Step-by-step explanation:
cos (105) = cos( 60 + 45) = cos 60 cos 45 - sin60 sin45
= 1/2 * sqrt (2) /2 - sqrt(3)/2 * sqrt (2)/2
= sqrt (2)/4 - sqrt(6)/4
= 1/4 (sqrt(2) - sqrt (6) )
A basketball team sells tickets that cost$10,$20, $30 the team has sold 3322 tickets overall.It has sold 191 more $20 tickets than $10 tickets.The total sales are 64, 180.How many tickets of each kind have been sold
Answer:
1022 of $10 tickets, 1326 of $20 tickets, 948 of VIP $30 tickets
Answer:
$10 tickets = 1,119
$20 tickets = 1,310
$30 tickets = 893
Step-by-step explanation:
x = $10 tickets, y = $20 tickets, z = $30 tickets
10x + 20y + 30z = 64,180
x + y + z = 3,322
y = 191 + x
therefore;
10x + 20(191+x) + 30z = 64,180 eqn 1
x + (191 + x) + z = 3,322 eqn 2
make z the subject of eqn 2
z = 3,322 - x - (191 + x)
z = 3,322 - 191 - x - x
z = 3131 - 2x
put z in eqn 1
10x + 20(191+x) + 30(3131 - 2x) = 64,180
10x + 3820 + 20x + 93,930 - 60x = 64,180
10x + 20x - 60x = 64,180 - 3820 - 93,930
-30x = -33,570
x = 1,119
put x = 1,119 in z
z = 3131 - 2(1119)
z = 893
put x = 1,119 in y
y = 191 + 1119
= 1,310
10(1119) + 20(1310) + 30(893) = 64,180
1119 + 1310 + 893 = 3,322
Find the exact value of cos(5pi/6)cos(pi/12)+sin(5pi/6)sin(pi/12)
if there are 15 cubs and 4 lionesses, what is the ratio of cubs to lionesses?
Answer:
15 : 4
Step-by-step explanation:
Given that,
→ 4 lionesses
→ 15 cubs
Then the ratio of cubs to lionesses,
→ x = No. of cubs : No. of lionesses
→ [ x = 15 : 4 ]
Hence, the ratio is 15 : 4.
14. Factor 64a³-8b³. Explain all steps.
The expression 64a³ - 8b³ can be factored as 8 (8a³ - b³).
Given a cubic expression.
64a³ - 8b³
We have to factor this expression.
Factoring is the method of taking the common terms outside of an expression which contains more than one terms.
This is also a form of simplification.
Consider the expression,
64a³ - 8b³
Here 8 is a common factor of both 64a³ and 8b³.
64a³ - 8b³ = 8 (8a³ - b³)
Hence the factored form of the given expression is 64a³ - 8b³ = 8 (8a³ - b³).
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Post Falls High School in Idaho has 1160 students and is growing by 22 students per year. Richmond High School in Indiana has 1900 students and is shrinking by 15 students per year.
A number Q is at least -2 and less than 6
Answer:
Q=-8
Step-by-step explanation:
Q-2-6
Event A and B are independent. Suppose P(B) = 0.4 and P(A and B) = 0.13. Find P(A).
The required probability is 0.325 or 32.5%.
Event A and B are independent. Suppose P(B) = 0.4 and P(A and B) = 0.13.
Given: P(B) = 0.4P(A and B) = 0.13
Formula used: We know that when two events A and B are independent, then P(A and B) = P(A) × P(B)
Hence, the formula for finding P(A) can be given by:P(A) = P(A and B) / P(B)
Now, let's put the given values in the formula:P(A) = 0.13 / 0.4P(A) = 0.325
So, the probability of event A is 0.325 or 32.5% (approx).
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Hafsa has planted a total of 40 plants in her new garden. 22 of these are flowering cacti. What percentage of the plants are flowering cacti?
Answer:
55%
Step-by-step explanation:
22 ÷ 40 × 100 = 55
Hope this could help you
you have been cruising at fl 230, and you forget to set your altimeter to the local altimeter setting during your descent. if field elevation is 303 feet and the altimeter setting is 30.02, what will your altimeter indicate after landing?
The altimeter will indicate a reading of 22,697 feet.
Standard deviation is a measure of variability in a dataset. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean. This measure indicates how much variation exists in a dataset.
If you are at an altitude of Flight Level 230 (23,000 feet) and forget to set your altimeter to the local altimeter setting during descent, your altimeter will indicate different readings depending on the field elevation and the local altimeter setting.
To calculate the difference between the two, we use the standard deviation formula. Specifically, we calculate the difference between the local altimeter setting and the field elevation, and subtract that difference from the Flight Level. The standard deviation formula then looks like this:
Flight Level - (Local Altimeter Setting - Field Elevation)
In our example, the equation would look like this:
23,000 - (30.02 - 303) = 22,697
It is important to note that when making such calculations, the Flight Level should always be expressed in feet, rather than in thousands of feet.
By using the standard deviation formula and keeping track of settings like local altimeter setting and field elevation, pilots can ensure that their altimeter readings are accurate and that their aircraft will land safely
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F(x)=2(x-3)^2-1 I NEED HELP
Answer:
2x^2 −12x+17
Step-by-step explanation:
i think i did that right?
show work by factoring completely
30x^3 + 22x^2 + 4x
Given:
The expression is
\(30x^3+22x^2+4\)
To find:
Factorized form of given expression.
Solution:
We have,
\(30x^3+22x^2+4\)
\(=2x(15x^2+11x+2)\)
Splitting the middle term, we get
\(=2x(15x^2+6x+5x+2)\)
\(=2x(3x(5x+2)+1(5x+2))\)
\(=2x(3x+1)(5x+2)\)
Therefore, the complete factorized form of given expression is \(2x(3x+1)(5x+2)\).
Simplify
1-(cos^2)theta/(sin^2 )theta
A. 1
B. sin^2 theta
C. cos^2 theta
D. tan^2 theta
How many pencils did kyle purchase?
Answer:
he purchased 12 pencils
Step-by-step explanation:
1.24x12=14.88
14.88-20= 5.12
also this kid i knew has the same pfp
A power failure on the bridge of a Great Lakes freighter has resulted in the ship's navigator having to do her own calculations. She measures the angle between the ship's course and a lighthouse on shore as 32°. After the ship has travelled 1500 m, she measures the angle to be 72°. Determine if the ship was closer to or farther from the lighthouse at the second sighting, and by what distance. (4 marks)
It is impossible to measure the length of a particular swamp directly. Kendra put a stake in the ground and measured from the stake to opposite ends of the swamp, the results being 410 m and 805 m. She measured the angle between the distances to be 57°. What is the length of the swamp? (4 marks)
Answer:
1) The ship is closer
2) 675.73 m
Step-by-step explanation:
1) The given parameters are;
The initial angle between the ship's course and the lighthouse = 32°
The final angle between the ship's course and the lighthouse = 72°
The distance traveled by the sip between he two positions = 1500 m
Therefore we have a triangle formed between the distance covered by the ship and the two distances of the ship from the lighthouse, a and b
Where;
a = The initial distance fro the lighthouse
b = The final distance fro the lighthouse
The angles of the triangle are
32°, (180 - 72) = 108° and 180 - 32 - 108 = 40°
By sine rule we have;
1500/(sin(40)) = a/(sin(108)) = b/(sin(32)) =
Therefore, a = sin(108°) × 1500/(sin(40°)) = 2219.37 m
b = (sin(32°)) × 1500/(sin(40°)) = 1236.61 m
Therefore, a > b
The initial distance fro the lighthouse > The final distance fro the lighthouse, which shows that the ship is closer
2) By cosine rule we have
a² = b² + c² - 2× b×c×cos(A)
Where the given measurements by Kendra are;
410 m and 805 m with an included (in between) angle of 57°, we have;
Let b = 410 m, c = 805 m, and A = 57°, we have;
a² = 410^2 + 805^2 - 2× 410×805×cos(57 degrees) = 456608.77 m²
a = The length of the stream = 675.73 m.
4•(2+5)^2 -5^2 how do I solve this?
Answer:
4•(2+5)^2 -5^2 = 171
Step-by-step explanation:
Do BIDMAS
(brackets, indices, division, multipy, add, sub)
so brackets
4*7^2-5^2
then do the indices
4*49-25
then the multiply
196-25
= 171
Hope this helps
Answer: Brackets => 4 x (7)^2 - 5^2
Indices/Orders => 4 x 49 - 25
Multiplication => 196 - 25
Subtraction => 171
Which of these statements best describes the relation shown?
a relation that is not a function
a function that is one-to-many
a function that is one-to-one
a function that is many-to-one
Answer:
a
Step-by-step explanation:
A function that is many-to-one because for different inputs we are getting the same output option (D) is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that:
A table represents the value of input and output.
As we can see for the value of x = -5
The value of y is 10
For the value of x = 5
The value of y is the same as 10
Which shows the many-to-one mapping.
And many to one represents the relationship as a function.
Thus, a function that is many-to-one because for different inputs we are getting the same output.
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Two cars travel at the same speed to different destinations. Car A reaches its destination in 12 minutes. Car B reaches its destination in 18 minutes. Car B travels 4 miles farther than Car A. How fast do the cars travel? Write your answer as a fraction in simplest form.
Answer:
chatGPT
Step-by-step explanation:
Let's denote the speed of each car as v, and the distance that Car A travels as d. Then we can set up two equations based on the information given:
d = v * (12/60) (since Car A reaches its destination in 12 minutes)
d + 4 = v * (18/60) (since Car B travels 4 miles farther than Car A and reaches its destination in 18 minutes)
Simplifying the equations by multiplying both sides by 60 (to convert the minutes to hours) and canceling out v, we get:
12v = 60d
18v = 60d + 240
Subtracting the first equation from the second, we get:
6v = 240
Therefore:
v = 240/6 = 40
So the cars travel at a speed of 40 miles per hour.
Directions: Find the inverse of each number.
Additive
-2 =
18 =
-30 =
2/5 =
Multiplicative
8/9 =
12/15 =
-6 =
10 =
Answer:
Additive
-2 = 2
18 = -18
-30 = 30
2/5 = -2/5
Multiplicative
8/9 = 9/8
12/15 = 15/12
-6 = -1/6
10 = 1/10
Step-by-step explanation:
an additive inverse is a number you must add to another number to get 0
(think of it as the negative version of the number)
{but WHY? In math, you can imagine comparing numbers on a number line. If we are finding the opposite of a number, we want to find the same distance from 0, but on the opposite side of 0. So, 2 would be two to the right of 0, -2 would be two to the left of 0}
-2 + 2 = 0
18 - 18 = 0
-30 + 30 = 0
2/5 - 2/5 = 0
a multiplicative inverse is a number that you multiply by another number to get 1.
We are finding the "reciprocal" of a number; you are essentially flipping it as a fraction
(reciprocal of 2 = 1/2 {remember, 2 is the same thing as 2/1 } ; reciprocal of 1 / 8 = 8)
note: reciprocal is being used interchangeably with multiplicative inverse here
8/9 · 9/8 = 1
12/15 · 15/12 = 1
-6 · -1/6 = 1 {-6 = -6/1}
10 · 1/10 = 1 {10 = 10/1}
hope this helps!! have a lovely day :)
Answer:
Additive: number that you add to get 0
2
-18
30
-2/5
Multiplicative: number that you multiply to get 1
9/8
15/12
-1/6
1/10
hope this is helpful!! ^u^
Which is the most accurate estimate of 27% of 39?
A. 1/3 x 40
B. 1/2 x 40
C. 1/4 x 40
D. 2/3 x 40
Answer:
A
Step-by-step explanation:
You Welcome
How do I work this out ?
Answer:
protractor
Step-by-step explanation:
use a protractor or an online protractor
Which equation represents linear functions
Answer:
I know that A is one of the answers.
Mr jones pays $423.22 for his car payment and $98.30 for his car insurance every month how much is mr jones paying per month for his automotive bills
The total payment done by Mr. Jones every month as he pays $423.22 for car payment and $98.30 for car insurance every month is equal to $ 521.52.
As given,
Payment done for car every month = $423.22
Payment done for car insurance = $98.30
Total payment done by Mr. Jones every month = $ (423.22 + 98.30)
= $521.52
Therefore, the total payment done by Mr. Jones every month as he pays $423.22 for car payments and $98.30 for car insurance every month is equal to $ 521.52.
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The total cost of a pair of pants and a jacket was $59.01. If the price of the pair of pants was $1.49 less than the jacket, what was the price of the pair of pants? Express your answer as a simplified fraction or a decimal rounded to two places.
Answer:
The answer is 788
Answer:
28.52?
Step-by-step explanation:
3x+1 = 5x-9. what is the value of x?
Answer:
X equals 5
Step-by-step explanation:
3x+1=5x-9
3(5)+1=5(5)-9
15+1=25-9
16=16
4z + 5 = -3z - 8
Z =
Answer:
\(z = - \frac{13}{7} \)
Step-by-step explanation:
1) Add 3z to both sides.
\(4 z+ 5 + 3z = - 8\)
2) Simplify 4z + 4 + 3z to 7z + 5.
\(7z + 5 = - 8\)
3) Subtract 5 from both sides.
\(7z = - 8 - 5\)
4) Simplify -8-5 to -13.
\(7z = - 13\)
5) Divide both sides by 7.
\(z = - \frac{13}{7} \)
Therefore, the answer is z = - 13/7.
tamie uses 2/3 of a cup of water with 1/6 of a pound of flour to make a paste for a sculpture she is creating how many cups of water does she need to mix 1 pound of flower to create the same paste
Answer: 12/18
Step-by-step explanation:
For a quick explanation, all you need to do is multiply 1/6 by 6 to get 1 whole and do the same to 2/3 so it’s proportional again.
The number of cups of water she needs to mix is 4.
Given that,
Tamie uses two-third of a cup of water with one-sixth of a pound of flour to make a paste for a sculpture.
Based on the above information, the calculation is as follows:
\(= \frac{2}{3} \div \frac{1}{6} \\\\= \frac{2\times 6}{3\times 1 }\)
= 4
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you may have found the limit from one side instead of from both sides as notated. how might you consider the limit as x approaches a from both sides?
LHL is equal to RHL then limit exist
LHL is not equal to RHL then limit does not exist.
As per the given data the graph of the function is given
Here we have to determine the limit at the indicated value of a, if it was exists.
You may have found the limit from one side instead of from both sides as notated.
Now we have to find:
\($\lim _{x \rightarrow a} f(x)$\) when a = 1
We find the left hand side limit and the right hand side limit at a = 1
So,
The Left hand limit is \($\lim _{\mathrm{x} \rightarrow 1^{-}} \mathrm{f}(\mathrm{x})=\frac{3}{2}$\)
The Right hand limit is \($\lim _{x \rightarrow 1^{+}}\) f(x) = 3
Here \($\lim _{x \rightarrow 1^{-}} f(x) \neq \lim _{x \rightarrow 1^{+}} f(x)$\)
Hence \($\lim _{x \rightarrow a}\) f(x) = DNE
From the graph we find the left hand limit and the right hand limit:
If Left hand limit = Right hand limit then limit exist
If then Left hand limit ≠ Right hand limit then limit does not exist.
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Use the graph of the given function f to determine the limit at the indicated value of a, if it exists.(If an answer does not exist, enter DNE.)
Graph attached at the end of solution
you may have found the limit from one side instead of from both sides as notated. how might you consider the limit as x approaches a from both sides?
which is not true for the mean of the sampling distribution?it depends on the sample size.it is the same as the population parameter.it is the mean of the statistic for all of the samples in the distribution.none of these answers.
The correct option is option (b) . The statement that mean of the sampling distribution is same as the population parameters is not true .
Sampling Distribution:
A statistical sampling distribution is a type of probability distribution constructed by drawing a large number of random samples of a specified size from the same population. These distributions are useful for understanding how sample statistics vary from sample to sample. Mean of sampling distribution:
The distribution of the values of the sample mean (x- bar) in replicate samples is called the x -bar sampling distribution.
Central Limit Theorem :
For populations with finite mean μ and finite nonzero variance σₓ, the sampling distribution of the mean approaches a normal distribution with mean μ and variance σₓ/N, and for large N (sample size) become.
The theorem tells us that mean of samplingdistribution is depends on sample size
X -bar , mean of measurements for a sample of size n. The distribution of the X bar is its sampling distribution, see distribution of the mean µ X- bar = µ ( means of samples in distribution )Hence, the correct option is option (c) which gives the false or not true statement about mean of sampling distribution.
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when the values in the independent variable and the values in the dependent variable move together in a pattern or are correlated there is a demonstration of .
There is evidence of association when the values of the independent variable as well as the values of the dependent variable follow a pattern or are connected.
Form, direction, strength, & outliers can all be used to define a connection between two numerical variables. A positive connection is considered to exist when one variable rises as the other rises.
An independent variable is precisely just what sounds like. It is a stand-alone variable that is unaffected by the other factors you are attempting to assess. Age, for instance, could be an independent factor.
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Brian buys a computer for £2100.
It depreciates at a rate of 1% per year.
How much will it be worth in 6 years?
Give your answer to the nearest penny where appropriate.
Answer:
it will be 1974
Step-by-step explanation:
2100*6/100
=126
Answer:
1997.08 pounds at the beginning of 6 years.
Step-by-step explanation:
If you start at 2100 pounds, and it depreciates by .01 every year, you would start by doing this. It wouldn't just be subtracting 21 each year because the value depreciates and 1% would come off the new depreciated value each year.
1st year - 2100*.01 = 21
2100-21 = 2079
2nd year - 2079*.01 = 20.79
2079 - 20.79 = 2058.21
3rd year - 2058.21*.01 = 20.58
2058.21-20.58 = 2037.63
4th year - 2037.63*.01 = 20.38
2037.63-20.38 = 2017.25
5th year - 2017.25*.01 = 20.17
2017.25 - 20.17 = 1997.08
6th year - at the beginning of the 6th year, it would be worth 1997.08.
At the end of the 6th year, it would be: 1997.08*.01 = 19.97. 1997.08-19.97 = 1977.11