Answers
Answer:
1). Option (b)
2). Option (d)
3). Option (d)
Step-by-step explanation:
Question (1)
For Pythagoras triplet,
(Largest number)² = (Number 1)² + (Number 2)²
a). 5² = 5² + 2²
25 = 25 + 4
25 = 29
Not True.
b). 5² = 3² + 4²
25 = 9 + 16
25 = 25
True.
c). 10² = 1² + 5²
100 = 1 + 25
100 = 26
Not true.
d). 2² = 2²+ 2²
4 = 4 + 4
4 = 8
Not true.
Therefore, Option (b) is correct.
Question (2)
1 - [tex]\frac{1}{5}[/tex] = [tex]\frac{5}{5}-\frac{1}{5}[/tex]
= [tex]\frac{5-1}{5}[/tex]
= [tex]\frac{4}{5}[/tex]
Therefore, Option (d) is the answer.
Question (3)
Property of triangle → Sum of lengths of two sides of a triangle should be greater than the measure of third side.
a). 6 + 3 > 2 ⇒ 9 > 2 [True]
6 + 2 > 3 ⇒ 8 > 3 [True]
2 + 3 > 6 ⇒ 5 > 6 [False]
Triangle is not possible.
b). 2 + 8 > 3 → 10 > 3 [True]
8 + 3 > 2 → 11 > 2 [True]
2 + 3 > 8 → 5 > 8 [False]
Triangle is not possible.
c). 5.5 + 2.5 > 2.5 → 8 > 2.5 [True]
5.5 + 2.5 > 2.5 → 8 > 2.5 [True]
2.5 + 2.5 > 5.5 → 5 > 5.5 [False]
Triangle is not possible.
d). 3 + 6 > 7 → 9 > 7 [True]
3 + 7 > 6 → 10 > 6 [True]
7 + 6 > 3 → 13 > 3 [True]
These are the sides of a triangle.
Therefore, Option D is the answer.
Related Questions
Find the solution to the system of equations.
You can use the interactive graph below to find the solution.
\begin{cases} y=-7x+3 \\\\ y=-x-3 \end{cases}
⎩
⎪
⎪
⎨
⎪
⎪
⎧
y=−7x+3
y=−x−3
Answers
Answer:
(1,-4)
Step-by-step explanation:
Given:
y = −7x+3
y = −x−3
Computation:
y = −7x+3......eq1
y = −x−3.......eq2
Eq 1 - 2
-6x + 6 = 0
x = 1
So,
y = −7x+3
y = −7(1)+3
y = -4
So,
(1,-4)
Nick earns 3.5%
commission on every
car he sells. How much
would he earn if he sold
a $14.000 car?
Answers
The amount he would earn is $490.
What does multiplication mean?
Multiplication is the process of determining the product of a number. It is determined by following some mathematical processes. The sign used to represent multiplication is ×.
How much will he earn?Commission = 3.5% x $14,000
0.035 x $14,000 = $490
To learn more about multiplication, please check: https://brainly.com/question/13814687
how many men have a waist measurement of more than 85cm
Answers
Answer:
29
Step-by-step explanation:
A music store marks up the instruments it sells by 30%.
If the price tag on a trumpet says $104, how much did the store pay for it?
Answers
A. $ 58.50
B. $ 80
C. No, it did not mark up 30%.
Step-by-step explanation:Since,
A. We have,
Mark up percentage = 30%
Actual price = $ 45,
B. We have,
SP = $ 104,
C. We have,
AP = $ 75,
SP = $100,
Thus, mark up percentage =
= 33.33 %
Hence, store did not mark up the price by 30%.
The life span of a domestic cat is normally distributed with a mean of 15.7 years and a standard deviation of 1.6 years. a. Find the probability that a cat will live to be older than 14 years. b. Find the probability that a cat will live between 14 and 18 years. c. If a cat lives to be over 18 years, would that be unusual? Why or why not? d. How old would a cat have to be to be older than 90% of other cats?
Answers
Answer
a. 0.856
b. 0.78071
c. It is not unusual
d. 13.65 years old
Step-by-step explanation:
The life span of a domestic cat is normally distributed with a mean of 15.7 years and a standard deviation of 1.6 years.
We solve this question using z score formula:
z = (x-μ)/σ, where
x is the raw score
μ is the population mean
σ is the population standard deviation.
a. Find the probability that a cat will live to be older than 14 years.
For x > 14 years
z = 14 - 15.7/1.6
z = -1.0625
Probability value from Z-Table:
P(x<14) = 0.144
P(x>14) = 1 - P(x<14) = 0.856
b. Find the probability that a cat will live between 14 and 18 years.
For x = 14 years
z = 14 - 15.7/1.6
z = -1.0625
Probability value from Z-Table:
P(x = 14) = 0.144
For x = 18 years
z = 18 - 15.7/1.6
z= 1.4375
Probability value from Z-Table:
P(x = 18) = 0.92471
The probability that a cat will live between 14 and 18 years is calculated as:
P(x = 18) - P(x = 14)
0.92471 - 0.144
= 0.78071
c. If a cat lives to be over 18 years, would that be unusual? Why or why not?
For x > 18 years
z = 18 - 15.7/1.6
z= 1.4375
Probability value from Z-Table:
P(x<18) = 0.92471
P(x>18) = 1 - P(x<18) = 0.075288
Converting this to percentage:
0.075288 × 100 = 7.5288%
Hence, 7.5288% of the cats live to be over 18 years. Hence, it is not unusual.
d. How old would a cat have to be to be older than 90% of other cats?
From the question above, 10% of the cats would be older than 90% of other cats.
Hence, we find the z score of the 10th percentile
= -1.282
Hence,
-1.282 = x - 15.7/1.6
Cross Multiply
-1.282 × 1.6 = x - 15.7
- 2.0512 = x - 15.7
x = 15.7 -2.0512
x = 13.6488 years old
Approximately = 13.65 years old
A national consumer agency selected independent random samples of 45 owners of newer cars (less than five years old) and 40 owners of older cars (more than five years old) to estimate the difference in mean dollar cost of yearly routine maintenance, such as oil changes, tire rotations, filters, and wiper blades. The agency found the mean dollar cost per year for newer cars was $195 with a standard deviation of $46. For older cars, the mean was $286 with a standard deviation of $58. Which of the following represents the 95 percent confidence interval to estimate the difference (newer minus older) in the mean dollar cost of routine maintenance between newer and older cars?
A. (195 - 286) + 1.992 underroot46/45 + 58/40
B. (286 - 195) + 1.992 underroot46^2/45+ 58^2/40
C. (195 - 286)+ 1.992 underrot 140² 158²/45+40
D. (286 - 195) + 1.992 46 1582 45 +40
E. (195-286) +1.992 462 + 58 45 40
Answers
Answer:
(195 - 286) ± 1.992 * sqrt((46^2/45) + (58^2/40))
Step-by-step explanation:
Given that:
NEWER CARS:
Sample size = n1 = 45
Standard deviation s1 = 46
Mean = m1 = 195
OLDER CARS:
Sample size = n2 = 40
Standard DEVIATION s2 = 58
Mean = m2 = 286
Confidence interval at 95% ; α = 1 - 0.95 = 0.05 ; 0.05 / 2 = 0.025
Confidence interval is calculated thus : (newer--older)
(m1 - m2) ± Tcritical * standard error
Mean difference = m1 - m2; (195 - 286)
Tcritical = Tn1+n2-2, α/2 = T(45+40)-2 = T83, 0.025 = 1.99 (T value calculator)
Standard error (E) = sqrt((s1²/n1) + (s2²/n2))
E = sqrt((46^2/45) + (58^2/40))
Hence, confidence interval:
(195 - 286) ± 1.992 * sqrt((46^2/45) + (58^2/40))
The 95% confidence interval for estimating the difference in the mean dollar cost of the routine maintenance between newer and older cars is given by:
[tex]CI=(\overline{x_1} - \overline{x_2}) \pm t_{critical} \sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}[/tex]
Given that:The first sample consists of owners of newer cars
First sample's size = [tex]n_1 =45[/tex]First sample's mean = [tex]\overline{x_1}=\$195[/tex]First sample's standard deviation = [tex]s_1 = \$46[/tex]The second sample consists of owner of older cars.
Second sample's size = [tex]n_2 = 40[/tex]Second sample's mean = [tex]\overline{x_2}=\$286[/tex]Second sample's standard deviation = [tex]s_2 = \$58[/tex]To find:95% confidence interval for difference between both samples' means.
Calculations and Explanations:Since the sample sizes are > 30, thus we can use the z table for finding the Confidence interval.
The CI is given as:
[tex]CI=(\overline{x_1} - \overline{x_2}) \pm t_{critical} \sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}[/tex]
For 0.95 probability confidence, we have t at 40+45-3= t at 83 at 0.05/2 is 1.992 (from T tables)
Thus,
[tex]CI=(195-268) \pm 1.992 \sqrt{\dfrac{46^2}{45} + \dfrac{58^2}{40}}[/tex]
Learn more about confidence interval here:
https://brainly.com/question/4249560
Solve the following equations | 3x + 3/7 | = 2 1/3
Answers
Answer:
X∈[tex]\frac{5}{63}, -\frac{23}{63}[/tex]
Step-by-step explanation:
Where did the 45% come from. It states 55% in question
Answers
Answer:
is this a question......
Ellen already knew 50 appetizer recipes before starting culinary school, and she will learn 4 new appetizer recipes during each week of school. After 73 weeks of culinary school, how many total appetizer recipes will Ellen know? Write and solve an equation to find the answer.
Answers
Answer:
342
Step-by-step explanation:
50+4x=y
x=73
At 5:00 p.m., Antonio turned on the oven. While the oven preheated, the temperature in the oven increased from 72°F to 400°F over a 10-minute period. The oven remained at 400°F for 45 minutes until Antonio turned it off. It took 60 minutes for the temperature in the oven to cool, returning to 72°F at 6:55 p.m. Which statement best explains whether or not the temperature in the oven is a function of the time?
Answers
Answer: It is a function because at any given time the oven was exactly one temperature.
Step-by-step explanation:
It is given that:
At 5:00 p.m., Antonio turned on the oven.
The oven remained at 400°F for 45 minutes until Antonio turned it off.
It took 60 minutes for the temperature in the oven to cool, returning to 72°F at 6:55 p.m.
) Buyers are charged a shipping fee of $4.75 for each scarf order.
Which expression can you use to find the total price of a scarf order?
Answers
Answer:
huh can you put the whole question?
Step-by-step explanation:
Put all the answers
Step-by-step explanation:
What is the answer I need help pls
Answers
Answer:
The answers are,
-3, -7
-2, 4
0, 2
2, 8
3, 11
Step-by-step explanation:
You just plug in the domain values into the equation and solve for f(x), so your domain number is your x value and the y value(f(x) value) is the answer
16 is what percent of 20?
Answers
Answer:
3.2
Step-by-step explanation:
0.8 * 100 = 80
Solution: 80%
Pls help me with this ASAP
Answers
A tank is being filled up with water. At t=0, we know that the tank holds 150 gallons of
water, and after one hour ( t=1) , it holds 180 gallon of water.
Answers
Answer:
What is the question?
Step-by-step explanation:
Answer: The initial value is 150 and the rate of change is 30
150+30x=y
Which substitution method should be the best used to solve which system of equations
Answers
Answer: 6x+2y=1
Step-by-step explanation:
because it just is
In a class of 12 boys and 8 girls, two students need to be chosen for classroom jobs.
What is the probability that Mary gets selected?
Answers
Answer:
55 percent chance or 11/20 or 0.55
Step-by-step explanation
Which of the following is not a solution of the equation y=3x-4?
A. 2,2
B. 0,-4
C. 4,8
D. -1,-1
Answers
2 = 3(2) - 4, true
-4 = 3(0) - 4, true
8 = 3(4) - 4, true
-1 = 3(-1) - 4, false
Solution: D
HELP!!! STATS!!!
A random sample of 100 felony trials showed a sample mean waiting time between arrest and trial = 173 days with a population standard deviation of waiting times = 28 days. Find a 99% confidence interval for the population mean waiting time.
Stats question, I'm really stck please help me!
Answers
Answer:
The 99% confidence interval is [tex] 165.776 < \mu < 180.224 [/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 100
The sample mean is [tex]\= x = 173 \ days[/tex]
The population standard deviation is [tex]\sigma = 28 \ days[/tex]
From the question we are told the confidence level is 99% , hence the level of significance is
[tex]\alpha = (100 - 99 ) \%[/tex]
=> [tex]\alpha = 0.01[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 2.58 [/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
[tex]E = 2.58 * \frac{28 }{\sqrt{100} }[/tex]
=> [tex]E = 7.224 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
=> [tex] 173 -7.224 < \mu < 173 + 7.224 [/tex]
=> [tex] 165.776 < \mu < 180.224 [/tex]
what is m% of n please help
Answers
m% of n would technically be some amount of n. To find m%, you would have to do n * 0.m to find your answer
plz help this is very confusing
Answers
Answer:
[tex] x \ge 15 [/tex]
Step-by-step explanation:
An isosceles ∆ has 2 equal sides. The perimeter of a ∆ is the sum of all its sides.
Given that the perimeter of the triangle above is "at least 137 ft", this means the sum of all its sides is equal to or greater than 137 ft.
Thus, using inequality, this can be represented as:
[tex] 2(2x + 7) + 4x + 3 \ge 137 [/tex]
Solve for x
[tex] 4x + 14 + 4x + 3 \ge 137 [/tex]
Add like terms
[tex] 8x + 17 \ge 137 [/tex]
Subtract 17 from both sides
[tex] 8x + 17 - 17 \ge 137 - 17 [/tex]
[tex] 8x \ge 120 [/tex]
Divide both sides by 8
[tex] \frac{8x}{8} \ge \frac{120}{8} [/tex]
[tex] x \ge 15 [/tex]
Which expressions are equivalent to 6a(5+d) ?
Select each correct answer.
30a+6ad
30ad
30a+(6a⋅d)
(6a⋅5)+(6a⋅d)
11a + d
Answers
Answer: A is correct i think
Step-by-step explanation: 6a x 5 = 30a
6a x d = 6ad
Answer:
A
Step-by-step explanation:
Lourdes recorded in this table the change in her dog's weight, in ounces, each month. Which statement can be suppor by the data in the table? Change in Dog's Weight January February March April May +6 +4 -2 +1 -5
A) Lourdes dog gained weight in more months than it lost weight because there are more positive numbers than ne numbers.
B) Lourdes' dog lost weight in more months that it gained weight because the digit 5 is the greatest digit and it is a ne number.
C) Lourdes dog gained weight every month because it is getting older.
D) Lourdes dog lost weight every month because the change in May is a negative number.
Answers
Answer:
A). Lourdes dog gained weight in more months than it lost weight because there are more positive numbers then negative numbers
Luis is buying flour for his bakery, and he buys 8 sacks of flour for $25.75 each. He also has to pay $36.50 for delivery. How much is Luis paying in total for his flour order? (pls help this is a test)
Answers
4. The perimeters of the rectangle and the triangle below are equal. Find the value of x.
Answers
Answer:
x=6
Step-by-step explanation:
the perimeter of the rectangle is equal to 2x + 16.
the perimeter of the triangle is equal to 3x + 10.
since they are equal now you can solve by saying 2x + 16 = 3x + 10
Now you solve for x
2x + 16 = 3x + 10
2x + 6 = 3x
6 = x
Please help!!! I will mark brainliest :)))
Answers
Answer:
its the first top one the 3rd one and the bottom one
Step-by-step explanation:
Robert bough 3/4 pound of grapes and divided them into 6 equal portions.
What is the weight of each portion?
*
Answers
Answer: The answer should be 0.125
Step-by-step explanation:
-3(1)+(-3)(-1) =
+()]
-3(1) + (-3)(-1)=-3[0]
-3(1)+(-3)(-1) =
_
+(-3)(-1) =
+
Answers
Answer:
³⅜
Step-by-step explanation:
⁴⁵⅖
+⁷⅝×⅖i
I HOPE IT HELP TYSM
Answer:
i dunno
Step-by-step explanation:
8. Given: AD perpendicullar DB, DB perpendicullar BC, AB = CD Prove: AB||DC
Answers
Step-by-step explanation:
Angle ADB = Angle CBD = 90° (given)
Side AB = Side DC (given)
Common side DB / BD
By HL congruence, triangles ABD and CDB are congruent.
Therefore Angle ABD = Angle CDB
=> Line AB is parallel to Line DC (Z angles)
Find the value of x. Everything is in the photo.
Answers
Answer:
27
Step-by-step explanation:
Note that since VX and XZ are both line segments, <VWX and <XYZ both equal 180 (also known as a straight angle). Also, note that the sum of the angles in a triangle are 180 degrees. Now, let’s start.
Finding angles of the triangle:
<WYX = <XYZ - <WYZ = 180 - 4x
<XWY = <XWV - <VWY = 180 - 6x
Using the sum of angles in a triangle and substituting these values in:
180 = <X + <WYX + <XWY = 90 + (180 - 4x) + (180-6x) = 450 - 10x
270 = 10x
27 = x
We are done! I hope this helps! :)