By applying the Empirical Rule, the value of x is equal to: A. 8.
What is the Empirical Rule?The Empirical Rule is also known as the 68-95-99.7 rule and it simply refers to a statistical rule which states that the middle 95% of a normal distribution would be within two (2) standard deviations of its mean.
This ultimately implies that, 95% of a normal distribution would fall within two (2) standard deviations of its mean in accordance with the Empirical Rule.
By applying the Empirical Rule, the value of x is given by:
x = μ + 2σ
Substituting the given points into the formula, we have;
x = 4 + 2(2)
x = 4 + 4
x = 8.
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Complete Question:
Suppose X ~ N(4, 2). What value of x is two standard deviations to the right of the mean?
8
10
7
6
write two numbers that multiply to 54 and add to -21
This is the solution to a 2 degree equation:
[tex]x^2-21x+54=0[/tex]The two numbers that multiply to 54 and add to -21 are the roots of this equation.
We can find the solution of an equation with this form:
[tex]ax^2+bx+c=0[/tex]With this formula:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]For this problem, a = 1, b = -21 and c = 54:
[tex]x=\frac{21\pm\sqrt[]{(-21)^2-4\cdot1\cdot54}}{2\cdot1}=\frac{21\pm\sqrt[]{441-216}}{2}=\frac{21\pm\sqrt[]{225}}{2}=\frac{21\pm15}{2}[/tex]The two numbers are:
[tex]\begin{gathered} x_1=\frac{21+15}{2}=\frac{36}{2}=18 \\ x_2=\frac{21-15}{2}=\frac{6}{2}=3 \end{gathered}[/tex]The numbers are -18 and -3 (they must be negative so they add up to a negative number)
If this trapezoid is moved through the translation (x+3, y-2), what will the coordinates of B’ be?
The coordinates of B' in the image of the trapezoid upon translation would be; (-2, 2).
What would be the coordinates of B' after the translation (x+3, y-2) has been done on the trapezoid?It follows from the task content that the coordinates of the point, B' on the trapezoid after the translation (x+3, y-2) has been carried out is to be determined.
On this note, since it follows from the image attached that the coordinates pair of point B, in the trapezoid's pre-image is; (-5, 4).
It simply follows that upon carrying out the transformation; (x+3, y-2) on the trapezoid, the coordinates pair of point B is; (-5+3, 4 -2).
Hence, the required coordinate pair of point B' is; (-2, 2).
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Find the value of AB.D1312mo8AB = [?]
A={1,2,6} B= {x | x is an odd whole number less than 8}. Find A∪B.
The value of set A union set B is A ∪ B = { 1, 2, 3, 5, 6, 7 }.
Consider the set,
A = { 1, 2, 3 }
And, B = { x | x is an odd whole number less than 8 }
An integer's parity determines whether it is even or odd. If an integer is a multiple of two, it is even; otherwise, it is odd.
Therefore, all the numbers less than 8 are:
1, 3, 5, 7
Therefore, the set B will be:
B = { 1, 3, 5, 7 }
In set theory, the set containing every element in a collection is the union of all its sets.
So,
A ∪ B = { 1, 2, 6 } ∪ { 1, 3, 5, 7 }
A ∪ B = { 1, 2, 3, 5, 6, 7 }
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What is the last step in this process?
A, Find the difference between partial products
B, Find the sum of partial products
C, The last step is already complete
Answer:
B. Find the sum of partial products.
Step-by-step explanation:
pls help thx i don’t know what to do here options are a)0.3125b)2.2c)6.6d)3.2
Given:
The graph for height and width.
[tex]Height=constant\times width[/tex]Required:
What is the value of the constant in the equation?
Explanation:
From graph, we can evaluate respective values in equation and can get value of constant as:
[tex]\begin{gathered} height=constant\times weight \\ 1.6=constant\times0.5 \\ constant=3.2 \end{gathered}[/tex]Answer:
The value of constant equals 3.2
p= principal amount, 0.12= the interest charged; p+0.12p=224 . write a problem based on the given information
Step 1: Let's review the information given to us to answer the problem correctly:
• p = Principal
,• 0.12 = Interest rate
,• 224 = Future value
Step 2: Let's write a problem based on this information, using the Simple Interest Formula, as follows:
A = P(1 + rt), where:
A = Final amount
P = Principal
r = Annual interest rate
t = Time in years
224 = P (1 + 0.12t)
224 = 1.12Pt
Pt = 224/1.12
Pt = 200
If P = 200, then t = 1
Step 3: Let's interpret the answer and the problem we just wrote.
What is the amount of principal and the time of deposit for a savings account that earns 12% annually, and shows a final balance of $ 224?
Answer: $ 200 and the period of time is 1 year.
4. In 2017, chicken consumption in pounds consumed for 100 randomly selected people hasa mean * = 55.2 pounds and a standard deviation s = 23 pounds. Construct a 90%confidence interval the mean weight of chicken consumption in 2017.
(a)
The given parameters are:
[tex]\begin{gathered} \text{Mean}=\bar{X}=55.2 \\ \text{Standard deviation}=\sigma=23 \\ Sample\text{ size}=n=100 \\ z=1.644854\text{ (90\% confidence ineterval)} \end{gathered}[/tex](b)
The formula to find the margin of error for a 90% confidence interval is given below:
[tex]E=z\times\frac{\sigma}{\sqrt[]{n}}[/tex]Substitute the value from part (a), to get
[tex]\begin{gathered} E=1.644854\times\frac{23}{\sqrt[]{100}} \\ =1.644854\times\frac{23}{10} \\ =3.7832 \end{gathered}[/tex]Thus, the margin of error is 3.7832.
(d)
The given sample's confidence interval is,
[tex]55.2\pm3.7832[/tex]So, the confidence interval is (51.42 to 58.98).
(d)
For 90% confidence interval, the mean weight of chicken consumption is between 51.42 pounds and 58.98 pounds.
Write the equation in point-slope form of the line that passes through the given point with the given slope.
(3, 1); m = 2
Answer:m = (y – y1)/ (x – x1)
⇒ y – y1 = m(x – x1)….(i)
Step-by-step explanation:
A jogger goes 0.8 mi east and then turns south. If the jogger finishes 1.7 mi fromthe starting point, how far south did the jogger go?
We can use Pythagoras theorem:
[tex]\begin{gathered} H^2=a^2+b^2 \\ \\ \end{gathered}[/tex]Where H=hypotenuse and "a" and "b" are the other sides of the triangule.
In the current problem, we have:
H = 1.7, a = 0.8, b=?
Then:
a basketball player averages 13.5 points per game. there are 22 games in a season. at this rate, how many points would the player score in an entire season
In order to find the total player score, we just need to multiply the average of the player by the number of games in the season. So we have:
[tex]\text{total score}=22\cdot13.5=297[/tex]So the player score in the entire season would be 297.
The perimeter of a parallelogram is 72 meters . The width of the parallelogram is 4 meters less than its length. Write an equation that could be used to find the length of the parallelogram.
4L = 64
Explanation: The perimeter of a parallelogram (like most other quadrilaterals) is defined as;
P = 2 (L + W)
Where P is the perimeter, L is the length and W is the width. Note that the width is given as 4 metres less than its length, hence if the length is L then the width shall be L-4. The perimeter can now be expressed as follows:
P = 2 (L + [L-4])
If the perimeter is 72, then
72 = 2 (L + L - 4)
72 = 2 (2L - 4)
By expanding the bracket on the right hand side we now have;
72 = 4L - 8
Add 8 to both sides of the equation
72 + 8 = 4L - 8 + 8
80 = 4L
Therefore the equation is 4L = 80
And the Length is 20 metres.
Lookout station A is 12 miles from the fire. Lookout station B is 39 miles from station A. The angle at station A is 52°. Find the distance between Station B and the fire.
Therefore, in order to find out the distance from station b to the fire, we must use the sine formula, as we know that sine is the opposite side divided by the hypotenuse.
We want to find out the opposite side and we already have the hypotenuse that is 12 miles.
So:
[tex]\begin{gathered} \sin52=\text{ }\frac{x}{12} \\ 12(\sin52)=x \\ 12(0.788)=x \\ 9.456=x \end{gathered}[/tex]Therefore, station B i 09.456 miles from the fire.
I need help solving: c= 8a-3b and solve for a
hello
[tex]c=8a-3b[/tex]solve for a
step 1
add 3b to both sides of the equation
reason; we're doing this so that we take -3b to the other side of the equation so the we can have a and it's coefficient on one side of the equation
[tex]\begin{gathered} c=8a-3b \\ c+3b=8a-3b+3b \\ c+3b=8a \end{gathered}[/tex]or we can simply say take -3b to the other side of the equation in order to make it easy to equate a
but note that whenever a variable or real number crosses an equality or inequality sign, the sign changes from either positve (+ve) to negative (-ve) or negative (-ve) to positive (+ve).
in this case, -3b
now we have our equation almost set
step 2
divide both sides by 8 to solve for a
[tex]\begin{gathered} 8a=c+3b \\ \frac{8a}{8}=\frac{c+3b}{8} \\ a=\frac{c+3b}{8} \end{gathered}[/tex]Question 5(Multiple Choice Worth 2 points)
(Multi-Step Linear Equations MC)
Find the value of x in the following equation:
3.6(2x + 5) = 7.2x + 18
No solution
Infinite solutions
x = 0
x = 2.3
The Linear equation 3.6(2x + 5) = 7.2x + 18.3 has no solution except when x is put to be zero.
The provided equation is 3.6(2x + 5) = 7.2x + 18.
This is a linear equation in one variable.
We have to solve the equation for x,
We can solve it by simplifying it,
3.6(2x + 5) = 7.2x + 18
7.2x + 18 = 7.2x + 18
7.2x = 7.2x
7.2x - 7.2x = 0
(7.2-7.2)x = 0
(0)x = 0
x =0/0
Hence, there can not be any value of x.
But, if we put x = 0 in the equation,
Then,
3.6(2(0) + 5) = 7.2(0) + 18
18 = 18
So, x = 0 is satisfying the equation.
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a(n)=3n-7 what is the sum of the 1st and 5th terms of sequence
Answer: 4
Step-by-step explanation:
To find the first term you replace n with 1.
a(1) = 3(1) -7
a(1) = -4
Now that you have the first term you must find the fifth term by filling in 5 for n.
a(5) = 3(5) - 7
a(5) = 15 - 7
a(5) = 8
Now that we have both terms simply add them together to find the sum.
-4 + 8 = 4
Slope is 1 and (-2,1) is on the line
Answer:
y = x + 3
Step-by-step explanation:
Write the equation?
Use:
m (slope) = 1
x = -2
y = 1
y=mx + b
1 = 1(-2) +B
1 = -2 + b Add 2 to both sides
3 = b
y = mx + b
y = 1x + 3
y = x + 3
help fast please!!!!!!
Answer:
B is correct.
Step-by-step explanation:
[tex] \frac{5.96 \times {10}^{4} }{2.98 \times {10}^{3} } = 2 \times 10 = 20[/tex]
a dealer paid 720 kina for a radio and sold it so as to gain 37.5%. find the selling price
Cost: 720 kina
Earnings: 37.5%
Then, the selling price should be:
100% + 37.5% = 137.5% of 720 kina
=> 137.5*720/100 = 990 kina
The selling price was 990 kina.
Hello i did this question on my own because I thought I understood it but it was wrong I got 1/2
Given a number 'a', we have the following general rule for exponent:
[tex]a^{-n}=\frac{1}{a^n}[/tex]in this case, we have:
[tex]3^{-4}=\frac{1}{3^4}=\frac{1}{81}[/tex]ONLY (e) questionThe turning points of the graph are ___Type in ordered pair, round each coordinate to two decimal places
Answer:
[tex]\begin{gathered} (-4.85,-243) \\ (-1.5,136.69) \\ (1.85,-243) \end{gathered}[/tex]Explanation:
Given the function:
[tex]f(x)=3 x\left(x^{2}-9\right)(x+6)[/tex]The graph of f(x) is attached below:
From the graph, the turning points are:
[tex]\begin{gathered} (-4.85,-243) \\ (-1.5,136.69) \\ (1.85,-243) \end{gathered}[/tex]Which of these expressions entered into a graphing calculator willreturn the probability that 45 or fewer heads come up when flipping acoin 100 times?
Prob P = Heads/ flips
. = (n,p,c)
Here n is number of flips
. p is prob of 1 success
. c number of sucess
Then ANSWER IS
OPTION A) binomcdf (100,0.5, 45)
A rectangular piece of cardboard that is 10 inches by 14 inches has squares of length x inches on a side cut from each corner. (Assume that 0 < x < 5.) If the flaps of the figure are folded up, an open box is formed. Represent the volume of this box in the form of a polynomial function V(x).
This is an aproximation of the described situation. We are taking 4 squares of side lenght x from each corner.
The dashed lines mark up what would be the base of the box. The blue scrabbled areas will be the sides of the box.
Recall that to calculate the volume of the box, we need to multiply the lenghts of each side of the base and then multiply it by the height of the box. So, to calculate the volume we need to determine the lenght of the dashed lined.
Let us calculate the lenght of the black dashed lines. Notice that the horizontal side has a total lenght of 14. So, since we are taking 2 squares of side x, we have that the lenght of the dashed line plus twice the lenght x, we get the total lenght of the side. That is
[tex]\text{Black dashed line + 2x = 14}[/tex]Then the lenght of the black dashed line is 14-2x.
In the same manner, we can calculate the red dashed lines' lenght. It is 10-2x. Now, our box would be
In the picture, the green line represents the height. Comparing the blue and red lines, we have that the lenght of the green line corresponds to the lenght of the side of the square (x).
So now, we know that the volume of the box is
height * lenght of the base * width of the base = (14-2x)*(10-2x) * (x)
which is a polynomial of the variable x.
The ordered pair below is form an inverse variation.find the constant of variation.(8,6)
We have that an inverse variation can be represented by the following equation:
[tex]\begin{gathered} k=xy \\ or \\ y=\frac{k}{x} \end{gathered}[/tex]In this case we have the ordered pair (8,6), then, we have the following constant of variation:
[tex]\begin{gathered} (x,y)=(8,6) \\ \Rightarrow k=(8)(6)=48 \\ k=48 \end{gathered}[/tex]therefore, the constant of variation is k = 48
How many lines of symmetry does the figure have
○ 8
○ 7
○ 9
○0
Answer:
7
Step-by-step explanation:
First count the sides and draw a line above the shape and you will it's 7
A substance has a mass of 53 grams. Its volume is 12 ml3. What is thedensity? Round to the nearest Tenth. (1 number after decimal) & be sure toinclude the correct label.Your answerThe density of sulfur is 2.1g/cm3. If you have a volume of 6 cm3, what is the poinmass? Round to the nearest Tenth.
1) Gathering the data
mass = 53 g
V = 12 ml
The density is given using the following formula:
[tex]\begin{gathered} d=\frac{m}{V} \\ d\text{ =}\frac{53}{12\text{ }} \\ d=4.42\text{ g/ml} \end{gathered}[/tex]Please solve math question FAST
Answer:
Solution below.
Step-by-step explanation:
This question tests on the concept of percentages and comparing current and previous values.
Lets analyse the first statement from the question.
Taylor earned 15% more each week in September than in July.
We know that the formula for percentage change:
((Final Value - Initial Value) ÷ Initial Value) × 100
Comparing July and September,
we know that the change is 15% and the Final Value (September) is $207.
So we can substitute values into the formula to find the value for July.
[tex] \frac{207 - july}{july} \times 100 = 15 \\ \frac{207 - july}{july} = \frac{15}{100} \\ 207 - july = 0.15july \\ 1.15july = 207 \\ july = \frac{207}{1.15} \\ = 180[/tex]
Now we know Taylor earned $180 in July, we can use the same formula to find the amount she earned in August. Given Initial Value (July) = $180 and percentage change = 10% (She earns 10% more in August than in July)
[tex] \frac{sep - 180}{180} \times 100 = 10 \\ \frac{sep - 180}{180} = \frac{10}{100} \\ \frac{sep - 180}{180} = 0.1 \\ sep - 180 = 0.1 \times 180 \\ sep - 180 = 18 \\ sep = 18 + 180 \\ = 198[/tex]
Therefore, Taylor earns $198 per week in September.
The function C(x) = 10x +3,000 represents the cost to produce a number of items. How many items should beproduced so that the average cost is less than $30?Provide your answer
Given:
The cost function is C(x) = 10x + 3000.
Explanation:
The equation for the average cost is,
[tex]\begin{gathered} A(x)=\frac{C(x)}{x} \\ =\frac{10x+3000}{x} \end{gathered}[/tex]The inequality for x is,
[tex]\frac{10x+3000}{x}<30[/tex]Solve the inequality for x.
[tex]\begin{gathered} \frac{10x+3000}{x}\cdot x<30\cdot x \\ 10x+3000-10x<30x-10 \\ \frac{3000}{20}<\frac{20x}{20} \\ 150So the number of items should be more than 150.
What is the area of the corn field?
Answer:
23x-3
Step-by-step explanation:
5x+2+8x-11+4x+3+3+2x+4x Got this from adding the area around the field
5x+8x+4x+2x+4x+2-11+3+3 I grouped like-terms
23x+2-11+3+3 I added like-terms
23x-3 Then I got
7 A total of 340 gallons of oil is divided between two tanks. If at least half of the oil is pumped into the first tank, which number line represents that possible amount of oil in the second tank? (A 400 100 200 300 B 300 400 200 100 tot 200 300 400 100 O HH 300 400 100 200
Half of 340 gallons is:
[tex]170\text{ gallons.}[/tex]Let x represent the amount of oil in the second tank, we know that at least 170 gallons were pumped into the first tank, therefore, at most the other half is in the second tank:
[tex]x\ge170.[/tex]Answer: The above inequality in the number line is represented as follows:
