Answer:
The number of groupings is 45
Explanation:
Given that the professor decided he was only going to grade 8 out of 10 HW problems he assigned.
We want to calculate the number of ways the professor can grade the HW.
Which is a conbination;
[tex]10C8[/tex]Solving we have;
[tex]\begin{gathered} n=10C8=\frac{10!}{8!(10-8)!} \\ n=45 \end{gathered}[/tex]Therefore, the number of groupings is 45
Given a right triangle, what is the measure of 2B if ZA = 35º and b = 7?(Round your answer to the nearest degree.)
Let us make a drawing of the triangle:
Let's remember that the three angles of a triangle add up to 180 degrees. Then,
[tex]\measuredangle A+\measuredangle B+\measuredangle C=180\degree[/tex]Since our triangle is right, we have
[tex]\measuredangle C=90\degree[/tex]Thus
[tex]35\degree+\measuredangle B+90\degree=180\degree[/tex][tex]\measuredangle B=180\degree-90\degree-35\degree=55\degree[/tex]This means that the answer is 55°.
Question #1: The International Special Olympics were held in New York City. The USA team won 25 medals; Gold
[8], Silver [10], and Bronze [7]. Using the table below, construct a frequency distribution table that includes both
the relative frequency and the frequency percentage.
Class Level rf f%
Gold
Silver
Bronze
The frequency distribution table includes both the relative frequency and the frequency percentage given below.
Class Level Relative frequency frequency %
Gold 8/25 × 100 = 0.032 32%
Silver 10/25 × 100 = 0.04 40%
Bronze 7/25 × 100 = 0.028 28%
What is Relative frequency?The Relative frequency is an estimate or estimator of a probability in terms of statistics.
In straightforward situations, where the outcome of a trial just establishes whether the predetermined event has taken place, modeling using a binomial distribution may be suitable, and the empirical estimate is then the maximum likelihood estimate.
If specific conditions for the prior distribution of the probability are met, it is the Bayesian estimate for the same case. If a trial produces additional data, the relative frequency can be enhanced by adding new hypotheses in the form of a statistical model; if this model is fitted, it can be used to determine an estimate of the likelihood of the desired event.
To learn more about Relative frequency from the given link
https://brainly.com/question/16832475
#SPJ4
HELP ASAP!
Put (-3y + 6 < x) in slope-intercept form.
Step-by-step explanation:
so slope intercept form is y=mx+b or in this case y<mx+b
so you just need to solve for y
start by subtracting 6 from both sides getting -3y< x + 6 than you just divided by a -3 when you divide by a negative number you have to change the inequality so you would get y> -(x+6)/3 that would be your answer hopefully that helps. have a great day
14. A poll was taken of 13,875 working adults aged 40-70 to determine their level of education. The participants were classified by sex and by level of education. The results are shown below.Education LevelMaleFemaleTotalHigh School or Less299934306429Bachelor's Degree315131736324Master's Degree4975061003Ph.D.5465119Total6701717413,875A person is selected at random. Compute the following probabilities.(a) What is the probability that the selected person is a male? (b) What is the probability that the selected person does not have a Ph.D.? (c) What is the probability that the selected person has a Master's degree? (d) What is the probability that the selected person is female and has a Master's degree?
Part a
What is the probability that the selected person is a male?
P=6,701/13,875
P=0.4830
Part b
What is the probability that the selected person does not have a Ph.D.?
P=1-119/13,875
P=0.9914
Part c
What is the probability that the selected person has a Master's degree?
P=1,003/13,875
P=0.0723
Part d
What is the probability that the selected person is female and has a Master's degree?
P=506/13,875
P=0.0365
Is TAG BAG? IF so, identif th similarity postulate or theorem that applies
Step 1
Given;
[tex]Triangle\text{ TAG \textasciitilde Triangle BAG}[/tex]Required; To find the similarity postulate or theorem that applies.
Step 2
Both triangles share one side AG
They also have a common angle;
[tex]90^o[/tex]Side AG = 10 units and ∠AGT ≅ ∠AGB.
Thus, options A and B are discarded.
Step 3
Now, as for the SAS criteria, we need two sides to be congruent and their included angles to be congruent.
But, as no other information is given, we cannot determine whether the given triangles are congruent or not.
Therefore, the answer is; Option D
[tex]cannot\text{ be determined}[/tex]f(x +h)-f(x)For the function defined as follows, find (a) f(x + h), (b) f(x + h) – f(x), and (c)f(x)= 4/x
Given the function:
[tex]f(x)=\frac{4}{x}[/tex]We will find the following:
a) f(x+h)
So, we will substitute with x = x+h
[tex]f(x+h)=\frac{4}{x+h}[/tex]b) f(x+h) - f(x)
[tex]\begin{gathered} f(x+h)-f(x)=\frac{4}{x+h}-\frac{4}{x} \\ \\ f(x+h)-f(x)=\frac{4x-4(x+h)}{x(x+h)} \\ \\ f(x+h)-f(x)=\frac{4x-4x-4h}{x(x+h)} \\ \\ f(x+h)-f(x)=\frac{-4h}{x(x+h)} \end{gathered}[/tex]c) [f(x+h) - f(x)]/h
[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{-4h}{x(x+h)\cdot h} \\ \\ \frac{f(x+h)-f(x)}{h}=\frac{-4}{x(x+h)} \end{gathered}[/tex]A grain silo is shown below:168 ft6 ftWhat is the volume of grain that could completely fill this silo, rounded to the nearest whole number? Use22/7 for pi
Solution
Step 1
[tex]\begin{gathered} \text{The volume of the silo = volume of a cylinder + volume of the } \\ \text{ hemisphere} \\ The\text{ volume of the silo = }\pi r^2h\text{ + }\frac{2}{3}\pi r^3 \end{gathered}[/tex]Step 2
[tex]\begin{gathered} \text{h = 168} \\ \text{r = 6} \end{gathered}[/tex]Step 3
[tex]\begin{gathered} Volume\text{ = }\frac{22}{7}\times6^2\times\text{ 168 + }\frac{2}{3}\times\frac{22}{7}\times\text{ 6}^5 \\ Volume\text{ = }19008\text{ + 452.5714286} \\ Volume\text{ =19460.571 } \end{gathered}[/tex]Final answer
19461
Use the Trapezoidal Rule to approximate ∫2−1ex2dx using n=4. Round your answer to the nearest hundredth.
Give ordered pairs that are solutions and graph the equation.2y = 5x – 10Complete the ordered pairs so they are solutions to the given equation.
Answer:
The equation is given below as
[tex]2y=5x-10[/tex]Concept:
To calculate the value of y when x=0, we will substitute the x=0 in the equation above and solve for y
By substituting the values, we will have
When x=0
[tex]\begin{gathered} 2y=5x-10 \\ 2y=5(0)-10 \\ 2y=-10 \\ \frac{2y}{2}=-\frac{10}{2} \\ y=-5 \\ (0,-5) \end{gathered}[/tex]When x=1
[tex]\begin{gathered} 2y=5x-10 \\ 2y=5(1)-10 \\ 2y=5-10 \\ 2y=-5 \\ \frac{2y}{2}=-\frac{5}{2} \\ y=-2.5 \\ (0,-2.5) \end{gathered}[/tex]When x=2
[tex]\begin{gathered} 2y=5x-10 \\ 2y=5(2)-10 \\ 2y=10-10 \\ 2y=0 \\ \frac{2y}{2}=\frac{0}{2} \\ y=0 \\ (2,0) \end{gathered}[/tex]When x=3
[tex]\begin{gathered} 2y=5x-10 \\ 2y=5(3)-10 \\ 2y=15-10 \\ 2y=5 \\ \frac{2y}{2}=\frac{5}{2} \\ y=2.5 \\ (3,2.5) \end{gathered}[/tex]When x=4
[tex]\begin{gathered} 2y=5x-10 \\ 2y=5(4)-10 \\ 2y=20-10 \\ 2y=10 \\ \frac{2y}{2}=\frac{10}{2} \\ y=5 \\ (4,5) \end{gathered}[/tex]Hence,
By graphing using the ordered pairs below, we will have
[tex]\begin{gathered} (2,0) \\ (0,-5) \end{gathered}[/tex]A small jet can fly 889 miles in 3.5 hours with a tailwind but only 651 miles in 3.5 hours into a headwind. Find the speed of the jet in still air and the speed of the wind.
Given:
[tex]\begin{gathered} D_{is\tan ace\text{ travelled during tail wind}}=889miles \\ T_{\text{ime taken during tail wind}}=3.5hours \\ D_{is\tan ce\text{ travelled during headwind}}=651miles \\ T_{\text{ime taken during headwind}}=3.5hours \end{gathered}[/tex]To Determine: The speed of the jet in still air and the speed of the wind
Represent the speed of the jet in still air and the speed of the wind with unknowns
[tex]\begin{gathered} T_{he\text{ sp}eed\text{ of the jet in still air}}=x \\ T_{he\text{ sp}ed\text{ of the wind}}=y \end{gathered}[/tex]Note that the speed, distance, and time is related by the formula below
[tex]S_{\text{peed}}=\frac{D_{is\tan ce}}{T_{\text{ime}}}[/tex]Calculate the speed during the tailwind and the headwind
[tex]S_{\text{peed during tail wind}}=\frac{889}{3.5}=254milesperhour[/tex][tex]S_{\text{peed during headwind}}=\frac{651}{3.5}=186milesperhour[/tex]Note that during the tailwild, the speed of the wind and the speed of the jet in still air are in the same direction. Also during the headwind, the speed of the wind and the speed of the jet in still air are in opposite direction. Therefore average speed during the tailwind and the headwind would be
[tex]\begin{gathered} equation1\colon x+y=254 \\ equation2\colon x-y=186 \end{gathered}[/tex]Combine the two equations: Add equation 1 and equation 2 to eliminate y as shown below
[tex]\begin{gathered} x+x-y+y=254+186 \\ 2x=440 \\ x=\frac{440}{2} \\ x=220\text{ miles per hour} \end{gathered}[/tex]Substitute x = 220 in equation 1
[tex]\begin{gathered} x+y=254 \\ 220+y=254 \\ y=254-220 \\ y=34\text{ miles per hour} \end{gathered}[/tex]Hence:
The speed of the jet in still air is 220 miles per hour
The speed of the wind is 34 miles per hour
Find the area of the triangle. Round to the nearest tenth. a=28.5 b=33.4 c=22.3
solution
for this case we can use the Herons formula given by:
[tex]A=\sqrt[]{s(s-a)(s-b)(s-c)}[/tex]Where s is the semiperimeter given by:
[tex]s=\frac{a+b+c}{2}=\frac{33.4+28.5+22.3}{2}=42.1[/tex]And we can find the area on this way:
[tex]A=\sqrt[]{42.1(42.1-33.4)(42.1-28.5)(42.1-22.3)}=314.05[/tex]And rounded to the nearest tenth would be:
314.1
I'll upload pictures
Find similar triangles
Triangle PQS is similar to triangle PSR
Reason for this similarity is
RS/ PS = PS / QS
In consecuence
PS^2 = RS • QS
PART 3
RS = 4, RQ= 16. Find RP
Then
RP ^2 = RQ • RS
RP = √ (4•16) = 8
Which expression is equivalent to 3 (m + 2) – 6 (2m + 4)? 15m + 30 15m + 3 - 9m - 18 -9m + 30
To expand and then simplify the expression:
[tex]3(m+2)-6(2m+4)[/tex]We can follow the next steps:
1. Apply the distributive property:
[tex]3m+3\cdot2-12m-6\cdot4=3m+6-12m-24[/tex]Then, we need to algebraically sum the like terms:
[tex]3m-12m+6-24=-9m-18[/tex]Then, the equivalent expression for that given in the question is -9m - 18. It could be also -9(m+2) (using -9 as a common factor).
Neglecting air resistance, the distance (d) that an object fallsvaries directly as the square of the time (t) it has been falling.If an object falls 64 feet in 2 seconds, determine the distanceit will fall in 6 seconds.
where a is a constant, we can find a with the first statement:
"an object falls 64 feet in 2 seconds"
so:
[tex]\begin{gathered} 64=a(2)^2 \\ a=\frac{64}{2^2} \\ a=16 \end{gathered}[/tex]the complete equation is
[tex]d(t)=16t^2[/tex]now "determine the distance for 6seconds"
so, replace t=6 and find d
[tex]\begin{gathered} d(t)=16(6)^2 \\ d(t)=576ft \end{gathered}[/tex]the distance is 576ft
which property is illustrated by the statement 8 + 2 equals 2 + 8? A. Associative B. commutative C. Distributive D. Identity
8+2=2+8 is result of the commutative property. Then, the answer is option B
Kenneth read a total of 320 pages over 32 hours. After a total of 42 hours of reading this week, how many pages will Kenneth have read in all? Assume the relationship is directly proportional.
From the question, we can deduce the following:
320 pages ==> 32 hours
Let's find how many pages Kenneth will read in 42 hours.
We have:
32 hours = 320 pages
42 hours = x pages
Apply the proportionality equation and solve for x.
[tex]\frac{320}{32}=\frac{x}{42}[/tex]Cross multiply:
[tex]\begin{gathered} 32x=320\times42 \\ \\ 32x=13440 \end{gathered}[/tex]Divide both sides by 32:
[tex]\begin{gathered} \frac{32x}{x}=\frac{13440}{32} \\ \\ x=420 \end{gathered}[/tex]Therefore, Kenneth will read 420 pages after a total of 42 hours.
ANSWER:
420 pages.
The Honeywell HQ17 air cleaner takes twice as long as the EV25 to clean the samevolume of air. Together the two machines can clean the air in a 25-ft by 24-ft banquetroom in 10 minutes. How long would it take each machine working alone to clean the airin the room?
Given:
The Honeywell HQ17 air cleaner takes twice as long as the EV25 to clean the same
volume of air.
Let, x be the time taken by Honeywell EV25 air cleaner.
And 2x be the time taken by Honeywell HQ17 air cleaner.
Together the two machines can clean the air in 10 min.
[tex]\begin{gathered} x+2x=10 \\ 3x=10 \\ x=\frac{10}{3}=3.33\text{ min} \end{gathered}[/tex]So, time takes by Honeywell HQ17 air cleaner is,
[tex]2x=2(\frac{10}{3})=6.67\text{ min}[/tex]Answer:
The time taken by Honeywell EV25 air cleaner is 3.33 min.
The time taken by Honeywell HQ17 air cleaner is 6.67 min.
What are the dimensions of a parallelogram in terms of the demensioms of the circle?
If we divide a circle into a number of equal segments then stack them in a row head-to-tail, the new shape is a parallelogram with bumpy sides, with the same area as the circle.
We can conclude the following:
1. The base of a parallelogram is approximately equal to half the circumference of the circle
2. The height of the parallelogram is approximately equal to the radius of the circle
3. The area of the parallelogram is equal to the area of the circle.
Hi, can you help me to solve this problem, please!!!
The given parabola is:
[tex]y=-3x^2+3x-6[/tex]It is written in the form:
[tex]y=ax^2+bx+c[/tex]The axis of symmetry is given by the following formula:
[tex]x=-\frac{b}{2a}[/tex]Where a=-3 and b=3. Replace these values and solve for x:
[tex]\begin{gathered} x=-\frac{3}{2(-3)}=-\frac{3}{-6}=\frac{3}{6} \\ \text{Divide numerator and denominator by 3 to simplify} \\ x=\frac{3/3}{6/3}=\frac{1}{2} \end{gathered}[/tex]Therefore, the axis of symmetry is x=1/2
Compare two sequence 2 4 6 8 102 4 8 16 32
The given sequences are
[tex]\begin{gathered} 2,4,6,8,10\rightarrow(1) \\ 2,4,8,16,32\rightarrow(2) \end{gathered}[/tex]In the sequence (1):
[tex]\begin{gathered} 4-2=2 \\ 6-4=2 \\ 8-6=2 \\ 10-8=2 \end{gathered}[/tex]There is a common difference of 2
Then it is an arithmetic sequence
In the sequence (2):
[tex]\begin{gathered} \frac{4}{2}=2 \\ \frac{8}{4}=2 \\ \frac{16}{8}=2 \\ \frac{32}{16}=2 \end{gathered}[/tex]There is a common ratio of 2
Then it is a geometric sequence
The first sequence is increasing by 2
The second sequence is multiplying by 2
USMZABC = 40'and BỎ is the anglebisector of ZABC3y+6B.3x-134-2xD5y-18MZABD =[ ? 1°Enter
We want to calculate the value of
[tex]3x-1[/tex]However, x is unknown. For BD is "angle bisector"
[tex]3x-1=34-2x[/tex]Let us solve that equation for x:
[tex]3x+2x=34+1[/tex](-2x was sent to the left-hand side, and -1 was sent to the right-hand side)
[tex]5x=35[/tex][tex]x=7[/tex]Then,
[tex]3x-1=3(7)-1=21-1=20[/tex]Thus,
[tex]m\measuredangle ABD=20[/tex]Answer the question below based on the two quadratic functions.Function 2хyFunction 1f(x) = x2 + 4x - 3-7-8-2.-1012.-7-41Which function has the graph with the smaller minimum value and what is the minimum value?Function 1 has the smaller minimum value of -2.Function 2 has the smaller minimum value of -1.Function 1 has the smaller minimum value of -7.O Function 2 has the smaller minimum value of -8.
1. Plotting the function or creating a table with values.
This is what you did, and you got that for x=-2 the functions reaches the minimum, to y= -7
Now, since you already know the minmum value for the first function, you can see that the first answer is false while the third one is true. But, is that value (-7) smaller than the minimum for function 2?
Looking at the table, we can see that function 2 reaches the minimum for x = -1, and it is equal to y = -8.
Since -8 < -7, function 2 minimum is smaller than function 1 minimum.
Then, answer #4 is the correct one.
Mrs. Burke's biology class has 128 students, classified by academic year and major, as illustrated in the table. Mrs. Burke randomly chooses one student to collectyesterday's work.Mrs. Burke's Biology ClassAcademic Year Biology MajorsFreshmenSophomoresJuniorsSeniors19171617Non-Biology Majors17141018Step 2 of 2: What is the probability that she selects a senior, given that she chooses a biology major? Enter a fraction or round your answer to 4 decimal places, ifnecessary.
Total: 128 students
1. The probability that she selects a senior, given that she chooses a biology major is given by:
[tex]P=\frac{seniors}{biolog\text{y majors}}=\frac{17}{19+17+16+17}=\frac{17}{69}=0.2464[/tex]Answer: 0.2464
The diagonales of this rhombus are 3 meterse and 8 meters
Area of a rhombus = 1/2 x d1 x d2
d1= diagonal 1 = 8m
d2 = diagonal 2 = 3m
Replacing:
A = 1/2 x 8 x 3 = 12 m2
The graph below has the same shape as the graph of G(x) = x?, but it isshifted down five units and to the left four units. Complete its equation. Enterexponents using the caret (1); for example, enter x2 as x^2. Do not include"F(x) =" in your answer
Assume the random variable x is normally distributed with mean μ = 83 and standard deviation o=4. Find the indicated probability.P(70
SOLUTION
Given the question in the image on the question tab;
[tex]P(70Now, we are going to find;[tex]P(-3.25[tex]Using\text{ statistical table for normal distribution; the probability is:}[/tex][tex]0.0662301762265\times100=6.623\%[/tex]
Final answer:
[tex]\begin{equation*} 6.623\% \end{equation*}[/tex]Let f(x) = 3x – 3 and g(x) = x + 5. Find f(g(x)) and g(f(x)).
given data:
[tex]\begin{gathered} f\mleft(x\mright)=3x-3 \\ g\mleft(x\mright)=x+5 \end{gathered}[/tex]to find:
[tex]f\mleft(g\mleft(x\mright)\mright)\text{ and }g\mleft(f\mleft(x\mright)\mright)[/tex][tex]\begin{gathered} g(x)=x+5 \\ =f(x+5) \\ =3(x+5)-3 \\ =3x+12 \end{gathered}[/tex][tex]\begin{gathered} f(x)=3x-3 \\ =g(3x-3) \\ =(3x-3)+5 \\ =3x+2 \end{gathered}[/tex]which is in an equation of the line through (0,0) and (-8,-5)?
To finde the equation of the line troughh the points (0;0) and (-8;-5) first you must find the slope of the line. You have to use the next formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Replacing the points in the previous formula
[tex]m=\frac{-5-0}{-8-0}=\frac{5}{8}[/tex]As the line passes trough the origin of coordinates (point (0;0)) the equation is:
[tex]y=\frac{5}{8}x[/tex]So the answer is y= 5/8 x (option B)
*Be sure to simplify fractions and rationalize denominators if necessary.
As given by the question
There are given that the vector:
[tex]\vec{v}=\vec{2i}+\vec{3j}[/tex]Now,
From the formula to find the unit vector in same direction is:
[tex]\vec{u}=\frac{\vec{v}}{\lvert\vec{v}\rvert}[/tex]Then,
[tex]\begin{gathered} \vec{u}=\frac{\vec{v}}{\lvert\vec{v}\rvert} \\ \vec{u}=\frac{\vec{2i}+\vec{3j}}{\lvert\vec{2i}+\vec{3j}\rvert} \\ \vec{u}=\frac{\vec{2i}+\vec{3j}}{\lvert\sqrt[]{2^2+3^2}\rvert} \end{gathered}[/tex]Then,
[tex]\begin{gathered} \vec{u}=\frac{\vec{2i}+\vec{3j}}{\sqrt[]{2^2+3^2}} \\ \vec{u}=\frac{\vec{2i}+\vec{3j}}{\sqrt[]{4+9}} \\ \vec{u}=\frac{\vec{2i}+\vec{3j}}{\sqrt[]{13}} \end{gathered}[/tex]Then,
Rationalize the denominator:
So,
[tex]\begin{gathered} \vec{u}=\frac{\vec{2i}+\vec{3j}}{\sqrt[]{13}} \\ \vec{u}=\frac{\vec{2i}+\vec{3j}}{\sqrt[]{13}}\times\frac{\sqrt[]{13}}{\sqrt[]{13}} \\ \vec{u}=\frac{\vec{\sqrt[]{13}(2i}+\vec{3j})}{13} \\ \vec{u}=\frac{2\sqrt[]{13}}{13}i+\frac{3\sqrt[]{13}}{13}j \end{gathered}[/tex]Hence, the unit vector is shown below:
[tex]\vec{u}=\frac{2\sqrt[]{13}}{13}i+\frac{3\sqrt[]{13}}{13}j[/tex]c 1150Solve for the length of the arc, to the nearest tenth.2.08.016.150.3
ANSWER
8.0
EXPLANATION
If the central angle θ is in degrees and the radius is r, the length of the arc 's' is:
[tex]s=\frac{\theta}{360}\times2\pi r[/tex]In this problem θ = 115º, r = 4: