Answer:
The p-value of the test is 0.0007 < 0.05, indicating that the the snowfall for the 1993-1994 winters was higher than the previous 20-year average.
Step-by-step explanation:
20-year mean snowfall in the Denver/Boulder region is 28.76 inches. Test if the snowfall for the 1993-1994 winters has higher than the previous 20-year average.
At the null hypothesis, we test if the average was the same, that is, of 28.76 inches. So
[tex]H_0: \mu = 28.76[/tex]
At the alternate hypothesis, we test if the average incresaed, that is, it was higher than 28.76 inches. So
[tex]H_1: \mu > 28.76[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
28.76 is tested at the null hypothesis:
This means that [tex]\mu = 28.76[/tex]
Standard deviation of 7.5 inches. However, for the winter of 1993-1994, the average snowfall for a sample of 32 different locations was 33 inches.
This means that [tex]\sigma = 7.5, X = 33, n = 32[/tex].
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{33 - 28.76}{\frac{7.5}{\sqrt{32}}}[/tex]
[tex]z = 3.2[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample mean above 33, which is 1 subtracted by the p-value of z = 3.2. In this question, we consider the standard level [tex]\alpha = 0.05[/tex].
Looking at the z-table, z = 3.2 has a p-value of 0.9993.
1 - 0.9993 = 0.0007
The p-value of the test is 0.0007 < 0.05, indicating that the the snowfall for the 1993-1994 winters was higher than the previous 20-year average.
Need help ASAP NO LINKS
Answer:
9
Step-by-step explanation:
5(n-2)=35
5n-10=35
5n=35+10
5n=45
n=45/5
n=9
Please mark me as brainliest
Mia cut a piece of felt into 3 equal
sections. She used 1 section for an art project. What fraction of the felt did Mia use for the art
project?
(1 Point)
Answer:
[tex] \frac{1}{3} [/tex]
Step-by-step explanation:
Mia used One Third of the felt for her art project. 3/3 would be the whole felt together. Since one part of three sections was used up then this means that 1/3 was used.
The concentration of a pollutant in a lake is 85 parts per million (ppm) and is increasing at a rate of 4.6% each year. A possible formula for the concentration C as a function of year tis:
(a) C 85 +4.6t
(b) C-85-4.6t .
(c) C-85 +0.046t
(d) C-85 -0.046
(e) C = 85 (0.046)
(f) C-85 (0.954)
(g) C = 85 (1.046)
(h) C-85(1.46)
(i) C85(0.46)
(j) C-4.6 (0.85)
Answer:
[tex]C(t) = 85(1.046)^t[/tex], and the correct answer is given by option g.
Step-by-step explanation:
Equation for an concentration increasing exponentially:
The concentration after t years, considering that it increases exponentially, is given by the following equation:
[tex]C(t) = C(0)(1 + r)^t[/tex]
In which C(0) is the initial concentration and r is the growth rate, as a decimal.
The concentration of a pollutant in a lake is 85 parts per million (ppm) and is increasing at a rate of 4.6% each year.
This means that [tex]A(0) = 85, r = 0.046[/tex]. Thus
[tex]C(t) = C(0)(1 + r)^t[/tex]
[tex]C(t) = 85(1 + 0.046)^t[/tex]
[tex]C(t) = 85(1.046)^t[/tex], and the correct answer is given by option g.
1. What is the discriminant of the equation 5x2 - 20x + 20 = 0?
Answer:
0
Step-by-step explanation:
D = 20²-4(5)(20) = 400-400 = 0
What is the equivalent recursive definition for an = 12+ (n - 1)3?
A. a1 = 3, An = An-1 + 12
B. a1 = 12, An = 30n-1
C. a1 = 12, Un = On-1 +3
D. a1 = n, an= 1201-1+3
Answer:
[tex]A_1 = 12[/tex]
[tex]A_n = A_{n-1} + 3[/tex]
Step-by-step explanation:
Given
[tex]A_n =12+(n-1)3[/tex]
Required
Write as recursive
We have:
[tex]A_n =12+(n-1)3[/tex]
Open bracket
[tex]A_n =12+3n-3[/tex]
[tex]A_n =12-3+3n[/tex]
[tex]A_n =9+3n[/tex]
Calculate few terms
[tex]A_1 =9+3*1 = 9 + 3 = 12[/tex]
[tex]A_2 =9+3*2 = 9 + 6 = 15[/tex]
[tex]A_3 =9+3*3 = 9 + 9 = 18[/tex]
The above shows that the rule is to add 3.
So, we have:
[tex]A_1 = 12[/tex]
[tex]A_n = A_{n-1} + 3[/tex]
The measure of _A is 18° greater than the measure of _B. The two angles are complementary. Find the
measure of each angle.
The m_A is
1° m
and m_B is
Answer:
angle A=54 degree
angle B =36 degree
Step-by-step explanation:
let angle B be x
angle A=x+18
since they are complementary angles sum of these two angles will be 90 degree
x+x+18=90
2x=90-18
2x=72
x=72/2
x=36 degree
substitute the value of x to find angle A and angle B
for angle A
x+18
36+18
54 degree
for angle B
angle B =x
=36 degree
Now that we know that 2π is about 6.28, π2 is about 9.86, and 58−−√ is between 7 and 8, which choice represents the correct order of these expressions from least to greatest: 58−−√, 2π, π2, 8?
Answer:
use miss r sir hope I helped you
Find the surface area of the regular pyramid
Answer:
surface are of the pyramid =(1/2×6×5.2)+(3×1/2×6×10) =15.6+90 =105.6 yd²3. (a) Find the elasticity of the demand function p2 + 2p +
4 = 49 at p = 6.
(b) How will a price increase affect total revenue?
Answer:
6^2+12+4=49
36+16=49
52=49
therefore.3
7. The fastest ever Formula 1 qualifying lap at Silverstone is 1 minute, 29.6 seconds.
The fastest ever racing lap is 1 minute, 30.9 seconds.
How many tenths of a second quicker is the qualifying lap?
Answer:
1.3 seconds ; 13 tenth of a second
Step-by-step explanation:
Fastest ever qualifying lap = 1 minute 29.6 seconds
Fastest ever racing lap = 1 minute 30.9 seconds
The difference :
1 minute 30.9 seconds - 1 minute 29.6
30.9 seconds - 29.6 seconds = 1.3 seconds
1.3 seconds = 1.3/0. 1 = 13 tenth of a second
please helppppppppp me
What is the value of a?
A. 12
B. 15
C. 17.25
D. 21.25
Answer:
the answer is a.12
i think
Answer:
17.25
Step-by-step explanation:
The graph of g(x) resembles the graph of f(x) = x2, but it has been changed.
Which of these is the equation of g(x)?
Answer:
B. g(x)=x²-3 b is my answer
1.Ramu deposited Rs. 10,000 in a bank where interest is compounded
half yearly. If the rate of interest is 10% annually. How much amount he
will get after a year?
3
Answer:
Future value, A = $10,500
Step-by-step explanation:
Given the following data;
Principal = Rs. 10,000
Interest rate compounded half yearly = 10% = 10/2 = 5%
Time = 1 year
To find the future value, we would use the compound interest formula;
[tex] A = P(1 + \frac{r}{100})^{t}[/tex]
Where;
A is the future value. P is the principal or starting amount. r is annual interest rate. n is the number of times the interest is compounded in a year. t is the number of years for the compound interest.Substituting into the equation, we have;
[tex] A = 10000(1 + \frac{5}{100})^{1}[/tex]
[tex] A = 10000(1 + 0.05)[/tex]
[tex] A = 10000(1.05)[/tex]
Future value, A = $10,500
HELP ME PLEASEEEEEEEEEEEEEEEEEE
Answer:
y = 3/2x + 15
Step-by-step explanation:
change f(x) to 'y='
interchange 'x' and 'y' then solve for 'y':
y = 2/3x - 10
x = 2/3y - 10
x+10 = 2/3y
multiply each side by 3/2 to get:
y = 3/2x + 15
verify that A(3, 1), B(0, 5), and C(-1, -1) are the vertices of a right triangle.
- ⅘ x = 8.....................
im actually in middle school btw dunno why it says college
Answer:
-10
Step-by-step explanation:
See image below:)
Answer:
x = -10
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
-4/5x = 8
Step 2: Solve for x
[Division Property of Equality] Divide -4/5 on both sides: x = 8 / -4/5Divide: x = -10[12÷(9-6)]+4×6
please help
The answer is 28 ez.
Answer:
the answer is 28
Step-by-step explanation:
What is the greatest prime you must consider to test whether 4295 is prime?
Answer:
5
Step-by-step explanation:
4295/5 = 859
4295 is divisible by the prime number 5
no need to test any higher priime
Will mark Brainlest help plsssss
Answer:
45 is answer I guess cuz my teacher taught me just like that
The radius of a circle is 9in. Find it’s circumference in terms of
[tex]{ \bf{ \underbrace{Given :}}}[/tex]
Radius of the circle "[tex]r[/tex]" = 9 in.
[tex]{ \bf{ \underbrace{To\:find:}}}[/tex]
The circumference of the circle.
[tex]{ \bf{ \underbrace{Solution :}}}[/tex]
[tex]\sf\orange{The\:circumference \:of\:the\:circle\:is\:56.52\:in.}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
We know that,
[tex]\sf\purple{Circumference\:of\:a\:circle \:=\:2πr }[/tex]
[tex] = 2 \times 3.14 \times 9 \: in \\ \\ = 56.52 \: in[/tex]
Therefore, the circumference of the circle is 56.52 in.
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}[/tex]
10)
X + 80
70°
A) 5
C) -10
B) 8
D) 7
Answer:
C: x=-10
Step-by-step explanation:
Alternate interior angles are congruent to each other meaning that x+80=70 making x equal to -10. I hope this helped and this is one of my favorite units so post more these questions :)
Multiply each term number below by 5 to form a sequence
Answer:
Multiply the numbers by 5
Step-by-step explanation:
Mark me brainlist?
What is the quotient when (-12x9 + 3x7 + 24x6) is divided by 6x?
plllzzz im new and i neeed help
find the volume of the following composite object. enter your answer as an integer in the box
Answer:
4082
Step-by-step explanation:
Given
The composite object
Required
The volume
The object is a mix of a cone and a hemisphere
Such that:
Cone
[tex]r = 10cm[/tex] ---- radius (r = 20/2)
[tex]h = 19cm[/tex]
Hemisphere
[tex]r=10cm[/tex]
The volume of the cone is:
[tex]V_1 = \frac{1}{3}\pi r^2h[/tex]
[tex]V_1 = \frac{1}{3}\pi * 10^2 * 19[/tex]
[tex]V_1 = \frac{1900}{3}\pi[/tex]
The volume of the hemisphere is:
[tex]V_2 = \frac{2}{3}\pi r^3[/tex]
[tex]V_2 = \frac{2}{3}\pi 10^3[/tex]
[tex]V_2 = \frac{2000}{3}\pi[/tex]
So, the volume of the object is:
[tex]V = V_1 + V_2[/tex]
[tex]V = \frac{1900}{3}\pi + \frac{2000}{3}\pi[/tex]
[tex]V = \frac{3900}{3}\pi[/tex]
[tex]V = 1300\pi[/tex]
[tex]V = 1300 * 3.14[/tex]
[tex]V = 4082[/tex]
A six-character license plate can be any three letters of the alphabet, followed by any three numerical digits. How many different license plates are possible?
Answer:
17,576,000 different license plates are possible.
Step-by-step explanation:
Fundamental counting principle:
States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.
In this question:
For each letter, there are 26 possible outcomes.
For each digit, 10 possible outcomes.
So
L - L - L - D - D - D
Number of possible outcomes:
26 - 26 - 26 - 10 - 10 - 10
Each character of the license plate is independent, so, by the fundamental counting principle:
26*26*26*10*10*10 = 17,576,000
17,576,000 different license plates are possible.
write three ratios equivalent to the given ration 7/2
Answer:
(7*2 / 2*2) = 14/4 = 3.5
(7*3 / 2*3) = 21/6 = 3.5
(7*4 / 2*4) = 28/8 = 3.5
Step-by-step explanation:
just multiply or divide both number by the same quantity and you will maintain the ratio
Lisa played two rounds of
miniature golf. Her score was –3 in the
first round and +2 in the second round.
What was Lisa's score after two
rounds?
Answer:
-1 I think so.....
n please rate this
Find the area
76 sq meters
60 sq meters
30.5 sq meters
65 sq meters
Step-by-step explanation:
2*10+((4+10)x8)/2
=20+14*8/2
=76 sq meters
Which of the following triangles have three sides of different length? A. acute B. scalene C.equilateral D. right
Answer:
scalene
hope this helps
have a good day :)
Step-by-step explanation: