Step-by-step explanation:
Given,
a student (Charles) bought a car and sold it in 15 % profit for $4669.
we have the formula,
[tex]cp = \frac{sp \times 100}{100 + p\%} [/tex]
so,
[tex]cp = \frac{4669 \times 100}{100 + 15} [/tex]
by simplifying it we get,
CP is $4060.
Therefore, the cp was $4060.
Hope it helps...
Use Demoivres Theorem to find (-square root 3 +i)^6
Answer:
[tex]z=(-\sqrt{3}+i)^6[/tex] = -64
Step-by-step explanation:
You have the following complex number:
[tex]z=(-\sqrt{3}+i)^6[/tex] (1)
The Demoivres theorem stables the following:
[tex]z^n=r^n(cos(n\theta)+i sin(n\theta))[/tex] (2)
In this case you have n=6
In order to use the theorem you first find r and θ, as follow:
[tex]r=\sqrt{3+1}=2\\\\\theta=tan^{-1}(\frac{1}{\sqrt{3}})=30\°[/tex]
Next, you replace these values into the equation (2) with n=6:
[tex]z^6=(2)^6[cos(6*30\°)+isin(6*30\°)]\\\\z^6=64[-1+i0]=-64[/tex]
Then, the solution is -64
Answer:
A) -64
Step-by-step explanation:
Edge 2021
Lily is 14 years older than her little brother Ezekiel. In 8 years, Lily will be twice as old as Ezekiel will be then. What is Lily and Ezekiel's combined age?
Answer:
30 years
Step-by-step explanation:
let the age of Ezekiel be x years
Given
Lily is 14 years older than her little brother Ezekiel
Age of Lily = x + 14 years
Next condition
after 8 years\
age of Ezekiel = x+8
age of Lily = x + 8 +14 = x + 22 years
Given
. In 8 years, Lily will be twice as old as Ezekiel will be then.
Thus,
x + 22 = 2(x+8)
=> x + 22 = 2x + 16
=> 22-16 = 2x -x
=> x = 6
Thus, age of Ezekiel = 8 years
age of lily = 8+14 = 22 years
sum of their age = 22 + 8 = 30 years answer.
Find the volume o the sphere.
Answer:
The volume of sphere is 267.95 units³.
Step-by-step explanation:
Given that the formula of volume of sphere is V = 4/3×π×r³ where r represents radius. Then, you have to substitute the values into the formula :
[tex]v = \frac{4}{3} \times \pi \times {r}^{3} [/tex]
[tex]let \: r = 4[/tex]
[tex]v = \frac{4}{3} \times \pi \times {4}^{3} [/tex]
[tex]v = \frac{4}{3} \times \pi \times 64[/tex]
[tex]v = \frac{256}{3} \times 3.14[/tex]
[tex]v = 267.95 \: {units}^{ 3} [/tex]
What is 36/100 added with 4/10
Answer:
0.76 or 19/25
Step-by-step explanation:
Convert 4/10 so that it has a common denominator with 36/100.
4/10 x 10/10 = 40/100
Now that the denominator is the same, just add the top values.
40/100 + 36/100 = 76/100
We can also simplify the answer to be 19/25 by dividing the top and bottom by 4.
Answer:
19/25Step-by-step explanation:
[tex]\frac{36}{100}+\frac{4}{10}\\Let\: first\: deal\: with\: ;\frac{36}{100}\\\mathrm{Cancel\:the\:common\:factor:}\:4\\=\frac{9}{25}\\\\=\frac{9}{25}+\frac{4}{10}\\Now \:lets \:deal \:with ; \frac{4}{10}\\\mathrm{Cancel\:the\:common\:factor:}\:2\\=\frac{2}{5}\\=\frac{9}{25}+\frac{2}{5}\\\mathrm{Prime\:factorization\:of\:}25:\quad 5\times\:5\\\mathrm{Prime\:factorization\:of\:}5:\quad 5\\\mathrm{Multiply\:each\:factor\:the\:greatest\:number\:of\:times\:it\:occurs\:in\:either\:}25\mathrm{\:or\:}5\\[/tex]
[tex]\lim_{n \to \infty} a_n =5\cdot \:5\\\\\mathrm{Multiply\:the\:numbers:}\:5\cdot \:5=25\\=25\\\mathrm{Multiply\:each\:numerator\:by\:the\:same\:amount\:needed\:to\:multiply\:its}\\\mathrm{corresponding\:denominator\:to\:turn\:it\:into\:the\:LCM}\:25\\\mathrm{For}\:\frac{2}{5}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}5\\\frac{2}{5}=\frac{2\times \:5}{5\times \:5}=\frac{10}{25}\\=\frac{9}{25}+\frac{10}{25}\\[/tex]
[tex]\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\=\frac{9+10}{25}\\\\=\frac{19}{25}[/tex]
The population, p, in thousands of a resort community is given by P(t)=700t/4t[tex]x^{2}[/tex]+9
Answer:
Step-by-step explanation:
pt=700 is basically evaluate it form the bottom to the top and u must mark me as brainly
Subtract the rational expressions: (x/x+2)-(2/x)
Simplify the following algebraic expression.
square root of 392x^7
Answer:
[tex] \sqrt{392 {x}^{7} } [/tex]
Simplify
that's
[tex] \sqrt{392} \times \sqrt{ {x}^{7} } \\ \\ = \sqrt{196 \times 2} \: \times \sqrt{ {x}^{7} } \\ \\ = 14 \sqrt{2} \times \sqrt{ {x}^{7} } \\ \\ = 14 \sqrt{2x ^{7} } [/tex]
Hope this helps you
Find the distance between the points (–9, 0) and (2, 5). Find the distance between the points (–9, 0) and (2, 5).
Answer:
sqrt( 146)
Step-by-step explanation:
To find the distance, we use the following formula
d = sqrt( ( x2-x1) ^2 + ( y2-y1) ^2)
sqrt( ( -9-2) ^2 + ( 0-5) ^2)
sqrt( ( -11) ^2 + ( -5) ^2)
sqrt( 121+25)
sqrt( 146)
(08.05 LC)The histogram shows the number of prizes won by different numbers of students at a quiz competition. Which of the following statements is correct regarding the number of students and the number of prizes won? A histogram titled Prizes Won is shown. The horizontal axis is labeled Number of Prizes with bins 0 to 5, 6 to 11, 12 to 17, and 18 to 23. The vertical axis labeled Students with values from 0 to 10 at intervals of 1. The first bin goes to 2, the second goes to 7, the third goes to 4, and the last goes to 10. A) A total of 10 students won all the prizes. B) Four students won 12, 13, 14, 15, 16, or 17 prizes. C) A total of 10 prizes were won by all the students. D) Four prizes were won by 12, 13, 14, 15, 16, or 17 students.
Answer: B.
Four students won 12, 13, 14, 15, 16, or 17 prizes
Answer:
Four students won 12, 13, 14, 15, 16, or 17 prizes!
Step-by-step explanation:
write the statement for 6x-3=9
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
The statement for [tex]6x - 3 = 9[/tex] is :
[tex]\boxed{Six (x) .minus. Three .equals. Nine.}[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hope this helped you.
Could you maybe give brainliest..?
❀*May*❀
Write the equation of a line through the given point with the given slope (0,6);m undefined
Answer:
x=0
Step-by-step explanation:
If the slope is undefined, the line is vertical
vertical lines are of the form
x =
Since the point is (0,6)
x=0
A study is done to see if the average age a "child" moves permanently out of his parents' home in the United States is at most 23. 43 U.S. Adults were surveyed. The sample average age was 24.2 with a standard deviation of 3.7. The p-value is
Answer:
The p-value is 2.1%.
Step-by-step explanation:
We are given that a study is done to see if the average age a "child" moves permanently out of his parents' home in the United States is at most 23. 43 U.S. Adults were surveyed.
The sample average age was 24.2 with a standard deviation of 3.7.
Let [tex]\mu[/tex] = true average age a "child" moves permanently out of his parents' home in the United States.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 23 {means that the average age a "child" moves permanently out of his parents' home in the United States is at most 23}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 23 {means that the average age a "child" moves permanently out of his parents' home in the United States is greater than 23}
The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample average age = 24.2
s = sample standard deviation =3.7
n = sample of U.S. Adults = 43
So, the test statistics = [tex]\frac{24.2-23}{\frac{3.7}{\sqrt{43} } }[/tex] ~ [tex]t_4_2[/tex]
= 2.127
The value of t-test statistics is 2.127.
Now, the p-value of the test statistics is given by;
P-value = P( [tex]t_4_2[/tex] > 2.127) = 0.021 or 2.1%
Write these numbers in standard form 906000000
Answer:
9.06×10 to the power of 8(8 is superscript above 10)
Answer:
9.06 x 10^8
Step-by-step explanation:
906000000 = 9.06 x 10^8
8 decimal places in
Find a formula for an for the arithmetic sequence.
Answer:
a(n)= a(n+1)+4
Step-by-step explanation:
The first terms of this sequence are: 4,0, -4, -8, -12
Let 4 be a0 and 0 a1.
● a1-a0 = 0-4
●a1-a0 = -4
●a1 = -4+a0
So this relation links the first term with the second one.
replace 1 in a1 with n.
0 in a0 will be n-1
● an = -4+a(n-1)
Add one in n
● a(n+1) = a(n)-4
● a(n) = a(n+1)+4
This afternoon, Vivek noticed that the temperature was above zero when the temperature was 17 5/8 degrees. Its evening now, and the temperature is -8 1/2 degrees. What does this mean?
Answer:
The temperature droped from 17 5/8° C to - 8 1/2° C = 26 1/8° C, simply add the 2 mixed fractions together and you'll get the temperture change.
Step-by-step explanation:
Convert to a mixed number:
209/8
Divide 209 by 8:
8 | 2 | 0 | 9
8 goes into 20 at most 2 times:
| | 2 | |
8 | 2 | 0 | 9 |
- | 1 | 6 | |
| | 4 | 9 |
8 goes into 49 at most 6 times:
| | 2 | 6 |
8 | 2 | 0 | 9 |
- | 1 | 6 | |
| | 4 | 9 |
| - | 4 | 8 |
| | | 1 |
Read off the results. The quotient is the number at the top and the remainder is the number at the bottom:
| | 2 | 6 | (quotient)
8 | 2 | 0 | 9 |
- | 1 | 6 | |
| | 4 | 9 |
| - | 4 | 8 |
| | | 1 | (remainder)
The quotient of 209/8 is 26 with remainder 1, so:
Answer: 26 1/8° C
using the horizontal line test, which of the following can be confused about the inverse of the graph?
Answer:
I think D
Step-by-step explanation:
Verticle or horizontal line test, it would be a function either way
How many even 3 digit positive integers can be written using the numbers 3,4,5,6,and 7?
Answer:
I got 45, but I may be wrong.
Step-by-step explanation:
When a number is even, the number must end in an even number. Here, the even numbers are 4 and 6, so the numbers we are going to create are all going to end in 4 and 6.
To answer this question, we just have to find as many possible combinations following the guidelines provided.
334
344
354
364
374
434
444
454
464
474
534
544
554
564
574
634
644
654
664
674
336
346
356
366
376
436
446
456
466
476
536
546
556
566
576
636
646
656
666
676
736
746
756
766
776
1. for what constant k must f(k) always equal the constant term of f(x) for any polynomial f(x) 2. If we multiply a polynomial by a constant, is the result a polynomial? 3. if deg(f+g) is less than both deg f and deg g, then must f and g have the same degree?
Answer:
1. k=0
2. yes, result is still a polynomial.
3. yes, f and g must have the same degree to have deg(f+g) < deg(f) or deg(g)
Step-by-step explanation:
1. for what constant k must f(k) always equal the constant term of f(x) for any polynomial f(x)
for k=0 any polynomial f(x) will reduce f(k) to the constant term.
2. If we multiply a polynomial by a constant, is the result a polynomial?
Yes, If we multiply a polynomial by a constant, the result is always a polynomial.
3. if deg(f+g) is less than both deg f and deg g, then must f and g have the same degree?
Yes.
If
deg(f+g) < deg(f) and
deg(f+g) < deg(g)
then it means that the two leading terms cancel out, which can happen only if f and g have the same degree.
find the slope for (-4,-2)(-3,-6)
Answer:
The slope is -4.
Step-by-step explanation:
The values -2 and -6 are 4 values apart.
The values -4 and -3 are 1 value apart.
Since the second coordinate is lower than the first one, the slope of this is negative.
4 / 1 = 1
Negating 1 gets us -1.
Hope this helped!
Answer:
[tex] \frac{y}{x} = \frac{ - 4}{1} = - 4[/tex]
Step-by-step explanation:
[tex]x = ( - 3) - ( - 4) = 1[/tex]
[tex]y = ( - 6) - ( - 2) = - 4[/tex]
A photoconductor film is manufactured at a nominal thickness of 25 mils. The product engineer wishes to increase the mean speed of the film and believes that this can be achieved by reducing the thickness of the film to 20 mils. Eight samples of each film thickness are manufactured in a pilot production process, and the film speed (in microjoules per square inch) is measured. For the 25-mil film, the sample data result is: Mean Standard deviation 1.15 0.11 For the 20-mil film the data yield: Mean Standard deviation 1.06 0.09 *Note: An increase in film speed would lower the value of the observation in microjoules per square inch. We may also assume the speeds of the film follow a normal distribution. Use this information to construct a 98% interval estimate for the difference in mean speed of the films. Does decreasing the thickness of the film increase the speed of the film?
Answer:
A 98% confidence interval estimate for the difference in mean speed of the films is [-0.042, 0.222].
Step-by-step explanation:
We are given that Eight samples of each film thickness are manufactured in a pilot production process, and the film speed (in microjoules per square inch) is measured.
For the 25-mil film, the sample data result is: Mean Standard deviation 1.15 0.11 and For the 20-mil film the data yield: Mean Standard deviation 1.06 0.09.
Firstly, the pivotal quantity for finding the confidence interval for the difference in population mean is given by;
P.Q. = [tex]\frac{(\bar X_1 -\bar X_2)-(\mu_1- \mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ~ [tex]t__n_1_+_n_2_-_2[/tex]
where, [tex]\bar X_1[/tex] = sample mean speed for the 25-mil film = 1.15
[tex]\bar X_1[/tex] = sample mean speed for the 20-mil film = 1.06
[tex]s_1[/tex] = sample standard deviation for the 25-mil film = 0.11
[tex]s_2[/tex] = sample standard deviation for the 20-mil film = 0.09
[tex]n_1[/tex] = sample of 25-mil film = 8
[tex]n_2[/tex] = sample of 20-mil film = 8
[tex]\mu_1[/tex] = population mean speed for the 25-mil film
[tex]\mu_2[/tex] = population mean speed for the 20-mil film
Also, [tex]s_p =\sqrt{\frac{(n_1-1)s_1^{2}+ (n_2-1)s_2^{2}}{n_1+n_2-2} }[/tex] = [tex]\sqrt{\frac{(8-1)\times 0.11^{2}+ (8-1)\times 0.09^{2}}{8+8-2} }[/tex] = 0.1005
Here for constructing a 98% confidence interval we have used a Two-sample t-test statistics because we don't know about population standard deviations.
So, 98% confidence interval for the difference in population means, ([tex]\mu_1-\mu_2[/tex]) is;
P(-2.624 < [tex]t_1_4[/tex] < 2.624) = 0.98 {As the critical value of t at 14 degrees of
freedom are -2.624 & 2.624 with P = 1%}
P(-2.624 < [tex]\frac{(\bar X_1 -\bar X_2)-(\mu_1- \mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] < 2.624) = 0.98
P( [tex]-2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] < [tex]2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] < ) = 0.98
P( [tex](\bar X_1-\bar X_2)-2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] < ([tex]\mu_1-\mu_2[/tex]) < [tex](\bar X_1-\bar X_2)+2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ) = 0.98
98% confidence interval for ([tex]\mu_1-\mu_2[/tex]) = [ [tex](\bar X_1-\bar X_2)-2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] , [tex](\bar X_1-\bar X_2)+2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ]
= [ [tex](1.15-1.06)-2.624 \times {0.1005 \times \sqrt{\frac{1}{8}+\frac{1}{8} } }[/tex] , [tex](1.15-1.06)+2.624 \times {0.1005 \times \sqrt{\frac{1}{8}+\frac{1}{8} } }[/tex] ]
= [-0.042, 0.222]
Therefore, a 98% confidence interval estimate for the difference in mean speed of the films is [-0.042, 0.222].
Since the above interval contains 0; this means that decreasing the thickness of the film doesn't increase the speed of the film.
Please answer in the form of an angle or degree
Step-by-step explanation:
angle A = angle B( Corresponding angles)
so,
5x - 5 = 3x + 13
=> 5x - 3x = 13 + 5
=> 2x = 18
=> x = 9
angle B = 3x + 13 = (3×9) + 13 = 27 + 13 = 40
Answer:
x=9, ∠B=40
Step-by-step explanation:
In this case, ∠A≅∠B, as they are corresponding angles. Therefore, if you set up the equation to be 5x-5=3x+13,
2x=18, x=9
∠B=3(9)+13=27+13=40
Pleased help with this
Answer:
A
Step-by-step explanation:
How do I tell if scatterplot is linear?
express 3.222......in p/q form
Answer:
3.22222...... = [tex]\frac{29}{9}[/tex]
Step-by-step explanation:
In this question we have to convert the number given in recurrent decimals into fraction.
Recurrent decimal number is 3.22222.......
Let x = 3.2222......... -------(1)
Multiply this expression by 10.
10x = 32.2222........... -------(2)
Now subtract the expression (1) from (2),
10x = 32.22222.....
x = 3.22222.......
9x = 29
x = [tex]\frac{29}{9}[/tex]
Therefore, recurrent decimal number can be written as [tex]\frac{29}{9}[/tex] which is in the form of [tex]\frac{p}{q}[/tex].
-6+4q+(-6q)−6+4q+(−6q)minus, 6, plus, 4, q, plus, left parenthesis, minus, 6, q, right parenthesis ?
Answer:
-16-5q
Step-by-step explanation:
-6+4q-6q-6+4q-6q-6+4q-6q= -18-6q
Answer:C
Step-by-step explanation: 100% correct I did it on Khan Academy
Shannon went to an auto repair shop and paid $339.50, which included parts that cost $112 and 3.5 hours of labor. Joni went to an auto repair shop and paid $455, which included parts that cost $310 and 2.5 hours of labor. Which correctly compares the cost of the labor? Shannon paid $7 more per hour for labor. Shannon paid $7 less per hour for labor. Joni paid $85 more per hour for labor. Joni paid $85 less per hour for labor.
for labor. Joni paid $85 less per hour for labor. explanation:
The correct comparison of the cost of labor between Shannon and Joni is that Shannon paid $7 more per hour for labor.
What is the cost?It refers to the total amount of the expenditure done on a product in manufacturing or procuring.
What is labor cost?It refers to the expenditure done on procuring labor for the work.
How to calculate per hour labor cost?In our situation Shannon paid total $339.50 in which the cost of the parts is $112 and 3.5 hours of labor. So,
labor cost Shannon Paid=339.50-112
=$227.50
labor cost per hour=227.50/3.5
=$6.5 per hour
Joni paid total $455 in which the cost of spare parts is $310 and rest is labor
labor cost paid by Joni=455-310
=$145
labor cost per hour=145/2.5
=$58 per hour
So by doing comparing we found that Shannon had paid $6 per hour extra for labor.
Learn more about cost at https://brainly.com/question/1153322
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If the wavelength of the violet color is 400 nm, what is the value of its frequency?
Hi there! Hopefully this helps!
-------------------------------------------------------------------------------------------------- The frequency is ~7.5*1014 Hz
Since visible light has a wavelength spectrum of ~400 nm to ~700 nm, Violet light has a wavelength of ~400 nm and a frequency of ~7.5*1014 Hz.
Step-by-step explanation:
Speed = wavelength × frequency
3×10⁸ m/s = (400×10⁻⁹ m) f
f = 7.5×10¹⁴
What single transformation maps Triangle ABC onto A’B’C’
Answer:
Your answer is B
Step-by-step explanation:
rotating about/around the origin taking a shape and rotating it with the same values but around the point (0,0). so rotating your shape ABC around (0,0) with the same value would give you the shape A'B'C'
what is the slop of y= -5+4x
Hey there! :)
Answer:
m = 4.
Step-by-step explanation:
We are given the formula y = -5 + 4x. Rearrange the equation to be in proper slope-intercept form (y = mx + b)
Where 'm' is the slope and 'b' is the y-intercept. Therefore:
y = -5 + 4x becomes y = 4x - 5
The 'm' value is equivalent to 4, so the slope of the equation is 4.
Answer:
4
Step-by-step explanation:
because of y= mx + b where m is the slope
m= 4 in the equation
A landscaping company charges $50 per cubic yard of mulch plus a delivery charge of $24. Find a
linear function which computes the total cost C(in dollars) to deliver a cubic yards of mulch.
C(x) =
Answer: c(x) = $50*x + $24
Step-by-step explanation:
First, this situation can be modeled with a linear equation like:
c(x) = s*x + b
where c is the cost, s is the slope, x is the number of cubic yards of mulch bought, and b is the y-intercept ( a constant that no depends on the number x)
Then we know that:
The company charges $50 per cubic yard, so the slope is $50
A delivery charge of $24, this delivery charge does not depend on x, so this is the y-intercept.
Then our equation is:
c(x) = $50*x + $24
This is:
"The cost of buying x cubic yards of mulch"