What is the value of h in the diagram below? If necessary, round your answer
to the nearest tenth of a unit.
A. 8.1
B. 9.1
C. 23
D. 3
Answers
Answer:
A - 8.1
Step-by-step explanation:
This is an example of similar shapes.
The length of MO is 18, and PO is 5.
So length of MP is 13. (18 - 5)
We need to separate this large triangle into 2 triangles:
Triangle NMP Triangle NPOIn problems including similar shapes, our unknown needs to be on top of the fraction in an equation.
NP (h) /
[tex]{\frac{NP}{MP}[/tex] = [tex]\frac{PO}{NP}[/tex]
[tex]\frac{h}{13}[/tex] = [tex]\frac{5}{h}[/tex]
Cross multiply
h² = 65
h = √65
h = 8.06
h = 8.1 (rounded)
Drawn out explanation below.
Hope this has answered your question.
Related Questions
pls i need help 15 points!!!!! The treehouse will be 8 feet off the ground. Peter will hang a rope, with knots tied for footholds. Each knot uses an additional 2 inches of rope. Write an expression for the length of the rope needed if Peter ties n knots and wants the rope to touch the ground. How many inches of rope are needed if there are 8 knots? Explain.
Answers
Answer:
Step-by-step explanation:
First, we can figure out how many additional inches of rope are needed. If there are 8 knots, 16 additional inches will be needed. Peter would need 9 feet 4 inches of rope, or 112 inches.
The formula for finding the length of the rope needed would be 8+2n.
Hope this helps!
Answer:
112 inches
Step-by-step explanation:
Each knot needs 2 inches of rope
There are 2 knots
2*8 = 16 inches
He wants 8 ft from the ground, but he wants it in inches
8 ft* 12 inches per foot = 96 inches for the rope
96+ 16 =112 inches of rope
please help.
create five word expressions that will need to be translated into an algebraic expression also provide a value for the variable mentioned in the expression.
Answers
Answer:
The answers are as follows.
Step-by-step explanation:
Expressions:
Product of 2 and x is 146 added with a number gives 14The product of six and a gives 1212 divided by y gives 26 subtract with a number and get 12Computation:
Product of 2 and x is 14
2(x) = 14
x = 7
6 added with a number gives 14
6+x = 14
x = 8
The product of six and a gives 12
6(a) = 12
a = 2
12 divided by y gives 2
12 / y = 2
y = 6
6 subtract from a number and get 12
x - 6 = 14
x = 20
how do you solve these problems?
Answers
Answer:
Step-by-step explanation:
Hello,
a. The area of region P is the area of the rectangle 1 * e minus the
[tex]\displaystyle \int\limits^0_1 {e^x} \, dx=[e^x]^{1}_{0}=e-1[/tex]
So this is e - (e-1) = e - e + 1 = 1
b. The area of region P is the area of the rectangle 1 * e minus P and minus the
[tex]\displaystyle \int\limits^0_1 {e^{-x}} \, dx=[-e^{-x}]^{1}_{0}=-e^{-1}+1[/tex]
So this is
[tex]e - 1 - (-e^{-1}+1) = e-1+e^{-1}-1=e+e^{-1}-2[/tex]
This is around 1.08616127...
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
please help me with this
Answers
Answer:
Step-by-step explanation:
Open box is in rectangular shape. cuboid that is open in the top
l = length = 30 - (2.5 + 2.5 ) = 30 - 5 = 25 cm
h = 2.5 cm
w = width = 30 - (2.5 + 2.5) = 30 - 5 = 25 cm
Surface Area = 2lh + 2wh + lw
= 2*25*2.5 + 2* 25*2.5 + 25*25
=125 + 125 + 625
= 875 square cm
Volume = lwh
= 25*25*2.5
= 1562.5 cubic cm
The focus of the problem set is to show your ability to prove similarity between two triangles that are congruent. True False
Answers
Answer:
true bc i am smart
Answer:
the answer is TRUEStep-by-step explanation:
If tan x°= z/10 and cos x°= 10/y , what is the value of sin x°?
A. sin x° = z/y
B. sin x° = y/z
C. sin x° = 10z
D. sin x° = 10y
Answers
Answer:
A. z/y
Step-by-step explanation:
Because the trig ratios are; tangent : opp/adj cos : adj/hyp sin : opp/hyp
because tan of x is z/10, z must be opposite
and because cos of x is 10/y, then y must be the hypotenuse
this means sin of x must be z/y
Answer:
A. sin x = z/y
Step-by-step explanation:
2. Kelsea needs a test average of at least 90 to get an "A-" this marking period in math. Her three test grades
are 87,91 and 86. What score must she get on her fourth test to receive at least an A- ?
Define variable:
Equation:
Solution:
can someone check this please :)
Answers
Answer:
Equation: 87 + 91 + 86 + x = 360
Solution: 264 + x = 360
x = 360 - 264
x = 96
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
First three Kelsea's test grades : 87, 91 and 86
2. What score must she get on her fourth test to receive at least an A- ?
Define variable: x that represents the grade needed by Kelsea on her fourth test to receive at least an A-
Equation: 87 + 91 + 86 + x = 360
Solution: 264 + x = 360
x = 360 - 264
x = 96
Now you can understand if the previous work you did is correct
What is the value of x? (Use only the digits 0 - 9 and the decimal point, if needed, to write the number.)
x + 12.66 = 18
Answers
Answer: 5.34
Step-by-step explanation: 18 - 12.66 = 5.34
PLEASE HELP I AM IN A RUSH: Jason has applied to be a camp counselor for the summer. The job pays $9 per hour. The equation to represent Jason’s job is y = 9x, where x is the number of hours he works and y is the total amount he earns. Mia has applied to be a lifeguard for the summer. The lifeguard job is three days a week with hours and pays as shown in the table below. Tuesday Thursday Saturday Hours worked 6 8 5 Amount paid $52.50 $70.00 $43.75 Which statement best describes the hourly rates? The two jobs pay the same hourly rate. The comparison cannot be made with the information given. Jason’s camp counselor job pays a higher hourly rate than Mia’s lifeguard job. Jason’s camp counselor job pays a lower hourly rate than Mia’s lifeguard job.
Answers
Answer:
C: Jason’s camp counselor job pays a higher hourly rate than Mia’s lifeguard job.
Step-by-step explanation:
given:
y = 9x for Jason
For Mia
Tue Thu Sat
6 8 5
Tuesday : 52.50 for 6 hyours => 8.75 / hour
Thursday : 70.00 for 8 hours => 8.75 / hour
Saturday : 43.75 for 5 hours => 8.75 / hour
Solution:
Therefore Mia makes 8.75 / hour
False : The two jobs pay the same hourly rate.
False : The comparison cannot be made with the information given.
True : Jason’s camp counselor job pays a higher hourly rate than Mia’s lifeguard job.
False : Jason’s camp counselor job pays a lower hourly rate than Mia’s lifeguard job.
Answer: C Jason’s camp counselor job pays a higher hourly rate than Mia’s lifeguard job.
Step-by-step explanation:
please help with this
Answers
Answer:
158m^3
Step-by-step explanation:
First, let's figure out the total amount of water in the tank.
It measures 4.5m by 6m by 8m. The volume of a rectangular prism is V=lwh.
Therefore, the volume is:
[tex]V=(4.5)(6)(8)=216 m^3[/tex]
We are told is it filled to the brim, so we can conclude that there are 216 cubic meters of water in the tank.
We used 58 cubic meters of water, so we simply need to subtract that from 216:
[tex]216m^3-58m^3=158m^3[/tex]
There is still 158 cubic meters of water left in the tank.
Answer:
158 m^3
Step-by-step explanation:
Volume of the tank
= 4.5 * 6 * 8
= 216 m^3.
So amount left in the tank
= 216 - 58
= 158 m^3.
Questions are attached
Answers
Answer:
V = 32 in^3
Step-by-step explanation:
The area of the triangle is (1/2)(base)(height), which here comes to:
(1/2)(4 in)(8 in) = 16 in^2.
The volume is (16 in^2)(height) = (16 in^2)(2 in) = 32 in^3
From the set {5, 15, 20}, use substitution to determine which value of x makes the inequality true. x + 10 >25 A . 20 B. 5 C. none of these D. 15
Answers
Answer:
A.
Step-by-step explanation:
If x=5
5 + 10 is less than 25.
If x=15
15+10 is equal to 25
If x =20
20+10 is greater than 25
Evaluate each limit. Give exact answers.
Answers
Answer:
Given that 1 and 4 are vertical asymtotes we have;
(a) -∞
(b) +∞
(c) +∞
(d) -∞
Step-by-step explanation:
(a) For the function;
[tex]\lim_{x\rightarrow 4^{-}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{x^{2}-5\cdot x+4} \right )[/tex]
We have the denominator given by the expression, x² - 5·x + 4 which can be factorized as (x - 4)(x - 1)
Therefore, as the function approaches 4 from the left [lim (x → 4⁻)] gives;
[tex]\lim_{x\rightarrow 4^{-}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(x - 1)\cdot (x - 4)} \right )[/tex] [tex]\lim_{x\rightarrow 4^{-}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(3.999 - 1)\cdot (3.999 - 4)} \right )[/tex] [tex]\lim_{x\rightarrow 4^{-}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(2.999)\cdot (-0.001)} \right )[/tex][tex]=- \infty[/tex]
(b) Similarly, we have;
[tex]\lim_{x\rightarrow 4^{+}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{x^{2}-5\cdot x+4} \right )[/tex]
We have the denominator given by the expression, x² - 5·x + 4 which can be factorized as (x - 4)(x - 1)
Therefore, as the function approaches 4 from the right [lim (x → 4⁺)] gives;
[tex]\lim_{x\rightarrow 4^{+}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(x - 1)\cdot (x - 4)} \right )[/tex] [tex]\lim_{x\rightarrow 4^{+}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(4.0001 - 1)\cdot (4.0001 - 4)} \right )[/tex] [tex]\lim_{x\rightarrow 4^{+}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(3.0001)\cdot (0.0001)} \right )[/tex][tex]= +\infty[/tex]
(c)
[tex]\lim_{x\rightarrow 1^{-}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{x^{2}-5\cdot x+4} \right )[/tex]
We have the denominator given by the expression, x² - 5·x + 4 which can be factorized as (x - 4)(x - 1)
Therefore, as the function approaches 1 from the left [lim (x → 1⁻)] gives;
[tex]\lim_{x\rightarrow 1 ^{-}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(x - 1)\cdot (x - 4)} \right )[/tex] [tex]\lim_{x\rightarrow 1^{-}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(0.999 - 1)\cdot (0.999 - 4)} \right )[/tex] [tex]\lim_{x\rightarrow 4^{+}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(-0.001)\cdot (-3.001)} \right )[/tex][tex]=+ \infty[/tex]
(d) As the function approaches 1 from the right [lim (x → 1⁺)]
We have;
[tex]\lim_{x\rightarrow 1^{+}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(1.0001 - 1)\cdot (1.0001 - 4)} \right )[/tex]= [tex]\lim_{x\rightarrow 1^{+}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(0.0001)\cdot (-2.999)} \right ) =- \infty[/tex]
In triangle ABC, angle B = 90 degrees. Semicircles are constructed on sides AB, AC, and BC, as shown below. Show that the total area of the shaded region is equal to the area of triangle ABC.
Answers
Explanation:
The area of a semicircle is given by ...
A = πr^2/2
where r is the radius. Here, we're given diameters, so in terms of diameter, the area of a semicircle is ...
A = π(d/2)^2/2 = (π/8)d^2
__
The area of the semicircle with diameter AC is ...
white area = (π/8)AC^2
The area of the semicircle with diameter BC is ...
left semicircle area = (π/8)BC^2
And the area of the semicircle with diameter AB is ...
right semicircle area = (π/8)AB^2
__
We can use the relationship between the areas to find the shaded area:
triangle area + left semicircle area + right semicircle area =
white area + shaded area
Then the shaded area is ...
shaded area = triangle area + left semicircle area + ...
right semicircle area - white area
__
Filling in the values for area from above, we have ...
shaded area = triangle area+ (π/8)BC^2 +(π/8)AB^2 -(π/8)AC^2
shaded area = triangle area + (π/8)(BC^2 +AB^2 -AC^2)
From the Pythagorean theorem, we know that ...
AC^2 = BC^2 +AB^2
Substituting this into the above equation gives ...
shaded area = triangle area + (π/8)((Bc^2 +AB^2 -(BC^2 +AB^2))
shaded area = triangle area + 0 . . . . simplify
shaded area = triangle area
Rectangle JKLM is rotated 90° clockwise about the origin. On a coordinate plane, rectangle J K L M has points (negative 4, 1), (negative 1, 1), (negative 1, negative 1), (negative 4, negative 1). What are the coordinates of J’? J’(–1, –4) J’(4, –1) J’(1, 4) J’(4, 1)
Answers
Answer:
(4,-1)
Step-by-step explanation:
The required coordinate of J is (1, 4). Hence the option c is correct.
Rectangle JKLM is rotated 90° clockwise about the origin.
On a coordinate plane, rectangle J K L M has points (negative 4, 1), (negative 1, 1), (negative 1, negative 1), (negative 4, negative 1).
Rectangle is four sided polygon whose opposites sides are equal and has angle of 90° between its sides.
While rotating the rectangle about origin clock wise, the new coordinates forms of rectangle J K L M has points ( 4, 1), (1, 1), (negative 1, 1), (negative1 , 4).
Thus, the required coordinate of J is (1, 4).
Learn more about rectangles here:
https://brainly.com/question/16021628
#SPJ2
Which two solid figures have the same volume?
Answers
Answer:
b
Step-by-step explanation:
Answer:
The answer is B.
Step-by-step explanation:
A painter leans a 25-foot ladder against the wall. The bottom of the ladder is 20 feet from the base of the wall. The painter then moves the bottom of the ladder 13 feet closer to the wall. How much higher is the top of the ladder on the wall?
Answers
Answer:
9 ft
Step-by-step explanation:
a²+b²=c²
20²+b²=25²
400=b²=625
b²=625-400
b²=225
b=15 (the distance up the wall the ladder is to begin with)
20-13=7
7²+b²=25²
49+b²=625
b²=625-49
b²=576
b=24 (The distance up the wall the ladder is after moving it)
24-15=9
Select the correct answer from each drop-down menu.
The given equation has been solved in the table.
Step
Statement
1
= 15
- - 6 =
- - 6 + 6 = 15 +
+4
- = 21
N
3
4.
2
-2 - 21
5
y = -42
Use the table to complete each statement.
In step 2, the
In step 4, the
property of equality was applied.
property of equality was applied.
V
Reset
Next
Answers
Answer:
Step 2: addition property of equality
Step 4: multiplication property of equality
Step-by-step explanation:
=>In step 2, from step 1, where you have [tex] -\frac{y}{2} - 6 = 15 [/tex] , to make -6 cross over to the other side of the equation, the addition property of equality was applied. That would ensure the equation remains balanced. Thus, 6 is added to both sides of the equation.
[tex] -\frac{y}{2} - 6 + 6 = 15 + 6 [/tex]
[tex] = -\frac{y}{2} = 21 [/tex]
=>In step 4, the multiplication property of equality was used as both sides of the equation were multiplied by -2, to balance the equation and also solve for y.
Answer:
Step 2 > addition
Step 4 > multiplication
Step-by-step explanation:
help please. Find the length of x.
Answers
Answer:
x=10
Step-by-step explanation:
The triangles are similar so we can use ratios to solve
6.5 (6.5+6.5)
------ = -----------------------
5 x
6.5 (13)
------ = -----------------------
5 x
Using cross products
6.5x = 65
Divide by 6.5
6.5x/6.5 = 65/6.5
x = 10
What is the length of DF?
Answers
Answer:
7.06
Step-by-step explanation:
17/8 = 15/DF
DF = 7.06
I think that’s right
A machining company needs to manufacture more than 20 fixtures in a day. The company uses five identical machines to make the fixtures. If each machine produces x fixtures, which inequality represents this situation? A. 5x > 20 B. 5x 20 + 5 D. 5x < 20 + 5
Answers
Answer:
A. 5x>20
Step-by-step explanation:
Because the company has to produce more than 20 fixtures you need greater than 20 and you have 5 machines time the number they produce.
Hope this helps, if it does please mark brainliest!!
Hi I really need help on this problem. Thank you!
Answers
Answer:
9
Step-by-step explanation:
because the angle is 45 deg, it is 1/8 of the full circle
the arc it intercepts will also be 1/8 the circumference of the full circle
72*1/8=9
In lowa, the Hoosiers basketball team won half of its first twelve games. There are a total of
24 games in the season. In order to make it to the playoffs, the Hoosiers need to win three
fourths of their remaining games. If the team is able to win exactly three fourths of their
games, how many total games will they have won at the end of their 24-game season before
the playoffs begin?
Answers
Answer:
18
Step-by-step explanation:
3/4 of 24 is 18
question 9: consecutive angles in a parallelogram are___ A: cute B: congruent C: parallel D: Supplementary E: Convex
Answers
Answer:
Consecutive angles in a parallelogram are, D supplementary.
Step-by-step explanation:
Consecutive angles in a parallelogram will always sum to 180 degrees.
Answer:
Supplementary
Step-by-step explanation:
Correct answer in Ap3x. Just took the quiz.
what is the product of the reciprocal of 5,the reciprocal of 18, and the reciprocal of -3 please provide a explanation :)
Answers
Answer:
1/5, 1/18, and 1/-3
Step-by-step explanation:
a reciprocal reverses a fraction
for example:
5=5/1
reciprocal=1/5
hope this helps:)
Answer:
1/5, 1/18, -1/3
Step-by-step:
The simple answer is just to to make that number under one.
Example: 5 is the reciprocal then 1/5 was the start number. Vise-versa. Hope this helps!
In its first year of operations, Roma Company reports the following. Earned revenues of $53,000 ($45,000 cash received from customers). Incurred expenses of $29,500 ($23,050 cash paid toward them). Prepaid $8,750 cash for costs that will not be expensed until next year.
Answers
Complete question :
In its first year of operations, Roma Company reports the following. Earned revenues of $53,000 ($45,000 cash received from customers). Incurred expenses of $29,500 ($23,050 cash paid toward them). Prepaid $8,750 cash for costs that will not be expensed until next year. calculate the first year's net income under both the cash basis and the accrual basis of accounting.
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following :
Earned revenue = $53,000
Cash received from customers = $45000
Incurred expenses = $29,500
Cash paid towards incurred expenses = $23,050
Cash which will not be expensed till next year = $8,750
Cash Accounting:
Cash received $45,000
Expenses ($23,050 + $8750) = $31,800
Net Income $(45,000 - 31,800) = $13,200
Accrual Accounting :
Revenue earned $53,000
Expenses incurred $29,500
Net income $(53,000 - 29,500) = $23500
Plz help me -5=-1/6b
Answers
Answer:
b = 30
Step-by-step explanation:
-5=-1/6b
Multiply each side by -6 to isolate b
-5 * -6 = -6 * -1/6 b
30 = b
For the given term, find the binomial raised to the power, whose expansion it came from: 15(5)^2 (-1/2 x) ^4
A. (5+1/2 x)^6
B. (Y- 1/2 x) ^6
C. (5- 1/2 x) ^6
D. (-5 + (- 1/2 x))^6
Answers
Answer:
C. [tex](5-\frac{1}{2})^6[/tex]
Step-by-step explanation:
Given
[tex]15(5)^2(-\frac{1}{2})^4[/tex]
Required
Determine which binomial expansion it came from
The first step is to add the powers of he expression in brackets;
[tex]Sum = 2 + 4[/tex]
[tex]Sum = 6[/tex]
Each term of a binomial expansion are always of the form:
[tex](a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......[/tex]
Where n = the sum above
[tex]n = 6[/tex]
Compare [tex]15(5)^2(-\frac{1}{2})^4[/tex] to the above general form of binomial expansion
[tex](a+b)^n = ......+15(5)^2(-\frac{1}{2})^4+.......[/tex]
Substitute 6 for n
[tex](a+b)^6 = ......+15(5)^2(-\frac{1}{2})^4+.......[/tex]
[Next is to solve for a and b]
From the above expression, the power of (5) is 2
Express 2 as 6 - 4
[tex](a+b)^6 = ......+15(5)^{6-4}(-\frac{1}{2})^4+.......[/tex]
By direct comparison of
[tex](a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......[/tex]
and
[tex](a+b)^6 = ......+15(5)^{6-4}(-\frac{1}{2})^4+.......[/tex]
We have;
[tex]^nC_ra^{n-r}b^r= 15(5)^{6-4}(-\frac{1}{2})^4[/tex]
Further comparison gives
[tex]^nC_r = 15[/tex]
[tex]a^{n-r} =(5)^{6-4}[/tex]
[tex]b^r= (-\frac{1}{2})^4[/tex]
[Solving for a]
By direct comparison of [tex]a^{n-r} =(5)^{6-4}[/tex]
[tex]a = 5[/tex]
[tex]n = 6[/tex]
[tex]r = 4[/tex]
[Solving for b]
By direct comparison of [tex]b^r= (-\frac{1}{2})^4[/tex]
[tex]r = 4[/tex]
[tex]b = \frac{-1}{2}[/tex]
Substitute values for a, b, n and r in
[tex](a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......[/tex]
[tex](5+\frac{-1}{2})^6 = ......+ ^6C_4(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]
[tex](5-\frac{1}{2})^6 = ......+ ^6C_4(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]
Solve for [tex]^6C_4[/tex]
[tex](5-\frac{1}{2})^6 = ......+ \frac{6!}{(6-4)!4!)}*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]
[tex](5-\frac{1}{2})^6 = ......+ \frac{6!}{2!!4!}*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]
[tex](5-\frac{1}{2})^6 = ......+ \frac{6*5*4!}{2*1*!4!}*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]
[tex](5-\frac{1}{2})^6 = ......+ \frac{6*5}{2*1}*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]
[tex](5-\frac{1}{2})^6 = ......+ \frac{30}{2}*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]
[tex](5-\frac{1}{2})^6 = ......+15*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]
[tex](5-\frac{1}{2})^6 = ......+15(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]
[tex](5-\frac{1}{2})^6 = ......+15(5)^2(\frac{-1}{2})^4+.......[/tex]
Check the list of options for the expression on the left hand side
The correct answer is [tex](5-\frac{1}{2})^6[/tex]
Suppose a hardware manufacturer is checking its nails to make sure they are of the right length. A quality control investigator collects a sample of 100 nails and measures their lengths, finding that their mean is 2.000cm with a sample standard deviation of 0.002cm. Suppose the investigator knows that nearly all of the nail population produced will be within 2 standard deviations. What will be the most likely upper bound on the length of a randomly chosen nail from all nails manufactured by the company?
Answers
Answer:
The upper bound on the length of a randomly chosen nail from all nails manufactured by the company is 2.004 cm.
Step-by-step explanation:
According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.
Then, the mean of the sample means is given by,
[tex]\mu_{\bar x}=\bar x[/tex]
And the standard deviation of the sample means (also known as the standard error) is given by,
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
In this case the sample of nails selected is quite large, i.e. n = 100 > 30.
So, the sampling distribution of sample mean length of nails will be approximately normal.
Then according to the Empirical rule, 95% of the normal distribution is contained in the range,
[tex]\mu\pm 2\cdot \frac{s}{\sqrt{n}}[/tex]
Compute the upper bound as follows:
[tex]\text{Upper Bound}=\mu\pm 2\cdot \frac{s}{\sqrt{n}}[/tex]
[tex]=2+(2\times\frac{0.002}{\sqrt{100}})\\\\=2+0.0004\\\\=2.004[/tex]
Thus, the upper bound on the length of a randomly chosen nail from all nails manufactured by the company is 2.004 cm.
Which value makes the inequality x^2 ≥ x false?
A. -1/4
B. 0
C. 1/4
D. 1
Answers
Answer:
D
Step-by-step explanation:
cas if x =1
then 1^2>or=1
1is not >or=1