Answer:
7 + 6
5 + 11
Step-by-step explanation:
the lengths of the two shorter sides of a triangle must add up to more than the length of the third side.
3 + 4 = 7 ≤ 8 no
7 + 6 = 13 > 12 yes
5 + 11 = 16 > 13 yes
4 + 6 = 10 ≤ 12 no
4 + 6 = 10 ≤ 10 no
===================================================
Explanation:
We'll use the triangle inequality theorem. Recall that this theorem says that a triangle is only possible if and only if adding any two sides leads to a sum larger than the third side.
Let's say we had a triangle with sides a,b,c. Such a triangle is only possible if all three conditions hold true
a+b > cb+c > aa+c > b----------------
Let's go through each answer choice to see if those conditions hold up.
Choice A. We have a = 3, b = 4, c = 8. Note that a+b = 3+4 = 7 which is not greater than c = 8. Therefore a+b > c is false, and we cannot make a triangle here. We don't need to check the other inequalities. I recommend you trying it out by cutting out slips of paper of these lengths. You'll find a triangle cannot be constructed. We can rule out choice A.Choice B. We have a = 7, b = 6 and c = 12. We can see that a+b = 7+6 = 13 which is larger than c = 12. So far, so good. Then note that b+c = 6+12 = 18 which is larger than a = 7. Finally, a+c = 7+12 = 19 which is larger than b = 6. Picking any two sides, adding them up, leads to a sum larger than the third side. A triangle is possible in this case. Choice B is one of the answers.Choice C. This time a = 5, b = 11, c = 13. You should find that a triangle is possible following the same steps as done in choice B above. Adding any two sides leads to a sum larger than the third side. Choice C is one of the answers. Choice D. Now we have a = 4, b = 6, c = 12. Then note a+b = 4+6 = 10 which is too small compared to c = 12. Meaning a+b > c is false. A triangle isn't possible. Cross choice D off the list.Choice E. In this case, a = 4, b = 6 and c = 10. Adding the first two values gets us a+b = 4+6 = 10 which is not larger than c = 10. If you used slips of paper, you'd find that a straight line is formed rather than a triangle. Cross choice E off the list.To wrap things up, only choice B and choice C are possible triangles because adding any two sides leads to a sum larger than the third side.
Probability and Statistics
Acellus
The probability distribution for a
random variable x is given in the table.
Help Resources
-10
-5
0
5
10
15
20
.20
.15
.05
.1
Probability
.25
.1
.15
Find the probability that x> 5
The probability distribution for a random variable x is given in the table x > 5 is 0.5.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
P(E) = Number of favorable outcomes / total number of outcomes
We are given that;
The table
Now,
Using these facts, we can find the probability that x > 5 from the given table:
The possible values of x that are greater than 5 are 10, 15, and 20. We need to add their probabilities to get the probability of x > 5.
The probability of x = 10 is 0.25, the probability of x = 15 is 0.1, and the probability of x = 20 is 0.15. Adding them together, we get:
P(x > 5) = P(x = 10) + P(x = 15) + P(x = 20)
P(x > 5) = 0.25 + 0.1 + 0.15
P(x > 5) = 0.5
Therefore, the probability will be 0.5.
Learn more about probability here;
https://brainly.com/question/9326835
#SPJ7
This is worth 30 points
Answer:
There's 3 questions which one do I answer?
Step-by-step explanation:
PLEASE HELP MEEEEEEEEE
Answer:
Step-by-step explanation:
How find the length of a hypotenuse triangle
Answer:
Step-by-step explanation:
A hypotenuse is calculated on a triangle with a right angle. The hypotenuse is the side opposite the sides with the right angle. The equation is a^2 + b^2=c^2 where the hypotenuse is the square root of c.
If f(x) = -x^3+ 2x^2 - 3, find f(2).
PLEASE PLEASE
Answer:
Step-by-step explanation:
f(x) = -x^3+ 2x^2 - 3
Putting value of x = 2
F(2) = - (2)^3 + 2(2)^2 - 3
= - 8 + 8 - 3
= - 3
Option B is the correct answer
ILL GIVE BRAINLYEST TO WHOEVER IS CORRECT PLEASE
The dot plots show the amounts, in dollars, that two
waiters made in tips at different tables.
Waiter A: Tips (dollars)
4 6 8 10 12 14 16 18 20 22 24
Waiter B: Tips (dollars)
4 6 8 10 12 14 16 18 20 22 24
Which of the following statements is correct?
A. The mean for waiter B is higher than the mean for waiter A.
B. The mean for waiter A is the same as the mean for waiter B.
C. The mean for waiter A is higher than the mean for waiter B.
O D. There are more tips shown for waiter A than for waiter B in the dot
plots.
Answer:
A The mean for waiter B is higher than the mean for waiter A.
Answer:
The mean for waiter B is higher than the mean for waiter A.
Step-by-step explanation:
Test approved
plz plz plz plz help me plz it is due in 1 hour and no links plz
Answer:
B
Step-by-step explanation:
The formula for the area of a triangle is given as:
A = ½*base*height
A = ½*b*h
A = (bh)2
If we know the area (A) and the base, to find the height, the following would be done:
Divide both sides by b
A/b = h/2
Multiply both sides by 2
[tex] \frac{A}{b} * 2 = h [/tex]
As we can see here, to find the base, we would divide the area by the vase, then multiply what we get by 2.
A company making tires for bikes is concerned about the exact width of their cyclocross tires. The company has a lower specification limit of 22.8 mm and an upper specification limit of 23.2 mm. The standard deviation is 0.15 mm and the mean is 23 mm. (Round your answer to 4 decimal places.) What is the process capability index for the process
Answer:
For this process, the capability index is 0.4444
Step-by-step explanation:
Given the data in the question;
Lower specification limit = 22.8 mm
Upper specification limit = 23.2 mm
The standard deviation σ = 0.15 mm
Mean μ = 23
capability index Cpk = ?
Now, Using the formula;
Cpk = min{ [(USL - μ)/3σ], [(μ - LSL)/3σ]
where USL is the Upper specification limit, LSL is the Lower specification limit, σ is the standard deviation, μ is the mean
so we substitute
Cpk = min{ [(23.2 - 23 )/(3×0.15)], [(23 - 22.8)/(3×0.15)] }
Cpk = min{ [0.2 / 0.45 ], [0.2 / 0.45] }
Cpk = min{ [ 0.4444 ], [0.4444] }
Therefore, for this process, the capability index is 0.4444
What is the vertex of x2 + 8x + 12?
Answer:
(-4,-4)
YW :))
Or you could of just looked it up cause thats what I did!!
A school has found from past records that the average scores for boys is 75 in a sample of 45 boys, and the average scores for girls is 85 in a sample of 30 girls. The population standard deviations for boys' and girls' scores were 25 and 17, respectively. The 90% confidence interval for the difference of the population means is approximately (_____, −2.022). Assume that the distributions of the scores of men and women are normally distributed. Round your answer to two decimal places.
Confidence Level Corresponding zc Value
90% confidence zc=1.645
95% confidence zc=1.96
99% confidence zc=2.576
Answer:
The 90% confidence interval for the difference of the population means is approximately (-17.98, -2.02).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem estabilishes 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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Boys:
Mean of 75, sample of 45, standard deviation of 25.
This means that [tex]\mu_B = 75, s_B = \frac{25}{\sqrt{45}}[/tex]
Girls:
Mean of 85, sample of 30, standard deviation of 17.
This means that [tex]\mu_G = 85, s_G = \frac{17}{\sqrt{30}}[/tex]
Distribution of the difference of mean grades of boys and girls:
[tex]\mu = \mu_B - \mu_G = 75 - 85 = -10[/tex]
[tex]s = \sqrt{s_B^2+s_G^2} = \sqrt{(\frac{25}{\sqrt{45}})^2+(\frac{17}{\sqrt{30}})^2} = 4.85[/tex]
Confidence interval:
As stated, the critical value is [tex]z = 1.645[/tex]
The margin of error is of:
[tex]M = zs = 1.645*4.85 = 7.98[/tex]
Lower bound:
[tex]\mu - M = -10 - 7.98 = -17.98[/tex]
Upper bound:
[tex]\mu + M = -10 + 7.98 = -2.02[/tex]
The 90% confidence interval for the difference of the population means is approximately (-17.98, -2.02).
17. Calculate the profit and loss percent if CP is RS 480 andSP is RS420
Answer:
there is no profit there is loss because CP is greater than SP
Step-by-step explanation:
loss=CP-SP
=Rs480-Rs420
=Rs60
loss%=loss/cp*100%
=60/480*100%
=6000/480
=12.5%
Based on the graph, how many distinct real number solutions does the equation x3 – 3x2 + 4 = 0 have?
Answer:
2 solutions
-1 and 2
Step-by-step explanation:
Pls help I’ll brainlest and add extra points asap
Step-by-step explanation:
1. E
2. G
3. I
4. J
5. H
6. F
7. A
8. D
9. B
10. C
(2v-3u)-(v-4u)+(v+4u)
Answer:
2v + 5u
Step-by-step explanation:
Fifteen students were asked how many board games they played last week. The responses are summarized in the table.
Number of
Board Games
Played
Number of
Students
0
5
6
1
2.
3
3
1
Find the mean and median number of board games played by the students.
Drag numbers to the blanks to show your answer.
mean
median
0
0.5
1
1.5
2
2.5
3
Answer:
Mean - 1.5
Median - 1.5
Step-by-step explanation:
Median = middle number
Means = all numbers added up and divided by how many are there
angle d is a vertical angle to angle f. The measure of angle d is 53 degrees. What is the measure of angle f?
Answer:
53 degrees
Step-by-step explanation:
Answer:
53
Step-by-step explanation:
Angle D = Angle F as they are vertical angles :)))
Sam's first six scores were 90, 80, 90, 80, 80, and 100. What is the median of these scores?
Answer:
85
Step-by-step explanation:
Nina purchases a gallon of milk for $3 and some tomatoes for $2 per pound
from the grocery store. Which equation represents the relationship
between the number of poundsp of tomatoes purchased and the total
amount x Nina spent at the grocery store? *
Answer:
x = 3 + 2p (2p is 2 times p)
The inside diameter of a randomly selected piston ring is a normally distributed random variable with mean 12 cm and standard deviation 0.04 cm. (a) What is the diameter that is exceeded by only 5% of the piston rings
Answer:
[tex]x=12.07[/tex]
Step-by-step explanation:
From the question we are told that:
Mean [tex]\=x =12cm[/tex]
Standard deviation [tex]\sigma=0.04[/tex]
Significance level [tex]\alpha=5\%=0.05[/tex]
Therefore
Confidence level [tex]95\%=0.95[/tex]
From table [tex]P(z<1.645)=0.95[/tex]
Generally the equation for Z-score is mathematically given by
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]x=z\sigma+\mu[/tex]
[tex]x=1.645*0.04+12[/tex]
[tex]x=12.07[/tex]
An election ballot asks voters to select four city commissioners from a group of fourteen candidates. In how many ways can this be done ?
Find the volume of the pyramid. Write your answer as a fraction or mixed number.
2 ft
1 ft
2 ft
Answer:
V=lwh /3
Step-by-step explanation:
Admission to a Museum is $30 for adults and $20 for students. The freshman class is attending a field trip
with teacher chaperones. Mr. Frees collects $6050 total from teachers and students, and 297 total people
go on the field trip. How many students and teachers attended?
Use s for # of students and a for # of adults
A) Write the equation representing the total number of people who went to the Museum
B) Write the equation representing the total amount of money collected
Now solve your system on your own paper
C) Number of students attending:
D) Number of adults attending:
Submit Question
9514 1404 393
Answer:
A) a + s = 297
B) 30a +20s = 6050
C) 286 students
D) 11 adults
Step-by-step explanation:
A) Total people is the sum of the numbers of adults and students:
a + s = 297
__
B) Total revenue is the sum of revenue from each class of attendees:
30a +20s = 6050
The solution is ...
30a + 20(297 -a) = 6050 . . . there were 297-a students
10a = 110 . . . . . . . . . . . . . . . . subtract 5940
a = 11
s = 297 -11 = 286
__
C) 286 students attended.
__
D) 11 adults attended.
Which of the following properties is shown in the question below?
Answer:
C. Associative property of multiplication
Step-by-step explanation:
The associative property of multiplication states that the way in which factors are grouped in a multiplication problem does not change the product.
Jada ran 15.25 kilometers. Han ran 8,500 meters. Who ran farther?
Answer:
15.25 km =15,250 m
so Jada ran further
Answer:
Jada ran farther
Step-by-step explanation:
First, convert 8,500 to kilometers.
8,500 ÷ 1,000 = 8.5
15.25 > 8.5
Have a wonderful day!
9. A shipping box is shaped like a rectangular prism. The dimensions of the box are in inches, as shown below.
(w+5) inches
(w+4) inches."
(2w) inches
Which expression describes the volume, in cubic inches, of the box?
A. 2w3 + 9w + 20
B. 243 + 182 + 402
C. 2u2 + 18w + 40
D. 2w2 + 4w+5
Given:
The dimensions of the box are (w+5) inches, (w+4) inches, (2w) inches.
To find:
The expression that describes the volume of the box.
Solution:
We know that the volume of a rectangular prism is:
[tex]V=length\times breadth \times height[/tex]
Substituting the given values, we get
[tex]V=(w+5)\times (w+4) \times 2w[/tex]
[tex]V=(w^2+5w+4w+20)2w[/tex]
[tex]V=(w^2+9w+20)2w[/tex]
Using distribution property, we get
[tex]V=(w^2)2w+(9w)2w+(20)2w[/tex]
[tex]V=2w^3+18w^2+40w[/tex]
Therefore, the volume of the box is [tex]2w^3+18w^2+40w[/tex] cubic inches.
Note: All the options are incorrect.
please help me pass please I need the most help ever is someone knows how to do these pls hmu on at ixgweeb
Answer:
tanx=b/c
sinx=b/a
cosx=c/a
Step-by-step explanation:
Answer:
REVENGE
Step-by-step explanation:
Every child who comes to Dr. Dean's dental office gets to choose a goody bag to take home.
There are 6 toothbrush colors and 8 toothpaste flavors to choose from. There are also 3
flavors of dental floss. Finally, Dr. Dean lets children choose from 5 different stickers for the
outside of the goody bag. How many different goody bags can a child make?
Answer:
720
Step-by-step explanation:
I think you just have to do
6x8x3x5
a car company uses the table below to show customers the appropriate amount of gas used when a car has been driven a certain number of miles.
if the car always uses the same amount of gas each time, how many gallons of gas would be needed to travel 480 miles?
A. 20
B. 24
C. 33
D. 39
Answer:
B. 24
Step-by-step explanation:
This is a simple ratio.If 1 mile = 0.05 gallons of gasoline, then 480 miles = 24 gallons of gasoline!Alex is making a blanket for her nephew. The blanket has a length of 5 ft and a width of 4 ft. She is going to sew ribbon edging around the perimeter of the blanket. The edging costs $3 per yard. How much will it cost for Alex to get the amount of ribbon edging that she needs? Help Resa 5 ft Skip 4 ft 4 ft 5 ft HINT: There are 3 feet in one yard.
She will need 6 yards. the permiter is 16 which 5 wouldnt be enough
Fifty seven percent (57%) of the students applying to a university are accepted. In other words, there is a 57% probability of being accepted. A sample of 12 applicants has been selected. Using Excel, answer the questions below. Please, round your solutions to 4 decimal places (if your answer has less than 4 decimals, it is okay to leave it as it is).