Answer:
a) 0.0147 = 1.47% probability that none of them graduates from the local community college.
b) 0.9398 = 93.98% probability that at most four will graduate from the local community college.
c) The expected number that will graduate is 2.85.
Step-by-step explanation:
For each student, there are only two possible outcomes. Either they will graduate, or they will not. The probability of a student graduating is independent of any other student graduating, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
57% of students who enter the college as freshmen go on to graduate.
This means that [tex]p = 0.57[/tex]
Five freshmen are randomly selected.
This means that [tex]n = 5[/tex]
a. What is the probability that none of them graduates from the local community college?
This is P(X = 0). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.57)^{0}.(0.43)^{5} = 0.0147[/tex]
0.0147 = 1.47% probability that none of them graduates from the local community college.
b. What is the probability that at most four will graduate from the local community college?
This is:
[tex]P(X \leq 4) = 1 - P(X = 5)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{5,5}.(0.57)^{5}.(0.43)^{0} = 0.0602[/tex]
So
[tex]P(X \leq 4) = 1 - P(X = 5) = 1 - 0.0602 = 0.9398[/tex]
0.9398 = 93.98% probability that at most four will graduate from the local community college.
c. What is the expected number that will graduate?
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
In this question:
[tex]E(X) = 5*0.57 = 2.85[/tex]
The expected number that will graduate is 2.85.
Starting from point A, a boat sales due south for 4 miles, then due east for 5 miles, then due south again for 6 miles. How far is the boat from point A?
Answer:
17 miles
By adding the miles they have traveled, you get you total distance.
Matthew participates in a study that is looking at how confident students at SUNY Albany are. The mean score on the scale is 50. The distribution has a standard deviation of 10 and is normally distributed. Matthew scores a 65. What percentage of people could be expected to score the same as Matthew or higher on this scale
Answer:
The percentage of people that could be expected to score the same as Matthew or higher on this scale is:
= 93.3%.
Step-by-step explanation:
a) Data and Calculations:
Mean score on the scale, μ = 50
Distribution's standard deviation, σ = 10
Matthew scores, x = 65
Calculating the Z-score:
Z-score = (x – μ) / σ
= (65-50)/10
= 1.5
The probability based on a Z-score of 1.5 is 0.93319
Therefore, the percentage of people that could be expected to score the same as Matthew or higher on this scale is 93.3%.
A river is 212 mile long. What is the length of the river on a map, if the scale is 1 inch : 50 miles?
Answer:
4.24 inches
Step-by-step explanation:
1 inch / 50 miles = x / 212 miles Cross multiply
1 inch * 212 miles = 50 miles * x Divide by 50 miles
1 inch * 212 miles / 50 miles = x
x = 4.24 inches.
How much is 0.24 of an inch?
0.24 * 50 = 12
So 0.24 inches represents 12 miles.
If a woman makes $32,000 a year receives a cost of living increase 2.2% what will her new salary be?
Answer:
$32 704
Step-by-step explanation:
(102.2÷100) × 32 000 = $32 704
The sum of a number and 2 times its reciprocal is -3
Answer:
(-2,-1)
Step-by-step explanation:
let the number=x
its reciprocal=1/x
x+2(1/x)=-3
x+2/x=-3
x²+2=-3x
x²+3x+2=0
(x+2)(x+1)=0
x=-2,-1
9. What is the value of x if the quadrilateral is a rhombus? 15 5x 4x+3
I don’t think I got the right answer?
Answer:
it's third option the one who says 10 units up
Select the line segment.
Answer:
i think you need to attach a fine for us to do so?
Step-by-step explanation:
Answer:
I can't tell you without the problem
When four times a number is added to 8 times the number, the result is 36. What is the number
Let the number = X
4x + 8x = 36
Simplify:
12x = 36
Divide both sides by 12:
x = 3
The number is 3
If f(x) =4x2 - 8x - 20 and g(x) = 2x + a, find the value of a so that the y-intercept of the graph of the composite function (fog)(x) is (0, 25).
Answer:
The possible values are a = -2.5 or a = 4.5.
