Answer:
There are at least two runners whose times are less than 9 seconds apart.
Step-by-step explanation:
Let's assume that Tₙ is the time of the n-th runner, we know that:
6 min < Tₙ < 7 min
knowing that:
1 min = 60 s
We can rewrite this as:
6*60 s < Tₙ < 7*60 s
360 s < Tₙ < 420 s
We know that there are 7 runners, and we want to see if we can conclude that there are two runners whose times are less than nine seconds.
So, the smallest time allowed in seconds is 361 seconds (the first value larger than 360 seg) while the largest time allowed is 419 seconds (the largest time allowed smallest than 420 seconds).
Now, let's assume that the first runner has the smallest time:
then:
T₁ = 361 s
Now let's add 9 seconds to the time of each runner (here we want to check that we can have all the runners with exactly 9 seconds apart in their times, so we will prove that the statement is false), then:
T₂ = 361s + 9s = 370s
T₃ = 370s + 9s = 379s
T₄ = 379s + 9s = 388s
T₄ = 388s + 9s = 397s
T₅ = 397s + 9s = 406s
T₆ = 406s + 9s = 415s
T₇ = 415s + 9s = 424s
But 424s > 420s
So this is not allowed (as the maximum time allowed was 419 s), so at least two of the runners must have times that are less than 9 seconds apart.
Then; Can you conclude that there are two runners whose times are less than nine seconds apart? Yes.
Yes conclude that there are two runners whose times are less than nine seconds apart.
Given that,
Number of members = 7
Their mile times are all faster than 7 minutes but not faster than 6 minutes.
We have to determine,
Can you conclude that there are two runners whose times are less than nine seconds apart.
According to the question,
Let's assume that Tₙ is the time of the nth runner,
Then,
[tex]6 min < T_n < 7 min\\\\And \ 1 min = 60 s\\\\6\times 60 s < T_n < 7\times 60 s\\\\360 \ sec < T_n < 420 \ sec[/tex]
There are 7 runners, conclude that there are two runners whose times are less than nine seconds.
So, The smallest time allowed in seconds is 361 seconds (the first value larger than 360 seconds).
While the largest time allowed is 419 seconds (the largest time allowed smallest than 420 seconds).
Therefore,
Let's assume that the first runner has the smallest time:
T₁ = 361 s
Adding 9 seconds to the time of each runner to check that all the runners with exactly 9 seconds apart in their times.
So, prove that the statement is false
Then:
[tex]T_2 = 361s + 9s = 370s\\\\T_3 = 370s + 9s = 379s\\\\T_4 = 379s + 9s = 388s\\\\T_5 = 388s + 9s = 397s\\\\T_6= 397s + 9s = 406s\\\\T_7 = 406s + 9s = 415s\\\\T_8 = 415s + 9s = 424s[/tex]
Here, [tex]424s>420s[/tex]
So, There is not allowed (as the maximum time allowed was 419 s), T least two of the runners must have times that are less than 9 seconds apart.
Therefore, Yes conclude that there are two runners whose times are less than nine seconds apart.
To know more about Probability click the link given below.
https://brainly.com/question/23431320
One side of a triangle is 3 times longer than the shortest side and the third side is 4 centimeters longer than the shortest side. The perimeter of the triangle is 64.
How long is the shortest side of the triangle?
Answer:
First side is: 12cm
Second side is: 36cm
Third side is: 16cm
Step-by-step explanation:
Let x represent the shorter side
Then 3x represents the second side, and
x + 4 represents the third side.
Perimeter of three sides:
P = x + 3x + (x + 4)
Perimeter is 64, so
64 = x + 3x + (x + 4)
64 = 5x + 4
60 = 5x
12 = x
First side is x: 12cm
Second side is 3x: 3(12) = 36cm
Third side is x + 4: 12 + 4 = 16cm
Is my answer correct?
9514 1404 393
Answer:
yes
Step-by-step explanation:
By the "rule of 72", the amount will be doubled in 72/I years, where I is the annual interest rate in percent. That is, it can be estimated to take 72/4 = 18 years to double the $240 investment to $480. It would take another 18 years to double it again to $960. So, to achieve a balance of $1500 will be expected to take more than 36 years. The only reasonable answer choice is the one you have selected.
__
The exact solution is ...
log (1500/240)/log(1 +0.04) ≈ 46.72 years ≈ 47 years.
30 POINTS NO CAP PUT REALL STUFF
If it takes Laine 3 hours to wash the windows of one house, Leslie 4 hours to wash the same windows, and Lance 5 hours to wash the same windows, how long would it take them all working together to wash the windows on THREE houses?
3.8 hours
2.6 hours
5 hours
0.08 hours
Answer:
The answer would be C. 5 Hours
Step-by-step explanation:
Hopes this helps and good luck :)
(Functions and Relations) Answer getting brainliest!!
Answer:
D
Step-by-step explanation:
Have a nice day
Can any one help?
Solve the following equations:
Answer:
2- x=16/3 or 5.3
4- x=8
Step-by-step explanation:
yeah
In a triangle, the measure of the first angle is twice the measure of the second angle. The measure of the third angle is 80° more than the measure of the second angle. Use the fact that the sum of the measures of the three angles of a triangle is 180° to find the measure of each angle. what is the measure of the first angle?
Answer:
The measure of the first angle is 50°.
Step-by-step explanation:
Let the three angles be a, b, and c.
The measure of the first angle is twice the measure of the second angle. In other words:
[tex]a=2b[/tex]
The measure of the third angle is 80° more than the measure of the second angle. In other words:
[tex]c=b+80[/tex]
And since the interior angles of a triangle must equal 180°:
[tex]a+b+c=180[/tex]
Substitute a and c:
[tex](2b)+b+(b+80)=180[/tex]
Combine like terms:
[tex]4b+80=180[/tex]
Subtract 80 from both sides:
[tex]4b=100[/tex]
And divide both sides by four:
[tex]b=25^\circ[/tex]
So, the measure of the second angle is 25°.
Since the measure of the first is twice the second, the measure of the first angle is 50°.
(And since the measure of the third is 80° than the second, the measure of the third angle is 105°.)
An object dropped from a height of 500 feet has a height, h(t), in feet after t seconds have elapsed, such that h(t)=500−16t^2. Express t as a function of height h, and find the time to reach a height of 100 feet
Step-by-step explanation:
the answer is in the above image
The height of a triangle is 8 m more than twice the length of the base . The area of the triangle is 21 m^2 find the height of the triangle
Answer:12
Step-by-step explanation:cumquat
simplify 6to the power of-3 over 6 to the power of5
1/1679616 or 5.9537418 times 10 to the power of -7
The vertices of a triangle are as follows: (4,) (6,7) and (8,0) If you dilate the triangle by a scale factor of 3, what are the vertices of the new triangle
1. (12,12) (6,7) (24,3)
2. (4,12) (6,21) (8,0)
3. (12,4) (18,7) (24,0)
4. (12,12) (18,21) (24,0)
Answer:
(12, 12), (18, 21), (24, 0)
Step-by-step explanation:
To dilate a figure, you multiple each of the numbers in its coordinates by the scale factor.
The vertices of the new triangle is:
4. (12,12) (18,21) (24,0)
What are the vertices of the new triangle?We have:
The vertices of a triangle: (4, 4) (6,7) and (8,0)
We dilate the triangle by a scale factor of 3
To find the vertices of the new triangle after a dilation of 3, multiply the old vertices by 3. That is:
3 * (4, 4) => (12, 12)
3 * (6, 7) => (18, 21)
3 * (8,0) => (24, 0)
Therefore, the vertices of the new triangle is (12,12) (18,21) (24,0)
Learn more about dilation on:
brainly.com/question/28956841
#SPJ3
Solve for the value of v
Answer:
v = 9 because it is what would make a great answer
Step-by-step explanation:
the angles are supplementary, meaning it sums up to 180 degrees
so to find v, you have to find the total angle of v.
180- 105 equals 8v+3, or 75 equals 8v+3
subtract 75 with 3 leaving 72 equals 8v
v would equal 9
(6a + 6) + (3x - 2) + (2a + 4)
Answer:
8a+8+3x
Step-by-step explanation:
Just plus them! Nothing so harsh
Answer:
6a + 6 + 3x-2 + 2a +4=
= 6a +2a+3x+6-2+4=
= 8a+3x+8
Step-by-step explanation:
1. remove the () since the actions within them cannot be solved.
2.find the sum
Graph the line.
y=3x
Answer:
desmos(dot)com/calculator/gv8jsoui4w
Step-by-step explanation:
Create a table of appropriate x values e.g. x = 2 and substitute into y=3x which will be y=3*2 meaning y=6 at the point x=2. Repeat with different x values until you have enough points to draw a straight line.
Select the correct answer. How does the risk of needing insurance impact the cost of premlums? А. In some cases, higher risk results in lower costs. B. Higher risk always results in lower costs.
C. Higher risk always results in higher costs.
D In some cases, higher risk results in higher costs.
Answer:
A
Step-by-step explanation:
John shot 30 baskets in 5 minutes. At this rate how many minutes will it take him to shoot 90 baskets? What are the 2 units you are comparing?
Ans5 and 2
Step-by-step explanation:
Three relatives will share an inheritance of 196,800 in the ratio of 3 to 7 to 2. How many dollars of the inheritance will each of the relatives receive?
Answer:
49200
114800
32800
Step-by-step explanation:
196800/12=ans
ans * 3
ans * 7
ans * 2
Solve for b. b= V [?] 12 5 b Pythagorean Theorem: a2 + b2 = c2 Enter
[tex]\huge\bold{Given:}[/tex]
Length of the perpendicular "[tex]a[/tex]" = 5.
Length of the hypotenuse "[tex]c[/tex]" = 12.
[tex]\huge\bold{To\:find:}[/tex]
The length of the missing side ''[tex]b[/tex]".
[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]
The length of the missing side (base) "[tex]b[/tex]" is [tex]\boxed{√119}[/tex].
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
Using Pythagoras theorem, we have
[tex]({perpendicular})^{2} + ({base})^{2} = ({hypotenuse})^{2} \\ \\⇢ {a}^{2} + {b}^{2} = {c}^{2} \\\\ ⇢ {5}^{2} + {b}^{2} = {12}^{2} \\ \\⇢25 + {b}^{2} = 144 \\ \\⇢ {b}^{2} = 144 - 25 \\ \\⇢ {b}^{2} = 119 \\ \\⇢b = \sqrt{119} [/tex]
[tex]\sf\blue{Therefore,\:the\:length\:of\:the\:missing\:side\:"b"\:is\:√119.}[/tex]
[tex]\huge\bold{To\:verify :}[/tex]
[tex] {5}^{2} + { \sqrt{119} }^{2} = {12}^{2} \\\\ ⇝25 + 119 = 144 \\ \\⇝144 = 144 \\ \\⇝L.H.S.=R. H. S[/tex]
Hence verified. ✔
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{♡}}}}}[/tex]
Given m||n, find the value of x
Answer:
(i)Here ∠HGB=∠AGE(vertically opposite angles)
∠HGB=110
∘
Now, for parallel lines l and m, with transversal t.
∠HGB+∠GHD=180
∘
(Angles on the same side of the transversal are supplementary)
110
∘
+∠GHD=180
∘
∠GHD=180
∘
−110
∘
=70
∘
(ii)For parallel lines l and m with transversal a
∠AIE=∠CJI (corresponding angles)
⇒x=100
∘
Someone please help me?
Which is the decimal expansion of the following 1/5
Answer:
Decimal expansion of 1/5 = 0.2
Can someone please help me?
Answer:
A
Step-by-step explanation:
to find the inverse, there are two steps
1-interchange x and y
2-solve for y
so y=x+1/x
interchange to get x=y+1/y
and solving for y we multiply both sides by y to get xy=y+1
subtract both sides by y yielding xy-y=1
factor out y to get y(x-1)=1
then divide to get y=1/x-1
The Howards bought a $224,000 townhome. They made a down payment of $45,000 and took out a mortgage for the rest. Over the course of 30 years they
made monthly payments of $1073.21 on their mortgage until it was paid off.
th
total amount they ended un naying for the townhome
1 year = 12 months.
