Answer:
60
hope this helps
have a good day :)
Step-by-step explanation:
Answer:
60
Step-by-step explanation:
1) Find the two middle numbers: 50 and 70.
2) Take the average of both #'s to get your answer: 60.
prove that tan theta * sin theta = (1 - cos^2 theta)/(sqrt(1 - sin^2 theta))
Answer:
This identity holds as long as [tex]\displaystyle \theta \ne k\, \pi + \frac{\pi}{2}[/tex] for all integer [tex]k[/tex].
For the proof, make use of the fact that:
[tex]\displaystyle \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}[/tex] (definition of tangents,) and
[tex]\cos(\theta) = \sqrt{1 - \sin^{2}(\theta)}[/tex] (Pythagorean identity,) which is equivalent to [tex]1 - \cos^{2}(\theta) = \sin^{2}(\theta)[/tex].
Step-by-step explanation:
Assume that [tex]\displaystyle \theta \ne k\, \pi + \frac{\pi}{2}[/tex] for all integer [tex]k[/tex]. This requirement ensures that the [tex]\tan(\theta)[/tex] on the left-hand side takes a finite value. Doing so also ensures that the denominator [tex]\sqrt{1 - \sin^2(\theta)}[/tex] on the right-hand side is non-zero.
Make use of the fact that [tex]\displaystyle \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}[/tex] to rewrite the left-hand side:
[tex]\begin{aligned} & \tan(\theta) \cdot \sin(\theta) \\ =&\; \frac{\sin({\theta})}{\cos({\theta})} \cdot \sin(\theta) \\ =&\; \frac{\sin^{2}(\theta)}{\cos(\theta)}\end{aligned}[/tex].
Apply the Pythagorean identity [tex]\sin^{2}(\theta) = 1 - \cos^{2}(\theta)[/tex] and [tex]\cos(\theta) = \sqrt{1 - \sin^{2}(\theta)}[/tex] to rewrite this fraction:
[tex]\begin{aligned} & \frac{\sin^{2}(\theta)}{\cos(\theta)}\\ =\; &\frac{1 - \cos^{2}(\theta)}{\cos(\theta)}\\ =\; & \frac{1 - \cos^{2}(\theta)}{\sqrt{1 - \sin^{2}(\theta)}}\end{aligned}[/tex].
Hence, [tex]\displaystyle \tan(\theta) \cdot \sin(\theta) = \frac{1 - \cos^{2}(\theta)}{\sqrt{1 - \sin^{2}(\theta)}}[/tex].
The cost to make a path connecting all four landmarks is based on the proposal shown. The cost of path A is $29. The cost of path B is $59 The cost of path C is $32 The cost of path D is $38 Find the cost of the minimum spanning tree to connect all four landmarks?
Answer:
158
Step-by-step explanation:
The cost of the minimum spanning tree to connect all four landmarks will be $158.
What is Algebra?Algebra is the study of graphic formulas, while logic is the interpretation among those signs.
Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
The cost to make a path connecting all four landmarks is based on the proposal shown.
The cost of path A is $29.
The cost of path B is $59.
The cost of path C is $32.
The cost of path D is $38.
Then the cost of the minimum spanning tree to connect all four landmarks will be
Total cost = cost of path A + cost of path B + cost of path C + cost of path D
Total cost = $29 + $59 + $32 + $38
Simplify the expression, then we have
Total cost = $29 + $59 + $32 + $38
Total cost = $158
More about the Algebra link is given below.
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Question 6 of 10
Which expression gives the volume of a sphere with radius 7?
A 4/3pi(7^2)
B. 4/3pi (7^3)
C. 4pi(7^3)
D. 4pi(7^2)
Answer:
B. 4/3pi (7^3)
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
We know the radius is 7
V = 4/3 pi 7^3
Consider the following data. 15,−4,−10,8,14,−10,−2,−11
Step 1 of 3: Determine the mean of the given data
Step 2 of 3: Determine the median of the given data.
Step 3 of 3: Determine if the data set is unimodal, bimodal, multimodal, or has no mode. Identify the mode(s), if any exist.
Answer:
(a) The mean is 0
(b) The median is -30
(c) The mode is unimodal
Step-by-step explanation:
Given
[tex]Data: 15,-4,-10,8,14,-10,-2,-11[/tex]
Solving (a): The mean.
This is calculated using:
[tex]\bar x = \frac{\sum x}{n}[/tex]
So, we have:
[tex]\bar x =\frac{15-4-10+8+14-10-2-11}{8}[/tex]
[tex]\bar x =\frac{0}{8}[/tex]
[tex]\bar x =0[/tex]
Solving (b): The median
First, arrange the data
[tex]Sorted: -11,-10, -10, -4, -2,8,14,15[/tex]
There are 4 elements in the dataset. So, the median is the mean of the 4th and 5th item.
[tex]Median = \frac{-4-2}{2}[/tex]
[tex]Median = \frac{-6}{2}[/tex]
[tex]Median = -3[/tex]
Solving (c): The mode
The item that has occurs most is -10.
Hence, the mode is -10. The dataset is unimodal because it has only 1 mode (-10).
A colony contains 1500 bacteria. The population increases at a rate of 115% each hour. If x represents the number of hours elapsed, which function represents the scenario?
f(x) = 1500(1.15)x
f(x) = 1500(115)x
f(x) = 1500(2.15)x
f(x) = 1500(215)x
Answer:
C) f(x) = 1500(2.15)x
Step-by-step explanation:
Got it right on Edge :)
find the value of x, do not round until the final answer.
thank you!
Answer:
[tex]x\approx 5.48[/tex]
Step-by-step explanation:
Draw a line from the center of the circle O to the end of either side of the line marked as 4. This line represents two things:
A radius of the circleThe hypotenuse of a right triangle with legs 5.1 and 2In this case, both are important. Since [tex]x[/tex] is also a radius of the circle, the line must be equal to [tex]x[/tex], since all radii of a circle are equal. To find the length of this line, use the Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse of the triangle and [tex]a[/tex] and [tex]b[/tex] are the two legs of the triangle.
Since we're solving for the hypotenuse and the two legs are 5.1 and 2, we have:
[tex]5.1^2+2^2=c^2,\\26.01+4=c^2,\\c^2=30.01,\\c=5.47813836992\approx \boxed{5.48}[/tex] (round as necessary).
Juan borrowed $1500 from a credit union for 7 years and was charged simple interest at a rate of 2.97%. What is the amount of interest he paid at the end of the loan
Answer:
The amount of interest he paid at the end of the loan is $ 311.85.
Step-by-step explanation:
Given that Juan borrowed $ 1500 from a credit union for 7 years and was charged simple interest at a rate of 2.97%, to determine what is the amount of interest he paid at the end of the loan, the following calculation must be performed:
(1500 x 0.0297) x 7 = X
44.55 x 7 = X
311.85 = X
Therefore, the amount of interest he paid at the end of the loan is $ 311.85.
Wally bought a television for $987.00. The finance charge was $205 and she paid for it over 24 months. (Finance Ch arg e: #Months)(12) Amount Financed Use the formula Approximate APR to calculate her approximate APR. Round the answer to the nearest tenth.
Answer:
10.4%Step-by-step explanation:
Principal is $987.Finance charge is $205Time is 2 yearsAPR = ((Finance charge/Principal)/Time)*100% (simplified for this case)APR = ((205/987)/2)*100% = 10.4%Example 3:
In how many ways can a supermarket manager display 5 brands of cereals
in 3 spaces on a shelf?
Solution:
Answer:
10
Step-by-step explanation:
5
C
3
5!/(3!(5-3)!)
5!/(3!x2!)
120/12
10
In 10 ways can a supermarket manager display 5 brands of cereals
in 3 spaces on a shelf.
What is Combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.
Given:
Total brands of cereals= 5
Using Combination, C(n, r)
= n!/ r! (n- r)!
So, the number of ways
= C(5, 3)
= 5!/(3!(5-3)!) 5
= 5 x 4 x 3! / 3! x 2!
= 5 x 4 /2
= 10
Thus, the total number of ways is 10.
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What is 30 rounded to the nearest whole number percent?
Answer:
Thirty rounded to the nearest whole number percent is 30% (%=percent)
Step-by-step explanation:
Well, you see that if you have 30 out of one hundred then that's when all you have to do is go with the same number and just add percent or % to the end.
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Hope this Helps
This is just evidence
Which expression gives the measure of XYZ?
V
110°
w
D
42
O A. 110° - 42°
O B. 2(110° + 42°)
O c. 2(110° - 42°)
OD. 110° +420
Answer:
1/2( 110+42)
Step-by-step explanation:
Angle Formed by Two Chords= 1/2(sum of Intercepted Arcs)
<<XYZ = 1/2( 42+110)
All of the benches in a park are red or blue. The ratio of red benches to blue benches in the park is 3 : 4. Based on this information, which of the following statements is true?
A. For every 4 benches in the park, 3 are red.
B. For every 7 benches in the park, 4 are red.
C. For every 3 red benches in the park, there are 4 blue benches.
D. For every 3 red benches in the park, there are 7 blue benches.
(I'll give brainly, likes, follow, etc for anybody who answers this question with some explanation.)
Answer:
The answer is C
Step-by-step explanation:
3 : 4
^ ^
II II
red blue
one lap around a field is 4/5 of a mile .Adrian ran these laps . how far did he run?
Alex is planning to surround his pool ABCD with a single line of tiles. How many units of tile will he need to surround his pool? Round your answer to the nearest hundredth.
Answers:
8.96
10.48
13.42
20.42
Answer:19.82
Step-by-step explanation:
Got it right i did it on a test
What is the integer x
so that x/9
lies between 71/7
and 113/11 ?
Answer:
(A) 89 (B) 91 (C) 92 (D) 95 4.If |x−2| = p, where x < 2, then x+1 equals (A) −2 (B) 3− p (C) |2p−2| (D) 2p−2 5.A
Step-by-step explanation:
Following are the calculation to the find the value of x:
Given:
Please find the question.
To find:
x=?
Solution:
[tex]\frac{71}{7} <\frac{x}{9} < \frac{113}{11}\\\\10 <\frac{71}{7} < 11 \\\\10< \frac{113}{11}<11\\\\\frac{x}{9} >10\\\\x>90\\\\\text{When}\ x=91 \\\\\frac{71}{7} > \frac{91}{9}\\\\x=92\\\\ \frac{71}{7}< \frac{92}{9} <\frac{113}{11}\\\\[/tex]
so, x= 92 \\\\
by compare score value x= 92
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What is the equation of the line that passes through the point (1,7)and has a slope of -1
?
Answer:
y = -x + 8
Step-by-step explanation:
First, plug in the slope.
y = mx + b
y = -1x + b
y = -x + b
Then, plug in the point.
7 = -(1) + b
7 = -1 + b
8 = b
PLS HELP ASAP !!! WILL MARK BRAINLIEST !!
Answer:
c is equal to e
Step-by-step explanation: a
In the radius of a circle with an area of 10 inches squared is reduced by half what is the area of the new circle
Answer:
Hence when the radius is halved the area is divided by 4
2.5 inches^2
Step-by-step explanation:
Given data
Area= 10inches^2
We know that the expression for the area of a circle is given as
Area= πr^2
10= 3.142*r^2
10/3.142= r^2
r^2= 3.18
Square both sides
r= √3.18
r= 1.78 inches
Now let us half the radius and find the area of the new circle
r/2= 1.78/2
r= 0.89
Area of the new circle is
Area= 3.142*0.89^2
Area= 3.142*0.7921
Area= 2.5 inches^2
Find the equation of the least squares regression line. Show all calculations, and be sure to define any variables used.
A study of college football games shows that the number of holding penalties assessed has a mean of penalties per game and a standard deviation of penalties per game. What is the probability that, for a sample of college games to be played next week, the mean number of holding penalties will be penalties per game or less
Answer:
The probability that the mean number of holding penalties per game is of X or less is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is the mean number of penalties per game, [tex]\sigma[/tex] is the standard deviation and n is the number of games that will be sampled.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
We have that:
The mean number of penalties per game is [tex]\mu[/tex] and the standard deviation is [tex]\sigma[/tex].
Sample of n games:
This means that [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
What is the probability that, for a sample of college games to be played next week, the mean number of holding penalties will be X penalties per game or less?
The probability that the mean number of holding penalties per game is of X or less is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is the mean number of penalties per game, [tex]\sigma[/tex] is the standard deviation and n is the number of games that will be sampled.
a tv cost £800 plus VAT at 20% what is the total cost of the tv?
Answer:
Given:
Cost = £ 800
Tax = 20%
To find:
The total cost
Solution:
Total cost = Cost + Tax
Tax = 20 % of cost
20 / 100 * 800
Tax = £ 160
Hence,
Total cost = £ 800 + £ 160
Total cost = £ 960
There are 28 chocolate-covered peanuts in 1 ounce (oz). Jay bought a 62 oz. jar of chocolate-covered peanuts.
Problem:
audio
How many chocolate-covered peanuts were there in the jar that Jay bought?
Enter your answer in the box.
Answer:
1,736 chocolate cover peanuts
Step-by-step explanation:
do 28×62 hope this helps
Answer:
1736 chocolate-covered peanuts
Step-by-step explanation:
[tex]\frac{1}{62} :\frac{28}{y}[/tex]
1 · y = 62 · 28
y = 1736
A rectangular field is covered by circular sprinklers as
shown in the diagram. What percentage of the field is not
being watered by the sprinklers?
Answer:
21%
Step-by-step explanation:
Area of one sprinkler
a = πr²
a = π10²
a = 314.159 ft²
8 sprinklers
a = 8 * 314.159
a = 2,513.272
---------------------
area of field
a = lw
a = 80 * 40
a = 3200
------------------------
area not watered
a = 3200 - 2,513.272
a = 686.728
------------------
percentage not watered
p = 686.728 / 3200 * 100%
p = 21.46025%
Rounded
21%
Standard form for -3x^+ x=13
Answer:
to put the equation into standard for we must multiply the terms on the right side of the equation. To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.
Step-by-step explanation:
y
=
(
x
−
13
)
(
x
−
12
)
becomes:
y
=
(
x
×
x
)
−
(
x
×
12
)
−
(
13
×
x
)
+
(
13
×
12
)
y
=
x
2
−
12
x
−
13
x
+
156
We can now combine like terms:
y
=
x
2
+
(
−
12
−
13
)
x
+
156
y
=
x
2
+
(
−
25
)
x
+
156
y
=
x
2
−
25
x
+
156
PLEASE HELP
Libby flips a quarter 2 times in a row.
What is the probability of the quarter landing on heads at least 1 time?
A. 1/4
B. 1/3
C. 3/4
D. 1/2
HELP I WILL GIVE BRAINLYEST PLSSS HELP
Answer:
The answer is 0.5
Answer:
rhe answer is r= .50
Step-by-step explanation:
125-75=50
Five minivans and three trucks are traveling on a 3.0 mile circular track and complete a full lap in 98.0, 108.0, 113.0, 108.0, 102.0, 101.0, 85.0, and 95.0 seconds, respectively. Assuming all vehicles are traveling at constant speeds, what is the time-mean speed of the minivans
Answer:
The time-mean speed of the minivans is of 105.8 seconds.
Step-by-step explanation:
Mean of a data-set:
The mean of a data-set is the sum of all values in the data-set divided by the number of values.
Five minivans, times of: 98.0, 108.0, 113.0, 108.0, 102.0, in seconds.
Thus, the mean is:
[tex]M = \frac{98 + 108 + 113 + 108 + 102}{5} = 105.8[/tex]
The time-mean speed of the minivans is of 105.8 seconds.
Bill Dollar is playing a video game. After level one he has - 17 points. You decide to challenge Bill online and after level one you have a score that is 29 points less than Bill's score. What is your score?
Answer:
-46
Step-by-step explanation:
To find your score, take Bill's score which is -17 and if it is 29 less than, you subtract 29
So, - 17 - 29 is -46
The augmented matrix is given for a system of equations. If the system is consistent, find the general solution. Otherwise state that there is no solution.
[1 -5 -4
0 0 7]
A. X1 = - 4 + 5x2 X2 is free
B. (-4,7)
C. X1 = - 4 +5x2
X2=7
X3 is free
D. There is no solution.
Answer:
Option D (There is no solution) is the correct answer.
Step-by-step explanation:
According to the question, the matrix is:
⇒ [tex]\left[\begin{array}{ccc}1&-5&-4\\0&0&7\end{array}\right][/tex]
The linear equation will be:
⇒ [tex]x-5y=-4[/tex]
and
⇒ [tex]0.x+0.y=7[/tex]
i.e,
[tex]0=7[/tex] (Not possible)
Thus the above given matrix has no solution. So the above is the correct option.
Evaluate f(x) =
f(x) = x for x = 4.
3
Answer:
x=3
Step-by-step explanation:
