From a group of 15 women and 16 men, a researcher wants to randomly select 8 women and 8 men for a study. In how many ways can the study group be selected?A. 300,540,195B. 778,377,600C. 19,305OD. 82,818,450
Since we are talking about a group of people the order is not going to matter when we select the different people, then, start to make the combination for the group of women and the group of men separately.
[tex]\begin{gathered} women=15C8 \\ women=\frac{15!}{(15-8)!8!} \\ women=\frac{15\cdot14\cdot13\cdot12\cdot11\cdot10\cdot9}{7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1} \\ women=6435 \end{gathered}[/tex][tex]\begin{gathered} men=16C8 \\ men=\frac{16!}{(16-8)!8!} \\ men=\frac{16\cdot15\cdot14\cdot13\cdot12\cdot11\cdot10\cdot9}{8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1} \\ men=12870 \end{gathered}[/tex]then, multiply the results
[tex]\begin{gathered} 16C8\cdot15C8 \\ 12870\cdot6435 \\ 82,818,450 \end{gathered}[/tex]Evaluate.
{3 + [−5 (2−4) ÷ 2]} x 3
Answer choices:
−27
(negative 27)
−13
(negative 13)
18
(eighteen)
24
(Twenty-four)
Answer:
24
(twenty - four)
Step-by-step explanation:
Again we want to evaluate this using BPEMDAS
Which tell us in order which operations we do
Remember BPEMDAS means
Brackets
Parenthesis
Exponents
Multiplication/Division (going left to right)
Addition/Subtraction (going left to right)
{3 + [−5 (2−4) ÷ 2]} x 3
==> first we perform all operations in the innermost bracket
[3 + (−5(-2) ÷ 2)] x 3
==> we do the same thing as the first step, the operations in the inner most parenthesis. there is only multiplication and division here so we perform them going left to right
[3 + (10 ÷ 2)] x 3 ==> multiplication first because its before the division in the parenthesis
(3 + 5) x 3 ==> division next
==> next we do the final operations in the parenthesis 3+5
8 x 3
==> finally the multiplication
= 24
Can you tell me What is 4x16=?
Hello
This is a multiplication question and we can easily use our calculator for this question.
[tex]4\times16=64[/tex]From the above, the answer to 4 * 16 is 64
"A quadrilateral is a square if and only if it has four rightangles.Rewrite the biconditional statement to make itvalid.
Which statement is true of the function flx) = -3/x? Select three options. The function is always increasing. The function has a domain of all real numbers. The function has a range of tyl-
Notice that the given function:
1.- has a domain of all real numbers because you can always compute the cube root for all real numbers,
2.- the function has a range of all real numbers, and
3.- the function is a reflection of
[tex]y=\sqrt[3]{x}[/tex]over the x-axis.
Answer: Options 2, 3, and 4.
Using Euler's formula, how manyedges does a polyhedron with 20faces and 12 vertices have?[?] edges
Using Euler's Formula:
F + V - E = 2
Given:
F = 20, V = 12 and E = a
According to the formula:
20 + 12 - a = 2
32 - a = 2
a = 32 - 2
a = 30
ANSWER
30 edges
Graph the set on the number line. Then, write the set using interval notation.
(-5, 1)
Explanation:The given set:
{x | -5 < x < 1}
To draw the number line, the range of the line will be from -5 to 1.
Since there is no equal sign attached to the inequlaity, the dot or circle will not be shaded.
Plotting on the number line:
Writing the set in interval notation:
[tex]\begin{gathered} The\text{ parenthesis that will be used is ( ), since the inequality doesn't have equal sign attached} \\ \text{Hence, the interval is }(-5,\text{ 1)} \end{gathered}[/tex]In 30 words of your identify which form slope intercept or point slope would be better to use why
As indicated in the question, parallel lines have the same slope.
This means the slope of the fourth parallel line is also 2. A point on that line has been identified as;
[tex](3,15)[/tex]Using the point-lope form which is;
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{Where,} \\ x_1=3,y_1=15 \\ \text{The equation becomes;} \\ y-15=2(x-3) \end{gathered}[/tex]Further simplified, this now becomes;
[tex]\begin{gathered} y-15=2(x-3) \\ y-15=2x-6 \\ \text{Add 15 to both sides;} \\ y=2x+9 \end{gathered}[/tex]ANSWER:
It would be better to use the point-slope form to derive the equation of the 4th line because we already have the slope and one point on the equation.
if point c, shown on the coordinate plane below is reflected over both axes to create c what will be the coordinate of c
Explanation:
The coordinate of c in the plane looks like x= 3 while y = 2
This we assumed because there is no grid line to determine the numbers. The location shows it is within that coordinate
c (3, 2):
Reflecting acrossboth axes means reflecting across the y and reflection across the x axis
Reflection across y axis: (x, y) to (-x, y)
The coordinate of becomes: (-3, 2)
What can you say about the 3s in 43,862 and 75,398?4 grade student Lesson Place value relationship
Remember that a place value can be defined as the value represented by a digit in a number based on its position in the number. With decimal numbers, we can have a guide from the decimal point, and with natural numbers, we have a guide from the comma.
So, if we look at the numbers on the exercise we note that
- 3s in 43,862 is placed first before the comma indicating that their place is in the thousands.
- 3s in 75,398 is placed first after the comma indicating that its place is in the hundred.
Divide and round to the nearest hundredths place25.7 ÷ 0.3
85.67
Explanation:[tex]\frac{25.7}{0.3}[/tex]Using a calculator, the result is 85.6667
To the nearest hundredth: The hundredth position is at second 6. The next number after it is more than 5. So it would be rounded to 1 and added to the second 6
To the nearest hundredth, the answer is 85.67
Find the STANDARD equation for a line with slope 3 and y-intercept -2 Show work
We know that
• The slope is 3.
,• The y-intercept is -2.
We use the slope-intercept form to find an equation.
[tex]y=mx+b[/tex]Where m is the slope, and b is the y-intercept.
Replacing the given information, we have
[tex]y=3x-2[/tex]Now, we move all terms to the left side to express the linear equation in standard form.
Therefore, the standard form is[tex]-3x+y=-2[/tex]The equation y = kx represents a proportional relationship between x and y, where k is the constant of proportionality. For a moving object, the equation d = st represents a proportional relationship between distance (d) and speed (s) or between distance (d) and time (t). Explain the different ways that you can define the constant of proportionality for this equation. Then describe some other equations that represent proportional relationships in the real world and explain why they're useful. Research on the Internet, if needed.
d = st
if speed is constant, there is a proportional relation between distance (d) and time (t). The constant (s) can be defined as:
s = d/t
and you can compute it knowing the distance travelled in some time
if time is constant, there is a proportional relation between distance (d) and speed (s). The constant (t) can be defined as:
t = d/s
and you can compute it knowing the distance travelled at some speed.
Acceleration (a) is defined as:
a = s/t
this equation can be rewritten as:
s = at
where a is the constant of proportionality.
Another example is Hook's law, which states:
F = ke
where F is the force applied to a spring, k is the spring constant, and e is the extension of the spring.
list of financial formulas.Lisa invested $5300 in an account that pays an annual interest rate of 2.5%, compounded monthly. Answer each part. If necessary, refer to the(a) Find the amount in the account after one year, assuming no withdrawals are made.Do not round any intermediate computations, and round your answer to the nearest cent.X(b) Find the effective annual interest rate, expressed as a percentage.of a percent.Do not round any intermediate computations, and round your answer to the nearest hundredth%
Given:
Investment = $5300
annual interest rate = 2.5% compounded monthly
The amount A after time t can be computed using the formula:
[tex]\begin{gathered} A\text{ = P\lparen1 + }\frac{r}{n})^{nt}^ \\ \\ Where\text{ P is the principal} \\ r\text{ is the rate of interest} \\ n\text{ is the number of compounding periods } \\ and\text{ t is the time in years} \end{gathered}[/tex](a) The amount A after 1 year
Substituting the given values:
[tex]\begin{gathered} A\text{ = 5300\lparen1 + }\frac{0.025}{12})^{12\times1} \\ \text{= \$5434.0288} \end{gathered}[/tex]Answer:
Amount = $5434.03
please help me with mathHere’s a picture of the question
Answer:
a) Yes, triangles JNM and JLK are similar by the AA Similarity Postulate
b) JN = 4 in
c) LN = 1.5 in
JK = 3.5 in
d) Area ratio = 2.56 : 1
Explanation:
Given:
KL = 5 in
MN = 8 in
JL = 2.5 in
MK = 2.1 in
From triangle JLK and JNM, we can deduce the following;
[tex]\begin{gathered} \angle J\cong\angle J......Reflexive\text{ property of angles} \\ \angle M\cong\angle K......Corresponding\text{ angles are equal} \\ \angle N\cong\angle L.........Corresponding\text{ angles are equal} \end{gathered}[/tex]a) The AA Similarity theorem states that if two pairs of corresponding angles in two triangles are congruent, then the two triangles are similar. From the above, we can see that we have two pairs of corresponding angles that are congruent, so we can say that triangles JLK and JNM are similar.
b) Note that, in similar triangles, corresponding sides are equal in proportion.
So we can go ahead and solve for JN as seen below;
[tex]\begin{gathered} \frac{KL}{MN}=\frac{JL}{JN} \\ \frac{5}{8}=\frac{2.5}{JN} \\ 5JN=20 \\ JN=\frac{20}{5} \\ JN=4 \end{gathered}[/tex]So JN is 4 in
c)
[tex]\begin{gathered} JN=JL+LN \\ LN=JN-JL \\ LN=4-2.5 \\ LN=1.5\text{ in} \end{gathered}[/tex]So LN is 1.5 in
Let's find the length of JK;
[tex]\begin{gathered} \frac{KL}{MN}=\frac{JK}{JM} \\ \frac{KL}{MN}=\frac{JK}{JK+MK} \\ \frac{5}{8}=\frac{JK}{JK+2.1} \\ 5(JK+2.1)=8JK \\ 5JK+10.5=8JK \\ 8JK-5JK=10.5 \\ 3JK=10.5 \\ JK=\frac{10.5}{3} \\ JK=3.5\text{ in} \end{gathered}[/tex]So the length of JK is 3.5 in
d) The area ratio of two similar triangles is equal to the square of the ratio of any two corresponding sides.
So the ratio of triangle JNM to JKL is;
[tex]Area\text{ ratio}=\frac{8^2}{5^2}=\frac{64}{25}=\frac{2.56}{1}=2.56:1[/tex]You are designing a rectangda garden for the city park. The gardien is to have an area of 250 S feet, but you want to theamount of fending that you need to surround the garden. One length of the garden will not have a fence How many fees of lenong to you needto Surround the garden?
Consider the following picture
This is a sketch of the rectangular garden. We are given that the area of this rectangle is 200. Recall that the area of a rectangle is base * height. IN this case, we have the equation
[tex]\times\cdot\text{ y = 200}[/tex]Now, note that we want to minimize the amount of fence we use. This means, that we want to minimize the perimIn this case we are told that we are not putting fence on one side of the rectangle. Since we want the less amount of fence to be used, and since y is the lenght of the longest side, we will assume that we are not fencing one of the y sides. So the perimeter of this rectangle is sum of the three remaining sides. Hence the function we want to minimize is
[tex]y\text{ + 2x }[/tex]From the first equation, we can replace the value of y with 200/x. So the function we want to minimize is
[tex]\frac{200}{x}+2x[/tex]Since we want to find the minimum of this function, we proceed by calculating its' derivative, make it equal to zero and the find the value of x that makes the equation true.
So, recall that the derivative of a term x^n is n x ^(n-1). In the case of 1/x, the value of n is n=-1. Also, recall that the derivative of a sum is the sum of the derivatives. So, applying this rule we get that the derivative of the function is
[tex]200(-1)x^{^{\text{ -2}}}+2x^0=2\text{ - }\frac{200}{x^2}[/tex]No, we will make it equal to 0 and find the value of x that makes the equation true. So we get the equation
[tex]2\text{ - }\frac{200}{x^2}\text{ = 0 = }\frac{2x^2\text{ -200}}{x^2}[/tex]Since we have an equation of the form a/b =0 It must happen that a is 0. Then, we have the equation
[tex]2x^2\text{ -200 =0}[/tex]If we add 200 on both side, we get
[tex]2x^2\text{ = 200}[/tex]If we divide on both sides by 2, we get
[tex]\times^2\text{ = 100}[/tex]By taking the square root on both sides we get
[tex]\text{ x = 10 or x = -10}[/tex]Since x is a lenght, it should be positive. So we must have x = 10.
In this case, by replacing in the expression of y, we get that y = 200/10 = 20.
So we will need 2*10 + 20 = 40 feets long to surround the garden.
5A line passes through point (-8, 9) and has a slope of4Write an equation in Ax+By=C form for this line.Use integers for A, B, and C.
Point = (-8, 9)
slope = m = 5/4
Equation of the line
y - y1 = m(x - x1)
Substitution
y - 9 = 5/4(x + 8)
Expanding
4y - 36 = 5x + 40
General form
5x - 4y + 40 + 36 = 0
Equation of the line
5x - 4y + 76 = 0 5x - 4y = -76
A = 5 B = -4 C = 76 }}
Problem 2.
Point = (-10, -9)
slope = m = 1/2
Equation of the line
y - y1 = m(x - x1)
y + 9 = 1/2 (x + 10)
2y + 18 = x + 10
x - 2y = 18 - 10
x - 2y = 8
What is the theoretical probability that an odd number will berolled on a 6-sided die?
TIP
All possible outcome ; 1, 2 , 3, 4, 5, 6
Odd number ; 1, 3, 5
[tex]\begin{gathered} \text{Probability =}\frac{possible\text{ outcome of odd number}}{\text{Total possible outcome}} \\ \text{Probability}=\frac{3}{6}=\frac{1}{2} \\ \end{gathered}[/tex]Probability that an odd number will be
[tex]\frac{1}{2}[/tex]If f (p) = 3p – 1 andg(n)=n? + 2,what is (f.g)(x)?
This is a composition function, so:
[tex]\begin{gathered} f(p)=3p-1 \\ g(n)=n^2+2 \\ (f\circ g)(x)=f(g(x))=3\cdot g(x)-1 \\ (f\circ g)(x)=3(x^2+2)-1=3x^2+3\cdot2-1 \\ (f\circ g)(x)=3x^2+5 \end{gathered}[/tex]which of the following is not a line of symmetry in the figure below
From the graph the line of symmetry is the line that divides the shape into two equal halves
These lines are at
1) x = -4
2) y = 4
3) y = -x
An equation of a line that does not divides the shape into equal halves is not a line of symmetry
If a quadratic equation can be factored as (ax +b)(ex+d) = 0, what information do these factors provide about the graph of the equation?
Answer:
The 4th choice: The graph of the equation has roots at x = -b/a and x = -d/c
Explanation:
If we have an equation of the form
[tex](ax+b)(bx+c)=0[/tex]then it must be that either
[tex](ax+b)=0[/tex]or
[tex](bx+c)=0[/tex]The first equation gives
[tex]\begin{gathered} ax+b=0 \\ x=-\frac{b}{a} \end{gathered}[/tex]and the second equation gives
[tex]\begin{gathered} cx+d=0 \\ x=-\frac{d}{c} \end{gathered}[/tex]Hence, the roots of the equation turn out to be
[tex]x=-\frac{b}{a},x=-\frac{d}{c}[/tex]Therefore, we conclude that the equation of the form (ax + b) (cx + d) tells us about the roots of the function, and hence, choice 4 is correct.
a diver stands on a platform 15 ft above a lake. he doesn't dive off the platform and lands in the water below. His height (h) above the lake after X seconds is shown on the graph below. what is the maximum height the diver reached?
We are asked about the maximum height of the diver given the graph. we notice from the graph that the maximum point is h = 20 feet, therefore, the maximum height is 20 feet.
Which shows the correct substitution for: "Evaluate f(6)"f(x) = x + 5
f(x) = x + 5
Evaluate the function for x = 6
f(6) = 6 + 5
f(6) = 11
Whiteout graphing the function, describe what the graph would look like if b were 8.5
We have the function y=x+b.
This is a line with b as y-intercept.
When b gets larger, that graph moves parallel and up in the vertical axis.
That is because b is like a "floor" level when x=0, and, as the slope of the line stays the same, the lines stays parallel.
As b becomes negative, the graph goes in the opposite direction (down in the vertical axis).
The lines stays parallel, because the slope does not change.
22. Solve 3(5x – 4) < 15x.O x<4No solutionX >-4All Real Numbers
ANSWER
All real numbers
EXPLANATION
To solve this inequality, first, divide both sides by 3,
[tex]\begin{gathered} \frac{3\left(5x-4\right)}{3}\lt\frac{15x}{3} \\ \\ 5x-4\lt5x \end{gathered}[/tex]Then, subtract 5x from both sides of the inequality,
[tex]\begin{gathered} 5x-5x-4\lt5x-5x \\ \\ -4\lt0 \end{gathered}[/tex]-4 indeed is less than 0, and this is valid for any value of x in the real numbers - i.e. any real number for x satisfies the inequality.
Hence, the solution is all real numbers.
Find the slope from real world application. At pizza galore a two topping pizza costs $9. A pizza with four toppings costs $12. How much does each topping cost?
The slope is:
[tex]m=\frac{12-9}{4-2}[/tex][tex]m=\frac{3}{2}=1.5[/tex]Hence, each topping of the pizza cost $1.5
What is the inverse of the function f (x) = 3(x + 4)^2 – 2, such that x ≤ –4?A. f^-1(x)=-4 + square root of x/3+2B. f^-1(x)=-4 - square root of x/3+2C. f^-1(x)=-4 + square root of x+2/3D. f^-1(x)=-4 - square root of x+2/3
Given the following function:
f(x) = 3(x + 4)^2 – 2
Let's determine its inverse form.
*Change f(x) = y, swap x and y then solve for y.
[tex]\text{ f\lparen x\rparen= 3\lparen x + 4\rparen}^2\text{ - 2}[/tex][tex]\text{ y = 3\lparen x + 4\rparen}^2\text{ - 2}[/tex][tex]\text{ x = 3\lparen y + 4\rparen}^2\text{ - 2}[/tex][tex]\text{ 3\lparen y + 4\rparen}^2\text{ - 2 = x}[/tex][tex]\text{ 3\lparen y + 4\rparen}^2\text{ = x + 2}[/tex][tex]\text{ \lparen y + 4\rparen}^2\text{ = }\frac{\text{ x + 2 }}{\text{ 3}}[/tex][tex]\text{ y + 4 = }\sqrt{\frac{\text{ x + 2 }}{\text{ 3}}}[/tex][tex]\text{y = f}^{-1}(\text{x\rparen = -4 + }\sqrt{\frac{\text{ x + 2 }}{\text{ 3 }}}[/tex]Therefore, the answer is CHOICE C.
What is the area of this triangle? 1375 Ft 1500 ft 3300 ft 4500 ft
The area of the triangle is 1500 feet.
We are given a triangle. The length of the base of the triangle is 120 feet. The length of the altitude of the triangle is 25 feet. The area of a triangle is equal to half the product of its base and its altitude. The area indicated by the quantity indicates the extent of a region on a planar or curved surface. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina. So, the area of the triangle can be formulated as given below :
A = (1/2)*B*H = (1/2)*120*25 = 1500
To learn more about triangles, visit :
https://brainly.com/question/2773823
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Answer:
The area is 1500 feet.
The person above me is correct
Estimate the difference of the decimals below by rounding to the nearestwhole number. Enter your answer in the space provided.91.2764.310
The decimal number 91.276 is round off to the number 91 and number 4.310 is round off to the number 4.
Evaluate the difference between the number 91 and 4.
[tex]91-4=87[/tex]So answer is 87.
how do I find which of the following statements are true?
Verify each statement
Option A is true because M is between A and B
Option B
Is not true
because AM=AB/2
Option C
Is true
because M is the midpoint
Option D
Is not true
because M is between A and B
Option E
we have
Is true because AB=AM+MB ------> AB-AM=MB
Option F
Is true because AB=AM+MB
Option G
Is not true
because AB=2AM
Option H
Is true
because AB=2AM