Answer:
2 cm and 6 cm
Step-by-step explanation:
The product of the dimensions must be 12 cm². (All answer choices meet that requirement.)
Opposite sides of a rectangle are the same length, so the sum of the two dimensions must be half the perimeter, 8 cm. The sums of the answer choices are ...
8 cm7 cm9.5 cm13 cmOnly the first answer choice meets the requirement for a perimeter of 16 cm. The dimensions could be 2 cm and 6 cm.
6
×
2
Explanation:
For the rectangle
Length
=
ℓ
Breadth
=
b
Area is
12
cm
2
ℓ
b
=
12
Perimeter is
16
cm
2
(
ℓ
+
b
)
=
16
ℓ
+
b
=
8
Substitute
b
=
12
ℓ
from first equation
ℓ
+
12
ℓ
=
8
ℓ
2
+
12
=
8
ℓ
ℓ
2
−
8
ℓ
+
12
=
0
Use quadratic formula (
x
=
−
b
±
√
b
2
−
4
a
c
2
a
) to find
ℓ
ℓ
=
−
(
−
8
)
±
√
(
−
8
)
2
−
(
4
×
1
×
12
)
2
×
1
ℓ
=
8
±
√
16
2
ℓ
=
8
±
4
2
ℓ
1
=
8
+
4
2
=
6
ℓ
2
=
8
−
4
2
=
2
If
ℓ
1
is taken as length then
ℓ
2
is the breadth of the rectangle.
translate this sentence into an inequality. A cheetah can reach a speed of 70 mph. however, this speed can be maintained for no more than 1,640 feet. A. d>1,640 B. d_<1,640 C. d<1,640 D. d_>1,640
The answer is:
B. [tex]d\leq 1,640ft[/tex]
Why?From the statement we know that the cheetah can reach a speed of 70 mph, but it can be maintained for no more than 1,640 feet.
The expression "no more than" means that at least it can be reached but never exceeded, it involves that the distance can be less or equal than 1,640 feet but never more than that.
So, the correct option is:
B. [tex]d\leq 1,640ft[/tex]
Have a nice day!
Evaluate: 54-75+81-(-27)+53
Hi the answer is 344
Answer:
140
Step-by-step explanation:
54-75=-21
-21+81=60
60-(-27)=87 or 60+27=87
87+53=140
The function f(x)= x - 6x + 9 is shifted 5 units to the left to create g(x). What is
Answer:
g(x) = x^2 + 4x + 4
Step-by-step explanation:
In translation of functions, adding a constant to the domain values (x) of a function will move the graph to the left, while subtracting from the input of the function will move the graph to the right.
Given the function;
f(x) = x2 - 6x + 9
a shift 5 units to the left implies that we shall be adding the constant 5 to the x values of the function;
g(x) = f(x+5)
g(x) = (x+5)^2 - 6(x+5) + 9
g(x) = x^2 + 10x + 25 - 6x -30 + 9
g(x) = x^2 + 4x + 4
Use trigonometric ratios to solve the right triangle.
The length of leg DF is WARRAND -
The length of leg DE is
Answer:
DF = 21DE = 7√3Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you ...
Sin = Opposite/Hypotenuse
Side DF is opposite the marked angle, and the hypotenuse is EF, so ...
sin(60°) = (√3)/2 = DF/(14√3) . . . . . to solve, multiply by the denominator
DF = (√3)/2·(14√3) = 7·3 = 21
__
Likewise,
Cos = Adjacent/Hypotenuse
Side DE is adjacent to the marked angle, so ...
cos(60°) = 1/2 = DE/(14√3) . . . . . to solve, multiply by the denominator
DE = (1/2)(14√3) = 7√3
a ball is thrown with a slingshot at a velocity of 110ft/sec at an angle of 20 degrees above the ground from a height of 4.5 ft. approximentaly how long does is take for the ball to hit the ground. Acceleration due to gravity is 32ft/s^2
Answer:
[tex]t=2.47\ s[/tex]
The ball takes 2.47 seconds to touch the ground
Step-by-step explanation:
The equation that models the height of the ball in feet as a function of time is:
[tex]h(t) = h_0 + s_0t -16t ^ 2[/tex]
Where [tex]h_0[/tex] is the initial height, [tex]s_0[/tex] is the initial velocity and t is the time in seconds.
We know that the initial height is:
[tex]h_0 = 4.5\ ft[/tex]
The initial speed is:
[tex]s_0 = 110sin(20\°)\\\\s_0 = 37.62\ ft/s[/tex]
So the equation is:
[tex]h (t) = 4.5 + 37.62t -16t ^ 2[/tex]
The ball hits the ground when when [tex]h(t) = 0[/tex]
So
[tex]4.5 + 37.62t -16t ^ 2 = 0[/tex]
We use the quadratic formula to solve the equation for t
For a quadratic equation of the form
[tex]at^2 +bt + c[/tex]
The quadratic formula is:
[tex]t=\frac{-b\±\sqrt{b^2 -4ac}}{2a}[/tex]
In this case
[tex]a= -16\\\\b=37.62\\\\c=4.5[/tex]
Therefore
[tex]t=\frac{-37.62\±\sqrt{(37.62)^2 -4(-16)(4.5)}}{2(-16)}[/tex]
[tex]t_1=-0.114\ s\\\\t_2=2.47\ s[/tex]
We take the positive solution.
Finally the ball takes 2.47 seconds to touch the ground
It would take approximately B. 2.47 seconds
Serena is an account executive. She receives a base pay of $18 an hour plus a 15 percent bonus for all the sales she generates. Last week she generated $1,200 worth of sales. What is the minimum number of hours she could have worked to make $500?
PLEASE SHOW WORK.
Answer:
17.8 hours
Step-by-step explanation:
Serena's bonus on $1200 sales is 15%×$1200 = $180. In order to make $500 for the week, then she must have at least ...
$500 - 180 = $320
in hourly pay.
At $18 per hour, that requires she work $320/($18/h) = 17.77_7 h.
Serena must work a minimum of about 17.8 hours to make $500.
_____
Comment on the answer
The exact result of the computation is 17 7/9 hours. Many payroll departments record hours to the nearest 1/4 or 1/10 hour. For Serena's pay to be at least $500, she must work 17.8 (rounded to tenths) or 18.0 (rounded to quarters) hours.
Lisa has developed a new product, and knows that the graph of function R models her revenue from selling the item, after deducting expenses, when she charges x dollars per unit.
Lisa wants to restrict function R to only model selling prices for which she will make a profit. Which interval should she use as the domain of the function?
Answer:
Choice B is correct; (10, 60)
Step-by-step explanation:
For Lisa to make a profit, the function R should assume a value greater than 0;
R > 0
We are to determine the interval of x values for which the above expression will be true.
From the graph, R(x) = 0 when x = 10. As x increases from 10 to 60, the value of R(x) remains positive, that is;
R(x) ≥ 0 for values of x in the interval (10, 60)
The domain that she should use in order to only model selling prices for which she will make a profit is thus;
(10, 60)
Benji, a 12 kg Border terrier, requires daily injections of ampicillin 15% for 3 days. The dose rate is 7.5
mg/kg. How many mL per injection does Benji require? i just need to know how to set the problem up, using dimensional analysis.
The answer is:
Benji requires 90mL per injection.
Why?From the statement we know that dog's weight is 12 kg, and daily injections are required for 3 days, the dose rate is 7.5 mg/kg, so we need to calculate how many mL per injection does Benji require.
We have that:
[tex]Weight=12Kg\\\\Dose=7.5\frac{mL}{Kg}[/tex]
If the dose rate is 7.5 mL per each Kg, how many mL are required for 12 Kg? We can set it up using the following relation:
[tex]7.5mL=1Kg\\x=12Kg\\\\x=\frac{7.5mL*12Kg}{1Kg}=\frac{90mL.Kg}{1Kg}=90mL[/tex]
Hence, we have that there are needed 90 mL per injection.
Have a nice day!
Write an Explicit formula for a1 = –2, an = an – 1 + 4, n ≥ 2
A. an = –4n – 6
B. an = –2n – 6
C. an = 4n – 6
D. an = 4n + 6
According to the recursive formula,
[tex]a_2=a_1+4[/tex]
[tex]a_3=a_2+4=(a_1+4)+4=a_1+2\cdot4[/tex]
[tex]a_4=a_3+4=a_2+2\cdot4=a_1+3\cdot4[/tex]
and so on, with the general formula
[tex]a_n=a_1+(n-1)\cdot4[/tex]
Then
[tex]a_n=-2+4(n-1)=4n-6[/tex]
and the answer is C.
Answer:
C. an = 4n -6
Step-by-step explanation:
Only one of the offered choices gives a1=-2 for n=1.
___
The recursive formula tells you ...
a2 -a1 = 4
The only choices that increase by 4 when n increases by 1 are choices C and D. Of these, choice D gives a1=4·1+6 = 10 ≠ -2.
Choice C gives a1 = 4·1 -6 = -2, as required.
Three trucks delivered potatoes to a warehouse. The first truck delivered 5 7/8 tons of potatoes, the second one 6 1/2 tons more. If the three trucks delivered 25 tons of potatoes in total, then how many tons were delivered by the third truck?
Answer:
12 5/8 tons were delivered by the third truck
Step-by-step explanation:
25 = 6 4/8 + 5 7/8 + x
25 = 12 3/8 + x
- 12 3/8
12 5/8 = x
Answer:
6 3/4
Step-by-step explanation:
5 7/8 * 2 +6 1/2 + X = 25
Do the algebra.
x = 6 3/4
PLEASE ANSWER THIS... WILL VOTE FOR U
The answer is g(x) = (1/4 x)^2
It has a horizontal stretch of 4. Since it is horizontal it goes inside the parentheses and becomes the reciprocal of 4 which is 1/4
Hope this helped!
~Just a girl in love with Shawn Mendes
2nd term in expansion of the binomial theorem (4x+2y^3)^3 show work
I hope this helps with you
Two similar polygons have areas of 4 square inches and 64 square inches. The ratio of a pair of corresponding sides is 1/4. True False
Answer:
That is true
Step-by-step explanation:
The ratio is a one-to-one measure, literally a ratio of the sides in reduced form. The area is that one-to-one ratio squared.
Our numbers are already squared, so in order to find the one-to-one we have to take the square roots of both of them.
[tex]\frac{\sqrt{4} }{\sqrt{64} } =\frac{2}{8} =\frac{1}{4}[/tex].
Answer:
True
step-by-step explanation:
Just in case you needed a second opinion.
What measure of the cylinder do 26 and 34 describe?
diameter and height i think
Answer:
they describe diameter and height
26-diameter
34-height
Please Help!!!!
Will mark brainliest. Thank you so much for your help
Answer:
a)
[tex]y=400(2.5)^{x}[/tex]
b)
3,814,698
c)
16.08 weeks
Step-by-step explanation:
a)
The question presented here is similar to a compound interest problem. We are informed that there are 400 rice weevils at the beginning of the study. In a compound interest problem this value would be our Principal.
P = 400
Moreover, the population is expected to grow at a rate of 150% every week. This is equivalent to a rate of interest in a compound interest problem.
r = 150% = 1.5
The compound interest formula is given as;
[tex]A=P(1+r)^{n}[/tex]
We let y be the weevil population in any given week x. The formula that can be used to predict the weevil population is thus;
[tex]y=400(1+1.5)^{x}\\\\y=400(2.5)^{x}[/tex]
b)
The weevil population 10 weeks after the beginning of the study is simply the value of y when x = 10. We substitute x with 10 in the equation obtained from a) above;
[tex]y=400(2.5)^{10}\\\\y=3814697.3[/tex]
Therefore, the weevil population 10 weeks after the beginning of the study is approximately 3,814,698
c)
We are simply required to determine the value of x when y is
1,000,000,000
Substitute y with 1,000,000,000 in the equation obtained in a) above and solve for x;
[tex]1000000000=400(2.5)^{x}\\\\2.5^{x}=2500000\\\\xln(2.5)=ln(2500000)\\\\x=\frac{ln(2500000}{ln(2.5)}=16.0776[/tex]
The area of a triangle is 17.5 square meters. The height of the triangle is 3 meters less than twice its base. The base of the triangle is x meters. Complete the equation that represents this description and fill in the values for the base and height of the triangle.
Answer:
17.5 = (1/2)(x)(2x-3)base: 5 m; height: 7 mStep-by-step explanation:
The base is defined as x. The height is said to be 3 less than 2x, so is (2x-3).
The formula for the area of a triangle is ...
A = (1/2)bh
Filling in the given values, we have ...
17.5 = (1/2)x(2x-3)
35 = 2x^2 -3x . . . . multiply by 2
2x^2 -3x -35 = 0 . . . . put in standard form
(2x +7)(x -5) = 0 . . . . . factor
The base is 5 meters; the height is 2·5-3 = 7 meters.
The base and height of the triangle satisfying the given conditions are approximately 4.3 and 5.6 meters, respectively.
Explanation:The area of a triangle is given by the formula 1/2 * base * height. Here, the area is 17.5 square meters, the base of the triangle is x, and the height of the triangle is 3 meters less than twice its base, therefore the height is 2x-3. Plugging these values into the formula, we get 17.5 = 1/2 * x * (2x - 3).
To solve this equation for x, first simplify the right-hand side, yielding 17.5 = x*(2x - 3). Multiplying this out gives 17.5 = 2x^2 - 3x. Then, rearrange to get the equation in standard quadratic form, resulting in 2x^2 - 3x - 17.5 = 0.
Through using quadratic formula we can find the solution(s) to be approximately x = 4.3 or x = -2.0. Since a negative value for x ? the base of a triangle ? is not possible, we discard that solution. Thus, the base of the triangle is 4.3 meters, and the height would then be 2*4.3 - 3 = about 5.6 meters.
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If $22,000 is deposited in an account paying 3.85% interest compounded continuously, use the continuously compounded interest formula , A=Pe^rt, to find the balance in the account after 11 years.
A. $1,519,356.93
B. $33,600.60
C. $33,416.25
D. $25,416.25
Answer:
B
Step-by-step explanation:
In the equation for interest compounding continuously, the A stands for the amount after the compounding is done, the P is the initial amount invested, the e is Euler's number, the r is the rate in decimal form, and the t is the time in years that the money is invested. Setting up our equation with the given values looks like this:
[tex]A=22,000e^{(.0385)(11)}[/tex]
Multiply the rate with the time to simplify a bit to
[tex]A=22,000e^{.4235}[/tex]
Raise e to the power of .4235 on your calculator (hit 2nd then the ln button to get your e) and get
[tex]A=22,000(1.527297754)[/tex]
Multiply out to get $33600.55, but rounding up gives you B as your answer.
The balance in the account after 11 years is $33,600.6. Thus, the correct option is B.
What is continuous compounding?Theoretically, long-term average interest means that interest is continuously earned on a current account as well as reinvested into the balance to increase future interest earnings.
The equation is given as,
[tex]\rm P=P_o \times e^{rt}[/tex]
The balance in the account after 11 years is calculated as,
[tex]\rm P = \$22,000 \times e^{0.0385\times 11}[/tex]
Simplify the equation, then we have
P = $22,000 x 1.52729
P = $33,600.6
Thus, the correct option is B.
More about the continuous compounding link is given below.
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What is the determinant of m= {5 8 -5 4} ? 20 40 60 80
Answer:
60
Step-by-step explanation:
We have been given the matrix;
[tex]\left[\begin{array}{ccc}5&8\\-5&4\end{array}\right][/tex]
For a 2-by-2 matrix, the determinant is calculated as;
( product of elements in the leading diagonal) - (product of elements in the other diagonal)
determinant = ( 5*4) - (8*-5)
= 20 - (-40) = 60
Answer:
c. 60
Step-by-step explanation
math
Match the systems of linear equations with their solutions.
Answer:
The solutions of linear equations in the procedure
Step-by-step explanation:
Part 1) we have
x+y=-1 ----> equation A
-6x+2y=14 ----> equation B
Solve the system by elimination
Multiply the equation A by 6 both sides
6*(x+y)=-1*6
6x+6y=-6 -----> equation C
Adds equation C and equation B
6x+6y=-6
-6x+2y=14
-------------------
6y+2y=-6+14
8y=8
y=1
Find the value of x
substitute in the equation A
x+y=-1 ------> x+1=-1 ------> x=-2
The solution is the point (-2,1)
Part 2) we have
-4x+y=-9 -----> equation A
5x+2y=3 ------> equation B
Solve the system by elimination
Multiply the equation A by -2 both sides
-2*(-4x+y)=-9*(-2)
8x-2y=18 ------> equation C
Adds equation B and equation C
5x+2y=3
8x-2y=18
----------------
5x+8x=3+18
13x=21
x=21/13
Find the value of y
substitute in the equation A
-4x+y=-9 ------> -4(21/13)+y=-9 ----> y=-9+84/13 -----> y=-33/13
The solution is the point (21/13,-33/13)
Part 3) we have
-x+2y=4 ------> equation A
-3x+6y=11 -----> equation B
Multiply the equation A by 3 both sides
3*(-x+2y)=4*3 ------> -3x+6y=12
so
Line A and Line B are parallel lines with different y-intercept
therefore
The system has no solution
Part 4) we have
x-2y=-5 -----> equation A
5x+3y=27 ----> equation B
Solve the system by elimination
Multiply the equation A by -5 both sides
-5*(x-2y)=-5*(-5)
-5x+10y=25 -----> equation C
Adds equation B and equation C
5x+3y=27
-5x+10y=25
-------------------
3y+10y=27+25
13y=52
y=4
Find the value of x
Substitute in the equation A
x-2y=-5 -----> x-2(4)=-5 -----> x=-5+8 ------> x=3
The solution is the point (3,4)
Part 5) we have
6x+3y=-6 ------> equation A
2x+y=-2 ------> equation B
Multiply the equation B by 3 both sides
3*(2x+y)=-2*3
6x+3y=6
so
Line A and Line B is the same line
therefore
The system has infinite solutions
Part 6) we have
-7x+y=1 ------> equation A
14x-7y=28 -----> equation B
Solve the system by elimination
Multiply the equation A by 7 both sides
7*(-7x+y)=1*7
-49x+7y=7 -----> equation C
Adds equation B and equation C
14x-7y=28
-49x+7y=7
------------------
14x-49x=28+7
-35x=35
x=-1
Find the value of y
substitute in the equation A
-7x+y=1 -----> -7(-1)+y=1 ----> y=1-7 ----> y=-6
The solution is the point (-1,-6)
The sum of the numbers x, y, and z is 50. The ratio of x to y is 1:4, and the ratio of y and z is 4:5. What is the value of y?
Answer:
y = 20
Step-by-step explanation:
x+y+z = 50
x/y = 1/4 so y = 4x
Substitute y = 4x into x+y+z = 50
x + 4x + z = 50
5x + z = 50
y/z = 4/5 --> 4z = 5y so z =5/4 y
Substitute z =5/4 y into 5x + z = 50
5x + 5/4 y = 50
You can solve for x from these 2 equations
5x + 5/4 y = 50
y = 4x
Substitute y = 4x into 5x + 5/4 y = 50
5x + 5/4 (4x) = 50
5x + 5x = 50
10x = 50
x = 5
y = 4x = 4 (5) = 20
Answer
y = 20
The sum of the numbers x, y, and z is 50. The ratio of x to y is 1:4, and the ratio of y and z is 4:5
The value of y =20
Given :
The sum of the numbers x, y, and z is 50
The ratio of x to y is 1:4, and the ratio of y and z is 4:5.
The sum of the numbers x, y, and z is 50
The equation becomes [tex]x+y+z=50[/tex]
The ratio of x to y is 1:4
[tex]\frac{x}{y} =\frac{1}{4} \\4x=y\\y=4x[/tex]
Now use the second ratio . the ratio of y and z is 4:5
[tex]\frac{y}{z} =\frac{4}{5}\\5y=4z\\Replace \; y=4x\\5(4x)=4z\\20x=4z\\z=5x[/tex]
Replace y=4x and z=5x in the first equation
[tex]x+y+z=50\\x+4x+5x=50\\10x=50\\x=5[/tex]
Now we replace x with 5 and find out y
[tex]y=4x\\y=4(5)\\\y=20[/tex]
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(I need help as soon as i can! :-) Can you find the third angle measure in a triangle, if you know the other 2 angel measure?
Answer: Yes you can using the sum of internal angles in a triangle they add up to 180, so if you add the two given angle measures and them substract the result from 180 you will have the measure of the third angle. Hope this helps. :)
Step-by-step explanation:
The function f(x) is the wait time for an amusement park ride where x is the number of people in line. What is the practical domain for the function f(x)?
all integers
all whole numbers
all real numbers
all positive integers
Answer:
The domain would be the set of all whole numbers.
Step-by-step explanation:
Integers are { ......-3, -2, -1, 0, 1, 2, 3....}
Whole numbers are {0, 1, 2, 3, ...... }
Real numbers are all numbers except imaginary number,
Positive integers are {1, 2, 3, 4, ....}
Given,
In the function f(x),
x represents the number of people in line,
We know that number of people can not be negative and it can be 0,
Thus, the possible value of x are 0, 1, 2, 3,......
Also, the domain of a function is the set of all possible value of input,
Since, x represent the input for the function f(x),
Thus, the domain of f(x) would be the set of all whole number.
Second option is correct.
In triangle ABC, the side lengths are AB = 13, AC = 21, and BC = x. Write a compound inequality that represents the range of possible values for x.
Big fraction
Parentheses
Vertical bars
Square root
Root
Superscript (Ctrl+Up)
Subscript (Ctrl+Down)
Plus sign
Minus sign
Middle dot
Multiplication sign
Equals sign
Less-than sign
Greater-than sign
Less-than or equal to
Greater-than or equal to
Pi
Alpha
Beta
Epsilon
Theta
Lambda
Mu
Rho
Phi
Sine
Cosine
Tangent
Arcsine
Arccosine
Arctangent
Cosecant
Secant
Cotangent
Logarithm
Logarithm to base n
Natural logarithm
Bar accent
Right left arrow with under script
Right arrow with under script
Angle
Triangle
Parallel to
Perpendicular
Approximately equal to
Tilde operator
Degree sign
Intersection
Union
Summation with under and over scripts
Matrix with square brackets
The compound inequality representing the range of possible values for 'x' (side length BC) in the triangle ABC, given that side lengths AB=13 and AC=21, is 8 < x < 34.
Explanation:In the triangle ABC with side lengths, AB=13, AC=21, and BC=x, we use the triangle inequality theorem which states that the length of a side of a triangle is less than the sum of the lengths of the other two sides and more than the absolute difference between them. Applying this theorem to your specific situation, we get the compound inequality 8 < x < 34. This inequality represents the range of possible values for the side length x is BC.
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For triangle ABC with sides AB = 13, AC = 21, and BC = x, the range of possible values for x is[tex]\( 8 < x < 34 \)[/tex] based on the triangle inequality theorem.
In triangle ABC, the relationship among its side lengths is governed by the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.
For the given triangle with side lengths AB = 13, AC = 21, and BC = x, we can express this relationship as a compound inequality. Let \[tex]( a \), \( b \), and \( c \)[/tex] represent the lengths of the sides of the triangle. According to the triangle inequality theorem, we have:
[tex]\[ a + b > c \][/tex]
Substitute the given values:
[tex]\[ 13 + x > 21 \][/tex]
Now, solve for[tex]\( x \)[/tex]
[tex]\[ x > 8 \][/tex]
Similarly, for the other pair of sides:
[tex]\[ 21 + x > 13 \][/tex]
Solving for \( x \):
[tex]\[ x > -8 \][/tex]
However, since side lengths cannot be negative, we disregard the second inequality. Therefore, the compound inequality representing the range of possible values for [tex]\( x \) is \( 8 < x < 34 \).[/tex] This means that any value of [tex]\( x \)[/tex] between 8 and 34 (exclusive) will satisfy the conditions for the given triangle.
There are 40 students in an elementary statistics class. On the basis of years of experience, the instructor knows that the time needed to grade a randomly chosen first examination paper is a random variable with an expected value of 6 min and a standard deviation of 6 min.If a grading times are independent and the instructor begins grading at 6:50 P.M. and grades continuously, the (approximate probability that he is through grading before the 11:00 P.M. TV news begins is probability isIf the sports report begins at 11:10 P.M., the probability that he misses part of the report if he waits until grading is done before turning on the TV is
Final answer:
To determine the probability of the instructor finishing grading before 11:00 P.M., calculate the expected time to grade 40 exams, determine the standard deviation, and then use the z-score to find the corresponding probability from the standard normal distribution.
Explanation:
To tackle these statistics problems, there are several concepts we need to apply including expected value, standard deviation, the central limit theorem, hypothesis testing, and probability. Since only one problem can be answered at a time, I'll focus on the first one you've mentioned about the grading times for exams.
The instructor's time to grade each paper is a random variable with an expected value of 6 minutes and a standard deviation of 6 minutes. When considering the grading of 40 papers, we can use the central limit theorem which suggests that the sum of these independent random variables will be approximately normally distributed given the large number of papers (n=40).
We first calculate the expected total time to grade 40 exams by multiplying the individual exam time's expected value by the number of exams: 6 minutes/exam * 40 exams = 240 minutes. Then, we calculate the standard deviation for the total grading time: 6 minutes/exam * √40 ≈ 37.95 minutes.
To find the probability that the instructor finishes grading before 11:00 P.M., we need to calculate the number of minutes from 6:50 P.M. to 11:00 P.M., which is 250 minutes. Next, we convert this problem into a z-score problem where we find the z-score corresponding to 250 minutes. Finally, we look up this z-score in a standard normal distribution table (or use statistical software) to find the corresponding probability.
The diameter of a sphere is 12
inches. What is the appropriate
surface are, in square inches, of the
sphere if Surface Area = 4tr2?
Answer:
first u should find the radius .radius is half of diameter 12/2=6 so surface area of sphere is 4*3.142*6*6=452.448 square in
The diagram is not to scale.
Answer:
[tex]|AB|=30[/tex]
Step-by-step explanation:
From the diagram,
AO=OC=16 units, all radii of a circle are equal.
BO=OC+BC
BO=16+18
BO=34
A tangent to a circle will always meet the radius at right angles.
We use the Pythagoras Theorem to obtain:
[tex]|AB|^2+|AO|^2=|BO|^2[/tex]
[tex]|AB|^2+16^2=34^2[/tex]
[tex]|AB|^2+256=1156[/tex]
[tex]|AB|^2=1156-256[/tex]
[tex]|AB|^2=900[/tex]
Take positive square roots to get:
[tex]|AB|=\sqrt{900}[/tex]
[tex]|AB|=30[/tex]
Please help me ASAP!!!!
Answer: A, inside the circle.
Step-by-step explanation: Because the radius is wider than 4, (4,-1) would be just inside the circle instead of outside. Using the radius, you could determine that all points on the circle extend 5 units from its center, which means that the overall circumference would be past (4,-1).
Hope this helps,
LaciaMelodii :)
The fibrous protein core formed by elongated cells that contains melanin pigment is the______?
Answer:
Cortex layer
Step-by-step explanation:
The fibrous protein core of the hair, formed by elongated cells containing melanin pigment, is the cortex layer
Answer:
The fibrous protein core formed by elongated cells that contains melanin pigment is the cortex.
The maximum grade allowed between two stations in a rapid-transit rail system is 3.5%. Between station A and station B, which are 260260 ft apart, the tracks rise 7 and one half7
1
2 ft. What is the grade of the tracks between these two stations? Round the answer to the nearest tenth of a percent. Does this grade meet the rapid-transit rail standards?
The grade of the tracks between station A and station B is nothing%.
(Type an integer or decimal rounded to the nearest tenth as needed.)
Answer:
2.9%
Step-by-step explanation:
The problem says the stations are 260 feet apart. Assuming that this is the horizontal distance between them, then the grade is:
7.5 / 260 × 100% = 2.9%
This is less than the maximum of 3.5%, so it meets the standards.
Given: JK tangent, KH=16, HE=12 Find: JK.
Check the picture below.