Answer:
[tex]sinx=-\dfrac{12}{13}[/tex]
[tex]cosx=-\dfrac{5}{13}[/tex]
[tex]cotx=\dfrac{5}{12}[/tex]
Step-by-step explanation:
Given that:
[tex]\dfrac{12}{5} = tan(x)[/tex]
[tex]\pi <x < 3\pi/2[/tex]
i.e. x is in 3rd quadrant. So tan is positive.
To find:
sin(x), cos(x), and cot(x).
Solution:
Given that:
[tex]\dfrac{12}{5} = tan(x)[/tex]
We know by trigonometric identities that:
[tex]tan\theta =\dfrac{Perpendicular}{Base}[/tex]
Comparing with the given values:
[tex]\theta=x[/tex]
Perpendicular = 12 units
Base = 5 units
Using pythagorean theorem, we can find out hypotenuse:
According to pythagorean theorem:
[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}[/tex]
[tex]\Rightarrow Hypotenuse=\sqrt{12^2+5^2}\\\Rightarrow Hypotenuse=\sqrt{169} = 13 units[/tex]
We can easily find out the values of:
[tex]sinx, cos x\ and\ cot x[/tex]
[tex]sin\theta =\dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]sinx =\dfrac{12}{13}[/tex]
Given that x is in 3rd quadrant, sinx will be negative.
[tex]\therefore sinx =-\dfrac{12}{13}[/tex]
[tex]sin\theta =\dfrac{Base}{Hypotenuse}[/tex]
[tex]cosx =\dfrac{5}{13}[/tex]
Given that x is in 3rd quadrant, cosx will be negative.
[tex]\therefore cosx =-\dfrac{5}{13}[/tex]
[tex]cot\theta = \dfrac{1}{tan\theta}[/tex]
Given that x is in 3rd quadrant, cotx will be positive.
[tex]cotx = \dfrac{1}{\dfrac{12}{5}} = \dfrac{5}{12}[/tex]
Which monomial is a perfect cube? I I A 1x3 B 3x3 C 6x3 D 9x3
Answer:
option D 9x³
Step-by-step explanation:
the monomial 9x³ comes from (3x)³, which gives, 3×3×3×x×x×x= 9x³
9 is 3 times 3 and x³ is 3 times x. So here, 9x³ is a perfect cube
Don’t know this one
Answer:
B
Step-by-step explanation:
The answer is B because in order for the square root of a number to be equal to another number, the answer squared should be the number under the square root.
B. [tex](-4)^2\neq -16[/tex].
Hope this helps.
how many sixths are in 4
how many two-thirds are in 2
Answer:
24 sixths in 4 and 3 two-thirds
Step-by-step explanation:
6=24 sixths in 4
Answer:
24 sixth's are in 4 and 3 two-third's are in 2
Step-by-step explanation:
4 ÷ 1/6 = 4 * 6 = 24
2 ÷ 2/3 = 2 * 3/2 = 3
An object is dropped from the top of a tower with a height of 1160 feet. Neglecting air resistance, the height of the object at time t seconds is given by the
polynomial - 16t square + 1160. Find the height of the object at t = 1 second.
The height of the object at 1 second is feet.
Answer:
Height at t = 1 sec is 1144 ft
Step-by-step explanation:
Given:
Initial height of object = 1160 feet
Height of object after t seconds is given by the polynomial:
[tex]- 16t ^2+ 1160[/tex]
Let [tex]h(t)=- 16t ^2+ 1160[/tex]
Let us analyze the given equation once.
[tex]t^2[/tex] will always be positive.
and coefficient of [tex]t^2[/tex] is [tex]-16[/tex] i.e. negative value.
It means something is subtracted from 1160 ft (i.e. the initial height).
So, height will keep on decreasing with increasing value of t.
Also, given that the object is dropped from the top of a tower.
To find:
Height of object at t = 1 sec.
OR
[tex]h (1)[/tex] = ?
Solution:
Let us put t = 1 in the given equation: [tex]h(t)=- 16t ^2+ 1160[/tex]
[tex]h(1)=- 16\times 1 ^2+ 1160\\\Rightarrow h(1) = -16 + 1160\\\Rightarrow h(1) = 1144\ ft[/tex]
So, height of object at t = 1 sec is 1144 ft.
Identify the triangle that contains an acute angle for which the sine and cosine ratios are equal. Triangle A B C has angle measures 50 degrees, 40 degrees, and 90 degrees. Triangle A B C has angle measures 45 degrees, 45 degrees, 90 degrees. The lengths of sides A C and C B are congruent. Triangle A B C has angle measures 68 degrees, 22 degrees, and 90 degrees. Triangle A B C has angle measures 60 degrees, 30 degrees, and 90 degrees.
Answer:
The sine and cosine are equal for 45 degrees.
Choose the triangle that has a 45-deg angle.
Answer:
Answer is the second choice
Step-by-step explanation:
jut did it on edge
5. In the figure below, triangles CPW and
BHM are congruent. Which statement must be true?
Answer:
C. side CW ≅ side BM,
Step-by-step explanation:
When two triangles are said to be congruent, it means they have the same shape and size. This implies that their corresponding sides and corresponding angles are equal.
Therefore, given that triangles CPW and BHM are congruent, their corresponding sides should be equal.
Thus, the statement side CW ≅ side BM, must be true.
Other statements given are not true.
find the value of x...
Answer:
x = 7
Step-by-step explanation:
This problem can be solved using angular bisector theorem.
It states that if any angle of triangle is bisected by a line , then that line
divides the opposite side of that angle in same proportion as that of two other sides which contain the angle.
__________________________________
Here one angle is is divided into parts theta
Thus,
using angular bisector theorem
14/21 = 6/3x-12
=> 14(3x-12) = 21*6
=> 3x-12 = 21*6/14 = 9
=> 3x = 12+9 = 21
=> x = 21/3 = 7
Thus, x = 7
ga political candidate has asked you to conduct a poll to determine what percentage of people support her. if the candidate only wants a 8% margin of error at a 95% cnofidence level, what size of sample is needed
Answer: 151
Step-by-step explanation:
if prior population proportion is unknown , then the formula is used to find the sample size :
[tex]n=0.25(\frac{z_{\alpha/2}}{E})^2[/tex]
, where [tex]z_{\alpha/2}[/tex] = Two tailed critical value for significance level of [tex]\alpha.[/tex]
E = Margin of error.
Given : margin of error = 8%= .08
For 95% confidence level , two tailed critical value = 1.96
Now, the required sample size :
[tex]n=0.25(\frac{1.96}{0.08})^2\\\\=0.25(24.5)^2\\\\=150.0625\approx151[/tex]
Hence, the size of the sample needed = 151.
Find the value of x.
Answer:
[tex]\huge\boxed{x=\sqrt{66}}[/tex]
Step-by-step explanation:
ΔADC and ΔABD are similar (AAA)
Therefore the cooresponging sides are in proportion:
[tex]\dfrac{AD}{AC}=\dfrac{AB}{AD}[/tex]
Substitute
[tex]AD=x;\ AC=6+5=11;\ AB=6[/tex]
[tex]\dfrac{x}{11}=\dfrac{6}{x}[/tex] cross multiply
[tex](x)(x)=(11)(6)\\\\x^2=66\to x=\sqrt{66}[/tex]
Write an equation that is 10 less than 3 times a number y, multiplied by 2 and divided by 4. (10 less than 3 times a number y is to be done first)
Answer: (3y - 10)*2÷4
Step-by-step explanation:
Because 10 less than 3 times a number, y, is done first, it is in parenthesis. The 3 is there to represent the "three times" and the -10 is there to represent the "ten less". The *2 is there to represent the "multiplied by two" and the ÷4 is there to represent the "divided by 4"
Hope it helps, and tyvm <3
Answer:
[tex]\displaystyle \frac{2(3y - 10)}{4}[/tex]
Step-by-step explanation:
10 less than 3 times y.
The variable y is multiplied by 3, 10 is subtracted from 3 × y.
The result 3y - 10 is then multiplied by 2.
2(3y - 10) is then divided by 4.
Need help withGraph a circle
Step-by-step explanation:
The equation of this circle is:
(x-3)^2 +(y+5)^2 = 16
The equatiin of a circle in general is:
(x-a)^2 +(y-b)^2 = r^2
a and b are the coordinates of the center and r is the radius
● in the given equation: (x-3)^2 + (y+5)^2 = 16
-3 and 5 are the coordinates if the center so start by ploting the center in the point (-3,5)
16 is the radius multiplied by itself
16 is 4×4 so the radius is 4
Take a four unit radius from the center and strat drawing your circle using a compass
John had $800 Tasha has $500 Kyle had $300 Who had the most money.
Answer:
Step-by-step explanation:Josh
By comparing the given numbers, Jhon had most money.
How to compare integers?As you move to the right on the number line, integers get larger in value. As you move to the left on the number line, integers get smaller in value.
The rules of the ordering and the comparing of the integers are given below:
If we compare numbers with different signs, then the negative number is less than positive.If numbers are both positive, then this is the case when we compare whole numbers.If numbers are both negative, then we compare numbers without signs. The bigger is the positive number; the smaller is its corresponding negative number.Given that, John had $800 Tasha has $500 Kyle had $300.
Here, 300<500<800
Therefore, by comparing the given numbers, Jhon had most money.
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Sam invests $6000 in two different accounts. The first account paid 12 %, the second account paid 7 % in interest. At the end of the first year he had earned $590 in interest. How much was in each account? $_____ at 12% $_____ at 7%
Answer:
The amount in the account at 12% interest is $3400 and the amount in the second account at 7% interest is $2600
Step-by-step explanation:
Let x be the amount in the account at 12% interest
So, 6000-x is the amount in the second account at 7% interest
[tex]SI = \frac{P \times T \times R}{100}[/tex]
First account:[tex]SI=\frac{x \times 1 \times 12}{100}[/tex]
Second account : [tex]SI =\frac{(6000-x) \times 1 \times 7}{100}[/tex]
We are given that At the end of the first year he had earned $590 in interest.
So, [tex]\frac{x \times 1 \times 12}{100}+\frac{(6000-x) \times 1 \times 7}{100}=590\\x=3400[/tex]
So,the amount in the account at 12% interest is $3400
The amount in the second account at 7% interest =6000-x=6000-3400=2600
Hence the amount in the account at 12% interest is $3400 and the amount in the second account at 7% interest is $2600
Find the median of: 1, 3, 4, 6, 2, 4, 5, 6, 2, 3, 1, 4, 0, 4, 4, 4, 8, 9, 7, 4
Answer:
4
Step-by-step explanation:
1, 3, 4, 6, 2, 4, 5, 6, 2, 3, 1, 4, 0, 4, 4, 4, 8, 9, 7, 4
Arrange the numbers from smallest to largest
0,1, 1,2,2, 3,3, 4, 4,4,4,4,4 , 4, 5, 6, 6, 7, 8, 9,
There are 20 numbers
The middle number is between 10 and 11
0,1, 1,2,2, 3,3, 4, 4,4 ,4,4,4 , 4, 5, 6, 6, 7, 8, 9,
The median is 4
Solution,
Arranging the data in ascending order:
0,1,1,2,2,3,3,4,4,4,4,4,4,4,5,6,6,7,8,9
N(total number of items)= 20
Now,
Median:
[tex] (\frac{n + 1}{2)} ) ^{th \: item} \\ = (\frac{20 + 1}{2} ) ^{th \: item} \\ = \frac{21}{2} \\ = 10.5 \: th \: \: item[/tex]
Again,
Median:
[tex] \frac{10 \: th \: item + 11 \: th \: item}{2} \\ = \frac{4 + 4}{2} \\ = \frac{8}{2} \\ = 4[/tex]
Last winter Armand had StartFraction 5 Over 6 EndFraction of a row of stacked logs. At the end of the winter he had StartFraction 8 Over 15 EndFraction of the same row left. How much wood did he burn over the winter?
Answer:
3/10
Step-by-step explanation:
We have that the Armans last winter had 5/6 of a row of stacked logs and at the end of the winter he had 8/15 of the same row left, therefore:
Ambitious
First we have to do is that the denominator is the same.
in the case of 5/6 it would be 25/30
and for 8/15 it would be 16/30
Now if we can do the subtraction and it would be:
25/30 - 16/30 = 9/30 or what equals 3/10
3/10 was the amount of wood he burned in the winter
Answer:
D) 3/10 row
Step-by-step explanation:
true or false? the circumcenter of a triangle is the center of the only circle that can be inscribed about it
Answer:
TRUE
Step-by-step explanation:
The circumcenter of a triangle is the center of the only circle that can be circumscribed about it
Answer:
False
Step-by-step explanation:
help please please i give bralienst don't need to explain just put the number
Answer:
487 ÷ 14
Hope that helps.
Please answer this correctly
Answer:
2/7
Step-by-step explanation:
The numbers greater than 7 or less than 3 are 2 and 8.
2 numbers out of 7.
P(greater than 7 or less than 3) = 2/7
Answer:
2/7
Step-by-step explanation:
There are a total of 7 sample spaces also known as 2,3,4,5,6,7,8. Now we have to find a number greater than 7 and less than 3. 2 is less than 3, and 8 is greater than 7, so two numbers are selected. This would become 2/7 because out of all of the 7 outcomes, only two are selected.
Suppose H is an ntimesn matrix. If the equation Hxequalsc is inconsistent for some c in set of real numbers R Superscript n, what can you say about the equation Hxequals0? Why?
Answer:
The answer is explained below
Step-by-step explanation:
Given that, the equation H*x = c is inconsistent for some c in R^n, we can say that the equation A*x = b has at least one solution for each b in R^n of IMT (Inverse Matrix Theorem) is not fulfilled.
Thanks to this we can say that by equivalence of theorem statement, the equation H*x = 0 will not have only the trivial solution. It will have non-trivial solutions too.
When exchanging US Dollars (USD) for Philippine Peso (PHP) the number of Philippine Pesos received is directly proportional to the number of US Dollars to be exchanged. If 550 USD can be converted into 24,334.75 PHP.
Find the constant of proportionality k.
k= ______ (If needed, round answer to 3 decimal places.)
Using the k from above find the amount of PHP given that you have 900 USD to convert. You will receive ________ PHP (If needed, round answer to 2 decimal places.)
Answer:
(a)k=44.245
(b)39820.50 PHP
Step-by-step explanation:
Part A
Let the number of PHP =y
Let the number of USD =x
The number of Philippine Pesos(y) received is directly proportional to the number of US Dollars(x) to be exchanged.
The equation of proportion is: y=kx
If 550 USD can be converted into 24,334.75 PHP.
x=550y=24,334.75Substitution into y=kx gives:
[tex]24,334.75=550k\\$Divide both sides by 550$\\k=24,334.75 \div 550\\k=44.245[/tex]
The constant of proportionality k=44.245
Part B
The equation connecting y and x then becomes:
y=44.245x
If x=900 USD
Then:
y=44.245 X 900
y= 39820.50
Therefore, given that you have 900 USD to convert. You will receive 39820.50 PHP
What is the length of Line segment B C?
11
23
40
60
Answer:
40
Step-by-step explanation:
An isosceles triangle is a triangle that has 2 congruent/equal sides and 2 congruent angles.
Side AB and side BC are the same length (the red tick marks shows that the sides are congruent)
Since they are the same length, you can set them equal to each other
Side AB = Side BC
x + 17 = 2x - 6 Subtract x on both sides
17 = x - 6 Add 6 on both sides
23 = x
Now that you know "x", you can find the length of Side BC:
2x - 6 Plug in 23 for "x"
2(23) - 6
46 - 6 = 40
Answer:
Yes, the answer is C! (40)
quanto e 500x6-51-5x50
Answer:
2699
Step-by-step explanation:
you do all the multiplication first
500×6= 3000
5 ×50 = 250
so it becomes
3000-51-250 = 2699
Answer:
2699
Step-by-step explanation:
Two parallel lines are crossed by a transversal.What is the value of d?
Step-by-step explanation:
if there is any confusion then again ask me always with you
Answer:
d = 125
Step-by-step explanation:
E2020
pls mark Brainliest
A daffodil grows 0.05m every day. Plot the growth of the flower if the initial length of the daffodil is 0.8m and hence give the length of the daffodil on the 8th day.
Answer:
1.2m
Step-by-step explanation:
You must first find out how much the daffodil grew over the 8 days:
0.05 x 8 = 0.4
Then you must add how much it grew to the original height:
0.4 + 0.8 = 1.2
Hope this helps you out! : )
the length of the daffodil on the 8th day is 1.2m.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
A daffodil grows 0.05m every day.
the initial length of the daffodil is 0.8m.
You must first find out how much the daffodil grew over the 8 days:
0.05 x 8 = 0.4
Then you must add how much it grew to the original height:
0.4 + 0.8 = 1.2
hence, the length of the daffodil on the 8th day is 1.2m.
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Katie is making hair clips to sell at the craft fair. To make each hair clip, she uses 1 barrette and 1 precut ribbon. The barrettes are sold in packs of 12, and the precut ribbons are sold in packs of 9. How many packs of each item does she need to buy to make the least number of hair clips with no supplies left over?
Answer:
3 packs of barrettes and 4 packs of ribbons.
Step-by-step explanation:
All we need to do here is to find the least common multiple between 12 and 9.
We can factor both of these numbers to do so.
12: 3*4: 3*2*2
9: 3*3
We can cancel out one 3 (since it appears in both prime factorizations) and multiply what we have left to find the LCM.
2*2*3*3=36
This means that she will be making 36 clips/needs 36 of each item.
36/12=3
3 packs of barretes.
36/9=4
4 packs of ribbons.
You want to be able to withdraw $4000 a month for 30 years how much would you need to have in your account with an APR of 3.4% to accomplish this goal
Answer:
$904,510.28
Step-by-step explanation:
If we assume the withdrawals are at the beginning of the month, we can use the annuity-due formula.
P = A(1 +r/n)(1 -(1 +r/n)^(-nt))/(r/n)
where r is the APR, n is the number of times interest is compounded per year (12), A is the amount withdrawn, and t is the number of years.
Filling in your values, we have ...
P = $4000(1 +.034/12)(1 -(1 +.034/12)^(-12·30))/(.034/12)
P = $904,510.28
You need to have $904,510.28 in your account when you begin withdrawals.
Answer:
You need to have $904,510.28 in your account when you begin
How many different words can be formed with the letters AAAABBCCD (not necessarily meaningful words)?
Please help me with this. Other answers did not work.
Answer:
the answer is 9! ÷ (4! * 2! * 2!)
Step-by-step explanation:
The different words that can be formed with the letters AAAABBCCD will be 3780.
What is permutation?
The permutation is a mathematical calculation of the number of ways a particular set can be arranged, where the order of the arrangement matters.
We have,
AAAABBCCD
i.e.
Total number of letters = 9
Letter A repeated = 4 times
Letter B repeated = 2 times
Letter C repeated = 2 times
Now,
Using the permutation formula,
Permutation (ⁿPr) = n! / r!
So,
Number of ways = 9! / [ 4! × 2! × 2!] = [9 × 8 × 7 × 6 × 5 × 4!] / [ 4! × 2! × 2!] = 3780
Hence we can say that the different words that can be formed with the letters AAAABBCCD will be 3780.
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What is the sqr root of x times the sqr root of x?
Answer:
Just x
Step-by-step explanation:
√x times √x equals √x²
√x² = x
Hippocrates magazine states that 32 percent of all Americans take multiple vitamins regularly. Suppose a researcher surveyed 750 people to test this claim and found that 261 did regularly take a multiple vitamin. Is this sufficient evidence to conclude that the actual percentage is different from 32% at the 5% significance level?
Select the [p-value, Decision to Reject (RHo) or Failure to Reject (FRHo)1.
a) [p-value = 0.069, FRHI
b) [p-value = 0.009, RH01
c) [p-value = 0.009, FRHol
d) [p-value = 0.019, FRH)]
e) [p-value = 0.019, RHo]
Answer:
Step-by-step explanation:
We would set up the hypothesis test.
For the null hypothesis,
p = 0.32
For the alternative hypothesis,
p ≠ 0.32
This is a two tailed test
Considering the population proportion, probability of success, p = 0.32
q = probability of failure = 1 - p
q = 1 - 0.32 = 0.68
Considering the sample,
Sample proportion, P = x/n
Where
x = number of success = 261
n = number of samples = 750
P = 261/750 = 0.35
We would determine the test statistic which is the z score
z = (P - p)/√pq/n
z = (0.35 - 0.32)/√(0.32 × 0.68)/750 = 1.8
Recall, population proportion, p = 0.32
The difference between sample proportion and population proportion(P - p) is 0.35 - 0.32 = 0.03
Since the curve is symmetrical and it is a two tailed test, the p for the left tail is 0.32 - 0.03 = 0.29
the p for the right tail is 0.32 + 0.03 = 0.35
These proportions are lower and higher than the null proportion. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area
From the normal distribution table, the area above the z score in the right tail 1 - 0.9641 = 0.0359
We would double this area to include the area in the right tail of z = 0.44 Thus
p = 0.0359 × 2 = 0.07
Since alpha, 0.05 < the p value, 0.07 then we would fail to reject the null hypothesis. Therefore, this is not sufficient evidence to conclude that the actual percentage is different from 32% at the 5% significance level.
The number of hours worked per year per person in a state is normally distributed with a standard deviation of 39. A sample of 15 people is selected at random, and the number of hours worked per year per person is given below. Calculate the 98% confidence interval for the mean hours worked per year in this state. Round your answers to the nearest integer and use ascending order.Time205120612162216721692171218021832186219521962198220522102211
Answer:
[tex]2169.67-2.624\frac{48.72}{\sqrt{15}}=2136.66[/tex]
[tex]2169.67+2.624\frac{48.72}{\sqrt{15}}=2202.68[/tex]
And the confidence interval would be given by (2137, 2203)
Step-by-step explanation:
2051 ,2061 ,2162 ,2167 , 2169 ,2171 , 2180 , 2183 , 2186 , 2195 , 2196 , 2198 , 2205 , 2210 ,2211
We can calculate the mean and deviation with these formulas:
[tex]\bar X= \sum_{i=1}^n \frac{x_i}{n}[/tex] (2)
[tex]s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}[/tex] (3)
And we got:
[tex]\bar X=2169.67[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean
s=48.72 represent the sample standard deviation
n=15 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=15-1=14[/tex]
Since the Confidence is 0.98 or 98%, the significance is [tex]\alpha=0.02[/tex] and [tex]\alpha/2 =0.01[/tex], and using excel we calculate the critical value [tex]t_{\alpha/2}=2.624[/tex]
Now we have everything in order to replace into formula (1):
[tex]2169.67-2.624\frac{48.72}{\sqrt{15}}=2136.66[/tex]
[tex]2169.67+2.624\frac{48.72}{\sqrt{15}}=2202.68[/tex]
And the confidence interval would be given by (2137, 2203)