Answer:
Test statistic = 1.818
Reject H0
Step-by-step explanation:
H0 : μ = 90
H1 : μ > 90
xbar = 94 ; s = 22 ; n = 100
The test statistic : (xbar - μ) ÷ (s/√(n))
Test statistic = (94 - 90) ÷ (22/√100)
Test statistic = 4 ÷ 2.2
T = 1.818
The critical value :
At α = 0.10
Degree of freedom = n - 1 = 100 - 1 = 99
Tcritical(0.10, 99) = 1.290
Decison region :
Reject H0 if Test statistic > |Tcritical |
1.818 > 1.290
We reject H0
Write the sum of three odd consecutive integers if the last one is m-2
Answer:
the sum is 3m-12
Step-by-step explanation:
The nunbers are:
[tex]m-2\\m-4\\m-6\\the~sum~is:\\sum=(m-2)+(m-4)+(m-6)\\sum=m-2+m-4+m-6=m+m+m-2-4-6\\sum=3m-12[/tex]
The sum of three odd consecutive integers is 3m - 12
What are odd integers?"These are the integers which are not divisible by 2."
For given question,
We need to find the sum of three consecutive odd integers.
Let x, x + 2, x + 4 be three consecutive odd integers.
We have been given the last one is m - 2
This means x + 4 = m - 2
So, the second odd integer would be,
x + 2 = m - 4
and the first odd integer would be,
x = m - 6
, we find the sum of the three odd consecutive integers.
⇒ (m - 6) + (m - 4) + (m - 2)
= m + m + m - 6 - 4 - 2
= 3m - (6 + 4 + 2)
= 3m - 12
Therefore, the sum of three odd consecutive integers is 3m - 12
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9.
For a normal distribution with mean 20 and standard deviation 5, approximately what percent of
the observations will be between 5 and 35?
A. 50%
B. 68%
C. 95%
D. 99.7%
Answer: D. 99.7%
Step-by-step explanation:
Scores that lies within the first deviation(1σ) =
(20 - 5) to (20 + 5) → 15 to 25
Scores that lies within the second deviation(2σ) =
(20 - 5 - 5) to (20 + 5 + 5) → 10 to 30
Scores that lies within the third deviation(3σ) =
(20 - 5 - 5 - 5) to (20 + 5 + 5 + 5) → 5 to 35
As shown by the distribution graph below, 99.73% of the scores lies within the third deviation(3σ).
Use the tangent to find the unknown side lengths.
Answer:
4.076
Step-by-step explanation:
tan27°= |AC|/8
8*tan27°= 4.076
Use the tangent to find the unknown side lengths.
This is the answer
Ac= 4.07
Ab=8.97
Find the area of the rectangle shown.
914
323
323
914
The solution is
Answer: The answer is 295,222.
Step-by-step explanation: The area of a rectangle is base times height, which is 914 x 323. If you do the math correctly, you will get 295,222.
[tex] \huge\boxed{\mathfrak{Answer}}[/tex]
Length (l) = 914 units
Breadth (b) = 323 units
Area = ?
Area of a rectangle (a) = l × b ----> use this formula
[tex]a = l \times b \\ a = 914 \times 323 \\ a = 295222 \: \: sq.units[/tex]
=> The area of the rectangle is 295222 sq.units.
What is the value of x?
Answer:
22
Step-by-step explanation:
3x-14= 4(x-9)
3×-14= 4x-36
4x-36-3x+14=0
×-22÷0
x=22
Write the equation of the line with the given conditions. passing through (-1, -7) and perpendicular to the line with equation 4x + 5y = 31
Answer:
y = 5/4 x - 23/4
Step-by-step explanation:
4x + 5y = 31
5y = - 4x +31
y = -4/5 x + 31/5
⊥ slope = 5/4
-7 = 5/4 (-1) + B
-28 = -5 + 4b
-23 = 4B
b = -23/4
Jordan rides a bike from Clovis to Millerton Lake. On the flatland Jordan travels at 36 mph for 1 hour, and in the mountains rides for 3 hours traveling at 20 miles per hour. Which of the following choices is the average speed for the trip?
Answer:
24 mph
Step-by-step explanation:
1 hour of 36 mph
3 hours of 20 mph
(36 + 20 + 20 + 20)/4
96/4
24
Answer:
24 mph
Step-by-step explanation:
36 miles = 1 hour
60 miles = 3 hours
36+60= 96
1+3+4
96/4= 24
A quality control expert at Glotech computers wants to test their new monitors. The production manager claims they have a mean life of 82 months with a standard deviation of 7 months. If the claim is true, what is the probability that the mean monitor life would be greater than 83.8 months in a sample of 71 monitors
Answer:
0.015 = 1.5% probability that the mean monitor life would be greater than 83.8 months in a sample of 71 monitors
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 life of 82 months with a standard deviation of 7 months.
This means that [tex]\mu = 82, \sigma = 7[/tex]
Sample of 71
This means that [tex]n = 71, s = \frac{7}{\sqrt{71}}[/tex]
What is the probability that the mean monitor life would be greater than 83.8 months?
1 subtracted by the p-value of Z when X = 83.8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{83.8 - 82}{\frac{7}{\sqrt{71}}}[/tex]
[tex]Z = 2.17[/tex]
[tex]Z = 2.17[/tex] has a p-value of 0.985.
1 - 0.985 = 0.015
0.015 = 1.5% probability that the mean monitor life would be greater than 83.8 months in a sample of 71 monitors
The total number of labor hours for a construction project by week x is given by: Week 1 4 7 10 13 16 19 Total hours 25 158 1254 5633 9280 10,010 10,100 Look at its scatter plot, an appropriate model for this data is:
Answer:
Logistic model
Step-by-step explanation:
A scatter plot is a mathematical representation or diagram which is used to shoe the relation between two given variables. It uses the Cartesian coordinates which is used to display the values for a typically two variables for the given set of data.
In the context, a scatter plot is made between two variables. The two variables are the total number of hours and the number of weeks.
From the graph shown, we can say that model is a logistic model as the shape of the graph is S shaped.
Therefore, the appropriate model for the data given is logistic model.
How do I find the missing number?
Answer:
to find the missing number is all u have to do is understand the problem and silve the problem!
Step-by-step explanation:
paki brainly po
Help me with this question, please!!
Answer:
4yz^2
Step-by-step Explanation:
Please help :)
Solve 3(m-4)=33
Thanks so much :)
Answer:
3(m-4)=33
3m-12=33
3m=45
m=15
Check:
3(15-4)=33
3(11)=33
33=33
Hope This Helps!!!
Answer:
m = 15
Step-by-step explanation:
3 ( m - 4 ) = 33
Solve for m
3 ( m - 4 ) = 33
Divide both side by 3
[tex]\small \sf \frac{3(m-4)}{3} = \frac{33}{3} \\ [/tex]
m - 4 = 11
Add 4 to both side
m - 4 + 4 = 11 + 4
m = 15
please help please help
Answer:
1. number line or 3
2. D
3. E and K
4. B
5. A
Brainliest please~
Bond is 20 years older than Jude and 10 years older than John. If the sum of the ages of Bond,Jude and John is 90,how old is Bond?
Answer:
hey hi mate
Ur answer is
bond 40John 20Jude 30Step-by-step explanation:
u have to think
hope u like it
plz mark it as brainliest
tiene 40 años de edad
bond 40
jude 20
joh 30
40+20+30 = 90
solve this fast please… and thank you so much :)
Answer:
hi
Step-by-step explanation:
To teach computer programming to employees, many firms use on the job training. A human resources administrator wishes to review the performance of trainees on the final test of the training. The mean of the test scores is 72 with a standard deviation of 5. The distribution of test scores is approximately normal. Find the z-score for a trainee, given a score of 82.
Answer:
The z-score for the trainee is of 2.
Step-by-step explanation:
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.
The mean of the test scores is 72 with a standard deviation of 5.
This means that [tex]\mu = 72, \sigma = 5[/tex]
Find the z-score for a trainee, given a score of 82.
