Answer: C
Step-by-step explanation:
In the quadrant IV, it is only a cos θ that is positive.
Given that tan θ = –8∕15
Where tan θ = opposite ÷ adjacent
Where opposite = 8 and adjacent = 15
We can find the hypothenus by using pythagorean theorem
Hypothenus = sqrt(15^2 + 8^2)
Hypothenus = sqrt(289)
Hypothenus = 17.
Sin θ = opposite ÷ hypothenus
Sin θ = 8/17
Since Sin θ is also negative in the fourth quadrant, therefore
Sin θ = - 8/17
Option C is correct.
The
is calculated by putting the data in
order and selecting the middle value.
The
is the data value that occurs the
most in a set of data.
The
is the difference between the
maximum and minimum values of a data set.
The
is the sum of the data divided by
the number of data values.
The answer choices are mean, median, Mode, range.
Answer:
median, mode, range, mean
Step-by-step explanation
the median is found by putting the data in order and selecting the middle value
the mode is the value that occurs the most often
the range is the difference between the greatest and least value
and the mean is the sum of all the values divided by the number of values
Answer:
The ✔ median is calculated by putting the data in order and selecting the middle value.
The ✔ mode is the data value that occurs the most in a set of data.
The ✔ range is the difference between the maximum and minimum values of a data set.
The ✔ mean is the sum of the data divided by the number of data values.
Students were asked how many pairs of shoes they owned. Their responses were 8, 2, 1, 5, 7, 6, 2, 2, 8, and 3.
The mean of the data is 4.4.
The median of the data is 4 .
The mode of the data is 2 .
The range of the data is 7 .
Step-by-step explanation:
Just took the test from E D G E N U I T Y....
hope this helps :P
PLEASE HELP!!!!!!! i will give brainliest
Yes they are independent because P(California) = 0.55 approximately and P(California | Brand B) = 0.55 approximately as well
===================================================
Explanation:
P(California) is notation that means "probability the person is from California". There are 150 people from California out of 275 total. Therefore, the probability is 150/275 = 0.5454 approximately which rounds to 0.55
Now if I told you "this person prefers brand B", then you would focus your attention solely on the brand B column. The other columns are ignored because you know they don't prefer anything else. With this narrower view, we see that 54 Californians prefer this brand out of 99 total. The probability becomes 54/99 = 0.5454 which rounds to 0.55. We get the same as before.
The notation P(California | Brand B) means "the probability they are from California given they prefer brand B". The vertical line is not the uppercase letter i or lowercase letter L. It is simply a vertical line. In probability notation that vertical line means "given".
We've shown that P(California | Brand B) = 0.55 approximately. The fact that they prefer brand B does not change the original probability. So the two events are independent. If liking brand B did change the probability, then the events would be dependent.
Formulate the recursive formula for the following geometric sequence. {-16, 4, -1,...}
Answer:
Step-by-step explanation:
Common ratio = 2nd term/1st term = 4/-16 = -1/4
[tex]a_{n}=a_{n-1}*r\\a_{n}=a_{n-1}*\frac{-1}{4}\\\\a_{n}=\frac{-1}{4}a_{n-1}[/tex]
Answer:
Common ratio = 2nd term/1st term = 4/-16 = -1/4
Step-by-step explanation:
Find the vertex of the given function. f(x) = |x + 1| - 7 The vertex is at (, )
Answer: The vertex of the function is (-1, -7).
Step-by-step explanation: We are given to find the vertex of the following function.
We know that the vertex of the function is given by (h, k).
So, for the given function f(x), the vertex will be (-1, -7).
The graph of the function f(x) is shown in the attached figure, where the vertex is at the point (-1, -7).
Thus, the vertex of the function is (-1, -7).
The vertex of the function f(x) = |x + 1| - 7 is (-1,-7)
How to determine the vertex?The function is given as:
f(x) = |x + 1| - 7
The above function is an absolute value function
An absolute value function is represented as:
f(x) = a|x – h| + k
Where, the vertex is (h,k)
So, we have:
(h,k) = (-1,-7)
Hence, the vertex of the function f(x) = |x + 1| - 7 is (-1,-7)
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(99^2-98^2)/197+(98^2-97^2)/195+(97^2-96^2)/193+ ... +(2^2-1^2)/3
plz help
Answer:
99
Step-by-step explanation:
(99^2-98^2)/197+(98^2-97^2)/195+(97^2-96^2)/193+ ... +(2^2-1^2)/3
each term can be written as:
(a²- b²)/(a+b)= (a+b)(a-b)/(a+b)= a-bso the sum will look as:
99 -98+ 98- 97 + 97- 96 + ... +2- 1= 99-1= 98(all middle terms get cancelled leaving only 99 and -1 in the equation)
Why is the median listed at 55 when none of the data points is 55?
Answer: If there is an even amount of numbers in the list, the median is the average of the two middle most numbers, once they are in least to greatest.
Step-by-step explanation:
A bird species in danger of extinction has a population that is decreasing exponentially (A = A0e^kt). Five years ago, the population was at 1400 and today only 1000 of the birds are alive. Once the population drops below 100, the situation will be irreversible. When will this happen?
Answer:
It'll take approximately 34 years from today.
Step-by-step explanation:
in order to solve this problem we first need to find the rate of change, "k", to do that we will use the given information where the population was 1400 five years ago and its now 1000. Applying this data to the equation gives us:
[tex]A = A_0*e^{k*t}\\1000 = 1400*e^{5*k}\\1400*e^{5*k} = 1000\\e^{5*k} = \frac{1000}{1400}\\ln(e^{5*k}) = ln(\frac{1000}{1400})\\5*k = ln(1000) - ln(1400) \\k = \frac{ln(1000) - ln(1400)}{5} = -0.06729[/tex]
We now know the value for "k", we can estimate how many years it will take for the bird population to dip below 100. We have:
[tex]100 = 1000*e^{-0.06729*t}\\e^{-0.06729*t} = \frac{100}{1000}\\ln(e^{-0.06729*t} = \frac{1}{10}\\-0.06729*t = ln(0.1)\\t = -\frac{ln(0.1)}{0.06729} = 34.22[/tex]
It'll take approximately 34 years from today.
Pls help summer homework :D C:
Answer:
C) None of the above
Step-by-step explanation:
Reason is V is a shorter distance and q is longer they need to be subtraction but the other way round to enable the correct subtraction we can show (q-V) which means the longer distance minus the shorter distance.
These triangles are NOT similar! Why not?
Use calculations AND words to explain.
Answer:
Similar triangles are (roughly speaking) triangles that have the same angles and the same ratio of the length of their sides
We can use ratios to show that the triangles are not similar
14:20 as a fraction is 14/20 as a decimal is 0.7
12:16 as a fraction is 12/16 as a decimal is 0.75
The side lengths are not the same proportion as shown by the different decimal, so the triangles are not similar
Use the linear combination method to solve this system of equations. What is the value of x? A. Negative 2.4 x minus 3.6 y = 1.2. 2.4 x + 1.2 y = 1.2. B. Negative 1 C. 0 D. 1
Answer:
x=1 , y = -1
Step-by-step explanation:
-2.4x-3.6y = 1.2
2.4x+1.2y = 1.2
Add the equations together
-2.4x-3.6y = 1.2
2.4x+1.2y = 1.2
---------------------------
-2.4 y = 2.4
Divide by -2.4
y = -1
Now find x
2.4x +1.2y = 1.2
2.4x +1.2(-1) = 1.2
2.4x -1.2 = 1.2
Add 1.2 to each side
2.4x -1.2+1.2 = 1.2+1.2
2.4x = 2.4
Divide by 2.4
x = 1
Answer:
x=1
Step-by-step explanation:
Marco has a sandbox that is 3 feet long, 5 feet wide, and
foot deep. How many cubic feet of sand does he need to fill the
sandbox completely?