30 years x 12 months per year = 360 total months
Multiply total months by monthly payment:
360 months x 1,073.21 per month = $386,355.60 total monthly payments for 30 years.
Now add the down payment to the total monthly amount:
$386,355.60 + $45,000 = $431,355.60
Total amount paid: $431,355.60
Researchers at a medical school conducted a study to test the effectiveness of a new drug for lowering cholesterol. The 52 subjects who volunteered for the study were each given a randomly generated number. Subjects with an odd number were given the new drug, while those with an even number were given a placebo. Cholesterol levels before and after the treatment were measured for each subject, and the differences were computed.
This study is an example of ______________ study. The difference in cholesterol level is _____________ the variable. The treatment with drug or placebo is the ____________ variable.
Answer:
1. An Experimental
2. Dependent
3. Independent
Step-by-step explanation:
Considering the description of how the research was carried out, it can be concluded that This study is an example of AN EXPERIMENTAL study. This because the researcher is trying to study the effectiveness of a new drug for lowering cholesterol
The difference in cholesterol level is the DEPENDENT variable. This is because the difference in cholesterol level is what the researcher wants to determine.
The treatment with a drug or placebo is the INDEPENDENT variable. This is because this is what the researcher manipulates to determine the difference in cholesterol level which is the dependent variable in this experimental study.
In a certain region, there is a 0.1 probability that any checked passerine bird's nest will
contain a cuckoo egg. If three passerine nests are checked, what is the probability that
at least two of them contain a cuckoo egg?
Answer:
Probability of at least two cuckoo eggs is 0.738.
Step-by-step explanation:
probability of cuckoo egg = 0.1
probability of not a cuckoo egg = 1 - 0.1 = 0.9
Probability of at least two cuckoo eggs is
= Probability of two cuckoo eggs x probability of 1 not cuckoo egg +
probability of three cuckoo eggs
= 0.1 x 0.1 x 0.9 + 0.9 x 0.9 x 0.9
= 0.009 + 0.729
= 0.738
(Will mark brainlest ) help me to find the value of x or theta (step by step)
Answer:
X = 6
Step-by-step explanation:
sin○ = opposite side/hypotenuse
sin 45 = 3 root2/x
1/root2 = 3 root2/x
x = 3 × 2
x = 6
Answer:
x=6 cm
Step-by-step explanation:
take 45 degree as reference angle
using sin rule
sin 45 =opposite/hypotenuse
[tex]\frac{1}{\sqrt{2} } =\frac{3\sqrt{2} }{x}[/tex]
do cross multiplication
[tex]x=\sqrt{2} * 3\sqrt{2}[/tex]
x=6
2 1/3 - (-5) =
what does it equal
Answer:
7 1/3
Step-by-step explanation:
See image below:)
What is the image point of (1,-7) after the transformation T-3,-1 degrees R180 degrees?
Answer:
first hust rotate 180 and next reflect it over x axis.
the given point (-7,3) id in second quadrant but after rotation it will be in fourth quadrant.
afterwards you have to refect that point over x-axis which gives you the image of the points on first quadrant ie. (7,1).
Evaluate: (ƒ − g)(−2)
From the graph,
f(-2) = 0
and, g(-2) = 0
(ƒ − g)(−2)= f(-2)-g(-2) = 0
OPTION B is the correct answer
You have 3 five dollar bills and 4 ten dollar bills in your pocket. If you pull out 2 bills, what is the probability they are both tens?
Answer: I think its 4%
Step-by-step explanation: 3+4=7 7/2=3.5
Answer:
1/14
Step-by-step explanation:
Which measure of central tendency best describes the data set below?
{0, 80, 85, 88, 90, 95}
A. the mean, 73
B. the mode, none
C. the range, 95
D. the median, 86.5
Answer:
The correct answer would be D, the median 86.5. In this set of data most of the values are in the 80's or 90's.
Step-by-step explanation:
d point is the answer
Answer:
D) The median, 86.5
Step-by-step explanation:
Most of the data is clustered in the 80s. Therefore, D is correct.
