We have to find the minimum sample size.
The margin of error that it is aimed is ±0.2 hours from the real mean.
The population standard deviation is 0.8 hours.
The desired level of confidence is 96%. This corresponds to a z-score of 2.054.
We can relate sample size with the given information as:
[tex]\begin{gathered} e=\frac{\sigma}{\sqrt{n}}\cdot z \\ \sqrt{n}=\frac{\sigma}{e}\cdot z \\ n=(\frac{\sigma\cdot z}{e})^2 \end{gathered}[/tex]If we replace e = 0.2, σ = 0.8 and z = 2.054 we can calculate the sample size n as:
[tex]\begin{gathered} n=(\frac{0.8*2.054}{0.2})^2 \\ \\ n=(8.216)^2 \\ n\approx67.5 \\ n\approx68 \end{gathered}[/tex]Answer: the sample size has to be at least 68 people.
W
the scatterplot shows the time spent studying compared to test scores for Mr Stones 8th grade class predicted score that a student would earn if she studied for 7 hours on your answer to the nearest whole number into your answer in the Box
the straight line is
i have to the table i just need to know the expected value of X, please help, statistics
Total number of camera = 7
Defective camera = 5
Sample selected = 2
when x = 0
P(x=0) = 2/7 × 1/6 = 2/42
P(x=1) = [2/7 × 5/6] + [5/7 × 2/6] = 20/42
P(x=2) = 5/7 × 4/6 = 20/42
So,
E(x) = [0×2/42] + [1×20/42] + [2×20/42]
E(x) = 1.43
A rectangle is twice as long as it is wide. If the length and width are both increased by 5 cm, the resulting rectangle has an area of 50cm^2. Find the dimensions of the original rectangle to the nearest hundredth.
Considering the sides of the rectangle are:
w = width
l = lenght
Since it is twice as long as it is wide:
l = 2w
The area of a rectangle (A) is the product of the width and length.
Then,
A = lw
Knowing that: If the length and width are both increased by 5 cm, the resulting rectangle has an area of 50cm^2, then:
[tex]50=(l+5)*(w+5)[/tex]Substituting l by 2w:
[tex]50=(2w+5)*(w+5)[/tex]Solving the multiplications:
[tex]\begin{gathered} 50=2w*w+2w*5+5*w+5*5 \\ 50=2w^2+10w+5w+25 \\ 50=2w^2+15w+25 \end{gathered}[/tex]Subtracting 50 from both sides:
[tex]\begin{gathered} 50-50=2w^2+15w+25-50 \\ 2w^2+15w-25=0 \end{gathered}[/tex]To find w, use the quadratic formula.
For a quadratic equation ax² + bx + c = 0, the quadratic formula is:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]In this question:
x = w
a = 2
b = 15
c = -25
Substituting the values:
[tex]\begin{gathered} w=\frac{-15\pm\sqrt{(-15)^2-4*2*(-25)}}{2*2} \\ w=\frac{-15\pm\sqrt{225+200}}{4} \\ w=\frac{-15\pm20.62}{4} \\ w_1=\frac{-15-20.62}{4}=\frac{-35.62}{4}=-8.90 \\ w_2=\frac{-15+20.62}{4}=\frac{5.62}{4}=1.40 \end{gathered}[/tex]Since the measure must be posite, width = 1.40 cm.
Also, l = 2w.
Then, l = 2*1.40
l = 2.80 cm.
Answer:
width = 1.40 cm
length = 2.80 cm.
2 poin #1 You start by adding $5 to your bank account, each week after that you will double what you are depositing. Week 1 you would deposit $10, week 2 $20 and so on. How much money would you be depositing on week 10?
the initial money deposit is 5 $ in the starting
Differentiate. y = (x2 - 2x + 6) ex O (2x - 2) et O (x2 + 4x + 4) et 0 (x² + 4) ex 03 + 4x + 6 ex 3 400
Differentiate y
so,
[tex]\begin{gathered} y^{\prime}=(2x-2)\cdot e^x+(x^2-2x+6)\cdot e^x \\ y^{\prime}=(2x-2+x^2-2x+6)\cdot e^x \\ y^{\prime}=(x^2+4)\cdot e^x \end{gathered}[/tex]so, the answer is option 3
=======================================================
Note: we have used the rule of y = f(x) * g(x)
y' = f'(x) * g(x) + f(x) * g'(x)
Please help me I dont know how to simplify it
The experession is:
[tex]-\frac{6}{5}-\frac{2}{3}v+\frac{4}{15}+\frac{1}{3}v[/tex]In this case, we can multiply the first fraction by 3/3, and reorganice like:
[tex]\begin{gathered} -\frac{6}{5}\frac{3}{3}-\frac{2}{3}v+\frac{4}{15}+\frac{1}{3}v \\ -\frac{18}{15}+\frac{4}{15}-\frac{2}{3}v+\frac{1}{3}v \end{gathered}[/tex]and we can sum the fraction with common denominator:
[tex]-\frac{14}{15}-\frac{1}{3}v[/tex]and thats all we can simplify it
a gardener planted flowers of different colors. 3/10 of the flowers are Yellow.3/4 of the remaining flowers are green.The rest of the flowers are purple.
Mr.Jackson made a one time deposit of $57,000 into his retirement account when he was 25 years old. The account has an annual interest rate of 3.35%. If Mr.Jackson checks this retirement account when he is 72 years old. A. How much will he have earned in interest?B. What will be the total amount in his retirement account.
First we have to calculate how many yeas has pass from the date of the deposit and when he is 72 years old so:
[tex]72-25=47[/tex]So has pass 47 yeas, now we can calculate how much will he have earned in interest like this:
[tex]57000(1+0.035)^{47}=287125.19[/tex]so in interes will be the resto of this value minus the initial amound:
[tex]287125.19-57000=230125.19[/tex]In interest he earned 203,125.19 and the total amount is: 287,125.19
PLEASE HELP WITH GEOMETRY IVE ASKED THIS SO MANY TIMES AND NO ONE IS ANSWERING
A trapezoid is a quadrilateral as it has 4 sides. An Isosceles trapezoid has parallel bases.The legs of an Isosceles trapezoid are congruent, the lower base angles are congruent and the upper base angles are also congruent. The diagonals are also congruent.
Let's use a diagram to represent the Isosceles trapezoid.
ABCD is an Isosceles trapezoid with the bases AB and CD. Therefore,
[tex]OA\cong OB[/tex][tex]\begin{gathered} AC\cong BD \\ \operatorname{Re}ason\colon\text{ The legs of Isosceles trapezoid are congruent} \end{gathered}[/tex][tex]\begin{gathered} \angle CAB\cong\angle DBA \\ \text{ Reason: }The\text{ upper base angles of an Isosceles trapezoid are congruent} \end{gathered}[/tex][tex]\begin{gathered} \angle ACD\cong\angle BDC \\ \text{ Reason: The lower base angles of an Isosceles trapezoid are congruent} \end{gathered}[/tex]Note :
[tex]AB||CD[/tex]The Floor Area of a Guest Room in the diagram is 12 x 8. If the room expanded to 40% increase, what are the new dimensions of the room?
First let's calculate the initial area, by multiplying the dimensions:
[tex]\begin{gathered} A=12\cdot8 \\ A=96 \end{gathered}[/tex]Now, let's increase this area by 40%, multiplying it by 1.4:
[tex]A=96\cdot1.4=134.4[/tex]Finally, to find the new dimensions, we just need to multiply them, knowing that they have the proportion of 12:8
[tex]\begin{gathered} x\cdot y=134.4 \\ \frac{x}{y}=\frac{12}{8}\to8x=12y\to x=\frac{12}{8}y \\ \\ (\frac{12}{8}y)\cdot y=134.4 \\ y^2=134.4\cdot\frac{8}{12} \\ y^2=89.6 \\ y=9.466 \\ \\ x=\frac{12}{8}y=\frac{12}{8}\cdot9.466=14.199 \end{gathered}[/tex]So the new dimensions are 14.199 and 9.466
On the unit circle standard position and angle of which measure is CO terminal with an angle that measures pie radians?
answer is the first option
3pi
use the discriminant to find the nature of the solutions to the following quadratic equation3x^2 -2x-4=0Two different irrational number solutionsOne repeated irrational number solutiontwo different rational number solutionsOne repeated rational number solutiontwo imaginary number solution
The quadratic equation is
3x^2 - 2x - 4
using completing the square method
firstly, to solve a quadratic equation the coefficient x^2 must be 1
divide through by 3
3x^2/3 -2x/3 - 4/3 = 0
make the linear expression a perfect square
x^2 - 2x/3 = 4/3
make -2x/3 a perfect square
x^2 - 2x/3 x 1/ 2 = 4/3
x^2 - 2x/6 = 4/3
square -2x/6
x^2 -(2x/6)^2 = 4/3
add the perfect square to both sides
x^2 - (2x/6)^2 = 4/3 + (2/6)^2
(x - 2/6)^2 = 4/3 + 4/36
solve the left hand side of the equation
4/3 + 4/36
lcm is 36
4 * 12 + 4 *1 / 36
48 + 4 / 36
52/36
(x - 2/6)^2 = 52/36
find the squareroot of both sides
[tex]\begin{gathered} \text{x -2/6 }\pm\text{ }\sqrt[]{\frac{52}{36}_{}} \\ x\text{ = 2/6 }\pm\text{ }\frac{\sqrt[]{52}}{6} \\ \end{gathered}[/tex]square root of 52 is 7.211
x = 2 + 7.211 / 6 0r 2 - 7.211 / 6
x = 9.211 / 6 or -5.211/6
x = 1.53 or -0.8685
the answer is two different rational number solutions
Can you please help me with Math?
19) the proportion of shining day to all day is:
[tex]4\colon5[/tex]So if the month have 30 days then we have to multiplay the ratio for 6 so:
[tex]\begin{gathered} 6\cdot4\colon6\cdot5 \\ 24\colon30 \end{gathered}[/tex]So there was 24 shining day out of 30 so now we can calculate the percentage with a rule of 3
[tex]\begin{gathered} 30\to100 \\ 24\to x \end{gathered}[/tex]and the equation is:
[tex]\begin{gathered} x=\frac{100\cdot24}{30} \\ x=80 \end{gathered}[/tex]So the 80% of the days wwere shining
1.3719691094 rounded 5 decimal places
1.3719691094 rounded 5 decimal places is
[tex]1.37197[/tex]in which 9 in the 6th position convert the 6 in the 5th position into 7.
This shape is a Rhombus. What do you know about angle 1 and angle 2?
Since the shape is a rhombus we will have that angles 1 & 2 are complementary angles (The sum of both of them adds to 90°).
Need an equation that makes a parabola from soccer ball over soccer dummy and into the garbage can
Answer:
The position of David Beckham is at (2,0) and the position of the garbage can is (38,0). Note that these two points would be the roots of the parabola we are going to draw.
Now since we have the roots, we can construct the equation of the parabola as
[tex]-a(x-2)(x-38)[/tex]where a is a constant.
We choose a = 0.05 and get
[tex]-0.05(x-2)(x-38)[/tex]16+2x=22 solve for x
16+2x=22 solve for x
step 1
subtract 16 both sides
2x=22-16
2x=6
step 2
Divide by 2 both sides
x=6/2
x=3
therefore
the ananswer is
x=3Using an appropriate diagram be able to prove the TriangleProportionality theorem and/or its converse.
The converse of Basic Proportionality Theorem: If a line divides any two sides of a triangle in the same ratio, then the line must be parallel to the third side.
From the sketch,
[tex]\frac{CD}{DA}=\frac{CE}{EB}[/tex]Take the reciprocal
[tex]\frac{DA}{CD}=\frac{EB}{CE}[/tex][tex]\text{Add 1 TO BOTH SIDES}[/tex][tex]\frac{DA}{CD}+1=\frac{EB}{CE}+1[/tex]Any number divided by itself is 1, so we can replace 1 with CD/CD or CE/CE
so that
[tex]\frac{CD}{CD}+\frac{DA}{CD}=\frac{CE}{CE}+\frac{EB}{CE}[/tex]Combine terms using our common denominator
[tex]\frac{CD+DA}{CD}=\frac{CE+EB}{CE}[/tex]from the diagram, we can see that
CA=CD+DA
and
CB=CE+EB
Then
[tex]\frac{CA}{CD}=\frac{CB}{CE}[/tex]Since the triangles have SAS for triangle similarity.
This means that
[tex]\text{Triangle ABD is similar to Triangle }CDE[/tex]Solve /x-5/=3A. x=2, x=8B. x=-8, x=8C. x=-2, x=2D. x=-8, x=-2
According to the given data we have the following equation:
|x-5|=3
In order to solve the equation above we would make the following:
[tex]\mathrm{Apply\: absolute\: rule}\colon\quad \mathrm{If}\: |u|\: =\: a,\: a>0\: \mathrm{then}\: u\: =\: a\: \quad \mathrm{or}\quad \: u\: =\: -a[/tex]So, if x-5=-3. x=-3+5. x=2
Therefore the value of x would be 2
if x-5=3.x=3+5.x=8
Therefore the value of x would be 8.
Therefore, the combine solution would be:
x=2
x=8
Use the equation of the line of best fit to fill in the blanks below Give exact answers, not rounded approximations
Explanation:
The equation for the line of best fit is given as:
[tex]y=0.6x+19.85[/tex]Part A
Number of Hours Worked: 8.1
Observed Amount (from the table): 24.71
Predicted Amount:
[tex]\begin{gathered} y=0.6x+19.85 \\ =0.6(8.1)+19.85 \\ =24.71 \end{gathered}[/tex]Residual: The residual is the difference between the actual and predicted values.
[tex]\begin{gathered} \text{ Residual}=\text{ Actual Value-Predicted Value} \\ =24.71-24.71 \\ =0 \end{gathered}[/tex]Part B
Number of Hours Worked: 10.00
Observed Amount (from the table): 21.50
Predicted Amount:
[tex]\begin{gathered} y=0.6x+19.85 \\ =0.6(10)+19.85 \\ =25.85 \end{gathered}[/tex]Residual: The residual is the difference between the actual and predicted values.
[tex]\begin{gathered} \text{ Residual}=\text{ Actual Value-Predicted Value} \\ =21.50-25.85 \\ =-4.35 \end{gathered}[/tex]Answer:
The completed table is attached below:
A six-sided biased die is weighted in such a way that the probability of obtaining a "one" is 3/7 The die is tossed 10 times. Find the probability of obtaining (a) at most four "ones".
The probability of obtaining (a) at most four "ones" will be; 91.31%.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The first step is using the binomial distribution which is = np or n (1-p)
The binomial distribution will be n = 10 and p = 3/7;
np = 10 x 3/7 = 4.2
n(1-p) = 200 x (4/7)
= 166.67
We can see that Both n(1-p) and np are much higher than 5,
Therefore,
P(Y ≤ 40.5) = P(z ≤ (40.5-μ)/σ)
= P(z≤1.36)
= 0.9131
= 91.31%
Thus, the probability of obtaining (a) at most four "ones" will be; 91.31%.
Learn more about probability here;
https://brainly.com/question/9326835
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3s+2t=-4-6s-10t=-7Value of s
Answer :
s = -3
Explanation :
Using method of substitution by expressing one equation to only one variable.
Equation 1 : 3s + 2t = -4
Equation 2 : -6s - 10t = -7
Express equation 1 as t in terms of s :
[tex]\begin{gathered} 3s+2t=-4 \\ 2t=-3s-4 \\ t=\frac{-3s-4}{2} \end{gathered}[/tex]Substitute t to the equation 2 :
[tex]\begin{gathered} -6s-10t=-7 \\ -6s-10(\frac{-3s-4}{2})=-7 \\ -6s-5(-3s-4)=-7 \\ -6s+15s+20=-7 \\ 9s=-7-20 \\ 9s=-27 \\ s=-\frac{27}{9}=-3 \end{gathered}[/tex]The answer is s = -3
Does the set of numbers represent a Pythagorean Triple. 4,5,6YesNo
representNo
Explanation
to find if the numbers represent a Pythagorean triple, we need check if it is possible to make a rigth triangle with those side lengths
the bigger number will be the hypotenuse, then
Let
[tex]\begin{gathered} 6\rightarrow hypotenuse \\ 4\rightarrow side1 \\ 5\text{ }\rightarrow side2 \end{gathered}[/tex]now, the Pythagoras theorem is
[tex]\text{side}1^2+side2^2=hypotenuse^2[/tex]then , replace
[tex]\begin{gathered} 4^2+5^2=6^2 \\ 24+25=36 \\ 49=36,\text{ false, then 4.5,6 NOT represent a Pythagorean triple} \end{gathered}[/tex]I hope this helps you.
[tex]undefined[/tex]In DGE, DG = 8, GE = 17, and DE = 15. What is the length of DF? Round to the nearest hundred
Answer:
7.06 units
Explanation:
The given side lengths are indicated in the diagram below:
Using similar triangles, we have:
[tex]\begin{gathered} \frac{GF}{8}=\frac{8}{17} \\ 17GF=64 \\ GF=\frac{64}{17} \\ GF=3.76 \end{gathered}[/tex]Next, apply Pythagorean Theorem to triangle DGF.
[tex]\begin{gathered} DG^2=DF^2+GF^2 \\ 8^2=DF^2+3.76^2 \\ DF^2=8^2-3.76^2 \\ DF^2=49.8624 \\ DF^{}=\sqrt{49.8624} \\ DF\approx7.06\text{ units} \end{gathered}[/tex]The length of DF is approximately 7.06 units (to the nearest hundred).
1 Felipe surveyed students at his school. He found that 78 students own a cell phone and 57 of those students own an MP3 player. There are 13 students that do not own a cell phone, but own an MP3 player. Nine students do not own either device Construct a two-way table summarizing the MP3 Player No MP3 Player Total Cell Phone No Cell Phone Total 1 2 3 4 5
students that own a cell phone but don't own an MP3: 78 - 57 = 21
total number of student with no cell phone: 13 + 9 = 22
total number of student with a MP3 player: 57 + 13 = 70
total number of student without a MP3 player: 21 + 9 = 30
total number of students: 70 + 30 = 78 + 22 = 100
MP3 player no MP3 player Total
cell phone 57 21 78
no cell phone 13 9 22
Total 70 30 100
Mrs. Kelly is making pizzas and she uses 20 slices of pepperoni on each pizza how many pepperoni slices will she need if she makes seven pizza
Given Mrs. Kelly uses 20 slices of pepperoni on each pizza.
If whe makes seven pizzas let the slices of pepperoni be x.
Then x is equal to
[tex]x=7\times20=140[/tex]Verona is solving the equation -3+4x=9. In order to isolate the variable term using the subtraction property of equality, which number should she subtract from both sides of the equation. A: -4B: -3C: 3D: 4
In order to solve the equation, we should do:
[tex]\begin{gathered} -3+4x=9 \\ -3+4x+3=9+3 \\ 4x=12 \\ x=\frac{12}{4} \\ x=3 \end{gathered}[/tex]Then, in the step to isolate the variable term (4x), we should add 3 to both sides of the equality (see step 2).
Answer: C: 3.
A service station attendant is paid time-and-a-half for working over 40 hours per week. Last week the attendant worked 47 h and earned $580.75. Find the attendant's regular hourly wage.
the attendant's regular hourly wage is $11.50
Explanation:let the regular pay = p
time and the half is the amount paid for overtime:
time and the half = p + 1/2p = p + 0.5p
time and the half = 1.5p
40 hours is the normal hours. Hence, the cost per hour is P
7 hours is the over time. The cost per hour 1.5p
Total earned = $580.75
p(40) + 1.5p(7) = 580.75
40p + 10.5p = 580.75
50.5p = 580.75
divide both sides by 50.5:
50.5p/50.5 = 580.75/50.5
p = 11.5
Hence, the attendant's regular hourly wage is $11.50
A group of friends wants to go to the music park they have no more than $275 to spend on parking and admission parking is $18.25 and tickets cost $39.50 per person including tax write in and sold in any quality which can be used to determine X the number of people who can go to the amusement park
Money available = 275
Parking cost = 18.25
Cost of each ticket = 39.50
x = number of people
The total cost, parking cost + ( number of people * price of each ticket ) , must be less or equal to the money available (275)
18.25+ 39.50x ≤ 275
Solve for x:
39.50x ≤ 275 -18.25
39.50x ≤ 256.75
x ≤ 256.75 / 39.50
x ≤ 6.5
The width of a rectangular room is 1 foot less than the length. if the area of the room is 6 square feet, Find the dimensions of the room
Dimension: 2ft by 3ft
Explanations:Let the length of the rectangle be L
Let the width of the triangle be W
The formula for calculating the area of a rectangle is expressed as:
A = LW
Since the area of the room is 6 square feet, hence;
6 = LW ..................................1
If the width of a rectangular room is 1 foot less than the length, then;
W = L - 1 ...............................2
Substitute equation 2 into 1 to have:
6 = L(L - 1)
6 = L² - L
Swap sides
L² - L = 6
L² - L - 6 = 0
Factorize the resulting quadratic expressions:
L² - 2L + 3L - 6 = 0
L(L - 2) + 3(L - 2) = 0
(L + 3)(L - 2) = 0
L + 3 = 0 and L - 2 = 0
L = -3 and L = 2
Since the dimension cannot be negative, hence L = 2ft
Recall that LW = 6
W = 6/L
W = 6/2
W = 3ft
Hence the dimension of the room will be 2 feet by 3 feet