Step-by-step explanation:
so, we pick the first one. the probability this person swims is 0.45.
if yes, then we pick the second one. this one has also a probability of swimming of 0.45.
combined with the probability of the first one being a swimmer this is now 0.45×0.45.
the same with the third pick.
and we have the probability that all 3 swim of
0.45×0.45×0.45 = 0.45³ = 0.091125
that is rounded about 0.09 or 9%.
Give the digits in the hundred thousands place and the ten thousands place.
746,089
Answer:
Hundred thousands - 7
Ten Thousands- 4
Step-by-step explanation:
(b) Notice that x=0.5 meter when θ = 45o. By approximately how many radians should you increase θ if you want the x coordinate of the point R to decrease to x = 0.45 meters? Use the tangent line approximation.
The angle is increased in approximately 0.095 radians (5.443°) for [tex]x = 0.45\,m[/tex].
Based on the statement we construct the geometric diagram, by definition of tangent we have expressions for the initial and final angles ([tex]\theta_{1}[/tex], [tex]\theta_{2}[/tex]), in radians, of the figure:
Initial triangle
[tex]\tan \theta_{1} = \frac{y_{1}}{x_{1}}[/tex] (1)
Final triangle
[tex]\tan \theta_{2} = \frac{y_{2}}{x_{2}}[/tex] (2)
By using (2), the equivalence [tex]\theta_{2} = \theta_{1}+\Delta \theta[/tex] and trigonometric identities we have the following expression:
[tex]\frac{y_{2}}{x_{2}} = \frac{\tan \theta_{1}+\tan \theta_{2}}{1-\tan \theta_{1}\cdot \tan \theta_{2}}[/tex] (3)
By (1), we simplify the expression:
[tex]\frac{y_{2}}{x_{2}} = \frac{\frac{y_{1}}{x_{1}} + \tan \Delta \theta}{1-\frac{y_{1}}{x_{1}}\cdot \tan \Delta \theta}[/tex] (3b)
If [tex]0 \le \Delta \theta \le \frac{\pi}{6}[/tex], then we can use the following approximation:
[tex]\tan \Delta\theta \approx \Delta \theta[/tex] (4)
Then, we reduce (3b) into an entirely algebraic expression:
[tex]\frac{y_{2}}{x_{2}} = \frac{\frac{y_{1}}{x_{1}}+\Delta \theta }{1-\frac{y_{1}}{x_{1}}\cdot \Delta \theta }[/tex] (3c)
Where [tex]y_{2} = \sqrt{r^{2}-x_{2}^{2}}[/tex].
Now we clear [tex]\Delta \theta[/tex] within the formula:
[tex]\Delta \theta = \frac{\frac{y_{2}}{x_{2}}-\frac{y_{1}}{x_{1}}}{\frac{y_{1}}{x_{1}}\cdot \left(1+\frac{y_{2}}{x_{2}} \right) }[/tex] (5)
If we know that [tex]x_{1} = y_{1} = 0.5[/tex], [tex]r = 0.707[/tex] and [tex]x_{2} = 0.45[/tex], then we estimate the angle change:
[tex]y_{2} = \sqrt{0.707^{2}-0.45^{2}}[/tex]
[tex]y_{2} \approx 0.545[/tex]
[tex]\Delta \theta = \frac{\frac{0.545}{0.45}-1 }{1\cdot \left(1+\frac{0.545}{0.45} \right)}[/tex]
[tex]\Delta \theta = 0.095[/tex]
As [tex]\Delta \theta < \frac{\pi}{6}[/tex], then the result seems to be reasonable. The angle is increased in approximately 0.095 radians (5.443°) for [tex]x = 0.45\,m[/tex].
We kindly invite to check this question on trigonometric identities: https://brainly.com/question/24836845
Write $1.50 to $12.00 as a ratio in fraction form in lowest terms.
Answer:
1/8
Step-by-step explanation:
If 20% of the students were boys, what fraction were girls?
Answer:
Girls are 4/5 of the students.
Step-by-step explanation:
boys + girls = 100% of students.
If 20% of the students are boys then 80% are girls
80% = 80/100 = 4/5
June, Gavyn and Alex share some sweets in the ratio 5:3:2. June gets 42 more sweets than Alex. How many sweets does Gavyn get?
