The correct options for the given parts are as follows
(a) Two-sample t-test.
(b) x1 bar - x2 bar = 12.1 - 11.2 = 0.9
(c) p - value = 0.031
(d) The null hypothesis is rejected. There is sufficient evidence of a difference between the mean height of two cacti.
(e) The test result is statistically significant.
(f) Type I error, which means the scientist concluded there is a significant difference between average height of cacti in Africa and cacti in Mexico, when in reality there is no difference.
What is sample statistics?
Any number calculated from your sample data is referred to as a sample statistic (or simply a statistic). The sample average, median, sample standard deviation, and percentiles are a few examples. Because a statistic is based on data obtained through random sampling, which is a random experiment, it is a random variable.
a) Since there are two independent samples and we want to compare population means. We must use: Two-sample t-test.
b) The value of the sample statistic to test those hypotheses is:
x1 bar - x2 bar = 12.1 - 11.2 = 0.9
c) This is two-tailed test. For p-value, use excel formula =TDIST(2.169,202,2).
p - value = 0.031
d) Since p-value is less than 0.05, correct option is:
The null hypothesis is rejected. There is sufficient evidence of a difference between the mean height of two cacti.
e) Since p-value is less than 0.05, correct option is:
-The test result is statistically significant.
f) Since null hypothesis is rejected, we might have been made Type I error. The correct option is:
-Type I error, which means the scientist concluded there is a significant difference between average height of cacti in Africa and cacti in Mexico, when in reality there is no difference.
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What is the measure of ABC
Answer:
Step-by-step explanation:
find x
7x+10=2x+40+3x
2x=30
x=15
ABD = 7(15)+10 = 115
ABD + ABC =180
115+ABC=180
ABC=65
Which statements are true for the functions g(x) = x2 and h(x) = –x2 ? Check all that apply.
For any value of x, g(x) will always be greater than h(x).
For any value of x, h(x) will always be greater than g(x).
g(x) > h(x) for x = -1.
g(x) < h(x) for x = 3.
For positive values of x, g(x) > h(x).
For negative values of x, g(x) > h(x).
The statements that are true for functions g(x) = x² and h(x) = -x² are given as follows:
g(x) > h(x) for x = -1.For positive values of x, g(x) > h(x).For negative values of x, g(x) > h(x).What is the relation between the functions?The functions for this problem are defined as follows:
g(x) = x².h(x) = -x².The function h(x) is given by the multiplication of the function g(x) by -1, meaning that it is the reflection over the x-axis of the function g(x).
The two quadratic functions share the same vertex at the origin, meaning that it cannot be affirmed that one function will always be greater than the other for all values of x.
However, considering that the x² function is non-negative in all it's domain, the reflected function -x² will be non-positive at all it's domain, they are equal only at the origin, which is the vertex, all for all remaining non-zero values, g(x) is greater than h(x).
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Xp-rx=ah
Solve for P
(Steps needed)
The value of p in the equation is as follows:
p = ah / x + rHow to find the subject of a formula?The subject of a formula is the variable which is expressed in terms of the other variables.
In other words, the subject of the formula is the variable which is on the left hand side of the formula.
Therefore, let's make p the subject of the formula in the equation xp - rx = ah.
xp - rx = ah
add rx to both sides of the equation
xp - rx = ah
xp - rx + rx = ah + rx
xp = ah + rx
divide both sides by x
xp = ah + rx
xp / x = ah / x + rx / x
Therefore, the value of p = ah / x + r
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A smoothie recipe calls for 2 1\4 cups of frozen mango if the recipe serves two how many cups of frozen mango is needed the serve one
Answer: 1 1/8
Step-by-step explanation:
1/4 in half is equivalent to 1/8
the quotient of two polynomial expressions is a rational expression.
Yes, The quotient of two polynomial expressions is a rational expression. so the statement is true
Polynomial Expression
A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division (No division operation by a variable).
Rational expression
A rational expression is the quotient of two polynomial expressions where the denominator is not equal to zero.
Consider two polynomial p(x) & q(x)
and q(x) [tex]\neq[/tex] 0
then the quotient is a rational expression
so the statement is true.
Yes, The quotient of two polynomial expressions is a rational expression. so the statement is true
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**I WILL MARK BRAINLIEST AND GIVE 58 POINTS**
Decide which situations can be represented by the system of equations y= x + 9 and x + y = 300.
1. Kiran scores 300 career goals. There are 9 more games to play.
2. Mrs. Ardoin and Mrs. Thomason measure the length of their lawns. They notice that Mrs. Ardoin's lawn is 9 yards longer, and their lengths add up to exactly 300 yards .
3. University View Academy took a count of their faculty. They found that there are 9 more male faculty members than female, and their total number of faculty members is 300.
Kayla tried to find the median from the following table, which shows the number of chin-ups she did
last week. However, she made a mistake.
Day
Number of chin-ups
Here is Kayla's work:
=
5+7+9+4+5
5
30
5
Mon Tue Wed Thu Fri
5 7 9 4 5
= 6
"The median is 6 chin-ups per day."
What mistake did Kayla make?
Answer:
Kayla Calculated the Mean instead of the median.
Step-by-step explanation:
If Kayla's work is the sum of all the numbers, she is calculating the mean.
you toss a pair of six-sided dice. (a) determine the number of possible pairs of outcomes. (recall that there are six possible outcomes for each die.)
36 is the number of possible pairs of outcomes by probability.
What is a probability answer?
Mathematics' branch of probability, where probability is the likelihood that any event will occur, deals with the occurrence of random events.
The probability value is given as a number between 0 and 1. Probabilities are always between 0 and 1. The basic probability formula is: Probability = Number of Favorable Outcomes / Total Number of Outcomes.
We have two dice in this question. A die is known to be make up of 6 faces.
Therefore the number of faces for two dice = 6*6 = 36
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if the probability that a certain tennis player will serve an ace is 1 4 , what is the probability that he will serve exactly four aces out of seven serves? (assume that the seven serves are independent. round your answer to four decimal places.)
The probability that he will serve exactly four aces out of seven serves is 5.7 %.
Given :
if the probability that a certain tennis player will serve an ace is 1 / 4 .
If we let p stand for the probability of a succes, then p = 1/4, and ( 1 - p ) = 3/4. (1-p) is the probability that he will NOT serve an ace.
Formula for probability:
P (m successes in n trials) = ( nCm ) * p^m * ( 1 - p )^( n - m ).
= 7C4 * ( 1/4 )^4 * ( 3/4 )^( 7 - 4 )
= 7! / ( 7 - 4 )! 4! * 1/256 * 27/64
= 7 * 6 * 5 / 3 * 2 * 1 / 256 * 27/64
= 35/256 * 27/64
= 945/16384
= 0.057
= 0.057 * 100 %
= 5.7 %
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I am too tired to think, please help my daughter finish her homework
Answer: 3(p-5) + 2s
Step-by-step explanation:
Let p represent the henna powder, we know that she has a discount of $5 dollar for every henna powder, and she will buy 3.
So the equation is 3(p-5), plus the two bottles, we get the equation
3(p-5) + 2s
How do you evaluate 12P7?
The evaluation of 12P7 through permutation is 3991680.
This is a question of permutations . The capital letter P is a symbol for permutations. A permutation is a word that describes the number of ways things can be ordered or arranged. In other words , a permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters.
The formula for permutation is P(n,r)=n! (n−r)!
Hence , 12P7 = 12!/(12-7)!
⇒ 12!/5!
⇒ 12×11×10×9×8×7×6×5!/5!
Now , cancelling 5! from both denominator and numerator, we get
⇒ 12×11×10×9×8×7×6
⇒ 3991680
Therefore , the answer is 3991680.
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(3.65u − 11) − (−5 + 8.7u)
Answer:
73u/ - 11
Step-by-step explanation:
Answer:
-5.05. U -6
Step-by-step explanation:
Distribute the Negative Sign:=3.65u−11+−1(−5+8.7u)=3.65u+−11+(−1)(−5)+−1(8.7u)=3.65u+−11+5+−8.7uCombine Like Terms:=3.65u+−11+5+−8.7u=(3.65u+−8.7u)+(−11+5)=−5.05u+−6
if n is an integer and n3 is divisible by 24, what is the largest number that must be a factor of n?
If n is an integer and n3 is divisible by 24, The largest number that must be a factor of n is 8.
N3 is a number that is divisible by 24, meaning it can be expressed as 24k, where k is an integer.
This can further be expressed as 8(3k), meaning that 8 is the largest number that is a factor of 24, and therefore must also be a factor of n3. Consequently, the largest number that must be a factor of n3 is 8.
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A second investment account starts with $2,000 and grows by $150 each year. How much money would be in this account in 10 years?
Answer: He would have $1,500 alone from making $150 each year, and the total would be $3,500.
Step-by-step explanation: To find how much money he makes in 10 years (not including the $2,000) we would multiply 150 by 10 to get 1500.
Now, we need to add 2000 + 1500, and we get 3,500.
I hope this helps!
television viewers often express doubts about the validity of certain commercials. in an attempt to answer their critics, a large advertiser wants to estimate the true proportion of consumers who believe what is shown in commercials. preliminary studies indicate that about 40% of those surveyed believe what is shown in commercials. what is the minimum number of consumers that should be sampled by the advertiser to be 95% confident that their estimate will fall within 2% of the true population proportion? a) 2305 b) 2327 c) 2285 d) 2317 e) 2292 f) none of the above
2327 is the minimal number of consumers that should be sampled by the advertiser to be 95% confident that their estimate will fall within 2% of the genuine population proportion.
Given that,
TV viewers frequently doubt the validity of particular advertising. In an attempt to counter their critics, a large advertiser wants to determine the true proportion of consumers who believe what is depicted in ads. About 40% of individuals examined, according to preliminary studies, seem to believe what is depicted in advertisements.
We have to find what is the minimal number of consumers that should be sampled by the advertiser to be 95% confident that their estimate will fall within 2% of the genuine population proportion.
We know that,
Let
Population proportion (p)= 0.40
Margin of error = 2% = 0.02
Confidence level = 95% = 0.95
α = 1- 0.95 = 0.05
α/2 = 0.025
Let's find out the Z critical value using excel for the 95% confidence level,
Use the following excel command.
= ABS(NORMSINV(α/2))
= ABS(NORMSINV(0.025))
We will get, Z critical value = 2.17009
Sample size (n) = p(1-p)×(Zα/2)/E
n = 0.40(1-0.40)({2.17009}÷{0.05})²
Sample size (n) = 2327
Therefore, 2327 is the minimal number of consumers that should be sampled by the advertiser to be 95% confident that their estimate will fall within 2% of the genuine population proportion.
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find the weight of a pumpkin hanging from two scales, if scale one reads 44 n, scale two reads 46 n, and the angle θ between the strings coming from the two scales is 72 degrees.
The pumpkin hangs between the two scales and weighs 58.77 N.
Explain the term resultant force?The entire force operating on the item or body, combined with the body's direction, is referred to as the resultant force. Once the object is at rest or moving at the same speed as the object, then resultant force is zero.The given data is-
a = 44 N when reading from scale one.b = 46 N when reading on scale two.Ф = 72° is the angle between both the two scales.The result of the 2 scale readings is equal to the weight of a pumpkin swinging from the two scales.
The two forces combine to create resultant force;
R² = a² + b² - 2abcos(θ)
R² = 44² + 46² - 2(44)(46)cos(72)
R² = 3454.97
R = 58.77
Consequently, the pumpkin's weight on the two scales is 58.77 N.
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-6x – 9y = 0
-24x = 36y
infinite
none
or one solution?
Answer:
No solution
Step-by-step explanation:
-6x - 9y = 0
-24x -36y = 0
Multiply the top equation by -4 and add that to the second equation
24x + 36y = -4
-24x - 36y = 0
0 + 0 = -4
0 ≠ -4 Since this is a false statement, the answer is no solution.
luianne works as a waitress at a local emerald monday restaurant. her regular hourly wage is $15.50. she regularly works 40 hours per week. what is her regular weekly pay?
Luianne earns $4340 weekly by working as waitress at a local emerald Monday restaurant.
As per the known fact, one week comprises of seven days. Concerning this, the formula to be used for calculation is -
Regular weekly pay = Numbers of hours of work × number of days in a week × pay per hour
Keep the values in formula to find the regular weekly pay
Regular weekly pay = 40 × 7 × 15.50
Performing multiplication on Right Hand Side of the equation
Regular weekly pay = 4340
Hence, she earns $4340 weekly.
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(b) Use the defining formula to compute the sample standard deviation s_ Recall the defining formula used to compute the sample standard deviation $ where x is a F = member of the data set, x is the mean, and n is number of data values Before using the formula, we must determine x and n There are five values in the data set 1, 2, 4, 7, 8, so n Calculate the mean X by taking the average of the data values, which is dividing the sum of the data values by the number of data values: 1 + 2 + 4 + 7 + 8 22 Step 3 In order to use the defining formula for sample standard deviation, it is helpful to first calculate (x each data value in the data set 1, 2, 4, 7, 8. for Use the values in the data set and the previously determined mean, x = 4.4,to complete the following table_ 4.4 4.4 4.4 4.4 4.4 X-* ~3.4 0.4 3.6 11.56 5.76 6.76 (iX?
The standard deviation is 4.95.
The standard deviation is the average amount of variability in your dataset. It tells you, on average, how far each value lies from the mean.
A high standard deviation means that values are generally far from the mean, while a low standard deviation indicates that values are clustered close to the mean. The standard deviation and the mean together can tell you where most of the values in your frequency distribution lie if they follow a normal distribution.
Dataset: 1,2,4,7,8
So, n = 5 (because the sample size is 5)
We calculate the mean X by taking the average of the data values, which is dividing the sum of the data values by the number of data values:
X = 1+2+4+7+8/5
X=22/5 = 4.4
So, the average is 4.4
For standard deviation calculation,
$ = [tex]{\sqrt{(x-X)^2/n-1} }[/tex]
Thus, the standard deviation is 4.95.
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HELP MEEEEEEEEEEEEEEEEEEEEEEEE PLEASEEEEEEEEEEEEEEEEEEEEE!!!!!!!!!!!!!!!!!!!!!!!
What is the smallest degree of rotation that will map a regular 16-agon (a 16 sided figure) onto itself?
The smallest degree of rotation that will map a regular 16-agon onto itself is 22.5 degrees.
What is a degree?
A degree is a unit of measurement used to express angles. It is defined as 1/360th of a full rotation, or 1/2π radians.
To see this, note that a regular 16-agon has 16 sides, and each angle between sides measures 180(16-2)/16 = 135 degrees. Therefore, to rotate the 16-agon so that it maps onto itself, we must rotate it an integer multiple of 135 degrees.
However, we want the smallest such angle, so we must find the smallest integer multiple of 135 degrees that is greater than or equal to 360 degrees (since a full rotation maps the figure onto itself). The smallest such multiple is 2, which is equal to 270 degrees.
The smallest degree of rotation that will map the 16-agon onto itself is 270 degrees / 2 = 135 degrees / 2 = 22.5 degrees.
Hence, The smallest degree of rotation that will map a regular 16-agon onto itself is 22.5 degrees.
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how do you know if a system of two linear equations has one solution, multiple solutions or no solutions?
A system of linear equations has one solution when the graphs intersect at a point.
A system of linear equations has no solution when the graphs are parallel.
A system of linear equations has infinite solutions when the graphs are on the exact same line.
The graphs attached below show the linear equations that have one solution, multiple solutions, and no solutions.
A linear equation in two variables of the form axe + by + c = 0, where a, b, c R, a 0, and b 0. By comparing the coefficients of the equations while taking the system of linear equations into consideration, we may determine how many solutions there are. Additionally, we can use a graphical way to determine whether the equation system has a single solution or an infinite number of solutions.
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When matter burns: Mechanical energy is changed to heat energy. Light energy is changed to heat energy. Chemical energy is changed to heat energy.
Answer:
Chemical energy is changed to heat energy.
Step-by-step explanation:
The population of pets in Mr. Jones neighborhood in Bartlett has declined in the pass year by roughly 30%. Residents hypothesize that this is due to predation by coyotes. The current pets in Mr. Jones neighborhood is 90. Approximately how many pets were there originally?
Answer:
128 4/7
Step-by-step explanation:
100%-30%=70%
90=.7X
900=7X
128 4/7=X
a club elects a president, vice-president, and secretary-treasurer. how many sets of officers are possible if there are 13 members and any member can be elected to each position? no person can hold more than one office.
The number of different sets of officers possible is 1716 sets.
The number of sets of officers possible is the number of ways people can be chosen for the given posts.
Since there are 13 people available for the post of president,
The choice can be made in
13 ways.
For the post of the Vice-President, there are 12 likely candidates. Hence, the choice can be made in
12 ways
Similarly for the post of treasurer, there are 11 likely candidates available. Hence, the choice can be made in 11 different ways.
Hence, the total number of sets of officers possible are
13 X 12 X 11
= 1716 sets.
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Help meeeeee I don’t knowwwwwwwww
Answer:
# of adult tickets = 10
# of child tickets = 4
Step-by-step explanation:
a = # of adult tickets
c = # of child tickets
a + c = 14
a = 14-c
9a + 5c = 110
9(14-c) + 5c =110
126 - 9c + 5c = 110
-4c = 110-126 = -16
c = -16/-4 = 4
a = 14-4 = 10
what percentage of observed variation in hardness can be explained by the linear relationship between hardness and elapsed time? (round your answer to one decimal place.)
95.1% of the proportion of observed variation in hardness can be explained by the simple linear regression model relationship between hardness and elapsed time.
Linear regression model:
In statistics, linear regression model defined the relationship between a dependent variable, y, and one or more independent variables, X.
Given,
Here we need to find the percentage of observed variation in hardness can be explained by the linear relationship between hardness and elapsed time.
In order to find the percentage we must know the definition of observed variation which means the combined variation that is derived from all sources.
In order to solve this let us consider that the linear regression model is used by statisticians to predict the value of the response variable for given values of the predictor variables.
So, if there are two variables involved in the regression analysis, then the model is called a bivariate one.
Where as If there are more than two independent variables, then the regression model is known as the multiple regression model.
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PLS HELP I AM OFFERING 50 POINTS
The midpoints of the sides of a triangle are given. find the vertices of the original triangle. explain your process and how you can check the answer
P (2, 1), Q (4, 5), R(7, 4)
please explain how to solve this
Answer:
Step-by-step explanation:
Step 1
1 of 5
Graph the three points and connect them to create the mid segments of the triangle:
Use midsegments of triangles in the coordinate plane.
Use the Triangle Midsegment Theorem to fi nd distances.
Using the Midsegment of a Triangle
A midsegment of a triangle is a segment that connects the
midpoints of two sides of the triangle. Every triangle has
three midsegments, which form the midsegment triangle.
The midsegments of △ABC at the right are MP —, MN —,
and NP —. The midsegment triangle is △MNP.
Using Midsegments in the Coordinate Plane
In △JKL, show that midsegment MN — is parallel to JL —
and that MN =
1
—2 JL.
SOLUTION
Step 1 Find the coordinates of M and N by fi nding
the midpoints of JK — and KL —.
M (—
−6 + (−2)
2
, —
1 + 5
2
) = M ( −8 —
2
, 6
—
2
) = M(−4, 3)
N (—
−2 + 2
2
, —
5 + (−1)
2
) = N ( 0
—
2
, 4
—
2
) = N(0, 2)
Step 2 Find and compare the slopes of MN — and JL —.
slope of MN —= —
2 − 3
0 − (−4) = −
1
—
4
slope of JL — = —
−1 − 1
2 − (−6) = −
2
—
8
= −
1
—
4
Because the slopes are the same, MN — is parallel to JL —.
Step 3 Find and compare the lengths of MN — and JL —.
MN = √——
[0 − (−4)]2 + (2 − 3)2 = √—
16 + 1 = √—
17
JL = √———
[2 − (−6)]2 + (−1 − 1)2 = √—
64 + 4 = √—
68 = 2 √—
17
JL = √———
[2 − (−6)]2 + (−1 − 1)2 = √—
64 + 4 = √—
68 = 2 √—
17
Because √—
17 =
1
—2
(2 √—
17 ) , MN =
1
—2 JL.
Monitoring Progress onitoring Progress Help in English and Spanish at BigIdeasMath.com
Use the graph of △ABC.
1. In △ABC, show that midsegment DE — is parallel
to AC — and that DE =
1
—2 AC.
2. Find the coordinates of the endpoints of
midsegment EF —, which is opposite AB —. Show
that EF — is parallel to AB — and that EF =
1
—2 AB.
READING
In the fi gure for Example 1,
midsegment MN — can be
called “the midsegment
opposite JL —.”
midsegment of a triangle,
p. 330
Previous
midpoint
parallel
slope
coordinate proof
Core Vocabulary Core Vocabulary
A C
P
N
M
B
x
y
4
6
−2
−6 −4 −2
M
N
K(−2, 5)
J(−6, 1)
L(2, −1)
x
y
−4
−6
−2 2 4 6
D
E
C(5, 0)
B(−1, 4)
A(
Please help soon, functions problem! Thanks!
Answer:
5
Step-by-step explanation:
x=-1 doesn't fit in the range -1<x<2 since x>-1, not x=-1.
Hence, x=-1 fits in the range x<=-1 since (x<-1 or x=-1) which is true.
Hence, the expression -x+4 should be used
g(-1) =
-x + 4 =
-(-1) + 4 = ==> plugin -1 for x
1 + 4 = 5 ==> Negating a negative number is equal to taking a positive
number
If θ is an angle in standard position and its terminal side passes through the point (2,-1), find the exact value of \tan\thetatanθ in simplest radical form.
The exact value of tanθ is -1/2
What is the trigonometric ratio?
Trigonometric ratios are the ratios of a right triangle's sides. The sine (sin), cosine (cos), and tangent (tan) are three often used trigonometric ratios. There are other trigonometric ratios which are reciprocals of these ratios.
Given:
θ is an angle in standard position and its terminal side passes through the point (2,-1).
To find:
The exact value of tanθ in simplest radical form.
If θ is an angle in standard position and its terminal side passes through the point (x,y), then the exact value of tanθ is:
tanθ = y/x
It is given that, θ is an angle in standard position and its terminal side passes through the point (2,-1),. So, t he exact value of tanθ is:
tanθ = -1/2
Therefore, the required value is tanθ = -1/2
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