Step-by-step explanation:
Composite function:
The composite function of f(x) and g(x) is given by:
[tex](f \circ g)(x) = f(g(x))[/tex]
In this case:
[tex]f(x) = 4x^2 - 8x - 20[/tex]
[tex]g(x) = 2x + a[/tex]
So
[tex](f \circ g)(x) = f(g(x)) = f(2x + a) = 4(2x + a)^2 - 8(2x + a) - 20 = 4(4x^2 + 4ax + a^2) - 16x - 8a - 20 = 16x^2 + 16ax + 4a^2 - 16x - 8a - 20 = 16x^2 +(16a-16)x + 4a^2 - 8a - 20[/tex]
Value of a so that the y-intercept of the graph of the composite function (fog)(x) is (0, 25).
This means that when [tex]x = 0, f(g(x)) = 25[/tex]. So
[tex]4a^2 - 8a - 20 = 25[/tex]
[tex]4a^2 - 8a - 45 = 0[/tex]
Solving a quadratic equation, by Bhaskara:
[tex]\Delta = (-8)^2 - 4(4)(-45) = 784[/tex]
[tex]x_{1} = \frac{-(-8) + \sqrt{784}}{2*(4)} = \frac{36}{8} = 4.5[/tex]
[tex]x_{2} = \frac{-(-8) - \sqrt{784}}{2*(4)} = -\frac{20}{8} = -2.5[/tex]
The possible values are a = -2.5 or a = 4.5.
Find the distance between the points (3,4) and (–8,4)
Answer:
distance = 11
Step-by-step explanation:
distance = [tex]\sqrt{[3-(-8)]^{2} +(4-4)^{2}}[/tex]
= [tex]\sqrt{11^{2} }[/tex]
= 11
Which pair of functions are inverses of each other?
O A. f(x) = f and g(x) = 8x?
O B. f(x) = 4 + 9 and g(x) = 4x - 9
O C. Ax) = 5x – 9 and g(x) = 149
O D. f(x) = 3 - 7 and g(x) = 247
I need help with this question.
Answer:
Step-by-step explanation:
f(x-2) means that x is happening sooner or a shift to the left and
+4 means that the whole function moves up 4.
The 1st choice looks good
Uma lâmpada de incandescência traz os seguintes dados inscritos no seu bulbo. U= 220 V e P = 100 W. Conhecendo as relações U = R. i e P = U. i , pode-se afirmar que o valor da resistência R da lâmpada durante o funcionamento é, em omhs:
Answer:
The resistance is 484 ohm.
Step-by-step explanation:
An incandescent lamp has the following data inscribed on its bulb. U= 220 V and P = 100 W. Knowing the relations U = R. i and P = U. i , it can be stated that the value of the resistance R of the lamp during operation is, in omhs:
P = 100 W
V = 220 V
Let the current is I.
P = V I
100 = 220 I
I = 0.45 A
Now,
V = I R
220 = 0.45 x R
R = 484 ohm
The resistance is 484 ohm.
Answer correctly and 40 points. Thx. Will report if wrong. ASAP plz! Thx!
Answer:
-7
Step-by-step explanation:
if you multiply by 7 positive it wont work because u cant cancel 7x out and a fraction wont work because theres no fraction involved in this so ur answer is A
Need help on this ASAP
Answer:
The answer is C
Step-by-step explanation:
The intersection of those figures results to a point
6. Calculate the area of the octagon in the
figure below.
Answer:
[tex]41\text{ [units squared]}[/tex]
Step-by-step explanation:
The octagon is irregular, meaning not all sides have equal length. However, we can break it up into other shapes to find the area.
The octagon shown in the figure is a composite figure as it's composed of other shapes. In the octagon, let's break it up into:
4 triangles (corners)3 rectangles (one in the middle, two on top after you remove triangles)Formulas:
Area of rectangle with length [tex]l[/tex] and width [tex]w[/tex]: [tex]A=lw[/tex] Area of triangle with base [tex]b[/tex] and height [tex]h[/tex]: [tex]A=\frac{1}{2}bh[/tex]Area of triangles:
All four triangles we broke the octagon into are congruent. Each has a base of 2 and a height of 2.
Thus, the total area of one is [tex]A=\frac{1}{2}\cdot 2\cdot 2=2\text{ square units}[/tex]
The area of all four is then [tex]2\cdot 4=8[/tex] units squared.
Area of rectangles:
The two smaller rectangles are also congruent. Each has a length of 3 and a width of 2. Therefore, each of them have an area of [tex]3\cdot 2=6[/tex] units squared, and the both of them have a total area of [tex]6\cdot 2=12[/tex] units squared.
The last rectangle has a width of 7 and a height of 3 for a total area of [tex]7\cdot 3=21[/tex] units squared.
Therefore, the area of the entire octagon is [tex]8+12+21=\boxed{41\text{ [units squared]}}[/tex]
what is the sum of a 7 term geometric series if the first term is 6 the last term is -24576 and the common ratio is -4
Answer:
Sum = 19,662
Step-by-step explanation:
Given that this is a finite geometric series (meaning it stops at a specific term or in this case -24,576), we can use this formula:
[tex]\frac{a(1-r^n)}{1-r}[/tex], where a is the first term, r is the common ratio, and n is the number of terms.
Substituting for everything and simplifying gives us:
[tex]\frac{6(1-(-4)^7)}{1-(-4)} \\\\\frac{6(16385}{5}\\ \\\frac{98310}{5}\\ \\19662[/tex]
1) Write an equation in slope-intercept form of the line with slope of 6 and y-intercept of -3. Then graph the line. 2) Write an equation in point-slope form of the line with slope -3/5 that contains(-10 ,8). Then graph the line.
Answer:
An equation in the slope-intercept form is:
y = a*x + b
Where a is the slope, and b is the y-intercept.
a)
Here we have a slope of 6 and a y-intercept of -3
Then the equation is:
y = 6*x - 3
Now we want to graph this.
To graph it, we first need to find two points (x, y) that belong to this equation, then we can graph the points, and connect them with a line.
To find the points, we evaluate in two different values of x.
x = 0
y = 6*0 - 3 = -3
Then we have the point (0, -3)
x = 1
y = 6*1 - 3 = 3
Then we have the point (1, 3)
The graph of this line can be seen in the image below (the red one)
b) Similar to before, here the slope is -3/5, then the equation is something like:
y = (-3/5)*x + b
Now we also know that the line passes through the point (-10, 8)
This means that when x = -10, we must have y = 8
Replacing these two in the equation we get:
8 = (-3/5)*-10 + b
8 = 6 + b
8 - 6 = 2 = b
Then this equation is:
y = (-3/5)*X + 2
The graph can be found in the same way as before, the graph of this function can also be seen in the image below (the green one)
What is the GCF of 1683t, 4085, and 68t??
O 4
O 483t
O 8
O 8837
Answer:I’m pretty sure ( not 100% thou ) the awnser would be A) 4
Zero is not a real number True or
False
Help me please with this maths question thank you
Answer:
Step-by-step explanation:
A)
The opposite sides of a rectangle are equal. The width make this obvious because both of them are x.
B)
The lengths are not so obvious, but it is never the less true. The two sides are obvious and they are therefore true.
4x + 1 = 2x + 12 Subtract 1 from both sides.
- 1 -1
4x = 2x + 11 Subtract 2x from both sides
-2x -2x
2x = 11 Divide by 2
x = 11/2
x = 5.5
C)
P = L + L + w + w
P = 4(5.5) + 1 + 2(5.5) + 12 + 5.5 + 5.5
P = 22 + 1 + 11 + 12 + 11
P = 23 + 23 + 11
P = 57
Can someone do these for me and list the number because I’m struggling rn. And I’m having a breakdown lol.
Answer:
Step-by-step explanation:
First remove the parentheses.
As the sign outside the second parentheses is a + then the signs of the terms inside stay the same.
So the first one + (-3x +2) is just -3x + 2.
All the others on the left column are answered in the same way.
No. 4:
(-2x + 10 + (-8x - 1) Just remove the parentheses, we get:
-2x + 10 - 8x - 1 (we leave out the + before the second parentheses).
= -2x - 8x + 10 - 1
= -10x + 9
6. 8x + 8 + ( -6x - 1)
= 8x + 8 - 6x - 1
= 8x - 6x + 8 - 1
= 2x + 7.
- the other expressions on the right side column are solved in the same way.
were should i go shopping for fidgets
Answer:
Amazon
Step-by-step explanation:
Determine which statements about the relationship are true. Choose two options. g is the dependent variable. u is the dependent variable. g is the independent variable. u is the independent variable. The two variables cannot be labeled as independent or dependent without a table of values.
Answer:
1) g is the dependent variable.(A)
2) u is the independent variable.(D)
Step-by-step explanation:
What is the scare root of 85 roused to nearest tenth?
Answer:
9.2
Step-by-step explanation:
You can do this calculation with a calculator by taking the square root of 85.
Hi there!
»»————- ★ ————-««
I believe your answer is:
9.2
»»————- ★ ————-««
Here’s why:
Assuming that you mean "the square root of 85 rounded to the nearest tenth..."
⸻⸻⸻⸻
[tex]\boxed{\text{Calculating the Answer...}}\\\\\rightarrow \sqrt{85} = 9.21954445729....[/tex]
⸻⸻⸻⸻
Since the digit to the right of the tenth (the 1) is less than or equal to four, we round down.
⸻⸻⸻⸻
[tex]9.21954445729...\approx\boxed{9.2}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
HELPPP PLEASEEE! I tried everything from adding to dividing, subtracting, multiplying but still no correct answer. Can someone help me out here please? I am not sure where to start either now. Thank you for your time.
You have some data points labeled by [tex]x[/tex]. They form the set {3, 5, 7}.
The mean, [tex]\bar x[/tex], is the average of these values:
[tex]\bar x = \dfrac{3+5+7}3 = \dfrac{15}3 = 5[/tex]
Then in the column labeled [tex]x-\bar x[/tex], what you're doing is computing the difference between each data point [tex]x[/tex] and the mean [tex]\bar x[/tex]:
[tex]x=3 \implies x-\bar x = 3 - 5 = -2[/tex]
[tex]x=5 \implies x-\bar x = 5-5 = 0[/tex]
[tex]x=7 \implies x-\bar x = 7 - 5 = 2[/tex]
These are sometimes called "residuals".
In the next column, you square these values:
[tex]x=3 \implies (x-\bar x)^2 = (-2)^2 = 4[/tex]
[tex]x=5 \implies (x-\bar x)^2 = 0^2 = 0[/tex]
[tex]x=7 \implies (x-\bar x)^2 = 2^2 = 4[/tex]
and the variance of the data is the sum of these so-called "squared residuals".
what is the value of -2x²y³ when ×=2 and y=4?
Answer:
1024
Step-by-step explanation:
Given :-
x = 2 y = 4Value of -2x²y³
2x³ y³2 * (2)³ * (4)³2 * 8 * 64 1024Answer:
254
Step-by-step explanation:
^ <- this is the square sign
-2x^y^3
x=2
y=4
put x values in to x place and y value in to y place.
-2(2)^2(4)^3
Find the squares and - it with 2
-2(4)(64)
2-256=254
:. the value of -2x^2y^3 =254
That the answer.
Hope this is what you asked.
Help and explain explain !!!!!!!!!!
Answer:
[tex]x=-1\text{ or }x=11[/tex]
Step-by-step explanation:
For [tex]a=|b|[/tex], we have two cases:
[tex]\begin{cases}a=b,\\a=-b\end{cases}[/tex]
Therefore, for [tex]18=|15-3x|[/tex], we have the following cases:
[tex]\begin{cases}18=15-3x,\\18=-(15-3x)\end{cases}[/tex]
Solving, we have:
[tex]\begin{cases}18=15-3x, -3x=3, x=\boxed{-1},\\18=-(15-3x), 18=-15+3x, 33=3x, x=\boxed{11}\end{cases}[/tex].
Therefore,
[tex]\implies \boxed{x=-1\text{ or }x=11}[/tex]
Find the value of x. What is the value of x?
Answer:
x = 16
Step-by-step explanation:
The product of the lengths theorem is a property that can be sued to describe the relationships of the sides between the tangents and secants in a circle. One of these products states the following;
The distance between the point of tangency and its intersection point with the exterior secant squared is equal to the product of the exterior secant times the interior secant.
This essentially means the following equation can be formed;
[tex](AB)^2=(DC)(CB)[/tex]
Substitute,
[tex]12^2=x*9[/tex]
Simplify,
[tex]144=9x[/tex]
Inverse operations,
[tex]\frac{144}{9}=x\\\\16=x[/tex]
Answer:
[tex]\boxed{\sf x=7}[/tex]
Step-by-step explanation:
By Targent-secant theorem...
[tex]\sf 9(x + 9) = {12}^{2} [/tex]
Use the distributive property to multiply 9 by x+9.
[tex]\sf 9x+81= {12}^{2} [/tex]
Now, let calculate 12 to the power of 2 and get 144.
[tex]\sf 9x+81=144[/tex]
Subtract 81 from both sides.
[tex]\sf 9x=63[/tex]
Divide both sides by 9.
[tex] \sf \cfrac{ 9x}{9} = \cfrac{63}{9} [/tex]
[tex]\sf x=7[/tex]
