In a normal distribution, about _% of the data lie within 1 standard deviation below and 2 standard deviations above the mean
Answers
ANSWER
81.8%
EXPLANATION
The percentage of data that lies between 1 standard deviation below and 2 standard deviations above the mean is the sum of the percentages between those two values,
So this is,
[tex]34.1\%+34.1\operatorname{\%}+13.6\operatorname{\%}=81.8\operatorname{\%}[/tex]Hence, 81.8% of the data lies within 1 SD below and 2 SD above the mean.
Related Questions
Write the first four terms in the expansion of: (x + y)^8
Answers
Given:
[tex](x+y)^8[/tex]We will write the first four terms of the expansion.
the general rule of the expansion is as follows:
[tex](x+y)^n=x^n+n*x^{n-1}*y+...+nCr*x^{n-r}*y^r+...+y^n[/tex]So, the answer will be, the first four terms are:
[tex]x^8+8x^7y+28x^6y^2+56x^5y^3[/tex]Given \sin A=-\frac{6}{\sqrt{61}}sinA=−
61
6
and that angle AA is in Quadrant IV, find the exact value of \cos AcosA in simplest radical form using a rational denominator.
Answers
The value of Cos A is postive in fourth quadrant , Cos A=5/[tex]\sqrt{61}[/tex]
Here we can solve the problem using the Pythagoras theorem . Hence we draw triangle with the details given in the question.
It is given that A is lying in IV quadrant . So that Sin A is less than zero and thus Cos A will be positive value.
As the value of sinθ= -6/[tex]\sqrt{61}[/tex]=Altitude/ Hypotenuse . Thus here with the help of Pythagoras theorem we can solve the problem.
That is ,
[tex]Base^{2} =Hypotenuse ^{2} -Altittude ^{2} \\B^{2} =\sqrt{61}^{2} -36\\B= \sqrt{25}=5[/tex]
We know that Base\Hypotenuse =Cos A. Which is positive and in fourth quadrant .
Thus we get answer as Cos A=5/[tex]\sqrt{61}[/tex]
To know more about Pythagoras theorem here:
https://brainly.in/question/2829237
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A translation maps ABC onto A'B'C'. Use the coordinates A(-3, 0), B(4, 2), B'(0, 0), and C'(6, 3) to determine the translation vector and thecoordinates of C.
Answers
Given that a translation maps triangle ABC onto A'B'C'.
with coordinates;
[tex]\begin{gathered} A(-3,0) \\ B(4,2) \\ B^{\prime}(0,0) \\ C^{\prime}(6,3) \end{gathered}[/tex]Let us find the translation vector;
[tex]\begin{gathered} B(4,2)\rightarrow B^{\prime}(0,0) \\ \\ <0-4,0-2> \\ <-4,-2> \end{gathered}[/tex]Therefore, the translation vector is;
[tex]<-4,-2>[/tex]Solving for point C;
[tex]\begin{gathered} C(x,y)\rightarrow C^{\prime}(x-4,y-2)=C^{\prime}(6,3) \\ \\ x-4=6 \\ x=6+4 \\ x=10 \\ y-2=3 \\ y=3+2 \\ y=5 \\ C(10,5) \end{gathered}[/tex]Therefore, the coordinate of C is;
[tex]undefined[/tex]Keith needs to build a bridge across a pond . he has been able to collect the following measurements. about how long his bridge need to be ?a) 11. 9 ftb) 8.4 ftc) 7. 7 ftd) 6.4 ft
Answers
In order to find the length of the bridge, we can use the tangent relation of the angle 50°.
The tangent relation is the length of the opposite side to the angle over the length of the adjacent side to the angle.
So we have that:
[tex]\begin{gathered} \tan (50\degree)=\frac{x}{10} \\ 1.1917=\frac{x}{10} \\ x=10\cdot1.1917 \\ x=11.917 \end{gathered}[/tex]So the length of the bridge is 11.9 ft, therefore the correct option is A.
In a recent year, 29.7% of all registered doctors were female. If there were 42,300 female registered doctors that year, what was the total number of registered doctors?Round your answer to the nearest whole number.
Answers
ANSWER
142,424 doctors
EXPLANATION
We have that 29.7% of all registered doctors were female and 42,300 female doctors were registered that year.
Let the total number of registered doctors that year be x.
This means that 29.7% of x is 42,300.
Therefore:
[tex]\begin{gathered} \frac{29.7}{100}\cdot\text{ x = 42300} \\ \text{Divide both sides by 29.7 and multiply by 100:} \\ x\text{ = }\frac{\text{42300 }\cdot\text{ 100}}{29.7} \\ x\text{ }\cong\text{ 142,424 doctors} \end{gathered}[/tex]A total of 142,424 doctors were registered that year.
a) Write a multiplication expression without exponents that is equivalent to 3^3b) how many factors of 3 did you write
Answers
hello
the question given is to find an expression that's equivalent to the exponent of 3^3
[tex]3^3=27[/tex]now we just simply look for another way to write 3^3 to give 27
[tex]3^3=3\times3\times3[/tex]the answer to the question is 3*3*3
b)
the number of factors of three here is one
Which of these expressions CANNOT be simplified by combining like terms? CLEAR CHECK 5ab3 +7 - 3a²b2 + a'b – 10 5ab3 + 3a2b2 + ab - 10 5ab3 + 3a2b2 + a363 - 10ab 5ab3 + 26(3ab2) + a’b – 10
Answers
Which of these expressions CANNOT be simplified by combining like terms?
The answer:
to simplify the terms , the terms must be similar like ab and 3ab the result will be 4ab.
So for our giving options:
1) 5ab3 +7 - 3a²b2 + a'b – 10
2) 5ab3 + 3a2b2 + ab - 10
3) 5ab3 + 3a2b2 + a363 - 10ab
4) 5ab3 + 26(3ab2) + a’b – 10
so, as shown at the options:
option 1) Can be simplified to 5ab3 - 3a²b2 + a'b – 3
becuse it has only two like terms {7 - 10}
Option 2) CANNOT be simplified
Becuse, it is not contain like terms
Option 3) CANNOT be simplified
Becuse, it is not contain like terms
Option 4) CANNOT be simplified
Becuse, it is not contain like terms
So, the answer is all: All expressions CANNOT be simplified by combining like terms except the first expressions.
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Solve this system of equations:3x - 2y = -8y=3/2x - 2
Answers
The system of equations that we have are:
3x - 2y = -8 ________(1)
y = 3/2x - 2 ________(2)
Multiply both sides in (2) by 2x:
=> 2xy = 3 - 4x ______(3)
From (1), make y the subject of the formula:
3x + 8 = 2y
=> y = 3x/2 + 4
Put this into (3):
2x(3x/2 + 4) = 3 - 4x
Open the bracket:
[tex]3x^2\text{ + 8x = 3 - 4x}[/tex]Collect like terms:
[tex]3x^2\text{ + 8x + 4x = 3}[/tex][tex]3x^2\text{ + 12x - 3 = 0}[/tex]We
The perimeter of a rectangle is 84. The length is 2 1/2 times the width. Find the dimensions of the rectangle.
Answers
The Solution:
Given:
The perimeter of a rectangle is 84.
We are asked to find the dimensions ( that is, length and width) of the rectangle.
Let the length of the rectangle be L and W for the width.
So,
[tex]L=2\frac{1}{2}of\text{ W}=\frac{5}{2}W[/tex]By formula, the perimeter of a rectangle is:
[tex]\begin{gathered} P=2(L+W) \\ \\ In\text{ this case,} \\ P=perimeter=84 \\ W=width=? \\ L=length=\frac{5}{2}W \end{gathered}[/tex]Substitute these values in the formula, we get:
[tex]84=2(\frac{5}{2}W+W)[/tex]Dividing both sides by 2, we get:
[tex]\begin{gathered} 42=\frac{5}{2}W+W \\ \\ 42=\frac{5W+2W}{2} \\ \\ 42=\frac{7W}{2} \end{gathered}[/tex]Cross multiplying, we get:
[tex]\begin{gathered} 7W=2\times42 \\ 7W=84 \end{gathered}[/tex]Dividing both sides by 7, we get:
[tex]W=\frac{84}{7}=12[/tex]To find the length L, we shall put 12 for W.
[tex]L=\frac{5}{2}W=\frac{5}{2}\times12=5\times6=30[/tex]Therefore, the dimensions of the rectangle is 30 by 12.
Length = 30 units
Width = 12 units
what is -3 2 / 3 + (-2 5/6) need help asap!!
Answers
A piggy bank contains 4 quarters, 18 dimes, 10 nickels, and 8 pennies. A coin is chosen at random, not replaced, then another is chosen. Find each probability. P(worth at least 10 cents, then penny)
Answers
The probability of choosing a coin that is worth at leas 10 cents is:
[tex]P=\frac{22}{40}=\frac{11}{20}[/tex]then the probability of obtaining a penny is:
[tex]P=\frac{8}{39}[/tex]Then the probability to obtain a coin of at least 10 cents and then a penny is:
[tex]P=\frac{11}{20}\cdot\frac{8}{39}=\frac{22}{195}[/tex]-5n = 20Help don’t have time
Answers
Simplify the equation.
[tex]\begin{gathered} -5n=20 \\ n=\frac{20}{-5} \\ =-4 \end{gathered}[/tex]So value of n is -4.
2. Given: -2x =4y +62(2y+3) =3x -5What is the solution (x,y)?I
Answers
this is a 2x2 system of equations.
Let:
-2x = 4y + 6 (1)
and
2(2y+3) = 3x - 5 (2)
Let's rewrite (1) as:
2x + 4y = -6 (1)
and (2) as:
3x - 4y = 11 (2)
Now, from (1)
Let's solve for x:
2x + 4y = -6
Subtract 4y from both sides:
2x + 4y - 4y = -6 - 4y
2x = -6 - 4y
Divide both sides by 2:
2x/2 = (-6 - 4y)/2
x = -3 - 2y (3)
Replacing (3) into (2)
3x - 4y = 11
3(-3 - 2y) - 4y = 11
Using distributive property:
-9 - 6y - 4y = 11
Add like terms:
-10y - 9 = 11
Add 9 to both sides:
-10y - 9 + 9 = 11 + 9
-10y = 20
Divide both sides by -10:
(-10y)/-10 = 20/-10
y = -2
Finally, replace the value of y into (3)
x = -3 - 2y
x = -3 - 2(-2)
x = -3 + 4
x = 1
Therefore the solution is :
x= 1 and y=-2
(x,y) = (1,-2)
hi I am working on an assignment and i came up on a question that I did not understand please help me understand and answer this please
Answers
Solution
Step 1:
Write the two equations:
2x + 3y = 12
2x + y = 6
2x = 6 - y
[tex]\begin{gathered} 6\text{ - y + 3y = 12} \\ 2y\text{ = 12 - 6} \\ \\ 2y\text{ = 6} \\ \\ y\text{ = 3} \end{gathered}[/tex]Answer
The first step in solving by substitution would be to solve the second equation for x, since the coefficient is 2.
First
y = 6 - 2x
y = 3
Someone please help me on this type of problem, I tried multiple times but still got correct answer. :(
Answers
ANSWER
P(both girls) = 3/20
EXPLANATION
The probability of the event E where the teacher selects one student from each grade and both are girls is:
[tex]P(E)=P(girl\text{ 7th)}\cdot P(girl\text{ 8th)}[/tex]The probability of selecting a girl from 7th grade is:
[tex]P(\text{girl 7th)}=\frac{\text{ \# of girls in 7th grade}}{\text{ \# of students in 7th grade}}=\frac{5}{10}=\frac{1}{2}[/tex]The probability of selecting a girl from 8th grade is:
[tex]P(\text{girl 8th)}=\frac{\text{ \# of girls in8th grade}}{\text{ \# of students in 8th grade}}=\frac{3}{10}[/tex]The probability of event E is then:
[tex]P(E)=\frac{1}{2}\cdot\frac{3}{10}=\frac{3}{20}[/tex]A study of a local high school tried to determine the mean amount of money that eachstudent had saved. The study surveyed a random sample of 74 students in the highschool and found a mean savings of 2600 dollars with a standard deviation of 1400dollars. At the 95% confidence level, find the margin of error for the mean, roundingto the nearest whole number. (Do not write +).
Answers
To calculate the margin of error, we use the formula:
[tex]M_{\gamma}=z_{\gamma}\sqrt[]{\frac{\sigma^2}{n}}[/tex]So, we got n, the number of students, sigma, the standard deviation, and gamma, the confidence level. z for 95% is 1.64, so:
[tex]M_{95\text{ \%}}=1.64\sqrt[]{\frac{1400^2}{74}}=1.64\frac{1400}{\sqrt[]{74}}=266.9\approx267[/tex]So, the margin of error goes from mean - 267 to mean + 267:
[tex]undefined[/tex]Look at the system of equations shown in the graph. What is the solution to the system?
Answers
Solution
A solution to a system of linear equations is the point of intersection of both lines when graphed.
Parallel lines do not ever cross so there are zero solutions.
However, there could be a chance that there is a solution because often, the equation of two lines that look parallel are actually the same line, in which case the system will produce an infinite number of solutions.
The way to be sure is just to pick an x value randomly and put it in both equations and see if the answers are equal. If it is really two parallel lines, they will not be equal otherwise, they will be equal.
Hence from the graph, we will first get the equation for both lines
Line 1
[tex]\begin{gathered} y_2=-4 \\ y_1=2 \\ x_2=0 \\ x_1=-2 \\ \text{Hence the equation of the line is given as} \\ y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)_{} \end{gathered}[/tex][tex]\begin{gathered} y\text{ -(2)=}\frac{-4-(2)_{}}{0-(-2)}(x-(-2)) \\ y-2=\frac{-6}{2}(x+2) \\ y-2\text{ = -3x}-6 \\ y\text{ = -3x -}6+2 \\ y\text{ = -3x-4} \end{gathered}[/tex]For line 2
[tex]\begin{gathered} y_1=4 \\ y_2=\text{ 1} \\ x_2=0 \\ x_1=-1 \\ \text{The equation of the line is} \\ y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ \text{After susbstitution} \\ y\text{ -4=}\frac{1-4}{0-(-1)}(x-(-1)) \\ y-4\text{ = }\frac{-3}{1}(x+1) \\ y-4=-3x-3 \\ y\text{ = -3x-3+4} \\ y\text{ = -3x+1} \end{gathered}[/tex]So picking a random value of x= -1
we will have
[tex]\begin{gathered} \text{Line 1} \\ y\text{ = -3(-1)-4} \\ y=3-4 \\ y\text{ = -1} \\ \text{Line 2} \\ y\text{ = -3(-1)+1} \\ y=\text{ 3+1} \\ y\text{ =4} \end{gathered}[/tex]Since both values of y using a constant random value of x gives us different answers, the lines, therefore, are not images of each other and the system has no solution.
Final answer------ No solution
during blowing pratice marley rolled 14 strikes out of 70 attemps what percent of marleys attempts were strikes enter anwser
Answers
we know that
To find out the percentage, divide the number of strikes by the total attemps, and multiply by 100
so
(14/70)(100)=20%
therefore
the answer is
20%I sent pic for help. This question has 4 parts
Answers
Explanation
Skewness refers to a distortion or asymmetry that deviates from the symmetrical bell curve, or normal distribution, in a set of data.
There are two main things that make a distribution skewed left: The mean is to the left of the peak. This is the main definition behind “skewness”, which is technically a measure of the distribution of values around the mean. The tail is longer on the left.
A "skewed right" distribution is one in which the tail is on the right side. A "skewed left" distribution is one in which the tail is on the left side. The above histogram is for a distribution that is skewed right.
From the given question
Part B
Since the answer to part A is option C
We can infer from the definition above that the tail is on the right-hand side
Therefore, It is Right-Skewed.
In the diagram, RSTU ~ ABCD. Find the ratio of their perimeter
Answers
The ratio of their perimeters is the same ratio between corresponding sides.
Looking at the image, the side ST corresponds to the side BC.
Calculating their ratio, we have:
[tex]\begin{gathered} \text{ratio}=\frac{ST}{BC} \\ \text{ratio}=\frac{12}{8} \\ \text{ratio}=\frac{3}{2} \end{gathered}[/tex]So the ratio of their perimeters is 3 : 2
Given the equilateral triangle ABC; AE, BD, & CF are altitude intersecting at point G. How many right triangles are in the diagram?
Answers
Solution
Given the equilateral triangle ABC;
The following are the numbers of right triangles:
[tex]\begin{gathered} CFB \\ CFA \\ CEA \\ AEB \\ CDB \\ BDA \\ FHD \\ FHE \\ DJE \\ DJF \\ EID \\ EIF \end{gathered}[/tex]There are 12 right triangles in the diagram.
solving for x - (6x -5) = 2x+6 2
Answers
we have
[tex]\frac{6x-5}{2}=2x+6[/tex]step 1
Multiply by 2 both sides
[tex]\begin{gathered} 6x-5=2(2x+6) \\ 6x-5=4x+12 \end{gathered}[/tex]step 2
Group terms
[tex]6x-4x=12+5[/tex]Combine like terms
[tex]2x=17[/tex]divide by 2 both sides
[tex]\begin{gathered} x=\frac{17}{2} \\ x=8.5 \end{gathered}[/tex]Verify
substitute the value of x in the original expression
[tex]\begin{gathered} \frac{6(8.5)-5}{2}=2(8.5)+6 \\ 23=23 \end{gathered}[/tex]is ok
the value of x satisfy the equation
7.8.1y varies directly as x. y = 50 when x= 5. Find y when x= 16.y =(Simplify your answer.)
Answers
If y varies directly as x
x=5 when y= 50
so we can assumme the next equation
y=10x
so
x=16 y=10(16)=160
9+1=91, 8+2=75, 7+3=61, 6+4=49, 5+5=39, 3+7=?
Answers
We can note the following pattern:
[tex]\begin{gathered} 9^2+1+9=81+10=91 \\ 8^2+2+9=64+11=75 \end{gathered}[/tex]and
[tex]7^2+3+9=49+12=61[/tex]Similarly,
[tex]\begin{gathered} 6^2+4+9=36+13=49 \\ 5^2+5+9=25+14=39 \end{gathered}[/tex]So, our pattern matches with the given results.
By applying this pattern to the question, we have
[tex]3+7\Rightarrow3^2+7+9=9+16=25[/tex]Therefore, the answer is: 7+3=25
Find the smallest positive integer N that satisfies all of the following conditions: • N is a square.
• N is a cube.
• N is an odd number.
• N is divisible by twelve different prime numbers. How many digits does this number N have?
Answers
Answer:
16
Step-by-step explanation:
first primes: 2,3,5,7,11,13,17,19,23,29,31,37,41
then,cube 2 and square 3 to get 3.6510032e+15 which has 15+1=16 digits
find the derivative of [tex]h(x) = {4}^{ \frac{x}{2} } \sin(2x) [/tex]
Answers
The given expression is:
[tex]\begin{gathered} \\ h(x)={4}^{\frac{x}{2}}\sin (2x) \end{gathered}[/tex]To find the derivative, use the product rule:
[tex]\begin{gathered} \frac{dh}{dx}=\text{ U}\frac{dV}{dx}+V\frac{dU}{dx} \\ U=4^{\frac{x}{2}} \\ \frac{dU}{dx}=\text{ }\frac{4^{\frac{x}{2}}\ln 4}{2} \\ V\text{ = sin(2x)} \\ \frac{dV}{dx}=\text{ 2}\cos (2x) \end{gathered}[/tex]Substitute, U, V, dU/dx, and dV/dx into the product rule given above:
[tex]undefined[/tex]simply 3y- 2y/ - 3/4
Answers
Given:
[tex]3y-\frac{2y-3}{4}[/tex]The difference of w and 3 is less than 29
Answers
The difference of w and 3 is less than 29
so
w-3 < 29the image is downloading now
Problem N 2
A number x increased by 4 is greater than -19
x+4 > -19Problem N 3
The quotient of c and 2 is at least -23
[tex]\frac{c}{2}\ge-23[/tex]4. Solve the equation using square roots.x2 + 10 = 9x^2+10x=9
Answers
Given:
The area of the playground is 204 square yd.
The width of the playground is 5 yd longer than its length.
Let, w be the with of the playground and l is length.
[tex]w=5+l[/tex]The area is given as,
[tex]\begin{gathered} A=l\times w \\ 204=l\times(l+5) \\ l^2+5l-204=0 \\ Use\text{ quadratic formula:} \\ l=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a},a=1,b=5,c=-204 \\ l=\frac{-5\pm\sqrt[]{5^2-4\times1\times(-204)}}{2} \\ l=\frac{-5\pm\: 29}{2} \\ l=\frac{-5+29}{2},l=\frac{-5-29}{2} \\ l=12,l=-17 \end{gathered}[/tex]As length can not be negative.
Hence, length = l =12 yd
Width = w = l +5 = 12+5 =17 yd.
Answer: owidth is 17 yds.
(8 + 9m) -3 =step by step how to solve
Answers
Given the expression :
[tex](8+9m)-3[/tex]We need to simplify the expression , so, combine the like terms
[tex]\begin{gathered} 8+9m-3 \\ =(8-3)+9m \\ \\ =5+9m \end{gathered}[/tex]