Step-by-step explanation:
sin(2x) + cos(3x)
Use double angle formula sin(2x) = 2 sin x cos x.
Use triple angle formula cos(3x) = 4 cos³x − 3 cos x.
Substitute:
2 sin x cos x + 4 cos³x − 3 cos x
1) Determine which events are mutually exclusive and which are not, when a single card is drawn from a deck. a. Getting a 7 and getting a jack b. Getting a club and getting a king c. Getting a face card and getting an ace d. Getting a face card and getting a spade
Answer:
The events a) and c) are mutually exclusive.
Step-by-step explanation:
a) This is mutually exclusive, each card has a unique value between 2 and 10, or it is a jack, queen, king, or an Ace. A single card cant have two different values at the same time.
b) This is not mutually exclusive, since you can get a king of clubs. Each card can have any combination of one suit and one value.
c) A face card is either a Jack, a Queen or a King, it is not an Ace. For the same argument of a), a card cant have two different values, therefore this event is mutually exclusive.
d) This is not mutually exclusive, since a card can have any suit independently of the value it has (same argument than b), therefore, a card can be a face card and a spade at the exact time.
Therefore, events a and c are mutually exclusive.
a) Getting a 7 and getting a jack: Mutually exclusive events
b) Getting a club and getting a king: Not mutually exclusive events
c) Getting a face card and getting an ace: Mutually exclusive events
d) Getting a face card and getting a spade: Not mutually exclusive events
A standard deck of cards has 52 cards having 13 ranks each of 4 suites. The 13 ranks are
[tex]\text{Ranks}=\{Ace,2,3,4,5,6,7,8,9,10,Jack,Queen,King\}[/tex]
and the suites are
[tex]Suites=\{Clubs,Diamonds,Hearts,Spades\}[/tex]
a) Getting a 7 and getting a jack:
Since a 7 and a Jack are different rank elements, you either pick a 7 of a suite, or a Jack of a suite, but never both. So, the events are mutually exclusive.
b) Getting a club and getting a king:
Since a Club is a suite and a King is a Rank, the sample space will have a King of Clubs card. So, the events are not mutually exclusive.
c) Getting a face card and getting an ace:
A face card is a card with a face on it. Faces are Ranks, but an Ace is also a Rank. The sample space contains cards with only one Rank per card. So, the events are mutually exclusive.
d) Getting a face card and getting a spade:
Faces are Ranks, and a Spade is a suite. The sample space will contain face cards for the Spade suite of cards. So, the events are not mutually exclusive.
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Which statement illustrates the distributive property?
3(4+5)= 3(4)+5
3(4+5)= 3(4)+3(5)
3[(4)+(5)] = 3(4)+3(5)
3[(4)(5)] = [3(4) ][ 3(5)]
Answer:
3(4+5)= 3(4)+3(5)
Step-by-step explanation:
Answer:
3(4+5)= 3(4)+3(5)
Step-by-step explanation:
Recall the equation for a circle with center ( h , k ) and radius r . At what point in the first quadrant does the line with equation y = 2.5 x + 3 intersect the circle with radius 4 and center (0, 3)?
Answer:
The point at which the line y = 2.5·x + 3 intersect with the circle of radius 4 and center (0, 3) is x = 1.49
Step-by-step explanation:
Here we have the equation of a circle = (x - h)² + (y-k)² = r²
Where (h, k) is the coordinate of the center
Therefore, we have
(x - 0)² + (y - 3)² = 4²
Which gives x² + (y - 3)² = 16
Since the line y = 2.5·x + 3 we have
x² + ( (2.5·x + 3 ) - 3)² = 16
x² + (2.5·x)² = 16
x² + 6.25·x² = 16
7.25·x² = 16
x² = 16/7.25 = 2.21
x = 1.49
That is the line y = 2.5·x + 3 intersect with the circle of radius 4 and center (0, 3) at x = 1.49.
The point of intersection in the first quadrant of the given line y = 2.5x + 3 and the given circle x² + (y - 3)² = 16, can be found by substituting the equation of the line into the equation of the circle and then solving for x and y.
Explanation:The subject of this question is the intersection of a line and a circle in the first quadrant of a coordinate plane. The circle is defined by the equation (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. For a circle with center at the origin (0, 3) and radius 4, the equation is x² + (y - 3)² = 16.
The line is defined by the equation y = 2.5x + 3. To find the intersection point, we substitute this equation into the equation of the circle, resulting in x² + (2.5x)² - 6x + 9 = 16. Solving this quadratic equation gives the x-coordinates of the intersection points. Since we are only interested in the first quadrant, we pick the positive root. Substituting this value of x into y = 2.5x +3 gives the corresponding y-coordinate, defining the point of intersection in the first quadrant.
Learn more about Intersection of line and circle here:https://brainly.com/question/34183150
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One hundred students are enrolled in State University's course on introductory physics for math and science majors. In the group, 60 students are math majors and 40 are science majors. Sarah is in the class. She got all As in her high school science courses, and she would like to be a chemist someday. She lives on campus. Her boyfriend is also in the class. There is a _________________ chance that Sarah is a science major.
Answer:
40%
Step-by-step explanation:
Total Number of Students in Introductory Physics Course =100
Number of Math Majors = 60
Number of Science Majors = 40
Relevant Facts
Sarah got all As in her high school science coursesShe would like to be a chemist someday which is Science RelatedTherefore, there is a 40 out of 100 chance that Sarah is a science major.
Expressed in percentage, there is a 40% chance that Sarah is a science major.
There is a 40% chance that Sarah is a science major.
To determine the probability that Sarah is a science major, we use the information given about the composition of the student group. There are 100 students in total, 60 of whom are math majors, and 40 are science majors.
To find the probability that Sarah is a science major, we simply take the number of science majors and divide it by the total number of students. Therefore, the probability (P) is calculated as:
P(Sarah is a science major) = Number of Science Majors / Total Number of Students = 40/100 = 0.40 or 40%.So, there is a 40% chance that Sarah is a science major.
There were 30 voters. Exactly 10% of voters chose which candidate?
Candidate A-12
Candidate B-3
Candidate C-6
Candidate D-9
Answer:
CANDIDATE B
Step-by-step explanation:
I need help asap :):):)
Answer: m + 4
Step-by-step explanation:
Expressions don't have equal signs and the values are separated by a symbol/s.
Answer:
m+4
An expression is the problem.
Ex: 2+3=5 2+3 Would be the expression here
The number of bacteria grown in a lab can be modeled by p(t)=300(2)^4t ,where t is the number of hours. Which expression is equivalent to ?
1) 300 (8)^t
2) 300 (16)^t
3) 300^t (4)^t
4) 300^2t (2)^2t
Answer:
2. 300(16)∧t
Step-by-step explanation:
p(t) = 300(2)∧4t
where b is the number of hours
2∧4t =2∧4(t) 2 x2 x2 x2 = 16∧t
p(t) = 300(2)∧4t = 300(16)∧t
Need help
Please tell me
A supermarket gives a 10% discount on the marked prices of all items during the sale. Find the following marked prices:
1)the amount of discount given and
2)the sale prices: a)$45 b)$110
Answer:
For a $45 purchase the discount would be $-4.5
the sales price $40.5
For a $110 purchase the discount is $-11
The sales price $99
Step-by-step explanation:
To find the discount on an item first multiply the original cost of the item by the percentage discounted. in this case,
$45 × 0.10 = $4.5
$110 × 0.10 =$11
$4.5 and $11 are respective discount amounts
now simply subtract the amount of the discount from the original price
$110 - $11 = $99
$45 - $4.5 = $40.5
These are your final sale prices after discount.
The selling price of a chair is N14 000. The trader gives a 25% discount for cash. What is the cash price?
Answer:N10500
Step-by-step explanation:
10%of 14000=1400
20%=1400x2=2800
5%=1400 divided by 2=700
25%=2800+700=3500
14000-3500=10500
hope this helps
A decision model that presumes an environment where problems are clearly defined, all possible action alternatives are known, and the consequences of the alternatives are clear is known as a ________ decision model.
a. behavioral.
b. classical.
c. optimizing.
d. satisficing.
Answer:
B. Classical
Step-by-step explanation:
By definition, classic decision model is where the problems are clearly defined, all possible actions and alternatives are known, and the consequences of the alternatives are clear.
what is the are of a rectangle with the height of 2x^4 and a width of x^2+8x+15?
Answer:
the length is x+5
Step-by-step explanation:
1.(x^2+8x+15)/(x+3)
2.(x+5)(x+3)(x+3)X=5
Answer:
2x^6 + 16x^5 + 30x^4
Step-by-step explanation:
You just need to multiply the two together; it's the same as any rectangle.
Central Park in New York City is rectangular with a length of 2.5 miles and a width of 0.5 during an afternoon it's population density is about 15 acre find the number of people in the park that afternoon one square mile is equal to 640 acres
Answer:
12,000 people were present
Step-by-step explanation:
In this question, we are asked to calculate the number of people in a park on an afternoon given the measurements of the park and its population density.
Firstly, we calculate the area of the park.
Mathematically the area is the product of the length and width = 0.5 * 2.5 = 1.25 square miles
Let’s convert this to acres. From the question, we know that one square mile is 640 acres, this mean that 1.25 square mile would be 1.25 * 640 = 800 acres
Now let’s consider the population density of 15 people per acre, the number of people present is thus 800 * 15 = 12,000 people
What is the value of s?
Answer:
The answer to your question is 33°
Step-by-step explanation:
Data
∠1 = 39°
∠2 = 108°
∠3 = ?
Process
To solve this problem, remember that the sum of the internal angles in a triangle equals 180°.
Then,
∠1 + ∠2 + ∠3 = 180°
-Substitution
39° + 108° + ∠3 = 180°
-Solve for ∠3
∠3 = 180 - 39 - 108
-Simplification
∠3 = 180° - 147°
-Result
∠3 = 33°Find the perimeter of the polygon.
W: 4ft
L: 7ft
How do I slove it?
If your looking to solve the perimeter, your looking for the total distance around the box. Add up the length of each of the 4 sides. The formula would be: (w x 2)+(Lx2)
(4x2)+(7x2)=
8+14=
22
perimeter is "22"
Who is the snoozer?
Davis: the snoozer was either Rawls or Charlton
Rawls: neither Vongy nor I was asleep
Charlton: both Rawls and Davis are lying
Bobbins: only one of the Rawls or Davis is telling the truth.
Vongy: Bobbins is a liar.
When the board chairperson (she was not questioned) was consulted, she said that three of the board members always tell the truth and two of them always lie. Who slept in the board meeting?
Answer:
Charlton is the snoozer!
Step-by-step explanation:
"If Charlton is telling the truth, that means that both Davis and Rawls are the liars; in particular, Vongy is telling the truth, which would mean that Bobbins is also a liar, contradicting the fact that there are only two liars and there three truth-tellers.
So Charlton is lying. That means that at most one of Davis and Rawls are lying.
If Bobbins is telling the truth, then the second liar must be one of Rawls and Davis, which would again mean that Vongy is telling the truth, making Bobbins a third liar; this is impossible, so Bobbins is lying.
So we now know that the two liars are Charlton and Bobbins, and the remaining three are truth-tellers.
Therefore, the snoozer is either Rawls or Charlton (since Davis is telling the truth), but cannot be Rawls (since Rawls is telling the truth).
So Charlton is the one who fell asleep."
Jake, Elijah, and Zaire had 65 Pokemon cards. Jake had two more cards than Elijah, and Elijah had three more cards than Zaire. How many cards did Jake have?
Answer: Jake has 24 cards
Step-by-step explanation:
Let x represent the number of Pokemon cards that Elijah has.
Jake had two more cards than Elijah. It means that the number of cards that Jake has is x + 2
Elijah had three more cards than Zaire. It means that the number of cards that Zaire has is x - 3
Jake, Elijah, and Zaire had 65 Pokemon cards. It means that
x + x + 2 + x - 3 = 65
3x - 1 = 65
3x = 65 + 1 = 66
x = 66/3 = 22
The number of cards that Jake has is
x + 2 = 22 + 2 = 24
Answer:
24
Step-by-step explanation:
Given:
Total number of cards, T = 65
Let's take number of Elijah's cards as E
Jake's cards = J
Zaires's cards= Z
So we have,
J+E+Z = 65
We are told Jake had 2 more than Elijah=
J= E+2
Elijah had 3 more than Zaire. number of Zaire's card will be=
Z= E-3
We now have:
E+2+E-3+E = 65
3E = 65+1
3E = 66
E = 66/3
E=22
Number of Elijah's card is 22
We are told Jake had 2 more cards than Elijah. Therefore number of Jake's cards will be=
E + 2
= 22 + 2 = 24
Number of Jake's cards = 24
Find the greatest common factor of 44 and 16.
Answer:
4
Step-by-step explanation:
If you prime factorization both
for 16 you get 2^4= 2^2*2^2
for 44 you get 2^2*11
they both have 2^2 so 4
Look at the attached picture⤴
Hope it will help u...
3+3
(This is just to get you points or complete challenges)
Answer:
6
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
Using 3.14 as an approximation for pi, find the diameter, circumference, and area of the circle with a radius of 5 cm. Do NOT include units in your answer. Part A Diameter Part B Centimeter Part C Area
The diameter of this circle is 10, the circumference is 31.4 and the area is 58.5.
Because the diameter of a circle is twice its radius, we have:
d = 2*r
d = 2*5 = 10
The following formula calculates the circumference of a circle:
2*pi*r = circumference
2*3.14*5 circumference
10 times 3.14 equals 31.4
The following formula calculates the area of a circle:
area = pi*r²
area = 3.14*(5)²
area = 3.14*25
area = 78.5
This circle has a diameter of 10, a circumference of 31.4, and an area of 58.5.
Complete question:
Find the diameter, circumference, and area of the circle with a radius of 5 cm.
What is the probability that you turn to page 45?
Type your answer in the format:
3/4
with no spaces.
Answer:
1/60
Step-by-step explanation:
Solve the equation
45÷x=3/4
Brainliest would be appreciated
The points scored by a basketball team in its last 5 games are shown. The mean amount of points is 83.2. The median is 72 points. Which measure of center best describes the data? Show work or explain.(5pts.)5.Armand is training for a video game competition. He wants to practice an average of 40 minutes a day. His training log for the week is below. A.How many minutes does he need to practice on Sunday to meet his goal? Show work.(10pts.)6.Show work:(5 pts.)Points Scored73707271130Monday53Tuesday24Wednesday35Thursday60Friday20Saturday65Sunday
Answer:
1. The median is a much more precise measure of the team's perfomance & it showcases the true picture of the team's average performance
2. This implies that Armand needs to train for 23 minutes on Sunday
Step-by-step explanation:
The mean (also called arithmetic mean) is the central value of a given set of data; gotten by dividing the sum of the values in the data set by the number of items in the data set.
Mathematically,
Mean (m) = ∑ [tex]\frac{x_i}{n}[/tex]
where [tex]x_{i}[/tex] = the sample
n = the number of items in the sample
The median is the central value in a distribution or given set of data after the data has been arranged sequentially either in ascending or descending degree. In simpler terms, it is regarded as the 'middle number'. The basic advantage of the median over the mean is that unlike the mean which can be skewed by outliers (extremely high or low values) in a data set, the median stays close to presenting a true value
1.
Data for the basketball team in its last 5 games = 73, 70, 72, 71, 130
Mean (m) = (73 + 70 + 72 + 71 + 130) ÷ 5
Mean (m) = 416 ÷ 5 = 83.2
Arranging the data sequentqially, we have: 70, 71, 72, 73, 130
Median ([tex]{\displaystyle a}[/tex]) = 72
The median is a much more precise measure of the team's perfomance & it showcases the true picture of the team's average performance. The mean was skewed by the result of the team's last game where the team scored 130 points (an outlier)
2.
Armand's training data (the week begins on Monday & ends on Sunday):
Monday = 53 minutes, Tuesday = 24 minutes, Wednesday = 35 minutes,
Thursday = 60 minutes, Friday = 20 minutes, Saturday = 65 minutes,
Sunday = ?
Since Armand intends to practise an average of 40 minutes for the week (7 days), we calculate thus
Mean (m) = sum of time Armand spends training ÷ number of days Armand spends training
Target Mean = 40 minutes, sum of time = 53 + 24 + 35 + 60 + 20 + 65 + x = 257 + x
where x = minutes Armand needs to practice on Sunday to meet his goal
number of days = 7
40 = (257 + x) ÷ 7
Make x the subject of the formula, we have:
257 + x = 40 * 7
x = 280 - 257 = 23
x = 23 minutes
This implies that Armand needs to train for 23 minutes on Sunday if he is to make his targeted weekly average of 40 minutes
The North Colony Trail at Royal Gorge, Colorado, is 18 miles long. Stacey has hiked four miles to a resting spot. She hikes the rest of the trail at two miles per hour. How far from the beginning of the trail is stacy six hours after leaving the resting spot?
Answer:
Stacey is 16 miles far from the beginning of the trail.
Step-by-step explanation:
Given:
Stacey's total hike journey to NCT, Colorado = 18 miles
Distance covered by her to, a resting spot = 4 miles
We have to find:
How far from the beginning of the trail is Stacey [tex]6[/tex] hours after leaving the resting spot.
According to the question.
Distance remaining = [tex](18-4) = 14[/tex] miles
Time taken = [tex]6[/tex] hours Speed maintained = [tex]2[/tex] mph
After leaving the resting spot she has covered a distance :
⇒ [tex]Distance = speed\times time[/tex]
⇒ [tex]Distance = 2\times 6[/tex]
⇒ [tex]Distance = 12[/tex] miles.
In [tex]6[/tex] hours she has covered [tex]12[/tex] miles and also she has covered [tex]4[/tex] miles before stopping here.
From the beginning she has covered :
⇒ [tex]Total\ distance =(4+12)[/tex]
⇒ [tex]Total\ distance = 16[/tex] miles.
Stacey is 16 miles far from the beginning of the trail.
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Proving the Parallelogram Diagonal Theorem
Given: ABCD is a parallelogram.
Diagonals AC, BD intersect at E.
Prove: AE CE and BE DE
Statements
✓ 1. ABCD is a parallelogram
Reasons
1. given
Correctl Assemble the next
statement.
) Intro
From the given parameters with reasons and statements, we have proven that AE = CE and BE = DE from; Properties of Parallelogram and ASA Congruence Postulate.
How to do a two - column proof?Statement 1; ABCD is a parallelogram
Reasons 1; given
Statement 2; ∠ABE and ∠CDE are alternate Interior angles
Reason 2; Definition of Alternate Interior angles
Statement 3; ∠BAE and ∠DCE are alternate Interior angles
Reason 3; Definition of Alternate Interior angles
Statement 4; AB = CD
Reason 4; Parallelogram side theorem
We want to prove that AE = CE and BE = DE
From properties of parallelogram, we can say that ∠CBD = ∠ABD and also ∠BCA = ∠DAC
Thus, it means that; ΔBEC ≅ ΔAED
Thus, from ASA Congruency postulate, we can say that;
AE ≅ CE and BE ≅ ED
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A jar contains 3 marbles marked with the numbers 1 through 3. You pick a marble at random. What is the probability of not picking the marble marked with the number 2? Enter your answer as a simplified fraction. The probability of not picking the marble marked with the number 2 is
Answer:
2/3
Step-by-step explanation:
Every 8 days the cafeteria sells pizza and every 10 days they sell banana pudding. Today they had both, how many days till they sell both again?
Answer:
40 days
Step-by-step explanation:
The next that the two lineup is forty days.
8,16,24,32,40
10,20,30,40
40 is when they meet up
Jolly Blue Giant Health Insurance (JBGHI) is concerned about rising lab test costs and would like to know what proportion of the positive lab tests for prostate cancer are actually proven correct through subsequent biopsy. JBGHI demands a sample large enough to ensure an error of ±2 percent with 90 percent confidence. What is the necessary sample size?
Answer:
Hence, the minimum required sample size (n) should be = 1692
Step-by-step explanation:
Solution:-
- The estimation error, E = 2%
- The confidence level, CI = 90 %
- Since the proportion of the positive lab tests for prostate cancer are actually proven correct through subsequent biopsy are unknown we will assume the corresponding proportion to be p = 0.58
- The required sample size is a function of confidence value and error of estimation (E):
[tex]n = p*( 1 - p ) * (\frac{Z-critical}{E})^2[/tex]
Where,
- The critical value of the confidence level = 90% would be:
significance level ( α ) = 1 - CI = 1 - 0.90 = 0.1
Z-critical = Z_α/2 = Z_0.05 = 1.645
- The required sample size (n) can be calculated:
[tex]n = 0.5*( 1 - 0.5 ) * (\frac{1.645}{0.02})^2\\\\n = 1691.265[/tex]
- Hence, the minimum required sample size (n) should be = 1692
If a pyramid has a scale factor of five applied to it what is the volume scale factor
Answer:
125
Step-by-step explanation:
The volume scale factor is the cube of the scale factor of linear dimensions:
5³ = 125
The volume scale factor is 125.
Bed & Bath, a retailing company, has two departments—Hardware and Linens. The company's most recent monthly contribution format income statement follows: Department Total Hardware Linens Sales $ 4,190,000 $ 3,110,000 $ 1,080,000 Variable expenses 1,264,000 858,000 406,000 Contribution margin 2,926,000 2,252,000 674,000 Fixed expenses 2,290,000 1,480,000 810,000 Net operating income (loss) $ 636,000 $ 772,000 $ (136,000 ) A study indicates that $373,000 of the fixed expenses being charged to Linens are sunk costs or allocated costs that will continue even if the Linens Department is dropped. In addition, the elimination of the Linens Department will result in a 15% decrease in the sales of the Hardware Department.
Answer:
By eliminating Linens department net operating income fell by $574,800.00
Step-by-step explanation:
The question requires that the monthly contribution income statement be prepared when the Linens is closed or eliminated,incorporating the unavoidable fixed costs of $373,000 as well as the fall in sales of Hardware by 15%.
Monthly Contribution Income Statement:
Sales($3,110,000)*(1-15%) $2,643,500.00
Variable expenses($858,000)*(1-15%) ($729,300.00)
Contribution margin $1,914,200.00
Fixed expenses($1,480,000+$373,000) ($1,853,000.00)
Net operating income $61,200.00
Reduction in net operating=$636,000-$61,200.00=$574,800
Alternatively:
Lost contribution from closing Linens department $674,000.00
Lost contribution from Hardware(15%*$2,252,000) $ 337,800.00
Total lost contribution $1,011,800.00
Less avoidable fixed costs($810,000-$373,000) ($437,000.00)
Reduction in profits company-wide $574,800.00
The sunk costs, allocated costs, and the impact on the Hardware Department's sales and profitability, dropping the Linens Department appears to be a financially prudent decision for Bed & Bath.
Sunk Costs and Allocated Costs:
- $373,000 of the fixed expenses allocated to the Linens Department are sunk costs or allocated costs. These costs will continue even if the Linens Department is dropped. They should not be considered in the decision-making process as they will not change with the elimination of the department.
2. Impact on Hardware Department:
- Dropping the Linens Department will result in a 15% decrease in the sales of the Hardware Department. This means that the sales of the Hardware Department will decrease by $1,110,000 (15% of $3,110,000, Linens sales). This decrease in sales will impact the contribution margin of the Hardware Department.
3. Contribution Margin Calculation:
- The contribution margin of the Hardware Department before dropping Linens is $2,252,000. With a 15% decrease in sales, the new contribution margin for the Hardware Department is $1,142,000.
4. Net Operating Income:
- The net operating income of the Hardware Department after dropping the Linens Department is calculated by subtracting the fixed expenses of the Hardware Department and the revised contribution margin from the total sales.
5. Overall Impact:
- Dropping the Linens Department will result in a positive impact on the overall net operating income of Bed & Bath. The increased net operating income from the Hardware Department ($772,000) will offset the loss from dropping the Linens Department ($136,000).
Considering the sunk costs, allocated costs, and the impact on the Hardware Department's sales and profitability, dropping the Linens Department appears to be a financially prudent decision for Bed & Bath.
What is the value of d
Answer:71.5
Step-by-step explanation:
2d+37+1+38=2d+76=180
180-76=2d+143
143divided by 2 =71.5
Answer:
d = 57 degrees.
Step-by-step explanation:
The 3 angles in a triangle add up to 180 degrees, so:
2d + 1 + 38 + 27 = 180
2d = 180 - (1 + 38 + 27)
2d = 180 - 66 = 114
d = 114/2
d = 57 degrees.