If a normally distributed data set has a mean of81 and a standard deviation of 6, which of thefollowing represents approximately 95% of thedata?
Answers
95% of the data is represented as 69 to 93 (option G)
Explanation:Given:
mean of data = 81
standard deviation = 6
To find:
The option that represents 95% of the data
To determine the right option, we will apply the empirical rule (68-95-99.7%):
68% of the data will fall within 1 standard deviation
95% of the data will fall within 2 standard deviation
99.5% of the data will fall within 3 standard deviation
[tex]\begin{gathered} 2\text{ standard deviation is represented as:} \\ \mu\text{ }\pm\text{ 2\sigma} \\ where\text{ \mu = mean, \sigma = standard deviation} \end{gathered}[/tex]substitute the values:
[tex]\begin{gathered} μ\pm2σ\text{ = 81 }\pm\text{ 2\lparen6\rparen} \\ =\text{ 81 }\pm\text{ 12} \\ 81\text{ }\pm\text{ 12 means 81 - 12 , 81 + 12} \\ =\text{ 69, 93} \\ This\text{ means 95\% of the data is represented from 69 to 93 \lparen option G\rparen} \end{gathered}[/tex]Related Questions
SHOW THE PROPORTION YOU ARE SETTING UP.Four out of 10 adults in a certain city buy their drugs at large drug stores. If this city has 34,000 adults, how many of these adults would you expectto buy their drugs at large drug stores?
Answers
You know that 4 out of 10 adults buy their drugs at large drug stores. To calculate the value of the proportion you have to divide 4 by 10
[tex]\begin{gathered} p=\frac{4}{10} \\ p=0.4 \end{gathered}[/tex]The city has n=34,000 adults, to determine the expected number of adults that buy at large drugstores, you have to multiply the total number of adults by the proportion:
[tex]E(X)=np[/tex]n=34,000 and p=0.4
[tex]\begin{gathered} E(X)=34000\cdot0.4 \\ E(X)=13600 \end{gathered}[/tex]Out of the 34,000 you could expect 13,600 adults to buy at large drug stores.
In circle C with m BCD= 48°, find the angle measure of minor arc BD.DB
Answers
Notice that angle BCD is a central angle, therefore, the measure of its arc will be the same as the measure of the angle, therefore, the measure of the minor arc BD is 48 degrees
i forgot how i solved this, what im getting is 4x -24 which is wrong
Answers
Answer:
[tex](4x^2+22x-12)cm^2[/tex]Explanation:
From the given figure:
• The base of the triangle, b = (4x-2) cm
,• The perpendicular height, h = (2x+12) cm
The area of a triangle is calculated using the formula:
[tex]A=\frac{1}{2}bh[/tex]Substitute the given expressions:
[tex]\begin{gathered} A=\frac{1}{2}(4x-2)(2x+12) \\ Factor\text{ }4x-2\implies4x-2=2(2x-1) \\ A=\frac{1}{2}\times2(2x-1)(2x+12) \\ A=(2x-1)(2x+12) \end{gathered}[/tex]Next, open the brackets:
[tex]\begin{gathered} A=2x(2x+12)-1(2x+12) \\ =4x^2+24x-2x-12 \\ =(4x^2+22x-12)cm^2 \end{gathered}[/tex]The area of the triangle is:
[tex](4x^2+22x-12)cm^2[/tex]V11, -14 and w -19, 15 are the influence of the line segment what is the midpoint M of that line segment right the coordinates as decimals are integers
Answers
Step 1: Problem
Mid-point of V ( 11, -14 ) and W ( -19, 15 )
Step 2: Concept
[tex]\begin{gathered} coordinatesofthe\text{mid}-po\text{ int = ( x , y )} \\ x\text{ = }\frac{x_1+x_2}{2} \\ y\text{ = }\frac{y_1+y_2}{2} \end{gathered}[/tex]Step 3: Method
Substitute the given data to find the coordinates of the mid-point
Given data
x1 = 11
y1 = -14
x2 = -19
y2 = 15
[tex]\begin{gathered} x\text{ = }\frac{-\text{ 19 + 11}}{2}\text{ = }\frac{\text{ -}8}{2}\text{ = -}4 \\ y\text{ = }\frac{15\text{ +(-14)}}{2}\text{ = }\frac{1}{2}\text{ = }0.5 \end{gathered}[/tex]Step 4: Final answer
The coordinates of the mid-point = ( -4 , 0.5 )
A piece of wire 5/4 m long is to be cut into 20 pieces of the same length. What is the length of each piece?Each piece is ____ m long.(Simplify your answer. Type an integer or a fraction.)
Answers
When we divide a fraction by a number, that's equivalent to multiplying the first fraction by the inverse of that number.
In this problem, we need to divide the fraction 5/4 by 20. So we obtain:
[tex]\frac{5}{4}\colon20=\frac{5}{4}\cdot\frac{1}{20}[/tex]Now, we need to multiply the numerator of the first fraction by the numerator of the second one, and the denominator of the first fraction by the denominators of the second one:
[tex]\frac{5}{4}\cdot\frac{1}{20}=\frac{5\cdot1}{4\cdot20}=\frac{5}{80}[/tex]Now, we need to simplify the answer. To do so, we can divide both the numerator and the denominator by 5:
[tex]\frac{5\colon5}{80\colon5}=\frac{1}{16}[/tex]Therefore:
Each piece is 1/16 m long.
what is the graph of x= 1 ?
Answers
The given equation x = 1 represents a horizontal lines that passes thourgh (1, 0).
Hence, the graph isThe answer is D.A student finished 45 of her homework problems in class. If the ratio of problems shefinished to problems she still had left was 9:4, how many homework problems did shehave total?
Answers
The ratio between the amount of problems she finished and the problems she still had left is given by the division between those amount. Since this ratio is 9:4, if we call the amount of homework she still has left as x, we have the following relation
[tex]\frac{45}{x}=\frac{9}{4}[/tex]Solving for x, we have
[tex]\begin{gathered} \frac{45}{x}=\frac{9}{4} \\ \frac{x}{45}=\frac{4}{9} \\ x=\frac{4}{9}\cdot45 \\ x=\frac{4\cdot45}{9} \\ x=\frac{180}{9} \\ x=20 \end{gathered}[/tex]She still has 20 problems left to solve. The total amount of problems is given by the sum between the problems she already finished and the problems left to solve, then, the total amount of problems is
[tex]45+20=65[/tex]65 problems.
hello can u help me please5.Admission to the Basketball Hall of Fame in Springfield is $5.00 per student. A group of students bought admission tickets. One student spent an extra $9.00 for a poster. The total amount they spent was $34.00. How many students were in the group?a.4b.5c.6d.7
Answers
Given:
The price per student for the admission, m=$5.
Extra amount spent by a student, c=$ 9.
Total amount spent, T=$34.
Let x be the number of students. Then, the expression for the total amount is,
[tex]T=mx+c[/tex]Substitute values and solve for x.
[tex]\begin{gathered} 34=5x+9 \\ 34-9=5x \\ 25=5x \\ x=\frac{25}{5} \\ x=5 \end{gathered}[/tex]Therefore, the number of students is 5.
Option (b) is correct.
i inserted a picture of the question can you make it very shorta -4 b 8c 4d -8
Answers
a. -4
Explanation
the average rate of change is given by:
[tex]\begin{gathered} rateofch=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ where \\ P1(x_1,y_1)\text{ is the start point} \\ P2(x_2,y_2)\text{ is the end point} \end{gathered}[/tex]then
Let
[tex]\begin{gathered} x_1=1 \\ f(x_1)=0 \end{gathered}[/tex]and
[tex]\begin{gathered} x_2=3 \\ f(x_2)=-8 \end{gathered}[/tex]hence
P1(1,0)
P2(3,-8)
now, replace in the formula
[tex]\begin{gathered} rateofch=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ \text{rate of change=}\frac{-8-0}{3-1}=\frac{-8}{2}=-4 \\ \text{rate of change=-}4 \end{gathered}[/tex]therefore, the answer is
a. -4
I hope th
The side walls of a regular quadrilateral pyramid are equilateral triangles with sides equal to 8 cm. Calculate the pyramid:1) the sum of the lengths of all the sides;2) the area of the base;3) the length of the height of the side wall;4) the area of the side wall.
Answers
a) 64cm
b) 64 square cm
c) 4√3 cm
d) 16√3 square cm
Explanations:A regular quadrilateral pyramid with equilateral triangles is as shown below;
1) The pyramid has 8 side lengths, hence the sum of the length of all the sides is given as:
[tex]\begin{gathered} Sum\text{ of side lengths}=8\times8cm \\ Sum\text{ of side lengths}=64cm \end{gathered}[/tex]2) Since the triangular sides are equilateral, the base of the pyramid will be a square with side length of 8cm. The area of the base is expressed as:
[tex]\begin{gathered} A=length\times length \\ A=8cm\times8cm \\ A=64cm^2 \end{gathered}[/tex]3) Since one side wall is an equilateral triangle, the height will be perpendicular to the base as shown:
In order to determine the height, we will use the Pythagorean theorem as shown:
[tex]\begin{gathered} 8^2=h^2+4^2 \\ h^2=8^2-4^2 \\ h^2=64-16 \\ h^2=48 \\ h=\sqrt{48}=4\sqrt{3}cm \\ \end{gathered}[/tex]4) The area of the side wall is equivalent to the area of the triangle expressed as:
[tex]\begin{gathered} Area\text{ of side wall}=\frac{1}{2}\times base\times height \\ Area\text{ of side wall}=\frac{1}{2}\times8cm\times4\sqrt{3} \\ Area\text{ of side wall}=16\sqrt{3}cm^2 \end{gathered}[/tex]S/14 = 14 a. -196 b. 196 C. 28 d. 0
Answers
In the given equation, the value of S is divided by 14, so to calculate the value of S you have to invert the operation, that is, multiply it by 14 so that both operations cancel each other.
And, for the equality to be valid, all operations made in one side of the = sign must be done on the other side as well. So, multiply both sides of the equation by 14:
[tex]\begin{gathered} \frac{14S}{14}=14\cdot14 \\ S=196 \end{gathered}[/tex]S=196 the correct choise is b.
WILL MARK BRAINLIEST Rectangle PQRS is shown above. Point C is the center of the rectangle.Maggle claims that there are transformations that preserve the length of the rectangle's sides. Which of the following transformations could be used to support Maggie's claim? select all that apply1.) a translation of 10 units to the right2.) a rotation of 90' clockwise about vortex Q3.) a reflection over the side RS4.) a diation of scale factor 1 through contor5.) a vertical stretch of scale factor 2 through contor C
Answers
With the given options;
(1) A translation of 10 units to the right will only map the rectangle onto a different location, but the lengths would remain as it were
(3) A reflection over the side RS will turn the rectangle into a mirror reflection of itself, and this means the sides remain the same measurement but is now being observed from the opposite side (but top now bwcomes bottom and vice versa).
(4) A dilation of scale factor 1 through center
solve equation. -2(y-1)=9
Answers
y = -7/2
Explanation:-2(y-1)=9
expand the bracket:
-2 × y -2 × -1 = 9
-2y + 2 = 9
collect like terms:
-2y = 9 -2
-2y = 7
Divide both sides by -2:
-2y/-2 = 7/-2
y = -7/2
List the potential rational zeros of the polynomial function. Do not find the zeros.f(x) = -4x^4 + 2x^2 - 3x + 6A± , ± , ± , ± , ± 1, ± 2, ± 3, ± 4, ± 6B± , ± , ± , ± , ± 1, ± 2, ± 3, ± 6C± , ± , ± , ± , ± , ± 1, ± 2, ± 4D± , ± , ± , ± , ± , ± 1, ± 2, ± 3, ± 6
Answers
Answer:
±1,±2,±3 and ±6
Explanation:
We make use of the Rational Zero theorem below:
If a polynomial has integer coefficients, then every rational zero of f(x) has the form p/q where p is a factor of the constant term and q is a factor of the leading coefficient.
Given the function:
[tex]f\mleft(x\mright)=-4x^4+2x^2-3x+6[/tex]The steps to follow are given below.
Step 1: Determine all factors of the constant term and all factors of the leading coefficient.
The constant term is 6: Factors are ±1,±2,±3 and ±6
The leading coefficient is -4: Factors are ±1,±2, and ±4.
Step 2: Determine all possible values of p/q.
[tex]\begin{gathered} \frac{p}{q}=\pm\frac{1}{1},\pm\frac{2}{1},\pm\frac{2}{2},\pm\frac{3}{1},\pm\frac{6}{1},\pm\frac{6}{2} \\ =\pm1,\pm2,\pm1,\pm3,\pm6,\pm3 \\ =\pm1,\pm2,\pm3,\pm6 \end{gathered}[/tex]Therefore, the potential zeros are: ±1,±2,±3 and ±6.
Lucille wrote three numbers between 0.75 and 0.76 what numbers could she have written?
Answers
As an answer to this question, any decimal between 0.75 and 0.76 will do.
So let us choose the three numbers at random.
0.751 , 0.754, and 0.756 will do.
A total of $54,000 is invested at an annual interest rate of 5.25%. Find the balance after 6 years if it is compounded monthly.
Answers
Using the compound interest formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where:
A = Amount
P = Principal = 54000
r = Interest rate = 5.25% = 0.0525
n = Number of times the interest is compounded per year = 12
t = Number of years = 6
So:
[tex]\begin{gathered} A=54000(1+\frac{0.0525}{12})^{12\cdot6} \\ A\approx73943.18 \end{gathered}[/tex]Answer:
The balance is $73943.18
There are a total of 37800 members at club A and the ratio of club A to club B is 20:13. The ratio of 40 and older group is 70% of club B the ratio of under 40members in club A to club B is 176:39
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2.) Your unusual boss decided to offer you a fourthoption to complicate your decision.Your payment would be described by the functionP(x) = 95,000x + 200,000, with x representingdays you work and P representing dollars you earn.Explain the meaning of the function based on thissituation and then decide if you would take this optionover the other three choices.On the next slide, you use a graph to support yourdecision.
Answers
P(x) = 95,000x + 200,000
1. Consider the following functions. f(x) = 3x2 + x + 2 g(x) = 4x2 + 2(3x – 4) h(x) = 5(x2 - 1) a. Find f (x) - g(x). b. Find g(x) - h(x).
Answers
a.
Let's write function g(x) better:
[tex]g(x)=4x^2+2(3x-4)=4x^2+6x-8[/tex]Now we can do the substraction easier
[tex]f(x)-g(x)=(3x^2+x+2)-(4x^2+6x-8)_{}[/tex][tex]f(x)-g(x)=3x^2+x+2-4x^2-6x+8[/tex][tex]f(x)-g(x)=(3-4)x^2+(1-6)x+2^{}+8[/tex][tex]f\mleft(x\mright)-g\mleft(x\mright)=-x^2-5x+10[/tex]That's answer a
b.
We write h(x) better too:
[tex]h(x)=5(x^2-1)=5x^2-5[/tex]And do the same as before:
[tex]g(x)-h(x)=(4x^2+6x-8)-(5x^2-5)[/tex][tex]g(x)-h(x)=4x^2+6x-8-5x^2+5[/tex][tex]g(x)-h(x)=(4-5)x^2+6x-8+5[/tex][tex]g(x)-h(x)=-x^2+6x-3[/tex]That's answer b
Its says for pi do 3.14 and round to tje nearest hundredth.
Answers
EXPLANATION
Measure of the rectangular window:
length = 24 inches
width = 18 1/4 inches = 73/4 inches = 18.25 inches
The area is given by the following relationship:
[tex]\text{Area}_{wi\text{ndow}}=\text{length}\cdot\text{width}=24\cdot18.25=438in^2[/tex]The picture is as follows:
Find the equation of the line through the given points. (-8, 6) and (-8, 0)
Answers
The equation of a line is typically written as y=mx+b, where m is the slope and b the y-intercept.
The slope can be calculated like this:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this case you have x1=-8, y1=6, x2=-8 and y2=0. Replace this values on the slope formula
[tex]m=\frac{0-6}{-8-(-8)}=\frac{-6}{-8+8}=\frac{-6}{0}\text{ the slope is undefined}[/tex]An undefined slope indicates that you have a vertical line parallel to the y-axis.
This line will pass through all points in the plane with an x-coordinate=constant (c). In this case this constant will be -8
The equation is written in the form x = c, then the equation of this line will be
[tex]x=-8[/tex]PLEASE HELP ME ASAP PLEASE PLEASE PLEASE
jaren is selling lampshades at a craft fair. for the price per lampshade in dollars is f (x) and it is a function of the
Number of lampshades bought as shown by the graph below. What is the total cost of buying 10 lampshades from Janet's stall
Answers
According to the graphic the total cost of buying 10 lampshades is 8 dollars
question will be in picture
Answers
given:
[tex]-7\le x[/tex]so, the line that represents the given inequality will be: b
what is the slope of the line described by 5x+7y=19
Answers
Answer:
-5/7
Explanation:
Given the equation 5x+7y = 19
The standard form of an equation is y = mx+c
m is the slope
c is the intercept of a line
Make y the subject of the formula from the given equation
5x+7y = 19
7y = -5x + 19
Divide through by 7
7y/7 = -5x/7 + 19/7
y = -5/7 x + 19/7
Comparing with general formula;
mx = -5/7 x
m = -5/7
Hence the slope of the line is -5/7
Classify the following triangle as acute, obtuse, or rightO A. AcuteO B. ObtuseOc. RightOD. None of theseSUBMIT
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Given:
Triangle is given with the angles.
Given triangle is Acute
What percentage of 371 is 120?
Answers
This question is about percentages.
To know which percentage of 371 is 120, we just have to divide
[tex]\frac{120}{371}=0.32[/tex]Then, we multiply by 100 to express it in percentage
[tex]\text{0}.32\cdot100=32[/tex]Therefore, 120 represents 32% of 370, approximately.Miranda has $100.00 in a saving account that earns 10 percent interest, compounded annually. what wull the balance be after 1 year round to the nearest cent
Answers
5 lb of apples cost $8.20. How much is it for 1 lb?
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in pqr, what is the measurement of angle Q? 200 degrees871059010
Answers
In the triangle PQR we know that its angles have the following measures:
∠P=(6x+5)º
∠Q=(11x-5)º
∠R=xº
To determine the measures of ∠Q, you have to determine the value of x first. To do so you have to keep in mind that the measure of the inner angles of any triangle is 180º, so, for this triangle, the measure of the inner angles can be expressed as:
[tex]\begin{gathered} \angle P+\angle Q+\angle R=180º \\ (6x+5)+(11x-5)+x=180º \end{gathered}[/tex]From this expression, we can calculate the value of x.
-First, take the parentheses away, order the like terms together and simplify them:
[tex]\begin{gathered} 6x+11x+x+5-5=180º \\ 18x=180º \end{gathered}[/tex]-Second, divide both sides by 18 to determine the value of x:
[tex]\begin{gathered} \frac{18x}{18}=\frac{180}{18} \\ x=10 \end{gathered}[/tex]Now that we know that the value of x is 10º, we can determine the measure of ∠Q by replacing this value on the given expression for its measure:
[tex]\begin{gathered} \angle Q=11x-5 \\ \angle Q=11\cdot10-5 \\ \angle Q=110-5 \\ \angle Q=105º \end{gathered}[/tex]∠Q=105º, the correct option is the third one.
In an octagon, five of the angles are equal and each of the other three angles is 24° greater than each of the five other ones. Determine the angles of the octagon anto
Answers
Given:
5 angles are equal: x
Each of the other angles is 24 greater than the other 5 angles: x+24
An octagon has 8 angles; the sum of the interior angles of an octaogn is 1080º
[tex]5x+3(x+24)=1080º[/tex]Use the equation above to solve x:
[tex]\begin{gathered} 5x+3x+72=1080 \\ 8x+72=1080 \\ 8x=1080-72 \\ 8x=1008 \\ x=\frac{1008}{8} \\ \\ x=126 \end{gathered}[/tex]The 5 angles that are equal measure 126º
The other 3 angles measure:
[tex]x+24=126+24=150º[/tex]Then, the angles of the octagon are: 126º,126º,126º,126º,126º,150º,150º,150º