Answer:
13,125 ducks
Step-by-step explanation:
The ratio of ducks:geese on the first day was:
175:63
On the last day (end of migration), he counted 4,725 geese.
To find the number of ducks using the same ratio, we are first going to divide 4,725 by 63 to find what number all the ducks and geese multiplied by:
4,725/63 = 75
The geese multiplied by 75. This means the ducks also multiplied by 75:
175*75 = 13,125
Barnaby counted 13,125 ducks.
Hope it helps (●'◡'●)
(a) The heights of male students in a college are thought to be normally distributed with mean 170 cm and standard deviation 7.
The heights of 5 male students from this college are measured and the sample mean was 174 cm.
Determine, at 5% level of significance, whether there is evidence that the mean height of the male students of this college is higher than 170 cm.
[6]
(b) (i) The result of a fitness trial is a random variable X which is normally distributed with mean μ and standard deviation 2.4 . A researcher uses the results from a random sample of 90 trials to calculate a
98% confidence interval for μ . What is the width of this interval?
[4]
(ii) Packets of fish food have weights that are distributed with standard deviation 2.3 g. A random sample of 200 packets is taken. The mean weight of this sample is found to be 99.2 g. Calculate a 99% confidence interval for the population mean weight.
[4]
(c) (i) Explain the difference between a point estimate and an interval
Estimate. [2]
(ii) The daily takings, $ x, for a shop were noted on 30 randomly chosen days. The takings are summarized by Σ x=31 500 and
Σ x2=33 141 816 .
Calculate unbiased estimates of the population mean and variance of the shop’s daily taking. [4
Answer:
the answer is 50 but I don't know if
Give two examples of addition of two mixed numbers with different denominators
SHOW ALL STEPS
Answer:
First Example: 3 1/2 + 4 3/4, Second Example: 6 3/8 + 7 9/15
Extra Example: 8 4/20 + 3 5/10
Step-by-step explanation:
First Example:
1/2 + 3/4
1/2 is equal to 2/4 so it is now compatible to be added to 3/4.
2/4 + 3/4
= 5/4
Now for the mixed numbers since its 3 and 4, 3 + 4 = 7.
Final answer is 7 5/4.
Second Example:
3/8 + 9/15
9/15 can be reduced to 3/5
Now the equation is 3/8 + 3/5
= 15/40 + 24/40 is an equivalent equation
15/40 + 24/40
= 39/40
Now for the mixed numbers since its 6 and 7, 6 + 7 = 13
Final answer is 13 39/40.
I am going to include one last example just in case you need one:
Third Example:
4/20 + 5/10
We can reduce these to
1/5 + 1/2
= 2/10 + 5/10 is the equivalent equation
2/10 + 5/10
= 7/10
Now for the mixed numbers since its 8 and 3, 8 + 3 = 11.
Final answer is 11 7/10.
I Hope this helps!
Calculate the pH of a buffer solution made by mixing 300 mL of 0.2 M acetic acid, CH3COOH, and 200 mL of 0.3 M of its salt sodium acetate, CH3COONa, to make 500 mL of solution. Ka for CH3COOH = 1.76×10–5
Answer:
Approximately [tex]4.75[/tex].
Step-by-step explanation:
Remark: this approach make use of the fact that in the original solution, the concentration of [tex]\rm CH_3COOH[/tex] and [tex]\rm CH_3COO^{-}[/tex] are equal.
[tex]{\rm CH_3COOH} \rightleftharpoons {\rm CH_3COO^{-}} + {\rm H^{+}}[/tex]
Since [tex]\rm CH_3COONa[/tex] is a salt soluble in water. Once in water, it would readily ionize to give [tex]\rm CH_3COO^{-}[/tex] and [tex]\rm Na^{+}[/tex] ions.
Assume that the [tex]\rm CH_3COOH[/tex] and [tex]\rm CH_3COO^{-}[/tex] ions in this solution did not disintegrate at all. The solution would contain:
[tex]0.3\; \rm L \times 0.2\; \rm mol \cdot L^{-1} = 0.06\; \rm mol[/tex] of [tex]\rm CH_3COOH[/tex], and
[tex]0.06\; \rm mol[/tex] of [tex]\rm CH_3COO^{-}[/tex] from [tex]0.2\; \rm L \times 0.3\; \rm mol \cdot L^{-1} = 0.06\; \rm mol[/tex] of [tex]\rm CH_3COONa[/tex].
Accordingly, the concentration of [tex]\rm CH_3COOH[/tex] and [tex]\rm CH_3COO^{-}[/tex] would be:
[tex]\begin{aligned} & c({\rm CH_3COOH}) \\ &= \frac{n({\rm CH_3COOH})}{V} \\ &= \frac{0.06\; \rm mol}{0.5\; \rm L} = 0.12\; \rm mol \cdot L^{-1} \end{aligned}[/tex].
[tex]\begin{aligned} & c({\rm CH_3COO^{-}}) \\ &= \frac{n({\rm CH_3COO^{-}})}{V} \\ &= \frac{0.06\; \rm mol}{0.5\; \rm L} = 0.12\; \rm mol \cdot L^{-1} \end{aligned}[/tex].
In other words, in this buffer solution, the initial concentration of the weak acid [tex]\rm CH_3COOH[/tex] is the same as that of its conjugate base, [tex]\rm CH_3COO^{-}[/tex].
Hence, once in equilibrium, the [tex]\rm pH[/tex] of this buffer solution would be the same as the [tex]{\rm pK}_{a}[/tex] of [tex]\rm CH_3COOH[/tex].
Calculate the [tex]{\rm pK}_{a}[/tex] of [tex]\rm CH_3COOH[/tex] from its [tex]{\rm K}_{a}[/tex]:
[tex]\begin{aligned} & {\rm pH}(\text{solution}) \\ &= {\rm pK}_{a} \\ &= -\log_{10}({\rm K}_{a}) \\ &= -\log_{10} (1.76 \times 10^{-5}) \\ &\approx 4.75\end{aligned}[/tex].
please help to solve this in written format
Answer:
50 dozen total
Step-by-step explanation:
8/12 & 10/12.... average 9/12
11/12 - 9/12 =
2/12x = 100
2x = 1200
x = 600/12
50 dozen total
Solve for X.
-6x + 14 < -28
AND 3x + 28 < 25
Answer:
1. -6x + 14 < -28
6x<42
x<7
2. 3x + 28 < 25
3x < -3
x<-1
Hope This Helps!!!
Sarah ordered 39 shirts that cost $8 each. She can sell each shirt for $16.19. She sold 32 shirts to customers. She had to return 7 shirts and pay a $1.4 charge for each returned shirt. Find Sarah's profit.
Answer:
$196.28
Step-by-step explanation:
Original cost: 39 × $8 = $312
Revenue: 32 × $16.19 = $518.08
Return charge: 7 × $1.4 = $9.8
$312 + $9.8 = total cost, which is $321.8
$518.08 - $321.8 = profit
Profit = $196.28
Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
Answer:
Slope = 2
Step-by-step explanation:
To find the slope of the line, you need to plot two points
My own two points will be: [tex](1,2)[/tex] and [tex](2,4)[/tex]
Now use the Slope-Formula to identify the slope of the line
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{4-2}{2-1}[/tex]
[tex]m=\frac{2}{1}[/tex]
[tex]m=2[/tex]
so the slope of the line in simplest form will be 2.
A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 47.0 and 57.0 minutes. Find the probability that a given class period runs between 51.25 and 51.5 minutes.
Answer:
0.025 = 2.5% probability that a given class period runs between 51.25 and 51.5 minutes.
Step-by-step explanation:
Uniform probability distribution:
An uniform distribution has two bounds, a and b.
The probability of finding a value between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
Uniformly distributed between 47.0 and 57.0 minutes.
This means that [tex]a = 47, b = 57[/tex]
Find the probability that a given class period runs between 51.25 and 51.5 minutes.
[tex]P(c \leq X \leq d) = \frac{51.5 - 51.25}{57 - 47} = 0.025[/tex]
0.025 = 2.5% probability that a given class period runs between 51.25 and 51.5 minutes.
The sum of 5 consecutive integers is 505. What is the second number in this sequence?
Answer:
The second number is 100.
Step-by-step explanation:
Let the first integer be x.
Then since the five integers are consecutive, the second integer will be (x + 1), the third (x + 2), fourth (x + 3), and the fifth (x + 4).
They total 505. Hence:
[tex]\displaystyle x+(x+1)+(x+2)+(x+3)+(x+4)=505[/tex]
Solve for x. Combine like terms:
[tex]5x+10=505[/tex]
Subtract 10 from both sides:
[tex]5x=495[/tex]
And divide both sides by five. Hence:
[tex]x=99[/tex]
Thus, our sequence is 99, 100, 101, 102, and 103.
The second number is 100.
using the 1 to 9 at the most time each, fill in the boxes to make a true statement
Answer:
2
Step-by-step explanation:
8*8 is 64
Since it looks like the empty box is an exponent, and there are 2 8s being multiplied, the answer is 2
If 2(x + 3) - 27 = 3[7 - 2(x + 19)], what is 2x - 5?
Answer:
D = -23
Step-by-step explanation:
Answer:
D) -23
Step-by-step explanation:
Definitely
Can someone help me with this question an my other work?
The product of 2 integers is 72. One number is two less than five times the other. Which equation can be used?
Answer:
should be (5y-2)y = 72
Step-by-step explanation:
since the product of the two is 72, it's true that xy = 72. and it is also true that x is equal to five times y minus 2, so you can rewrite x as 5y-2. plug that in for x in the first equation, and you're set. hope this helps :)
Two different formulas of an oxygenated motor fuel are being tested to study their road octane numbers. The variance of road octane number for formula 1 is σ12=1.5, and for formula 2 it is σ22=1.2. Two random samples of size n1=15 and n2=20 are tested, and the mean octane numbers observed are x¯1=89.0 fluid ounces and x¯2=92.2 fluid ounces. Assume normality.
a. Test the hypothesis that the formulations are equal versus the hypothesis that formulation 2 produces a higher mean road octane number than formulation 1. Calculate z0=
b. Calculate a 95% two-sided confidence interval on the mean difference road octane number.
Answer:
Step-by-step explanation:
a)
zo=(89.0-92.2)/sqrt((1.5/15)+(1.2/20))
zo=-8.00
p-value=0.0000
Reject the null hypothesis.
b)
95% confidence interval for difference
=(89-92.2)+/-1.96*sqrt((1.5/15)+(1.2/20))
=-3.2+/-0.78
=(-3.98, -2.42)
Hello, please help me!!
Answer:
0.14
Step-by-step explanation:
P(A|B) asks for the probability of A, given that B has happened. This is equal to the probability of A and B over the probability of B (see picture)
Here, the question is asking if someone is taking the bus given that they are a senior.
The probability of someone being a senior and taking the bus is 5/100, or 0.05 . The probability of someone being a senior is 35/100, or 0.35
Our answer is then 0.05/0.35 = 1/7 = 0.14
If X is a normal random variable with mean 6 and standard deviation 2.0, then find the value x such that P(X > x) is equal to .7054. Group of answer choices5.28
5.46
4.92
7.28
Answer:
Step-by-step explanation:
If X is a normal random variable with a mean of 6 and a standard deviation of 3.0, then find the value x such that P(Z>x)is equal to .7054.
-----
Find the z-value with a right tail of 0.7054
z = invNorm(1-0.7054) = -0.5400
x = zs+u
x = -5400*3+6 = 4.38
You buy a six pack of Gatorade for $9.00. What is the unit price or the price per bottle?
$1.50/bottle
$2/bottle
$1.75 per bottle
Answer:
The answer is $1.50/bottle.
Step-by-step explanation:
To get the unit price, you need to divide the total by the amount of bottles.
[tex]9.00/6=1.50[/tex]
The cost of 5 gallons of ice cream has a variance of 64 with a mean of 34 dollars during the summer. What is the probability that the sample mean would differ from the true mean by less than 1.1 dollars if a sample of 38 5-gallon pails is randomly selected
Answer:
0.5587 = 55.87% probability that the sample mean would differ from the true mean by less than 1.1 dollars.
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 cost of 5 gallons of ice cream has a variance of 64 with a mean of 34 dollars during the summer.
This means that [tex]\sigma = \sqrt{64} = 8, \mu = 34[/tex]
Sample of 38
This means that [tex]n = 38, s = \frac{8}{\sqrt{38}}[/tex]
What is the probability that the sample mean would differ from the true mean by less than 1.1 dollars ?
P-value of Z when X = 34 + 1.1 = 35.1 subtracted by the p-value of Z when X = 34 - 1.1 = 32.9. So
X = 35.1
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{35.1 - 34}{\frac{8}{\sqrt{38}}}[/tex]
[tex]Z = 0.77[/tex]
[tex]Z = 0.77[/tex] has a p-value of 0.77935
X = 32.9
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{32.9 - 34}{\frac{8}{\sqrt{38}}}[/tex]
[tex]Z = -0.77[/tex]
[tex]Z = -0.77[/tex] has a p-value of 0.22065
0.77935 - 0.22065 = 0.5587
0.5587 = 55.87% probability that the sample mean would differ from the true mean by less than 1.1 dollars.
Translate the sentence into an inequality. The product of w and 2 is less than 23.
Answer:
2w<23
Step-by-step explanation:
The product of w and 2 mean that w multiplied by 2
The product of -3x and (2x+5) is …
[tex]\huge{\boxed{\boxed{ Solution ⎇}}} \ [/tex]
[tex] - 3x \times (2x + 5) \\ = - 3x \times 2x + - 3x \times 5 \\ = - 6x ^{2} - 15x[/tex]
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ ツ
꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐
[tex] \huge\boxed{\mathfrak{Answer}}[/tex]
[tex] - 3x \times (2x + 5) \\ = - 3x \times 2x + - 3x \times 5 \\ = - 6x ^{2} - 15x [/tex]
Answer ⟶ - 6x² - 15x
Using law of sines please show process!!!
Let the <C=x
We know in a triangle
☆Sum of angles=180°
[tex]\\ \sf\longmapsto 51+26+x=180[/tex]
[tex]\\ \sf\longmapsto 77+x=180[/tex]
[tex]\\ \sf\longmapsto x=180-77[/tex]
[tex]\\ \sf\longmapsto x=103°[/tex]
PLS HELP please give an explanation if you don’t have one pls still give answer
The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a student's alarm clock has a 15.3% daily failure rate. Complete parts (a) through (d) below. a. What is the probability that the student's alarm clock will not work on the morning of an important final exam?
Answer:
[tex]Pr = 0.153[/tex]
Step-by-step explanation:
Given
[tex]p = 15.3\%[/tex]
Required
Probability of alarm not working
[tex]p = 15.3\%[/tex] implies that the alarm has a probability of not working on a given day.
So, the probability that the alarm will not work on an exam date is:
[tex]Pr = 15.3\%[/tex]
Express as decimal
[tex]Pr = 0.153[/tex]
answer quick it's urgent
Expand : (5xy+7)(5xy-7)
Answer:
[tex](5xy + 7)(5xy-7) = 25x^2 y^2 - 49[/tex]
Step-by-step explanation:
[tex](a - b)(a +b ) = a^2 - b^2 \\\\From \ given \ expression \ a = 5xy \ , \ b = 7\\\\Therefore , (5xy + 7 )(5xy - 7 ) = ( 5xy)^2 - ( 7)^2 \\[/tex]
[tex]= 25x^2 y^2 - 49[/tex]
Answer:
25x²y² - 49
Step-by-step explanation:
We can do this by using the a+b formula:
(a+b)(a-b)= a² - b²
So,
(5xy+7)(5xy-7)
=(5xy)² - 7²
= 25x²y² - 49
Another way we can do this by expanding the algebraic expression:
(5xy+7)(5xy-7)
= 5xy(5xy-7) + 7(5xy-7)
= 25x²y² - 35xy + 35xy - 49
= 25x²y²- 49
Is it possible to have a relation on the set {a, b, c} that is both symmetric and transitive but not reflexive
Answer:
Yes, it is possible to have a relation on the set {a, b, c} that is both symmetric and transitive but not reflexive
Step-by-step explanation:
Let
Set A={a,b,c}
Now, define a relation R on set A is given by
R={(a,a),(a,b),(b,a),(b,b)}
For reflexive
A relation is called reflexive if (a,a)[tex]\in R[/tex] for every element a[tex]\in A[/tex]
[tex](c,c)\notin R[/tex]
Therefore, the relation R is not reflexive.
For symmetric
If [tex](a,b)\in R[/tex] then [tex](b,a)\in R[/tex]
We have
[tex](a,b)\in R[/tex] and [tex](b,a)\in R[/tex]
Hence, R is symmetric.
For transitive
If (a,b)[tex]\in R[/tex] and (b,c)[tex]\in R[/tex] then (a,c)[tex]\in R[/tex]
Here,
[tex](a,a)\in R[/tex] and [tex](a,b)\in R[/tex]
[tex]\implies (a,b)\in R[/tex]
[tex](a,b)\in R[/tex] and [tex](b,a)\in R[/tex]
[tex]\implies (a,a)\in R[/tex]
Therefore, R is transitive.
Yes, it is possible to have a relation on the set {a, b, c} that is both symmetric and transitive but not reflexive.
Please answer i need help please i will give you brainlest please
Answer:
14) 4x+10=8x-26 (corresponding angles are equal)
4x-8x=-26-10
-4x=-36
x= -36/-4= 9
x=9
15) perimeter of rectangle= 2(l+b)
2( l+ [tex]\frac{2l}{3}[/tex]) = 40m
2l+ [tex]\frac{4l}{3}[/tex] =40
Take LCM as 3
[tex]\frac{2l}{1}[/tex] * [tex]\frac{3}{3}[/tex] + [tex]\frac{4l}{3}[/tex] =40
[tex]\frac{6l+4l}{3}[/tex] = 40
[tex]\frac{10l}{3}[/tex] = 40
10l=40*3
10l = 120
l= 120/10 =12 cm
l=12cm
b= 2/3 *12 = 8cm
16) 2:3:4
It can be written as 2x+3x+4x
sum of angles of a triangle =180 degree
so 2x+3x+4x=180
9x=180
x=180/9=20 degree
1st angle=2x=2*20= 40 degree
2nd angle= 3x=3*20 =60 degree
3rd angle= 4x=4*20= 80 degree
17) sum of interior angles of a pentagon is 540 degree
so, 125+88+128+60+x=540 degree
401 +x= 540 degree
x=540-401= 139 degree
Hope this helps
Please mark me as brainliest
help? haha
solve the equation below:)
3x - 5 = 10 + 2x
Step-by-step explanation:
3x-2x=5+10 [taking variables on one side and constant on other]
x=15
soln:
3x-5= 2x+10
3x -5+5=2x+10+5 [ adding 5 on both side]
3x=2x+15
3x-2x=2x+15-2x [subtracting 2x on both side]
x=15
Ans=15
Answer:
[tex]x = 15[/tex]
Step-by-step explanation:
[tex]3x - 5 = 10 + 2x[/tex]
[tex]3x - 2x = 10 + 5[/tex]
[tex]1x = 15[/tex]
[tex]x = 15[/tex]
Hope it is helpful.....Which function represents the graph below?
Answer:
The answer is the third one below
Paul writes newspaper articles. He earns a base rate of $500 per month and an additional $100 per article he writes. Last month he earned $2000.
Write an equation to determine the number of articles (a) he sold last month.
Answer:
Total earning last month with x articles is:
x*100 + 500This is same amount as 2000
The equation is:
100x + 500 = 2000Find the slope of the line that passes through the two points 2,-4 & 4,-1
Answer:
Step-by-step explanation:
I have this saved on my computer in notepad b/c this type of question get asked sooo often :/
point P1 (-4,-2) in the form (x1,y1)
point P2(3,1) in the form (x2,y2)
slope = m
m = (y2-y1) / (x2-x1)
My suggestion is copy that above and save it on your computer for questions like this
now use it
Point 1 , P1 = (2,-4) in the form (x1,y1)
Point 2 , P2 = (4,-1) in the form (x2,y2)
m = [ -1-(-4) ] / [ 4-2]
m = (-1+4) / 2
m = 3 / 2
so now we know the slope is 3/2 :)
