In a normal distribution, about 0.1% 2.2% 13.6% 1 SD % of the data lies between 1 and 3 standard deviations of the mean. Mean 13.6% 1 SD 2.2% 0.1% 3 SD
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Solution:
Given a normal distribution table;
The % of data that lies between 1SD and 3SD is
[tex]=13.6\%+2.2\%=15.8\%[/tex]Hence, the answer is 15.8%
Related Questions
Identify the arc length of MA in terms of pi and rounded to the nearest hundredth.
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To answer this question we will use the following formula for the arc length of a central angle θ degrees:
[tex]\begin{gathered} \frac{\theta}{180}\cdot\pi r, \\ \text{where r is the circumference's radius.} \end{gathered}[/tex]Assuming that Y is the circumference's center we get:
[tex]m\hat{AM}+m\hat{MH}=180^{\circ}.[/tex]Substituting mMH=88degrees we get:
[tex]m\hat{AM}+88^{\circ}=180^{\circ}\text{.}[/tex]Therefore:
[tex]\text{m}\hat{\text{AM}}=92^{\circ}\text{.}[/tex]Then the arc length of MA is:
[tex]\frac{92}{180}\cdot\pi\cdot16m\approx8.18\pi m\approx25.69m\text{.}[/tex]Answer: First option.
Please help me thank you I’ll send tutor a chart that goes with the question
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Answer:
As time increases, the number of flyers Justin has increased.
3 flyers per minute
62 flyers at t
Explanation:
Based on the table, we can see that when the time is greater the number of flyers is also greater. So, as time increases, the number of flyers Justin has increased.
Then, to know the rate, we need to use two columns of the table, so the rate will be equal to:
[tex]\frac{Flyers_2-Flyers_1}{Time_2-Time_1}[/tex]So, if we replace Time1 by 10, Flyers1 by 92, Time2 by 15, and Flyers2 by 107, we get:
[tex]\text{rate}=\frac{107-92}{15-10}=\frac{15}{5}=3[/tex]Therefore, the rate is 3 flyers per minute.
Now, to know how many flyers he has when he started printing, we need to extend the table. We see that every 5 minutes, the flyers increase by 15. So, at 0 and 5 minutes the number of flyers was:
Time 0 5 10
Flyers 77-15 = 62 92-15 = 77 92
Therefore, the number of flyers that he has when he started printing was the number of flyers at 0 minutes. So the answer of part b is 62 flyers
Convert this rational number
to its decimal form and round
to the nearest tenth
2/5
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Answer:
0.4
Step-by-step explanation:
First, divide 2 by 5. You should but a decimal because 5 doesn't go into 2, so you get 20. 5 does go into 20, 4 times.
ΔABC - ΔDEE B D X = [?] Ente
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Triangle ABC = Triangle DEF
Both triangles are similar
Hence, we will be using the similarity theorem
AB / DE = BC / EF
x / 3 = 8/6
Cross multiply
6 * x = 8 * 3
6x = 24
Divide both sides by 6
6x / 6 = 24/ 6
x = 24/ 6
x = 4
The answer is 4
He starts by finding the sum of the exterior angles of a Pentagon, which isand then he solves to find that x is
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The sum of the exterior angle of all polygons is same.
This is equal to 360
So, when we add all the exterior angles, this is equal to 360
Thus, mathematically;
[tex]\begin{gathered} x\text{ +2x + 78 + 77 + 3x+3 = 360} \\ \\ 6x\text{ + 158 = 360} \\ \\ 6x\text{ = 360-158} \\ \\ 6x\text{ = 202} \\ \\ x\text{ = }\frac{202}{6} \\ \\ x\text{ = 33}\frac{2}{3} \end{gathered}[/tex]coefficient. | The (blank) factor that appears before a varible. constant of proportionality. | The value of the ratio between (blank) quantities that are in a proportional relationship. equation.| A mathematical statement equating two (blank). proportional. | a relationship between two quantities such that as one value increases or (blank), the other value will increase or decrease by the same multiple.
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1st statement = constant number factor
2nd statement =variable
3rd statement = expression
4 th statement = decreses
is 16.5 a rational or irrational number
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a rational number can be expressed by a fraction, if you cant is am irrational number
so
16.5 can by expressed like
[tex]\frac{165}{10}[/tex]so is a rational number, you can simplify the fraction
[tex]\frac{165}{10}\longrightarrow\frac{33}{2}[/tex]ED has a midpoint at C.If CD=6+x and CE = 2x +1, what is the length of ED?5112210
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Answer: Length of ED = 22
Since according to the question and the diagram drawn above, C is the midpoint of ED;
ED = 2CE = 2CD
CE = CD
6 + x = 2x + 1
6 - 1 = 2x - x
x = 5
CD = 6 + x = 6 + 5
CD = 11
CE = 2x + 1
CE = 2(5) + 1 = 10 + 1
CE = 11
Also note from the line drawn that ED = CE + CD
Therefore, ED = 11 + 11
ED = 22
The vertex of parabola that opens downwards is at (0,4)
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The true statement is that the points of intersection are of equal distance from the y-axis.
What is parabola?A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight line which is known as the directrix.
Given that the vertex of a parabola that opens downward is at (0, 4).
The vertex of a second parabola is at (0, -4).
Therefore, the points of intersection are the distance from the y-axis.
This is because the symmetry axis of both parabolas is x = 0, thus the intersection points must be at same distance from x- axis and y-axis.
Learn more about this parabola here:
brainly.com/question/8158213
#SPJ1
The complete question is;
The vertex of a parabola that opens downward is at (0, 4). The vertex of a second parabola is at (0, –4). If the parabolas intersect at two points, which statement must be true?
The second parabola opens downward.
The second parabola opens upward.
The points of intersection are on the x-axis.
The points of intersection are of equal distance from the y-axis.
19. Does the following system have a unique solution? Why?4x-6y=-7-2x + 3y = 18
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Given,
The equations are
[tex]\begin{gathered} 4x-6y=-7..............(1) \\ -2x+3y=18............(2) \end{gathered}[/tex]To find: Does the following system have a unique solution? Why?
Solution:
The determinant of the given equations are
[tex]\begin{gathered} \begin{bmatrix}{4} & {-6} \\ {-2} & {3}\end{bmatrix}=\begin{bmatrix}{-7} & {} \\ {18} & {}\end{bmatrix} \\ 4\times3-(-6\times-2) \\ =12-12 \\ =0 \end{gathered}[/tex]For unique solutions, the condition is
[tex]\begin{gathered} \frac{a_1}{a_2}=\frac{b_1}{b_2} \\ \frac{4}{-2}=\frac{-6}{3} \\ -2=-2 \end{gathered}[/tex]Condition satisfied.
Hence, the given equations have a unique solution.
Create a list of steps, in order, that will solve the following equation.5(x-3)² + 4 = 129Solution steps:
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We want to solve the equation
[tex]5\cdot(x-3)^2+4=129[/tex]To solve this equation, we must isolate the variable on one side of the equation. So, noticed that the term with the x has multiple things (it is raised to the second power, multiplied by five, etc) so we begin by subtracting 4 on both sides. (Step 1)
So we get
[tex]5\cdot(x-3)^2=129\text{ -4 =125}[/tex]Now we divide both sides by 5 (Step 2), so we get
[tex](x-3)^2=\frac{125}{5}=25[/tex]now we take the square root on both sides (Step 3). Then we get
[tex]\sqrt[]{(x-3)^2}=\sqrt[]{25}=5=x\text{ -3}[/tex]Finally, we add 3 on both sides (Step 4). Then we get
[tex]x=5+3=8[/tex]2 points6. Which system of questions can be used to find the number of smallboxes, x, and the number of large boxes, y, on the pallet?*Small boxes and large boxes are stacked together on a pallet.The total number of boxes is 10.• The small boxes weigh 5 pound each.The large boxes weigh 12 pounds each.The total weight of the boxes is 78 pounds.O a. x + y = 7 and 5x + 12y = 10b. x + y = 10 and 5x + 12y = 10Ο Ο Ο ΟC. X + y = 10 and 5x + 12y = 78O d. x + y = 78 and 5x + 12y = 78
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Let x be the number of small boxes and y be the number of large boxes. Then, for the first statement, we can write
[tex]x+y=10[/tex]For the second statement, we can write
[tex]5x+12y=78[/tex]Then, the answer is option C.
In the diagram, A CAT ~ADOG. Find the value of I.С161810215DT248.3I =
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we where given two sides of the triangle without the third side
lets take the given sides to a and b
then let the third side be c which is also x
let a = 16
b = 10
c = x
using pythagoras theorem
x^2 = a^2 - b^2
x^2 = 16^2 - 10^2
x^2 = 256 - 100
x^2 = 156
therefore,
x = the square root of 156
x = 12
The florist charge $31.75 for eight roses and five carnations. For one rose and three carnations,it costs $5.75. What is the cost for each type of flower?
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Let's use the variable x to represent the cost of one rose and y to represent the cost of one carnation.
If 8 roses and 5 carnations cost $31.75, we can write the following equation:
[tex]8x+5y=31.75[/tex]If 1 rose and 3 carnations cost $5.75, we can write a second equation:
[tex]x+3y=5.75[/tex]From the second equation, we have x = 5.75 - 3y.
Using this value of x in the first equation, we have:
[tex]\begin{gathered} 8(5.75-3y)+5y=31.75\\ \\ 46-24y+5y=31.75\\ \\ -19y=31.75-46\\ \\ -19y=-14.25\\ \\ y=0.75 \end{gathered}[/tex]Now, calculating the cost of one rose, we have:
[tex]x=5.75-3y=5.75-3\cdot0.75=5.75-2.25=3.5[/tex]Therefore the cost of one rose is $3.50 and the cost of one carnation is $0.75.
What should be done to these equations to solve the system of equations by elimination? [tex]2x + y = 12 \\ 5x - 3y = -3[/tex]A: Divide the first equation by 2.B: Divide the second equation by 2.C: Multiply the first equation by 3.D: Multiply the second equation by 3.
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ANSWER:
C: Multiply the first equation by 3.
STEP-BY-STEP EXPLANATION:
We have the following the system of equations:
[tex]\begin{gathered} 2x+y=12 \\ 5x-3y=-3 \end{gathered}[/tex]To solve a system of equations by means of the elimination method, it must coincide in such a way that when adding equation 1 and equation 2, one of the variables are eliminated, that is, they are canceled.
Therefore, the option in this case is to multiply the first equation by 3, in this way, the first equation remains as 3y and the second remains as -3y, since when adding them, it is 0 and the variable y is canceled.
About 53.6% of the students in the class got a AA. If 15 students got an A, estimate the number of students in the class B. If the students got an A, find the actual number of students in the class
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For A.
we have that 15 students got an A that represents the 53.6%
In this case w need to find the 100%
15 is 53.6%
x is 100%
x is the total number of students in the class
[tex]x=\frac{\frac{100}{100}\times15}{\frac{53.6}{100}}[/tex][tex]x=\frac{15\cdot100}{53.6}[/tex][tex]x=27.98[/tex]A certain state uses the following progressivetax rate for calculating individual income tax:Income ProgressiveRange ($)Tax Rate0 - 20002%2001 - 9000 5%9001 and up5.4%Calculate the state income tax owed on a $60,000per year salarytax = $[?]your answer to the nearest whole dollar amount.
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Answer:
$3240
Explanation:
If the tax rate for $9001 and up is 5.4%, we can calculate the state income tax when the income is $60,000. So,
$60,000 x 5.4% = $60,000 x 5.4/100 = $3240
Therefore, the tax will be:
$3240
Hi! I just wanted to know may you please help me on knowing how to solve an inequality?
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When given an inequality, we solve it as if we were solving an equation but there is one important consideration: If we divide or multiply by a negative number the inequality gets inverted.
Recall that to solve an equation we add, subtract, multiply, etc. to isolate the variable, in the case of inequalities we do the same process.
Example 1. x+58>36, to solve the inequality for x, we have to put the variable by itself on one side of the inequality, to do that we have to eliminate whatever is next to the variable, in the case 58 is adding, therefore, we must subtract it, but to not alter the inequality we do the same to both sides of the inequality.
Adding -58 to both sides of the inequality we get:
[tex]\begin{gathered} x+58-58>36-58, \\ x>-22. \end{gathered}[/tex]Therefore, the solution to this inequality is x>-22.
Example 2. -3x+3<4:
Adding -3 to both sides of the inequality we get:
[tex]\begin{gathered} -3x+3-3<4-3, \\ -3x<1. \end{gathered}[/tex]Dividing by -3 we get:
[tex]\begin{gathered} \frac{-3x}{-3}>\frac{1}{-3}, \\ x>-\frac{1}{3}\text{.} \end{gathered}[/tex]A woman is traveling in her car at 50 miles per hour. How far will that woman travel in fifteen minutes if her speed is constant? (Distance = Rate x Time)
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we know that
Distance=ratex Time
where
Rate=50 mph
Time=15 min
Convert the time to hours
1 hour=60 min
so
15 min=15/60=0.25 hours
substitute in the formula
Distance=50x0.25
Distance=12.50 milesgiven: ∠D ≅ ∠C and ∠CAB ≅ ∠DBA. Prove ΔABC ≅ ΔBAD
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To prove that
[tex]\Delta ABC\cong\Delta BAD[/tex]We have to prove that they share at least 2 angles.
1.
[tex]\angle D\cong\angle C[/tex]This is a given fact.
2.
Notice that
[tex]\Delta ADE\cong\Delta\text{BEC}[/tex]Since they already share two angles: DEA and CEB (They are vertically opposite)
This way, we can conclude that:
[tex]\angle DAE\cong\angle\text{CBE}[/tex]In other words, the two angles on top of A and B are equal.
Therefore, we can conclude that
[tex]\angle DAB\cong\angle CBA[/tex]And since ΔABC and ΔBAD share two of their angles, we can conclude that they also share their third and that:
[tex]\Delta ABC\cong\Delta BAD[/tex]Q.E.D
Together 2 people earn $28000. One earned $2000 more than the other. How much is the smaller income?
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Let x be the smaller income and y be the bigger income.
So, if both earn together $28,000, then:
[tex]x+y=28000[/tex]If one earns $2000 more than the other, we can say the the bigger minus the smaller is equal to 2000, that is:
[tex]y-x=2000[/tex]Now, we can solve the second equation for y and input it into the first equation:
[tex]\begin{gathered} y-x=2000 \\ y=x+2000 \end{gathered}[/tex][tex]\begin{gathered} x+y=28000 \\ x+x+2000=28000 \\ 2x=28000-2000 \\ 2x=26000 \\ x=\frac{26000}{2} \\ x=13000 \end{gathered}[/tex]Thus, the smalle income is $13,000, alternative D.
An equation is shownn-5=17What is the value for n that makes the equation true
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Simplify the equation n-5=17.
[tex]\begin{gathered} n-5=17 \\ n=17+5 \\ =22 \end{gathered}[/tex]So value of n is 22.
I did 4/cos(62°) but it didn't give me any of the answer options
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we have that
tan(62)=x/4 ------> by opposite side divided by the adjacent side
solve for x
x=4*tan(62)
x=7.5 unitsWrite an explanation of how you solved the problem. Write the explanation so that another student could follow your thought process.
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Solution
- The solution steps are given below:
[tex]\begin{gathered} \sqrt{125} \\ 125\text{ can be written as:} \\ 125=5\times25 \\ \\ \text{ Thus, we have:} \\ \sqrt{125}=\sqrt{5\times25} \\ \\ \text{ Using the surd rule that:} \\ \sqrt{ab}=\sqrt{a}\times\sqrt{b} \\ \text{ We have:} \\ \\ \sqrt{5\times25}=\sqrt{5}\times\sqrt{25} \\ \\ \therefore\sqrt{125}=\sqrt{5}\times5 \\ \\ =5\sqrt{5} \end{gathered}[/tex]Final Answer
The answer is
[tex]5\sqrt{5}[/tex]The following list gives the number of pets for each of 14 students.1, 4, 4, 2, 3, 4, 3,0,0,0,3,0,0,1Send data to calculatorFind the modes of this data set.If there is more than one mode, write them separated by commas.If there is no mode, click on "No mode."
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Given:
The number of pets for each of 14 students is,
1, 4, 4, 2, 3, 4, 3,0,0,0,3,0,0,1.
Mode: It is the number that appears the most.
In the given data,
0 appears the most that is for 5 times.
So, the mode of the given data is 0.
Answer: Mode is 0.
Charlie is saving money to buy a game. So far he has saved $16, which is one-half of the total cost of the game. How much does the game cost?
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Answer:
If $16 is just one-half of the total cost of the game, then the cost of the game must be $32.
Explanation:
See the illustration below for 1/2.
Charlie has saved $16 already which is 1/2 of the total game cost.
As we can see above, Charlie needs 1/2 more to be able to buy a game. This means Charlie needs to save an additional $16.
In total, Charlie must saved $16 + $16 = $32 to buy the game.
The game cost must be $32.
A triangle has side lengths of 13 mm 18 mm in 14 mm classify it as a cute obtuse or right
Answers
Given
Sides
13 mm, 18 mm, 14 mm
Using the Pythagorean theorem, compare the square of the longest side to the sum of the other two sides
[tex]\begin{gathered} a^2+b^2\text{ ? }c^2 \\ 13^2+14^2\text{ ? }18^2 \\ 169+196\text{ ? }324 \\ 365>324 \end{gathered}[/tex]Since the sum of the square of two sides is greater than the square of the longest side, the triangle is acute.
A zero-coupon bond is a bond that is sold now at a discount and will pay its face value at the time when it matures; no interest payments are made.A zero-coupon bond can be redeemed in 20 years for $10,000. How much should you be willing to pay for it now if you want the following returns?(a) 8% compounded daily(b) 8% compounded continuously
Answers
EXPLANATION:
We are given a zero-coupon bond that will be worth $10,000 if redeemed in 20 years time at an annual rate of 8% compounded;
(a) Daily
(b) Continuously
The formula for compounding annually is given as follows;
[tex]A=P(1+r)^t[/tex]Here the variables are;
[tex]\begin{gathered} P=initial\text{ investment} \\ A=Amount\text{ after the period given} \\ r=rate\text{ of interest} \\ t=time\text{ period \lparen in years\rparen} \end{gathered}[/tex]Note that this zero-coupon bond will yield an amount of $10,000 after 20 years at the rate of 8%. This means we already have;
[tex]\begin{gathered} A=10,000 \\ r=0.08 \\ t=20 \end{gathered}[/tex](a) For interest compounded daily, we would use the adjusted formula which is;
[tex]A=P(1+\frac{r}{365})^{t\times365}[/tex]This assumes that there are 365 days in a year.
We now have;
[tex]10000=P(1+\frac{0.08}{365})^{20\times365}[/tex][tex]10000=P(1.00021917808)^{7300}[/tex][tex]10000=P(4.95216415047)[/tex]Now we divide both sides by 4.95216415047;
[tex]P=\frac{10000}{4.95216415047}[/tex][tex]P=2019.31916959[/tex]We can round this to 2 decimal places and we'll have;
[tex]P=2019.32[/tex](b) For interest compounded continuously, we would use the special formula which is;
[tex]A=Pe^{rt}[/tex]Note that the variable e is a mathematical constant whose value is approximately;
[tex]e=2.7183\text{ \lparen to }4\text{ }decimal\text{ }places)[/tex][tex]10000=Pe^{0.08\times365}[/tex][tex]10000=Pe^{29.2}[/tex]With the use of a calculator we have the following value;
[tex]\frac{10000}{e^{29.2}}=P[/tex]Use substitution to determine the solution of the system of equations. Write the solution as an ordered pair.x + 2y = 14y = 3x – 14solution =
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the first step:
we will rewrite the second equation to look like the first one
y=3x-14
lets subtract 3x from both sides
y-3x=-14
-3x+y=-14
our system of equations will look like
x+2y=14
-3x+y=-14
however, for a substitution method we can use:
x+2(3x-14)=14
i multiply 2 with the parenthesis
x+6x-28=14
7x=28+14
7x=42, x=42/7=6
x=6
y=3x-14
y=(3x6)-14=18-14=4
solution= 6,4
Use sigma notation to represent the sum of the first eight terms of the following sequence: 4,7. 10,
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To answer this question, we need to check the kind of sequence here. We have that the first three elements of the sequence are:
[tex]4,7,10[/tex]If we have the difference between the second element and the first element, and the difference between the third element and the second element, we have:
[tex]7-4=3,10-7=3[/tex]Thus, we have a common difference of 3. This is an arithmetic sequence. Then, we also have that:
[tex]a_n=a_1+(n-1)d[/tex]This is the formula for finding a general term in an arithmetic sequence, where:
• an is any term, n, in the sequence.
,• a1 is the first term in the sequence.
,• n the number of the term in the sequence.
,• d is the common difference of the sequence.
In this way, we have:
a1 = 4
d = 3