Answer:
42 sweets
Step-by-step explanation:
The ratios are 5 : 3 : 2 = 5x : 3x : 2x (x is a multiplier )
June gets 42 more sweets than Alex , then
5x = 2x + 42 ( subtract 2x from both sides )
3x = 42 ( divide both sides by 3 )
x = 14
Gavyn = 3x = 3 × 14 = 42 sweets
Answer:
42 sweets.
Step-by-step explanation:
First work out the number of parts:
5 + 3 + 2 = 10.
So June gets 5/10 = 1/2 of the sweets.
Alex gets 2/10 = 1/5.
Gavyn gets 3/10.
If the total number of sweets was x, then:
1/2 x - 1/5 x = 42
5/10x - 2/10 x = 42
3/10 x = 42
x = 42*10/3 = 140.
So Gavyn has 3/10 * 140 = 42.
Question 5 - Last night 20 mm of rain fell in 4 h. If it continues raining at the same rate, how
long will it take for 45 cm of rain to fall?
Answer:
Step-by-step explanation:
45 divided by two
The circle graph shows a family budgets it’s annual income.if the total annual income is 140,000, what amount is budgeted for auto expenses?
Answer: The amount budgeted for Auto Expenses is $18,200
Step-by-step explanation:
13 Percent of $140,000 is $18,200
0.13 times 140,000 :-)
Lcd of 4/5 , c/7 where c=3
Answer:
35
Step-by-step explanation:
I need to know that answer please help if you can
Answer:
$180
Step-by-step explanation:
y = 30x +150
30(1) + 150
= 180
The lcm of 5^3 and 5^2 is?
Answer:
5³
Step-by-step explanation:
5³ is the answer since it's the greater between the two numbers
Answer:
125
Step-by-step explanation:
This is because 5^2 *5 is 125 and 5^3 * 1 = 125 and the findings are both numbers have to be multiplied by a whole number to quantify a same identical multiple total number - we can check this by dividing by the smallest 125/5^2 = 5 and then the largest is 125/5^3 = 1 and we know there could not be a smaller whole number - The other workings would be to do a prim e factor tree of 125 = 5 25 5 and 5 = 5^3 and here we are told 5^3 is a multiple of 125 and 5^2 is also a multiple of 5^3 as it square fits 5 times into 125 as 5*25 is 125
Fdgbfrgrth Rheu Hyueheuhuhuhuheeuhuhuhe
6x+3>15 solve for a please
Answer:
x>2
Step-by-step explanation:
1) 6x+3 > 15
2) 6x > 15-3
3) 6x > 12
4) x > 12÷6
5) x > 2
Angles 1 and 2 are coresponding angles angle 1 is 3x+15 angle 2 is 4x-5 degrees.
what is the value of x
Answer:
10
Step-by-step explanation:
3x+15+4x-5=180
7x+10=180
7x=170
x=10
Jack bought a 1/4 pound of salami and 1 2/3 pounds of Ham at the deli. Both items are on sale for $12 per pound. What is the total cost?
Answer:
Salami: $3.00
Ham: $ 8.00
Step-by-step explanation:
12 * 1/4 = 12/4 = $3.00
12 * 2/3 = 24/3 = $8.00
The difference between
five-halves of a number and 17 is 48
Answer:
31, the five halves of is 6.2
Step-by-step explanation:
Solve the inequality 10y−3(y+2)>2y+4, and write the solution in interval notation.
Step-by-step explanation:
10y - 3(y + 2) > 2y + 4
10y - 3y - 6 > 2y + 4
(10 - 3 - 2)y > 4 + 6
5y > 10
y > 10/5
y > 2
[tex] \: [/tex]
Solution → y > 2
Interval Notation → [tex] \lang 2 , \infty\rang[/tex]
The solution in interval notation is: (2, ∞)
To solve the inequality 10y - 3(y + 2) > 2y + 4, follow these steps:
Step 1: Distribute the -3 on the left side of the inequality:
10y - 3y - 6 > 2y + 4
Step 2: Combine like terms:
(10y - 3y) - 6 > 2y + 4
7y - 6 > 2y + 4
Step 3: Get all the y terms on one side by subtracting 2y from both sides of the inequality:
7y - 2y - 6 > 2y - 2y + 4
5y - 6 > 4
Step 4: Get the constant term on the other side by adding 6 to both sides of the inequality:
5y - 6 + 6 > 4 + 6
5y > 10
Step 5: Finally, solve for y by dividing both sides by 5:
y > 10/5
y > 2
The solution to the inequality is y > 2. Now, let's write it in interval notation.
To know more about interval:
https://brainly.com/question/29126055
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There are 594 calories in six ounces of a certain ice cream. How many calories are there in two pounds?
1 pound=16 ounces
Before you try that problem, answer the question below.
How many ounces will you need to find the number of calories for?
Answer:
3,168 cal= 2lbs of Ice Cream
Step-by-step explanation:
I need to fin how many calories are in two pounds of that ceratin ice cream.
594cal/6=99cal
99cal=1 oz
16oz x 2 = 32oz
99 x 32 = 3,168 cal
There is 3,168 cal in two pounds of ceratin ice cream.
plz plz heelp me i need heelp
What equals 10³ I need to know
Answer:
1,000
Step-by-step explanation:
10 x 10 x 10 = 1,000
1000
Step-by-step explanation:
10³
=10×10×10
1000
The question is in the image! Please answer quickly.
Answer:
She thought the multiplication symbol was the addition symbol
actual answer: 1.39 x 10^12
Step-by-step explanation:
If it was addition, then she’d be correct;
6.75x10^6 + 0.2x10^6
= (6.75 + 0.2)x10^6
= 6.95x10^6
But really, it was a multiplication, meaning the answer really is;
(6.95x10^6)x(0.2x10^6)
= 1.39 x 10^12
3x-1 over 5 = x+1 over 3
I need asap
Answer:
(3x-1)/5= (x+1)/3
3(3x-1)=5(x+1)
then solve which the final answer will give you x=8
pls help with this pls
Answer:
1.5 songs/minutes
Step-by-step explanation:
30÷20 = 1.5
Third question please need help
Answer:
add 6 time 8 and get the answer like that.
Step-by-step explanation:
just keep adding that what you need to do ok.
PLEASE HELP! Economics
Answer:
B
Step-by-step explanation:
hope it helps, and im finding another question
Answer:
B. a German citizen
Step-by-step explanation:
I think I'm not sure.
Hello can someone please help me with this
Answer:
I would assume it is c. 1, because of rounding, but I'm only 70% sure.
Please answer this question no links please
Answer:
first I need to know what your question is to be able to answer this question sorry
Answer:
Ummm what is the question?
Step-by-step explanation:
Log2(x-1)+Log2(x+2) =2
Find X
Please answer right!
Answer:
Step-by-step explanation:
5x + 2 - 3x - 1 = 3x + 2
5x - 3x - 3x = - 2 + 1 + 2
5x - 6x = 1
-1x = 1
x = 1 / -1
x = -1
The variable r is directly proportional to the square of t, and r = 144 when t = 72.
Write the equation that expresses the relationship between the variables. (Let k represent the variation constant.)
Using the given data, solve for the variation constant k.
Answer:
k=0.023
Step-by-step explanation:
[tex]r \alpha {t }^{2} \\ r = k {t}^{2} \\ 144 = k \times {72 }^{2} \\ k = \frac{144}{ {72 }^{2} } \\ k = 0.023 \\ the \: eqn \: is \: therefore \\ r = 0.023 \times {t}^{2} [/tex]
The equation that expresses the relationship between the variables is r=kt and the variation constant k=2.
What is a proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".
Given that, the variable r is directly proportional to the square of t
Now, r∝t
r=kt
Here, r =144 when t =72
Thus, 144=k×72
k=2
Therefore, the equation that expresses the relationship between the variables is r=kt and the variation constant k=2.
To learn more about the proportional relationship visit:
brainly.com/question/12917806.
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For a project in his Geometry class, Ryan uses a mirror on the ground to measure the height of his school’s football goalpost. He walks a distance of 12.15 meters from the goalpost, then places a mirror on flat on the ground, marked with an X at the center. He then walks 3.4 more meters past the mirror, so that when he turns around and looks down at the mirror, he can see the top of the goalpost clearly marked in the X. His partner measures the distance from his eyes to the ground to be 1.35 meters. How tall is the goalpost? Round your answer to the nearest hundredth of a meter.
9514 1404 393
Answer:
4.82 m
Step-by-step explanation:
The mirror reflects light at the same angle the light hits it, so the triangles formed by the line of sight, the ground, and the objects involved are similar. This means corresponding lengths are proportional.
height/mirror distance = T/12.15 = 1.35/3.4
Multiplying by 12.15, we find the top of the goalpost to have a height of ...
T = 12.15(1.35/3.4) ≈ 4.82 . . . meters
The goalpost is about 4.82 meters high.
