Answer:
[tex]i^{54}=-1[/tex]
Step-by-step explanation:
First, recall the 4 basic imaginary exponents:
[tex]i^1=i \text{, }i^2=-1\text{, }i^3=-1\text{ and } i^4=1[/tex]
So, we want to find:
[tex]i^{54}[/tex]
This is the same as:
[tex]=i^{52}\cdot i^2[/tex]
52 is 4 times 13. Thus:
[tex]=(i^4)^{13}\cdot i^2[/tex]
Since we know that i to the fourth is 1:
[tex]=(1)^{13}\cdot i^2[/tex]
Simplify:
[tex]=i^2[/tex]
And this equals:
[tex]=-1[/tex]
So:
[tex]i^{54}=-1[/tex]
PLS HELP BEST ANSWER GETS BRAINLIEST\
A dog needs 4/3 liters of water for 2/5 of a day. How many liters of water does the dog need for an entire day? *
Answer:
A dog needs 4/3 liters of water 2/5 of a day, Therefore
he'll need 4/3 liters for 5/2 day or
4/3 * 5/2 = 20/6 = 10/3 liters or 3 and 1/3 liters per day
Step-by-step explanation:
Suppose that you roll two dice and don’t get to look at the outcome. Your friend looksat the outcome and tells you honestly that at least one of the dice came up 6. What isthe probability that the sum of your two dice is 8?
Answer:
2/11
Step-by-step explanation:
We have to calculate this by
p(B nA)/p(A)
= We have A¹ to be that none of the die roll gives us 6
P(A¹) = 5/6²
P(A) = 1 -5/6²
= 11/36
BnA = one die being 6 and summation being equal to 8
= BnA = (6,2)(2,6)
= P(BnA) = 2/36
Therefore we have (2/36)/(11/36)
= 2/11
Carl owns a company that washes the windows of office buildings. He recently signed a contract for a large office building and estimates that it would take 2 days for 4 workers to wash the windows. Write an equation to describe the relationship between time (t) and the number of workers (n), which are inversely proportional.
Answer:
t = 8 / n
Step-by-step explanation:
Time (t) and the number of workers (n), which are inversely proportional.
t = k (1/n)
t = k / n
Where,
t= time it will take workers to finish their job
n = number of workers doing the job
k = constant of proportionality
He estimates that it would take 2 days for 4 workers to wash the windows.
t= 2 days
n= 4 workers
t = k / n
2 = k / 4
Cross product
2*4 = k
8 = k
The relationship between time an number of workers is
t = k / n
t = 8 / n
Answer:
Step-by-step explanation:
t= 8/n
What is the common ratio of the geometric sequence below?
Answer:
The answer is option BStep-by-step explanation:
Since it's a geometric sequence, to find the common ratio divide the previous term by the next term.
That's
[tex] \frac{48}{ - 96} = - \frac{1}{2} [/tex]And also
[tex] \frac{ - 24}{48} = - \frac{1}{2} [/tex][tex] \frac{12}{ - 24} = - \frac{ 1}{2} [/tex]Also
[tex] \frac{ - 6}{12} = - \frac{1}{2} [/tex]Since the common ratio is the same for any of the terms chosen the common ratio of the sequence is
[tex] - \frac{1}{2} [/tex]Hope this helps you
Answer:
B. -1/2
Step-by-step explanation:
The common ratio is the ratio between two numbers next to each other To find the common ratio, divide a term by the preceding term.
For example, if the term is 48, divide by -96.
48/-96 = -1/2
Another example, if the term is -24, divide by 48.
-24/48= -1/2
Let’s try one more example. If the term is 12, divide by -24
12/-24= -1/2
Therefore, the common ratio is 1/2 and the correct answer is B.
Can someone show me how to get the answer to this step by step? It's Combining Like Terms. [tex]-9x^{2}[/tex] - 7 + [tex]4x[/tex] + [tex]10x^{2}[/tex] - 14x
Answer:
x² - 10x - 7
Step-by-step explanation:
See steps below:
- 9x² - 7 + 4x + 10x² - 14x = (-9x² + 10x²) + (4x - 14x) - 7 = ⇒ like terms combined in parenthesisx² - 10x - 7 ⇒ simplifiedSnow White is sewing stockings for the animals that visit her in the forest. When she looks around, she sees 38 legs. She knows that there are ten total animals: mice, deer, and birds. She also knows there are twice as many deer as mice. How many of each animal are there?
Answer:
B=1 M=6 D=3
Step-by-step explanation:
the equations are 4M+4D+2B=38
M+D+B=10
2D=M
step two: 4M+4D+2B=38 (multiply 2nd equation by -4)
-4M-4D-4B=-40
4M AND 4D cancels out and your left with -2B=-2 B=1
then you take the first equation and subsitute the third equation for M
step three: M+D+1 =10 (SUBSITUTE B WITH 1)
M+D=9
STEP FOUR: take the last equation (M+D=9) and subsitute 2D=M
2D+D=9
3D=9
D=3
subsitute D=3 into 2D=M so you get 2(3)=M M=6
DOUBLE CHECK USE THE SECOND EQUATION
M+D+B=1-
6+3+1=10
The required number of mice, deers, and birds are 3, 6, and 1 respectively.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements.
Here,
Let the number of mice be x and the number of birds is y
Number of Deers = 2x
There are a total of 10 animals,
mice + deer + bird = 10
x + 2x + y = 10
3x + y = 10
y = 10 - 3x - - - - - - -(1)
Legs of mouse = 4
Legs of deers = 4
Legs of birds = 2
Total number of legs = 38
4x + 4 * 2x + 2y = 38
4x + 8x + 2y =38
12x + 2y = 38 - - - - - - - (2)
Solving equations 1 and 2
12x + 2(10 -3x ) = 38
12x + 20 - 6x = 38
6x = 18
x = 3
Put x in equation 1
y = 10 - 3 * 3
y = 1
Now,
Mice= x = 3
Deers = 2x = 2 *3 = 6
Bird = y = 1
Thus, the required number of mice, deers, and birds are 3, 6, and 1 respectively.
Learn more about arithmetic here:
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The mean cost for a pint of frozen yogurt is $1.50, with a standard deviation of $0.10.
What is the value of the variance?
a.) $0.40
b.) $0.10
c.) $0.01
d.) $0.20
Answer:
The correct answer is:
0.01$ (c)
Step-by-step explanation:
Standard deviation is a measure of how spread out numbers are from the mean value. The formula for standard deviation is given by:
[tex]s = \sqrt{\frac{\sum(x - \bar x)}{n} } \\where:\\x = sample\ \\\bar x\ = mean\\n\ = number\ of\ samples\[/tex]
Variance is a measure of the squared differences from the mean.
Variance is simply the square of the standard deviation. It is mathematically shown as:
[tex]s^2 = \frac{\sum(x - \bar x)}{n} }[/tex]
Now in our example,
Stabnard deviation = $0.10
Variance = (standard deviation)²
Variance = (0.10)²
Variance = $0.01
Answer:
c.) $0.01
Step-by-step explanation:
Got it right.
Problem PageQuestion A circle has a radius of . Find the radian measure of the central angle that intercepts an arc of length . Do not round any intermediate computations, and round your answer to the nearest tenth
Answer:
0.1π radStep-by-step explanation:
The question is incomplete. Here is the complete question.
A circle has a radius of 19m . Find the radian measure of the central angle θ that intercepts an arc of length 5m. Do not round any intermediate computations, and round your answer to the nearest tenth.
The formula for calculating the length of an arc [tex]L = \frac{\theta}{360} * 2 \pi r[/tex]
θ is the central angle
r is the radius of the circle = 19m
L is the length of an arc = 5m
Substitute the given values into the formula and get the central angle θ
5 = θ/360 * 2(22/7)*19
5 = θ/2π * 119.4285714
θ/2π = 5/119.4285714
θ/2π = 0.041866
θ = 2π*0.041866
θ = 0.083732π
θ = 0.1π rad (to the nearest tenth)
Hence the radian measure of the central angle that intercepts an arc of length to the nearest tenth is 0.1π rad
112 equals 2 times the length minus 5
Answer:
l = 58.5
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Write out equation
112 = 2l - 5
Step 2: Isolate term l by adding 5 on both sides
117 = 2l
Step 3: Isolate l by dividing both sides by 2
117/2 = l
Step 4: Evaluate
l = 58.5
Answer:
[tex]\Large \boxed{l = \frac{117}{2}}[/tex]
Step-by-step explanation:
Let the length be [tex]l[/tex].
[tex]112 = 2 l - 5[/tex]
Adding 5 to both sides.
[tex]112 +5= 2 l - 5+5[/tex]
[tex]117 = 2 l[/tex]
Dividing both sides by 2.
[tex]\displaystyle \frac{117}{2} = \frac{2 l}{2}[/tex]
[tex]\displaystyle \frac{117}{2} = l[/tex]
Explain the order of operations you would use to evaluate (284) • 5-6+42. Then evaluate it.
Answer:
1456
Step-by-step explanation:
If there are parentheses what is inside comes first, then multiplication or division, last is addition and subtraction. If you have multiple division or multiplication you go in order left to right. Once it's down to addition and subtraction you also go left to right.
First we multiply 284 * 5 = 1420
Now we go in order.
1420 - 6 + 42
1414 + 42
1414 + 42 = 1456
The following rational equation has denominators that contain variables. for this equation, A. write the value or values of the variable that makes the denominator zero. These are the restrictions on the variable. B.
keeping the restrictions in mind, solve the equation.
3/x+4 + 2/x-4 = 16/(x+4)(x-4)
A. what is/ Are The value our values of the variable that make(s) the denominators zero?
x=
Answer:
A. -4 and 4
B. No solution.
Step-by-step explanation:
The given equation is
[tex]\dfrac{3}{x+4}+\dfrac{2}{x-4}=\dfrac{16}{(x+4)(x-4)}[/tex]
A.
Equate the denominators equal to 0 to find the restrictions on the variable.
[tex]x+4=0\Rightarrow x=-4[/tex]
[tex]x-4=0\Rightarrow x=4[/tex]
Therefore, [tex]x\neq -4,4[/tex].
B.
We have,
[tex]\dfrac{3}{x+4}+\dfrac{2}{x-4}=\dfrac{16}{(x+4)(x-4)}[/tex]
[tex]\dfrac{3(x-4)+2(x+4)}{(x+4)(x-4)}=\dfrac{16}{(x+4)(x-4)}[/tex]
Multiply both sides by (x-4)(x+4).
[tex]3x-12+2x+8=16[/tex]
[tex]5x-4=16[/tex]
Add 4 on both sides.
[tex]5x=16+4[/tex]
[tex]5x=20[/tex]
Divide both sides by 5.
[tex]x=4[/tex]
Here the solution is x=4 but it is the restricted value.
Therefore, the given equation has no solution.
For the given rational equation, we have that:
A. The values of the variable that make(s) the denominators zero are x = -4 and x = 4.B. The equation has no solution.Rational Equation:The rational equation given in this problem is:
[tex]\frac{3}{x + 4} + \frac{2}{x - 4} = \frac{16}{(x + 4)(x - 4)}[/tex]
Then, applying the least common factor:
[tex]\frac{3(x - 4) + 2(x + 4)}{(x + 4)(x - 4)} = \frac{16}{(x + 4)(x - 4)}[/tex]
[tex]\frac{5x - 4}{(x + 4)(x - 4)} - \frac{16}{(x + 4)(x - 4)} = 0[/tex]
[tex]\frac{5x - 20}{(x + 4)(x - 4)} = 0[/tex]
Item a:
The denominator cannot be zero, hence:
[tex](x + 4)(x - 4) \neq 0[/tex]
[tex]x \neq -4[/tex]
[tex]x \neq 4[/tex]
The values of the variable that make(s) the denominators zero are x = -4 and x = 4.
Item b:
[tex]5x - 20 = 0[/tex]
[tex]5x = 20[/tex]
[tex]x = \frac{20}{5}[/tex]
[tex]x = 4[/tex]
However, x = 4 makes the denominator zero, hence the equation has no solution.
You can learn more about rational functions at https://brainly.com/question/13136492
Evaluate.
(-4)=
(-7) = 0
Please help ASAP!!
(-4)³ = (-4)(-4)(-4) = 16(-4) = - 64
(-7)² = (-7)(-7) = 49
(-)×(-) = +
(-)×(+) = -
Solve for the indicated variable in each math formula. 1.C=2(3.14)r for r 2.A=1/2bh for b 3.y=Mx+b for x 4.A=1/2(a+b)h for h 5.V(3.14)r(r)h for h
Answer:
See below
Step-by-step explanation:
1. C = 2(3.14) for r
r = C / 3.28
2. A = 1/2 b h for b
b = A2 / h
3. y = Mx + b for x
y - b = Mx
x = (y - b) / M
4. A = 1/2 (a + b) h for h
A = (1/2a + 1/2b)h
A = 1/2ah + 1/2bh
A = (a + b) h / 2
h = 2A / (a + b)
5. V = (3.14) r² h for h
h = V / (3.14 r²)
Bell metal which is a form of bronze is used for casting bells. It is an alloy of copper and tin. To make bell metal requires 17 parts of copper to every 3 parts of tin. (6) (i) Express this requirement as a ratio (ii) Express the amount of tin required as a percentage of the total (iii) If the total amount of tin in a particular casting is 150 kg, find the amount of copper
Answer:
you need 17 parts copper and 3 parts tin in order to make brass
1. ratio of copper with respect to brass: 17:20
ratio of tin with respect to brass: 3:20
ratio of tin with respect to copper: 3:17
2. percentage of tin required in brass: fraction of tin in brass X 100
3/20 X 100 = 15%
3. if we used 150 kg tin in the alloy, then 150 kg is 15 % of the alloy
(from last answer)
150/x X 100 = 15%
x = 1000 kg
if the total brass formed is 1000 kg, and 150 kg of it is tin,
copper used = 1000 - 150 = 850 kg copper
5(6x+2)+4(5x+5)+4=50x+34
Answer:
0=0
Step-by-step explanation:
50x+34=50x+34
50x=50x
50x - 50x = 50x - 50x
0=0
Answer:
5(6x + 2)+4(5x+5)+4=50+34
multiply it then collect like terms
30x+15x+10+15+15+4=50+34
45x +54=50+34
so the 54 will cross over to the other side making it to be -54
45x=50+34-54
45x=30
the u divide both sides by 45
x= 45÷30
x=0.67
23. Due to an increase in taxes on electronic devices, the price of a 46" LED flat TV screen has increased
to £845, which is 30% increase of the original price.
What was the original price of the TV prior to the increase?
Answer:
£591.5
Step-by-step explanation:
First find the price increase by multiplying the new price by 30 percent . Then subtract the answer from the new price.
The original price of the TV prior to the increase is £650 and this can be determined by using the unitary method.
Given :
The price of a 46" LED flat TV screen has increased to £845, which is 30% increase of the original price.
The following steps can be used in order to determine the original price of the TV prior to the increase:
Step 1 - The unitary method can be used in order to determine the original price of the TV prior to the increase.
Step 2 - According to the given data, the increased price of the TV is £845 which is 130%.
Step 3 - Now, let the original price of the TV be 'x'.
Step 4 - So, the value of 'x' is:
[tex]x = \dfrac{100}{130}\times 845[/tex]
Step 5 - Simplify the above expression.
[tex]x = \dfrac{8450}{13}[/tex]
[tex]x = 650[/tex]
So, the original price of the TV prior to the increase is £650.
For more information, refer to the link given below:
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CAN SOMEONE PLEASE HELP ME ASAP PLEASEEEE!!!
Answer:
x = 12
Step-by-step explanation:
the other explanation might be confusing so here is the answer again to sum it up
The difference between the length and the
width of a rectangle is 5 centimeters. What is
the length (the longer side) of the rectangle, if
its perimeter is equal to 106 centimeters?
42 divided by 7 get a decimal answer
Answer:
6
Step-by-step explanation:
just put 6.00 bro it divides evenly
The Department of Transportation would like to test the hypothesis that the average age of cars on the road is less than 10 years. A random sample of 50 cars had an average age of 9.5 years. It is believed that the population standard deviation for the age of cars is 3.4 years. The Department of Transportation would like to set = 0.10. The critical value for this hypothesis test would be ________.
Answer:
0.1492
Step-by-step explanation:
Mean (m) = 9.5
Standard deviation (sd) = 3.4
Number of observations (n) = 50
Computing the test statistic :
X = 10
Z = (x - m) / standard error
Standard Error = sd/sqrt(n)
Z = (x - m) / (sd/sqrt(n))
Z = (10 - 9.5) / (3.4/sqrt(50))
Z = 0.5 / 0.4808326
Z = 1.0398 = 1.04
Using a P-value calculator, we can obtain the critical value with α = 0.10, hence, the critical value = 0.14917
= 0.1492
I WILL GIVE THE BRAINIEST
Which of the following could be a rational number?
A. the product of two irrational numbers.
B. the sum of two irrational numbers.
C. the product of a rational number and an irrational number.
D.the sum of a rational number and an irrational number
Answer:
A.
Step-by-step explanation:
the product of two irrational numbers
Answer:
the answer is A
Step-by-step explanation:
A. the product of two irrational numbers.
Lines L and M are parallel.
L
3/4
2/5
1/6
38° 7
-M
Find : m_3
belongs in the green box. [?]
?
o
Entor
Step-by-step explanation:
Hey, there!
Let's simply solve it.
As there is given that L and M are parallel. Use all the condition or properties of parallel lines.
Here use:
vertically opposite angle. coointerior angles sum is 180°.Now,
angle 6= 38° { Vertically opposite angle}.
angle 6 + angle 5 = 180° { as sum of coointerior angles are equal to 180°}
38°+angle 5 = 180°
or, angke 5 = 180°-38°
Therefore, angle 5 = 142°
Now, angle 3 = angle 5 { Vertically opposite angle}
Therefore, the measure of angle 3 is 142°.
[tex]hope \: it \: helps...[/tex]
Answer: 142
Step-by-step explanation:
Given the inequality 2y + 6 > 20 Graph a solution
Answer:
y > 7
Step-by-step explanation:
2y > 20-6
2y > 14
2y/2 > 14/2
y > 7
Answer: y>y (graphing see below)
Step-by-step explanation:
2y+6>20
2y>14
y>7
Hope this helps!! :)
Please let me know if you have any question
Money Eric returned from a trip to Las Vegas with
$300.00, which was 50% more money than he had at the
beginning of the trip. How much money did Eric have at
the beginning of his trip?
Answer:
$200
Step-by-step explanation:
money he has now is 150% of what he had in the beginning
300 = 1.5x
x = 200
if he had $200 in the beginning, you add half of that to itself (200 + 100 = 300)
Which of the following is the midpoint of a line segment with endpoints −4 and 7?(1 point) 1.5 0 5.5 −3
Answer:
1.5
Step-by-step explanation:
To find the midpoint, add the two coordinates and divide by 2
( -4+7)/2 =
3/2
1.5
The midpoint is 1.5
Answer:
1.5
Step-by-step explanation:
In this case the midpoint value is the average or mean of -4 and 7:
-4 + 7
--------- = 3/2 or 1.5
2
find the volume of the shaded figure by subtracting the smaller volume from the larger
Answer:
a. [tex] 9a^3 - 9ab^2 [/tex]
b. [tex] 9a(a^2 - b^2) [/tex]
Step-by-step explanation:
a.
[tex] Volume = l*w*h [/tex]
[tex] Volume_{smaller} = l*w*h [/tex]
Where, [tex] l = 9a, w = b, h = b [/tex]
[tex] Volume_{smaller} = 9a*b*b = 9ab^2 [/tex]
[tex] Volume_{larger} = l*w*h [/tex]
Where, [tex] l = 9a, w = a, h = a [/tex]
[tex] Volume_{smaller} = 9a*a*a = 9a^3 [/tex]
Volume of the shaded figure = [tex] 9a^3 - 9ab^2 [/tex]
b. [tex] 9a^3 - 9ab^2 [/tex] expressed in factored form:
Look for the term that is common to 9a³ and 9ab², then take outside the parenthesis.
[tex] 9a^3 - 9ab^2 = 9a(a^2 - b^2) [/tex]
Write an equation of a line with slope of that passes through (-6,9) and (1,-8) in point-slope form.
Answer:
[tex]y = - \frac{17}{7} x - 5 \frac{4}{7} [/tex]
Step-by-step explanation:
Please see attached picture for full solution.
The proper choice of toothbrush is important in dental care. On 14 patients, measures of Gingivitis were taken at the beginning of the experiment. After this, each was given an experimental toothbrush to be used for the next 45 days. Afterwards, dental exam measures were given again of these same individuals. The mean of the differences in scores was 5.5 with a sample standard deviation of 11.6. The mean score before the experiment was 56.4 with a sample standard deviation of 6.4 The mean score after the experiment was 60.6 with a sample standard deviation of 4.3 Let alpha = 0.05
What is the p value from the test of the previous hypothesis?
Answer:
The p-value of the test is 0.049.
Step-by-step explanation:
The dependent t-test (also known as the paired t-test or paired samples t-test) compares the two means associated groups to conclude if there is a statistically significant difference amid these two means.
In this case a paired t-test is used to determine whether the experimental toothbrush was effective or not.
The hypothesis for the test can be defined as follows:
H₀: The experimental toothbrush was not effective, i.e. d = 0.
Hₐ: The experimental toothbrush was effective, i.e. d < 0.
The information provided is:
[tex]\bar d=5.5\\S_{d}=11.6\\n=14[/tex]
Compute the test statistic value as follows:
[tex]t=\frac{\bar d}{S_{d}/\sqrt{n}}[/tex]
[tex]=\frac{5.5}{11.6/\sqrt{14}}\\\\=1.7740617\\\\\approx 1.774[/tex]
The test statistic value is 1.774.
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.
Compute the p-value of the test as follows:
[tex]p-value=P(t_{n-1}<1.774)[/tex]
[tex]=P(t_{13}<1.774)\\=0.049[/tex]
*Use a t-table.
The p-value of the test is 0.049.
p-value= 0.049 > α = 0.05
The null hypothesis will be rejected.
Thus, it can be concluded that experimental toothbrush was effective.
The distributive property of multiplication justifies which of the following statements? A 3x + 4(y – z) = 3x + 4(y) + 4(-z) B 3(x)+ 3(y) + 3(z) = 27(xyz) C 8 + (-8) = 0 D (a + b) + c = (c + a) + b
Answer:
The distributive property is used when we have to multiplicate a parenthesis:
[tex]a*(b+c) = ab+ac[/tex]
So the corrects andwer is A) 3x + 4(y-z) = 3x + 4y - 4z, because:
[tex]3x + 4(y-z) = 3x + 4*y + 4*(-z) = 3x + 4y - 4z[/tex]
B is incorrect, as [tex]3x + 3y + 3z 27\neq xyz[/tex]
C is correct, as a number plus his opposite is always 0.
D is correct, but that's the associate property as it's correct that for any three numbers of an associative set, there's another operation with verifies the equality.
Write the equivalent ratio
11:4= __:16
Answer:
the missing value is 44
Step-by-step explanation:
let the missing value be x
we can solve this by expressing both ratios as rational expressions
11:4 = x:16
[tex]\frac{11}{4} = \frac{x}{16}[/tex] (cross multiply the denominators to eliminate them)
(11)(16) = (4)(x)
4x = 176
x = 176 / 4
x = 44
hence the ration is
11:4 = 44 : 16