This is Z when X = 82. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{82 - 72}{5}[/tex]
[tex]Z = 2[/tex]
The z-score for the trainee is of 2.
Using the following image , find the value for x
Step-by-step explanation:
Here, two angles i.e, (x + 13)° and (4x + 2)° are forming a straight line, thus the sum of these two angles will be 180° because they are forming a linear pair.
[tex]\longrightarrow[/tex] (x + 13) + (4x + 2) = 180°
[tex]\longrightarrow[/tex] x + 13 + 4x + 2 = 180°
[tex]\longrightarrow[/tex] 5x + 15 = 180°
[tex]\longrightarrow[/tex] 5x = 180° ― 15
[tex]\longrightarrow[/tex] 5x = 165°
[tex]\longrightarrow[/tex] x = 165° ÷ 5
[tex]\longrightarrow[/tex] x = 33°
Therefore, the value of x is 33°.
Quick Check!
[tex]\longrightarrow[/tex] x + 13
[tex]\longrightarrow[/tex] (33 + 13)°
[tex]\longrightarrow[/tex] 46°
And, another angle :
[tex]\longrightarrow[/tex] (4x + 2)°
[tex]\longrightarrow[/tex] {4(33) + 2}°
[tex]\longrightarrow[/tex] (132 + 2)°
[tex]\longrightarrow[/tex] 134°
★ Sum of the angles should be 180° :
[tex]\longrightarrow[/tex] (x + 13) + (4x + 2) = 180°
[tex]\longrightarrow[/tex] 46° + 134° = 180°
[tex]\longrightarrow[/tex] 180° = 180°
L.H.S = R.H.S, hence verified!
The value of x is 33
What is an equation?"It is a mathematical statement which consists of equal symbol between two algebraic expressions."
What is linear pair of angles?"It is formed when two lines intersect each other at a single point. "" The angles are adjacent to each other.""The sum of angles of a linear pair is always 180° "What are supplementary angles?"Two angles are supplementary angles if the sum of the angles is 180° "
For given question,
angle (x + 13) and angle (4x + 2) form linear pair of angles.
So, these angles are supplementary angles.
⇒ (x + 13)° + (4x + 2)° = 180°
We solve above equation to find the value of x
⇒ x + 4x + 13 + 2 = 180
⇒ 5x + 15 = 180
⇒ 5x = 165
⇒ x = 33
Therefore, the value of x is 33
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I don’t think I got the right answer?
Answer:
it's third option the one who says 10 units up
Which is equivalent to (-m)4x n2 ?
Answer:
a.) m⁴n²
Step-by-step explanation:
( -m)⁴ × n ²
A negative base raised to an even powers equals a positive.
m ⁴ × n²
multiply the terms
m⁴n²
Answer:
a.) m⁴n²
Step-by-step explanation:
yea
For which equation is (4, 3) a solution?
Answer:
4 over 3
because is in side the bracket is part of inequalities
simple equation:
6m=12
Step-by-step explanation:
Divide both sides of the equation by the same term6m/6 =12/6
Cancel terms that are in both the numerator and denominatorDivide the numbersm=2
Answer:
m=2
Step-by-step explanation:
Divide 6 on both sides
6m / 6 = 12/6
m= 12/6 = 2
So, m=2
Verification:
LHS = 6m m=2
6 * 2 = 12
RHS = 12
Both the LHS and RHS are same, so our answer is correct
HELP! AAHHHHH SOMEBODY HELP!
If each square of the grid below is $0.5\text{ cm}$ by $0.5\text{ cm}$, how many square centimeters are in the area of the blue figure?
Answer:
8.50 cm²
Step-by-step explanation:
The dimension of each square is given as 0.5cm by 0.5cm
The area of the a square is, a²
Where, a = side length
Area of each square = 0.5² = 0.25cm
The number of blue colored squares = 34
The total area of the blue colored squares is :
34 * 0.25 = 8.50cm²
Sarah walks into a grocery store with no more than 20 dollars to spend and needs to buy at least 3.5 pounds of flour and at least 2 pounds of sugar. Flour is 2 dollars per pound and sugar is 1.5 dollars per pound. Let x the amount of flour purchased and y be the amount of sugar purchased? Which of the following systems of inequalities represents this situation?
Answer:
x ≥ 3.5
y ≥ 2
2x + 1.5y ≤ 20
Step-by-step explanation:
Given :
Total Amount to spend ≤ $20
Let:
Amount of flour purchased = x
Amount of sugar purchased = y
Cost :
Flour = $2 per pound
Sugar = $1.5 per pound
Pounds of :
flour to be purchased ≥ 3.5
Sugar to be purchased ≥ 2
Hence, the system of inequalities :
x ≥ 3.5
y ≥ 2
Total Cost of x + total cost of y must be less than or equal to total amount
2x + 1.5y ≤ 20
Answer: x ≥ 3.5
y ≥ 2
2x + 1.5y ≤ 20
Step-by-step explanation: To write a system of inequalities, it is important to determine the restrictions. One restriction is that Sarah wants to buy at least 3.5 pounds of flour. "At least" means that 3.5 is the smallest amount she would buy and 3.5 can be included. This is expressed as x ≥ 3.5. She also wants at least 2 pounds of sugar, so similar to the flour, this can be written as y ≥ 2. Finally, the cost can be expressed as 2x + 1.5y. This is a restriction because Sarah can spend up to $20, so 2x + 1.5y is less than or equal to $20, or 2x + 1.5y ≤ 20.
Find the volume (in cubic feet) of a cylindrical column with a diameter of 6 feet and a height of 28 feet. (Round your answer to one decimal place.)
Answer:
[tex]791.7\:\mathrm{ft^3}[/tex]
Step-by-step explanation:
The volume of a cylinder with radius [tex]r[/tex] and height [tex]h[/tex] is given by [tex]A_{cyl}=r^2h\pi[/tex].
By definition, all radii of a circle are exactly half of all diameters of the circle. Therefore, if the diameter of the circular base of the cylinder is 6 feet, the radius of it must be [tex]6\div 2=3\text{ feet}[/tex].
Now we can substitute [tex]r=3[/tex] and [tex]h=28[/tex] into our formula [tex]A_{cyl}=r^2h\pi[/tex]:
[tex]A=3^2\cdot 28\cdot \pi,\\A=9\cdot28\cdot \pi,\\A=791.681348705\approx \boxed{791.7\:\mathrm{ft^3}}[/tex]
3. L = 5 cm
W = 30 cm
H= 14
V=____
Answer:
Step-by-step explanation: as the formula to find volume is L*W*H
so v=lwh
= 5*30*14
= 2100cm^3
Write in simplest form
Answer:
(1/8x)-(5/6)
Step-by-step explanation:
-3/4x-1/3+7/8x-1/2
-6/8x-2/6+7/8x-3/6
-6/8x+7/8x-2/6-3/6
1/8x-5/6
Forces of 9 lbs and 13 lbs act at a 38º angle to each other. Find the magnitude of the resultant force and the angle that the resultant makes with each force.
Answer: [tex]R=20.84\ lb\quad 22.57^{\circ},15.43^{\circ}[/tex]
Step-by-step explanation:
Given
Two forces of 9 and 13 lbs acts [tex]38^{\circ}[/tex] angle to each other
The resultant of the two forces is given by
[tex]\Rightarrow R=\sqrt{a^2+b^2+2ab\cos \theta}[/tex]
Insert the values
[tex]\Rightarrow R=\sqrt{9^2+13^2+2(9)(13)\cos 38^{\circ}}\\\Rightarrow R=\sqrt{81+169+184.394}\\\Rightarrow R=\sqrt{434.394}\\\Rightarrow R=20.84\ lb[/tex]
Resultant makes an angle of
[tex]\Rightarrow \alpha=\tan^{-1}\left( \dfrac{b\sin \theta}{a+b\cos \theta}\right)\\\\\text{Considering 9 lb force along the x-axis}\\\\\Rightarrow \alpha =\tan^{-1}\left( \dfrac{13\sin 38^{\circ}}{9+13\cos 38^{\circ}}\right)\\\\\Rightarrow \alpha =\tan^{-1}(\dfrac{8}{19.244})\\\\\Rightarrow \alpha=22.57^{\circ}[/tex]
So, the resultant makes an angle of [tex]22.57^{\circ}[/tex] with 9 lb force
Angle made with 13 lb force is [tex]38^{\circ}-22.57^{\circ}=15.43^{\circ}[/tex]
Answer:
Step-by-step explanation:
Question 5 Multiple Choice Worth 1 points)
(01.03 MC)
Bunny Hill Ski Resort charges $35 for ski rental and $10 an hour to ski. Black Diamond Ski Resort charges $40 for ski rental and $5 an hour to ski. Create an equation to determine at what point
the cost of both ski slopes is the same.
Answer:
Bunny Hill Ski Resort:
y = 10x + 35
Diamond Ski Resort:
y = 5x + 40
Point where the cost is the same:
(1, 45)
Step-by-step explanation:
The question tells us that:
$35 and $40 are initial fees
$10 and $5 are hourly fees
This means that x and y will equal:
x = number of hours
y = total cost of ski rental after a number of hours
So we can form these 2 equations:
y = 10x + 35
y = 5x + 40
Now we are going to use System of Equations to find what point the cost of both ski slopes is the same.
Because they both equal y, we can set the equations equal to each other:
10x + 35 = 5x + 40
And we use basic algebra to solve for x:
10x + 35 = 5x + 40
(subtract 5x from both sides)
5x + 35 = 40
(subtract 35 from both sides)
5x = 5
(divide both sides by 5)
x = 1
Remember, x equals the number of hours.
That means when your rent out the skis for 1 hour, you will get the same price of $45 (you find the price by plugging in 1 into both of the equations)
Hope it helps (●'◡'●)
4 mangoes and Pears cost $24 while to Mangos in three pears cost $16. Write a pair of simulataneous equations in x and y to represent the information given. State clearly what x and y represent
Answer:
x- cost of mango, y- cost of pear, 4x+4y=24 and 2x+3y=16
Step-by-step explanation:
For this, you first must assign variables. In this case, let's say x is the cost of a mango and y is the cost of a pear.
Therefore the total cost for the first part can be given by 4x+4y=24.(or 4 × the cost of a mango + 4 × the cost of a pear = $24).
Following this method, the second equation can be given by 2x+3y=16.
** building upon this knowledge (extension)**
To solve simultaneous equations, we need like terms. To make like terms, we can multiply the entire second equation by 2. This gives 2 equations of 4x+4y=24 and 4x+6y=32.
We solve this by subtracting one equation from another, giving (4x-4x)+(6y-4y)=(32-24), or 2y=8.
We can divide by 2 to get y=4, meaning a pear costs $4.
By substituting y with 4, we can work out x. 4x+4×4=24, also known as 4x+16=24.
We can subtract 16 to get 4x=8, and divide by 4, giving x=2, or a mango costs $2.
**This content involves writing simultaneous equations, which you may wish to revise. I'm always happy to help!
Help please somebody ASAP
Answer:
[tex]\frac{-2x+11}{(x-4)(x+1)}[/tex]
Step-by-step explanation:
I don't think we can factor this so we'll have to multiply to make the denominators the same
[tex]\frac{3(x+1)}{(x^2-3x-4)(x+1)}-\frac{2(x^2-3x-4)}{(x+1)(x^2-3x-4)}\\\\\frac{3x+3-(2x^2-6x-8)}{(x^2-3x-4)(x+1)}=\frac{-2x^2+9x+11}{(x^2-3x-4)(x+1)}\\-2x^2+9x+11=(x+1)(-2x+11)\\\\x^2-3x-4=(x+1)(x-4)\\\frac{(x+1)(-2x+11)}{(x+1)(x-4)(x+1)}=\frac{-2x+11}{(x-4)(x+1)}[/tex]
