7x²+5x
Step-by-step explanation:(9x²+8x)-(2x²+3x)
We will subtract the like terms. That means that we will subtract [tex]2x^{2}[/tex] from [tex]9x^{2}[/tex] and 3x from 8x.
Choose the correct way to simplify 4(5-3) using the distributive property of multiplication over subtraction.
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▹ Answer
20 - 12 or 8 (depending on what you need to find)
▹ Step-by-Step Explanation
4(5 - 3)
Distribute 4 * 5 and 4 * -3
This will give 20 - 12
If you are looking for the final answer, it would be 8.
Hope this helps!
CloutAnswers ❁
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For every touchdown scored by the Timberwolves, the mascot does 333 back flips and the cheerleaders set off 666 confetti cannons.
How many touchdowns did the Timberwolves score if the cheerleaders set off 181818 confetti cannons?
Answer:
273 Touchdowns
Step-by-step explanation:
You divide the amount of confetti cannons set off by the amount of confetti cannons set off every time there is a touchdown scored. So in this case 181818 ÷ 666
Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. n^2-4n/3
Answer:
(n- 2/3)²
Step-by-step explanation:
Perfect square trinomial is: a²+2ab+b²= (a+b)²We have:
n² - 4n/3It can be put as:
n² -2×n×2/3Here we consider n = a and -2/3 = b, then
b²= (-2/3)²= 4/9Now we add 4/9 to a given binomial to make it perfect square:
n² - 2×n×3/2 + 4/9= (n- 2/3)²So, added 4/9 and got a perfect square (n- 2/3)²
Determine the best answer
6 points
MULTIPLE CHOICE Find the length of BC. (Lesson 10-2)
B
21 cm
C
168°
A 18°
C 168°
B 2.20 cm
D 30.79 cm
A
Answer:
angle of bc= 180-168= 12°
length of bc= 12/360 × π × diameter
= 12/360 × 22/7 × 21
= 12/360 × 66
= 2,20 cm (b)
Multiply.
(2x2 – 3x + 1)(x2 - 4x – 3)
Answer:
2x^4−11x^3+7x^2+5x−3
Step-by-step explanation:
The ^ means exponent
The reciprocal function of sine is: A. cosine B. cosecant C. secant D. tangent
Answer:
The reciprocal is cosecant that is option B
The reciprocal function of sine is cosecant.
What is a reciprocal function?It is the opposite of a function meaning by if a function is f(x) then the reciprocal function will be 1/f(x).
What is a trigonometric function?They are real function which relates with the angle of a right angle triangle to ratios of two sides.
How to find the reciprocal function?We have to find the reciprocal function of sine.
f=sine
Reciprocal of f=1/sine
=cosecant
Hence the reciprocal of sine is cosecant.
Learn more about trigonometry at https://brainly.com/question/24349828
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Write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
0
∑
i=1 (−3i+5)
Question:
Write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
30
∑ (−3i+5)
i=1
Answer:
The first three terms are : 2, -1 and -4
The last term is: -85
The sum of the sequence is: -1245
Step-by-step explanation:
Given;
==================================
30
∑ (−3i+5) -------------------(i)
i=1
==================================
Where the ith term aₙ is given by;
[tex]a_{i}[/tex] = [tex]-3i + 5[/tex] -------------------(ii)
(a) Therefore, to get the first three terms ([tex]a_1, a_2, a_3[/tex]), we substitute i=1,2 and 3 into equation (ii) as follows;
[tex]a_{1}[/tex] = [tex]-3(1) + 5[/tex] = 2
[tex]a_2 = -3(2) + 5 = -1[/tex]
[tex]a_3 = -3(3) + 5[/tex][tex]= -4[/tex]
Since the sum expression in equation (i) goes from i=1 to 30, then the last term of the sequence is when i = 30. This is given by;
[tex]a_{30} = -3(30) + 5 = -85[/tex]
(b) The sum [tex]s_n[/tex] of an arithmetic sequence is given by;
[tex]s_n = \frac{n}{2}[a_1 + a_n][/tex] -----------------(iii)
Where;
n = number of terms in the sequence = 30
[tex]a_1[/tex] = first term = 2
[tex]a_n[/tex] = last term = -85
Substitute the corresponding values of n, [tex]a_1[/tex] and [tex]a_n[/tex] into equation (iii) as follows;
[tex]s_n = \frac{30}{2}[2 + (-85)][/tex]
[tex]s_n[/tex] = 15[-83]
[tex]s_n[/tex] = -1245
Select the correct interpretation of the probability of getting an 11 when a pair of dice is rolled. Interpret an event as significant if its probability is less than or equal to 0.05. Select one: a. Significant at .055 b. Not significant at .945 c. Not significant at .055 d. Significant at .028
Answer:
c. Not significant at .055
Step-by-step explanation:
When a pair of dice is rolled, we have 6²=36 possible outcomes. Only 2 of these outcomes have a total score of 11:
When the first dice is 5 and the second is 6.When the first dice is 6 and the second is 5.Then, we can calculate the probability of getting 11 as the quotient between the successs outcomes and the total outcomes.
Then, the probability of getting 11 is:
[tex]P=\dfrac{X}{N}=\dfrac{2}{36}=0.055[/tex]
This probability is not equal or less than 0.05, so it is not significant at 0.055.
Find
dy/dx and d2y/dx2,
and find the slope and concavity (if possible) at the given value of the parameter. (If an answer does not exist, enter DNE.)
Parametric Equations Point
x = 5t, y = 6t − 1
t = 2
Answer:
dy/dx = slope = 6/5d²y/dx² = concavity = 0.Step-by-step explanation:
Given the parametric equation points x = 5t, y = 6t − 1 when t = 2
From x = 5t, t = x/5. Substituting t = x/5 into the second equation y = 6t − 1 we will have;
y = 6(x/5) - 1
y = 6/5 x - 1
The derivative of y with respect to x i.e dy/dx = 6/5 - 0. (Note that differential of any constant is zero).
dy/dx = 6/5
d²y/dx² = d/dx(dy/dx)
d²y/dx² = d/dx(6/5)
Since 6/5 is a constant, the derivative of 6/5 with respect to x will be zero.
d²y/dx² = 0.
Since the first derivative and the second derivative are both constant then, the slope m at the given parameter will be 6/5.
m = dy/dx = 6/5
The concavity is the value of the second derivative at the given value of the parameter.
The concavity d²y/dx² = 0.
Verify the identity.
sin 2 t / cos t = t - cost
Answer:
Step-by-step explanation:
The question is incorrect. Here is the correct question.
Verify the identity sin²t / cos t = sect - cost
Given the identity sin²t / cos t = sect - cost, to verify means we are to check if both sides are equivalent. To do that we are going to start the proof from any sides of the equation and solve until we get to the function at the opposite side.
Starting with the left hand equation (LHS)
sin²t / cos t ...1
From trigonometry identity, sin²t+ cos²t = 1
sin²t = 1- cos²t ... 2
Substituting eqn 2 into 1 we have:
= 1- cos²t/cost
= 1/cost - cos²t/cost
= 1/cost - cost
Also from trig. identity, 1/cost = sect
On replacing this identity in the resulting equation we will have;
= sect - cost (which is equivalent to the RHS)
This shows that sin²t / cos t = sect - cost (Identity Proved!)
An article gave the accompanying data on ultimate load (kN) for two different types of beams. Assuming the underlying distributions are Normal, calculate and interpret a 99% Cl for the difference between the true average load for the fiberglass beams and that for the carbon beams.
Type Sample size Sample Mean Sample SD
Fiberglass grid 26 33.4 2.2
Commercial carbon 26 42.8 4.3
grid
1. Calculate and interpret a 99% Cl for true average stance duration among elderly individuals.
2. Carry out a test of hypotheses at significance level 0.05 to decide whether true average stance duration is larger among elderly individuals than younger individuals.
Answer:
The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is (-11.937, -6.863).
Step-by-step explanation:
We have to calculate a 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams.
The sample 1 (Fiberglass), of size n1=26 has a mean of 33.4 and a standard deviation of 2.2.
The sample 2 (Carbon), of size n2=26 has a mean of 42.8 and a standard deviation of 4.3.
The difference between sample means is Md=-9.4.
[tex]M_d=M_1-M_2=33.4-42.8=-9.4[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{2.2^2}{26}+\dfrac{4.3^2}{26}}\\\\\\s_{M_d}=\sqrt{0.186+0.711}=\sqrt{0.897}=0.9473[/tex]
The critical t-value for a 99% confidence interval is t=2.678.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_{M_d}=2.678 \cdot 0.9473=2.537[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M_d-t \cdot s_{M_d} = -9.4-2.537=-11.937\\\\UL=M_d+t \cdot s_{M_d} = -9.4+2.537=-6.863[/tex]
The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is (-11.937, -6.863).
In this way, we can calculate the individual duration of each one and the duration time, knowing that the sample means:
The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is -11.937 and -6.863.
We have to calculate a 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams. The sample 1 (Fiberglass), of size n1=26 has a mean of 33.4 and a standard deviation of 2.2. The sample 2 (Carbon), of size n2=26 has a mean of 42.8 and a standard deviation of 4.3. The difference between sample means is Md=-9.4.
[tex]Sm_d= \sqrt{\frac{\sigma^2_1}{n_1} +\frac{\sigma^2_2}{n_2}} = \sqrt{(0.186)+(0.711) }= 0.9473[/tex]
The critical t-value for a 99% confidednce interval is t=2.678. The margin of error (MOE) can be calculated as:
[tex]MOE=t*8M_d = (2.678)(0.9473)= 2.537[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL= M_d-t*SM_d = -9.4-2.537= -11.937\\UL= M_d+t*SM_d= -9.4+2.537= -6.863[/tex]
The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is (-11.937, -6.863).
See more about statistics at brainly.com/question/2289255
factorise 12x² + x - 20
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▹ Answer
(3x + 4) * (4x - 5)
▹ Step-by-Step Explanation
12x² + x - 20
Rewrite
12x² + 16x - 15x - 20
Factor out
4x(3x + 4) - 15x - 20
4x(3x + 4) - 5(3x + 4)
Factor
(3x + 4) * (4x - 5)
Hope this helps!
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Brainliest is greatly appreciated!
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WILL GIVE BRAINLIEST PLEASE HELP
Answer:
the 3 one is the correct answer
Step-by-step explanation:
Answer: RS and SU
Step-by-step explanation:
Skew lines are lines that don't have points connected and are not parrelel to each other.
The only lines that are both not parrelel and have unconnected points are the lines RS and SU
Find the area of the yellow region.
Round to the nearest tenth.
15 cm
15 cm
Area = [ ? ] cm2
Answer:
48.3 cm²
Step-by-step explanation:
Let A be the area of the yellow region
A= the area of the square - the area of the quarter square
A= 15²-(15²*π)/4= 48.28≈ 48.3 cm²
Connie is packing for a trip. She has 18 pairs of shoes. If she has room to pack 5 pairs, how many ways can she choose which shoes to take?
Answer:
There are 8568 ways to combine the shoes.
Step-by-step explanation:
In this case Connie wants to create smaller subsets from a larger group of things, therefore we must do a combination, which can be applied by using the following formula:
[tex]C_{(n,r)} = \frac{n!}{r!*(n - r)!}[/tex]
In our case n = 18, which is the total number of shoes and r = 5, which is the subset she wants to create.
[tex]C_{(18,5)} = \frac{18!}{5!*(18 - 5)!} = \frac{18!}{5!*13!} = \frac{18*17*16*15*14*13!}{5!*13!}\\C_{(18,5)} = \frac{18*17*16*15*14}{5*4*3*2} = 8568[/tex]
There are 8568 ways to combine the shoes.
The number of ways can she choose which shoes to take is 8,568.
Given that,
Connie is packing for a trip. She has 18 pairs of shoes and she has room to pack 5 pairs.Based on the above information, the calculation is as follows:
[tex]= \frac{n!}{k!(n-k)!} \\\\= \frac{18!}{5!13!} \\\\= \frac{18\times 17\times 16\times\15\times \times 14}{5\times 4\times 3\times2\times 1}[/tex]
= 8,568
Therefore we can conclude that The number of ways can she choose which shoes to take is 8,568.
Learn more: brainly.com/question/17429689
What are the quadratic factors of the function represented by this graph?
Answer:
B. (x + 5)(x + 1)
Step-by-step explanation:
Since our roots are x = -5 and x = -1, we have:
x + 5 = 0
x + 1 = 0
Put that into quadratic binomials:
(x + 5)(x + 1)
The volume of a rectangular prism is given by the formula V = lwh, where l is the length of the prism, w is the width, and h is the height. Suppose a box in the shape of a rectangular prism has length (2a + 11), width (5a – 12), and height (a + 6). Which expression represents the volume of the box?
Answer:
Volume = 10a³ + 91a² + 54a - 792
Step-by-step explanation:
In the absence of answer choices, let's find the expression for the volume.
Given: Volume = length×width×height
V = lwh
length =(2a + 11)
width =(5a – 12)
height= (a + 6)
V = (2a + 11)(5a – 12) (a + 6)
Expand the first two brackets using distributive property
V = (10a² -24a +55a - 132)(a + 6)
Collect like terms
V = (10a² + 31a -132)(a + 6)
Expand the two brackets using distributive property
V = 10a³ + 31a² - 132a + 60a² + 186a - 792
Collect like terms
V = 10a³ + 91a² + 54a - 792
The expression that represents the volume of the box = 10a³ + 91a² + 54a - 792
Answer:
Volume = 10a³ + 91a² + 54a - 792
Step-by-step explanation:
A veteran treated 7 dogs this morning. The list gives the weights in pounds of each dog 41,36,20,36,62,5,6 find the range of the data set
Answer:
57
Step-by-step explanation:
The range of a data set is
Largest data value - Smallest data value
62 - 5
= 57
The range of the data set is 57 pounds.
Answer:
[tex]\boxed{\red{57}}[/tex]
Step-by-step explanation:
[tex]\blue {range \: \: of \: \: a \: \: data \: \: set \: \: means}[/tex]
you have to subtract the smallest value from the largest value in the data set.
[tex]\boxed{\green{largest \: \: value - smallest \: \: value}} \\ \boxed{\green{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 62 - 5}} \\ \: \: \: \: \: \: \: \: \boxed{\pink{ =57}}[/tex]
Find the product of 4 2/7 x 3 1/2
Answer:
Hey there!
The product of these two fractions would equal 15.
Hope this helps :)
Answer:
Hi! The answer to your question is 7 11/14 or rounded will be 15
Step-by-step explanation:
So first let’s take the whole numbers which is 4 and 3 if we add them up we will get 7.
Now we do LCD (least common denominator)
4/14+7/14=11/14
So the answer is 7 11/14 or 15
(In mixed number the answer is 7 11/14 and in whole the answer is 15)
Hope this helps! :)
A researcher wants to study the average miles run per day for marathon runners. In testing the hypotheses: H0: μ = 25 miles vs. H1: μ ≠ 25 miles, a random sample of 36 marathon runners drawn from a normal population whose standard deviation is 10, produced a mean of 22.8 miles weekly. What is the rejection region associated with 3% significance level?
Answer:
The calculated value |Z| = 1.325 < 1.881 at 0.03 level of significance
Null hypothesis is accepted
Alternative hypothesis is rejected
A researcher wants to study the average miles run per day for marathon runners is 25
Step-by-step explanation:
Step(i):-
Given sample size 'n' = 36
Given mean of the sample x⁻ = 22.8 miles
Given mean of the Population 'μ' = 25
Given standard deviation of the Population 'σ' = 10
Null hypothesis:-H₀: μ = 25
Alternative Hypothesis:H₁:μ ≠ 25
Level of significance = 3 % or 97%
The critical value Z₀.₉₇ = 1.881
Step(ii):-
Test statistic
[tex]Z = \frac{x^{-} - mean}{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{22.8 - 25}{\frac{10}{\sqrt{36} } }[/tex]
Z = -1.325
|Z| = |-1.325| = 1.325
The calculated value |Z| = 1.325 < 1.881 at 0.03 level of significance
Null hypothesis is accepted
Alternative hypothesis is rejected
conclusion:-
A researcher wants to study the average miles run per day for marathon runners is 25
In 1998, as an advertising campaign, the Nabisco Company announced a "1000 Chips Challenge," claiming that every 18-ounce bag of their Chips Ahoy cookies contained at least 1000 chocolate chips. Dedicated statistics students at the Air Force Academy (no kidding) purchased some randomly selected bags of cookies and counted the chocolate chips. Some of their data are given below. 1219 1214 1087 1200 1419 1121 1325 1345 1244 1258 1356 1132 1191 1270 1295 1135 Find a 95% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies.
Answer:
A 95% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies is [1187.96, 1288.44].
Step-by-step explanation:
We are given that statistics students at the Air Force Academy (no kidding) purchased some randomly selected bags of cookies and counted the chocolate chips.
Some of their data are given below; 1219, 1214, 1087, 1200, 1419, 1121, 1325, 1345, 1244, 1258, 1356, 1132, 1191, 1270, 1295, 1135.
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean number of chocolate chips = [tex]\frac{\sum X}{n}[/tex] = 1238.2
s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex] = 94.3
n = sample of car drivers = 16
[tex]\mu[/tex] = population mean number of chips in a bag
Here for constructing a 95% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.
So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-2.131 < [tex]t_1_5[/tex] < 2.131) = 0.95 {As the critical value of t at 15 degrees of
freedom are -2.131 & 2.131 with P = 2.5%}
P(-2.131 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.131) = 0.95
P( [tex]-2.131 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.131 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
P( [tex]\bar X-2.131 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.131 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.131 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.131 \times {\frac{s}{\sqrt{n} } }[/tex] ]
= [ [tex]1238.2-2.131 \times {\frac{94.3}{\sqrt{16} } }[/tex] , [tex]1238.2+2.131 \times {\frac{94.3}{\sqrt{16} } }[/tex] ]
= [1187.96, 1288.44]
Therefore, a 95% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies is [1187.96, 1288.44].
Which linear inequality is represented by the graph?
Oy>2/3x-2
O y<2/3x+2
Oy> 2/3x+1
Oy<2/3x1
Answer:
Option (4)
Step-by-step explanation:
From the graph attached,
A dotted line passes through two points (3, 1) and (-3, -3)
Let the equation of the given line is,
y = mx + b
where 'm' = slope of the line
b = y-intercept
Slope of a line passing through [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] is,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
For the given points,
m = [tex]\frac{1+3}{3+3}[/tex]
m = [tex]\frac{2}{3}[/tex]
y-intercept 'b' = -1
Therefore, equation of the given line will be,
[tex]y=\frac{2}{3}x-1[/tex]
Since graphed line is a dotted line so it's representing an inequality(having < or > sign)
And the shaded part is below the dotted line,
Inequality will be,
y < [tex]\frac{2}{3}x-1[/tex]
Therefore, Option (4) will be the answer.
Answer:
D
Step-by-step explanation:
Correct:)
Question
Drag each description to the correct location on the table.
Examine the equation to determine if the descriptions listed are key features of the function or not.
Answer:
Key Feature: - decreasing, As x approaches -(infinite), y approaches (infinite), As x approaches (infinite), y approaches a constant.
Not a Key feature: increasing, As x approaches (infinite) y approaches (infinite), As x approaches -(infinite) y approaches -(infinite), & As x approaches -(infinite) y approaches a constant.
Step-by-step explanation:
In the given the figure above, m∠BAC = 64° and m∠CBA = 56°. Part I: Find the m∠DEC. Part II: Explain the steps you took to arrive at your answer. Make sure to justify your answer by identifying any theorems, postulates, or definitions used.
Answer:
56, see step-by-step.
Step-by-step explanation:
1. AB is parallel to CD. 1. Given
BC is parallel to DE.
m<BAC=64 and m<CBA =56
2. m<BAC + m<CBA + m<BCA =180 2. The angles in a triangle add up to 180
3. 64+ 56+ m<BCA=180 3. Substitution property of equality.
4. 120 + m<BCA=180 4. Addition property of equality.
5. m<BCA=60 5. Subtraction property of equality.
6. BC is a transversal that cuts through parallel lines AB and CD.
6. Def. of transversal.
7. m<CBA = m<BCD 7. If two parallel lines are cut by a transversal, then alternate interior angles are congruent.
8. m<BCA+m>BCD+m<DCE= 180. 8. Angle addition postulate
9. 60+56+m<DCE=180. 9.substitution.
10. 116 + m<DCE =180 10. Addition property of equality.
11. M<DCE =64 11. Subtraction property of equality.
12. DC is a transversal that cuts through parallel line BC and DE.
12. Def of transversal.
13. m<EDC= m<BCD 13. If two parallel lines are cut by a transversal, then alternate interior angles are congruent.
14. m<EDC= 60. 14. Substitution property of equality.
15. m<EDC+m<DCE+m<Dec=180. 15. Angle addition postulate
16. 56+64+m<dec = 180.16 Substitution property of equality.
17. 120+ m<dec = 180. Addition property of equality.
18. m<dec = 60 18. Subtraction property of equality.
how do you solve this problem
Answer:
more info is needed
Step-by-step explanation:
How do you write 416.7 in scientific notation? ___× 10^____
Answer:
4.167(10²)
Step-by-step explanation:
Step 1: Put number into proper decimal form
416.7 = 4.167
Step 2: Figure out exponent
Since we are moving the decimal places 2 places to the right, our exponent is 2
Answer:
4.167 × 10^2
Step-by-step explanation:
= 4.167 × 10^2
(scientific notation)
= 4.167e2
(scientific e notation)
= 416.7 × 10^0
(engineering notation)
(one)
= 416.7
(real number)
A simple random sample of 44 adults is obtained from a normally distributed population, and each person's red blood cell count (in cells per microliter) is measured. The sample mean is 5.31 and the sample standard deviation is 0.51 . Use a 0.05 significance level and the given calculator display to test the claim that the sample is from a population with a mean less than 5.4 comma which is a value often used for the upper limit of the range of normal values. What do the results suggest about the sample group?
Answer:
There is not enough evidence to support the claim that the population mean is significantly less than 5.4.
This result suggest we may be making a Type II error, where a true alternative hypothesis does not have enough evidence to be supported.
If the same outcome would have been obtained with a bigger sample size, the power of the test is bigger and there is a higher probability of rejecting the null hypothesis.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the population mean is significantly less than 5.4.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=5.4\\\\H_a:\mu< 5.4[/tex]
The significance level is 0.05.
The sample has a size n=44.
The sample mean is M=5.31.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.51.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.51}{\sqrt{44}}=0.077[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{5.31-5.4}{0.077}=\dfrac{-0.09}{0.077}=-1.171[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=44-1=43[/tex]
This test is a left-tailed test, with 43 degrees of freedom and t=-1.171, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t<-1.171)=0.124[/tex]
As the P-value (0.124) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the population mean is significantly less than 5.4.
This result suggest we may be making a Type II error, where a true alternative hypothesis does not have enough evidence to be supported.
If the same outcome would have been obtained with a bigger sample size, the power of the test is bigger and there is a higher probability of rejecting the null hypothesis.
Solve 0=4x^2+12x+9
Simplify the expression to solve the equation
Answer:
x = -3/2
Step-by-step explanation:
0 = 4x² + 12x + 9
4x² + 12x + 9 = 0
(2x + 3)² = 0
2x + 3 = 0
2x = -3
x = -3/2
Hope this helps! :)
A circle is shown. Angles 3 and 4 intersect an arc with a measure of 106 degrees. Angles 1 and 2 intersect an arc with measure 58 degrees. Is the measure of ∠1 equal to the measure of ∠2? Why?
Answer:
yes, because they intercept the same arc
Step-by-step explanation:
Answer:
yes, because they intercept the same arc
Step-by-step explanation:
TIME REMAINING
53:46
What is the value of c?
O 4 units
5 units
6 units
0 7 units
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WY = a = 4
ZY = b = 3
As WYZ is forming a right angle triangle, therefore, we can use pythagorean theorem to find the value of c
a2+b2=c2 (4)2+(3)2=C2 16+9=C2 C2=25
Taking square root on both sides
√c2= √25 c=5
The value of c is 5 units.
The value of c is 5 units
The complete question is an illustration of a right-triangle, where the equation to calculate the value of c is:
c^2 = a^2 + b^2
The equation becomes
c^2 = 3^2 + 4^2
Evaluate the exponents
c^2 = 9 + 16
Evaluate the sum
c^2 = 25
Take the square root of both sides
c =5
Hence, the value of c is 5 units
Read more about right-triangles at:
https://brainly.com/question/2437195