Answer:
[tex]{ \tt{4 log_{4}(3100) }} \\ = { \tt{4 log_{4}(775 \times 4) }} \\ = { \tt{4 log_{4}(775) + 4 log_{4}(4) }} \\ = { \tt{4( (\frac{ log_{10}775 }{ log_{10}4 } ) +1)}} \\ = { \tt{4(4.8 + 1)}} \\ = { \tt{23.2}}[/tex]
An English professor assigns letter grades on a test according to the following scheme. A: Top 13% of scores B: Scores below the top 13% and above the bottom 55% C: Scores below the top 45% and above the bottom 20% D: Scores below the top 80% and above the bottom 9% F: Bottom 9% of scores Scores on the test are normally distributed with a mean of 78.8 and a standard deviation of 9.8. Find the numerical limits for a C grade. Round your answers to the nearest whole number, if necessary.
Answer:
Scores between 71 and 80 give a C grade.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Scores on the test are normally distributed with a mean of 78.8 and a standard deviation of 9.8.
This means that [tex]\mu = 78.8, \sigma = 9.8[/tex]
Find the numerical limits for a C grade.
Above the bottom 20%(20th percentile) and below the top 45%(below the 100 - 45 = 55th percentile).
20th percentile:
X when Z has a p-value of 0.2, so X when Z = -0.84.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.84 = \frac{X - 78.8}{9.8}[/tex]
[tex]X - 78.8 = -0.84*9.8[/tex]
[tex]X = 70.57[/tex]
So it rounds to 71.
55th percentile:
X when Z has a p-value of 0.55, so X when Z = 0.125.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.125 = \frac{X - 78.8}{9.8}[/tex]
[tex]X - 78.8 = 0.125*9.8[/tex]
[tex]X = 80[/tex]
Scores between 71 and 80 give a C grade.
I need two examples of rounding to the thousandths place. SHOW ALL WORK!
Answer:
3.418
Step-by-step explanation:
3.4175
3.4178
u round if the number behind it is higher than 5
Anne is building bookcases that are 3.1 feet long. How many complete shelves can be cut from a 12-foot board?
Answer: 3 shelves
Step-by-step explanation:
12 ÷ 3.1 = 3.87…
Since this is more than 3 but less than 4, we can build 3 full shelves with a leftover.
Since lim n→ infinity (.............) = ...........
Notice that
[tex]\dfrac{4n+1}{8n+2}=\dfrac{4n+1}{2(4n+1)}=\dfrac12[/tex]
So by the root test,
[tex]\displaystyle\lim_{n\to\infty}\sqrt[n]{\left|\left(\frac12\right)^{2n}\right|} = \frac14 < 1[/tex]
and so the series converges (absolutely).
Which best describes the relationship between the line that passes through the points (6, –1) and (11, 2) and the line that passes through the points (5, –7) and (8, –2)?
A. same line
B. neither perpendicular nor parallel
C. perpendicular
D. parallel
Answer:
Step-by-step explanation:
slope of line through (6,-1) and (11,2) = (-1 - 2)/(6 - 11) = 3/5
slope of line through (5,-7) and (8,-2) = (-7 - (-2))/(8 - 5) = -5/3
product of the slopes = -1, so the lines are perpendicular.
Consider the initial value problem
y' + 6y = {0 if 0 < or equal to t < or equal to 2
12 if 2 < or equal to t < or equal to 6
0 if 6 < or equal to t < or equal to infinity}
a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y(t) by Y(s). Do not move any terms from one side of the equation to the other (until you get to part (b) below).
b. Solve your equation for Y(s).
c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t).
y' + 6y = f(t)
where
[tex]f(t)=\begin{cases}0&\text{if }0\le t\le2\\12&\text{if }2<t\le6\\0&\text{if }6<t<\infty\end{cases}[/tex]
You can write f(t) in terms of the unit step (i.e. Heaviside theta) function u(t), which is defined as
[tex]u(t)=\begin{cases}0&\text{if }t<0\\1&\text{if }t\ge0\end{cases}[/tex]
Then the DE is written as
y' + 6y = 12 u (t - 2) - 12 u (t - 6)
(a) Take the Laplace transform of both sides:
LT[y' + 6y] = LT[12 u (t - 2) - 12 u (t - 6)]
s Y - y (0) + 6Y = 12 (exp(-2s) - exp(-6s))/s
(b) Solve for Y :
(s + 6) Y = 12 (exp(-2s) - exp(-6s))/s + y (0)
Y = 12 (exp(-2s) - exp(-6s))/(s (s + 6)) + y (0)/(s + 6)
(c) Take the inverse transform:
LT⁻¹ [Y] = LT⁻¹[12 (exp(-2s) - exp(-6s))/(s (s + 6)) + y (0)/(s + 6)]
y = 12 LT⁻¹ [(exp(-2s) - exp(-6s))/(s (s + 6))] + y (0) LT⁻¹ [1/(s + 6)]
y = 12 u (t - 2) LT⁻¹ [1/(s (s + 6))] - 12 u (t - 6) LT⁻¹ [1/(s (s + 6))] + y (0) exp(-6t )
For the remaining inverse transform, break up into partial fractions:
1/(s (s + 6)) = a/s + b/(s + 6)
1 = a (s + 6) + bs
1 = (a + b) s + 6a
==> 6a = 1, a + b = 0 ==> a = 1/6, b = -1/6
y = 2 u (t - 2) LT⁻¹ [1/s - 1/(s + 6)] - 2 u (t - 6) LT⁻¹ [1/s - 1/(s + 6)] + y (0) exp(-6t )
y = 2 u (t - 2) (1 - exp(-6t )) - 2 u (t - 6) (1 - exp(-6t )) + y (0) exp(-6t )
It costs $7.45 for 2.5 pounds of round steak. What is the unit rate?
A.$9.95 per pound
B.$18.63 per pound
C.$2.50 per pound
D.$2.98 per pound
Answer:
D.
Step-by-step explanation:
Since the unit rate is in dollars per pound, we divide the cost (in dollars) by the weight (in pounds.)
($7.45)/(2.5 lb) = $2.98 per pound
Answer: D.
Compute how many 7-digit numbers can be made from the digits 1, 2, 3, 4, 5, 6, 7 if there is no repetition and the odd digits must appear in an unbroken sequence. (Examples: 3571264 or 2413576 or 2467531, etc., but not 7234615.)
Answer:
Number of 7-digit numbers that can be made from the digit is 576
Step-by-step explanation:
Given the data in the question;
digits ⇒ 1, 2, 3, 4, 5, 6, 7
Number of odd numbers in the given digits = 4
Number of even numbers in the given digits = 3
now, we take the odd digits as a single unit.
so, number of ways the odd digits can be arranged with the unit will be 4!.
Now, lets consider the unit of 4 odd digits with 3 even digits.
there are 4 units.
so the number of possible arrangements of these 4 units = 4!
hence, Number of 7-digit numbers that can be made from the digits will be;
⇒ Number of possible arrangements of 4 units × Number of ways in which the odd digits can be arranged within the unit.
⇒ 4! × 4!
⇒ 576
Therefore, Number of 7-digit numbers that can be made from the digit is 576
find the value of X in each figure below
Answer:
168). C
169). C
170). C
Step-by-step explanation:
For the first angle, it is a right angle, so it measures 90 degrees.
x and 50 are complementary angles, meaning they add up to 90 degrees.
So, subtract 50 from 90 to get 40, which is equal to x.
45 and x are supplementary angles, meaning they add up to 180 degrees.
Subtract 45 from 180 to get 35 degrees, which is the measure of angle x.
All angles in a triangle add up to 180 degrees.
So, 70 + 56 = 126, 180 - 126 = 54.
Since the unknown angle is x - 5, 54 + 5 = 59, which the the measure of angle x - 5.
Polynomial: 3x^4 + 5x - 4; Divisor: x - 1
Answer:
3x³+3x²+3x+8+[tex]\frac{4}{x-1}[/tex]
Step-by-step explanation:
You can use synthetic division for this problem since the divisor is in (x-a) form. The fraction is the remainder over the divisor.
What is 5% of 483759????
Step-by-step explanation:
5% of 483759 is 24187.95
Answer: The answer is 24,187.95
Step-by-step explanation:
483759 Multiplied by 0.05 = 24,187.95
Tìm x không âm biết √x =3
Answer:
x=9
Step-by-step explanation:
[tex]\sqrt{x}[/tex]=3
[tex]\sqrt{x}[/tex]^2=3^2
x=9
There is a rack of 15 billiard balls. Balls numbered 1 through 8 are solid-colored. Balsa numbered 9 through 15 contain stripes. If one ball is selected at random, determine the odds for it being striped.
If one ball is selected at random, the odds for it being striped are 7 out of 15, or 7/15.
What do we know?
We know that there are 15 billiard balls.
We also know that balls numbered 1 through 8 are solid-colored, so we have 8 solid-colored balls.
And the other 7 balls are striped.
Now we want to find the probability for a randomly selected ball to be a striped ball.
Because all the balls have the same probability of being randomly selected, the probability of randomly selecting a striped ball is equal to the quotient between the number of striped balls (7) and the total number of balls (15).
Then we have:
P = 7/15 = 0.467
That quotient is also what is called the "odds"
So if one ball is selected at random, the odds for it being striped are 7 out of 15, or 7/15.
If you want to learn more, you can read:
https://brainly.com/question/23044118
In the picture below, which lines are lines of symmetry for the figure?
A. 1 and 3
B. only 3
C. 2
D. 1, 2, and 3
A line of symmetry would separate a shape to make multiple shapes that are exactly the same.
The answer is C.2
find the lateral surface area of this cylinder. round to the nearest tenth. r=5cm 5cm LSA (in the image)
Answer:
157 cm²
Step-by-step explanation:
A cylinder is given to us and we need to find out the lateral surface area of the cylinder . We can see that the ,
Height = 5cm
Radius = 5cm
We know that we can find the lateral surface area of the cylinder as ,
[tex]\rm\implies LSA_{cylinder}= 2\pi r h [/tex]
Substitute upon the respective values ,
[tex]\rm\implies LSA = 2 \times 3.14 \times 5cm \times 5cm [/tex]
Multiply the numbers ,
[tex]\rm\implies \boxed{\blue{\rm LSA = 157 \ cm^2 }}[/tex]
Hence the Lateral surface area of the cylinder is 157 cm² .
[tex] \setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{5cm}}\put(9,17.5){\sf{5cm}}\end{picture}[/tex]
Answer:
314.2 is the Surface area
Step-by-step explanation:
Hope it Helps! If you have any questions, feel free to comment! :)
2π(5)(5)+2π(5^2)
2π(25)+2[tex]\pi[/tex](25)
50π+50π=100π
314.2 is the answer. That's what we get after rounding up! :)
On her summer abroad in France, Jane bought a pair of shoes for 54.82 euros. The store owner only had francs to give her as change. She gave him 55 euros. How much did he give her back in francs
Answer:
0.19
Step-by-step explanation:
Jane bought a shoe for 54.82 euros
She gave the store owner 55 euros
= 55-54.82
= 0.18 euros to franc
= 0.18× 1.08222
= 0.19 franc
The lengths of the three sides of a triangle are 17, 18, and 19. Classify it as acute, obtuse, or right.
Answer:
acute
Step-by-step explanation:
That triangle is an obtuse triangle
1/2 sin x sin (2x) + Cos 3 x
Answer:
1.047734151
Step-by-step explanation:
Type into calculator
1/2sin(2x)+cos(3x)
If IC Rs 100 is equal to Rs 160 NC, convert IC Rs 150 into NC rupees.
Answer:
240 NC rupees.
Marilyn is retiring and wants to set up a 25-year annuity with 140 000 of her savings . The annuity earns 7.7 compounded monthly How much will Marilyn receive every month ?
Answer:
marilyn isrestiring and wants to set up a 25-year annuity earns 7.
If\[\displaystyle\frac{\sqrt{600} + \sqrt{150} + 4\sqrt{54}}{6\sqrt{32} - 3\sqrt{50} - \sqrt{72}} = a\sqrt{b},\]where $a$ and $b$ are integers and $b$ is as small as possible, find $a+b.$
9514 1404 393
Answer:
12
Step-by-step explanation:
Apparently, you want the sum a+b when ...
[tex]\[\displaystyle\frac{\sqrt{600} + \sqrt{150} + 4\sqrt{54}}{6\sqrt{32} - 3\sqrt{50} - \sqrt{72}} = a\sqrt{b},\][/tex]
A calculator can show you the expression on the left evaluates to √243. In simplest terms, that is 9√3, so we have a=9, b=3 and ...
a+b = 9+3 = 12
Answer:
12
Step-by-step explanation:
The Science Club arranged a trip to Smithsonian. Only 2/3 of the members were able to attend, which left one seat empty on the 25-passenger bus. How many members does the Science Club have?
Answer:
36 members
Step-by-step explanation:
Let x = the number of science club members
There are 24 people on the bus (1 seat empty on the 25 seat bus)
2/3 of the club attended and that equals 24 people on the bus
2/3x = 24
Multiply each side by 3/2
3/2 * 2/3x = 24 * 3/2
x = 36
A line with a slope of 4 passes through the point (2, 3) . What is its equation in slope -intercept form?
Answer:
y=4x-5
Step-by-step explanation:
Slope-intercept form is y=mx+b where m is the slope and b is the y intercept.
Plug in what you know to solve for b.
3 = 4(2) + b
3 = 8 + b
3-8 = b
b = -5
now put b and m back into the slope- int form.
y = 4x-5
If the cost, C, for manufacturing x units of a certain product is given by c=x^2-5x+65, find the number of units manufactured at a cost of 13,865.
9514 1404 393
Answer:
120
Step-by-step explanation:
I find it pretty easy to obtain the solution by graphing ...
c(x) -13865 = 0
The positive value of x that makes this so is x = 120.
120 units will have a cost of 13,865 to manufacture.
__
If you like to solve this algebraically, you can probably do it most easily by completing the square.
x^2 -5x = -65 +13865
x^2 -5x +6.25 = 13806.25 . . . . . add the square of (-5/2)
(x -2.5)² = 13806.25
x -2.5 = √13806.25 = 117.5 . . . . only the positive square root is interesting
x = 117.5 +2.5 = 120
The length of a rectangle is 2 cm longer than its width.
If the perimeter of the rectangle is 36 cm, find its area.
Answer:
80 cm^2
Step-by-step explanation:
Let the width of the rectangle equal x. This means the length is x + 2, as it is 2 cm longer than the width. The formula for perimeter is: P = 2l + 2w, and substitute in the values of the length, width, and perimeter:
P = 2l + 2w
36 = 2(x + 2) + 2(x)
36 = 2x + 4 + 2x
36 = 4x + 4
4x = 32
x = 8
x represents the width, so the width is 8 and the length is 10. Area is length times width, so the area is 8 x 10 or 80 cm^2.
Step-by-step explanation:
let x be the width
p=2l+2w
36=2(2)+2(x)
36=4+2x
36-4=2x
32/2=2x/2(simplify)
x=16
therefore the width is 16cm
area of the rectangle is l×w
=2×16
=32cm"
therefore the area is 32cm"
The diameter of a sphere is 4 centimeters. Which represents the volume of the sphere?
A) 32/3π cm^3
B) 8π cm^3
C) 64/3π cm^3
D) 16π cm^3
Answer:
32[tex]\pi[/tex]/3 cm³
Step-by-step explanation:
If the diameter is 4 cm, then the radius is 2 cm.
Use the sphere volume formula:
V = 4/3[tex]\pi[/tex]r³
Plug in the radius and solve:
V = 4/3[tex]\pi[/tex](2)³
V = 4/3[tex]\pi[/tex](8)
V = 32[tex]\pi[/tex]/3
So, the volume of the sphere is 32[tex]\pi[/tex]/3 cm³
The radius of a sphere is increasing at a rate of 5 mm/s. How fast is the volume increasing (in mm3/s) when the diameter is 40 mm
9514 1404 393
Answer:
8000π mm^3/s ≈ 25,133 mm^3/s
Step-by-step explanation:
The rate of change of volume is found by differentiating the volume formula with respect to time.
V = 4/3πr^3
V' = 4πr^2·r'
For the given numbers, this is ...
V' = 4π(20 mm)^2·(5 mm/s) = 8000π mm^3/s ≈ 25,133 mm^3/s
_____
Additional comment
By comparing the derivative to the area formula for a sphere, you see that the rate of change of volume is the product of the area and the rate of change of radius. This sort of relationship will be seen for a number of different shapes.
If my saving x$ grows 10% every year how much will I have in:
1 year
2 year
5 year
Answer:
[tex]1.1x, 1.21x, 1.61051x[/tex]
Step-by-step explanation:
If you saving grows [tex]10 \%[/tex] every year, then your saving is [tex]1.1\\[/tex] times your saving from last year. Therefore, after one year, you will have [tex]1.1x\\[/tex], then after [tex]2[/tex] years, you will have [tex](1.1)^2 \cdot x=1.21x[/tex], then after [tex]5[/tex] years, you will have [tex](1.1)^5 \cdot x = 1.61051x[/tex].
Answer:
$1.1x, $1.21x, $1.61x
Step-by-step explanation:
four consecutive numbers have a sum of –30. What number is x?
Answer:
- 9
Step-by-step explanation:
Let the four consecutive numbers be x, x + 1,
x + 2 and x + 3.
x + x + 1 + x + 2 + x + 3 = - 30
x + x + x + x + 1 + 2 + 3 = - 30
4x + 6 = - 30
4x = - 30 - 6
4x = - 36
x = - 36 / 4
x = - 9
classmate Date 8) Solve the word problems a) If 576 balls are arranged in equal number of rows and columns, find the numbers of rows.
Answer:
24
Step-by-step explanation:
The number of rows (x) should b equal to the number of columns (x).
x²=576
x=√576 taking the square root of the product
x=24
