Answer:
[tex]Charlie = 5 + x[/tex]
[tex]Danny = x - 8[/tex]
[tex]Eric = 3x[/tex]
Step-by-step explanation:
Given
Billy's Marble = x
Required
Determine a,b and c
a. Charlie's Marble
"5 more" means 5 + or + 5
Since Billy's Marble is represented with x, then Charlie's Marbles will be
[tex]Charlie = 5 + x[/tex]
b. Danny's Marbles
Having "8 fewer" means we have to subtract 8 from Billy's marble;
Since Billy's Marble is represented with x, then Danny's Marbles will be
[tex]Danny = x - 8[/tex]
c. Eric Marbles
Having "three times as " means we have to multiply Bill's marble by 3;
Since Billy's Marble is represented with x, then Danny's Marbles will be
[tex]Eric = 3 * x[/tex]
[tex]Eric = 3x[/tex]
Question
Find the sample variance of the following set of data:
12, 7, 6, 4, 11.
Select the correct answer below:
Answer:
Variance is 256
Step-by-step explanation:
Variance:
[tex]var = \frac{ ({ \sum x})^{2} }{n} - {( \frac{ \sum x}{n} })^{2} [/tex]
x is the number or item in the data
n is the number of terms
[tex]{ \tt{ \sum x = (12 + 7 + 6 + 4 + 11)}} \\ { \tt{ \sum x = 40}}[/tex]
Therefore:
[tex]variance = \frac{ {40}^{2} }{5} - { (\frac{40}{5}) }^{2} \\ \\ = 320 - 64 \\ variance = 256[/tex]
Brief and easy(if possible) explanation on how to do these?
Answer:
linear pairs are supplement which means it always equals to 180°
Find the value of NT
A. 4
B. 14
C. 12
D. 16
Answer:
14
Step-by-step explanation:
(segment piece) x (segment piece) = (segment piece) x (segment piece)
12*x = 8 * (x+2)
Distribute
12x = 8x+16
Subtract 8x
12x-8x = 8x+16-8x
4x = 16
Divide by 4
4x/4 = 16/4
x = 4
We want NT
NT = 8+x+2
= 10 +x
= 10 +4
= 14
If r=9 and 4r+3s=75, what is the value of s?
Answer:
s = 13Step-by-step explanation:
4r+3s=75 , r = 9
Since we know the value of r, we can substitute the value of r into the above equation to find s
That's
4( 9) + 3s = 75
36 + 3s = 75
Group like terms
3s = 75 - 36
3s = 39
Divide both sides by 3
That's
[tex] \frac{3s}{3} = \frac{39}{3} [/tex]
We have the final answer as
s = 13Hope this helps you
Georgianna claims that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons. We have a random sample of 20 children from the city, with a mean of 4.6 years of piano lessons and a standard deviation of 2.2 years. Required:Explicitly state and check all conditions necessary for inference on these data.
Answer:
The condition are
The Null hypothesis is [tex]H_o : \mu = 5[/tex]
The Alternative hypothesis is [tex]H_a : \mu < 5[/tex]
The check revealed that
There is sufficient evidence to support the claim that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 5 \ year[/tex]
The sample size is n = 20
The sample mean is [tex]\= x = 4.6 \ years[/tex]
The standard deviation is [tex]\sigma = 2.2 \ years[/tex]
The Null hypothesis is [tex]H_o : \mu = 5[/tex]
The Alternative hypothesis is [tex]H_a : \mu < 5[/tex]
So i will be making use of [tex]\alpha = 0.05[/tex] level of significance to test this claim
The critical value of [tex]\alpha[/tex] from the normal distribution table is [tex]Z_\alpha = 1.645[/tex]
Generally the test statistics is mathematically evaluated as
[tex]t = \frac{\= x - \mu}{ \frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 4.6 - 5}{ \frac{2.2}{\sqrt{20} } }[/tex]
[tex]t = -0.8131[/tex]
Looking at the value of t and [tex]Z_{\alpha }[/tex] we see that [tex]t < Z_{\alpha }[/tex] so we fail to reject the null hypothesis
This implies that there is sufficient evidence to support the claim that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons.
cooks are needed to prepare for a large party. Each cook can bake either 5 Large cakes or 14 small cakes per hour . The kitchen is available for 3 hours and 29 large cakes and 260 cakes need to be baked . How many cooks are required to bake the required number of cakes during the time the kitchen is available?
it was all about equating some values
to bake the required number of cakes during the available 3-hour time period, 7 cooks are required.
Let's determine the number of cooks required to bake the required number of cakes during the available time.
We have the following information:
- Each cook can bake either 5 large cakes or 14 small cakes per hour.
- The kitchen is available for 3 hours.
- We need to bake 29 large cakes and 260 cakes in total.
First, let's calculate the number of large cakes that can be baked by one cook in 3 hours:
1 cook can bake 5 large cakes/hour × 3 hours = 15 large cakes.
Next, let's calculate the number of small cakes that can be baked by one cook in 3 hours:
1 cook can bake 14 small cakes/hour × 3 hours = 42 small cakes.
Now, let's calculate the number of large cakes that can be baked by all the cooks in 3 hours:
Total number of large cakes = Number of cooks × Large cakes per cook per 3 hours
We need to bake 29 large cakes, so:
29 = Number of cooks × 15
Number of cooks = 29 / 15 ≈ 1.93
Since we can't have a fraction of a cook, we need to round up to the nearest whole number. Therefore, we need at least 2 cooks to bake the required number of large cakes.
Similarly, let's calculate the number of small cakes that can be baked by all the cooks in 3 hours:
Total number of small cakes = Number of cooks × Small cakes per cook per 3 hours
We need to bake 260 small cakes, so:
260 = Number of cooks × 42
Number of cooks = 260 / 42 ≈ 6.19
Again, rounding up to the nearest whole number, we need at least 7 cooks to bake the required number of small cakes.
Since we need to satisfy both requirements for large and small cakes, we choose the larger number of cooks required, which is 7 cooks.
Therefore, to bake the required number of cakes during the available 3-hour time period, 7 cooks are required.
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(a) Five friends are in a netball squad. In each game during the 21-round season, at least 3 of them are picked in the team. Prove that there will be at least 3 matches in which the same three friends are selected to play.
(b) How does the answer change if there are six friends instead of 5?
PLS ANSWER FAST!!!!
Answer:
(a) there are 10 sets of 3 friends, so in 21 games, at least one set must show 3 times
(b) there are 20 sets of 3 friends, so in 21 games, at least one set must show 2 times.
Step-by-step explanation:
(a) The number of combinations of 5 things taken 3 at a time is ...
5C3 = 5!/(3!·2!) = 5·4/2 = 10
There can be 10 games in which the same 3 friends do not show up. There can be 10 more games such that the same 3 friends show up exactly twice. In the 21st game, some set of 3 friends must show up 3 times.
__
(b) The number of combinations of 6 things taken 3 at a time is ...
6C3 = 6!/(3!·3!) = 6·5·4/(3·2) = 20
Hence, there can be 20 games in which the same 3 friends do not show up. In the 21st game, some set of 3 friends will show up a second time.
Find the sum (x^3+5x^2+3x-7)+(8x-6^2+6)
Find the difference (7x-3x^2+2)-(x^3+5x^2+2x-5)
Answer:
x^3 - x^2 + 11x - 1
-x^3 - 8x^2 + 5x + 7
Step-by-step explanation:
Find the sum
(x^3+5x^2+3x-7)+(8x-6x^2+6)
=x^3+5x^2+3x-7+8x-6x^+6
Collect like terms
=x^3 +5x^2-6x^2+3x+8x-7+6
Add the like terms
= x^3 - x^2 + 11x - 1
Find the difference (7x-3x^2+2)-(x^3+5x^2+2x-5)
(7x-3x^2+2)-(x^3+5x^2+2x-5)
= 7x-3x^2+2-x^3-5x^2-2x+5
Collect like terms
= -x^3-3x^2-5x^2+7x-2x+2+5
Add the like terms
= -x^3 - 8x^2 + 5x + 7
3
2
Vx
1
1
2 3 4 5 6 7 8 9 10 11 12 X
Magnets
Using equivalent ratios, which statements are true about the cost per magnet? Check all that apply.
The cost of 2 magnets is $1.
The cost of 9 magnets is $3.
The cost of 10 magnets is $3.
The cost of 4 magnets is $2.
The cost of 6 magnets is $2.
The cost of 3 magnets is $1.
Next
Submit
Save and Exit
Mark this and retum
Answer:
The cost of 3 magnets is $1
The cost of 9 magnets is $3
The cost of 6 magnets is $2
Step-by-step explanation:
The cost of magnets is calculated using the equivalent ratio. If 3 magnets cost $ then the multiple used for the calculations of more magnets is 3. The ratio for every magnet price is 1 : 3 which means every dollar will be equal to 3 magnets. The cost of 3 magnets is $1, the cost of 6 magnets is $2 and cost of 9 magnets is $3.
Sodas in a can are supposed to contain an average 12 oz. This particular brand has a standard deviation of 0.1 oz, with an average of 12.1 oz. If the can’s contents follow a Normal distribution, what is the probability that the mean contents of a six-pack are less than 12 oz?
Answer:
The probability is [tex]P(X < 12) = 0.99286[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 12 \ oz[/tex]
The standard deviation is [tex]\sigma = 0.1 \ oz[/tex]
The sample mean is [tex]\= x = 12.1 \ oz[/tex]
The sample size is n = 6 packs
The standard error of the mean is mathematically represented as
[tex]\sigma_{\= x } = \frac{\sigma}{\sqrt{n} }[/tex]
substituting values
[tex]\sigma_{\= x } = \frac{0.1}{\sqrt{6} }[/tex]
[tex]\sigma_{\= x } = 0.0408[/tex]
Given that the can’s contents follow a Normal distribution then then the probability that the mean contents of a six-pack are less than 12 oz is mathematically represented as
[tex]P(X < 12) = P ( \frac{X - \mu }{ \sigma_{\= x }} < \frac{\= x - \mu }{ \sigma_{\= x }} )[/tex]
Generally [tex]\frac{X - \mu }{ \sigma_{ \= x }} = Z (The \ standardized \ value \ of \ X )[/tex]
So
[tex]P(X < 12) = P ( Z < \frac{\= x - \mu }{ \sigma_{\= x }} )[/tex]
substituting values
[tex]P(X < 12) = P ( Z < \frac{12.2 -12 }{0.0408} )[/tex]
[tex]P(X < 12) = P ( Z < 2.45 )[/tex]
From the normal distribution table the value of [tex]P ( Z < 2.45 )[/tex] is
[tex]P (Z < 2.45)0.99286[/tex]
=> [tex]P(X < 12) = 0.99286[/tex]
The mean weight of newborn infants at a community hospital is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. Does the sample data show a significant increase in the average birthrate at a 5% level of significance?
A. Fail to reject the null hypothesis and conclude the mean is 6.6 lb.
B. Reject the null hypothesis and conclude the mean is lower than 6.6 lb.
C. Reject the null hypothesis and conclude the mean is greater than 6.6 lb.
D. Cannot calculate because the population standard deviation is unknown
Answer:
The correct option is A
Step-by-step explanation:
From the question we are told that
The population is [tex]\mu = 6.6[/tex]
The level of significance is [tex]\alpha = 5\% = 0.05[/tex]
The sample data is 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds
The Null hypothesis is [tex]H_o : \mu = 6.6[/tex]
The Alternative hypothesis is [tex]H_a : \mu > 6.6[/tex]
The critical value of the level of significance obtained from the normal distribution table is
[tex]Z_{\alpha } = Z_{0.05 } = 1.645[/tex]
Generally the sample mean is mathematically evaluated as
[tex]\=x = \frac{\sum x_i }{n}[/tex]
substituting values
[tex]\=x = \frac{9.0 + 7.3 + 6.0+ 8.8+ 6.8+ 8.4+6.6 }{7}[/tex]
[tex]\=x = 7.5571[/tex]
The standard deviation is mathematically evaluated as
[tex]\sigma = \sqrt{\frac{\sum [ x - \= x ]}{n} }[/tex]
substituting values
[tex]\sigma = \sqrt{\frac{ [ 9.0-7.5571]^2 + [7.3 -7.5571]^2 + [6.0-7.5571]^2 + [8.8- 7.5571]^2 + [6.8- 7.5571]^2 + [8.4 - 7.5571]^2+ [6.6- 7.5571]^2 }{7} }[/tex][tex]\sigma = 1.1774[/tex]
Generally the test statistic is mathematically evaluated as
[tex]t = \frac{\= x - \mu } { \frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{7.5571 - 6.6 } { \frac{1.1774 }{\sqrt{7} } }[/tex]
[tex]t = 1.4274[/tex]
Looking at the value of t and [tex]Z_{\alpha }[/tex] we see that [tex]t < Z_{\alpha }[/tex] hence we fail to reject the null hypothesis
What this implies is that there is no sufficient evidence to state that the sample data show as significant increase in the average birth rate
The conclusion is that the mean is [tex]\mu = 6.6 \ lb[/tex]
6. How many rational number are there Between ⅕and⁹/⁵
9514 1404 393
Answer:
an infinite number
Step-by-step explanation:
Between any pair of numbers, there are ...
an infinite number of rational numbers, and
an infinite number of irrational numbers
(x-1)(x-3)(x+5)(x+7)=297
First simplify the expression into polynomial form,
[tex](x-1)(x-3)(x+5)(x+7)=297[/tex]
[tex]x^4+8x^3-10x^2-104x+105=297[/tex]
[tex]x^4+8x^3-10x^2-104x-192=0[/tex]
Now factor into,
[tex](x-4)(x+8)(x^2+4x+6)=0[/tex]
Which means the solutions are,
[tex]x-4=0\implies\boxed{x_1=4}[/tex]
[tex]x+8=0\implies\boxed{x_2=-8}[/tex]
and then two complex solutions because determinant of the third factor [tex]D\lt0[/tex],
[tex]x^2+4x+6=0[/tex]
[tex]x^2+4x+4=-2[/tex]
[tex](x+2)^2=-2\implies\boxed{x_3=i\sqrt{2}-2},\boxed{x_4=-i\sqrt{2}-2}[/tex]
Hope this helps :)
Answer:
x=4
Step-by-step explanation:
(4-1)(4-3)(4+5)(4+7)=297
Use the substitution method to solve the system of equations. Choose the correct ordered pair. x + y = 3 y = 9 A. (–12, 9) B. (–6, 9) C. (6, 9) D. (12, 9)
B(-6,9)is the answer
have a great dayyyy.
Draw a Venn diagram and use the given information to fill in the number of elements in each region.
Answer: Check out the diagram below for the filled in boxes
14 goes in the first box (inside A, but outside B)
7 goes in the overlapping circle regions
5 goes in the third box (inside B, outside A)
3 goes in the box outside of the circles
==============================================================
Explanation:
[tex]n(A \cup B) = 26[/tex] means there are 26 items that are in A, B or both.
n(A) = 21 means there are 21 items in A
n(B) = 12 means there are 12 items in B
We don't know the value of [tex]n(A \cap B)[/tex] which is the number of items in both A and B at the same time. This is the intersecting or overlapping regions of the two circles. Let [tex]x = n(A \cap B)[/tex]
It turns out that adding n(A) to n(B), then subtracting off the stuff they have in common, leads to n(A u B) as shown below.
--------
[tex]n(A \cup B) = n(A) + n(B) - n(A \cap B)\\\\26 = 21+12 - x\\\\26 = 33 - x\\\\x+26 = 33\\\\x = 33-26\\\\x = 7\\\\n(A \cap B) = 7\\\\[/tex]
So there are 7 items in both regions.
This means there are [tex]n(A) - n(A \cap B) = 21 - 7 = 14[/tex] items that are in set A only. In other words, 14 items are in circle A, but not in circle B.
Notice how the values 14 and 7 add back up to 14+7 = 21, which represents everything in set A.
Similarly, there are [tex]n(B) - n(A \cap B) = 12 - 7 = 5[/tex] items that are in circle B, but not in circle A. The values 5 and 7 in circle B add to 5+7 = 12, matching with n(B) = 12.
The notation n(A') means the number of items that are not in set A. We're given n(A') = 8. We already know that 5 is outside circle A. So if 5+y = 8, then y = 3 must be the missing value for the box that is outside both circles.
Again the diagram is posted below with the filled in values.
A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.
The filled Venn diagram is given below.
What is a Venn diagram?A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.
We have,
n(A) = 21
This is the total of all the items included in Circle A.
n(B) = 12
This is the total of all the items included in Circle A.
n(A') = 8
The items that are not in circle A.
n(A U B ) = 26
The items that are in both circle A and circle B.
Now,
n (A U B) = n(A) + n(B) - n(A ∩ B)
26 = 21 + 12 - n(A ∩ B)
n(A ∩ B) = 33 - 26
n(A ∩ B) = 7
Thus,
The filled Venn diagram is given below.
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Calculate the derivative of the function. Then find the value of the derivative as specified:
f(x) = 5x + 9; f "(2)
A) f "(x) 0,f , (2)-0
B) f , (x)-9; f , (2) = 9
C)f"(x) = 5; f "(2) = 5
D) f '(x) 5x; f '(2) 10
The correct question is;
Calculate the derivative of the function. Then find the value of the derivative as specified:
f(x) = 5x + 9; f '(2)
A) f'(x) = 0; f'(2) = 0
B) f'(x) = 9; f '(2) = 9
C)f'(x) = 5; f'(2) = 5
D) f '(x) = 5x; f '(2) = 10
Answer:
Option C: f'(x) = 5 and f '(2) = 5
Step-by-step explanation:
We want to find the derivative of f(x) = 5x + 9.
Now, the derivative with respect to x will be;
f'(x) = 5
Now,we also want to find out f'(2)
This means we are to put 2 for x in the derivative function.
In the derivative function, we don't have x as we have just 5.
Thus,f'(2) = 5
Solve for y.
Z = yn
Answer:
y = z /n
Step-by-step explanation:
Answer:
y=z/n
Step-by-step explanation:
To isolate the y, divide both sides by n
Amira has 3/4 of a bag of cat food her cat eats 1/10 of a bag per week how many weeks will the food last
Find all excluded values for the expression.
That is, find all values of for which the expression is undefined.
3v
------
2v+10
If there is more than one value, separate them with commas.
Answer:
-5
Step-by-step explanation:
For an expression to be undefined, the denominator must be equal to 0
Therefore, we must equate the denominator in the expression to 0
2v + 10 = 0
2v = 0 - 10
2v = -10
v = -10/2
v = -5
So in order for the expression to be undefined, v must be equal to -5
What's the y-intercept of the function y=-2(2)* + 2?
Answer:
-2 is the y-intercept of this function.
Step-by-step explanation:
. Simplify the sum. (2u3 + 6u2 + 2) + (7u3 – 7u + 4)
Answer:
9u^3 + 6u^2 - 7u + 6
Step-by-step explanation:
John can jog twice as fast as he can walk. He was able to jog the first 5 miles to his grandmother's house, but then he tired and walked the remaining 2 miles. If the total trip took 0.9 hours, then what was his average jogging speed?
Step-by-step explanation:
Suppose, John walks with a speed x
Then, John can jog at a speed 2x
[tex]total \: time \: = \frac{total \: distance}{average \: speed} [/tex]
TOTAL TIME
[tex]0.9 = \frac{5}{2x} + \frac{2}{x} [/tex]
Further solving :
x = 5 mph
Average jogging speed (2x) = 10 mph
Answer:
10mph
Step-by-step explanation:
We know that John's total trip is 0.9 hours, so let's try to figure out how much of that time is spent jogging, and how much of it is spent walking.
We can do that by naming the time he takes to jog a mile y.
An equation would be:
5y+2(2y)=0.9
5y+4y=0.9
y=0.1
It takes him 0.1 hours, or 6 minutes to jog a mile.
Since he jogged 5 miles, his jogging time is 0.5 hours, or 30 minutes.
Now,
Let's name the speed he jogs x (miles per hour)
This allows us to set up another equation.
Note that:
Speed=distance/time
His jogging speed is x.
x=5/0.5
x=10
His average jogging speed is 10 miles an hour.
Divide 3 2/3 ÷ 2 1/3. Simplify the answer and write it as a mixed number.
Answer:
The answer is [tex]1 \frac{4}{7}[/tex]
Step-by-step explanation:
First, you convert [tex]3 \frac{2}{3}[/tex] to an improper fraction. That is [tex]\frac{11}{3}[/tex]. Do the same for the other number.
Next, use KFC, or Keep, Flip, Change.
Keep the first number
Flip the second
Change the operation. Division becomes Multiplication. You should've gotten [tex]\frac{11}{3}[/tex]x[tex]\frac{3}{7}[/tex].
You can simplify now. You would've gotten 11 * [tex]\frac{1}{7}[/tex]. Multiply and you would get [tex]\frac{11}{7}[/tex]. Simplify into a mixed number. The answer is [tex]1 \frac{4}{7}[/tex].
What is the exact distance from (−1, 4) to (6, −2)? square root of 80. units square root of 82. units square root of 85. units square root of 89. units
Answer:
[tex]\sqrt{85}[/tex].
Step-by-step explanation:
[tex]x[/tex]-coordinates:
First point: [tex]-1[/tex].Second point: [tex]6[/tex].Difference: [tex]|-1 - 6| = |-7| = 7[/tex].[tex]y[/tex]-coordinates:
First point: [tex]4[/tex].Second point: [tex]-2[/tex].Difference: [tex]|4 - (-2)| = |6| = 6[/tex].Refer to the diagram attached. Consider these two points as the two end points of the hypotenuse of a right triangle. The lengths of the two legs are equal to:
the difference between the two [tex]x[/tex]-coordinates, [tex]7[/tex], and the difference between the two [tex]y[/tex]-coordinates, [tex]6[/tex].Apply Pythagorean Theorem to find the length of the hypotenuse (which is equal to the distance between the two points in question.)
[tex]\begin{aligned}\text{Hypotenuse} &= \sqrt{(\text{First Leg})^2 + (\text{Second Leg})^2} \\ &= \sqrt{7^2 + 6^2} \\ &= \sqrt{85}\end{aligned}[/tex].
Answer:
C
Step-by-step explanation:
Which graph represents a linear function that has a slope of 0.5 and a y-intercept of 2?
On a coordinate plane, a line goes through points (negative 2, 0) and (0, 1).
On a coordinate plane, a line goes through points (0, 2) and (4, 0).
On a coordinate plane, a line goes through points (0, 2) and (2, 3).
On a coordinate plane, a line goes through points (negative 4, 0) and (0, 2).
Answer:
f(x)=1/2x+2
Step-by-step explanation:
Using formula y=mx+b.
m is 0.5 or 1/2 as stated above
f(x)= 1/2x+b
If it were y=1/2x, it would intersect at 0,0 and we want 0,2
so b should be 2
therefore
Y=1/2x+2
or
f(x)=1/2x+2
Answer:
D
Step-by-step explanation:
Commuting times for employees of a local company have a mean of 63 minutes and a standard deviation of 3 minutes. What does Chebyshev's Theorem say about the percentage of employees with commuting times between 54 minutes and 72minutes?
Answer: At-least 89% of employees with commuting times between 54 minutes and 72 minutes .
Step-by-step explanation:
Given: Commuting times for employees of a local company have a mean of 63 minutes and a standard deviation of 3 minutes.
Now, 54 minutes = (63 - 9) minutes
= (63 -3(3)) minutes
= Mean - 3 standard deviation
72 minutes = (63 + 9) minutes
=63 +3(3) minutes
= Mean + 3 standard deviation
According to Chebyshev's theorem, at least [tex]\dfrac{8}{9}[/tex] of the data lie within 3 standard deviations of the mean.
i.e. The percentage of employees with commuting times between 54 minutes and 72 minutes = [tex]\dfrac{8}{9}\times100\approx89\%[/tex]
Hence, at-least 89% of employees with commuting times between 54 minutes and 72 minutes .
Write the polar form of a complex number in standard form for [tex]25[cos(\frac{5\pi }{6}) + isin(\frac{5\pi }{6})][/tex]
Answer:
Standard Complex Form : [tex]-\frac{25\sqrt{3}}{2}+\frac{25}{2}i[/tex]
Step-by-step explanation:
We want to rewrite this expression in standard complex form. Let's first evaluate cos(5π / 6). Remember that cos(x) = sin(π / 2 - x). Therefore,
cos(5π / 6) = sin(π / 2 - 5π / 6),
π / 2 - 5π / 6 = - π / 3,
sin(- π / 3) = - sin(π / 3)
And we also know that sin(π / 3) = √3 / 2. So - sin(π / 3) = - √3 / 2 = cos(5π / 6).
Now let's evaluate the sin(5π / 6). Similar to cos(x) = sin(π / 2 - x), sin(x) = cos(π / 2 - x). So, sin(5π / 6) = cos(- π / 3). Now let's further simplify from here,
cos(- π / 3) = cos(π / 3)
We know that cos(π / 3) = 1 / 2. So, sin(5π / 6) = 1 / 2
Through substitution we receive the expression 25( - √3 / 2 + i(1 / 2) ). Further simplification results in the following expression. As you can see your solution is option a.
[tex]-\frac{25\sqrt{3}}{2}+\frac{25}{2}i[/tex]
What is the sum of the arithmetic sequence 3, 9, 15
if there are 34 terms?
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Work Shown:
a = first term = 3
d = common difference = 6
S(n) = sum of the first n terms of an arithmetic sequence
S(n) = (n/2)*(2a + d(n-1))
S(34) = (34/2)*(2*3 + 6(34-1))
S(34) = 3468
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Check:
3+9+15+21+27+33+39+45+51+57+63+69+75+81+87+93+99+105+111+117+123+129+135+141+147+153+159+165+171+177+183+189+195+201 = 3468
I used GeoGebra to generate the 34 terms shown above. You could do so by hand (start at 3; add 6 to each term to get the next one), but it's a tedious busywork type of problem in my opinion. It's best left to computer software.
If 7time the 7th of Ap. Is equal of 11 tomes its 11th term find 18th term
0 0
,
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There is a pair of x and y values that make each equation true in this system of equations
{5x + 3y = 8
{4x + 7y = 34
Explain why the same pair of values also make 9x + 10y = 42 true.
Given Equations
5x+3y=8--(1)4x+7y=34--(2)Let it has solution (x,y)
Add both
[tex]\\ \sf\longmapsto 5x+4x+3y+7y=8+34[/tex]
[tex]\\ \sf\longmapsto 9x+10y=42[/tex]
It will also have same solution (x,y)
The solution of the equations is (-2, 6) which satisfies the equation 9x + 10y = 42.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The system of linear equations is given below.
5x + 3y = 8 ...1
4x + 7y = 34 ...2
From equation 1, then we have
5x + 3y = 8
y = 8/3 - (5/3)x
Put in equation 2, then we have
4x + 7[8/3 - (5/3)x] = 34
12x + 56 - 35x = 102
-23x = 46
x = - 2
Then the value of y is calculated as,
y = 8/3 - (5/3)(-2)
y = 8/3 + 10/3
y = 18 / 3
y = 6
Let's check whether (-2, 6) satisfy the equation 9x + 10y = 42 or not. Then we have
9(-2) + 10(6) = 42
- 18 + 60 = 42
42 = 42
The solution of the equations is (-2, 6) which satisfies the equation 9x + 10y = 42.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
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