Answer:
[tex]\bar x = 107.11[/tex]
[tex]\sigma_x = 31.07[/tex]
Step-by-step explanation:
See comment for complete question
Given
[tex]x: 97\ 178\ 129\ 90\ 75\ 94\ 116\ 100\ 85[/tex]
Solving (a): The sample mean
This is calculated using:
[tex]\bar x = \frac{\sum x}{n}[/tex]
So, we have:
[tex]\bar x = \frac{97+ 178+ 129+ 90+ 75+ 94+ 116+ 100+ 85}{9}[/tex]
[tex]\bar x = \frac{964}{9}[/tex]
[tex]\bar x = 107.11[/tex]
Solving (b): The sample standard deviation
This is calculated as:
[tex]\sigma_x = \sqrt{\frac{\sum(x - \bar x)^2}{n-1}}[/tex]
So, we have:
[tex]\sigma_x = \sqrt{\frac{(97 - 107.11)^2 +.............+ (85- 107.11)^2 }{9-1}}[/tex]
[tex]\sigma_x = \sqrt{\frac{7720.8889}{8}}[/tex]
[tex]\sigma_x = \sqrt{965.1111125}[/tex]
[tex]\sigma_x = 31.07[/tex]
(2cosA+1) (2cosA-1)=2cos2A+1 prove that
To prove that: (2cosA+1) (2cosA-1) = 2cos2A+1
We try to solve one side of the equation to get the other side of the equation.
In this case, we'll solve the right hand side (2cos2A + 1) of the equation with the aim of getting the left hand side of the equation (2cosA + 1)(2cosA - 1)
Solving the right hand side: 2cos2A + 1
i. We know that cos2A = cos(A+A) = cosAcosA - sinAsinA
Therefore;
cos2A = cos²A - sin²A
ii. We also know that: cos²A + sin²A = 1
Therefore;
sin²A = 1 - cos²A
iii. Now re-write the right hand side by substituting the value of cos2A as follows;
2cos2A + 1 = 2(cos²A - sin²A) + 1
iv. Expand the result in (iii)
2cos2A + 1 = 2cos²A - 2sin²A + 1
v. Now substitute the value of sin²A in (ii) into the result in (iv)
2cos2A + 1 = 2cos²A - 2(1 - cos²A) + 1
vi. Solve the result in (v)
2cos2A + 1 = 2cos²A - 2 + 2cos²A + 1
2cos2A + 1 = 4cos²A - 2 + 1
2cos2A + 1 = 4cos²A - 1
2cos2A + 1 = (2cosA)² - 1²
vii. Remember that the difference of the square of two numbers is the product of the sum and difference of the two numbers. i.e
a² - b² = (a+b)(a-b)
This means that if we put a = 2cosA and b = 1, the result from (vi) can be re-written as;
2cos2A + 1 = (2cosA)² - 1²
2cos2A + 1 = (2cosA + 1)(2cosA - 1)
Since, we have been able to arrive at the left hand side of the given equation, then we can conclude that;
(2cosA + 1)(2cosA - 1) = 2cos2A + 1
Answer:
[tex]\boxed{\sf LHS = RHS }[/tex]
Step-by-step explanation:
We need to prove that ,
[tex]\sf\implies (2 cosA +1)(2cosA-1) = 2cos2A+1[/tex]
We can start by taking RHS and will try to obtain the LHS . The RHS is ,
[tex]\sf\implies RHS= 2cos2A + 1 [/tex]
We know that , cos2A = 2cos²A - 1 ,
[tex]\sf\implies RHS= 2(2cos^2-1)-1 [/tex]
Simplify the bracket ,
[tex]\sf\implies RHS= 4cos^2A - 2 +1 [/tex]
Add the constants ,
[tex]\sf\implies RHS= 4cos^2-1 [/tex]
Write each term in form of square of a number ,
[tex]\sf\implies RHS= (2cos^2A)^2-1^2 [/tex]
Using (a+b)(a-b) = a² - b² , we have ,
[tex]\sf\implies RHS= (2cosA+1)(2cosA-1) [/tex]
This equals to LHS , therefore ,
[tex]\sf\implies \boxed{\pink{\textsf{\textbf{ RHS= LHS }}}} [/tex]
Hence Proved !
Please answer of question num 20 and 21 only please
Answer:
Iam going to do question 21
Step-by-step explanation:
1/7*x=2
1/7x=2
x=2:1/7
x=2*7/1
x=14
I’m stuck please help .
Answer:
me too
Step-by-step explanation:
me too
How many x-intercepts are in the quadratic equation y = 7x2 − 2x − 1
Answer:
There are 2 x intercepts
how do you write in numerals
Answer:
Basic numbersNumbers up to nine should always be written in words, anything higher than nine can be written in numerals. Alternatively, some guides suggest that if you can write the number in two words or fewer then use words rather than number.hope it's helpful for u !! stay safe ...Step-by-step explanation:
1 : a conventional symbol that represents a number. 2 numerals plural : numbers that designate by year a school or college class and that are awarded for distinction in an extracurricular activity. Other Words from numeral Synonyms Example Sentences Learn More About numeral.A numeral is a symbol or name that stands for a number. Examples: 3, 49 and twelve are all numerals. So the number is an idea, the numeral is how we write it.hope it helps.stay safe healthy and happy...PLZZZZ HELPP WILL GIVE BRAINLIEST
Two sides and the non-included right angle of one right triangle are congruent to the corresponding parts of another right triangle. Which congruence theorem can be used to prove that the triangles are congruent?
AAS
SSS
SAS
HL
Answer:
HL
Step-by-step explanation:
Since both triangles are right angle triangles that means one angle is 90°. other two sides are given congruent .
that means lengths of hypotenuse and the leg of the one right angle triangle is equal to the corresponding other hypotenuse and leg of other triangle.
This fulfills the condition of HL congruency.
Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.)
g(t) =
4 + t + t2
t
G(t) =
Step-by-step explanation:
[tex]G(t) =\displaystyle \int (4 + t + t^2)dt[/tex]
[tex]\:\:\:\:\:\:\:=4t + \frac{1}{2}t^2 + \frac{1}{3}t^3 + C[/tex]
Check:
[tex]\dfrac{d}{dt}(4t + \frac{1}{2}t^2 + \frac{1}{3}t^3+C)= 4 + t + t^2 =g(t)[/tex]
Help ! ASAP please and thank you !!
that alot of work shhheeshhh
It is believed that students who begin studying for final exams a week before the test score differently than students who wait until the night before. Suppose you want to test the hypothesis that students who study one week before score less than students who study the night before. A hypothesis test for two independent samples is run based on your data and a p-value is calculated to be 0.2789. What is the appropriate conclusion
Answer:
The p-value is 0.2789 > 0.05, which means that the appropriate conclusion is that the students do not score differently.
Step-by-step explanation:
It is believed that students who begin studying for final exams a week before the test score differently than students who wait until the night before.
At the null hypothesis, we test if the two means are equal, that is, the subtraction of them is 0.
[tex]H_0: \mu_1 - \mu_2 = 0[/tex]
At the alternative hypothesis, we test if the two means are different, that is, the subtraction of them is different of 0. So
[tex]H_1: \mu_1 - \mu_2 \neq 0[/tex]
A hypothesis test for two independent samples is run based on your data and a p-value is calculated to be 0.2789.
Considering a standard significance level of 0.02789, the p-value is 0.2789 > 0.05, which means that the appropriate conclusion is that the students do not score differently.
The function f(x) is shown below.
х
-6
-3
f(x)
1
2
5
3
Coon
0
If g(x) is the inverse of f(x), what is the value of f(g(2))?
-6
оооо
5
Answer:
[tex]f(g(2)) = 2[/tex]
Step-by-step explanation:
Given
[tex]x \to f(x)[/tex]
[tex]-6 \to 1[/tex]
[tex]-3 \to 2[/tex]
[tex]g(x) = f^{-1}(x)[/tex] --- inverse
Required
[tex]f(g(2))[/tex]
For two functions f(x) and g(x) where f(x) and g(x)are inverse;
[tex]f(g(x)) = x[/tex]
So, by comparison:
[tex]f(g(2)) = 2[/tex]
You want to send postcards to 15 friends. In the shop there are only 3 kinds of postcards. In how many ways can you send the postcards, if
Answer:
455 ways
Step-by-step explanation:
Given
[tex]n = 15[/tex] --- friends
[tex]r = 3[/tex] -- available postcard kinds
Required
Ways of sending the cards
The question is an illustration of combination and the formula is:
[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]
So, we have:
[tex]^{15}C_3 = \frac{15!}{(15 - 3)!3!}[/tex]
[tex]^{15}C_3 = \frac{15!}{12!*3!}[/tex]
Expand
[tex]^{15}C_3 = \frac{15*14*13*12!}{12!*3*2*1}[/tex]
[tex]^{15}C_3 = \frac{15*14*13}{3*2*1}[/tex]
[tex]^{15}C_3 = \frac{2730}{6}[/tex]
[tex]^{15}C_3 = 455[/tex]
EXERCISE 3 Date:......... A shop sells a pencil at ¢500.00 and pen at 42,000.00. (a) If Afua bought 8 pencils and 5 pens, how much did she pay altogether for them? (b) The price of a pencil is increased by 20% and a pen by 10%. Find how much she will pay for 10 pencils and 8 pens.
Answer:
ok so its is 5 dollars for a pencil and 420 dollars for a pen(dang)
a40+2100=2140
now
b6 pencil 462 pen
60+3696=3756
Hope This Helps!!!
(a) Afua paid ¢44,500.00 for 8 pencils and 5 pens.
(b) Afua will pay ¢71,400.00 for 10 pencils and 8 pens after the price increase.
(a) To find how much Afua paid altogether for 8 pencils and 5 pens, we need to calculate the total cost for each item and then add them together.
Given:
Cost of a pencil, [tex]Pencil_{cost}[/tex] = ¢500.00
Cost of a pen, [tex]Pen_{cost}[/tex] = ¢42,000.00
Number of pencils bought, [tex]n_{pencils}[/tex] = 8
Number of pens bought, [tex]n_{pens}[/tex] = 5
Total cost of pencils,
[tex]Total_{pencil}_{cost} = Pencil_{cost} * n_{pencils}[/tex]
= ¢500.00 × 8
= ¢4,000.00
Total cost of pens,
[tex]Total_{pen}_{cost} = Pen_{cost} * n_{pens}[/tex]
= ¢42,000.00 × 5
= ¢210,000.00
Altogether, [tex]Total_{cost} = Total_{pencil}_{cost} + Total_{pen}_{cost}[/tex]
= ¢4,000.00 + ¢210,000.00
= ¢214,000.00.
Therefore, Afua paid ¢214,000.00 for 8 pencils and 5 pens.
(b) Now, let's calculate the new total cost after the price increase.
The price of a pencil increased by 20%, which means the new pencil cost is:
[tex]New_{pencil}_{cost}[/tex] = [tex]Pencil_{cost}[/tex]+ (20% × [tex]Pencil_{cost}[/tex])
= ¢500.00 + (0.20 × ¢500.00)
= ¢500.00 + ¢100.00
= ¢600.00
Similarly, the price of a pen increased by 10%, which means the new pen cost is:
[tex]New_{pen}_{cost}[/tex] = [tex]Pen_{cost}[/tex] + (10% × [tex]Pen_{cost}[/tex])
= ¢42,000.00 + (0.10 × ¢42,000.00)
= ¢42,000.00 + ¢4,200.00
= ¢46,200.00
Now, we can find the total cost for 10 pencils and 8 pens with the increased prices:
Number of pencils to be bought, [tex]n_{pencils}_{new}[/tex] = 10
Number of pens to be bought, [tex]n_{pens}_{new}[/tex] = 8
Total cost of pencils with new prices,
[tex]Total_{pencil}_{cost}_{new}[/tex] =[tex]New_{pencil}_{cost}[/tex] × [tex]n_{pencils}_{new}[/tex]
= ¢600.00 × 10
= ¢6,000.00
Total cost of pens with new prices,
[tex]Total_{pen}_{cost}_{new}[/tex] = [tex]New_{pen}_{cost}[/tex] × [tex]n_{pens}_{new}[/tex]
= ¢46,200.00 × 8
= ¢369,600.00
Altogether, [tex]New_{total}_{cost}[/tex] = [tex]Total_{pencil}_{cost}_{new}[/tex] + [tex]Total_{pen}_{cost}_{new}[/tex]
= ¢6,000.00 + ¢369,600.00
= ¢375,600.00
Therefore, Afua will pay ¢375,600.00 for 10 pencils and 8 pens with the increased prices.
To know more about Price here
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Your money grows at a rate of 8% a year if you originally invest $2,000 what is the function that represents your money after t years
Answer:
2000*(1.08)^t where t is years after deposit
Step-by-step explanation:
Fill in the table using this function rule.
y=-10x+3
9514 1404 393
Answer:
see below
Step-by-step explanation:
Put the x-value in the equation and do the arithmetic.
For example, ...
for x = -5,
y = -10(-5) +3 = 50 +3 = 53
Use quadratic regression to find the
equation for the parabola going
through these 3 points.
(-4, 7) (6, -33) (10, -105)
HELP PLZ
Answer:
[tex]y= -x^{2} -2x+15[/tex]
Step-by-step explanation:
[tex]y= -x^{2} -2x+15[/tex]
Quality control. As part of a quality control process for computer chips, an engineer at a factory randomly samples 212 chips during a week of production to test the current rate of chips with severe defects. She finds that 27 of the chips are defective.
(a) What population is under consideration in the data set?
(b) What parameter is being estimated?
(c) What is the point estimate for the parameter?
(d) What is the name of the statistic can we use to measure the uncertainty of the point estimate?
(e) Compute the value from part (d) for this context.
(f) The historical rate of defects is 10%. Should the engineer be surprised by the observed rate of defects
during the current week?
(g) Suppose the true population value was found to be 10%. If we use this proportion to recompute the value in part (e) using p = 0.1 instead of pˆ, does the resulting value change much?
Answer:
See Explanation
Step-by-step explanation:
According to the Question,
Given That, As part of a quality control process for computer chips, an engineer at a factory randomly samples 212 chips during a week of production to test the current rate of chips with severe defects. She finds that 27 of the chips are defective.(a) The sample is from all computer chips manufactured at the factory during the week of production. We might be tempted to generalize the population to represent all weeks, but we should exercise caution here since the rate of defects may change over time.
(b) The fraction of computer chips manufactured at the factory during the week of production that had defects.
(c) Estimate the parameter using the data: phat = 27/212 = 0.127.
(d) Standard error (or SE).
(e) Compute the SE using phat = 0.127 in place of p:
SE ≈ √(phat(1−phat)/n) = 0.023.
(f) The standard error is the standard deviation of phat. A value of 0.10 would be about one standard error away from the observed value, which would not represent a very uncommon deviation. (Usually beyond about 2 standard errors is a good rule of thumb.) The engineer should not be surprised.
(g) Recomputed standard error using p = 0.1: SE = 0.021. This value isn't very different, which is typical when the standard error is computed using relatively similar proportions (and even sometimes when those proportions are quite different!).
Which of the following is an x-intercept of the function, f(x) = x3 – x2 - 8x +12?
O A. -4
B. 3
C. 4
D. -3
8-6•4+10divided by 2 =
some pleaseeeeee help!!
f(x) = 3x + 4 + 2
g(x) = 4
Find (f +g)(x).
Answer:
3x^2 + 10x
Step-by-step explanation:
If u wrote it correctly it would be ((x+4+2)+4)(x)
Which of the following is a polynomial
A. 1-5x^2/x
b. 11x
c. 2x^2- square root x
d. 3x^2+6x
Answer:
B and D are polynomial
Step-by-step explanation:
An algebraic expression with non-zero coefficients and variables having non-negative integers as exponents is called a polynomial.
A)
If it is [tex]1 -\frac{5x^{2}}{x }=1-5x[/tex] , then it is a polynomial.
But if it is [tex]\frac{1-5x^{2}}{x}[/tex] then it is not a polynomial
5. There are 8 sections of seats in an auditorium. Each section contains at least 150 seats but not more than 200 seats. Which of the following could be the number of seats in this auditorium? (A) 800 (B) 1,000 (C) 1,100 (D) 1,300 (E) 1,700
Answer:
1300
Step-by-step explanation:
Given that :
Number of sections = 8
Number of seats per section, x ;
150 ≤ x ≤ 200
The possible Number of seats in the auditorium :
Number of seats per section * number of sections
150 * 8 ≤ x ≤ 200 * 8
1200 ≤ x ≤ 1600
The possible Number of seats will lie within 1200 and 1600
From the options, only 1300 lie within this range
Find the area of the figure below, formed from a triangle and a parallelogram.
144 square millimeters
120 square millimeters
72 square millimeters
96 square millimeters
total area =A1+A2+A3
A1=1/2b*h
A1=1/2*8mm*6mm
A1=24mmsquare
A2=1/2b*h
A2=1/2*8mm*6mm
A2=24mmsquare
A3=b*h
A3=8mm*6mm
A3=48mmsquare
Atotal=24mmsquare+24mmsquare+48mmsquare
Atotal=96mmsquare
Helppp and explain than you
Answer:
1) x = 2
Step-by-step explanation:
Hope it helps. I'll try to solve the second one too
9514 1404 393
Answer:
x = 2(-5, 4, 6)Step-by-step explanation:
1. Substitution can work for this.
2x +3(4x -5) = 13
14x = 28 . . . . . add 15
x = 2 . . . . . . . divide by 14
__
2. The equation z=6 eliminates all but the 1st and 3rd choices. Using that value in the first equation gives ...
x + y + 6 = 5
x + y = -1
Only the 3rd choice satisfies this equation.
(x, y, z) = (-5, 4, 6)
Using the quadratic formula, which of the following are the zeros of the quadratic equation below? y=x^2-x-5
Answer:
The roots(Zeros) are
x=2.7913 and -1.7913
Use multiplication to solve the proportion.
y/9 = 44/54
Answer: [tex]y=7\dfrac{1}{3}[/tex].
Step-by-step explanation:
[tex]\dfrac{y}{9} =\dfrac{44}{54} \\\\y \times 54=44 \times 9\\\\54y=396\\\\54y \div 54=396 \div 54\\\\y=7\dfrac{1}{3}[/tex]
Subtract 8 1/5 - 4 2/5 . Simplify the answer and write as a mixed number.
Answer:
[tex]3\frac{4}{5}[/tex]
Step-by-step explanation:
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]3\frac{4}{5}[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Calculating the answer...}}\\\\8\frac{1}{5}-4 \frac{2}{5}\\-------------\\\text{Converting the mixed numbers into improper fractions...}\\\\\rightarrow 8\frac{1}{5} =\frac{41}{5}\\\\\rightarrow 4\frac{2}{5}=\frac{22}{5} \\-------------\\\frac{41}{5} -\frac{22}{5}\\\\\rightarrow\boxed{ \frac{19}{5}}\\-------------\\\\text{5 would go into 19 3 times with 4 as the remainder.}\\\\\frac{19}{5}=\boxed{3\frac{4}{5}}\\-------------\\\text{\textbf{Therefore:}}\\\\[/tex]
[tex]8\frac{1}{5}-4\frac{2}{5}=\boxed{3\frac{4}{5}}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
The head of maintenance at XYZ Rent-A-Car believes that the mean number of miles between services is 4959 miles, with a standard deviation of 448 miles. If he is correct, what is the probability that the mean of a sample of 43 cars would differ from the population mean by less than 111 miles
Answer:
0.8948 = 89.48% probability that the mean of a sample of 43 cars would differ from the population mean by less than 111 miles
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The mean number of miles between services is 4959 miles, with a standard deviation of 448 miles
This means that [tex]\mu = 4959, \sigma = 448[/tex]
Sample of 43:
This means that [tex]n = 43, s = \frac{448}{\sqrt{43}}[/tex]
What is the probability that the mean of a sample of 43 cars would differ from the population mean by less than 111 miles?
p-value of Z when X = 4959 + 111 = 5070 subtracted by the p-value of Z when X = 4959 - 111 = 4848, that is, probability the sample mean is between these two values.
X = 5070
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{5070 - 4959}{\frac{448}{\sqrt{43}}}[/tex]
[tex]Z = 1.62[/tex]
[tex]Z = 1.62[/tex] has a p-value of 0.9474
X = 4848
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{4848 - 4959}{\frac{448}{\sqrt{43}}}[/tex]
[tex]Z = -1.62[/tex]
[tex]Z = -1.62[/tex] has a p-value of 0.0526
0.9474 - 0.0526 = 0.8948
0.8948 = 89.48% probability that the mean of a sample of 43 cars would differ from the population mean by less than 111 miles
Which pair of points have equal x-coordinates?
Answer:
A. Q and R
Step-by-step explanation:
The x-axis is the horizontal line. The y-axis is the vertical line.
On the x-axis, go to the left, all the way to -5.
Look at the line that goes through -5 vertically. You will see that that line intersects with both Q and R.
This means that Q and R have equal x-coordinates, -5.
They're x and y coordinates would be
Q- (-5, 6)
R- (-5, -7)
I hope this helps!
Answer: Q and R
Step-by-step explanation:
See since in the photo the Q coordinate(Q) is directly above the R coordinate(R), that can only mean that they have the same X coordinate(X) or else it wouldn't be possible for Q to be right above R. The reason Q is right above R is because their Y coordinates(Y) are different, not because of X.
I hope this helps!
Formular for quadratic equation almighty formular
[tex]x = \frac{ - b \frac{ + }{} \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
The population of a bacteria colony is growing exponentially, doubling every 6 hours. If there are 150 bacteria currently present, how many (to the nearest ten bacteria) will be present in 10 hours
Answer:
If rounded to the nearest 10 bacteria, then it would be 500 bacteria.
Step-by-step explanation:
First multiply 150 by two in order to get 300, that leaves 4 hours to figure out. From there you can figure out the rest by seeing that 4 is 2/3 of 6. I converted it into the decimal number .66. Multiply 300 by .66 to get 198 and then add it to 300 to get 498. Then just round it up to the nearest 10 bacteria which leaves you with the final answer of 500 bacteria.