We want to find [tex]x[/tex] such that
[tex]\mathrm{Pr}(X \le x) = 0.81[/tex]
where [tex]X[/tex] is the random variable for test scores, and [tex]X\sim\mathrm{Normal}(63,9.3^2)[/tex].
Transform [tex]X[/tex] to [tex]Z\sim\mathrm{Normal}(0,1)[/tex] using the relation
[tex]X = \mu + \sigma Z \implies Z = \drac{X-63}{9.3}[/tex]
so that
[tex]\mathrm{Pr}(X \le x) = \mathrm{Pr}\left(\dfrac{X-63}{9.3} \le \dfrac{x-63}{9.3}\right) = \mathrm{Pr}\left(Z \le \dfrac{x-63}{9.3}\right) = 0.81[/tex]
Applying the inverse CDF of [tex]Z[/tex] (denoted by [tex]\Phi^{-1}[/tex]), we have
[tex]\dfrac{x-63}{9.3} = \Phi^{-1}(0.81) \approx 0.8779[/tex]
Solve for [tex]x[/tex].
[tex]\dfrac{x-63}{9.3} \approx 0.8779[/tex]
[tex]x-63 \approx 8.1644[/tex]
[tex]x \approx 76.1644[/tex]
Then the cutoff test score for the 81% percentile is [tex]P_{81} \approx \boxed{76}[/tex].
Find the measure of Angle BAC.
Applying the inscribed angle theorem, the measure of angle BAC is: 110°.
What is the Inscribed Angle Theorem?According to the inscribed angle theorem, the measure of angle BAC is half the measure of the intercepted arc, x + 50°.
x - 30 + x + 50 = 360
2x + 20 = 360
2x = 360 - 20
2x = 340
x = 170
m∠BAC = 1/2(x + 50)
Plug in the value of x
m∠BAC = 1/2(170 + 50)
m∠BAC = 110°
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You are on the Arithmetic Reasoning section.
Q: If 12 men are needed to run 4 machines. How many men are needed to
run 20?
A. 24
B. 48
C. 60
D. 80
Answer:that will be c 60
Step-by-step explanation: Because 12/4 but than the machines turn to 20 so 4x5 equals 20 so you got to do it to both sides
12x5=60 so its 60 men to run 20 machines
area of regular polygon?
[tex]\huge\purple{Hi!}[/tex]
The area of a regular polygon is one-half the product of its apothem and its perimeter.
Prove that :-
(sinA + secA)² + (cosA + cosecA)² = 1 + secAcosecA
May this answers be helps you to solve
Uncle Bill has planted fruits in the farm and 7/12 is watermelon.2/3 of the watermelon section is ruined from the storm.The rest is planted with lemon which isn’t ruined.What is the fraction of his farm which isn’t ruined?
The fraction of his farm which isn’t ruined is 11/18
Fractions and proportionFractions are written as a ratio of two integers. The given question will be solved using the method of proportion.
If Uncle Bill has planted fruits in the farm and 7/12 is watermelon, and 2/3 of the watermelon section is ruined from the storm, the fraction ruined from the storm is;
Fraction ruined from the storm = 2/3* (7/12)
Simplify to its lowest term to have:
Fraction ruined from the storm = 7/18
Determine the fraction of the firm that is not ruined
Fraction not ruined = 1 - 7/18
Fraction not ruined = 11/18
Hence the fraction of his farm which isn’t ruined is 11/18 if uncle Bill has planted fruits in the farm and 7/12 is watermelon.
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QUESTION IS DOW BELOW 5 POINTS EACH PLEASE HELP PLEASE HELP PLEASE HELP
Applying the central angle theorem, we have:
a. angle BAC.
b. arc BEC
c. arc BC
d. Measure of arc BEC = 260°
e. Measure of arc BC = 100°
What is the Central Angle Theorem?According to the central angle theorem, the central angle that is suspended at the center of a circle by two line segments (usually radii) have a measure that is equal to the measure of the intercepted arc. That is:
Measure of central angle = measure of intercepted arc.
What is a Major and a Minor Arc?
A major arc have a measure that is greater than 180 degrees or half a circle, while minor arcs have a measure that is less than 180 degrees or half a circle.
a. A central angle in the image given is: angle BAC.
b. One major arc in the given circle is arc BEC (greater than half a half a circle/180 degrees).
c. One minor arc in the given circle is arc BC (less than half a half a circle/180 degrees).
d. m∠BEC = 360 - 100
m∠BEC = 260°
m∠BEC = measure of arc BEC [central angle theorem].
Measure of arc BEC = 260°
e. Measure of arc BC = m∠BAC [central angle theorem].
Measure of arc BC = 100°
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72 is 15% of what number?
Answer: 480
Step-by-step explanation:
72/3 is 5% of the number we are looking for.
72/3=24
24*20 will be 100%
480 is 100%
72 is 15% of what number?
Quantity %
72---------------15
x---------------100
We solve
[tex]\boldsymbol{\sf{x=\dfrac{72\times100 }{15}=\dfrac{7200}{15}=480 }}[/tex]
Answer: 72 is 15% of 480.
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Solve Log6( x) = -2
ASAP HELP ME WITH THIS
Answer:
isosceles trapezoind
Step-by-step explanation:
An isosceles trapezoid is a trapezoid with congruent base angles.
How many lines can be drawn through points J and K?
Answer:
show the image because we cant answer it if there's no picture or image
Step-by-step explanation:
A bird flies 50km everyday to collect food for his offspring and 20km to drink water. To fly this distance takes him 1 hour and 40 minutes. What’s his average speed during flight?
Answer:
Step-by-step explanation:
speed = 50 km / hr.
distance = 20 km
time = distance / speed.
time = ( / 50) hr.
speed = 2 km/hrs
PLEASE help with question ASAP ASAP
Answer:
No classification is guaranteed.
5. A Government of Canada V39065 issue 90-day T-bill achieved its highest rate of return on May
24, 2000, with a yield of 5.74%. It realized its lowest rate of return on February 26, 2010, with
a yield of 0.16%. Calculate the purchase price of a $100,000 T-bill on each of these dates. In
dollars, how much more yield did an investor realize in 2000 than in 2010?
Based on the yields to the Canadian government's T-bills, the purchase price of a $100,000 T-bill on each of these dates are:
May 24, 2000 = $98,565February 26, 2010 = $99,960The yield to the investor in 2010 more than 2000 was $1,395.
What was the price of the T-Bills?On May 24, 2000, the price was:
= 100,000 x ( 1 - 5.74% x 90/360 days)
= $98,565
On February 26, 2010, the price was:
= 100,000 x (1 - 0.16% x 90/360)
= $99,960
The difference in yield is:
= (100,000 - 98,565) - (100,000 - 99,960)
= $1,395
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What would the first step be in solving the equation 4/7x = 21
❄ Hi there,
the first step in solving this inequality is
multiplying (both sides) by 7[tex]\sf{\dfrac{4}{7}x\times7=21\times7}[/tex]. Look what happens on the left side!
[tex]\sf{4x=147}[/tex]
Multiplying both sides of an equation, or inequality, by the fraction's denominator, is a nice little trick when you need to get rid of fractions to solve in terms of a variable.
Finish solving for x by dividing both sides by 4 –
[tex]\sf{x=\dfrac{147}{4}}[/tex]
❄
Please help
Use the parabola tool to graph the quadratic function f(x)=−2(x+4)^2−3
Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
Due to length restrictions, we kindly invite to read the explanation of this question and the image of parabola on Cartesian plane attached below to see the results.
How to graph a quadratic function
To graph a parabola, we shall follow the following procedure:
Mark the vertex of the parabola on the Cartesian plane.Mark at least two pairs of values on the Cartesian plane, one on the right of the vertex and other on the left of the vertex.Match the points to create the resulting curves.By following all the steps, we generate the curve with the help of a graphing tool.
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Consider the function f(x)=x
Describe the transformation of g(x)=2f(x-4)+2
The parent function ____ will undergo ____ transformations. The first transformation is a _____ reflect by a factor of ______. Next, the graph will shift ______ units to the ______. Finally, the graph will shift _____ units ____.
Please help me!
The parent function f(x) = x will undergo 3 transformations. The first transformation is vertically stretched by a factor of 2. Next, the graph will shift 4 units to the right. Finally, the graph will shift 2 units up
How to determine the transformation?The function is given as:
f(x) = x
This represents the parent function.
Start by stretching the function vertically by a factor of 2
This gives
f'(x) = 2x
Next, we shift the graph 4 units to the right
This gives
f''(x) = 2(x - 4)
Finally, we shift the graph 2 units up
This gives
f'''(x) = 2(x - 4) + 2
The number of transformations above is 3
Hence, the complete statement is:
The parent function f(x) = x will undergo 3 transformations. The first transformation is vertically stretched by a factor of 2. Next, the graph will shift 4 units to the right. Finally, the graph will shift 2 units up
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What expression is equivalent to (9x^2 + 2x -7)(x - 4)
Answer: C
Step-by-step explanation:
We can use the expanding rule to get that one if the expressions is
(9x^2 + 2x - 7)x + (9x^2 + 2x - 7)(-4)
At Roxas Middle School, every student studies Spanish, Chinese, or both Spanish and Chinese. There are $374$ students enrolled at the school, and $100$ of these students study both Spanish and Chinese. Also, the number of students studying Spanish is twice the number studying Chinese. How many students at Roxas Middle School study Spanish?
Based on the number of students at Roxas Middle School and the number of students studying Chinese and Spanish, the number of students who study Spanish is 182 students.
What number of students study Spanish?The first thing to do is to find out the number of students who are studying either Spanish or Chinese:
= Total number of students - Students studying both Spanish and Chinese
= 374 - 100
= 274 students
Then, assuming the number of students studying Chinese alone is x, the expression to find them would be:
274 = 2x + x
Solving gives:
2x + x = 274
3x = 274
x = 274 / 3
x = 91 students
The number studying Spanish is twice this number so will be:
= 91 x 2
= 182 students
In conclusion, there are 182 student studying Spanish.
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2.
David swam 800 m in 20 minutes. Find his average speed in m/min.
Answer:
40 meters a minute
Step-by-step explanation:
800m - 20 min
800/20
40m-1 min
(sin alpha +cos alpha )2
Step-by-step explanation:
sin alpha^2 + 2sin alpha* cos alpha + cos alpha^2
sin alpha^2 + cos alpha^2 +2sin alpha* cos alpha
1+ 2sin alpha* cos alpha
1+sin2 alpha
what is angle JLK?
a. 23 degrees
b. 24 degrees
c. 67 degrees
d. 134 degrees
Answer:
Answer is c, 67.
Step-by-step explanation:
So angle L and K are going to be the same, and so its going to be:
46+2n=180, since 180* inside a triangle and n= both L and K.
180-46=134
134/2=67
Both K and L will be 67.
Answer is c, 67.
To check, 46+67+67=180
The measure of angle JLK is 67 degree.
What is a triangle?A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.
The angle L and K are going to be the same;
46+2n=180,
Since 180 inside a triangle and n= both L and K.
180-46=134
134/2=67
Both K and L will be 67.
The answer is c, 67.
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Find the solution of the differential equation that satisfies the given initial condition. dy/dx=x/y , y(0)=-1
Separating variables, we have
[tex]\dfrac{dy}{dx} = \dfrac xy \implies y\,dy = x\,dx[/tex]
Integrate both sides.
[tex]\displaystyle \int y\,dy = \int x\,dx[/tex]
[tex]\dfrac12 y^2 = \dfrac12 x^2 + C[/tex]
Given that [tex]y(0)=-1[/tex], we find
[tex]\dfrac12 (-1)^2 = \dfrac12 0^2 + C \implies C = \dfrac12[/tex]
Then the particular solution is
[tex]\dfrac12 y^2 = \dfrac12 x^2 + \dfrac12[/tex]
[tex]y^2 = x^2 + 1[/tex]
[tex]y = \pm\sqrt{x^2 + 1}[/tex]
and because [tex]y(0)=-1[/tex], we take the negative solution to accommodate this initial value.
[tex]\boxed{y(x) = -\sqrt{x^2+1}}[/tex]
A 1L IV contains 60meq of kcal. The IV was discontinued after 400ml has infused. How much lvl did the patient receive
If a 1L IV contains 60meq of kcal and the IV was discontinued after 400ml has infused, then the amount of IV received by the patient is 24meq of kcal.
Calculation for the Amount of IV
It is given that,
1L IV contains 60meq of kcal
⇒ 1000 mL of IV contains 60meq of kcal
⇒ 1 mL of IV will contain 60 / 1000 meq of kcal
As per the question,
The amount of IV infused in the patient = 400 mL
⇒ The amount of IV received by the patient in meq of kcal = 400 × (60 / 1000)
= 4 × 6
= 24 meq of kcal
Hence, the patient receives 24meq of kcal amount of IV.
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Trapezoid FGHJ is inscribed in P as shown. If FG = 24, JH = 10, and the diameter of P is 26, find the area of the trapezoid. (Hint: draw in auxiliary lines). Round to the nearest tenth if necessary.
Answer:
221
Step-by-step explanation:
If the diameter is 26, the radius is 13 (which is the same as the perpendicular from P to JH)
So, the area is
[tex]\frac{1}{2}(13)(24+10)=221[/tex]
Which choice shows 40 + 30+ 10 rewritten correctly using the commutative property and then simplified correctly?
Answer:
40 + 10 + 30 = 50 + 30 = 80
Step-by-step explanation:
40 + 10 + 30 = 50 + 30 = 80
Answer:
10(4+3+1)
Step-by-step explanation:
Expand 40+30+10 by the distributive property:: 10(4+3+1)
If f(x) = 5x, what is ƒ˜¹ (x)?
[tex]y = 5x \\ switch \: y \: and \: x \\ x = 5y \\ solve \: for \:y \\ y = \frac{x}{5} [/tex]
se the FOIL method to evaluate the expression: (5+2)(4-5)
The FOIL method is a method of expanding two given brackets by following the required steps. Thus using the FOIL method, the required answer is: -7
Expansion of brackets may be done using different methods, but these methods would give the same answer. Some methods that can be used are the binomial expansion method, FOIL method, etc.
The FOIL method is a shortened form of the steps required for the process. These required steps are First, Outside, Inside, and last.
Thus to expand the given brackets in the question, we have;
(5+2)(4-5) = 5(4 - 5) + 2(4 - 5)
= 20 - 25 + 8 - 10
= 28 - 35
(5+2)(4-5) = -7
Thus using the FOIL method, the answer to the question is -7.
Quick check: (5+2)(4-5) = (7)(-1)
= -7
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Elliot borrows $3,000 from a bank that is charging three percent simple interest per year. If he pays the loan back in six months, how much interest will he pay? $30.00
$45.00
$90.00
$300.00
Answer:
The answer to that question depends
beacuse where ever you are it changes like uk you can pay 100€
or japan it can be around 1000¥
Decreasing the number of years of a loan decreases the amount of interest repaid over the term of the loan. Suppose a dental hygienist has the option of a 30-year loan or a 25-year loan of $345,000 at an annual interest rate of 3.75%.
(a)
a) Calculate the monthly payment (in dollars) for each loan. (Round your answers to the nearest cent.)
30-year loan
25-year loan
b) Calculate the savings in interest (in dollars) by using the 25-year loan. (Round your answer to the nearest cent.)
Answer:
a) 30 yr: $1597.75; 25 yr: $1773.75
b) $43065.00
Step-by-step explanation:
The monthly payment for each loan can be found using the amortization formula, or a spreadsheet or calculator. The shorter 25-year loan has fewer and larger payments, but the net result is less interest paid.
a)The attached calculator shows the monthly payments to be ...
30 year loan: $1597.75 monthly
25 year loan: $1773.75 monthly
b)The number of payments is the product of 12 payments per year and the number of years. The total repaid is the monthly payment times the number of payments.
The difference in amounts repaid is the difference in interest charged.
360×1597.75 -300×1773.75 = $43065 . . . . savings using 25-year loan
__
Additional comment
The monthly payment on a loan of principal P at annual rate r for t years is ...
A = P(r/12)/(1 -(1 +r/12)^(-12t))
Some calculators and all spreadsheets have built-in functions for calculating this amount.
The wall, shown above in Figure 105.1401, has an overall length that is 37’ and 8 1/4" . Three receptacle outlets are to be installed in this wall. L2 is twice as long as L1 . L1 should be _____' _____''.
Since L₂ is twice as long as L₁, the length of L₁ should be 12' and 6 3/4".
How to calculate the length (L₁)?First of all, we would convert the value of the overall length in feet to inches as follows:
1 feet = 12 inches
37 × 8 1/4 feet = X inches
Cross-multiplying, we have:
X = 1809/4 inches.
Since L₂ is twice as long as L₁, we have:
L₂ = 2L₁
Also, the overall length is given by:
T = 2L₁ + 2L₂
T = L₂ + 2L₂
T = 3L₂
1809/4 = 3L₂
L₂ = 1809/4 × 1/3
L₂ = 1809/12
L₂ = 150.75''
L₂ = 12' and 6 3/4".
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