Answer: M=32°
Step-by-step explanation:
The identity sin²(x)+cos²(x)=1 can help us figure out the value of M. You can see that the problem's format fits exactly the identity. Since x is the same in the identity, we know that M=32°.
A committee of 4 people is chosen from 7 women and 7 men. How many different committees are possible that consist of 2 women and 2 men?
Answer: 441
Step-by-step explanation:
2 men from 7 will be the members of committee that makes 7*6/2=21 outputs
2 women from 7 will be the members of committee that makes 7*6/2=21 outputs as well.
Total number of outputs is 21*21=441
The number of ways different committees are possible that consist of 2 women and 2 men is 441.
What is binomial?Two terms joined by a plus or minus sign make up a mathematical expression are termed as binomial.
What is the binomial coefficient?The positive integers that appear as coefficients in the binomial theorem are known as binomial coefficients in mathematics. A binomial coefficient is typically written and indexed by the two integers n ≥ k ≥ 0.
There are the binomial coefficient "7 choose 2", i.e. [tex]\frac{7!}{2!5!}=21[/tex] ways to choose 2 people from a set of 7 people.
So, there are 21 ways to choose 2 men and 21 ways to choose 2 women. This means that there is [tex]21^2 = 441[/tex] ways to choose both 2 men and 2 women.
Learn more about application of binomial coefficient from given link.
https://brainly.com/question/14216809
#SPJ2
In a large school, it was found that 69% of students are taking a math class, 70% of student are taking an English class, and 50% of students are taking both.
A. True
B. False
Answer:
P(Math or English) = 0.89
Step-by-step explanation: This solution will only be applicable if finding the probability that a randomly selected student is taking a math class or an English class.
Lets study the meaning of or , and on probability. The use of the word or means that you are calculating the probability
that either event A or event B happened
Both events do not have to happen
The use of the word and, means that both event A and B have to happened
The addition rules are: # P(A or B) = P(A) + P(B) ⇒ mutually exclusive (events cannot happen
at the same time)
P(A or B) = P(A) + P(B) - P(A and B) ⇒ non-mutually exclusive (if they
have at least one outcome in common)
The union is written as A ∪ B or “A or B”.
The Both is written as A ∩ B or “A and B”
Lets solve the question
The probability of taking Math class 69%
The probability of taking English class 70%
The probability of taking both classes is 50%
P(Math) = 69% = 0.69
P(English) = 70% = 0.70
P(Math and English) = 50% = 0.50
To find P(Math or English) use the rule of non-mutually exclusive
P(A or B) = P(A) + P(B) - P(A and B)
P(Math or English) = P(Math) + P(English) - P(Math and English)
Lets substitute the values of P(Math) , P(English) , P(Math and English)
in the rule P(Math or English) = 0.69 + 0.70 - 0.50 = 0.89
P(Math or English) = 0.89
P(Math or English) = 0.89
This solution will only be applicable if we are to find the probability that a randomly selected student is taking a math class or an English class.
Which of the following indicates the subtraction property of equality when solving the equation 86 – 2 (9x + 4) = 12x + 18 A) 2(9x + 4) = 86 – 12x – 18 B) x = 2 C) –2(9x + 4) = 12x + 18 – 86 D) 86 – 18x – 8 = 12x + 18
Answer:
D) 86 – 18x – 8 = 12x + 18
X = 2
Step-by-step explanation:
86 – 2 (9x + 4) = 12x + 18
This question has a straight forward answer...
It's just to open up the bracket and ensure that the negative sign before the bracket multiply the values in the bracket exactly.
So opening up the bracket gives us this as the answer
86 - 18x -8 = 12x +18
86-18-8 = 12x+ 18x
60 = 30x
X = 2
me Left:1:23:57
Mandeep Sharma: Attempt 1
Question 1 (2 points)
A scientist records the internal temperature of a kiln that has been turned off for maintenance after
a limestone calcination reaction as 794 °C. He then leaves the room to allow the kiln cool further.
The room temperature is 25°C. An equation that models the temperature of the cooling kiln (T in °C,
t in min) is as follows:
T(t) = 1.0.73l/3.7 + 25
How fast is the reaction cooling rate (%T lost/min) to the nearest whole number?
Your Answer:
Answer
Answer:
c and I will talk to you later today or tomorrow morning and then I will
Step-by-step explanation:
email to you later today to see you and the kids are doing well and that you
Please answer this correctly without making mistakes
Answer: Anything above 2
Step-by-step explanation:
Answer: 3,4,5,6,7,8,9 (Any of these digits work)
Step-by-step explanation:
We want to find a digit that makes the number greater than 3260.2. There are many digits that can fit in there.
3318.7≥3260.2
Here, we plugged in a 3. that makes this sentence true because 3318.7 is greater than or equal to 3260.2. Since 3 works, we know that any digit greater than 3 would fit.
The rectangle has an area of 60 square feet. Find its dimensions (in ft). (x + 4) feet smaller value ___________________ ft larger value ____________________ ft
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
The rectangle has an area of 60 square feet. Find its dimensions (in ft) if the length of the rectangle is 4 ft more than its widh.
smaller value ___________________ ft
larger value ____________________ ft
Answer:
Smaller value = 6 ft
Larger value = 10 ft
Step-by-step explanation:
Recall that the area of a rectangle is given by
[tex]Area = W \times L[/tex]
Where W is the width and L is the length of the rectangle.
It is given that the rectangle has an area of 60 square feet.
[tex]Area = 60 \: ft^2 \\\\60 = W \times L \\\\[/tex]
It is also given that the length of the rectangle is 4 ft more than its width
[tex]L = W + 4[/tex]
Substitute [tex]L = W + 4[/tex] into the above equation
[tex]60 = W \times (W + 4) \\\\60 = W^2 + 4W \\\\W^2 + 4W - 60 = 0 \\\\[/tex]
So we are left with a quadratic equation.
We may solve the quadratic equation using the factorization method
[tex]W^2 + 10W - 6W - 60 \\\\W(W + 10) – 6(W + 10) \\\\(W + 10) (W - 6) = 0 \\\\[/tex]
So,
[tex](W + 10) = 0 \\\\W = -10 \\\\[/tex]
Since width cannot be negative, discard the negative value of W
[tex](W - 6) = 0 \\\\W = 6 \: ft \\\\[/tex]
The length of the rectangle is
[tex]L = W + 4 \\\\L = 6 + 4 \\\\L = 10 \: ft \\\\[/tex]
Therefore, the dimensions of the rectangle are
Smaller value = 6 ft
Larger value = 10 ft
Verification:
[tex]Area = W \times L \\\\Area = 6 \times 10 \\\\Area = 60 \: ft^2 \\\\[/tex]
Hence verified.
Identify which quadrant of the coordinate plane the point (−3, 15) lies in.
Answer:
Quadrant II.
Step-by-step explanation:
Quadrant | has positive x and y coordinates.
Quadrant || has negative x and positive y coordinates.
Quadrant ||| has negative x and y coordinates.
Quadrant |V has positive x and negative y coordinates.
Since -3 is negative and 15 is positive, the answer is Quadrant II.
Write the Maclaurin series for f(x) = x^7e^x5. (2 points) a) the summation from n equals 1 to infinity of the quotient of x to the 7th power and n factorial b) the summation from n equals 0 to infinity of the quotient of x to the 12th power and the quantity n plus 5 factorial c) the summation from n equals 0 to infinity of the quotient of x to the quantity 5 times n plus 7 power and n factorial d) the product of x raised to the 5 times n power and the summation from n equals 1 to infinity of the quotient of x to the 7th power and n factorial
Recall that
[tex]e^x=\displaystyle\sum_{n=0}^\infty\frac{x^n}{n!}[/tex]
Then
[tex]e^{x^5}=\displaystyle\sum_{n=0}^\infty\frac{x^{5n}}{n!}[/tex]
and
[tex]x^7e^{x^5}=\displaystyle\sum_{n=0}^\infty\frac{x^{5n+7}}{n!}[/tex]
As Devine rides her bike, she picks up a nail in her front tire. The height, h, of the nail from the ground as she rides her bike over time, t, in seconds, is modelled by the equation below: As Devine rides her bike, she picks up a nail in her front tire. The height, h, of the nail from the ground as she rides her bike over time, t, in seconds, is modelled by the equation below:f(x)=-14 cos(720(t-10))+14
Using the equation, determine the following. Show your work for part marks.
a) What is the diameter of the bike wheel?
b) How long does it take the tire to rotate 3 times?
c) What is the minimum height of the nail? Does this height make sense? Why?
Step-by-step explanation:
a) The diameter of the wheel is the distance between the minimum and maximum. In other words, it's double the amplitude.
d = 2 × 14 = 28.
b) The period of the wave is:
720 = 2π / T
T = π/360
So the time for 3 revolution is:
3T = π/120
3T = 0.026 seconds
c) The minimum here is when cosine = 1.
h(t) = -14(1) + 14
h(t) = 0
This makes sense, since the minimum height is when the nail is at the bottom of the wheel, or at the ground.
A random sample of college football players had an average height of 64.55 inches. Based on this sample, (63.2, 65.9) found to be a 92% confidence interval for the population mean height of college football players. A. We are 92% confident that the population mean height of college football players is between 63.2 and 65.9 inches.B. We are 92% confident that the population mean height of college football palyers is 64.55 inches.C. A 92% of college football players have height between 63.2 and 65.9 inches.D. There is a 92% chance that the population mean height of college football players is between 63 2 and 65.9 inches.
Answer:
A. We are 92% confident that the population mean height of college football players is between 63.2 and 65.9 inches.
Step-by-step explanation:
Confidence interval:
x% confidence
Of a sample
Between a and b.
Interpretation: We are x% sure(or there is a x% probability/chance) that the population mean is between a and b.
In this question:
92% confidence interval for the average height of football players is (63.2, 65.9).
Interpretation: We are 92% sure that the true average height of all college football players, that is, the population mean, is in this interval.
The correct answer is:
A. We are 92% confident that the population mean height of college football players is between 63.2 and 65.9 inches.
I NEED HELP ASAP PLEASE! :)
Answer:
option 1
Step-by-step explanation:
[tex]r=\sqrt{(5\sqrt{2})^{2}+(-5\sqrt{2})^{2} } \\\\=\sqrt{25*2+25*2}\\\\ =\sqrt{50+50}\\\\=\sqrt{100}\\\\=10[/tex]
[tex]x=tan^{-1}(\frac{-5\sqrt{2}}{5\sqrt{2}})\\\\x=tan^{-1} (-1)\\x=\frac{7\pi}{4}[/tex]
[tex]re^{ix}=10e^{i\frac{7\pi}{4}}[/tex]
SOMEBODY HELP
Jill bought 7 books more than Sam. If Sam and Jill together have 25 books, find the
number of books Sam has.
Answer:
Jill bought 16 books and Sam bought 9 books
Step-by-step explanation:
Let the number of books that Jill bought be j.
Let the number of books that Sam bought be s.
Jill bought 7 more books than Sam:
j = 7 + s
They bought 25 books altogether:
j + s = 25
Put j = 7 + s into the second equation:
7 + s + s = 25
7 + 2s = 25
2s = 25 - 7 = 18
s = 18/2 = 9 books
Therefore:
j = 7 + s = 7 + 9
s = 16 books
Jill bought 16 books and Sam bought 9 books.
Choose the name of this figure.
A.
line
B.
angle
c.
line segment
D.
ray
Answer:
we dont see aa figure
Step-by-step explanation:
In a jar of coins, 18 out of the 40 coins are dimes. Express the fraction of the coins
that are dimes in three different ways below: (a) as a fraction, (b) as a decimal, and (c) as a percent.
Use long division to determine the decimal.
(a) as a fraction
(b) as a decimal
(c) as a percent
Answer:
Percent: 20%
Fraction: 1/5
Decimal: 0.20
Step-by-step explanation:
8:40*100 =
( 8*100):40 =
800:40 = 20%
Percent to fraction:
20%=20/100
= 0.2
=0.2×10/10
=2/10
=1/5
Percent to decimal:
20/100 = 0.20
Which functions have an axis of symmetry of x = -2? Check all that apply. A. f(x) = x^2 + 4x + 3 B. f(x) = x^2 - 4x - 5 C. f(x) = x^2 + 6x + 2 D. f(x) = -2x^2 - 8x + 1 E. f(x) = -2x^2 + 8x - 2
Answer:
A. f(x) = x^2 + 4x + 3
D. f(x) = -2x^2 - 8x + 1
Step-by-step explanation:
The axis of symmetry is found by h = -b/2a where ax^2 +bx +c
A. f(x) = x^2 + 4x + 3
h = -4/2*1 = -2 x=-2
B. f(x) = x^2 - 4x - 5
h = - -4/2*1 = 4/2 =2 x=2 not -2
C. f(x) = x^2 + 6x + 2
h = -6/2*1 = -3/2 = x=-3/2 not -2
D. f(x) = -2x^2 - 8x + 1
h = - -8/2*-2 = 8/-4 =-2 x=-2
E. f(x) = -2x^2 + 8x - 2
h = - 8/2*-2 = -8/-4 =2 x=2 not -2
Answer:
Hey there! The answer to this question is
A. f(x) = x^2 + 4x + 3
D. f(x) = -2x^2 - 8x + 1
Please answer this correctly without making mistakes
Answer:
A digit that makes this sentence true is 4.
Step-by-step explanation:
Since the first digit in the number to the left is 3, you simply have to find a digit greater than 3. Here are the possibilities:
4
5
6
7
8
and
9
Out of any of these you can choose, I chose 4.
9514 1404 393
Answer:
3, or any greater digit
Step-by-step explanation:
Suppose the digit is 'd'. Then the value on the right is ...
69.436 +100d
Subtracting the value on the left, we want the difference greater than 0.
69.436 +100d - 352.934 > 0
100d -293.498 > 0 . . . . simplify
100d > 293.498 . . . . . . . add 293.498
d > 2.93498 . . . . . . . . . . divide by 100
That is d is any single digit greater than 2.9. Those digits are ...
d ∈ {3, 4, 5, 6, 7, 8, 9}
Any digit 3 or greater makes the sentence true.
PLEASE HELP ME! Simplify the expression 3 4 (1440) + 295.25 + (-33.50) to determine how much money the theater brought in.
Answer:
1341.75
Step-by-step explanation:
I did the math :)
The guy above me is correct
Which of the following is not an example of a quadratic function?
1. f(x)= (3x-2)(4x +7) 2. f(x) = (2x-1)2
3. f(x)= -7x²+8X
4. f(x)= 8x4–3x+5x2
Answer:
4. f(x) = 8x^4 – 3x + 5x^2
Step-by-step explanation:
In choices 1., 2., and 3., each function is a 2nd degree function since the term with the highest degree has an exponent of 2 on x. In choice 4., the function is a 4th degree function since there is a term with x^4, and that is the highest exponent on x.
Answer: 4. f(x) = 8x^4 – 3x + 5x^2
Pls hurry least to greatest
Answer:
First choice
Step-by-step explanation:
Start by arranging the exponents of 10 in ascending order.
9.4 * 10^-8, 9.25 * 10^-6, 2.5 * 10^3, 7 * 10^3
The exponents are in ascending order, -8, -6, 3, 3
Since the last two exponents are equal, we must compare the numbers that multiply the powers of 10. They are 2.5 and 7. Since 2.5 < 7, ascending order is 2.5, 7. That means the line above is in ascending order.
Answer: First choice
A sample of 17 patients in a hospital had these hemoglobin readings 112 120 98 55 71 35 99 142 64 150 150 55 100 132 20 70 93 find a 95% confidence interval for the hemoglobin reading for all the patienta in the hospital
Answer:
The 95% confidence interval for the hemoglobin reading for all the patients in the hospital is (72, 112).
Step-by-step explanation:
The (1 - α)% confidence interval for the population mean, when the population standard deviation is not provided is:
[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\cdot \frac{s}{\sqrt{n}}[/tex]
The data provided is:
S = {112, 120, 98, 55, 71, 35, 99, 142, 64, 150, 150, 55, 100, 132, 20, 70, 93}
Compute the sample mean and sample standard deviation as follows:
[tex]\bar x=\frac{1}{n}\sum X=\frac{1}{17}\times[112+120+98+...+93]=92.1176\\\\s=\sqrt{\frac{1}{n-1}\sum (x-\bar x)^{2}}=\sqrt{\frac{1}{17-1}\times 25041.7647}=39.56[/tex]
The critical value of t for 95% confidence level and n - 1 = 16 degrees of freedom is:
[tex]t_{\alpha/2, (n-1)}=t_{0.05/2, 16}=2.120[/tex]
*Use a t-table.
Compute the 95% confidence interval for the hemoglobin reading for all the patients in the hospital as follows:
[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\cdot \frac{s}{\sqrt{n}}[/tex]
[tex]=92.1176\pm 2.120\times\frac{39.56}{\sqrt{17}}\\\\=92.1176\pm 20.3408\\\\=(71.7768, 112.4584)\\\\\approx (72, 112)[/tex]
Thus, the 95% confidence interval for the hemoglobin reading for all the patients in the hospital is (72, 112).
Betty can mow a lawn in 60 minutes. Melissa can mow the same lawn in 30 minutes. How long does it take for both Betty and Melissa to mow the lawn if they are working together? Express your answer as a reduced fraction.
Answer:
20 minutes
Step-by-step explanation:
Melissa works as fast as two Bettys, so working together, they get the job done at the rate 3 Bettys could do it. That time is (60 minutes)/3 = 20 minutes.
Working together, Betty and Melissa can mow the lawn in 20 minutes.
_____
You can also think in terms of mowing rates as lawns per minute. The total mowing rate is ...
Betty's rate + Melissa's rate = (1/60 lawns/min) +(1/30 lawns/min)
= (1/60 +2/60) lawns/min = 1/20 lawns/min
The inverse rate is then ...
20/1 min/lawn
Together, they take 20 minutes to mow 1 lawn.
Determine whether the parallelogram is a rhombus, rectangle, square, or none. Explain.
Q(1, 3), R(3, 4), S(5, 3), T(3, 2)
Select one:
A. QRST is a rhombus that is not a square because its diagonals are perpendicular but not congruent.
B. QRST is a rectangle that is not a square because its diagonals are congruent but not perpendicular.
C. QRST is a square because its diagonals are both perpendicular and congruent.
D. QRST is none of these because its diagonals are neither congruent nor perpendicular.
Answer:
Step-by-step explanation:
The diagonals of the given parallelogram are QS and RT. We would first determine if its diagonals are congruent.
QS = √(1 - 5)² + (3 - 3)² = 16
RT = √(3 - 3)² + (4 - 2)² = 4
Since QS ≠ RT, it means that they are not congruent and this means that the parallelogram is not a rectangle.
Let us check if the diagonals are perpendicular.
Slope of QS = (3 - 3)/(5 - 1) = 0/4
Slope of RT = (2 - 4)/(3 - 3) = - 2/0
The slopes are not opposite reciprocals. It means that the diagonals are not perpendicular. Therefore, the correct option is
D. QRST is none of these because its diagonals are neither congruent nor perpendicular.
The Gold Bar has a trapezium cross-sectional area Gold has a density of 19.3 grams per
Answer: 22.3 quarter
Step-by-step explanation:
Answer:
13.896 kg
Step-by-step explanation:
Charles's law states that at constant pressure, the volume of a fixed amount of gas varies directly with its temperature measured in Kelvins. A gas has a volume of 250 ml at 300°K. a.) Write an equation for the relationship between volume and temperature. b.) What is the volume if the temperature increases at 420°K?
Answer:
equation is pv=nRT
p, n, R are constants
so, v is directly proportional to Temperature
v1/v2=T1/T2
250/v2=300/420
v2=350
If sin t=0.29 and sin w = 0.43, both t and w are positive, and the angles determined by t and w are in quadrant 2, then which of the following statements is true? Explain your selection
a. t>w
b. w>t
c. cannot be determined
Answer:
a. t>w
Step-by-step explanation:
Sin t= 0.29
t = sin^-1(0.29)
t= 16.86°
Sin w= 0.43
W = sin^-1(0.43)
W= 25.47°
Angles in the second quadrant are positive in sine and they are generally determined by subtracting the initial value from 180°
For t= 180°-16.86°
t = 163.14°
For w = 180°-25.47°
W= 154.53°
163.14°>154.53°
t>w
Let f(x)= |x| and g(x) = x+2. What are the domain and range of (fog)(x)?
If [tex]f(x)=\mid x\mid[/tex] and [tex]g(x)=x+2[/tex] then [tex]f(g(x))=\mid x+2\mid[/tex].
The domain is [tex]x\in(-\infty, +\infty)=\mathbb{R}[/tex].
The range is [tex]y\in[2,+\infty)[/tex].
Hope this helps.
Answer:
D) domain: all real numbersrange: y>0Step-by-step explanation:
with range there is a horizontal line under the > sign, just as a side note:D
BRANLIEST?
i need help please!!!
Answer:
1 = 95
2 = 77
3 = 85
4 = 103
Step-by-step explanation:
Inscribed angles are half their arc that their 2 lines intersect.
the linear equation y=2x represents the cost y of x pounds of pears. which order pair lies on the graph of the equation? A. (2,4) B. (1,0) C.(10,5) D. (4,12)
Answer:
A. (2, 4)
Step-by-step explanation:
The ordered pairs represent (x, y). Since you have y =2x, this is the same as ...
(x, 2x)
That is, the second number in the pair needs to be twice the first number in the pair. Since you know your times tables, you know that this is not the case for (1, 0), (10, 5) or (4, 12). Those values of x would give (1, 2), (10, 20), (4, 8).
It is the case that you have (x, 2x) for (2, 4).
The point (2, 4) lies on the graph of y = 2x.
Point p is the centroid of jkl. Kr=72 and Pq=30 what is kp?
Answer:
B (48)
Step-by-step explanation:
One particular property of medians is the 2/3 ratio. Basically, the centroid separates the median into two line segments, and the longer line segment is 2/3 of the median length. So, 72 x 2/3 is 48.
What are the angle measurements of angles 1 &4 for #1 & measurements of angles 1-3 on #2?
Answer:
1. To find m∠1, we can notice that ∠1 and 46° are complementary, meaning they add up to 90° This means that m∠1 = 90 - 46 = 44°. We can do the same for ∠4. In this case, ∠4 = 90 - 23 = 67°.
2. To find m∠1, we can use the exterior angle formula which means that the measure of an exterior angle is equal to the sum of both of its remote interior angles. This means that ∠1 = 52 + 62 = 114°. To find ∠2 we can do 180 - 52 - 62 = 66° because the sum of all angles in a triangle is 180°. Since ∠2 and ∠3 are vertical angles, ∠3 = ∠2 = 66°.