The confidence interval for the mean score of the 30 randomly selected students is: 99% CI {78.26, 89.73}
What is confidence interval?Confidence interval is the range of values for which which is expected to have the values at a certain percentage of the times.
How to construct a 99% confidence intervalGiven data form the question
99% confidence interval
30 randomly selected students
mean sample = 84
Standard deviation = 12.2
Definition of variables
confidence level, CI = 99%
mean sample, X = 84
standard deviation, SD = 12.2
Z score, z = 2.576
from z table z score of 99%confidence interval = 2.576sample size, n = 30
The formula for the confidence interval is given by
[tex]CI=X+Z\frac{SD}{\sqrt{n} }[/tex] OR [tex]CI=X-Z\frac{SD}{\sqrt{n} }[/tex]
[tex]=84+2.576\frac{12.2}{\sqrt{30} }[/tex]
=[tex]=84+2.576*2.2274[/tex]
= 84 + 5.7378 OR 84 - 5.7378
= 89.7378 OR 78.2622
= 89.73 to 78.26
The confidence interval for the mean score of all students is 78.26 to 89.78
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What is f(2) - f(0) answer choices:A) 1B) 2C) 3D) 4
The points of the graph of a function f(x) have the form (x,f(x)). This means that the values of f(0) and f(2) are the y-values of the points in the graph that have 0 and 2 as their x-values. If you look at the graph you'll notice that the points (0,1) and (2,4) are part of the graph which implies that:
[tex]\begin{gathered} (0,f(0))=(0,1)\rightarrow f(0)=1 \\ (2,f(2))=(2,4)\rightarrow f(2)=4 \end{gathered}[/tex]Then we get:
[tex]f(2)-f(0)=4-1=3[/tex]AnswerThen the answer is option C.
Joseph owns a 50 inch TV and it measures 50 inch on the diagonal. if the television is 40 inches across the bottom find the height of the TV
Let's draw the tv with the given values.
Note that we will form a right triangle with heigh of h, base of 40 and a hypotenuse of 50.
The Pythagorean Theorem is :
[tex]c^2=a^2+b^2[/tex]where c is the hypotenuse, a and b are the legs of the triangle.
Using the formula above. we will have :
[tex]\begin{gathered} 50^2=40^2+h^2 \\ 2500=1600+h^2 \\ h^2=2500-1600 \\ h^2=900 \\ \sqrt[]{h^2}=\sqrt[]{900} \\ h=30 \end{gathered}[/tex]The answer is 30 inches
4. Find the slope of the two points: (-3,-2) & (5, -8)
Enter Numerical value ONLY. NO Decimals
Try Again!
5. Find the slope of the two points: (6, 10) and (-2, 10) *
Enter Numerical value ONLY. NO Decimals
Your answer
This is a required question
Answer:
The slope of (-3, -2) and (5, -8) is -3/4
The slope of (6, 10) and (-2, 10 ) is 0
Step-by-step explanation:
[tex]\frac{-8 - (-2)}{5 - (-3)} = \frac{-6}{8} = -\frac{3}{4}[/tex]
and
[tex]\frac{10 - 10}{-2 - 6} = \frac{0}{-8} = 0[/tex]
How many degrees was ABCDE rotated? (submit your answer as a number)
If a figure has a vertex, (x, y) and it is rotated 180 degrees counterclockwise, the corresponding vertex of the new image would have a coordinate of (- x, - y)
Looking at the given figure, we would compare the corresponding coordinates of a given vertex. Looking at vertex A,
For the original figure, the coordinate is (1, 3)
For the ratated figure, the coordinate of A' is (- 1, - 3)
This corresponds to what was we stated earlier
Thus, it was rotated 180 degrees in the counterclockwise direction
Which of the following measurements form a right triangle? Select all that apply.
We are asked to find which of the measurements form a right triangle.
A right triangle is a triangle that has an angle of 90°, and also we can use the Pythagorean theorem in them.
The Pythagorean theorem tells us that the sum of the two legs of the triangle squared is equal to the hypotenuse squared:
[tex]a^2+b^2=c^2[/tex]Where a and b are the legs of the triangle and c is the Hypotenuse. Also, in the right triangle, the hypotenuse is the longest side of the triangle.
We will use the Pythagorean theorem formula on all of the options using the first two given measures as a and b, and check that we the third measure as the value of c.
Option A. 7in, 24in, and 25 in.
We define:
[tex]\begin{gathered} a=7 \\ b=24 \end{gathered}[/tex]And apply the Pythagorean theorem:
[tex]7^2+24^2=c^2[/tex]And we solve for c. If the result for x is 25, the triangle will be a right triangle, if not, this will not be an answer.
-Solving for c:
[tex]\begin{gathered} 49+576=c^2 \\ 625=c^2 \end{gathered}[/tex]Taking the square root of both sides we find c:
[tex]\begin{gathered} \sqrt[]{625}=c \\ 25=c \end{gathered}[/tex]Since we get the third measure as the value of c option A is a right triangle.
Option B. 18ft, 23ft, and 29 ft.
we do the same as did with option A. First, define a and b:
[tex]\begin{gathered} a=18 \\ b=23 \end{gathered}[/tex]Apply the Pythagorean theorem:
[tex]18^2+23^2=c^2[/tex]And solve for c:
[tex]\begin{gathered} 324+529=c^2 \\ 853=c^2 \\ \sqrt[]{853}=c \\ 29.2=c \end{gathered}[/tex]We get 29.2 instead of just 29, thus option B is NOT a right triangle.
Option C. 10in, 24in, and 26 in.
Define a and b:
[tex]\begin{gathered} a=10 \\ b=24 \end{gathered}[/tex]Apply the Pythagorean theorem:
[tex]10^2+24^2=c^2[/tex]Solve for c:
[tex]\begin{gathered} 100+576=c^2 \\ 676=c^2 \\ \sqrt[]{676}=c \\ 26=c \end{gathered}[/tex]We get 26 which is the third measure given, thus, option C is a right triangle.
Option D. 10yd, 15yd, and 20yd.
Define a and b:
[tex]\begin{gathered} a=10 \\ b=15 \end{gathered}[/tex]Apply the Pythagorean theorem:
[tex]\begin{gathered} 10^2+15^2=c^2 \\ 100+225=c^2 \\ 325=c^2 \\ \sqrt[]{325}=c \\ 18.03=c \end{gathered}[/tex]We don't get 20yd as the value of c, thus, option D is NOT a right triangle.
Option E. 15mm, 18mm, and 24 mm
Define a and b:
[tex]\begin{gathered} a=15 \\ b=18 \end{gathered}[/tex]Apply the Pythagorean theorem
[tex]\begin{gathered} 15^2+18^2=c^2 \\ 225+324=c^2 \\ 549=c^2 \\ \sqrt[]{549}=c \\ 23.43=c \end{gathered}[/tex]We don't get 24 as the value of c, thus, option E is Not a right triangle.
Answer:
Option A and Option C are right triangles.
if angle 2 = 106 degrees, what is the measurement of angle 6 ? ( better explanation in picture )
angle 2 and angle 6 are corresponding angles.
Since the lines crossed by the trnasversal are parallel, corresponding angles are congruent. (equal)
angle 6 = 106°
Please provide deep explanation, so i can understand and learn. Thank you
Assume the height of the box is x.
5 reams of paper have 5 x 500 = 2500 sheets of paper.
This means that each sheet of paper has a thickness of x/2500.
Two sheets of paper have a thickness of 2 times x/2500.
Simplifying the fraction:
[tex]2\cdot\frac{x}{2500}=\frac{x}{1250}[/tex]Two sheets of paper have a thickness of 1/1250th of the height of the box.
Assume the height is x = 20 cm, then two sheets are 20/1250 = 0.016 cm thick.
What is the volume of this sphere? Use a ~ 3.14 and round your answer to the nearest! hundredth. 5 m cubic meters
We will have the following:
[tex]V=\frac{4}{3}\pi r^3[/tex]Now, we replace the values and solve:
[tex]V=\frac{4}{3}(3.14)(5)^3\Rightarrow V\approx523.33[/tex]So, the volume of the sphere is approximately 523.33 cubic meters.
***Example with an 8 m radius***
If the radius of the sphere were of 8 meters, we would have:
[tex]V=\frac{4}{3}(3.14)(8)^3\Rightarrow V\approx2143.57[/tex]So, the volume of such a sphere would be approximately 2143.57 cubic meters.
Mario constructs a scale model of a building with a rectangular base. His model is 4.2 inches in length and 2 inches in width. The scale of the model is 1 inch = 15 feet What is the actual area, in square feet, of the base of the building?
First let's use two rules of three to determine the actual dimensions of the building.
For the length, we have:
[tex]\begin{gathered} 1\text{ inch}\to15\text{ feet} \\ 4.2\text{ inches}\to x\text{ feet} \\ \\ \frac{1}{4.2}=\frac{15}{x} \\ x=15\cdot4.2=63 \end{gathered}[/tex]For the width:
[tex]\begin{gathered} 1\text{ inch}\to15\text{ feet} \\ 2\text{ inches}\to x\text{ feet} \\ \\ \frac{1}{2}=\frac{15}{x} \\ x=15\cdot2=30 \end{gathered}[/tex]Now, calculating the area of the building base, we have:
[tex]\text{Area}=63\cdot30=1890\text{ ft2}[/tex]So the area of the building base is 1890 ft².
In solving for the inverse function for y = sqrt(3x + 2) - 1 , which of the following represents the first step?
we know that
The first step to find out the inverse of the function is to exchange the variables (x for y and y for x)
therefore
the answer is the second optionA machine that makes
toy spinners operates for 8 hours each
day. The machine makes 7,829 toy
spinners in
day. About how
many toy
spinners does the machine make each
hour?
Using the unitary method, the number of toy spinners the machines will make in an hour is 2069.
The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
A machine makes 7829 toy spinners in a day.
The machines operate for 8 hours each day to make the toy spinners.
So,
8 hours = 7829
Then by using the unitary method the number of toy spinners the machines will make each hour will be:
8 hours = 7829
24 hours = x toy spinner
Toys in one hour = ( 7829/ 24 ) × 8
Toys in one hour = 326.20833 × 8
Toys in one hour = 2609.6667
Toys in one hour = 2069
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Based on the graph of f(x) shown here what is f^-1(8).
Answer
2
Explanation:
f⁻¹(8) is equal to the value of x that makes f(x) = 8. So, taking into account the graph, we get:
Therefore, f⁻¹(8) = 2. So the answer is 2
h(r) = (r +1)(r+8)1) What are the zeros of the function?Write the smaller r first, and the larger second.smaller r =larger s 2) What is the vertex of the parabola
For the zeros of the function, we have to solve h(r)=0, therefore:
[tex]\begin{gathered} h(r)=(r+1)(r+8) \\ h(r)=0 \\ \Rightarrow(r+1)(r+8)=0 \\ \Rightarrow r=-1\text{ or } \\ r=-8 \end{gathered}[/tex]then, the smaller r is -8 and the larger is -1.
Now, to find the vertex of the parabola, we can find the x-coordinate of the vertex from the general rule:
[tex]\begin{gathered} f(x)=ax^2+bx+c \\ \text{ x-coordinate: -b/2a} \end{gathered}[/tex]In this case, we have the following:
[tex]\begin{gathered} h(r)=(r+1)(r+8)=r^2+8r+r+8=r^2+9r+8 \\ \Rightarrow a=1,b=9 \\ \Rightarrow-\frac{b}{2a}=-\frac{9}{2(1)}=-\frac{9}{2} \end{gathered}[/tex]now that we have the x-coordinate of the vertex, we just evaluate the function on that point to find the y-coordinate of the vertex:
[tex]h(-\frac{9}{2})=(-\frac{9}{2}+1)(-\frac{9}{2}+8)=(-\frac{7}{2})(\frac{7}{2})=-\frac{49}{4}[/tex]therefore, the vertex of the parabola is the point (-9/2,-49/4)
For each equation, choose the statement that describes its solution. If applicable, give the solution.
w=2
All real numbers are solutions
1) In this question, let's solve each equation, and then we can check whether there are solutions, which one would be.
2) Let's begin with the first one, top to bottom
[tex]\begin{gathered} 2(w-1)+4w=3(w-1)+7 \\ 2w-2+4w=3w-3+7 \\ 6w-2=3w+4 \\ 6w-3w=4+2 \\ 3w=6 \\ \frac{3w}{3}=\frac{6}{3} \\ w=2 \end{gathered}[/tex]Note that we distributed the factors outside the parenthesis over the terms inside.
So for the first one, we can check w=2
3) Moving on to the 2nd equation, we can state:
[tex]\begin{gathered} 6(y+1)-10=4(y-1)+2y \\ 6y+6-10=4y-4+2y \\ 6y-4y-2y=4-4 \\ 6y-6y=0 \\ 0y=0 \end{gathered}[/tex]So, there are infinite solutions for this equation, or All real numbers are solutions
0896. Calculate the atomic mass of copper if copper-63 is 69.17% abundant and copper-65 is30.83% abundant.
The atomic mass of the copper is
[tex]63\times69.17\text{ \% + 65}\times30.83\text{ \%}[/tex]solve the above expression
[tex]63\times\frac{69.17}{100}+65\times\frac{30.83}{100}[/tex][tex]63\times\frac{6917}{10000}+65\times\frac{3083}{10000}[/tex][tex]46.35+20.03=66.38[/tex]So the atomic weight of the mixture is 66.36 .
Hello! I need some help with this homework question, please? The question is posted in the image below. Q7
SOLUTION
Since -3 is a zero of the function then x=-3
This implies
x+3 is a factor of the polynomial
Following the same procedure, since 2 and 5 are zeros then
x-2 and x-5 are factors
Hence the polynomial can be written as
[tex]y=a(x+3)(x-2)(x-5)[/tex]Since the graph passes through the point (7,300)
Substitute x=7 and y=300 into the equation
This gives
[tex]300=a(7+3)(7-2)(7-5)[/tex]Solve the equation for a
[tex]\begin{gathered} 300=a(10)(5)(2) \\ 300=100a \\ a=\frac{300}{100} \\ a=3 \end{gathered}[/tex]Substitute a into the equation of the polynomial
[tex]y=3(x+3)(x-2)(x-5)[/tex]Therefore the answer is
[tex]y=3(x+3)(x-2)(x-5)[/tex]
L1 : y=−4x+3L2 : y=4x−1
Answer:
Assuming you're trying to find where the lines intersect (their solution), the point where they intersect is (1/2 , 1).
Step-by-step explanation:
When you are trying to find the point where two lines intersect, you have to find the x and y values of that point. To do that, just set the lines equal to each other.
First, since y must equal y:
y = y
-4x + 3 = 4x - 1
Now solve for x:
-8x + 3 = -4
-8x = -4
8x = 4
x = 1/2
We just found the x value of the shared point. Now we need to find the y value of that point. Again, since the two lines share this point, plugging in the x value will result in the same y value for both lines.
So just plug in x to any of the equations: (I think y=4x-1 is easier)
y(1/2) = 4(1/2) - 1 or y = 4(1/2) - 1 (it doesn't matter how you write it)
y(1/2) = 2 - 1 or y = 2 - 1
y(1/2) = 1
So the point is:
(1/2 , 1)
To check you can plug in the y value you find, 1 in this case, and solve for x. If you get the same x value as before, everything is correct.
So:
(1) = -4x + 3
-2 = -4x
1/2 = x or x = 1/2
Great! Everything is correct.
This may seem like a very long process, but it is very easy. Just find the x and y values that the lines share by setting the lines equal to each other.
if 1ml = 0.00011 then 9ml= _____
if 1ml = 0.00011 then 9ml=
Apply proportion
0.00011/1=x/9
solve for x
x=9*0.00011
x=0.00099
answer is
0.00099Find the union of E and L.Find the intersection of E and L.Write your answers using set notation (in roster form).
For the intersection operation we have to look what elements both sets have in common, in this case both E and L has the number 8. Then the second answer is:
[tex]E\cap L=\lbrace8\rbrace[/tex]Now, the union operation adds the all elements into a single set without repetition, in this case the first answer is:
[tex]E\cup L=\lbrace-2,1,2,3,6,7,8\rbrace[/tex]−1= 8x+2i need help with this problem,
Given
-1 = 8x + 2
Answer
-1 = 8x + 2
-1 -2 =8x
-3 = 8x
x = -3/8
Please help me, i struggle with these types of problems
Solution
[tex]\begin{gathered} 11x-3=9x+15 \\ \\ 2x=18 \\ \\ x=9 \end{gathered}[/tex]Therefore, we find m < 7
[tex]\begin{gathered} 11x-3 \\ \\ 11(9)-3 \\ \\ 99-3 \\ \\ 96\degree \end{gathered}[/tex]D(-9,4) E(-3,4) F(-3,10) G(-9,10) rotation 180 clockwise
Answer:
D = (9,-4) E = (3,-4) F= (3, -10) G=(9,-10)
Step-by-step explanation:
Simply switch the signs (- or +)
Ex: rotate (9,1) 180 degrees
Your answer would be (-9,-1)
A leaking pond loses 16 gallons of water in 47 hours. How many gallons of water will it lose in 33 hours?
A leaking pond loses 16 gallons of water in 47 hours.
How many gallons of water will it lose in 33 hours?
To solve this question we can use a rule of three:
16 gallons is to 47 hours as x gallons is to 33 hours:
[tex]\frac{16}{47}=\frac{x}{33}\Longrightarrow x=\frac{33\cdot16}{47}=\frac{528}{47}=\text{ 11.23}[/tex]Answer:
11.23 gallons
(0,1), (2,4), (4,7) (9.1)}Domain:Range:
The domain of an ordered pair are its first elements and its range are all the second elements of the ordered pair.
So, the domain ={0,2,4,9}
Range={1,4,7,1}
A team won 5 and lost 2 of their first 7 games. The team continued to win at this rate and won w games in the 28-game season. Which of the following proportions could be used to determine w? 2. 7 28 B 2 5 28 5 7 28 D U NICT 28
Answer:
C. 5/7 = w/28
Explanation:
We're told from the question, the team won 5 and lost 2 of their first 7 games and later continued to win at this rate and won w games in the 28-game season.
Since w represents the number of games won in a 28-game season, in order to create a proportion to determine the value of w, we have to consider the number of games won (which was 5) in 1st 7 games.
So the proportion can then be written as;
[tex]\frac{5}{7}=\frac{w}{28}[/tex]A cookie recipe calls for 3/4 of a cup of flour and makes 2dozen cookies. How many cookies can Julia make if she has 12cups of flour and wants to use it all
Given that 3/4 of a cup of flour is used to cook 2 dozen cookies,
[tex]\frac{3}{4}\text{ cup of flour}\equiv2\text{ dozen cookies}[/tex]Consider the conversion,
[tex]1\text{ dozen}=12\text{ units}[/tex]So it follows that,
[tex]\frac{3}{4}\text{ cup of flour}\equiv2\cdot12=24\text{ cookies}[/tex]Multiply both sides by 4/3 as follows,
[tex]\begin{gathered} \frac{3}{4}\cdot\frac{4}{3}\text{ cups of flour}\equiv24\cdot\frac{4}{3}\text{ cookies} \\ 1\text{ cup of flour}\equiv32\text{ cookies} \end{gathered}[/tex]So, 32 cookies can be cooked using 1 cup pf flour.
Given that Julia has 12 cups of flour, so the number of cookies that she can cook, is calculated as,
[tex]12\text{ cups of flour}\equiv32\cdot12=384\text{ cookies.}[/tex]Thus, Julia can make 384 cookies if she uses 12 cups of flour.
Which region labeled in the graph below would represent the solution (the final shaded area) to the system of linear inequalities:≤12−3<−23+1
Since both inequalities include the less than symbol, <, the shaded region must be below the two lines.
The intersection (common) of the shaded regions, which are both below the two lines, is region D.
which fraction remains in the quotient when 4,028 is divided by 32
We get that
[tex]\frac{4028}{32}=\frac{1007}{8}=\frac{1000}{8}+\frac{7}{8}=125+\frac{7}{8}[/tex]so the fractions that remains is 7/8
Could I please get help with finding the correct statements and reasonings. I think I messed up line number four because it keeps saying the line is incorrect and that I can not validate it l but
Answer:
Step-by-step explanation:
[tex]undefined[/tex]translating words into algebraic symbols its not -70 or -7
translating words into algebraic symbols
a number x = x
decreased by seventy = -7
y= x-70
___________________
Answer
x-70