Answer:
Choice D
Step-by-step explanation:
[tex]3\dfrac{1}{2}\cdot 5 \cdot \dfrac{1}{2}= 3.5\cdot 5\cdot 0.5=8.75 = 8\dfrac{3}{4}[/tex]
Hope this helps!
Cubic feet would be volume.
Volume = length x width x height
Volume = 3 1/2 x 5 x 1/2 = 8 3/4 cubic feet.
Use the interactive to graph a line with the given points: (–1,7) and (1,–1) The coordinates of the y-intercept of the line are.
Answer:
The y-intercept would be 6.25
Step-by-step explanation:
I found this by taking the two points and making it into a y = mx + b line.
Answer:
(0,3)
Step-by-step explanation:
We can use the slope-intercept form to find the y-intercept.
First, we need to find the slope of the line.
We are given the points (-1,7) and (1,-1).
[tex]m=\frac{rise}{run}=\frac{-1-7}{1+1}=\frac{-8}{2}=-4[/tex]
The slope is -4.
Slope-intercept is [tex]y=mx+b[/tex].
We can replace 'y' and 'x' with one of the points given, 'm' with the slope, and solve for 'b'. "B" would be the y-intercept.
I will use (-1,7):
[tex]7=-4(-1)+b\\\\7=4+b\\\\7-4=4-4+b\\\\\boxed{3=b}[/tex]
The line's equation is [tex]y=-4x+3[/tex].
Therefore, the y-intercept is '3'. The coordinates of the y-intercept is (0,3).
The number of unread emails in Bryan’s account is 100. This number grows by 15 unread emails a day. The function N(t)=100+15t represents the relation between the number of unread emails, N, and the time, t, measured in days.
Answer:
Independent variable = t
Dependent variable = N
Step-by-step explanation:
Given that the function N(t)=100+15t represents the relation between the number of unread emails, N, and the time, t, measured in days
The independent variable is an input which can be controlled. In the function
N(t)=100+15t
The independent variable is t
While the dependent variable is the output of a function when independent variable has been substituted.
In the function N(t)=100+15t
The number of unread messages depends on the number of time t measured in days as the number of unread messages N is a function of t.
Therefore, the independent variable is N.
Pete, Chris, and Dina realized that the number of A’s they each received on their report cards were in a ratio of 4:2:5. If Pete got 14 more A’s than Chris, how many A’s did Dina get?
Answer:
[tex]Dina= 35[/tex]
Step-by-step explanation:
Given
[tex]Ratio = 4:2:5[/tex]
Peter = 14 more A's than Chris
Required
How many A’s did Dina get?
The order of the ratio is Peter: Chris: Dina
This implies that
[tex]Peter: Chris: Dina = 4:2:5[/tex]
Considering Peter and Chris
[tex]Peter: Chris = 4:2[/tex]
Let the number of Chris' A's be represented by A
This implies that:
Peter's = 14 + A
And as such;
[tex]14 + A : A = 4 : 2[/tex]
Convert ratio to division
[tex]\frac{14 + A}{ A} = \frac{4}{ 2}[/tex]
Multiply both sides by A
[tex]A * \frac{14 + A}{ A} = \frac{4}{ 2}* A[/tex]
[tex]14 + A = \frac{4}{ 2}* A[/tex]
[tex]14 + A = 2* A[/tex]
[tex]14 + A = 2 A[/tex]
Subtract A from both sides
[tex]14 + A-A = 2 A-A[/tex]
[tex]14 = A[/tex]
This means that;
Chris answered 14 while Pete answered 28 (14 + 14)
Considering Chris and Dana
[tex]Chris :Dana = 2:5[/tex]
Replace Chris with 14
[tex]14:Dana = 2:5[/tex]
Convert ratio to division
[tex]\frac{14}{ Dina} = \frac{2}{5}[/tex]
Cross Multiplication
[tex]Dina * 2 = 14 * 5[/tex]
Divide both sides by 2
[tex]\frac{Dina * 2}{2} = \frac{14 * 5}{2}[/tex]
[tex]Dina= \frac{14 * 5}{2}[/tex]
[tex]Dina= \frac{70}{2}[/tex]
[tex]Dina= 35[/tex]
Hence, Dina had 35 A's
Which number completes the inequality? 1.01 less-than blank less-than 1.17, less-than 1.20 1.008 1.08 1.18 1.8
Answer:
1.08
Step-by-step explanation:
1.01 < x < 1.17
x ≠ 1.20
x ≠ 1.008
x = 1.08
x ≠ 1.18
x ≠ 1.8
The number that completes the inequality is 1.08:
1.01 < 1.08 < 1.17, < 1.20
Option C is the correct answer.
We have,
To determine which number completes the inequality, we need to find the number that is greater than 1.01 but less than both 1.17 and 1.20.
Among the given options, the number that satisfies this condition is 1.08.
Thus,
The number that completes the inequality is 1.08:
1.01 < 1.08 < 1.17, < 1.20
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Problem 1 Given: HJ=4x+9, JK=3x+3, and KH=33 Find: x, HJ, and JK x= Answer HJ= Answer JK= Answer
Answer:
Step-by-step explanation:
The triangle is an equilateral triangle
One side is A
The radius is A/2
What is the area of the center triangle?
Answer:
[tex]Orange\ area = A^2(\sqrt{3}/4 - \pi/8) = 0.0403A^2[/tex]
Step-by-step explanation:
First let's find the area of the triangle, using the formula:
[tex]Area\_triangle = side^2\sqrt{3}/4[/tex]
[tex]Area\_triangle = A^2\sqrt{3}/4[/tex]
Now, let's find the area of each circular sector of 60° (internal angle of a equilateral triangle):
[tex]Area\_sector = \pi*radius^2*60/360[/tex]
[tex]Area\_sector = \pi*(A/2)^2/6[/tex]
[tex]Area\_sector = \pi*A^2/24[/tex]
Now, To calculate the orange area in the center, we have:
[tex]Orange\ area = Area\_triangle - 3*Area\_sector[/tex]
[tex]Orange\ area = A^2\sqrt{3}/4 - \pi*A^2/8[/tex]
[tex]Orange\ area = A^2(\sqrt{3}/4 - \pi/8)[/tex]
[tex]Orange\ area = 0.0403A^2[/tex]
Karin wants to use the distributive property to mentally find the value of 19⋅42+19⋅58. Which expression can she use?
Answer:
[tex]19( 42+ 58)[/tex]
Step-by-step explanation:
[tex]19 \cdot 42+19 \cdot 58\\[/tex]
The common factor is 19
[tex]19( 42+ 58)[/tex]
Answer:
A
Step-by-step explanation:
dont know how explain.
can anyone help? soh cah toa trig question to the nearest tenth of a foot?
Answer:
About 2.7 feet
Step-by-step explanation:
The tangent of an angle is equivalent to the length of the opposite side divided by the length of the adjacent side:
[tex]\tan 44=\dfrac{x}{2.8}\\\\x=2.8 \cdot \tan 44\approx 2.7[/tex]
Hope this helps!
Answer:
x = 2.7 feet
Step-by-step explanation:
Use tan to find the value of x
tan 44 = [tex]\frac{x}{2.8}[/tex] Simplify
0.9657 = [tex]\frac{x}{2.8}[/tex] Multiply both sides by 2.8
x = 2.70396 Round this answer to the nearest tenth of a foot
x = 2.7 feet
Find the value of y.
Answer:
y = [tex]\frac{4\sqrt{3} }{3}[/tex]
Step-by-step explanation:
We are working with 30-60-90 triangles, and to solve for y we need to know the hypotenuse of the smaller triangle.
You can get that by finding the smaller value of the larger triangle.
[tex]\frac{8}{\sqrt{3} } =\frac{x}{1}[/tex]
x[tex]\sqrt{3}[/tex] = 8
x = [tex]\frac{8}{\sqrt{3} }[/tex]
x = [tex]\frac{8\sqrt{3} }{3}[/tex]
That is the hypotenuse of the smaller triangle. To find y...
[tex]\frac{(\frac{8\sqrt{3} }{3}) }{2} =\frac{y}{1}[/tex]
2y = [tex]\frac{8\sqrt{3} }{3}[/tex]
y = [tex]\frac{4\sqrt{3} }{3}[/tex]
Hope this helps!
Which system of inequalities has a solution set that is a line?
[x+y23
[x+y s3
[x+y2-3
Extysa
0
[x+y>3
(x + y <3
(x+y> -3
(x+y<3
Answer:
x + y ≥ 3
x + y ≤ 3
Step-by-step explanation:
In the picture attached, the problem is shown.
The solution to the system:
x + y ≥ 3
x + y ≤ 3
is the line x + y = 3
In order to get a solution to a system of inequalities that is a line, we need the same equation on the left (here, x + y), the same constant on the right (here, 3), and the ≥ sign in one inequality and the sign ≤ in the other one.
A car travels 3 hours at 50mph; then travels 40mph for 7 hours. How many miles does it travel during the 10 hours?
Answer: 430 miles
Step-by-step explanation:
Distance = speed x time
1) D = 50 x 3 = 150
2) D = 40 x 7 = 280
Total distance travelled = 150+280 = 430
A large jar contains 25% blue marbles. A sample contains 9 blue marbles, 15 red marbles, and 16 green marbles.
What is pˆ, the sample proportion of blue marbles?
Enter your answer, as a simplified fraction, in the box.
Answer:
Proportion of blue marbles in in sample = 9/40
Step-by-step explanation:
Total number of blue marbles in a jar is given by 25%
Lets find the probability of blue marble in the jar of the given sample:
Proportion of blue marbles in in sample = Total number of blue marbles in sample/ Total number of marbles in sample
Where
Total number of blue marbles in sample = 9
Total number of marbles in sample = 9 + 15 + 16
Total number of marbles in sample = 40
SO
Proportion of blue marbles in in sample = 9/40
or
Proportion of blue marbles in in sample = 9/40
At a company picnic, 1/2 of the people are employees. 2/5 are employees' spouses. What percent are neither?
Answer:
10% of the people at the picnic are neither.
Step-by-step explanation:
To get the answer,
1/2 + 2/5 = 9/10
10/10 - 9/10 = 1/10
1/10 = 10%
Thanks, I hope I got this right!
In how many months were there more than two days with thunderstorms?
Answer:
5
Step-by-step explanation:
March,May,June,July,August
Which statement correctly describes the graph of y = x + 7?
Answer: C
Step-by-step explanation:
The slope stays the same but the y-intercept is moved up 7 units.
Determine the vertical asymptote for the rational function f(x) = x-4 over 3x +2
Answer: (b) x = -2/3
Step-by-step explanation:
The vertical asymptote is the restriction on x.
The denominator cannot be equal to zero so that it the restriction.
Set the denominator equal to zero and solve for x to find the asymptote.
3x + 2 = 0
3x = -2
x = -2/3
The chef in a restaurant makes a large kettle of soup each day. The restaurant sells the soup in different-sized bowls.
At 7 p.m the kettle contains 20 3/8 cups of soup. A server scoops 5/8 cup from the kettle into a small bowl. How many cups of soup are left in the kettle?
Answer: 79/4
Step-by-step explanation:
The kettle contains 20 3/8 cups of soup = 163/8 cups
A server scoops 5/8 cup from the kettle
So,
163/8 - 5/8 = 158/8 = 79/4
Choose the correct conversion of 25 grams to milligrams. A. 0.025 B. 0.25 C. 250 D. 25,000
Answer:25000 because 1 m is equal to 1000mm
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In right triangle RST, ∠T is a right angle, m∠S=41∘, and ST=8. What is the measurement of RT? Enter the correct value. If necessary, round your answer to two decimal places, like this: 42.53
Answer:
RT is 6.95 units long
Step-by-step explanation:
Use tan to find the unknown measurement
tan 41 = x/8 Simplify
0.8692 = x/8 Multiply both sides by 8
6.9536 = x