Answer:
Hello,
What is tan 30°?
[tex]tan(30^o)=\dfrac {\sqrt{3} }{3}[/tex]
Step-by-step explanation:
[tex]sin(30^o)=\dfrac{1}{2} \\\\cos(30^o)=\dfrac{\sqrt{3} }{2} \\\\\\tan(30^o)=\dfrac{sin(30^o)}{cos(30^o)} \\tan(30^o)=\dfrac{\dfrac{1}{2} } { \dfrac{\sqrt{3} }{2} }\\\\ =\dfrac {1*2}{2*\sqrt{3} }\\\\ =\dfrac {\sqrt{3} }{3}[/tex]
The value of tan 30° is 1/√3
What is tangent of an angle?The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.
In other words, it is the ratio of sine and cosine function of an acute angle such that the value of cosine function should not equal to zero.
Tan 30° = sin 30° / cos 30°
We know that, sin 30° = 1/2
cos 30° = √3/2
Therefore,
Tan 30° = 1/2 ÷ √3/2
Tan 30° = 1/2 x 2/√3
Tan 30° = 1/√3
Hence, the value of tan 30° is 1/√3
Learn more about tangent of an angle, click;
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A school sports team contains 68 students. 33 do field events, 40 do track events, 23 do swimming, 14 do both field and track events, 8 do both swimming and field events. If 15 students do field events only and 10 do both swimming and track events, how many students do a. Swimming only b. Track events only c. All three events?
Answer:
a. 9 students
b. 20 students
c. 4 students
Polygon mnopq is dialated by scale factor of 0.8 with the origin as the center dilation resulting in the image MNOPQ the coordinates of point M are (2,4) and the coordinates of point N are (3,5). The slope of MN is?
9514 1404 393
Answer:
1
Step-by-step explanation:
The slope is given by the formula ...
slope = (y2 -y1)/(x2 -x1)
slope = (5 -4)/(3 -2) = 1/1 = 1
The slope of MN is 1.
__
Dilation does not change the slope.
A^2 + 2AB +B^2
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Find the fraction equivalent to 5/7 with: a) numerator 25 b) denominator 42
Answer:
a) 25/35
b) 30/42
Step-by-step explanation:
a)
Variable x = denominator if numerator is 25
5/7 = 25/x
5 × x = 7 × 25
5x = 175
x = 35
b)
Variable y = numerator if denominator is 42
5/7 = y/42
5 × 42 = 7 × y
210 = 7y
30 = y
25/35
30/42
To get 25/35 multiply by 5
To get 30/42 multiply by 6
Given that the supply and demand function for the product type is Qd = [tex]\sqrt{260-p}[/tex],
Qs = [tex]\sqrt{p-14}[/tex]. consumer surplus ??.
WILL GIVE BRAINLIEST
Complete the equation describing how
x and y are related.
х
-3
-2
-1
0
1
2
3
y
12
8
4
0
-4
-8
-12
y = [? ]x
Answer:
[tex]y=4x[/tex]
Answer:
y = -4x
hope that helped.........
Solve the system of equations.
3x + 4y + 3z = 5
2x + 2y + 3z = 5
5x+ 6y+7z = 7
a. (x = 13, y=-6, z = -2)
b. (x = 15, y = -8, z = -4)
c. (x = 16, y = -9, z = -1)
d. (x = 14, y = -7, z = 3)
Answer:
x = 14
y = -7
z = -3
but this is none of the provided answer options !
Step-by-step explanation:
it's really easy by principle. it's just some work to do.
we try to find equations to express one variable in terms of the others.
but one thing there is : your teacher made a mistake.
the right solution is x = 14, y = -7, z = -3
your teacher made a typo at d.
but the right answer should be d.
just to give you an idea how this can be done (and also to prove that there is a mistake by the teacher):
we can directly try to transform one expression into one that describes x by y and z.
and then another to describe e.g. z by y. and then solve the third one just for y. and then we get the other 2 by these other expressions.
or we can e.g. add or subtract one equation to/from another. this is one of these cases, because we can find really simple expressions that way :
we do
5x + 6y + 7z = 7
- (3x + 4y + 3z = 5)
- (2x + 2y + 3z = 5)
---------------------------
0x + 0y + z = -3
=> z = -3
3x + 4y - 3×3 = 5
3x = -4y + 14
x = (-4y + 14)/3
2×(-4y + 14)/3 + 2y - 9 = 5
(-8y + 28)/3 + 2y = 14
-8y + 28 + 6y = 42
-2y = 14
y = -7
x = (-4×-7 + 14)/3 = (28+14)/3 = 42/3 = 14
Assume x and y are two odd numbers and x/y is an integer.
