We can solve this question by using the fact that a normal distribution is symmetric and using the empirical rules. The empirical rules are
• 68% of the data falls within one standard deviation of the mean.
• 95% of the data falls within two standard deviations of the mean.
• 99.7% of the data falls within three standard deviations of the mean.
In our problem, the mean is 28 and the standard deviation is equal to 4. Our interval is 24(one standard deviation below the mean) and 36(2 standard deviations above the mean)
[tex](24,36)=(28-4,28+8)=(28-\sigma,28+2\sigma)[/tex]Our area is the area that falls within one standard deviation of the mean plus the area between one standard deviation and two on the positive side. The first area is 68% of the data, and the second area we can calculate using the fact that a bell curve is symmetric. Since 68% of data falls within one standard deviation and 95% of the data falls within two standard deviations of the mean, the difference between them represents the data that falls between one standard deviation and two standard deviation.
[tex]95-68=27[/tex]Since the distribution is symmetric, the data that falls between one standard deviation and two standard deviation on the positive side is half of this value.
[tex]\frac{27}{2}=13.5[/tex]Now, we just add this value to 68% and we're going to have our answer.
[tex]68+13.5=81.5[/tex]The percentage of employees worked between 24 and 36 hours is 81.5%.
a Density is the ratio of mass to volume. An object with a volume of 25 cubic centimeters (cm?) has a mass of 125 grams (g). What is the density, in g/cm", of the object? A 5 B. 25 C. 100 D. 3125
The density is a ratio, defined as
[tex]\rho=\frac{m}{v}[/tex]replace in the ratio of density
[tex]\rho=\frac{125g}{25\operatorname{cm}3}[/tex]the density will be
[tex]\rho=\frac{5g}{\operatorname{cm}3}[/tex]27,9,3,1,1/3,1/9....Write the sigma notation for the infinite series. ________________
Given
Series,
[tex]27,9,3,1,\frac{1}{3},\frac{1}{9},...[/tex]Find
Write the sigma notation for the infinite series.
Explanation
as we see the given series is a geometric series .
here , a = 27
common ratio , r = 9/27 = 1/3
so ,
[tex]\begin{gathered} \sum_{n\mathop{=}1}^{\infty}ar^{n-1} \\ \\ \sum_{n\mathop{=}1}^{\infty}(27)(\frac{1}{3})^{n-1} \\ \\ \sum_{n\mathop{=}1}^{\infty}(\frac{1}{3})^{-3}(\frac{1}{3})^{n-1} \\ \\ \sum_{n\mathop{=}1}^{\infty}(\frac{1}{3})^{n-4} \end{gathered}[/tex]Final Answer
Hence , the sigma notation for the infinite series is
[tex]\sum_{n\mathop{=}1}^{\infty}(\frac{1}{3})^{n-4}[/tex]the number of girls is 75% of the number of boys.There are 28 students altogether. how many are girls and how many are boys?use a tape diagram
Let x be the number of boys
Let the number of girls be 75% of x = 75x/100
Boys + girls = 28
75x/100 + x = 28
0.75x + x = 28
1.75x = 28
Divide both-side of the equation by 1.75
x = 16
There a
Travis was walking to school when hesaw some friends walking a block aheadof him. After running to catch up with hisfriends, his heart was beating 24 beatsevery 10 seconds. At this rate, how manytimes would his heart beat in 3 minutes?
his heart would beat 432 times in 3 minutes
Explanation
we can easily solve this by using a rule of three,
then
Step 1
to do that we need the same measure unit for the time, let's use seconds
so, we need to convert 3 minutes into seconds,
the equivalence is
[tex]1\text{ minute = 60 seconds}[/tex]hence, to convert from minutes into seconds just mutlply by 60
then
[tex]3\text{ minutes}\Rightarrow3\cdot60\text{ seconds=180 seconds}[/tex]Step 2
now, let's make the proportion
let x represents the number of times his heart would be in 180 seconds( 3 minutes)
so
[tex]\begin{gathered} \text{if} \\ 24\text{ beats}\Rightarrow10\text{ s} \\ \text{then} \\ x\text{ beats}\Rightarrow180\text{ s} \end{gathered}[/tex]so, the proportion is
[tex]\begin{gathered} \frac{24\text{ beats}}{10\text{ s}}=\frac{x}{180\text{ s}} \\ \frac{24}{10}=\frac{x}{180} \\ \end{gathered}[/tex]finally, to solve for x multiply both sides by of the equation by 180 and reduce
[tex]\begin{gathered} \frac{24}{10}=\frac{x}{180} \\ \frac{24}{10}\cdot180=\frac{x}{180}\cdot180 \\ \frac{4320}{10}=x \\ 432=x \end{gathered}[/tex]therefore, his heart would beat 432 times in 3 minutes
I hope this helps you
a debt company wants to build a uniquely shaped decks how many square feet of wood will the company need to cover the deck designer below shaped like a regular pentagon a trapezoid the height of the trapezoid is 4.5 ft round your answer to one decimal place to find the area of the Pentagon divided into 5 similar triangles you see if I could the radius at the Pentagon the distance from each vertex Center is 4.25 ft
72.2 square feet of wood will the company need to cover the deck designer shaped like a regular pentagon and a trapezoid.
To find the total wood required we need to add the area of pentagon and area of trapezoid.
Firstly we will draw the 5 similar triangle in the pentagon as shown below:
Lets name one triangle as ABC.
Given, radius of pentagon = 4.25 ft. (Let x)
Now, in triangle ABC,
BD=DC=2.5 ft. (half of the BC)
By applying Pythagoras theorem,
[tex]AB^{2} =AD^{2} +BD^{2} \\AD=\sqrt{AB^{2} -BD^{2} } \\AD=\sqrt{11.81} \\AD=3.44 ft.[/tex]
We know that AD is the height of triangle ABC.
So, Height = AD = 3.44 ft.
Area of triangle ABC = [tex]\frac{1}{2}[/tex] * base * height
=[tex]\frac{1}{2}[/tex] * 5 ft. 3.44 ft. = 8.59 square feet.
Area of pentagon = area of 5 similar triangle
= 5 * area of triangle ABC
= 5 * 8.59 = 42.96 square feet
Area of trapezoid = [tex]\frac{1}{2}[/tex] * (sum of the parallel side) * height
= [tex]\frac{1}{2}[/tex] * (5+8) * 4.5
= [tex]\frac{1}{2}[/tex] * 13 * 4.5 = 29.25 square feet.
Total square feet of wood required = area of pentagon + area of trapezoid
= 42.96 + 29.25 = 72.21 square feet
Rounding to one decimal place 72.21 square feet ≈ 72.2 square feet.
Thus, 72.2 square feet of wood will the company need to cover the deck designer shaped like a regular pentagon and a trapezoid.
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Elisa designed a flower garden in the shape of a square with a side length of 10 feet. She plans to build a walkway along the diagonal. What is the closest measure of the length of the walkway?
A square has all equal sides, then each side has a measure of feet
The diagonal can be found using the following formula:
[tex]d=\sqrt[]{2a}[/tex]Where a represents a side.
Replacing:
[tex]\begin{gathered} d=\sqrt[]{2(10)} \\ d=\sqrt[]{20} \\ d=14.1421 \end{gathered}[/tex]Hence, the closest measure of the walkway length is 14.1421 feet.
Find the volume of a pyramid with a square base, where the side length of the base is10 m and the height of the pyramid is 7.2 m. Round your answer to the nearesttenth of a cubic meter.
hello
to find the volume of the figure, we need to know the formula of a pyramid with a square base
once we know that, we can proceed to simply substitute the values into the equation
[tex]\begin{gathered} \text{volume}=\frac{1}{3}\times l^2\times h \\ l=\text{side length} \\ h=\text{height} \end{gathered}[/tex][tex]\begin{gathered} l=10m \\ h=7.2m \end{gathered}[/tex][tex]\begin{gathered} \text{volume}=\frac{1}{3}\times10^2\times7.2 \\ \text{volume}=\frac{100\times7.2}{3} \\ \text{volume}=240m^3 \end{gathered}[/tex]the volume of the figure is 240m^3
Find the measure of the following numbered angles and the feason: Measure Reason 1 1 3 1 m
Answer
Explanation
Using the image,
Mobile Cookies delivers packs of cookies which cost $2.60 per package to deliver. The fixed cost to run the delivery truck is $252 per day. If the company charges $5.60 per pack, how many packages must be delivered daily to make a profit of $33?
95 packages must be delivered daily to make a profit of $33.
What is the meaning of profit?
Profit is the term used to describe the financial gain experienced when the revenue from a commercial activity exceeds the costs, costs, and taxes associated with maintaining that activity.
Given that the delivers cost per packets is $2.60 and the cost to run a truck is $252.
Assume that they need deliver x packs of cookies to make a profit of $33.
The total cost to deliver x packs of cookies is $(2.60x + 252).
Given that company charges $5.60 per pack.
The revenue is $5.60x.
The total profit is $(5.60x - (2.60x + 252)) = $(5.60x - 2.60x - 252) = $(3x - 252).
Given that the profit is $33.
Thus 3x - 252 = 33
Add 252 on both sides:
3x = 285
Divide both sides by 3:
x = 95.
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On a certain day the probability of rain is 80% probability of thunder is 3/5 and the probability of both is 2/5. What is the probability that it will rain or thunder?
The probability it will rain or thunder = 100%
Explanation:Probability it will rain = 80%
P(rain) = 4/5 (simplest term in fraction)
Probability of thunder = 3/5
P(thunder) = 3/5
Probability of both rain and thunder = 2/5
P(rain and thunder) = 2/5
We need to find the probability of rain or thinder = P(rain or thunder)
To find the probability of P(rain or thunder), we will apply the formula for the addition rule on any two events:
[tex]P(A\text{ or B\rparen = P\lparen A\rparen +}P(B)\text{ - P\lparen A and B\rparen}[/tex]Applying the formula in our question:
[tex]P(rain\text{ or thunder\rparen = P\lparen rain\rparen + P\lparen thunder\rparen - P\lparen rain and thunder\rparen}[/tex]substitute the values in order to find the probability:
[tex]\begin{gathered} P(rain\text{ or thunder\rparen = }\frac{4}{5}\text{ + }\frac{3}{5}-\text{ }\frac{2}{5} \\ \\ P(rain\text{ or thunder\rparen = }\frac{4\text{ + 3 - 2}}{5} \\ P(rain\text{ or thunder\rparen = }\frac{5}{5} \\ \\ P(rain\text{ or thunder\rparen = 1} \end{gathered}[/tex]In percentage, the probability it will rain or thunder = 100%
Which of the following is a quadratic equation that has the roots x = 5 and x = 6?
Answer:
the quadratic equation that has the roots x=5 and x=6 is;
[tex]x^2-11x=-30[/tex]Explanatio
We want to derive the quadratic equation that has the roots x=5 and x=6;
To derive the equation, we have;
[tex](x-5)(x-6)=0[/tex]Expanding;
[tex]\begin{gathered} x^2-5x-6x+30=0 \\ x^2-11x+30=0 \\ x^2-11x=-30 \end{gathered}[/tex]Therefore, the quadratic equation that has the roots x=5 and x=6 is;
[tex]x^2-11x=-30[/tex]the figure below has a point marked with a large dot.first rotate the figure 90 degrees counterclockwise about the origin.then give the coordinates of the Mark point in the original figure in the final figure.
When we do a 90 degree counterclockwise rotation about the origin, a point moves from ( x,y) to ( -y,x)
Using the point with the blue dot
It is originally at (2,-3)
It will move to (3,2)
$7.400 at 10.5% for 1/4 yearsTo find the ending balance from the equation given using simple interest
Given:
$7.400 at 10.5% for 1/4 years
To find:
The ending balance from the equation given using simple interest
The ending balance here the total amount that will be gotten after the duration of 1/4 years
Using simple interest formula:
[tex]\begin{gathered} \text{I = PRT} \\ I\text{ = interest = ?} \\ P\text{ = principal = \$7400} \\ R\text{ = rate = 10.5\% = 0.105} \\ T\text{ = time = }\frac{1}{4}year \end{gathered}[/tex]substitute the values in the formula:
[tex]\begin{gathered} I\text{ = 7400 }\times\text{ 0.105 }\times\text{ }\frac{1}{4} \\ \\ I=\text{ 194.25} \end{gathered}[/tex]The ending balance = Interest + Principal
[tex]\begin{gathered} The\text{ ending balance = 194.25 + 7400} \\ \\ The\text{ ending balance = \$7594.25} \end{gathered}[/tex]I need to make my birthday into a polynomial my birthday is 11/01/2005
EXPLANATION:
To express a number or value as a polynomial we must take into account some steps:
-The polynomial may or may not have grouping signs.
-The polynomial can have more than one variable, constants and exponents.
-A polynomial must be ordered, the monomials that form it must be written from highest to lowest degree.
Since a polynomial is an algebraic expression that shows the sum of monomials and we have 3 separate monomials, so we must do the following:
[tex]\begin{gathered} (11)\rightarrow a\text{ monomial} \\ (01)\rightarrow a\text{ monomial} \\ (2005)\rightarrow a\text{ monomial} \\ \text{Now }we\text{ add }the\text{ t}hree\text{ }monomials\colon \\ (2005+11+01);\text{ there }the\text{ poly}nomial\text{ }must\text{ be organized }from \\ highest\text{ }to\text{ lowe}st\text{ }coefficient; \\ \text{ANSWER: (2005+11+01)} \end{gathered}[/tex]how do you do how do you point plot on a graph
To point plots on a graph, take the following steps:
1. Identify the x-coordinates and y-coordinates from the variable/data you have. It should be written in this form: (x, y)
2. Label both axes on the graph(x-axis and y-axis). The x-axis is usually on the horizontal line while the y axis is the horizontal line.
3. Start plotting your first 2 points on both axes (usually the numbers on first row). Plot the x value and also plot the y value at the appropriate points
4. Finally, Continue plotting the numbers by pointing each point on the graph (take them in rows)
If a different number in domain of a function have different outputs the function is called?
A function is a rule that assigns each input exactly one output. We call the output the image of the input. The set of all inputs for a function is called the domain.
A function is one-to-one if no two elements in the domain correspond to the same element in the range.
Thus, if a different number in the domain of a function has different outputs the function is called a one-to-one function
x + y =5x + y =5one solution no solutions infinity many solutions
We have the same equation twice, then there are infinity many solutions
Under her cell phone plan, Ella pays a flat cost of $58.50 per month and $3 per gigabyte, or part of a gigabyte. (For example, if she used 2.3 gigabytes, she would have to pay for 3 whole gigabytes.) She wants to keep her bill under $65 per month. What is the maximum whole number of gigabytes of data she can use while staying within her budget?
The maximum number of gigabytes of data she can use while staying within her budget is 2 gigabytes.
Given that Ella pays a flat cost of $58.50, and per gigabyte used have to pay $3. If she uses g gigabytes she has to pay $3xg.
Now we have to find the maximum whole number of gigabytes data, she can use within her budget.
Her budget is less than $65.
We can create a inequality expression for this, as follows.
58.50+3g< 65
Calculating further, we get
3g<65-58.50
3g<6.5
g<6.5/3
g<2.163.
Therefore, the maximum whole of gigabytes, she should use to keep the expense within budget is 2 gigabytes.
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7th grade math I'm stuckhelp me fill in the blanks!
ok
item price before tax sales tax price including tax
pillow 8 8 x 0.0725 = 0.58 8 + 0.58 = $8.58
blanket 22 22 x0.0725 = 1.595 22 + 1.595 = $23.595
trash can 14.5 14.5 x 0.0725 = 1.051 14.5 + 0.0725 =$15.55
A student has 42 coins worth a total of $5.90. Each coin is either a nickel (five cents) or a quarter (twenty-five cents). If x is the number of nickels, then x can be determined from the equation---
Given
no. of coins = 42
worth of coins = $5.90
Find
number of nickels
Explanation
The number of quaters is 42 - x
0.05x + 0.25(42 - x) = 5.9
-0.2x + 10.5 = 5.9
-0.2x = -4.6
x = 23
Final Answer
Number of Nickels, x = 23
I need HELP PLS!!! ITS HARD TO DO I NEED HELP
ANSWER:
B.
[tex]x^{\frac{7}{6}}[/tex]STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]\mleft(\sqrt{x}\mright)\mleft(\sqrt[3]{x^2}\mright)[/tex]We simplify and we have:
[tex]\begin{gathered} (\sqrt[]{x})=x^{\frac{1}{2}} \\ (\sqrt[3]{x^2})=x^{\frac{2}{3}} \\ \text{therefore:} \\ x^{\frac{1}{2}}\cdot x^{\frac{2}{3}}=x^{\frac{1}{2}+\frac{2}{3}} \\ \frac{1}{2}+\frac{2}{3}=\frac{1\cdot3+2\cdot2}{2\cdot3}=\frac{3+4}{6}=\frac{7}{6} \\ x^{\frac{7}{6}} \end{gathered}[/tex]Simplify the following trig expressions to an expression involving at most one trig function
we know that:
• cot x = adjacent /opposite
,• secx = hypotaneus / adjacent
,• cscx = hypotaneus / opposite
Therefore , our expression can be re-rewritten as follows :
(cot x * secx) /(cosec x)
→{adj /opp * hyp /adj }/( hyp/opp)... [note that adj cancels each other ]
→(hyp /opp)/ hyp/opp
→(hyp /opp) * (opp /hyp) .......( each variable cancels each other)
→1*1
= 1
the 4000N boat picks up 5 passengers who each weigh 500N. what is the total mass of the boat and passengers
The weight of the boat is 4000 N
and each passenger weigh 500 N,
then the total weigh of boat and passengers is:
4000 N + 5 * 500 N = 4000 + 2500 = 6500 N
Kim typed a 36-word paragraph in 2/3 minute. What is his typing speed, in words per minute?
ANSWER
54 words per minute
EXPLANATION
We want to know how much words he can write in 1 minute, so we have to find the ratio of words to minutes by dividing the number of words he wrot
Solve for q.
-18q+ 18q+ 2q + 14 = 4
q=
Answer:
q = -5
Step-by-step explanation:
Collect like terms
-18q + 18q + 2q = 4 - 14
-18q + 20q = -10
2q = -10
Divide both sides by 2
2q/2 = -10/2
q = -5
If Angle A is acute and Angle B is obtuse and Angle A is 2X+5 and Angle B is 6X+55, then how many degrees would Angle A be?
Angle A is 35° and Angle B is 145°
Supplementary angles are angles that give 180° when added together
Angle A and Angle B are supplementary angles such that
∠A + ∠B = 180°
Given that ∠A is acute angle and ∠B is obtuse angle
also , ∠A = 2x+5 and ∠B = 6x+55
using supplementary angle property ,
2x+5 + 6x+55 = 180
solving for x ,
8x + 60 = 180
x = 15
8x = 180 - 60
8x = 120
∠A = 2x+5
substituting value of x
∠A = 2(15)+ 5 = 30+5
∠A = 35°
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find the standard deviation of 3, 7, 4, 6, 5 if necessary, round your answer to the nearest tenth
3, 7, 4, 6, 5
First, find the mean.
Mean = Sum of the values / number of values
Mean = (3+7+4+6+5) /5 = 25/5 = 5
Then, find the variance:
Calculate each value difference from the mean
5-3 = 2
7-5 = 2
5-4= 1
6-5=1
5-5= 0
Square each difference, add them, and divide by the number of values.
Variance : (2^2+2^2+1^2+1^2+0^2 )/ 5 = (4+4+1+1) /5 = 10 /5 = 2
Standard deviation= square root of the variance:
√2 = 1.4
twice a number is 24a. 2- n = 24b. 2 + n = 24c. 2 / n = 24 d. 2n = 24
Answer:
d. 2n = 24
Explanation:
Let the number be n
Twice the number = 2 x n
The word 'is" is the equality sign.
Therefore, the expression twice a number is 24 in mathematical symbol is:
[tex]2n=24[/tex]Which of the following is an equation of a line parallel to the equaticy = 4x+12O A. y=-x-2y4O B. y = -4x – 2O c. y = 4x-2O O D. y=-x-2
Given
The equation of the line is,
[tex]y=4x+1[/tex]To find the equation of the line parallel to y=4x+1.
Explanation:
It is given that,
The equation of the line is,
[tex]y=4x+1[/tex]Since two parallel lines have same slope.
Then,
The slope of the line parallel to y=4x+1 is, 4.
Therefore, the equation of the line parallel to y=4x+1 is of the form,
[tex]y=4x+k[/tex]Hence, the equation of the line parallel to y=4x+1 is c) y=4x-2.
Let f(x)=8x+5 and g(x)=6x^2+2x after simplifying (f+g)(x)=
We have to find (f+g)(x), where:
[tex]\begin{gathered} f(x)=8x+5 \\ g(x)=6x^2+2x \end{gathered}[/tex]We can write:
[tex](f+g)(x)=f(x)+g(x)=(8x+5)+(6x^2+2x)=6x^2+10x+5[/tex]Answer: (f+g)(x) = 6x^2+10x+5