Solution :
Given :
mean weight of the dogs, [tex]$\overline x$[/tex] = 69
Number of dogs, n = 37
Standard deviation, σ = 9.2
Confidence interval = 90%
At 90% confidence interval for the true population mean dog weight is given by :
[tex]$= \overline x \pm \frac{\sigma}{\sqrt n} \times z_{0.05}$[/tex]
[tex]$= 69\pm \frac{9.2}{\sqrt_{37}}} \times 1.64485$[/tex]
[tex]$=69 \pm 2.487799$[/tex]
= (66.5122, 71.4878)
The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.974 g and a standard deviation of 0.325 g. The company that produces these cigarettes claims that it has now reduced the amount of nicotine. The supporting evidence consists of a sample of 48 cigarettes with a mean nicotine amount of 0.918 g. Assuming that the given mean and standard deviation have NOT changed, find the probability of randomly seleting 32 cigarettes with a mean of 0.917 g or less.
P(M < 0.917 g) = __________
Answer:
P(M < 0.917 g) = 0.1611.
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.
Mean of 0.974 g and a standard deviation of 0.325 g.
This means that [tex]\mu = 0.974, \sigma = 0.325[/tex]
Sample of 32:
This means that [tex]n = 32, s = \frac{0.325}{\sqrt{32}}[/tex]
Fnd the probability of randomly selecting 32 cigarettes with a mean of 0.917 g or less.
This is the p-value of Z when X = 0.917. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.917 - 0.974}{\frac{0.325}{\sqrt{32}}}[/tex]
[tex]Z = -0.99[/tex]
[tex]Z = -0.99[/tex] has a p-value of 0.1611.
So
P(M < 0.917 g) = 0.1611.
An angle measures. What is the measure of its complement? (b) An angle measures 48 . What is measure 26 of its supplement?
Write the equation of the line passing through the point (6,-9) with slope -5/6.
Answer:
The equation is y = -5/6 x-4
Step-by-step explanation:
The equation of a line in slope intercept form is
y = mx+b where m is the slope and b is the y intercept
y = -5/6 x+b
Substitute in the point
-9 = -5/6(6) +b
-9 = -5+b
Add 5 to each side
-4 = b
The equation is y = -5/6 x-4
approximate 10.54 to the nearest ten
Answer:
11 because <.5 is rounded to the next ten
You want to test the claim that the average age of students at Gorka College is greater than the average age of students at Yapoah College. You take a simple random sample of 53 people from Gorka and compute an average age of 21.2 (years) and a standard deviation of 1.1. Then you take a simple random sample of 46 students from Yapoah College and compute an average age of 20.7 and a standard deviation of 1.2.
Compute the t-statistic for testing the alternative hypothesis that the average age of Gorka students is greater than the average age of Yapoah students (set things up so that t is positive).
What are the degrees of freedom (using the conservative method)?
What is the P-value?
Is there significant evidence at the 0.05 level to support the hypothesis that the average age of Gorka students is higher than for Yapoah?
Answer:
Kindly check explanation
Step-by-step explanation:
The hypothesis :
H0 : μ1 = μ2
H1 : μ1 > μ2
Given :
x1 = 21.1 ; n1 = 53 ; s1 = 1.1
x2 = 20.7 ; n2 = 46 ; s2 = 1.2
The test statistic :
(x1 - x2) / √[(s1²/n1 + s2²/n2)]
(21.1 - 20.7) / √[(1.1²/53 + 1.2²/46)]
0.4 / 0.2326682
Test statistic = 1.719
The degree of freedom using the conservative method :
Comparing :
Degree of freedom = n - 1
Degree of freedom 1 = 53 - 1 = 52
Degree of freedom 2 = 46 - 1 = 45
Smaller degree of freedom is chosen ;
The Pvalue from Test statistic, using df = 45
Pvalue = 0.0462
Pvalue < α ; Hence, there is significant evidence to conclude that average age of Gorka student is higher than Yaphoa.
What is the 100th term of 1, 6, 11, 16
Answer:
496
Step-by-step explanation:
a+99d
1+ 99 (5)
1+ 495
Which step in the solution contains the first error ?? Please helpp
Answer:
step 4 I believe
Step-by-step explanation:
1. Leo ran around the track three times. The track was 400 meters. How many kilometers did he run altogether?
What is Start Fraction 5 Over 8 End Fraction divided by One-fourth?
Answer:
2.5
Step-by-step explanation:
5/8 ÷ 1/4
Division sign changes to multiplication and the reciprocal of the divisior is used to multiply instead :
5/8 * 4/1
= (5*4) / (8*1)
= 20 / 8
= 2.5
Which of the following pairs consists of equivalent fractions? .4/6 and 3/5 or 9/16 and 3/32 or 18/48 and 15/40 or 7/10 and 10/7
Answer:
18/48 and 15/40
Step-by-step explanation:
18/48 = 3/8
15/40 = 3/8
•°• 18/48 is equivalent to 15/40
Find Trig Ratios (with Radicals)
Answer:
the answer is 45 + 5-75 is equals to 30 +5
What is f(-2) for f(x)=(1/2)x^2
Answer:
[tex]{ \bf{f(x) = \frac{1}{2} {x}^{2} }} \\ \\ { \tt{f( - 2) = \frac{1}{2} {( - 2)}^{2} }} \\ = 2[/tex]
Insert a digit to make numbers that are divisible by 24 if it is possible: 83...8
plz i need help fast
Answer:
2
Step-by-step explanation:
8328÷24=347
hope this is helpful
Write an equation and solve for angle G? Show work
Answer:
50
Step-by-step explanation:
Complementary angles mean that the sum of the angles given is 90°. Therefore, as G and H are complementary, this means that G+H=90
G+H=90
(2x+10) + (x+20) = 90
Add values on left side
3x+30=90
Subtract 30 from both sides
3x=60
Divide both sides by 3
x=20
Since we now know the value of x, we can plug that in to G (2x+10) to get 2(20)+10 = 50 = G
The triangle has area of 72cm^2 and base of 18cm find the perpendicular height of the triangle
Answer:
The height is 8 cm
Step-by-step explanation:
The area of a triangle is
A = 1/2 bh
72 = 1/2 (18)h
72 = 9h
Divide each side by 9
72/9 = 9h/9
8 = h
The height is 8 cm
Answer:
8cm
Step-by-step explanation:
let y represent height
Area of a triangle=½base×height=72cm²
72cm²=½×18cm×y
72cm²=9cmy
72cm²/9cm=9cmy/9cm
8cm=y
Any help 13 points
If the price of tacos is $1.75, how many will consumers buy?
Answer:
B-100 If the price of tacos is $1.75, th consumers will buy 100 tacos
A group of campers is going to occupy campsites at a campground. There are 16 campsites from which to choose. In how many ways can the campsites be chosen?
Answer:
The campsites can be chosen in 5,765,760 different ways.
Step-by-step explanation:
Given that a group of campers is going to occupy 6 campsites at a campground, and there are 16 campsites from which to choose, to determine in how many ways the campsites can be chosen, the following calculation must be performed:
16 x 15 x 14 x 13 x 12 x 11 = X
240 x 182 x 132 = X
240 x 24,024 = X
5,765,760 = X
Therefore, the campsites can be chosen in 5,765,760 different ways.
Help Me Pls i need it now
Nonsense = Report
Answer:
8,6,3, v= 144
4,8,6, v=192
15,10,6, v=900
Step-by-step explanation:
Answer:
This geometric questions are very very simple let's start to solve all steps
Step-by-step explanation:
L means long of Prism and look at 8 and 6 for first prism. Which one is longest of course 8
w means wide =6
h means high=3 and
V means Volume: You must multiply by 3, 6,8 to find volume, so we can say Volume 3*6*8=144 easily
what is the area of the rectangle?
answers: 120 m
120 m2
120m3
120 cubic meters
top of the rectangle: 12 m
bottom of the rectangle:12 m
side of the rectangle: 10 m
side of the rectangle:10 m
Answer:
B
Step-by-step explanation:
Area = L * W
L = 12 m
W = 10 m
Area = 12 m * 10 m
Area = 120 m^2
Answer;
A. 120m²
Step-by-step explanation:Given That :-
Length of rectangle = 12mWidth of rectangle = 10mTo find :-
Area of rectangle.Solution :-
[tex]\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered} \sf Length = 12m\: \: \: \: \: \: \: \: \: \: \: \\ \begin{gathered}\begin{gathered}\boxed{\begin{array}{}\bf { \red{}}\\{\qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }{}\\ { \sf{ }}\\ { \sf{ }} \\ \\ { \sf{ }}\end{array}}\end{gathered}\end{gathered} \sf \: Width = 10m \end{gathered}\end{gathered} \end{gathered} \end{gathered}[/tex]
The area of a rectangle is equal to the length times the width.
Length × WidthSubstitute the values of the length l =12 and width w = 10 into the formula for the area of a rectangle.
12m × 10mMultiply 12m by 10m
12m × 10m= 120m²Hence, Area of rectangle is 120m² which means option A. is correct answer.
What is the output of the following function for x=2
F(x)= 2x^4-x^3+5x-9
Answer:25
Step-by-step explanation:
PLEASE ANSWER ASAP FOR BRANLIEST!!!!!!!!!!!!
Answer:
1. zero
2. seven over eight
3. one over three
4. one
5. one over two
PLEASE GIVE BRAINLYIST!!
Write the indicated event in set notation.When four coins are tossed, the first three tosses come up the same.[Hint: when four coins are tossed, the following 16 outcomes are possible:HHHH HHHT HHTH HHTTHTHH HTHT HTTH HTTTTHHH THHT THTH THTTTTHH TTHT TTTH TTTT ]a. (HHH, TTT) b. (HHHT, TTTH) c. (HHHT, TTTH, HTTT, THHH) d. (HHHH, HHHT, TTTH, TTTT)
Answer:
[tex]Outcomes = \{HHHH, HHHT,TTTH, TTTT\}[/tex]
Step-by-step explanation:
Given
[tex]S = \{HHHH, HHHT, HHTH, HHTT,HTHH, HTHT, HTTH, HTTT, THHH, THHT,[/tex]
[tex]THTH, THTT,TTHH, TTHT, TTTH, TTTT\}[/tex]
Required
The outcomes where the first three tosses are the same
To do this, we list out the outcomes that the first three are HHH or TTT.
So, we have:
[tex]Outcomes = \{HHHH, HHHT,TTTH, TTTT\}[/tex]
solve for x in the equation 9- x/4=2
Answer:
9-x/4=2
[tex] \frac{36 - x}{4} = 2[/tex]
[tex]36 - x = 2 \times 4[/tex]
[tex]36 - x = 8[/tex]
[tex] 36 - 8 = x[/tex]
[tex]28 = x[/tex]
[tex]x = 28[/tex]
9 - x/4 = 2
(36 - x)/4 = 2
36 - x = 8
36 - 8 = x
x = 28
I hope you understand...
Mark me as brainliest...
Susan uses the function p(x) = 4x to determine the perimeter of a square when she knows the side length, x. Which statements are true about the function?
The perimeter is the dependent variable.
The length of the side of the square is the dependent variable.
The value of p(x) depends on the value of x.
The length of the side of the square is the independent variable.
The value p(x) can be found by multiplying p by x.
The perimeter is the independent variable.
Answer:
Step-by-step explanation:
The perimeter is the dependent variable. TRUE
The length of the side of the square is the dependent variable. FALSE
The value of p(x) depends on the value of x. TRUE
The length of the side of the square is the independent variable. TRUE
The value p(x) can be found by multiplying p by x. FALSE
The perimeter is the independent variable. FALSE
Noel and Casey both start at the same place. Noel walks due south and Casey walks due east. After some time has passed, Noel is 6 miles south and Casey is 8 miles east. At this time, Noel is walking at a rate of 2 mph and Casey is walking at a rate of 1 mph. How fast is the distance between them increasing at this time
Answer:
2.04 miles per hour
Step-by-step explanation:
Given
Noel
[tex]n_1 =6miles[/tex]
[tex]r_1 = 2mph[/tex]
Casey
[tex]c_1 = 8miles[/tex]
[tex]r_2 =1mph[/tex]
Required
The rate at which the distance increases
Their movement forms a right triangle and the distance between them is the hypotenuse.
At [tex]n_1 =6miles[/tex] and [tex]c_1 = 8miles[/tex]
The distance between them is:
[tex]d_1 = \sqrt{n_1^2 + c_1^2}[/tex]
[tex]d_1 = \sqrt{6^2 + 8^2}[/tex]
[tex]d_1 = \sqrt{100}[/tex]
[tex]d_1 = 10miles[/tex]
After 1 hour, their new position is:
New = Old + Rate * Time
[tex]n_2 = n_1 + r_1 * 1[/tex]
[tex]n_2 = 6 + 2 * 1 = 8[/tex]
And:
[tex]c_2 = c_1 + r_2 * 1[/tex]
[tex]c_2 = 8 + 1 * 1 = 9[/tex]
So, the distance between them is now:
[tex]d_2 = \sqrt{n_2^2 + c_2^2}[/tex]
[tex]d_2 = \sqrt{8^2 + 9^2}[/tex]
[tex]d_2 = \sqrt{145}[/tex]
[tex]d_2 = 12.04[/tex]
The rate of change is:
[tex]\triangle d = d_2 -d_1[/tex]
[tex]\triangle d = 12.04 -10[/tex]
[tex]\triangle d = 2.04[/tex]
z =x^2-y^2 for find the domain
Answer:
R^2
Step-by-step explanation:
The domain for z =x^2-y^2 is R^2 ,where is the set of all real numbers.
Find f(5) for f(x)-1/9(3)*
O A. 27
O B. 81
O C. 9
O D. 3
Complete the point-slope equation of the line through (-5,7) and (-4,0)
y-7=?
12. Mr. Ellis bought several rose bushes
for $65 each. He was charged a $15
delivery fee. If r represents the number
of rose bushes, which expression
can be used to find the total cost of
Mr. Ellis' purchase?
A 150 - 65
B 65r + 15
c 15(r + 65)
D 651 - 15
Answer:
B
Step-by-step explanation:
Because every rose bush costs $65 and it's charged with a $15 delivery fee.
add negative 4 plus negative 6
-10
thats it, thats what i know