Which of the following statements are true?
I. x + y is odd
2. xy is odd.
3. x/y is odd
4. x-y is odd
Answer:
Let us check these out one at a time:
1. x + y is odd. FALSE. The sum of 2 odd numbers is even.
2. xy is odd. TRUE. The product of 2 odd numbers is odd.
3. x/y is odd. TRUE. The ratio of 2 odd numbers is odd, if the ratio is an integer.
4. x - y is odd. FALSE. The difference of 2 odd numbers is even.
Only statements 2 and 3 are TRUE, so that makes (C) the correct answer.
Sandra ride her bike 5 times as many miles as Barbara. If b, the distance Barbara rode equals 3.4 miles what is the correct expression and the distance Sandra rode
Answer:
b + 5; when b = 3.4 the distance Sandra rode is 17 miles.
Step-by-step explanation:
A line passes through the point (-3, -3) and has a slope of 1/2 What is the equation of the line?
Answer:
y= 1/2x-3/2
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = 1/2x+b
Using the point for x and y we can find b
-3 = 1/2(-3)+b
-3 = -3/2 +b
-6/2 = -3/2+b
Add 3/2 to each side
-6/2 +3/2 = b
-3/2 = b
y= 1/2x-3/2
Answer:
Step-by-step explanation:
y + 3 = 1/2(x + 3)
y + 3 = 1/2x + 3/2
y + 6/2 = 1/2x + 3/2
y = 1/2x - 3/2
If the slope of a wheelchair ramp is 1/11 then what is the angle of inclination to the nearest tenth of a degree?
Answer
4.8 degrees to the nearest tenth.
Step-by-step explanation:
The slope = rise / run = opposite side / adjacent side.
So the angle of inclination is the angle whose tangent is 1/12.
To the nearest tenth of a degree it is 4.8 degrees.
7. Ten samples of 15 parts each were taken from an ongoing process to establish a p-chart for control. a. Develop a p-Chart for 95 percent confidence (1.96 standard deviation). b. Based on the plotted data points, what comments can you make
Answer: Hello the table related to your question is attached below
answer:
a) attached below
b) The process is out of control because two ( 2 ) values from the defect rate table are out of the control limits at 95% as seen in the p-chart in question ( A )
Step-by-step explanation:
a) p-chart for 95% confidence
std = 1.96
Total defects = ∑ number of defective items in the sample = 10
number of samples = 10
sample size ( n ) = 15
The P value for the process is calculated as :
Total defects / ( number of sample * sample size )
= 10 / ( 15 * 10 ) = 10 / 150 = 0.067
standard deviation ( σ ) = [tex]\sqrt{\frac{p(1-p)}{n } } = \sqrt{\frac{0.067(1-0.067)}{15} }[/tex] = 0.065
next we determine the limits ( i.e. upper and lower )
UCL = p + zSp = 0.067 + 1.96(0.065 ) = 0.194
LCL = p - zSp = 0.067 - 1.96(0.065) = -0.060 ≈ 0 ( because LCL ≠ negative)
attached below is the required p-chart
b) The process is out of control because two ( 2 ) values from the defect rate table are out of the control limits at 95% as seen in the p-chart in question ( A )
Natalie's team needs to make a decision on how to handle a big product recall. People on the team have a lot of strong opinions. Management wants everyone to come to a consensus and to find a solution that everyone can support. What's the best way to get to a consensus? a) Everyone on the team talks until the entire team agrees on one decision. O b) Everyone on the team discusses options and then votes. O c) The team passes the decision-making responsibility to an outside person. O di The team leader makes a decision without input from the other members.
What is the length of BC in the right triangle below?
B
00
A
15
с
A. 17
B. 60
C. 17
D. 289
Using Pythagorean Theorem
[tex]\\ \sf\longmapsto H^2=P^2+B^2[/tex]
[tex]\\ \sf\longmapsto H^2=8^2+15^2[/tex]
[tex]\\ \sf\longmapsto H^2=64+225[/tex]
[tex]\\ \sf\longmapsto H^2=289[/tex]
[tex]\\ \sf\longmapsto H=\sqrt{289}[/tex]
[tex]\\ \sf\longmapsto H=17[/tex]
BC=17PLZ HELPPPPPPPPPPPPPPPPPPP
Assume a random variable representing the amount of time it takes for a customer service representative to pick up has a uniform distribution between 15 and 20 minutes. What is the probability that a randomly selected application from this distribution took less than 18 minutes
Answer:
0.6 = 60% probability that a randomly selected application from this distribution took less than 18 minutes.
Step-by-step explanation:
Uniform probability distribution:
An uniform distribution has two bounds, a and b.
The probability of finding a value of at lower than x is:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
The probability of finding a value between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
The probability of finding a value above x is:
[tex]P(X > x) = \frac{b - x}{b - a}[/tex]
Uniform distribution between 15 and 20 minutes.
This means that [tex]a = 15, b = 20[/tex]
What is the probability that a randomly selected application from this distribution took less than 18 minutes?
[tex]P(X < 18) = \frac{18 - 15}{20 - 15} = 0.6[/tex]
0.6 = 60% probability that a randomly selected application from this distribution took less than 18 minutes.
Fill in the blank with a number to make the expression a perfect square.
u^2- 18u +
Answer:
u^2- 18u +81 = (u-9)^2
Step-by-step explanation:
u^2- 18u +
Take the u coefficient
-18
Divide by 2
-18/2 = -9
Square it
(-9)^2 = 81
u^2- 18u +81 = (u-9)^2
Answer:
The blank should contain 81
Step-by-step explanation:
E = u^2 - 18u + (-18/2)^2
E = (u^2 - 18u + 9^2)
E = (u - 9)^2
To be perfectly correct what you have there is a perfect square, but you need to subtract out (9/2)^2 to make it a valid statement.
E = (u - 9)^2 - 81
divide 111001 by 1101
Based on the fact that you asked this three times and got the same answer three times, I suspect the interpretation made by the users that posted those answers was incorrect, and that you meant to ask about dividing in base 2.
We have
111001₂ = 1×2⁵ + 1×2⁴ + 1×2³ + 1×2⁰ = 57
1101₂ = 1×2³ + 1×2² + 1×2⁰ = 13
and 57/13 = (4×13 + 5)/13 = 4 + 5/13.
4 = 2² is already a power of 2, so we have
111001₂/1101₂ = 1×2² + 5/13
we just need to convert 5/13. To do this, we look for consecutive negative powers of 2 that 5/13 falls between, then expand 5/13 as the sum of the smaller power of 2 and some remainder term. For instance,
• 1/4 < 5/13 < 1/2, and
5/13 - 1/4 = (20 - 13)/52= 7/52
so that
5/13 = 1/4 + 7/52
or
5/13 = 1×2 ⁻² + 7/52
Then a partial conversion into base 2 gives us
111001₂/1101₂ = 1×2² + 1×2 ⁻² + 7/52
111001₂/1101₂ = 100.01₂ + 7/52
Continuing in this fashion, we find
• 1/8 < 7/52 < 1/4, and
7/52 = 1/8 + 1/104
==> 111001₂/1101₂ = 100.011₂ + 1/104
• 1/128 < 1/104 < 1/64, and
1/104 = 1/128 + 3/1664
==> 111001₂/1101₂ = 100.0110001₂ + 3/1664
• 1/1024 < 3/1664 < 1/512, and
3/1664 = 1/1024 + 11/13312
==> 111001₂/1101₂ = 100.0110001001₂ + 11/13312
• 1/2048 < 11/13312 < 1/1024, and
11/13312 = 1/2048 + 9/26624
==> 111001₂/1101₂ = 100.01100010011₂ + 9/26624
• 1/4096 < 9/26624 < 1/2048, and
9/26624 = 1/4096 + 5/53248
==> 111001₂/1101₂ = 100.011000100111₂ + 5/53248
and so on.
It turns out that this pattern repeats, so that
[tex]\displaystyle \frac{111001_2}{1101_2} = 100.\overline{011000100111}_2[/tex]
Which number is divisible by 5? 99 45 83 94
Answer:
45
Step-by-step explanation:
because 5•9=45 so yeah that's the answer
The distribution of sample means uses
to measure how much distance
is expected on average between a sample mean and the population mean.
re
o the standard error of M
none of these
the standard deviation of the sample
the standard deviation of the population
< Previous
Next
Answer:
A: the standard error of the mean
Step-by-step explanation:
The most frequently used measure to determine how much difference there is between population mean and sample mean is by calculating the standard deviation of the sampling distribution of the mean. This standard deviation is also referred to as the sew Station.
how many feet is 2 1/2 miles
Answer:
13200 ft
Step-by-step explanation:
1 mi = 5280 ft
5280 ft x 2.5 = 13200 ft
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Hallar el noveno término de la progresión aritmética 8, 13, 18,…
Answer:18
Step-by-step explanation:
Destiny just received two separate gifts from her great-great-grandmother.
The first gift is a box of 18 chocolate candy bars, and the second gift is a pack of 12 cookies.
Destiny wants to use all of the chocolate candy bars and cookies to make identical snack bags for her cousins.
What is the greatest number of snack bags that Destiny can make?
Answer:
Destiny will be able to create 12 identical snack bags.
Step-by-step explanation:
Given that a snack bag will be 1 chocolate candy bar, and 1 cookie, we have to subtract 1 chocolate for every cookie she has, and that will leave us with 6 chocolate bars left. The equation for this is 18 - 12 = 6.
a. 6
b. 10
c. 7
d. 9
Answer:
6
Step-by-step explanation:
21-20 = 1
20-18 =2
18 -15 = 3
15-11 = 4
We are subtracting 1 more each time
11-5 = 6
3（6x+3）=63 How to do it
Map Reading. A map is drawn so that every 3.3 inches on the map corresponds to an actual distance of 120
miles. If the actual distance between the two cities is 440 miles, how far apărt are they on the map?
The two cities are
inches apart on the map.
write 6x10x10x10x10 with an expont
Answer:
6x10^4
Step-by-step explanation:
help
What is 5 added to 3 4?
6. 12
Answer:
8.4
Step-by-step explanation:
jjdijendjndoendidnie
SAT scores are normally distributed with a mean of 1,500 and a standard deviation of 300. An administrator at a college is interested in estimating the average SAT score of first-year students. If the administrator would like to limit the margin of error of the 88% confidence interval to 15 points, how many students should the administrator sample? Make sure to give a whole number answer.
Answer:
The administrator should sample 968 students.
Step-by-step explanation:
We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.88}{2} = 0.06[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a p-value of [tex]1 - 0.06 = 0.94[/tex], so Z = 1.555.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Standard deviation of 300.
This means that [tex]n = 300[/tex]
If the administrator would like to limit the margin of error of the 88% confidence interval to 15 points, how many students should the administrator sample?
This is n for which M = 15. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]15 = 1.555\frac{300}{\sqrt{n}}[/tex]
[tex]15\sqrt{n} = 300*1.555[/tex]
Dividing both sides by 15
[tex]\sqrt{n} = 20*1.555[/tex]
[tex](\sqrt{n})^2 = (20*1.555)^2[/tex]
[tex]n = 967.2[/tex]
Rounding up:
The administrator should sample 968 students.
Please help I’m really stuck!!
Step 1: Solve for one variable
---I will be using the first equation and solving for a.
a + c = 405
a = 405 - c
Step 2: Substitute into the other equation
---Now that we have a value for a, we can substitute that value into the second equation. Then, we can solve for c.
12a + 5c = 3950
12(405 - c) + 5c = 3950
4860 - 12c + 5c = 3950
-12c + 5c = -910
-7c = -910
c = 130
Step 3: Plug back into the first equation
---We now know one variable, which means we can plug back into our first equation and solve for the other.
a = 405 - c
a = 405 - 130
a = 275
Answer: 275 adults, 130 children
Hope this helps!
