Answer:
21cm; 28cm; 14cm
Step-by-step explanation:
There is no info in the problem/s text which one of the triangle's side is 21 cm. That is why we have to try all possible variants.
Let the triangle is ABC . Let the AK is the angle A bisector and BM is median.
Let O is AK and BM cross point.
Have a look to triangle ABM. AO is the bisector and AOB=AOM=90 degrees (means that AO is as bisector as altitude)
=> triangle ABM is isosceles => AB=AM (1)
1. Let AC=21 So AM=21/2=10.5 cm
So AB=10.5 cm as well. So BC= P-AB-AC=63-21-10.5=31.5 cm
Such triangle doesn' t exist ( is impossible), because the triangle's inequality doesn't fulfill. AB+AC>BC ( We have 21+10.5=31.5 => AB+AC=BC)
2. Let AB=21 So AM=21 and AC=42 .So BC= P-AB-AC=63-21-42=0 cm- such triangle doesn't exist.
3. Finally let BC=21 cm. So AB+AC= 63-21=42 cm
We know (1) that AB=AM so AC=2*AB. So AB+AC=AB+2*AB=3*AB
=>3*AB=42=> AB=14 cm => AC=2*14=28 cm.
Let check if this triangle exists ( if the triangle's inequality fulfills).
BC+AB>AC 21+14>28 - correct=> the triangle with the sides' length 21cm,14 cm, 28cm exists.
This variant is the only possible solution of the given problem.
I travelled at 60km/h and took 2 hours for a certain journey. How long would it have taken me if I had travelled at 50km/h?
Answer:
2 hours and 24 minutes
Step-by-step explanation:
2 hours at 60 km/h means you have travelled 2*60=120 km
120 km at 50 km/h takes 120/50 = 2.4 hours
2.4 hours is 2 hours and 0.4*60 = 24 minutes.
Chang knows one side of a triangle is 13 cm. Which set of two sides is possible for the lengths of the other two side
bf this triangle?
O 5 cm and 8 cm
O 6 cm and 7 cm
O 7 cm and 2 cm
8 cm and 9 cm
Answer:
It's (D) 8 cm and 9 cm. Hope this helps you!
Step-by-step explanation:
The other 2 sides added have to be greater than 13.
Answer:
8 and 9
Step-by-step explanation:
The triangle inequality states that the sum of the two shortest sides must be greater than the longest side.
Let's check the first one. 5 + 8 > 13 → 13 > 13 which is false.
6 + 7 > 13 → 13 > 13 which is false.
7 + 2 > 13 → 9 > 13 which is false.
8 + 9 > 13 → 17 > 13 which is true.
3) BRAINLIEST & 10+ POINTS!!! If a 4 foot blade of a propeller completes 22 revolutions per second, find the angular speed of the blade in radians per second. ~Round your answer to the nearest hundredth. Angular speed = _______________ radians/second
Answer:
44π rads per seconds
Step-by-step explanation:
Already the speed of the 4 foot blade is given as 22 revolutions per sec.
What we have to do is just to convert the 22 revolutions per second to radians.
1 rev = 360°
360° = 2π
So the speed is actually equal to
22 *360 = 7920° per second
Or
22*2π = 44π rad per seconds
What ever way the answers are both same.
It is believed that 11% of all Americans are left-handed. In a random sample of 100 students from a particular college with 10123 students, 14 were left-handed. Find a 98% confidence interval for the percentage of all students at this particular college who are left-handed.
Answer:
Step-by-step explanation:
We can calculate this confidence interval using the population proportion calculation. To do this we must find p' and q'
Where p' = 14/100= 0.14 (no of left handed sample promotion)
q' = 1-p' = 1-0.14= 0.86
Since the requested confidence level is CL = 0.98, then α = 1 – CL = 1 – 0.98 = 0.02/2= 0.01, z (0.01) = 2.326
Using p' - z alpha √(p'q'/n) for the lower interval - 0.14-2.326√(0.14*0.86/100)
= -2.186√0.00325
= -2.186*0.057
= 12.46%
Using p' + z alpha √(p'q'/n)
0.14+2.326√(0.14*0.86/100)
= 0.466*0.057
= 26.5%
Thus we estimate with 98% confidence that between 12% and 27% of all Americans are left handed.
Jenna worked 13 hours more than Jose last month. If Jenna worked 9 hours for every 4 hours that Jose worked, how many hours did they each work?
Which is the graph of the equation v- 1 = (-3)?
Step-by-step explanation:
The equation is v-1 = -3
V-1 = -3 add one in both sides v -1 +1 = -3+1 v = -2Here is the graph :
Find the sum. Please
Answer:
[tex]\dfrac{2y^2 +12y -8}{y^3-3y+2}[/tex]
Step-by-step explanation:
It usually works to factor the denominators, so you can determine the least common denominator.
[tex]\dfrac{2y}{y^2-2y+1}+\dfrac{8}{y^2+y-2}=\dfrac{2y}{(y-1)^2}+\dfrac{8}{(y-1)(y+2)}\\\\=\dfrac{2y(y+2)}{(y-1)^2(y+2)}+\dfrac{8(y-1)}{(y-1)^2(y+2)}=\dfrac{2y^2+4y+8y-8}{(y-1)^2(y+2)}\\\\=\boxed{\dfrac{2y^2 +12y -8}{y^3-3y+2}}[/tex]
Write 0000 using the am/pm clock.
Answer:
12am
Step-by-step explanation:
Answer:
12:00 am or midnight
Step-by-step explanation:
00 00 hrs in 12-hours clock is 12:00 am or 12:00 o'clock midnight.
Please help me
And explain
Answer: 144
Step-by-step explanation:
ABD plus DBC makes up ABC so when you add the two it will give you a whole (76+68).
PLSSSSSSS HELP WILL MARK BRAINLIEST Doug owns a lawn mowing and landscaping business. The income from the business is given by the function f(x) = 2x + 54, where f(x) is the income in dollars and x is the area in square meters of lawn mowed. If he has earned {204, 344, 450, 482} dollars in the last four months, what are the corresponding areas of lawn he mowed?
Answer:
i think this person answered but idrk perseusharrison79
Step-by-step explanation:
For 2 parallelograms, the corresponding side lengths are 1 inch and x inches, and 2 inches and 6 inches.
Not drawn to scale
StartFraction 1 over x EndFraction = StartFraction 2 over 6 EndFraction
StartFraction 1 over x EndFraction = StartFraction 6 over 2 EndFraction
StartFraction 1 over 6 EndFraction = StartFraction 2 over x EndFraction
One-half = StartFraction 6 over x EndFraction
Step-by-step explanation:
By about how much will f (x comma y comma z )equalsln StartRoot x squared plus y squared plus z squared EndRoot change if the point Upper P (x comma y comma z )moves from Upper P 0 (6 comma 4 comma 12 )a distance of dsequals0.1 unit in the direction of 3 Bold i plus 6 Bold j minus 2 Bold k?
Answer:
pls format
Step-by-step explanation:
Explain the importance of factoring.
Answer:
Factoring is a useful skill in real life. Common applications include: dividing something into equal pieces, exchanging money, comparing prices, understanding time, and making calculations during travel.
Sorry if this is a little wordy, I can get carried away with this sort of thing
anyway, hope this helped and answered your question :)
CAN SOMEONE PLEASE HELP ME THIS IS DUE SOON!!
Answer:
95 ft²
Step-by-step explanation:
Given:
regular pyramid with,
Square base of side length (s) = 5 ft
Slant height (l) = 7 ft
Required:
Surface area
Solution:
Surface area of a regular pyramid = ½*P*l + B
Where,
P = perimeter of the square base = 4(s) = 4(5) = 20 ft
l = slant height = 7 ft
B = area of base = s² = 5² = 25 ft²
Surface area = ½*20*7 + 25
= 10*7 + 25
= 70 + 25
Surface area of regular pyramid = 95 ft²
Which expression is equivalent to [tex]4^7*4^{-5}[/tex]? A. [tex]4^{12}[/tex] B. [tex]4^2[/tex] C. [tex]4^{-2}[/tex] D. [tex]4^{-35}[/tex]
Answer:
B. [tex]4^2[/tex]
Step-by-step explanation:
[tex]4^7 \times 4^{-5}[/tex]
Apply rule (if bases are same) : [tex]a^b \times a^c = a^{b + c}[/tex]
[tex]4^{7 + -5}[/tex]
Add exponents.
[tex]=4^2[/tex]
Answer:
[tex] {4}^{2} [/tex]Step by step explanation
[tex] {4}^{7} \times {4}^{ - 5} [/tex]
Use product law of indices
i.e
[tex] {x}^{m} \times {x}^{n} = {x}^{m + n} [/tex]
( powers are added in multiplication of same base)
[tex] = {4}^{7 + ( - 5)} [/tex]
[tex] = {4}^{7 - 5} [/tex]
[tex] = {4}^{2} [/tex]
Hope this helps...
Best regards!
A random sample of soil specimens was obtained, and the amount of organic matter (%) in the soil was determined for each specimen, resulting in the accompanying data (from "Engineering Properties of Soil," Soil Science, 1998: 93–102).1.10 5.09 0.97 1.59 4.60 0.32 0.55 1.450.14 4.47 1.20 3.50 5.02 4.67 5.22 2.693.98 3.17 3.03 2.21 0.69 4.47 3.31 1.170.76 1.17 1.57 2.62 1.66 2.05The values of the sample mean, sample standard deviation,and (estimated) standard error of the mean are2.481, 1.616, and .295, respectively. Does this data suggestthat the true average percentage of organic matterin such soil is something other than 3%? Carry out atest of the appropriate hypotheses at significance level.10. Would your conclusion be different if a 5 .05 hadbeen used? [Note: A normal probability plot of the datashows an acceptable pattern in light of the reasonablylarge sample size.]
Answer:
We conclude that the true average percentage of organic matter in such soil is something other than 3% at 10% significance level.
We conclude that the true average percentage of organic matter in such soil is 3% at 5% significance level.
Step-by-step explanation:
We are given a random sample of soil specimens was obtained, and the amount of organic matter (%) in the soil was determined for each specimen;
1.10, 5.09, 0.97, 1.59, 4.60, 0.32, 0.55, 1.45, 0.14, 4.47, 1.20, 3.50, 5.02, 4.67, 5.22, 2.69, 3.98, 3.17, 3.03, 2.21, 0.69, 4.47, 3.31, 1.17, 0.76, 1.17, 1.57, 2.62, 1.66, 2.05.
Let [tex]\mu[/tex] = true average percentage of organic matter
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 3% {means that the true average percentage of organic matter in such soil is 3%}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu \neq[/tex] 3% {means that the true average percentage of organic matter in such soil is something other than 3%}
The test statistics that will be used here is One-sample t-test statistics because we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean percentage of organic matter = 2.481%
s = sample standard deviation = 1.616%
n = sample of soil specimens = 30
So, the test statistics = [tex]\frac{2.481-3}{\frac{1.616}{\sqrt{30} } }[/tex] ~ [tex]t_2_9[/tex]
= -1.76
The value of t-test statistics is -1.76.
(a) Now, at 10% level of significance the t table gives a critical value of -1.699 and 1.699 at 29 degrees of freedom for the two-tailed test.
Since the value of our test statistics doesn't lie within the range of critical values of t, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the true average percentage of organic matter in such soil is something other than 3% at 10% significance level.
(b) Now, at 5% level of significance the t table gives a critical value of -2.045 and 2.045 at 29 degrees of freedom for the two-tailed test.
Since the value of our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.
Therefore, we conclude that the true average percentage of organic matter in such soil is 3% at 5% significance level.
1- if angle A = 30, then its complementary is -- and its supplementary is
2- If a triangle has an area of 360, and its base = 10, what is its height?
3- if two triangles have the same angle measures, then the triangles are
4. What is the definition of similar triangles?
5- One of triangle congruence tests is SSS, what are 3 other congruent tests
6- What is a regular polygon?
7- If a rectangle has an area of 240 and a length of 24, what is the width?
8- Colinear points lie on the same
9- 3 non-colinear points determine a
10- The sum of 2 supplementary angles add up to -------
1 - complementary = 90- 30 = 60
suplementary = 180- 30 = 150
2 - area = hb/2 = 360 = hb/2 = h = 72
3 - similar
4- see number 3
5 - asa, ssa, sas
6 - polygon that had all equal angle measures and sides (equiangular and equilateral)
7 - length x width = area so
240 / 24 = 10
8 - line
9 - triangle
10 - 180, as see in question 1
vote me brainliest ):>
19.25 tons equal Lbs
Answer:
38500lbs
Step-by-step explanation:
2000 lbs is one tone
if we have 19.25 tons, we need to multiply 19.25x2000
The answer is 38500 lb
Answer:
38,500 pounds
Step-by-step explanation:
Every ton is 2,000 pounds.
We want to find out how many pounds are in 19.25 tons.
Set up a proportion.
pounds/tons=pounds/tons
2,000 pounds/ 1 ton= x pounds / 19.25 tons
2,000/1= x /19.25
x is being divided by 19.25. The inverse of division is multiplication. Multiply both sides by 19.25.
19.25*2,000/1= x/19.25 *19.25
19.25*2000=x
38,500=x
There are 38,500 pounds in 19.25 tons.
For a large sporting event the broadcasters sold 51 ad slots for a total revenue of $136 million. What was the mean price per ad slot?
Answer:
$2.67 million
Step-by-step explanation:
Average price per slot is found by dividing total price by total slots:
($136 million)/(51 slots) ≈ $2.67 million/slot
The mean price per ad slot was $2.67 million.
solve the inequality:8x+3>2x-15
8x + 3 > 2x - 15
8x - 2x > -15 - 3
6x > -18
x > -3
Answer:
x > -3
Step-by-step explanation:
8x + 3 > 2x - 15
Add -3 and -2x on both sides.
8x - 2x > -15 - 3
6x > -18
Divide 6 into both sides.
x > -18/6
x > -3
The tens digit in a two digit number is 4 greater than one’s digit. If we interchange the digits in the number, we obtain a new number that, when added to the original number, results in the sum of 88. Find this number
Answer:
The original digit is 62
Step-by-step explanation:
Let the Tens be represented with T
Let the Units be represented with U
Given:
Unknown Two digit number
Required:
Determine the number
Since, it's a two digit number, then the number can be represented as;
[tex]T * 10 + U[/tex]
From the first sentence, we have that;
[tex]T = 4 + U[/tex]
[tex]T = 4+U[/tex]
Interchanging the digit, we have the new digit to be [tex]U * 10 + T[/tex]
So;
[tex](U * 10 + T) + (T * 10+ U) = 88[/tex]
[tex]10U + T + 10T + U= 88[/tex]
Collect Like Terms
[tex]10U + U + T + 10T = 88[/tex]
[tex]11U + 11T = 88[/tex]
Divide through by 11
[tex]U + T = 8[/tex]
Recall that [tex]T = 4+U[/tex]
[tex]U + T = 8[/tex] becomes
[tex]U + 4 + U = 8[/tex]
Collect like terms
[tex]U + U = 8 - 4[/tex]
[tex]2U = 4[/tex]
Divide both sides by 2
[tex]U = 2[/tex]
Substitute 2 for U in [tex]T = 4+U[/tex]
[tex]T = 4 + 2[/tex]
[tex]T = 6[/tex]
Recall that the original digit is [tex]T * 10 + U[/tex]
Substitute 6 for T and 2 for U
[tex]T * 10 + U[/tex]
[tex]6 * 10 + 2[/tex]
[tex]60 + 2[/tex]
[tex]62[/tex]
Hence, the original digit is 62
Which is the first step in simplifying 4(3x-2)+6x(2-1)
Answer:
4(3x-2)+6x(2x-1)
12x-8+12^2x-6x
12x-6x +12^2x-8
6x+12^2x-8
Answer:
the first step in simplifying 4(3x-2)+6x(2-1) is to do subtract 1 from 2 in the second set of parenthesis. That will get you 4(3x-2)+6x(1)
The equation completely simplified is 18x-8
-look in the step-by-step explanation if you want to know all the steps to simplifyinh the equation
Step-by-step explanation:
Now if you want to know the rest here it is:
Then use the Distributive Property:
-distribute the 4 into (3x-2) to get 12x-8
-then distribut the 6x into (1) to get 6x
Your equation is now 12x-8+6x
Finally, add 12x and 6x to simplify the equation as much as you can
you get 18x-8 as you final, most simplified answer
The mean arrival rate of flights at Philadelphia International Airport is 195 flights or less per hour with a historical standard deviation of 13 flights. To increase arrivals, a new air traffic control procedure is implemented. In the next 30 days, the arrival rate per day is given in the data vector below called flights. Air traffic control manager wants to test if there is sufficient evidence that arrival rate has increased.
flights <- c(210, 215, 200, 189, 200, 213, 202, 181, 197, 199,
193, 209, 215, 192, 179, 196, 225, 199, 196, 210,
199, 188, 174, 176, 202, 195, 195, 208, 222, 221)
a) Find sample mean and sample standard deviation of arrival rate using R functions mean() and sd().
b) Is this a left-tailed, right-tailed or two-tailed test? Formulate the null and alternative hypothesis.
c) What is the statistical decision at the significance level α = .01?
Answer:
a) The sample mean is M=200.
The sample standard deviation is s=13.19.
b) Right-tailed. The null and alternative hypothesis are:
[tex]H_0: \mu=195\\\\H_a:\mu> 195[/tex]
c) At a significance level of 0.01, there is notenough evidence to support the claim that the arrival rate is significantly higher than 195.
Step-by-step explanation:
We start by calculating the sample and standard deviation.
The sample size is n=30.
The sample mean is M=200.
The sample standard deviation is s=13.19.
[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{30}(210+215+200+. . .+221)\\\\\\M=\dfrac{6000}{30}\\\\\\M=200\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{29}((210-200)^2+(215-200)^2+(200-200)^2+. . . +(221-200)^2)}\\\\\\s=\sqrt{\dfrac{5048}{29}}\\\\\\s=\sqrt{174.07}=13.19\\\\\\[/tex]
This is a hypothesis test for the population mean.
The claim is that the arrival rate is significantly higher than 195. As we are interested in only the higher tail for a significant effect, this is a right-tailed test.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=195\\\\H_a:\mu> 195[/tex]
The significance level is 0.01.
The standard deviation of the population is known and has a value of σ=13.
We can calculate the standard error as:
[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{13}{\sqrt{30}}=2.373[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{200-195}{2.373}=\dfrac{5}{2.373}=2.107[/tex]
This test is a right-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z>2.107)=0.018[/tex]
As the P-value (0.018) is bigger than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
At a significance level of 0.01, there is notenough evidence to support the claim that the arrival rate is significantly higher than 195.
Which is NOT supported by this graph?
30
25
20
15
10
Profit
5
(dollars)
0
-10
-15
Cars Washed
Answer:
D -price of car wash keeps getting higher
Answer: The price of a car wash keeps getting higher
Step-by-step explanation:
HELP!! Im not sure what i did wrong!!
I'm not sure what exactly you did wrong, but I agree with you that the sample size is too small, so the correct answer will probably be the fourth options. Hope that this gives you some confidence, and 'm sorry not to be able to help you any further...
Mexican currency is the peso. One Mexican peso is currently equal to 0.055 U.S. dollars. If a traveler exchanges $400 for Mexican pesos, how many pesos will he receive? Round to the nearest peso.
Answer:
7,273 Pesos
Step-by-step explanation:
1 Peso = $0.055
The formula below converts pesos to dollars:
1 Peso x 0.055 = $1
The formula below converts dollars to pesos:
$1/0.055= 1 Pesos
We use the second formula because we are coverting
from dollars to pesos.
$400/0.055=7,273 Pesos
Answer:
22
Step-by-step explanation:
If one Mexican peso is .055 U.S dollars that means it has a greater value than the dollar so we can make the following ratio 1:.055. But if the .055 is a 400 1:400 we just multiply to get 22.
Which could be the side lengths of a triangle? (A) 2,2,4 (B) 3,4,7 (C) 4,5,8 (D) 5,5,10 (E) 7,3,10 PLEASE HELP
Answer:
(C) 4,5,8
Step-by-step explanation:
Since 4+5 = 9 and 9 is bigger than 8, that means that the side 8 can fit into the triangle without there being an open space.
Answer:
Option C { 4,5,8 }
Step-by-step explanation:
By the Triangle Inequality Theorem, the length of two sides together must be greater than the length of the remaining side. Respectively their difference must be less than the length of the another side.
* I like to memorize this concept by thinking about a door. The more you open the door, the greater the distance between the door and the wall - as they are proportional. That is how we concluded this theorem.
______
{ 2, 2, 4 } is our first option. The difference of 4 and 2 is equal to the remaining length, 2. { 3, 4, 7 } is not applicable as well, considering that the addition of 3 and 4 is equivalent to the length of the 3rd side, 7. However, the lengths { 4, 5,8 } have no such " errors. " It could be the side lengths of a possible triangle.
______
Solution = { 4,5,8 }
7 + x - 15 = -2.67 solve for x
Answer:
5.33
Step-by-step explanation:
Move your numbers so that they're separate from the variables. You should now have x = -2.67 + 8; x = 5.33
Answer:
x=5.33
Step-by-step explanation:
7+x-15=-2.67
7-15+x=-2.67
Add 7 and -15
-8+x=-2.67
Add 8 on both sides
which equal to 5.33
x=5.33
Based on data from the Greater New York Blood Program, when blood donors are randomly selected the probability of the having Group O blood is 0.45. Knowing that information, find the probability that AT LEAST ONE of the 5 donors has Group O blood type.
Answer:
The probability that at least one of the 5 donors has Group O blood type is 0.9497.
Step-by-step explanation:
We can model this as a binomial random variable, with n=5 (the sample size) and p=0.45.
The probability that exactly k donors have Group O blood type in the sample can be written as:
[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{5}{k} 0.45^{k} 0.55^{5-k}\\\\\\[/tex]
We have to calculate the probability P(x≥1). In this case it easy to substract from 1 the probabitity that x is exactly 0:
[tex]P(X\geq1)=1-P(x=0)\\\\\\P(x=0) = \dbinom{5}{0} p^{0}(1-p)^{5}=0.55^5=0.0503\\\\\\P(x\geq1)=1-0.0503=0.9497[/tex]
Find the area of the figure. Round to the nearest tenth if necessary. Use 3.14 for pi . 47.3 units2 41.1 units2 57.1 units2 66.2 units2
Answer:
41.1 units
Step-by-step explanation:
find the area of the triangle
1/2BH
1/2*8*4
4*4=16
find the area half of the circle
pi*R^2
3.14*4^2
3.14*16
50.24/2
^because it is a half circle you divide by 2
25.12+16=41.1
b. Parallelogram PQRS has base RS=14 m and an area of 70 m². What is the height of
the parallelogram?
Rs=14m and an area of 70m2
Answer
h = 5m
Step-by-step explanation:
area of a parallelogram is b * h
base = 14 m
h = ?
Area = 70 m²
Area = b * h
70 = 14 * h
h = 70 / 14
h = 5 m