Step-by-step explanation:
[tex] \sin( \alpha - \beta ) = \sin( \alpha ) \cos( \beta ) - \cos( \alpha ) \sin( \beta ) [/tex]
Using the Pythagorean theorem,
[tex] \cos( \alpha ) = \frac{4}{5} [/tex]
[tex] \sin( \beta ) = \frac{8}{10} [/tex]
[tex] \sin( \alpha - \beta ) = ( \frac{3}{5} )( \frac{3}{5} ) - ( \frac{4}{5} )( \frac{4}{5} )[/tex]
[tex] \frac{9}{25} - \frac{16}{25} = \frac{ - 7}{25} [/tex]
Felipe transferred a balance of $3700 to a new credit card at the beginning of
the year. The card offered an introductory APR of 5.9% for the first 4 months
and a standard APR of 17.2% thereafter. If the card compounds interest
monthly, which of these expressions represents Felipe's balance at the end of
the year? (Assume that Felipe will make no payments or new purchases
during the year, and ignore any possible late payment fees.)
OA. ($3700) (1+0 052)*(1.0172)
B.
(83700)(1+0059) (1+0.172)
OC. ($3700)(1+0 59)*(1.0172)*
0.059
12
OD. $3700)(1+0.059)*(1+0.172)
The expression that represents Felipe's balance at the end of the year is 3700 x [tex]( 1 + \frac{0.059}{4}) ^{4}[/tex] x [tex](1 + \frac{0.172}{8})^{8}[/tex].
What is the expression that represents the balance?The equation that can be used to determine future value with compounding is:
FV = P (1 + r)^nm
Where:3700 x [tex]( 1 + \frac{0.059}{4}) ^{4}[/tex] x [tex](1 + \frac{0.172}{8})^{8}[/tex].
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In how many ways can 7 persons be arranged in a line such that (a) two particular persons are never together.
Answer:
3600 ways
Step-by-step explanation:
person A has 7 places to choose from :
→ He has 2 places ,one to the extreme left of the line ,the other to the extreme right of the line
If he chose one of those two ,person B will have 5 choices and the other 5 persons will have 5! Choices.
⇒ number of arrangements = 2×5×5! = 1 200
→ But Person A also , can choose one of the 5 places in between the two extremes .
If he chose one of those 5 ,person B will have 4 choices and the other 5 persons wil have 5! Choices.
⇒ number of arrangements = 5×4×5! = 2 400
In Total they can be arranged in :
1200 + 2400 = 3600 ways
Convert the degree measure to radian measure. Round to three decimal places.
75°
radians
The conversion from degree to radian will be 180° = π radian. Then the measure of angle 75° is 1.31 radians.
What is conversion?Conversion means to convert the same thing into different units.
Convert the degree measure to the radian measure.
⇒ 75°
We know the conversion is given as
180° = π radian
1° = π/180°
Then we have
75° = 75° x π/180° radian
75° = 1.30899 radian
75° ≅ 1.31 radian
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The weight of 3 cans of juice and 2 energy bars is 33.6 ounces. Four energy bars and two cans of juice weigh 27.2 ounces. How much does one energy bar weigh?
Answer:
1.8 ounces
Step-by-step explanation:
Let :
⇒ weight of a can of juice = x
⇒ weight of an energy bar = y
=============================================================
Equations formed :
3x + 2y = 33.64y + 2x = 27.2============================================================
Multiply Equation 1 by 2 :
⇒ 2 × (3x + 2y) = 2 × 33.6
⇒ 6x + 4y = 67.2 [Equation 3]
===========================================================
Subtract : Equation 3 - Equation 2
⇒ 6x + 4y - 4y - 2x = 67.2 - 27.2
⇒ 4x = 40
⇒ x = 10
===========================================================
Finding the weight of an energy bar :
⇒ 3(10) + 2y = 33.6
⇒ 2y = 3.6
⇒ y = 1.8 ounces
The diagram shows a right angled triangle. 11cm 8cm and x degrees. Find the size of angle x. Give your answer correct to 1 decimal place.
The size of the unknown angle "x"
Solution:We'll have to check which one is appropriate from SOHCAHTOA.
In this question hypotenuse and adjacent is given so, we'll have to use cos.
[tex]\large\boxed{Formula: cos \: (A)= \frac{adj}{hyp}}[/tex]
Let's solve!
Let's substitute the values according to the formula.
[tex]cos \: x= \frac{8}{11}[/tex]
We'll have to use cos inverse.
[tex]x= {cos}^{-1}( \frac{8}{11} )[/tex]
[tex]x= 43.34175823[/tex]
Now we'll have to round off to 1 decimal place.
The value in hundredths place is less than 5 so we won't have to round up.
So, the final answer is:
[tex]\large\boxed{x= 43.3°}[/tex]
Therefore, the size of the unknown angle "x" is 43.3°
Will give 50 points for the answer to this
Answer:
( 3, -2 )
Step-by-step explanation:
3, -2 is on the line so it is a solution
the rest of the points aren't in the shaded area or on the line therefore they are not a solution
Have a great day! :)
50 pts!!! Please answer without links!
The value of 'a' in the P(X≤a)=0.6 is 5 because at X =5 we get a probability of 0.7. a = 5 is the answer.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
From the graph:
P(X ≤ 1) = 0.05
P(X ≤ 2) = 0.1
P(X ≤ 3) = 0.15
P(X ≤ 4) = 0.2
P(X ≤ 5)= 0.2
Add all the probability:
P = 0.05+0.1+0.15+0.2+0.2 = 0.7
P(X≤a)=0.6 (that means the value of the area under the curve 'a' is 0.6)
So the value of a should be 5
Thus, the value of 'a' in the P(X≤a)=0.6 is 5 because at X =5 we get a probability of 0.7. a = 5 is the answer.
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Answer:
Put 5 in the input
if the equation of a function is a rational experssion the function is a rational
The statement "If the equation of a function is a rational expression the function is a rational" is true.
What is a rational number?If the value of a numerical expression is terminating then they are the rational number then they are called the rational number and if the value of a numerical expression is non-terminating then they are called an irrational number.
If the equation of a function is a rational expression the function is a rational, the statement is true.
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Which expression represents “2 times the difference of x and 5”?
Answer:
2(x-5)
Step-by-step explanation:
Hope this helps
Answer:
2 · (x - 5)
Step-by-step explanation:
2 · (x - 5)
2 ·
"2 times"
when multiplication- or "times" is said, it can be shown in multiple ways. Multiplication can be shown as a×b , a·b , (a)(b)
(x - 5)
"difference of x and 5"
when difference is noted, the first number listed is the one written first. The difference between 2 and x is ( 2 - x ); the difference between x and 2 is ( x - 2).
PLEASE HELP ASAP!!
The table of values represents the function g(x) and the graph shows the function f(x). Which statement about the functions is true?
-all of the x-intercepts of f(x) are common to those of g(x)
-f(x) and g(x) intersect at exactly two points
-the minimum value of f(x) is less than the minimum value of g(x)
-f(x) and g(x) have the same y-intercept
Using function concepts, it is found that the correct statement is given by:
all of the x-intercepts of f(x) are common to those of g(x).
What are the x-intercepts of the functions?They are the values of x when x = 0, hence:
For g(x), it is of x = -1 and x = 1.For f(x), it is of x = -1.Hence, the first statement is correct, and the x-intercept x = -1 of f(x) is common to the x-intercept x = -1 of g(x).
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please help question attached below!
Answer:
4.97
Step-by-step explanation:
h(x) = -3x² + 5
h(0.1)
x = 0.1
h(0.1) = -3(0.1)² + 5
0.1² = 0.01
-3(0.01) + 5
-3(0.01) = -0.03
-0.03 + 5 = 4.97
If f(x) = 3x +3, which of the following is the inverse of f(x)?
O
A. f-1(x) = 3(x-3)
5
OB. f-1(x) = 3(x+3)
5
O C. f-1(x) = 5(x+3)
3
O D. f-1(x) = 5(x-3)
3
The inverse function of f(x) = 3x + 3 is f-1(x) = 1/3x - 1
How to determine the inverse?The equation is given as:
f(x) = 3x + 3
Express f(x) as y
y = 3x + 3
Swap the positions of y and x
x = 3y + 3
Make y the subject
3y = x - 3
Divide by 3
y = 1/3x - 1
Replace y with the inverse function
f-1(x) = 1/3x - 1
Hence, the inverse function of f(x) = 3x + 3 is f-1(x) = 1/3x - 1
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8 marks] In how many ways can the letters of the word "UNDERDOG" be arranged such that the first and last letters are same and no two vowels are together?
The letters of the word "UNDERDOG" can be arranged in 144 ways.
Number of ways "UNDERDOG" can be arrangedThere are only two letters that are the same which are D, then the remaining letters are 6 letters.
V, E, O are vowels
N R G
The vowels are not joined together
For N, R, G A³3
There are 4 openings A³4
Hence:
A³4· A³3=4×3×2×3×2×1
A³4· A³3=144
Therefore the letters of the word "UNDERDOG" can be arranged in 144 ways.
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A water barrel has a total volume of 1.25 cubic meters (m3). Use the fact that 1 foot is approximately equal to 0.3048 m to convert this volume to cubic feet (ft3). Round your answer to the nearest tenth. Do not type the units in the space below.
Answer:
see the attachment photo!
Please help, having trouble. Show all work if you can :) Photo is attached.
Answer:
hope it helpssssssss youj
Nathan is considering two different job offers.
He was told by both companies that he would be paid a salary that is in the center of the salaries of the current employees
on his team. The two dot plots represent the annual salaries (in thousands of dollars) of the current employees on the teams
with whom Nathan would be working.
.
10
20 30 40 50
60
70
10
20
70
30 40 50 60
Company B
Company A
mean = 40
mean = 42
median = 35
median = 40
If the mean is used to determine Nathan's salary, he should choose company
If the median is used to determine Nathan's salary, he should choose company
The center of the data for company B is more accurately described by the
because the data is
1. If the mean is used to determine Nathan's salary, he should choose Company A.
2. If the median is used to determine Nathan's salary, he should choose Company A.
3. The center of the data for Company B is more accurately described by the Median because the data is not uniformly scattered and has extreme values or outliers.
What are the Mean and Median values?The Mean is the average value obtained after adding up a set of values and dividing the result by the number in the set.
The Median represents the middle value in an ordered list from smallest to largest.
Data and Calculations:Salaries Company A Company B
Year 1 10 10
Year 2 20 20
Year 3 30 70
Year 4 40 30
Year 5 50 40
Year 6 60 50
Year 7 70 60
Total 280 280
Mean 40 40
Median 40 35 (30 + 40)/2
Thus, Nathan should choose Company A whether the Mean or the Median is used to determine Nathan's salary.
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Answer: Company B
Company A
Median
Skewed Right
Step-by-step explanation:
for 12 days, Keisha keeps track of how much water she drinks per day. her results are shown below
1 1/2quarts 2 1/4quarts 2quarts 1 1/2quarts 1 3/4 quarts 1 1/2 quarts
1 1/4quarts 2quarts 2 1/4quarts 1 1/2quarts 2 quarts 1 /2quarts
what is the amount of water that Keisha drinks during 12 days ?
what is the average amount of water that Keisha drinks per day ?
at how many days did Keshia drink at least the average amount of water?
STRETCH YOUR THINKING on day 13 Keisha drinks 1 quart of water how does that affect the average amount of water she drinks ? EXPLAIN
The total amount of water that Kiesha drinks in 12 days is 20 quarts
The average amount of water she drinks per day is 1 2/3 quarts
The number of days that Keshia drinks at least the average amount of water is 6 days
If she drinks 1 quart of day 13, the average reduces.
What is the average ?The total amount of water drank in the 12 days can be determined by adding the quarts for each day together. When they are added together, the number is 20 quarts.
Average = total amount drank / number of days 1 2/3 quarts
New average = 20 + 1 / 13 = 21 / 13 = 1 7/13 quarts
The average reduces because the quart drank on the 13th day is less than the amount of water drank on the other days.
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HELPP PLEASE!!!
Harry is 5 years older than his sister, and the product of their
ages is 84.
Let h represent Harry's age, then h- 5 represents his
sister's age, and h (h-5) = 84 models the situation.
The equation can also be written as h² - 5h = 84.
Rewrite the equation so that it is in the form polynomial = 0.
Enter the polynomial, in standard form, in the box.
= 0
Answer:
See below
Step-by-step explanation:
h^2 - 5h = 84
h^2 - 5h - 84 = 0
The functoin f has zeros at -3 and 4 witch graph could represent function f
Since I don't see the graphs:
⇒ I am going to answer by the general format of what you should see
The function has zeros at -3, 4:
⇒ which means that the function must interest the x-axis at x = -3 and
x = 4
Hope that helps!
⇒look at the image I uploaded which shows a possible answer
Use the formula Area = (side)2 to find the area of the square.
3.
2.
1.
7m
5 yd
8 cm
Answer:
1. 5² is 25 yards
2. 7² is 49m
3. 8² is 64cm
4.draw a square, make one side 6 feet then do 6² which is 36feet
5. do the same thing then write 10 inches on one side and 10² is 100 inches.
6. 7x3= 21 ft
7. 5x4= 20 in.
8. 2x8= 16 yd
Step-by-step explanation:
common sense
River drove for 2 hours on the freeway, then decreased their speed by 20 miles per hour and drove for 2 more hours on a country road. If their total trip was 168 miles, then what was their speed on the freeway?
Answer:
Step-by-step explanation:
In ΔXYZ, x = 27 cm, y = 79 cm and ∠Z=142°. Find the length of z, to the nearest centimeter.
The value of side z will be equal to 99.32 cm.
What is trigonometry?The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle are termed trigonometry.
Given that:-
In ΔXYZ, x = 27 cm, y = 79 cm and ∠Z=142°
So by applying the formula given below:-
z² = x² + y² - 2xyCos(142)
z² = 79² + 27² - 2 ( 79 x 27 x Cos142 )
z = 99.32 cm
Hence the value of side z will be equal to 99.32 cm.
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PLEASE HELP NEEDS TO BE DONE IN 10 MINUTES!!!
Answer:
QR = 15 cm
PQ = 20 cm
Step-by-step explanation:
Use the Pythagorean theorem. [tex]a^{2} +b^{2} =c^{2}[/tex]
Find QR first since you know QP are SR.
[tex]a^{2} +b^{2} =c^{2}\\12^{2} +9^{2} =c^{2}\\144+81=c^2 \\225=c^2\\\sqrt{225} = \sqrt{c^2} \\c = 15[/tex]
QR = 15 cm
Now you can find PQ. First find the length of PR by adding PS and SR together.
16 + 9 = 25
[tex]a^{2} +b^{2} =c^{2}\\a^{2} +15^{2} =25^{2}\\a^{2} +225 =625\\a^{2} +225-225 =625-225\\\a^{2} = 400\\\sqrt{a^2} =\sqrt{400} \\a = 20[/tex]
PQ = 20 cm
Lashonda rolled a number cube 500 times and got the following results.
Outcome Rolled
1
2
3
4
5
6
Number of Rolls
77
89
73
69
110
82
Answer the following. Round your answers to the nearest thousandths.
(a) From Lashonda's results, compute the experimental probability of rolling an odd number.
0
(b) Assuming that the cube is fair, compute the theoretical probability of rolling an odd number.
0
(c) Assuming that the cube is fair, choose the statement below that is true.
O The larger the number of rolls, the greater the likelihood that the experimental probability
will be close to the theoretical probability.
O The smaller the number of rolls, the greater the likelihood that the experimental
probability
will be close to the theoretical probability.
The experimental probability will never be very close to the theoretical probability, no
X
Step-by-step explanation:
if I understand this correctly, then
1 was rolled 77 times
2 89 times
3 73 times
4 69 times
5 110 times
6 82 times
remember, a probability is always desired cases over total possible cases.
a)
the experimental probability to roll an odd number (1, 3, 5) is the number of desired cases (77 + 73 + 110) over the total cases (500).
260 / 500 = 26/50 = 13/25 = 0.52
b)
if the cube would be totally equal, so that every side has truly the same probability to appear we would have for every roll 6 total possible outcomes (1 .. 6), and 3 desired outcomes (1, 3, 5).
so the theoretical probability is
3/6 = 1/2 = 0.5
c)
if the cube is truly "fair" (all sides really have the same probability to show), then the first answer is true.
the more rolls of the die, the greater the likelihood that both probabilities will get closer and closer.
that is actually a main point of probabilities : to find the most likely behavior or structure of a large number of items or objects out of the structure or behavior of a smaller sample. or out of theoretical considerations that can be tested with smaller samples.
Jax drew an angle that turns through
80 one-degree angles. Which is the
measure of the angle Jax drew?
When Jax drew an angle that turns through 80 one-degree angles, the measure of the angle will be 80°.
How to depict the angle?It should be noted that when an angle turns through a particular degree, it'll be said to have an identical degree.
In this case, when Jax drew an angle that turns through 80 one-degree angles, the measure of the angle will be 80°.
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Charles has eight different winter scarves, and he wears three at a time. How many different ways can Charles wear three scarves? 6,720 56 112 336
Answer:
Ans= 6720 ways
Step-by-step explanation:
From Combination rule from Permutation and Combination, nCr
We use 8^C3 or 8C3,
8x7x6x5x4x3x2x1
-------------------------- =6,720
3x2x1
or
8x7x6x5x4x3! /3!, here the 3! cancels each other out, and we're left with 8x7x6x5x4, which equals 6720.
For her phone service, Charmaine pays a monthly fee of $15, and she pays an additional $0.05 per minute of use. The least she has been charged in a month is
$66.90.
What are the possible numbers of minutes she has used her phone in a month?
Use m for the number of minutes, and solve your inequality for m.
Step-by-step explanation:
after subtracting the monthly fee (which she has to pay, even if she does not make a single call) we have
66.9 - 15 = $51.90
for actual phone call minutes.
1 minute is $0.05
so, in the month with the lowest charge she had used
51.9 / 0.05 = 1038 minutes for calls.
since this was the minimum, for all the numbers of minutes m she used in a month we have
m >= 1038 minutes
Hi I’m really confused and it’s a new topic
[tex]\large\boxed{Formula:\frac{sum \: of \: interior \: angles}{n}}[/tex]
n means the number of sides.
Sum of interior angles of a dodecagon is 1800°
Let's substitute the values according to the formula.
[tex]\frac{1800}{12}[/tex]
[tex]\large\boxed{ = 150°}[/tex]
Now, we can find the size of one exterior angle.
[tex]\large\boxed{Formula:\frac{360}{n}}[/tex]
n means the number of sides.
A dodecagon has 12 sides.
Let's substitute the values according to the formula.
[tex]\frac{360}{12}[/tex]
[tex]\large\boxed{ = 30°}[/tex]
Hence, the size of 1 interior angle of a dodecagon is 150° and 1 exterior angle is 30°
100 points and i will mark brainiest.
What is 131072 divided by 2 to the power of 4
Answer:
1942
Step-by-step explanation:
31072 / (2^4) = 31072
Hope This Helped
Question
What is 131072 divided by 2 to the power of 4?
Solution in steps:
131072 / 2⁴ Find 2 to the power of 4131072 / 16 Divide 131072 by the value found at previous step8192 Calculated quotientAnswer:
8192
According to a 2017 Gallup survey, the percentage of individuals in the United States who are invested in the stock market by age is as shown in the following table.†
Age Range Percent of Individuals
Invested in Stock Market
18 to 29 31
30 to 49 62
50 to 64 62
65+ 54
If 2,000 individuals 18- to 29-years-old are randomly sampled, what is the expected number of 18- to 29-year-olds who invest in the stock market in this sample? What is the standard deviation of the number of 18- to 29-year-olds who invest in the stock market? (Round your answers to two decimal places.)
E(x)=
=
Answer: 75 people
Step-by-step explanation:
1).
we have percentage of people who invested in 18-29 year category
=31%
we need
n=40 people
this is
30% of x =40
or
0.3x=40
x=40/0.3 =133.33 or 134 people
2).
in 65+ category
percentage =54%
we need
n=40
this is
54% of x =40
or
0.54x=40
or
x=40/0.54 =70.07 or 75 people