whole figure:
72-2(2x3) = 60
Thus, 60cm^2 is your answer.
Question 3(Multiple Choice Worth 3 points)
(07.06)||||||
-10-9-8-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7 8 9 10
Which of the following inequalities best represents the graph above?
Ox<9
Ox>9
<|OT||||
Ox≤9
Ox≥9
Answer:
Please see attachment.
Step-by-step explanation:
Since there are no answer choices, I will just show you the graphs for each one.
Remember the dashed lines means it is either greater than, or less than.
The solid lines are either greater than or equal to, or less than or equal to.
Hope this helps!
If not, I am sorry.
The solutions of the equation given as |2/3x + 2| − 8 = 0 are x = 9 and x = -15
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
here, we have,
to determine the solutions of the equation:
The equation is given as:
|2/3x + 2| − 8 = 0
Start by adding 8 to both sides of the equation.
So, we have
|2/3x + 2| = 8
Next, we remove the absolute value expression
So, we have;
2/3x + 2 = 8 and 2/3x + 2 = -8
Subtract 2 from both sides of the equation
2/3x = 6 and 2/3x = -10
Multiply the equation by 3/2
x = 9 and x = -15
Hence, the solutions of the equation given as |2/3x + 2| − 8 = 0 are x = 9 and x = -15
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Complete question:
Determine the solutions of the equation:
|2/3x+2−8=0
Ox= -9 and x = 9
Ox= -15 and x = 4
Ox= -15 and x = 9
Ox= -15 and x = 15
HELP
Marbles: You have a bag with 3 red marbles, 4 blue marbles, and 5 green marbles. What is the probability of pulling out a red marble 3 times in a row, assuming you put each marble back into the bag before drawing another?
The probability of pulling out a red marble 3 times in a row will be 1/64.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
Marbles: You have a bag with 3 red marbles, 4 blue marbles, and 5 green marbles.
Then the probability of pulling out a red marble 3 times in a row will be
The total number of events will be
Total events = 3 + 4 + 5 = 12
The favorable event will be
Favorable event = 3
Then the probability will be
P = (3/12)(3/12)(3/12)
P = (1/4)(1/4)(1/4)
P = 1/64
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help me please i am struggling
Answer:
46 cm²
Step-by-step explanation:
Find the area of the rectangle and the triangle, then subtract. Take a look at the steps to know how.
The area of the rectangle:
10×7=70
Area of triangle:
1/2×6×8=24
Subtract the area of the triangle from the area of the rectangle.
70-24=46.
The area of the new shape is 46 cm².
It is cm² because it is a 2D object.
Hope this helps!
I need help fast please
Answer:
4
Step-by-step explanation:
The formula is P = 2(l +w)
w = P/2 - l = 20/2 - 6 = 4m
Write a formula for g(x) in terms of x.
The formula of g(x) is g(x) = -0.8x - 1.6
How to determine the formula of g(x)?The equation is given as:
-4x - 6 = 5y + 2
Subtract 2 from both sides
5y = -4x - 8
Divide through by 5
y = -0.8x - 1.6
Express as a function
g(x) = -0.8x - 1.6
Hence, the formula of g(x) is g(x) = -0.8x - 1.6
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Scores on IQ tests are normally distributed, with a mean of 100 and a standard deviation of 15. What is the score such that 10 percent of people taking the test achieve a higher score
Answer:
103.75 score
Step-by-step explanation:
10 % scored higher than the mean?
50% is the mean % so we need to look for the z score corresponding to 60 % from z-score table this is z-score of .25
.25 standard deviations (which is 15) above 100 =
.25 * 15 + 100 = 103.75 score
Which is bigger, a third of 45 or one-sixth c
138?
Applying the knowledge of fractions, the bigger one is: one-sixth of 138.
What are Fractions?Fractions can be defined as a part of a digit or number, and are not whole numbers. For example, a third is 1/3, one-sixth is 1/6, which are both fractions.
Therefore, let's evaluate each statement:
1/3 of 45 = 1/3 × 45 = 15
1/6 of 138 = 1/6 × 138 = 23
Therefore, the bigger of the two is: one-sixth of 138.
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Compute: -1 2/3 * 2 1/7
Answer:
Fraction form: -3 4/7
Decimal form: -3.57142
Step-by-step explanation:
convert mixed number to improper fractions
apply the fraction rule a/b * c/d = a * c / b * d
Factor the number
cancel the common factor
multiply the numbers
Conver improper fraction to mixed numbers
To get your final answer:
= -3 4/7
Hope this helps! :)
What is the answer to this
Answer: H
Step-by-step explanation:
TY:XY: = 2:5, not 3:5.
Answer:
H H H H H H H
Step-by-step explanation:
TY:XY: =2:5, NOT 3:5.
anybody can help me?
Graph C depicts the relation between No. of sweaters ( Nombre de chandails vendus ) and the fund raised in the campaign (Campagne de financements )
What is a Graph ?Graph is the statistical representation of data , It helps to observe large data systematically.
It is given that
Sale of one sweater gives $3
The relation between the amount raised for funding , M and the number of shirts sold , n is given by
M = 3n
It has to be found that which graph exactly depicts the relation and the condition as given
Graph C depicts the relation given as , The graph is between No. of sweaters ( Nombre de chandails vendus ) and the fund raised in the campaign (Campagne de financements ) , and for every 100 sweater , $300 is earned .
Therefore Graph C is the answer.
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What is the x-coordinate of the vertex of the parabola whose equation is y = 3x² + 9x?
o-3
o-1 1/12
o-2/3
Answer: x=-1,5.
Step-by-step explanation:
[tex]y=3x^2+9x\\\boxed {x=-\frac{b}{2a} }\\a=3,\ \ \ \ \ b=9.\\x=-\frac{9}{2*3}=-\frac{3}{2}=-1,5.[/tex]
Which of the following are possible equations of a parabola that has no real solutions and opens downward?
Oy=(x-4)2+2
Oy=-(x+4)²-2
Oy=(x-4) 2-2
Oy=-x²-2
Oy=-(x+4)² +2
Answer:
Oy= -(x+4)^2 -2
potentially Oy= -x^2 -2
Find x,y They have no other givens. Im not sure how to solve this.
Answer:
Step-by-step explanation:
If √5+√2=a+b√10 find a and b
Answer:
Firstly, we'll apply the below identity.
[tex]{\boxed{\sf{(a+b)^{2} = a^{2} + b^{2} +2ab}}}[/tex]
Applying the above identity.
⇒ (√5 + √2)²
⇒ (√5)² + (√2)² + 2×(√5)×(√2)
⇒ 5 + 2 + 2√10
⇒ 7 + 2√10
Comparing the LHS and RHS
⇒ 7 + 2√10 = a + b√10
∴ a = 7 and b = 2.