Answer:
z-method: (66.26, 75.18)
Step-by-step explanation:
We have the standard deviation for the population, which means that we use the z-distribution to solve this question.
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96\frac{16.25}{\sqrt{51}} = 4.46[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 70.72 - 4.46 = 66.26
The upper end of the interval is the sample mean added to M. So it is 70.72 + 4.46 = 75.18
The correct answer is z-method: (66.26, 75.18)
wrate 10 as a fraction of 30
Answer:
[tex]\frac{10}{30}[/tex]
Step-by-step explanation:
Answer:
10/30
Step-by-step explanation:
A natural number is choosen at random from the 100 natural number. what is the probability that number so chosen is devisible by 3?
Answer:
33/100
Step-by-step explanation:
The 100 natural numbers are from 1-100.
In order to find the total numbers divisible by 3, divide 100 by 3:
100/3 = 33.33
Put 33.33 into integer form:
33.33 ==> 33 numbers divisible by 3.
Divide 33 by 100 to get the probability: 33/100
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URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100
POINTS!!!
Answer: the answer is A
Step-by-step explanation:
i need big help on this question please
make g the subject of the formula w=7-/sqrt g
Answer:
Below
Step-by-step explanation:
w = 7 - sqrt (g) ?? ( syntax is unclear in your post)
sqrt(g) = 7-w
g = (7-w)^2
The Beta Club plans a dance as a fund-raiser. The band costs $650, decorations cost $45, and the refreshments cost $2.20 per person. The admission tickets are $6 each.
(a) How many tickets must be sold to break even?
(b) How many tickets must be sold to clear $700?
(c) If admission tickets are $7.50 each, how many must be sold to clear $700?
183 tickets must be sold to break even. The price at which a good or service must be provided in order to recoup its expenses of production.
How many tickets must be sold to break even?The price at which an asset must be sold in order to recover its acquisition and ownership costs is known as the break-even price. It can also be used to describe the price at which a good or service must be provided in order to recoup its expenses of production.The band costs $650,
decorations cost $45
refreshments cost $2.20 per person
let x be the no of ticket
Total cost = 650+ 45+ 2.20x
break even
tickets cost = $6
6x = 650+ 45+ 2.20x
6 x - 2.20x = 695
3.8 x = 695
x = 182.89
183 tickets must be sold to break even.
tickets must be sold to clear $700
700/6 =116.6
700/ 7.5 = 93.33
117 tickets must be sold to clear $700
94 tickets must be sold to clear $700, If admission tickets are $7.50 each.
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Compute the following and write in the form x+iy :
[tex]\frac{1+2i}{3-4i} + \frac{2-i}{5i}[/tex]
[tex] \Large{\boxed{\sf \dfrac{1 + 2i}{3 - 4i} + \dfrac{2 - i}{5i } = - \dfrac{2}{5}}} [/tex]
[tex] \\ [/tex]
Explanation:Given sum:
[tex] \sf \: \dfrac{1+2i}{3-4i} + \dfrac{2-i}{5i}[/tex]
[tex] \\ [/tex]
We can simplify the sum only if the denominators of the two fractions are the same. Since they are different, we have to multiply the numerator and the denominator of each fraction by the denominator of the other one.
[tex] \sf \: \dfrac{1+2i}{3-4i} + \dfrac{2-i}{5i} = \dfrac{5i(1 + 2i)}{5i(3 - 4i)} + \dfrac{(3 - 4i)(2 - i)}{(3 - 4i)5i} \\ \\ \\ \sf \: = \dfrac{5i + 10 {i}^{2} }{15i - 20 {i}^{2} } + \dfrac{6 - 3i - 8i + 4 {i}^{2} }{15i - 20 {i}^{2} } [/tex]
[tex] \\ [/tex]
Replace i² with -1:
[tex] \sf \dfrac{5i + 10 {i}^{2} }{15i - 20 {i}^{2} } + \dfrac{6 - 3i - 8i + 4 {i}^{2} }{15i - 20 {i}^{2} } \: \\ \\ \\ \\ \sf \: = \dfrac{5i + 10( - 1)}{15i - 20( - 1)} + \dfrac{ 6 - 11i + 4( - 1)}{15i - 20( - 1)} \\ \\ \\ \\ \sf = \dfrac{5i - 10}{20 + 15i} + \dfrac{2 - 11i}{20 + 15i} [/tex]
[tex] \\ [/tex]
Simplify the expression:
[tex] \sf = \dfrac{5i - 10}{20 + 15i} + \dfrac{2 - 11i}{20 + 15i} \\ \\ \\ \\ \sf \: = \dfrac{5i - 10 + 2 - 11i}{ 20 + 15i} = \sf \dfrac{ - 8 - 6i}{20 + 15i}[/tex]
[tex] \\ [/tex]
To write our solution in the x + iy form, also known as the algebraic form, we have to understand what the conjugate of a complex number is.
[tex] \textsf{Let z be our complex number, and} \: \overline{\sf z} \: \textsf{its conjugate.} [/tex]
[tex] \\ [/tex]
The conjugate of z, [tex] \overline{ \sf z}, [/tex] is the complex number formed of the same real part as z but of the opposite imaginary part.
Since x is the real part of z, and y is its imaginary part, this can be expressed as:
[tex] \sf If \: z = x + iy \:, then \: \overline{ \sf z} = x - iy [/tex]
[tex] \\ [/tex]
Now, we have to multiple both the denominator and the numerator of our fraction by the conjugate of its denominator:
[tex]\sf \dfrac{ - 8 - 6i}{20 + 15i} = \dfrac{( - 8 - 6i)( \overbrace{20 - 15i}^{ \overline{z}}) }{ (20 + 15i)( \underbrace{20 - 15i}_{ \overline{z}}) } \\ \\ \\ \sf = \dfrac{ - 160 + 120i - 120i + 90 {i}^{2} }{400 - 300i + 300i - 225 {i}^{2} } \\ \\ \\ \sf = \dfrac{ - 160 + 90 {i}^{2} }{400 - 225 {i}^{2} }[/tex]
[tex] \\ [/tex]
One more time, substitute -1 for i²:
[tex] \sf \: \dfrac{ - 160+ 90 {i}^{2} }{400 - 225 {i}^{2} } \: = \dfrac{ - 160 + 90( - 1)}{400 - 225( - 1)} \\ \\ \\ \sf = \boxed{\sf - \dfrac{ 250}{625}} [/tex]
[tex] \\ [/tex]
Finally, let's simplify our result:
[tex] \sf - \dfrac{250}{625} = - \dfrac{2 \times 125}{5 \times 125} = \boxed{ \boxed{ \sf - \dfrac{2}{5}}}[/tex]
[tex] \\ \\ [/tex]
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(x + 10)(3x² + 5x - 2)
To expand the expression (x + 10)(3x² + 5x - 2), we can use the distributive property, which states that for any numbers a, b, and c, the product (a + b)(c) can be written as a * c + b * c. Applying this property to the given expression, we get (x + 10)(3x² + 5x - 2) = (x * 3x² + 10 * 3x²) + (x * 5x + 10 * 5x) + (x * -2 + 10 * -2) = 3x³ + 30x² + 5x² + 50x - 2x - 20. Combining like terms, we get 3x³ + 35x² + 51x - 20. Thus, the expanded form of the expression (x + 10)(3x² + 5x - 2) is 3x³ + 35x² + 51x - 20.
ANSWER NOW NEED HELP
A red die, a blue die, and a green die
are rolled. Each die is labeled 1 to 6.
Find the probability of each event:
a) a 2 on the red die, a 3 on the blue
die, and a 4 on the green die
b) a 4 on the red die, an even number
on the blue die, and a number less
then 3 on the green die
Answer:
a)1/216
b)1/36
Step-by-step explanation:
p(2r)and p(3b) and p(4g)
1/6×1/6×1/6=1/216
p(4r) and p(even b) and p(no less than 3)
1/6×3/6×2/6=1/36
4.
a) Find four consecutive even integers such that twice the sum of the second and third exceeds 3 times the first by 32.
b) The difference between two numbers is 24. Find the numbers if their sum is 88.
5.
a) Separate 60 into two parts so that 3 times the smaller added to 6 more than 6 times the smaller = 60.
b) A train traveled 300 miles. How long did the trip take if the train was traveling at a rate of: Note * Use the d=rt formula (distance = rate * time). NOTE: You may not be able to solve for the variable. If you do not have enough information to solve for the variable then write the equation.
1) 50 mph
2) 70 mph
3) x mph
4) (x+10)mph
5) (x-5)mph
The first, second, third, and fourth consecutive even integers must be greater than 10, 12, 14, and 16 respectively.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Let the four consecutive even integers be n, (n + 2), (n + 4) and (n + 6).
Such that twice the sum of the second and third exceeds 3 times the first by 32.
2{(n + 2) + (n + 4)} > 3(n) + 32.
2n + 4 + 2n + 8 > 3n + 32.
4n - 3n > 32 - 12.
n > 10.
So, the consecutive even numbers must all be greater than 10.
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What is an equation of the line that passes through the points (-3, 8) and (6, 2)?
Answer:
y = (-2/3)x + 6
Step-by-step explanation:
To find the equation of the line that passes through the points (-3, 8) and (6, 2), we can use the slope-intercept form of the equation of a line, which is:
y = mx + b
where m is the slope of the line and b is the y-intercept, which is the point where the line crosses the y-axis.
To find the slope of the line, we can use the following formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line. Plugging in the coordinates of the two points given in the problem, we get:
m = (2 - 8) / (6 - (-3)) = -6/9 = -2/3
Next, we need to find the y-intercept of the line. This is the point where the line crosses the y-axis, which means that the x-coordinate of this point is 0. Since we know the slope of the line and one of the points that it passes through, we can use the point-slope form of the equation of a line to find the y-intercept:
y - y1 = m(x - x1)
Substituting the values we have calculated above and setting x = 0, we get:
y - 8 = (-2/3)(0 - (-3))
Solving for y, we find that the y-intercept is 8 - (2/3) * 3 = 8 - 2 = 6.
Therefore, the equation of the line that passes through the points (-3, 8) and (6, 2) is:
y = (-2/3)x + 6
Given the following piecewise function, evaluate ƒ(–2).
f(x) =
50+4 r
3x+3 x
2
2
Answer:
2
Step-by-step explanation:
Solve the equation for x
Answer:
Question 35x + 100 = 7x + 30
100 - 30 = 7x - 5x
70 = 2x
x = 35
Question 43y + 16 = 5y
16 = 5y - 3y
16 = 2y
y = 8
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-________________________________
5(x+20) = 7x + 30=> 5x + 100 = 7x + 30
=> 100 – 30 = 7x – 5x
=> 70 = 2x
=> x = 70/2
=> x = 35
The value of x is 35.
________________________________
3y + 16 = 5y=> 16 = 5y – 3y
=> 16 = 2y
=> y = 16/2
=> y = 8
The value of y is 8.
_______________________________
"A number n equals 7 more than half the number"
The number 'n' is equal to 14
In the question, we have been given that the number n is equal to 7 more than half of the number 'n'.
So in these linear equation-solving types of problems, first of all, we convert the written sentence into an equation.
So the equation for the following problem statement is -
n = 7 + n/2
{since we have been given the number equals 7 more than half of the number }
Solving the equation we have,
n = 14.
We can easily see that 14 is the number which is 7 more than half of itself.
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Find the width (in m) of the river in the illustration. (Round your answer to three significant digits.)
44°
100 m
Answer:
[tex]w \approx 96.6 \, \textrm{m}[/tex]
Step-by-step explanation:
See the attached image for my labeled diagram.
To solve for [tex]w[/tex], we can use the trigonometric ratio tangent.
[tex]\tan(\theta)=\dfrac{\textrm{opposite}}{\textrm{adjacent}}[/tex]
[tex]\tan(44\textdegree)=\dfrac{w}{100 \, \textrm{m}}[/tex]
↓ multiply both sides by 100m
[tex]100 \, \textrm{m} \cdot \tan(44\textdegree)=w[/tex]
↓ plug [tex]100\, \textrm{m} \cdot \tan(44\textdegree)[/tex] into a calculator
[tex]96.56887 \, \textrm{m} \approx w[/tex]
[tex]w \approx 96.56887 \, \textrm{m}[/tex]
↓ round to 3 significant figures
[tex]w \approx 96.6 \, \textrm{m}[/tex]
The average mass of Stephen, Shamsul and Saravanan is 64 kg. Stephen's mass is 72 kg Shamsul's mass is 1.5 times Saravanan's mass Calculate Shamsul's mass in kg.
Answer:
72kg
Step-by-step explanation:
Stephen = 72
Saravanan = x
Shamsul = (x • 1.5) since Shamsul's mass is 1.5 times Saravanan's mass
1. make an equation:
( 72 + x + (x • 1.5) ) ÷ 3 = 64
2. solve it:
( 72 + x + (x • 1.5) ) ÷ 3 = 64
( 72 + x + (x • 1.5) ) = 64 • 3
( 72 + x + (x • 1.5) ) = 192
x + 1.5x = 192 - 72
2.5x = 120
x = 120 ÷ 2.5
x = 48
Thus shamsul's mass is:
48 • 1.5 = 72kg
Solve for h. If you answer, you get 14 points
Answer: 24
Step-by-step explanation:
Answer:
h = 24
Step-by-step explanation:
Courtney would like to estimate the net worth of all people in the US. The distribution of net worth of people in the
US is strongly skewed to the right. Courtney selects an SRS of size n = 15 from this population and calculates the
sample mean. What is the shape of the distribution of the sample mean for all possible simple random samples of
size 15 from this population?
The distribution of the sample mean for all possible simple random samples of size 15 from the population of net worth in the US will be approximately normal, with a mean of μ and a standard deviation of σ/√15.
Courtney's estimate of the net worth of all people in the US is strongly skewed to the right. This means that the majority of the population has a net worth that is lower than the average net worth. When Courtney selects an SRS of size n = 15 from this population and calculates the sample mean, the shape of the distribution of the sample mean for all possible simple random samples of size 15 from this population will be approximately normal.
The Central Limit Theorem states that if a population has a mean of μ and a standard deviation of σ, then the sampling distribution of the sample mean will be approximately normal, no matter what the shape of the population distribution is, as long as the sample size is large enough. Since Courtney's sample size of 15 is large enough, the sampling distribution of the sample mean will be approximately normal.
The sample mean will have a mean of μ, which is the population mean, and a standard deviation of σ/√n, where n is the sample size. Since Courtney's sample size is 15, the standard deviation of the sample mean will be σ/√15. This means that the sample mean will be normally distributed with a mean of μ and a standard deviation of σ/√15.
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I need help, I’m trying to find the translation and scale factor.
Answer:
Translation: 4 to the right and 8 up.
Scale factor: 3
Step-by-step explanation:
If you move CDE 4 spaces to the right and 8 spaces up C and C' will match up. If you dilate (make bigger) CDE 3 times it will perfectly be C'D'E'.
6 Bob is flying to Croatia for a holiday. When he gets to the airport, he discovers that they
hove a new pricing system for luggage. 2 items of hand luggage plus 1 item to go in the hold
costs £86. 1 item of hand luggage and a piece of luggage to go in the hold costs £66. How
much does it cost to put an item of luggage in the hold?
DP BOOT
Answer:
£46
Step-by-step explanation:
You want to know the cost of luggage in the hold when 2 in the hand and 1 in the hold is £86, and 1 in the hand and 1 in the hold is £66.
RelationsLet 'a' and 'b' represent the costs of a piece of hand luggage and one in the hold, respectively. Then the given relations are ...
2a +b = 86
a +b = 66
SolutionSubtracting the first equation from twice the second gives ...
2(a +b) -(2a +b) = 2(66) -(86)
b = 46 . . . . . . . simplify
It costs £46 to put an item of luggage in the hold.
4. Caroline baked cookies from a recipe that called for 2 cup of sugar. She planned to triple the recipe.
How much sugar did she need?
Answer:
Step-by-step explanation: So First you would need to multiply 2x3 because if you need to triple two cups you have to multiply so the answer is 6 cups
3/4 of a peice of metal has a mass of 15kg. What is the mass of 2/5 of the peice of metal?
Answer:
Step-by-step explanation:
Let total mass be x
(3/4)*x=15
on solving
x=20
now,
mass of 2/5 of piece of metal is-
=> (2/5)*20
=> 8
Ans- 8kg
Find the linearization of f(x) = √ x at a = 4
Answer:
Step-by-step explanation:
To find the linearization of the function f(x) = sqrt(x) at x = a, we can use the linearization formula:
f(x) ≈ f(a) + f'(a) (x - a)
To use this formula, we first need to find the value of f(a) and f'(a). At x = a = 4, the value of f(x) is f(4) = sqrt(4) = 2. The derivative of f(x) is f'(x) = 1/(2 * sqrt(x)), so the value of f'(a) is f'(4) = 1/(2 * sqrt(4)) = 1/4.
Substituting these values into the linearization formula, we get:
f(x) ≈ 2 + 1/4 (x - 4)
This is the linearization of f(x) = sqrt(x) at x = 4. It is an approximation of the function f(x) that is valid for values of x that are close to 4.
Simplify using order of operations.
5³+28 /7-1
Answer:
128
Step-by-step explanation:
DO the "E"
125 + 28/7 -1 do the division next
125 + 4 - 1 now do the + or - or both
128
NO LINKS!! Write the first 5 terms of the geometric sequence
a1 = 6, r = 4
a1=
a2=
a3=
a4=
a5=
Step-by-step explanation:
since it is geometric sequence we will use the formula
[tex]tn = {ar}^{n - 1} [/tex]
a = 6
r = 4
The first term
T1(a) = 6
The second term
[tex]t2 = {a \times r}^{2 - 1} [/tex]
[tex]t2 = {6 \times 4}^{1 } = 24[/tex]
The Third Term
[tex]t3 = {a \times r}^{3 - 1} = {a \times r}^{2} [/tex]
[tex]t3 = {6 \times 4}^{2} = 6 \times 16 = 96[/tex]
The fourth term
[tex]t4 = {a \times r}^{4 - 1} = {a \times r}^{3} [/tex]
[tex]t4 = {6 \times 4}^{3} = 6 \times 64 = 384[/tex]
The fifth term
[tex]t5 = {a \times r}^{5 - 1} = {a \times r}^{4} [/tex]
[tex]t5 = {6 \times 4}^{4} = 6 \times 256 = 1,536[/tex]
i hope these helped
Answer:
6, 24, 96, 384, 1536, ...
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^{n-1}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]
Given:
a = 6r = 4Substitute the given values of a and r into the formula to create an equation for the nth term:
[tex]a_n=6(4)^{n-1}[/tex]
To find the first 5 terms of the geometric sequence, substitute n = 1 through 5 into the equation.
[tex]\begin{aligned}\implies a_1&=6(4)^{1-1}\\&=6(4)^{0}\\&=6(1)\\&=6\end{aligned}[/tex]
[tex]\begin{aligned}\implies a_2&=6(4)^{2-1}\\&=6(4)^{1}\\&=6(4)\\&=24\end{aligned}[/tex]
[tex]\begin{aligned}\implies a_3&=6(4)^{3-1}\\&=6(4)^{2}\\&=6(16)\\&=96\end{aligned}[/tex]
[tex]\begin{aligned}\implies a_4&=6(4)^{4-1}\\&=6(4)^{3}\\&=6(64)\\&=384\end{aligned}[/tex]
[tex]\begin{aligned}\implies a_5&=6(4)^{5-1}\\&=6(4)^{4}\\&=6(256)\\&=1536\end{aligned}[/tex]
Therefore, the first 5 terms of the given geometric sequence are:
6, 24, 96, 384, 1536, ...the speed of water in a whirl pool varies inversely with the radius. if the water speed is 2.5 feet per second at a radius of 30 feet what is the speed of the water at a radius of 3 feet
Answer:
Step-by-step explanation:
Let, the Speed of the water be 'x'
and the Radius be 'r'
Now, the speed of Water Varies inversely with the Radius
So, x ∝ 1/r
x = k/r -----------(i)
Here, k is the proportionality constant
Now,
Given that, x = 2.5 ft per sec
then, 30 ft,
So, from eq. (i)
2.5 = k/30
So, k = 75
Again From eq. (i)
x = 75/r
Now, if r = 3ft
then, x = 75/3
x = 25
Hence, Speed of the water (x) = 25 ft per sec.
a regular pentagon with side lengths of 9 units is translated 2 units to the left. what is the length of one side of the pentagon after translation, in units? 2
9
5
8
The length of one side of the pentagon after translation is 9 units
Step-by-step explanation:
To be clear, "A translation is an isometry that translates all points of a figure the same distance in the same direction." The dimensions of any geometric figure will never change as a result of translation. The figure's measurements won't change; it will simply be moved from one location to another.
This means that even after being translated 2 units to the left, a regular pentagon with sides of 9 units will still have a side length of 9 units.
The length of one side of the pentagon after translation is 9 units(option B)
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HELP ASAP!! READ CAREFULLY
Answer:
Step-by-step explanation:
There is a scale factor of 2 so since the trapezoid is 9 we can divide by 2 so AD is 4.5 and CB is 4.5
YZ is the same as ZW so 8
Using the scale factor we can divide 8 by 2 to get 4
Perimeters can be found from the sums so
ABCD would be 19 and WXYZ would be 38
Elizabeth has a 1,200-word report to be finished in 3 weeks.
During the first week, she wrote every day (Sunday to Saturday) and wrote a total of 525 words. For the second week, she plans to write every day according to the equation y = 55z where y is
the total number of words written after x days.
Use the drop-down menus to correctly complete the statements below.
Last week, Elizabeth wrote at a pace of
This week, she plans to write at a pace of
She will still need to write To complete report
Answer:
Step-by-step explanation: for the first part, 525/7 = 75.
for the second part, 55y = x, which means 55 words per day for a total of (55*7) or 385
for the third part, 1200-525-385=290, not totally sure, but I think this is the answer, the text was a bit blurry and I couldn't understand everything, try not to following this blindly and just see if it makes sense. Hope I could help
f(x) = 6x + 2 g(x) = -5x -9 Find the product of f and g.
Answer:30x^2 - 54x - 18
Step-by-step explanation: To find the product of f and g, we can simply multiply the expressions for f and g together. The product of f and g is:
(f * g)(x) = (6x + 2)(-5x - 9)
= -30x^2 - 54x - 18
So, the product of f and g is -30x^2 - 54x - 18
3x + 2 = 5x - (2x + 1).
Answer:
No solution
Step-by-step explanation: