Answer:
The answer should be (7, 5)
In a class of 20 students, all but 4 of the students put their names on a typed assignment. If the teacher randomly guesses, what is the probability that she correctly guesses which paper belongs to each of the four remaining students
Answer:
4.17%
(1/4)(1/3)(1/2)(1)
alternative you can say that there are 24 permutations of
4 items and that you have to guess 1 of them 1/24 = 4.17%
Step-by-step explanation:
0.25
0.333333333
0.5
1
the time it takes a runner to complete a race is inversely related to the speed of the runner if a runner can complete a race in 40 minutes while running at 8 mph how long will it take the runner to complete the race running at 9 mph t
A student-faculty government committee of 4 people is to be formed from 20 student
volunteers and 5 faculty volunteers.
a. If one person from the group of volunteers is chosen at random to draw the names
out of a hat, what is the probability that the person drawing the names is a student?
b. How many ways can the committee of four be formed if there are no restrictions on
composition.
C. How many ways can two of the students be chosen?
d. How many ways can 2 faculty be chosen?
e. What is the probability that the random selection of the four-person committee will
result in two students and two faculty?
the answer is c i just had this question your welcome
A system of equations is said to beinconsistentif the system has no solution. Show by usingthe pivot operation that the following system is inconsistent. Is the system equivalent to asystem in canonical form?
x1 + x2 - 3x3= 7
-2x1 + x2 +5x3 = 2
3x2 - x3 = 15
Answer:
The system is inconsistent
Step-by-step explanation:
Given the matrix system solutions in the attachment, we can see that the coefficient of the matrix rank has become zero. This shows that it has no solution.
Find the areas in that unit square PQRS, P(4,3), Q(4,1), S(-1,3), R(-1,1)
Answer:
Step-by-step explanation:
P(4,3), Q(4,1), S(-1,3), R(-1,1)
[tex]Distance =\sqrt{(x_{2}-x_{1})^{2}+(y_{2} -y_{1})^{2}}\\\\PQ= \sqrt{(4-4)^{2}+(1-3)^{2}}\\\\=\sqrt{(-2)^{2}}\\\\\=\sqrt{4}\\\\=2 \ units\\\\\\QS=\sqrt{(-1-4)^{2}+(3-1)^{2}}\\\\=\sqrt{(-5)^{2}+(2)^{2}}\\\\=\sqrt{25+4}\\\\=\sqrt{29}\ units\\\\\\SR =\sqrt{(-1-[-1])^{2}+(1-3)^{2}}\\\\=\sqrt{(-1+1)^{2}+(-2)^{2}}\\\\=\sqrt{0+4}\\\\= \sqrt{4}\\\\= 2 \\\\\\PR = \sqrt{(-1-4)^{2}+(1-3)^{2}}\\\\=\sqrt{(-5)^{2}+(-2)^{2}}\\\\=\sqrt{25+4}\\\\=\sqrt{29}\\\\[/tex]
PQRS is a rectangle
Area= length *breadth
= 2 * √29
= 2√29 sq.units
In the diagram below, trapezoid ABCD maps to trapezoid A’B’C’D’
Which angle corresponds to angle C
Answer:
C'
Step-by-step explanation:
Given
ABCD to A'B'C'D'
Required
Corresponding angle of C
ABCD to A'B'C'D' means that the following angles are corresponding
[tex]A \to A'[/tex]
[tex]B \to B'[/tex]
[tex]C \to C'[/tex]
[tex]D \to D'[/tex]
Hence, C' corresponds to C
Answer:
C
Step-by-step explanation:
I took the test :)
how to solve these questions?!
Answer:
1. x + 4 = 9
Hint: the word 'sum' generally refers to addition.
2. 10a = 70
3. [tex]\frac{3}{4} t[/tex] = 15
4. [tex]\frac{1}{4} x[/tex] - 4 = 4
Which ordered pair makes both inequalities true?
y < 3x – 1
y > –x + 4
Answer:
SECOND ONE
Step-by-step explanation:
The figure below shows two triangles on the coordinate grid: A coordinate grid is shown from positive 6 to negative 6 on the x axis and from positive 6 to negative 6 on the y axis. A triangle ABC is shown with vertex A on ordered pair negative 4, negative 1, vertex B on ordered pair negative 3, negative 1 and vertex C on ordered pair negative 4, negative 4. Another triangle A prime B prime C prime is shown with vertex A prime on ordered pair negative 1, 1, vertex B prime on ordered pair negative 2, 1, and vertex C prime on ordered pair negative 1, 4. What set of transformations is performed on triangle ABC to form triangle A′B′C′? A translation 5 units up, followed by a 270-degree counterclockwise rotation about the origin A 270-degree counterclockwise rotation about the origin, followed by a translation 5 units up A 180-degree counterclockwise rotation about the origin, followed by a translation 5 units to the right A translation 5 units to the right, followed by a 180-degree counterclockwise rotation about the origin
Option D. The set of transformation that is performed on this triangle (ABCD)' is A translation 5 units to the right, followed by a 180-degree counterclockwise rotation about the origin
How to solve for the transformationThe answer choices have been shown to have all solutions to be rotated around their origin.
To shift the triangle, It has to be done through the connection the points ABC ' to the origin in such a way that the line is extended as we can seen in the diagram.
Read more on reflection here:
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Would you rather?
buy 2 lollypops for $2
buy 30 lollypops for $40
Answer:
Buy 2 lollipops for $2.
Step-by-step explanation:
If you divide the total price by total items purchased, you get the price per unit. 2/2=1 or around $1, while 40/30=4/3 or around $1.3. You are paying 1$ per lollipop for the 2 lollipop choice and paying 1.3 dollars per lollipop for the 30 lollipop choice.
When two parallel lines are cut by a transversal, argles A and B are alternate Interior angles that each measure 105°. What is the measure of
each of the other alternate interior angles
Answer:
The angle for the other interior angel is 75°, all you have to do is subtract 180, from the 105
Step-by-step explanation:
Urgent help!!!
*Picture included
Answer:
3x+4
Step-by-step explanation:
When you factor 9x^2+24x+16, it factors to (3x+4)^2
Factoring 9x^2 - 16 factors to (3x+4)(3x-4)
Therefore the common factor is 3x+4
I hope this helps!
The proportion of brown M&M's in a milk chocolate packet is approximately 14% (Madison, 2013). Suppose a package of M&M's typically contains 52 M&M's
Answer:
7 brown M&Ms.
Step-by-step explanation:
This question is not complete, but I will assume that the final question is how many brown M&Ms will be in this package.
0.14 × 52 is our equation.
The answer is 7.28. We cannot have .28 of a brown M&M in a package (unless you count the broken ones) so there will be, on average, 7 brown M&Ms in a package.
(again, the question is incomplete, so this may not be the answer)
Joshua and his children went into a grocery store and will buy bananas and peaches. Each banana costs $0.70 and each peach costs $2. Joshua has a total of $25 to spend on bananas and peaches. Write an inequality that would represent the possible values for the number of bananas purchased, bb, and the number of peaches purchased, p.p.
What is the common ratio of the sequence? -2, 6, -18, 54,...
a.-3
b.-2
c.3
d.8
Answer:
a. -3
Step-by-step explanation:
-2 turns into 6 by multiplying it by -3.
the same from 6 to -18, from -18 to 54, ...
so, an/an+1 = -3
Which number produce a rational number when multiples by 1/5
Answer:
-2/3
Step-by-step explanation:
A rational number is a number that can be expressed by a fraction so when y add to fractions it’s a rational number.
Determine the equation of the line that is parallel to the given line, through the given point.
3x+2y = 10; (8,-11)
Answer:
[tex]y=-\frac{3}{2}x+1[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0)Parallel lines always have the same slope1) Determine the slope (m)
[tex]3x+2y = 10[/tex]
First, we must organize this given equation in slope-intercept form. This will help us identify its slope.
[tex]3x+2y = 10[/tex]
Subtract 3x from both sides
[tex]2y = -3x+10[/tex]
Divide both sides by 2
[tex]y = -\frac{3}{2} x+5[/tex]
Now, we can identify clearly that [tex]-\frac{3}{2}[/tex] is in the place of m in [tex]y=mx+b[/tex], making it the slope. Because parallel lines have the same slope, this makes the slope of the line we're currently solving for [tex]-\frac{3}{2}[/tex] as well. Plug this number into [tex]y=mx+b[/tex]:
[tex]y=-\frac{3}{2}x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=-\frac{3}{2}x+b[/tex]
Plug in the given point (8,-11) and solve for b
[tex]-11=-\frac{3}{2}(8)+b\\-11=-\frac{24}{2}+b\\-11=-12+b[/tex]
Add 12 to both sides
[tex]1=b[/tex]
Therefore, the y-intercept of the line is 1. Plug this back into [tex]y=-\frac{3}{2}x+b[/tex]:
[tex]y=-\frac{3}{2}x+1[/tex]
I hope this helps!
Use a Maclaurin series to obtain the Maclaurin series for the given function.
f(x)= 14x cos(1/15x^2)
Answer:
[tex]14x cos(\frac{1}{15}x^{2})=14 \sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{4k+1}}{(2k)!15^{2k}}[/tex]
Step-by-step explanation:
In order to find this Maclaurin series, we can start by using a known Maclaurin series and modify it according to our function. A pretty regular Maclaurin series is the cos series, where:
[tex]cos(x)=\sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{2k}}{(2k)!}[/tex]
So all we need to do is include the additional modifications to the series, for example, the angle of our current function is: [tex]\frac{1}{15}x^{2}[/tex] so for
[tex]cos(\frac{1}{15}x^{2})[/tex]
the modified series will look like this:
[tex]cos(\frac{1}{15}x^{2})=\sum _{k=0} ^{\infty} \frac{(-1)^{k}(\frac{1}{15}x^{2})^{2k}}{(2k)!}[/tex]
So we can use some algebra to simplify the series:
[tex]cos(\frac{1}{15}x^{2})=\sum _{k=0} ^{\infty} \frac{(-1)^{k}(\frac{1}{15^{2k}}x^{4k})}{(2k)!}[/tex]
which can be rewritten like this:
[tex]cos(\frac{1}{15}x^{2})=\sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{4k}}{(2k)!15^{2k}}[/tex]
So finally, we can multiply a 14x to the series so we get:
[tex]14xcos(\frac{1}{15}x^{2})=14x\sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{4k}}{(2k)!15^{2k}}[/tex]
We can input the x into the series by using power rules so we get:
[tex]14xcos(\frac{1}{15}x^{2})=14\sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{4k+1}}{(2k)!15^{2k}}[/tex]
And that will be our answer.
Figure A
Figure B
Figure C
3 ft
3 ft
Sf
3 ft
3 ft
5 ft
5 ft
3 ft
3 ft
Sft
3 ft
3 ft
Х
?.
None of the figures
(a) Which figures are rectangles?
Mark all that apply.
Figure A Figure B Figure C
(b) Which figures are squares?
Mark all that apply.
Figure A Figure B Figure C
(c) Which figures are parallelograms?
Mark all that apply.
Figure A
Figure B
Figure C
None of the figures
None of the figures
Answer:
a) Figure B and Figure C
b) Figure C
c) Figure A, Figure B, and Figure C
Step-by-step explanation:
a) Rectangles are shapes that have four sides, and four right angels. Right angles are angles that are 90 degrees.
The only shapes with four sides AND four right angles are Figure C and Figure B.
b) Squares are shapes with four EQUAL sides and four right angles. The only shape with four equal sides and four right angles is Figure C.
c) Parallelograms are any shapes with four sides. All of these shapes have four sides.
Hope this helps!
pls help with all the questions
Answer:
Step-by-step explanation:
Since, CD is an altitude, ∠CDB will be a right angle.
m∠CDB = m∠CDA = 90°
By applying triangle sum theorem in ΔABC,
m∠CAB + m∠CBA + m∠ACB = 180°
20° + m∠CBA + 90° = 180°
m∠CBA = 180° - 110°
= 70°
Therefore, m∠CBD = 70°
By applying triangle sum theorem in ΔBCD,
m∠BCD + m∠CDB + m∠DBC = 180°
m∠BCD + 90° + 70° = 180°
m∠BCD + 160° = 180°
m∠BCD = 20°
m∠CAD = m∠A = 20°
m∠ACD = 90° - m∠BCD
= 90° - 20°
m∠ACD = 70°
Which problem has a greater (bigger) answer? Solve both, choose the one that has the bigger answer and explain (1-2 sentences) how you found your
answer.
1) (2 + 3) (5 + 5)
2)2 + 3 x 5 + 5 =
I need help pleaseeee
Answer:
1) has bigger answer
Step-by-step explanation:
1)
solving parenthesis first we get
5 × 10
so, the answer = 50
2)
solving 3 × 5 first as we have to see multiplication first then addition
2 + 15 + 5
22
comparing both
50 > 22
so problem 1 has a bigger answer
help with this please !!
Answer:
B
Step-by-step explanation:
The coeffecients (I totally didn't spell that right) and variables match up.
Simplify the expression using the order of operations agreements.
-8÷2+2×8=
Answer:
12
Step-by-step explanation:
PEMDAS is the order
P = parenthesis
E = exponent
M = *
D = division
A = +
S = -
so first 8*2 = 16
and then -8/2 = -4
and then -4 + 16
= 12
!PLEASE HELP WILL GIVE BRAINLIEST!
An internet service charges $34 per month for internet access. Write an equation to represent the total cost based on the number of months of internet access.
Answer:
34m = c
Step-by-step explanation:
For every month (m) you pay 34 dollars. However many months youu use that service time 34 equals your total cost (c).
Answer:
[tex]let \: cost \: be \: { \bf{c}} \: and \: months \: be \: { \bf{n}} \\ { \bf{c \: \alpha \: n}} \\ { \bf{c = kn}} \\ 34 = (k \times 1) \\ k = 34 \: dollars \\ \\ { \boxed{ \bf{c = 34n}}}[/tex]
Find the limit of f as or show that the limit does not exist. Consider converting the function to polar coordinates to make finding the limit easier. f(x,y)
Answer:
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2} = 0[/tex]
Step-by-step explanation:
Given
[tex]f(x,y) = \frac{x^2 \sin^2y}{x^2+2y^2}[/tex]
Required
[tex]\lim_{(x,y) \to (0,0)} f(x,y)[/tex]
[tex]\lim_{(x,y) \to (0,0)} f(x,y)[/tex] becomes
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2}[/tex]
Multiply by 1
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2}\cdot 1[/tex]
Express 1 as
[tex]\frac{y^2}{y^2} = 1[/tex]
So, the expression becomes:
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2} \cdot \frac{y^2}{y^2}[/tex]
Rewrite as:
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 y^2}{x^2+2y^2} \cdot \frac{\sin^2y}{y^2}[/tex]
In limits:
[tex]\lim_{(x,y) \to (0,0)} \frac{\sin^2y}{y^2} \to 1[/tex]
So, we have:
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 y^2}{x^2+2y^2} *1[/tex]
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 y^2}{x^2+2y^2}[/tex]
Convert to polar coordinates; such that:
[tex]x = r\cos\theta;\ \ y = r\sin\theta;[/tex]
So, we have:
[tex]\lim_{(x,y) \to (0,0)} \frac{(r\cos\theta)^2 (r\sin\theta;)^2}{(r\cos\theta)^2+2(r\sin\theta;)^2}[/tex]
Expand
[tex]\lim_{(x,y) \to (0,0)} \frac{r^4\cos^2\theta\sin^2\theta}{r^2\cos^2\theta+2r^2\sin^2\theta}[/tex]
Factor out [tex]r^2[/tex]
[tex]\lim_{(x,y) \to (0,0)} \frac{r^4\cos^2\theta\sin^2\theta}{r^2(\cos^2\theta+2\sin^2\theta)}[/tex]
Cancel out [tex]r^2[/tex]
[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{\cos^2\theta+2\sin^2\theta}[/tex]
[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{\cos^2\theta+2\sin^2\theta}[/tex]
Express [tex]2\sin^2 \theta[/tex] as [tex]\sin^2\theta+\sin^2\theta[/tex]
So:
[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{\cos^2\theta+\sin^2\theta+\sin^2\theta}[/tex]
In trigonometry:
[tex]\cos^2\theta + \sin^2\theta = 1[/tex]
So, we have:
[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{1+\sin^2\theta}[/tex]
Evaluate the limits by substituting 0 for r
[tex]\frac{0^2 \cdot \cos^2\theta\sin^2\theta}{1+\sin^2\theta}[/tex]
[tex]\frac{0 \cdot \cos^2\theta\sin^2\theta}{1+\sin^2\theta}[/tex]
[tex]\frac{0}{1+\sin^2\theta}[/tex]
Since the denominator is non-zero; Then, the expression becomes 0 i.e.
[tex]\frac{0}{1+\sin^2\theta} = 0[/tex]
So,
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2} = 0[/tex]
A bus started from Kathmandu and reached khanikhola,26km far from Kathmandu, in one hour. if the bus had uniform acceleration, calculate the final velocity of the bus and acceleration.
Answer:
a = 0.0040 m/s², v = 14.4 m/s.
Step-by-step explanation:
Given that,
The distance between Kathmandu and Khanikhola, d = 26 km = 26000 m
Time, t = 1 hour = 3600 seconds
Let a is the acceleration of the bus. Using second equation of motion,
[tex]d=ut+\dfrac{1}{2}at^2[/tex]
Where
u is the initial speed of the bus, u = 0
So,
[tex]d=\dfrac{1}{2}at^2\\\\a=\dfrac{2d}{t^2}\\\\a=\dfrac{2\times 26000}{(3600)^2}\\\\a=0.0040\ m/s^2[/tex]
Now using first equation of motion.
Final velocity, v = u +at
So,
v = 0+0.0040(3600)
v = 14.4 m/s
Hence, this is the required solution.
FIND THE EQUATION OF THE LINE.
I NEED ANSWER WITH STEP BY STEP PLEASE
Given:
The graph of a line.
To find:
The equation for the given line.
Solution:
From the given graph, it is clear that the line passes through the points (0,-5) and (5,0). So, the equation of the line is:
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-(-5)=\dfrac{0-(-5)}{5-0}(x-0)[/tex]
[tex]y+5=\dfrac{5}{5}(x)[/tex]
[tex]y+5=x[/tex]
Subtract 5 from both sides.
[tex]y+5-5=x-5[/tex]
[tex]y=x-5[/tex]
Therefore, the equation of the given line is [tex]y=x-5[/tex].
Which of the following expressions would represent a class of 42 students divided equally into 7 groups?
Answer: [tex]7\sqrt{42}[/tex]
Step-by-step explanation:
42 students divided equally into 7 groups means 42 divided by 7, and [tex]7\sqrt{42}[/tex] is the only choice that shows that.
7√42. is the expressions would represent a class of 42 students divided equally into 7 groups
What is Division?A division is a process of splitting a specific amount into equal parts.
Given,
A class of forty two Forty two students divided equally into 7 groups.
Forty two students divided equally into seven groups means forty two divided by seven, and
this can be done by using 7√42.
42 students divided equally into 7 groups means forty two divided by seven
Hence 7√42. is the expressions would represent a class of 42 students divided equally into 7 groups
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At a hockey game, a vender sold a combined total of 228 sodas and hot dogs. The number of sodas sold was two times the number of hot dogs sold. Find the number of sodas and the number of hot dogs sold.
9514 1404 393
Answer:
152 sodas76 hot dogsStep-by-step explanation:
Of the items sold, sodas were 2/(2+1) = 2/3 of the total.
(2/3)(228) = 152 . . . sodas were sold
152/2 = 76 . . . . hot dogs were sold
Help! This is timed!
Answer: 5 ft i think so
Use the Pythagorean theorem