Answer:
The standard deviation of the sample mean is [tex]\sigma _ {\= x } = 2.711[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\= x = 60[/tex]
The standard deviation is [tex]\sigma = 21[/tex]
The sample size is [tex]n = 60[/tex]
Generally the standard deviation of the sample mean is mathematically represented as
[tex]\sigma _ {\= x } = \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]\sigma _ {\= x } = \frac{ 21 }{\sqrt{60} }[/tex]
[tex]\sigma _ {\= x } = 2.711[/tex]
please help Find: ∠a ∠b ∠c
Answer:
A-40
B-140
C-140
Step-by-step explanation:
b and c are supplementary angles to angle 40.
Therefore 180-40= 140.
and opposite angles in a quadrilateral are congruent to each other.
find the slope of a line that is perpendicular to the line y= - 1/3x+7
the slope of the line is 3
Write the expression as the logarithm of a single number or expression
4 In 2 +3 In 5
4 In 2 + 3 In 5-
(Simplify your answer.)
Answer:
ln(2000) = 7.601
Step-by-step explanation:
For this we need to know the rules of logarithms, specifically the product rule and the power rule. The product rule is simply ln(a*b) = ln(a) + ln(b). The power rule is simply ln(a^b) = b ln(a).
With these rules, let's begin to simplify the expression:
4 ln(2) + 3 ln(5)
= ln(2^4) + ln(5^3)
= ln(16) + ln(125)
= ln(16 * 125)
= ln(2000)
= 7.601
Hope this helps. Cheers.
A logarithm is a power to which a number must be raised in order to get some other number.
The value of the expression 4 log 2 + 3 log 5 as a single number is 3.30102.
What is a log?A logarithm is a power to which a number must be raised in order to get some other number.
Example:
log 10 = 1
log 100 = log 10² = 2 log 10 = 2 x 1 = 2
log 1000 = log 10³ = 3 log 10 = 3 x 1 = 3
log 0 = undefined
log 1 = 0
We have,
Some formulas for log:
log[tex]x^{n}[/tex] = n log x
log mn = log m + log n
Given,
4 log 2 + 3 log 5
= log [tex]2^{4}[/tex] + log [tex]5^{3}[/tex]
= log 16 + log 125
= log (16 x 125)
= log 2000
= 3.30102
Thus the value of the expression 4 log 2 + 3 log 5 as a single number is
3.30102.
Learn more about log here:
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19] After increasing the price of an article by 20%. The price was GHC
3000.00. What was the original price?
Step-by-step explanation:
Let the original price be x
After increasing by 20% the price is 3000
Thus,
x + ( x × 20%) = 3000
x + 20x/100 = 3000
x + x/5 = 3000
(5x + x)/5 = 3000
6x/5 = 3000
x = 3000 * 5/6
x = 2500
Hope it helps :)
PLESE HELPPP!!!!!!!!!!!!!!!!
Answer:
B. [tex]\frac{6}{2x^{2} - 5x}[/tex]
Step-by-step explanation:
The product of the ratioal expressions given above can be found as follows:
[tex] = \frac{2}{x} * \frac{3}{2x - 5} [/tex]
Multiply the denominators together, and the numerators together, separately to get a single expression
[tex] \frac{2(3)}{x(2x - 5)} [/tex]
[tex] = \frac{6}{x(2x) - x(5)} [/tex]
[tex]= \frac{6}{2x^{2} - 5x}[/tex]
The product of the expression [tex]\ = \frac{2}{x}*\frac{3}{2x - 5}[/tex] = [tex]\frac{6}{2x^{2} - 5x}[/tex]
The answer is B.
A local bottler, Fossil Cove, wants to ensure that an average of 16 ounces of beer is used to fill each bottle. Ben takes a random sample of 48 bottles and finds the average weight to be 15.8 ounces. Historically, the standard deviation has been 0.8 ounces.
Required:
a. Complete a hypothesis test (using the p-‐‐value approach). Interpret your results.
b. How would your answer change if instead of being given that the sample standard deviation was 0.8 ounces you were given the sample variance is 0.64?
Answer:
(a) The mean weight of beer used to fill each bottle is 16 ounces.
(b) The answer of part (a) would not change.
Step-by-step explanation:
A local bottler, Fossil Cove, wants to ensure that an average of 16 ounces of beer is used to fill each bottle.
Ben takes a random sample of n = 48 bottles and finds the average weight to be [tex]\bar x=[/tex] 15.8 ounces. Also it is known that the standard deviation is, σ = 0.8 ounces.
(a)
The hypothesis can be defined as follows:
H₀: The mean weight of beer used to fill each bottle is 16 ounces, i.e. μ = 16.
Hₐ: The mean weight of beer used to fill each bottle is not 16 ounces, i.e. μ ≠ 16.
Assume that the significance level of the test is, α = 0.05.
As the population standard deviation is provided, we will use a z-test for single mean.
Compute the test statistic value as follows:
[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}[/tex]
[tex]=\frac{15.8-16}{0.80/\sqrt{48}}\\\\=-1.732[/tex]
The test statistic value is -1.732.
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected.
Compute the p-value for the two-tailed test as follows:
[tex]p-value=2\cdot P(Z>-1.732)[/tex]
[tex]=2\times [1-P(Z<1.732)]\\\\=2\times [1-0.04182]\\\\=0.08364\\\\\approx 0.084[/tex]
*Use a z-table for the probability.
The p-value of the test is 0.084.
p-value = 0.084 > α = 0.05
The null hypothesis will not be rejected.
Thus, it can be concluded that the mean weight of beer used to fill each bottle is 16 ounces.
(b)
The standard deviation of a random variable is the square root of the variance.
[tex]SD=\sqrt{Variance}[/tex]
So, if the variance was 0.64, then the standard deviation will be:
[tex]SD=\sqrt{Variance}=\sqrt{0.64}=0.80[/tex]
Thus, the answer of part (a) would not change.
two boxes have the same volume. One box has a base that is 5 cm5\text{ cm}5 cm5, start text, space, c, m, end text by 5 cm5\text{ cm}5 cm5, start text, space, c, m, end text. The other box has a base that is 10 cm10\text{ cm}10 cm10, start text, space, c, m, end text by 10 cm10\text{ cm}10 cm10, start text, space, c, m, end text. How many times as tall is the box with the smaller base?
Answer:
The height of the box with the smaller base is 4 times that of the box with the larger base
Step-by-step explanation:
The volume of a box is the product of the base area and the height of the box, it is given as:
Volume = base area × height
For the smaller base box, it has a base of 5 cm by 5 cm, therefore the base area of the smaller base box = 5 cm × 5 cm = 25 cm². Let the height of the smaller base box be [tex]h_1[/tex]The volume of the small box = [tex]25*h_1[/tex]
For the larger base box, it has a base of 10 cm by 10 cm, therefore the base area of the larger base box = 10 cm × 10 cm = 100 cm². Let the height of the large base box be [tex]h_2[/tex]The volume of the larger base box = [tex]100*h_2[/tex]
Since both boxes have the same volume, therefore:
[tex]100*h_2[/tex] = [tex]25*h_1[/tex]
[tex]\frac{h_1}{h_2} =\frac{100}{25} \\\\\frac{h_1}{h_2}=4\\\\h_1=4h_2[/tex]
The height of the box with the smaller base is 4 times that of the box with the larger base
We can use the formula V=lwh to compare the volume in the two boxes.
First let's compare the volume of both boxes to see if they have the same height. To make it simple, let's use a height of 1 centimeter.
First the box with the smaller base.
V=lwh
V=5⋅5⋅1
V=25
Now the box with the larger base
V=lwh
V=10x10x1
V=100
We can set up an equation to find out how many times as tall the smaller box needs to be to have the same volume as the box with the larger base.
25·h=100
h=4
The boz with the smaller base is 4 times tall
hope it helped :)
Determine the values of \theta if sec\;\theta=-\frac{2}{\sqrt{3}}.
Answer:
See below.
Step-by-step explanation:
So, we have:
[tex]\sec(\theta)=-2/\sqrt{3}[/tex]
Recall that secant is simply the reciprocal of cosine. So we can:
[tex]\cos(\theta)=(\sec(\theta))^{-1}=(-2/\sqrt{3})^{-1}\\\cos(\theta)=-\sqrt{3}/2[/tex]
Now, recall the unit circle. Since cosine is negative, it must be in Quadrants II and/or III. The numerator is the square root of 3. The denominator is 2. The whole thing is negative. Therefore, this means that 150 or 5π/6 is a candidate. Therefore, due to reference angles, 180+30=210 or 7π/6 is also a candidate.
Therefore, the possible values for theta is
5π/6 +2nπ
and
7π/6 + 2nπ
really really need help!!!! Which Venn diagram has a shaded region that represents X n Z????
The answer is Diagram 4 or D
Explanation:
A Venn diagram is a type of model that represents sets, and their relationships. Additionally, each set is usually named with a letter and symbols such as ∪ or ∩ are used to represent specific zones of the diagram. In the case of the symbol ∩, this is used to represent the intersection between two sets. This means X ∩ Z represents the intersection between X and Z. Therefore, the correct representation is the fourth diagram, which shows in red only the intersection between these two sets.
Answer:
See below.
Step-by-step explanation:
None of the choices represent the intersection of sets X and Z, so there is some mistake with this problem. The question is not correct for these choices.
a parabola has an x-intercept at 2, its axis of symmetry is the line x=4, and the y-coordinate of its vertex is 6. Determine the equation of the parabola.
Answer:
The standard equation of the parabola is:
[tex]y=-\frac{3}{2}x^2+12x-18[/tex]
Step-by-step explanation:
An x intercept of 2 means that the point (2, 0) is in the graph of the parabola.
We can also write the general expression for the parabola in vertex form, since we can use the information on the coordinates of the vertex: (4, 6) - recall that the axis of symmetry of the parabola goes through the parabola's vertex, so the x-value of the vertex must be x=4.
[tex]y-y_{vertex}=a\,(x-x_{vertex})^2\\y-6=a\,(x-4)^2[/tex]
Now we can find the value of the parameter "a" by using the extra information about the point (2, 0) at which the parabola intercepts the x-axis:
[tex]y-6=a\,(x-4)^2\\0-6=a\,(2-4)^2\\-6=a\,4\\a=-\frac{6}{4} =-\frac{3}{2}[/tex]
Then the equation of the parabola becomes:
[tex]y-6=-\frac{3}{2} \,(x-4)^2\\y-6=-\frac{3}{2} (x^2-8x+16)\\y-6=-\frac{3}{2}x^2+12x-24\\y=-\frac{3}{2}x^2+12x-18[/tex]
A triangle has an area of 900m^2 . If a parallelogram has the same height and base as the triangle, what is the area of the parallelogram?
Answer:
area = 1800 m²
Step-by-step explanation:
area of one triangle = 900 m²
if a parallelogram has the same height and base as the triangle, then that means the area or the two triangle and shaped as a parallelogram
is twice the area given.
area = 900 * 2
area = 1800 m²
Mike can stitch 7 shirts in 42 hours
He can stitch 1 shirt in hours, and in 1 hour he can stitch of a shirt
Answer:
He stitched 1 shirt in 6 hours.
He can stitch 1/6 of a shirt in one hour
Step-by-step explanation:
Given Mike can stitch 7 shirts in 42 hours
No. of shirt stitch in one hour = total no of shirt stitch/total time taken
No. of shirt stitch in one hour = 7/42 = 1/6
Thus, he can stitch 1/6 of a shirt in one hour
Time taken to stitch 1 shirt = total time taken by him to stitch 7 shirts/ total no. of shirt stitch(i.e 7) = 42/6 = 6 hours.
Thus, he stitched 1 shirt in 6 hours.
Answer:
He can stitch 1/6 of a shirt in one hour
Step-by-step explanation:
Because he stitched 7 shirts in 42 hours
42/7 = 6
so 6 hours per shirt
In one hour:
1/6
PLS HELP!!!!ILL MARK YOU THE BRAINLISt
Translate into an algebraic expression and simplify if possible. C It would take Maya x minutes to rake the leaves and Carla y minutes, what portion of the leaves do they rake in one minute if they work together?
Answer:
(x+y)/xy or (1/x + 1/y) portion of the leaves
Step-by-step explanation:
Let the total work done to rake the leaves be a for representation.
Thus,
given Maya takes x minutes to rake the leaves
thus,
work done by may in x minutes = a
dividing both side by x
work done by maya in x/x = 1 minutes = a/x
similarly
given Calra takes y minutes to rake the leaves
thus,
work done by may in y minutes = a
dividing both side by y
work done by maya in y/y = 1 minutes = a/y
__________________________________
Total work done by both in 1 minutes = a/x + a/y = a(1/x+1/y) = a(x+y)/xy
Thus, if a is the total work , then they do (x+y)/xy of a work in one minute.
Thus, (x+y)/xy portion of leaves do they rake in one minute if they work together.
Solve for x in the equation x squared + 11 x + 121/4 = 125/4.
Step-by-step explanation:
x² + 11x + 121/4 = 125/4
x² + 11x + 121/4 - 125/4 = 0
x² + 11x - 1 = 0
after that apply quadratic formula
x = ( -b + or - √b² - 4ac ) ÷ 2a
x = (-11 + or - √11² - 4×1×-1 ) ÷ 2×1
+ = 0.090169....
- = -11.090168.....
x = 0.090 or x = -11.09
Maya is choosing between several pay plans for her new job. If she usually has monthly sales of about $5,000, which plan would allow Maya to earn the most money in a month? Plan Monthly base salary Commission rate A $500 8% B $600 7% C $700 6% D $800 5% plan A plan B plan C plan D
Answer:
Well Plan D
Step-by-step explanation:
Answer:
plan D.
Step-by-step explanation:
2021 edge
Solve the system using multiplication for the linear combination method. 6x – 3y = 3 –2x + 6y = 14 What is the solution to the system
Answer:
work is shown and pictured
Correct Answer would be
D: (2,3)
A word is anything of seven letters of the alphabet(26 letters) (no space in between). Repeated lettersare allowed. How many words are there?
Answer:
26^7=8 031 810 176
Step-by-step explanation:
The word has 7 letters. So the word have 7 places where any of 26 letters can be placed.
Any of 26 letters can stay at 1st place
Any of 26 letters can stay at 2-nd place (because letters can be repeated)
Any of 26 letters can stay at 3rd place
Any of 26 letters can stay at 4th place
Any of 26 letters can stay at 5th place
Any of 26 letters can stay at 6th place
Any of 26 letters can stay at 7th place
So N= 26*26*26*26*26*26*26=26^7=8 031 810 176
Which of the following is a correct tangent ratio for the figure?
Answer:
C) tan(39°) = 11/15
Step-by-step explanation:
SohCahToa
tangent = opposite / adjacent
The given angle is 39°. The angle directly opposite of 39° is 11 and the angle adjacent to 39° is 15.
Answer:
tan(39°) = 11∕15
Step-by-step explanation:
What are the x and y intercepts?
[tex]f(x) = \frac{(x - 3)(x + 4)(x - 1)}{(x + 2)(x - 12)} [/tex]
Answer:
(a)The x-intercepts are 3, -4 and 1.
(b)f(x)=-0.5
Step-by-step explanation:
Given the function:
[tex]f(x) = \dfrac{(x - 3)(x + 4)(x - 1)}{(x + 2)(x - 12)}[/tex]
The x-intercepts occurs when y=0The y-intercepts occurs when x=0x-Intercepts
When y=f(x)=0
[tex]f(x) = \dfrac{(x - 3)(x + 4)(x - 1)}{(x + 2)(x - 12)}=0\\(x - 3)(x + 4)(x - 1)=0\\x - 3=0$ or $ x + 4=0 $ or $ x - 1=0\\x=3$ or $ -4$ or $ 1[/tex]
The x-intercepts are 3, -4 and 1.
y-intercepts
When x=0
[tex]f(x) = \dfrac{(x - 3)(x + 4)(x - 1)}{(x + 2)(x - 12)}\\f(x) = \dfrac{(0 - 3)(0 + 4)(0 - 1)}{(0 + 2)(0 - 12)}\\= \dfrac{(- 3)( 4)( - 1)}{( 2)( - 12)}\\= \dfrac{12}{-24}\\\\=-0.5[/tex]
The y-intercept is -0.5
How do i solve this? F (x)=x³-2x²+x+1, then f (-x)=
Step-by-step explanation:
F (x)=x³-2x²+x+1,
Then F (-x)= - x³ - 2x² - x + 1
Tell me if I'm right.
Hope this helps.
Have a great day!
Here is a list of ages (years) of children in a room: 4, 3, 2, 10, 10, 6, 7 State the median.
Answer: 6
Step-by-step explanation:
Lets re- write the numbers in growing order.
2,3,4,6,7,10,10
The number that stays exactly in the middle of the the sequence is the median.
Number 6 stays in the middle. So 6 is the median
Answer
6Step by step explanation
Given data : 4 , 3 , 2 , 10 , 10 , 6 , 7
Arranging the data in ascending order, we have,
2 , 3 , 4 , 6 , 7 , 10 , 10
Here, n ( total number of items) = 7
Now, position of median:
[tex] {( \frac{n + 1}{2}) }^{th} [/tex] item
plug the value
[tex] = {( \frac{7 + 1}{2} )}^{th} [/tex] item
Add the numbers
[tex] =( { \frac{8}{2} )}^{th} [/tex] item
Divide
[tex] = {4}^{th} [/tex] item
i.e 4th item is the median
Median = 6
------------------------------------------------------------------------
Further more explanation:
Let's take another example:
please see the attached picture.
In the above series, the numbers are arranged in ascending order. Here, the fourth item 17 has three items before it and three items after it. So, 17 is the middle item in the series. 17 is called the median of the series.
Thus, Median is the value of the middle - most observation, when the data are arranged in ascending or descending order of magnitude.
Hope I helped..
Best regards!!
What is the slope of the line
described by -4X + 2Y = 16?
A. -2
B. -4
C. 4
D. 2
E. 16
Answer: THe slope is 2
SO answer d
Step-by-step explanation:
-4X + 2Y = 16 add 4x to the other side so equation is
2y=16+4x divided by 2
y=8+2x
46/100 46/1,000
which is greater
Answer:
46/100.
Step-by-step explanation:
46 / 100 = 0.46
46 / 1,000 = 0.046
0.046 < 0.46
So, 46/100 is greater than 46/1,000.
Hope this helps!
46/100 is greater because it equals 0.46 while 46/1000 would equal 0.046.
WILL GIVE YOU BRAINLIEST
Answer:
AB = 20 tan55°
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan55° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AB}{BC}[/tex] = [tex]\frac{AB}{20}[/tex] ( multiply both sides by 20 )
20 tan55° = AB
A manufacturing company has an old machine which produces 25 components per hour. The company has recently installed a new machine which produces 35 components per hour. Yesterday, both machines were in operation for different periods of time. If 430 components were produced when the total number of hours of operation was 14 hours, determine for how many hours each machine was in operation
Answer: old machine 150, new machine 280
Step-by-step explanation:
given data:
Old machine = 25t
New machine = 35t
where t = hrs
we dont know the time for old machine so we assume it to be ( t ),
while that of the new machine is ( 14-t ) hours for new machine, and sum of 430 components.
therefore;
25t +490 - 35t = 430
-10t = -60
divide both sides by -10
t = 6 hours for the first machine.
6hrs * 25 components /hr
= 150 component parts For old machine.
for new machine
= 14 - t ........... eq1.
where ( t = 6 ), substitute t into the equation
= 14 - 6
= 8 hours for the second machine
= 8 * 35
= 280 components parts
need help fast APR is an ____?
6th grade math help me, please. :)
Step-by-step explanation:
Hello there!!
no need to be panic we will help you, alright.
look solution in picture ok...
sorry for cutting in middle.
Hope it helps...
At time, t=0, Billy puts 625 into an account paying 6% simple interest. At the end of year 2, George puts 400 into an account paying interest at a force of interest, δt=16+t for t≥2. If both accounts continue to earn interest indefinitely at the levels given above, the amounts in both accounts will be equal at the end of year n. Calculate n.
Answer:
26
Step-by-step explanation:
Given that:
At time, t=0, Billy puts 625 into an account paying 6% simple interest
At the end of year 2, George puts 400 into an account paying interest at a force of interest, 1/(6+t), for all t ≥ 2.
If both accounts continue to earn interest indefinitely at the levels given above, the amounts in both accounts will be equal at the end of year n. Calculate n.
In order to calculate n;
Let K constant to be the value of time for both accounts
At time, t=0, the value of time K when Billy puts 625 into an account paying 6% simple interest is:
[tex]K = 625 \times (1+ 0.06 K)[/tex]
[tex]K = 625 +37.5 K[/tex]
At year end 2; George amount of 400 will grow at a force interest, then the value of [tex]K = 400 \times e^{\int\limits^2_k {\dfrac{1}{6+t}} \, dx }[/tex]
[tex]K =400 \times \dfrac{6+K}{6+2}[/tex]
[tex]K =400 \times \dfrac{6+K}{8}[/tex]
[tex]K =50 \times ({6+K})[/tex]
[tex]K =300+50K[/tex]
Therefore:
If K = K
Then:
625 + 37.5 = 300 +50 K
625-300 = 50 K - 37.5 K
325 = 12.5K
K = 325/12.5
K = 26
the amounts in both accounts at the end of year n = K = 26
Which ideas from the excerpt would be most appropriate to include in a summary? Select three options. Popular novels from the past often ask provocative questions that are important to consider today. Many Americans have given up and say that the nation is no longer great or a land of dreams. John Wayne, nicknamed Duke, was an iconic Hollywood actor and filmmaker. President Reagan believed that John Wayne would argue that he was not the last American hero, because there are many more. Duke Wayne died as a symbol of the Hollywood dream industry.
Answer:
Short answer A,B,D
Step-by-step explanation:
The ideas from the excerpt would be most appropriate to include in a summary are;
Popular novels from the past often ask provocative questions that are important to consider today. Many Americans have given up and say that the nation is no longer great or a land of dreams. President Reagan believed that John Wayne would argue that he was not the last American hero, because there are many more. What is a summary of a passage?Summary is known to be a form of quick or short review of what has happened in a specific passage.
The summary is regarded as a statement that present the main points of a passage as seen above.
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What does 0 = 0 mean regarding the solution to the system?
Answer:
It means the left side of the equation equals the right side of the equation regardless of the value of the variables. The solution is all real numbers for each variable
Step-by-step explanation: