Answer:
Step-by-step explanation:
4+6+10+10+15+17+19=81
Then you divide 81 by the numbers of the numbers given. Which is 7 numbers so it will be 81/7 which is 11.57 then you approximate it to 11.
find the mean of first five prime
numbers
Answer:
5.6
Step-by-step explanation:
(2+3+5+7+11)/5
=5.6
please someone help me to prove this...
Step-by-step explanation:
cos 20° cos 40° cos 60° cos 80°
Simplify cos 60° to ½.
½ cos 20° cos 40° cos 80°
We can use double angle formula, sin(2θ) = 2 sin θ cos θ. Multiply and divide by 2 sin 20°.
½ (2 sin 20° cos 20° cos 40° cos 80°) / (2 sin 20°)
½ (sin 40° cos 40° cos 80°) / (2 sin 20°)
Multiply and divide by 2 and use double angle formula again.
½ (2 sin 40° cos 40° cos 80°) / (4 sin 20°)
½ (sin 80° cos 80°) / (4 sin 20°)
Multiply and divide by 2 and use double angle formula again.
½ (2 sin 80° cos 80°) / (8 sin 20°)
½ (sin 160°) / (8 sin 20°)
Use phase shift identity sin θ = sin(180−θ).
½ (sin 20°) / (8 sin 20°)
1/16
In this case we have the equation cos(20°)(cos(40°)(cos(60°)(cos(80°) = 1 / 16, and are asked to prove that this equation is true. Let's start by using the property 'cos(s)cos(t) = cos(s + t) + cos(s - t) / 2.' Taking the bit 'cos(20°)(cos(40°)' we know that s should = 20°, and t should = 40°.
[tex]\mathrm{Using\:the\:following\:identity}:\quad \cos \left(s\right)\cos \left(t\right)=\frac{\cos \left(s+t\right)+\cos \left(s-t\right)}{2},[/tex]
[tex]\cos \left(20^{\circ \:}\right)\cos \left(40^{\circ \:}\right)=\frac{\cos \left(20^{\circ \:}+40^{\circ \:}\right)+\cos \left(20^{\circ \:}-40^{\circ \:}\right)}{2}\\[/tex]
[tex]\mathrm{Substituting\:the\:value\:back}:\frac{\cos \left(20^{\circ \:}+40^{\circ \:}\right)+\cos \left(20^{\circ \:}-40^{\circ \:}\right)}{2}\cos \left(60^{\circ \:}\right)\cos \left(80^{\circ \:}\right)[/tex]
[tex]\mathrm{Multiply\:fractions}:\quad \frac{\cos \left(60^{\circ \:}\right)\cos \left(80^{\circ \:}\right)\left(\cos \left(60^{\circ \:}\right)+\cos \left(-20^{\circ \:}\right)\right)}{2}[/tex]
This expression is indeed not simplified, but remember that we can use the identities 'cos(- 20°) = cos(20°)' and 'cos(60°) = 1 / 2.' Let's substitute one step and a time.
[tex]\cos \left(-20^{\circ \:}\right)=\cos \left(20^{\circ \:}\right): \frac{\cos \left(60^{\circ \:}\right)\cos \left(80^{\circ \:}\right)\left(\cos \left(60^{\circ \:}\right)+\cos \left(20^{\circ \:}\right)\right)}{2}[/tex]
[tex]\cos \left(60^{\circ \:}\right)=\frac{1}{2}:\frac{\frac{1}{2}\cos \left(80^{\circ \:}\right)\left(\frac{1}{2}+\cos \left(20^{\circ \:}\right)\right)}{2}[/tex]
[tex]\frac{\frac{1}{2}\cos \left(80^{\circ \:}\right)\left(\frac{1}{2}+\cos \left(20^{\circ \:}\right)\right)}{2} = \frac{\cos \left(80^{\circ \:}\right)\left(1+2\cos \left(20^{\circ \:}\right)\right)}{8}[/tex]
Now that we have this 'simplified expression,' if we take the numerator as a whole in decimal form, it will = 0.5. Respectively 0.5 / 8 = 1 / 2 / 8 = 1 / 16. Hence our equation is true.
[tex]\cos \left(80^{\circ \:\:}\right)\left(1+2\cos \left(20^{\circ \:\:}\right)\right) = 0.5,\\0.5 / 8 = (1 / 2) / 8 = 1 / 16[/tex]
The volume, in cubic feet, of a right cylindrical silo of height and radius is [tex]V = \pi r^2h[/tex] The height of the silo is h(r) = 3.5r. Which statements are true regarding the functions described?
A. To get a volume of 100 cubic feet, the radius must be 2 feet.
B. The domain of [tex]V(h(r))[/tex] is restricted to values of r greater than 0.
C. The output of V is the input of h
D. [tex]V(h(r)) = 3.5\pi r^3[/tex]
E. The volume depends on the radius of the cylinder
1. The domain of [tex]V (h(r))[/tex] is restricted to values of r greater than 0.
2. [tex]V(h(r)) = 3.5\pi r^3[/tex]
3. The volume depends on the radius of the cylinder
ray BD bisects ∠ABC m∠ABD if m∠ABC = 5/2 y and m∠DBC = (y+5)degrees
Step-by-step explanation:
BD bisects ∠ABC. Therefore:
m∠DBC = ½ m∠ABC
y + 5 = ½ (5/2 y)
y + 5 = 5/4 y
4y + 20 = 5y
y = 20
Therefore, m∠ABC = 50°, and m∠ABD = 25°.
Consider the line 9x - 5y = 2
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
Answer:
5y=9x-2
y=mx-b
m=slope
y=9/5x-2/5
m=9/5=1.8 slope of pArallel
slope of pARALLEL=-1/M SLOPE OF A LINE PERPENDICULAR
m=-5/9 slope of a line perpendiculr
PLEASE HELP ME ASP!!!!!!
Answer:
B
Step-by-step explanation:
First, note that the figure is a parallelogram.
The area of a parallelogram is given by:
[tex]A=bh[/tex]
Where b is the base length and h is the vertical height.
The base length is 5+2 or 7, and the vertical height is 2.
Thus:
[tex]A=7(2)\\A=14\text{ in}^2[/tex]
The answer is B.
What part of the expression is a factor? 12+5(-3n-8)
Answer:
5
Step-by-step explanation:
A factor is a number or an expression that is multiplying something.
5 is multiplying -3n + 8.
Answer: 5 is a factor.
What is another name for line P?
Answer:
Line CD
Step-by-step explanation:
The another name for line P is line [tex]\over (CD)[/tex].
It is required to find the another name for line P.
What is line?A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions. A line is made of a set of points which is extended in opposite directions infinitely. It is determined by two points in a two-dimensional plane. The two points which lie on the same line are said to be collinear points.
Given:
To answer this type of problem we have to know the axiom.
At least two points define a line.
Then I can call line p as (see below attached picture)
The line p cuts the 2 different points , point C and point D, so we can.t indicate a line in a single letter of the Western Alphabet.
Therefore, the another name for line P is line [tex]\over (CD)[/tex].
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i need help with the top one
Answer:
2. 14
4. -6
Step-by-step explanation:
#2
(x²-4y)/2, given x=4, y=-3
[(4)²-4(-3)]/2
=[16+12]/2
=28/2
=14
------------------------
#4
19-x², given x=-5
19-(-5)²
=19-25
=-6
Find the cosine ratio of angle 0
Answer: cos(0) = 1
hope this helped
Angle X and Y are supplementary. The measure of the angle X is 19° less than 2 times the measure of angle Y. What is the
measure of angle x?
Answer:
Supplementary angles add up to 180 degrees. The key phrase "less than" signifies you are going to subtract angle X from angle Y. Angle Y is 2 times the measure of angle X so you are going to multiply Y by 2. So right now you should have the equation 2y - 19 = 180. Then, plug it in. Add 19 to 180 to move it to the other side and then divide by 2.
Can somebody help me with this ?? :)
Which function has a domain of x 25 and a range of y s3?
Answer:
Step-by-step explanation:
The function has a domain x ≥ 5.
This is because the function remains real for (x - 5) ≥ 0 as negative within the square root is imaginary.
Hence, (x - 5) ≥ 0
⇒ x ≥ 5
Now, for all x values that are greater than equal to 5 the value of will be negative.
So,
⇒
⇒ y ≤ 3
Therefore, the range of the function is y ≤ 3. (Answer)
Note: Thanks rani
From the set {1, 2, 3, 4, 5}, find the lowest value of x that makes each inequality true. Arrange the inequalities in increasing order of the lowest value of x from the set that makes them true. 5x − 3x > 9 2x − 1 > 0 x + (x − 1) > 5
2x - 1 > 0 ( x = 1)
x + (x − 1) > 5 ( x = 3)
5x − 3x > 9 ( x = 5)
Answer:
2x - 1 > 0 ( x = 1)
x + (x − 1) > 5 ( x = 3)
5x − 3x > 9 ( x = 5)Step-by-step explanation:
PLS HELLP!!!!!!!!!!!!!!!!!!!!! Deandra is doing her math homework. Out of 24 problems total, she completed the first 12 problems in 1 hour and the last 12 problems in 3 hours. What is the unit rate for all 24 problems?
Answer:
24
Step-by-step explanation:
Imagine that you earned $8,425 in one year. If the government enforces a 15% income tax, how much money would you owe in taxes at the end of the year?
Answer: You would owe $1,263 and 75c! Have a fantastic day!
How to Multiply six and the reciprocal of the quotient of a number and seven?
Answer:
Let N be the unknown number
The we have 6 x reciprocal of N/7 which is 6 x 7/N which is 42/N
HOPE THIS HELPS YOU
Multiply six and the reciprocal of the quotient of a number and seven can be written as 42/M.
Where M is the number.
Given,
Multiply six and the reciprocal of the quotient of a number and seven.
We need to find this expression.
What does quotient mean?
It means to divide.
The quotient of a and b:
= a ÷ b.
= a / b
Find the expression.
Let the number be M.
Now,
The quotient of a number and 7 can be written as:
= M ÷ 7
= M / 7
Reciprocal of the quotient of a number and seven.
= 1 / (M/7)
= 7 / M
Now,
Multiply six and the reciprocal of the quotient of a number and seven.
It can be written as:
= 6 x 7 / M
= 42 / M
Thus multiply six and the reciprocal of the quotient of a number and seven can be written as 42/M.
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∠A and \angle B∠B are complementary angles. If m\angle A=(2x+10)^{\circ}∠A=(2x+10) ∘ and m\angle B=(3x+15)^{\circ}∠B=(3x+15) ∘ , then find the measure of \angle B∠B.
Answer:
[tex]54^\circ[/tex]
Step-by-step explanation:
Given :
[tex]m\angle A=(2x+10)^{\circ}[/tex]
[tex]m\angle B=(3x+15)^{\circ}[/tex]
And angles [tex]\angle A[/tex] and [tex]\angle B[/tex] are complementary angles.
To find:
The measure of [tex]\angle B[/tex].
Solution:
First of all, let us learn about complementary angles.
Complementary angles are the angles whose sum is equal to [tex]90^\circ[/tex].
And we are given that angles [tex]\angle A[/tex] and [tex]\angle B[/tex] are complementary angles.
Therefore [tex]\angle A[/tex] + [tex]\angle B[/tex] = [tex]90^\circ[/tex]
[tex]\Rightarrow 2x+10+3x+15=90\\\Rightarrow 5x+25=90\\\Rightarrow 5x=65\\\Rightarrow x =13[/tex]
Putting the value in [tex]\angle B[/tex].
[tex]m\angle B=(3\times 13+15)^{\circ} = 54^\circ[/tex]
Therefore, the answer is [tex]\bold{\angle B = 54^\circ}[/tex]
Which pair of numbers has 7 as its least common multiple? Group of answer choices 1, 7 3, 4 7, 21 14, 28
Answer:
7, 14, 14,21, and 28
Step-by-step explanation:
Only 1, 7 is pair of numbers that has 7 as its least common multiple.
Given that,
Pairs ( 1, 7 ), ( 3, 4 ), ( 7, 21), ( 14, 28).
A pair or pairs to be determined that have 7 as its least common multiple.
In mathematics, it deals with numbers of operations according to the statements.
What is Lowest Common Multiple?In arithmetic, LCM is defined as the lowest common multiple of two integers X and Y, usually represented as by LCM X, Y, and is the smallest favorable integer that is dividable by both X and Y.
Since the Least common multiple of pair of numbers has 7, this is only possible for 1 * 7, because the LCM of 1 and7 is 7. So from given option 1, 7 is the required pair.
Thus, only 1, 7 is pair of numbers that has 7 as its least common multiple.
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Solve for x. 2x + 2 = -8 X=???? Please help!?
x = - 5
Step-by-step explanation:2x + 2 = - 8
2x = - 8 - 2
2x = - 10
x = - 10 : 2
x = - 5
Answer:
x=-5
Step-by-step explanation:
1.) 2x+2=-8 start to isolate the variable by subtracting 2 to -8
2.) 2x=-10 divide both sides by 2
3.) x=-5
Hope this helped
Given: 2x + 3(x - 2) = 24
Prove: x = 6
Statements and Reasons?
Answer:
x=6
Step-by-step explanation:
first we'll use distributive property: we will distribute and multiply 3 by x and - 2
2x + 3x -6 = 24
then we'll add like terms which are 2x and 3x , 24 and 6 the sign of 6 will change from negative to positive:
2x + 3x =24 + 6
5x = 30
after that we will divide both sides by 5 in order to get x
5x/5 = 30/ 5
x = 6
Four more than twice a number is –10.
Four more than twice a number is –10 is the same as 2n + 4 = 10
Steps to solve:
2n + 4 = 10
~Subtract 4 to both sides
2n = 6
~Divide 2 to both sides
n = 3
Best of Luck!
Hours of
Training
10
20
30
40
50
60
70
Monthly
Pay
1220
1420
1620
1820
2020
2220
2420
According to the table, what is the monthly pay for a worker with 0 hours of
training?
Answer:
$1,020
Step-by-step explanation:
There is a $200 difference in the every monthly pay.
Because of this we know that the first month was an amount minus $200.
If we subtract 1220 and 200, you get the pay of 1020 for 0 hours.
help pls. Find the value of x.
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = 15 °}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{x + 30 ° + 100 ° + 3x - 10 ° = 180 °}[/tex]
( Sum of angle in straight line )
Collect like terms
⇒[tex] \sf{4x + 30 ° + 100 ° - 10 ° = 180 °}[/tex]
Calculate the sum or difference
⇒[tex] \sf{4x + 120 ° = 180 °} [/tex]
Move 120 to right hand side hand change it's sign
⇒[tex] \sf{4x = 180 ° - 120 °}[/tex]
Subtract 120 from 180
⇒[tex] \sf{4x = 60 ° }[/tex]
Divide both sides of the equation by 4
⇒[tex] \sf{ \frac{4x}{4} = \frac{60}{4} }[/tex]
Calculate
⇒[tex] \sf{x = 15 °}[/tex]
Hope I helped!
Best regards!!
On January 1st 2020 the populations of Japan and the Philippines were 126.5million and 109.6 respectively. Japan's population is currently decreasing by 0.2% per year while the population of the Philippines is increasing by 1.6% per year. If these rates of change remain constant, during which year will the two population be the same
In 422.5 years, the two populations will be the same
Let the year when the two populations will be the same be represented by x.
The equation to solve the question will be:
126.5 - 0.2x = 109.6 - 0.16x
Collect like terms
0.2x - 0.16x = 126.5 - 109.6
0.04x = 16.9
x = 16.9/0.04
x = 422.5
In conclusion, in 422.5 years, the two populations will be the same.
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How to round 1724.89 to the nearest tenths place ?
Answer:
1724.9
Step-by-step explanation:
1724.89 ≈ 1724.9
Answer:
1724.9
Step-by-step explanation:
If you want to round to tenths place, look at hundredths place.
If the digit in hundredths place is 5 or more than 5 (5,6,7,8,9), then add '1' to the tenth place.
Here, 9 is in hundredths place, so add 1 to 8
1724.9
These box plots show daily low temperatures for a sample of days in two
different towns.
Town A
10 15 20
30
55
Town B
5
20
30
40
55
0
5
10
15
20
45
50
55
60
25 30 35 40
Degrees (F)
Compare the shapes of the box plots.
O A. The distribution for town A is negatively skewed, but the
distribution for town B is symmetric.
B. The distributions for both towns are positively skewed.
C. The distributions for both towns are symmetric.
O D. The distribution for town A is positively skewed, but the
distribution for town B is symmetric.
D. The distribution for town A is positively skewed, but the
distribution for town B is symmetric.
The distribution for town A is positively skewed, but the distribution for town B is symmetric. The correct option is D.
What is box plots?Box plots, also known as box-and-whisker plots, are a way to visualize the distribution of a set of numerical data.
To compare the shapes of the box plots, we need to look at the position of the median, the length of the box, and the length of the whiskers.
In the box plot for town A, the median is closer to the bottom of the box, indicating that the lower half of the data is more spread out than the upper half.
The whisker on the left side of the box plot is longer than the whisker on the right side, which indicates that there are some extreme values on the lower end of the data. This is consistent with a positively skewed distribution.
In contrast, the box plot for town B has a symmetrical box, with the median located near the center.
The whiskers on both sides of the box plot are roughly the same length, indicating that there are no extreme values on either end of the data. This is consistent with a symmetric distribution.
Thus, the correct option is D.
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please help i need this answered as soon as possible!!! -Use ΔDEF, shown below, to answer the question that follows:
Answer:
X= 139
Step-by-step explanation:
the square on the E means its a right side so that would be 90 degrees. All triangles add up to 180. F would be 41 degrees. that mean X is 139 i think.
Answer:
36.083
Step-by-step explanation:
SOHCAHTOA
Cosine is adjacent over hypotenuse, so the
cos(49) = the adjacent side (x) || over the hypotenuse (55)
cos(49) = x/55
55cos(49) = x
x = 36.083
Complete the sequence,
13, 14, 27, 41,
Answer:
68
Step-by-step explanation:
We can see that the nth term would be the sum of the previous two terms. Continuing this would result in 68.
What two rational expressions sum to 2x+3/x^2-5x+4
Enter your answer by filling in the boxes. Enter your answer so that each rational expression is in simplified form.
Answer:
[tex] \frac{2x + 3}{(x- 1)(x - 4)} = \frac{-5}{3(x- 1)} + \frac{11}{3(x - 4)} [/tex]
Step-by-step explanation:
Given the rational expression: [tex] \frac{2x + 3}{x^2 - 5x + 4} [/tex], to express this in simplified form, we would need to apply the concept of partial fraction.
Step 1: factorise the denominator
[tex] x^2 - 5x + 4 [/tex]
[tex] x^2 - 4x - x + 4 [/tex]
[tex] (x^2 - 4x) - (x + 4) [/tex]
[tex] x(x - 4) - 1(x - 4) [/tex]
[tex] (x- 1)(x - 4) [/tex]
Thus, we now have: [tex] \frac{2x + 3}{(x- 1)(x - 4)} [/tex]
Step 2: Apply the concept of Partial Fraction
Let,
[tex] \frac{2x + 3}{(x- 1)(x - 4)} [/tex] = [tex] \frac{A}{x- 1} + \frac{B}{x - 4} [/tex]
Multiply both sides by (x - 1)(x - 4)
[tex] \frac{2x + 3}{(x- 1)(x - 4)} * (x - 1)(x - 4) [/tex] = [tex] (\frac{A}{x- 1} + \frac{B}{x - 4}) * (x - 1)(x - 4) [/tex]
[tex] 2x + 3 = A(x - 4) + B(x - 1) [/tex]
Step 3:
Substituting x = 4 in [tex] 2x + 3 = A(x - 4) + B(x - 1) [/tex]
[tex] 2(4) + 3 = A(4 - 4) + B(4 - 1) [/tex]
[tex] 8 + 3 = A(0) + B(3) [/tex]
[tex] 11 = 3B [/tex]
[tex] \frac{11}{3} = B [/tex]
[tex] B = \frac{11}{3} [/tex]
Substituting x = 1 in [tex] 2x + 3 = A(x - 4) + B(x - 1) [/tex]
[tex] 2(1) + 3 = A(1 - 4) + B(1 - 1) [/tex]
[tex] 2 + 3 = A(-3) + B(0) [/tex]
[tex] 5 = -3A [/tex]
[tex] \frac{5}{-3} = \frac{-3A}{-3} [/tex]
[tex] A = -\frac{5}{3} [/tex]
Step 4: Plug in the values of A and B into the original equation in step 2
[tex] \frac{2x + 3}{(x- 1)(x - 4)} = \frac{A}{x- 1} + \frac{B}{x - 4} [/tex]
[tex] \frac{2x + 3}{(x- 1)(x - 4)} = \frac{-5}{3(x- 1)} + \frac{11}{3(x - 4)} [/tex]
Answer:
Step-by-step explanation:
Given the rational expression: , to express this in simplified form, we would need to apply the concept of partial fraction.
Step 1: factorise the denominator
Thus, we now have:
Step 2: Apply the concept of Partial Fraction
Let,
=
Multiply both sides by (x - 1)(x - 4)
=
Step 3:
Substituting x = 4 in
Substituting x = 1 in
Step 4: Plug in the values of A and B into the original equation in step 2
Step-by-step explanation: