Answer:
71/84
Step-by-step explanation:
Answer:
1229/1764, 1231/1764, 179/252, 1255/1754 and 185/252.
Step-by-step explanation:
(5/6)^2 = 25/36
(6/7)^2 = 36/49
LCM of 36 and 49 is 1764
So 25/36 = 25 * 49 / 1764 = 1225/1764
and 36/49 = 36 * 36 / 1764 = 1296/1764
So the 5 rational numbers could be:
1229/1764, 1231/1764, 1253/1764 ( = 179/252), 1255/1764 and 1295/1764 (= 185/ 252).
A police car is located 40 feet on a small straight road perpendicular to main highway. A red car is driving along a highway in the direction of an intersection with that small road and is 180 feet away from the intersection. The police radar reads that the distance between the police car and the red car (this distance is straight between them - not on either road) is decreasing at a rate of 100 feet per second. How fast is the red car actually traveling along the road
Answer:
the red car is traveling at 102.44 ft/s along the road
Step-by-step explanation:
From the given information:
Let consider p be how far the car is up the road and q be how far the police is off the road.
Also, suppose that r is the distance between the police and the car.
Then, we can have a right triangle in which we can use the Pythagorean Theorem to calculate the r (distance between the cop and the car)
NOW,
p² + q² = r²
r² = 40² + 180²
r² = 1600 + 32400
r² = 34000
r = [tex]\sqrt{34000}[/tex]
r = 184.39
If we consider q' to be how fast the car is traveling down the road.
And, p' be how fast the police is traveling toward the road.
r' be how fast the distance between the police and the car is changing.
then , the derivative of our equation, p² + q² = r² with respect to time can now be:
2p(p') +2q(q') = 2r(r')
p(p') +q(q') = r(r')
By replacing our values; we have:
40(0) +180(y') = [tex]\sqrt{34000} \times 100[/tex] (given that the police is not moving p' =0)
180(y') = [tex]\sqrt{34000} \times 100[/tex]
[tex](y') = \dfrac{\sqrt{34000} \times 100}{180}[/tex]
[tex](y') = \dfrac{184.39 \times 100}{180}[/tex]
[tex]\mathbf{(y') = 102.44 \ ft/s}[/tex]
the red car is traveling at 102.44 ft/s along the road
The product of the roots of the equation x2 + x = 2 is: -2
Step-by-step explanation:
There are answers to this problem based on how we interpret this question.
If the question is x^2 + x =2
=> x = 1
Since, 1^2 + 1 = 2.
Another way to interpret this question is 2x+ x = 2
=> 3x = 2
=> x= 2/3
The answer differs based on how we interpret this question.
Hope this helps you.
Answer:
-2
Step-by-step explanation:
The EASIEST way to do this is using the laws of the sum and products of roots.
When you multiply two roots together, you simply get c/a
So, let's start:
x^2 + x = 2
subtract the 2 to get a quadratic equation equal to 0
x^2 + x -2 =0
Now,
a=1
b=1
c=-2
plug b and a into c/a
-(2/1)= -(2) = -2
The answer is -2.
It's NOT 1. the answer would be 1 IF it was adding the roots.
What is the equation of a circle centered at (1,-4) and a diameter 18?
Answer:
(x - 1)² + (y + 4)² = 81
Step-by-step explanation:
Circle Formula: (x - h)² + (y - k)² = r²
(h, k) is the center
2r = d
Step 1: Find r
18 = 2r
r = 9
Step 2: Plug known variables into formula
(x - 1)² + (y + 4)² = 9²
Step 3: Evaluate
(x - 1)² + (y + 4)² = 81
Answer:
(x-1)^2 + (y+4)^2 = 81
Step-by-step explanation:
The equation of a circle can be written as
(x-h)^2 + (y-k)^2 = r^2
where ( h,k) is the center and r is the radius
The center is ( 1,-4)
and the radius is d/2 = 18/2 = 9
(x-1)^2 + (y- -4)^2 = 9^2
(x-1)^2 + (y+4)^2 = 81
Manuel is saving money for college. He already has $250. He plans to
save another $50 per month,
Regardless of how many months he saves, how much does he save each
month?
Step-by-step explanation:
That is $250-$50=$200
why because he plans to
save $50 per month and
he already has$250to begin
so that explains what i did
the function y = a / x is given Which function will be obtained if the point P (-2,3) belongs to the graph of the given function
Answer:
The function is y = -6 / x.
Step-by-step explanation:
Since (-2, 3) belongs to the function, we know that x = -2, y = 3 is a solution to the function so when we plug those values in to solve for a, we get:
3 = a / (-2)
3 * (-2) = a / (-2) * (-2)
-6 = a so the function is y = -6 / x.
The office building is 111ft high. About how tall is this in meters.?
Answer:
Hey there!
11 meters is about 36 feet tall.
Let me know if this helps :)
Answer:
you answer is :33.8328
4' 1" − 1' 10" = Subtract measurement with Same Difference Theorem
Answer:
2' 3"
Step-by-step explanation:
Here 4' 1" − 1' 10" is certainly possible, but to carry out this operation we must borrow 1', or 12", from 4' 1":
4' 1" becomes 3' 13", and so the original problem becomes
3' 13" - 1' 10"
which in turn becomes 2' 3"
Multiply.
(7c+6)(-5c-4)
Simplify your answer.
Х
Answer:
120c
Step-by-step explanation:
7c(-5c)*(-4+6)
7c+5c*4+6
12c*10
120c
Answer:
the answer can be step by step explanation will be found in the answer was Matilda by 776 7 x 6 then the answer you will you - with the answer dancer used you New divide the answer that answer the simple your answer if we multiply you can contact me and say me in which is correct or wrong and I am a teacher
Find the distance between the points A(13, 2) and B(7, 10). The distance between the two points is
Answer:
The answer is 10 unitsStep-by-step explanation:
The distance between two points can be found by using the formula
[tex]d = \sqrt{( {x1 - x2})^{2} + ({y1 - y2})^{2} } [/tex]where
(x1 , y1) and (x2 , y2) are the points
From the question , the points are
A(13, 2) and B(7, 10)
The distance between them is
[tex] |AB| = \sqrt{( {13 - 7})^{2} + ({2 - 10})^{2} } \\ = \sqrt{ {6}^{2} + ( { - 8})^{2} } \\ = \sqrt{36 + 64} \\ = \sqrt{100} [/tex]We have the final answer as
10 unitsHope this helps you
At Geri’s school, 2 out of every 9 eighth-grade girls tried out for the volleyball team. If there are 216 eighth-grade girls at the school, how many tried out for the team?
Answer:
48 girls tried out for the team.
Step-by-step explanation:
The phrase "2 out of every 9" can be written as the fraction 2/9. To find our answer, all we have to do is 2/9 * 216 = 48 girls.
PLEASE ANSWER QUICKLY ASAP
READ QUESTIONS CAREFULLY
Answer:
see explanation
Step-by-step explanation:
Corresponding angles within the similar figures are congruent, thus
x = ∠ A = 52°
h = 7 × 1.5 = 10.5 cm
From B to A then divide by the scale factor, that is
w = 12 ÷ 1.5 = 8 cm
Julio wants to solve the system shown using the elimination method. Which is the best way to begin?
(x - 12y = 2
-4x + 7y = 12
Add the equations
b. Multiply each term in x - 12y = 2 by 4 and add it to the other original equation.
This system of equations has no solution, so Julio should not do anything.
d. Multiply each term in x - 12y = 2 by 4 and add it to the other original equation.
c.
Answer:
B. Multiply each term in x - 12y = 2 by 4 and add it to the other original equation.
Step-by-step explanation:
The expression are two linear equation and can be solved simultaneously
[tex]x - 12y = 2------------------1[/tex]
[tex]-4x + 7y = 12----------------------2[/tex]
1. we need to multiply each term in eqn 1 by 4 and add it to the other
original equation(2).
[tex]4x - 48y = 8----------------3\\-4x + 7y = 12---------------2\\\\[/tex]
Adding both 3 and 2 we have
[tex]4x - 48y = 8----------------3\\-4x + 7y = 12---------------2\\\\\\[/tex]
2. once we have gotten the value of y
we then substitute it in any of the equations to solve for x
Astrid is in charge of building a new fleet of ships. Each ship requires 404040 tons of wood, and accommodates 300300300 sailors. She receives a delivery of 444 tons of wood each day. The deliveries can continue for 100100100 days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least 210021002100 sailors.
To build the fleet of ships, Astrid must consider each of the given rates (i.e. the daily tons of wood, the sailors per ship, etc.). The available deliveries are enough to build ships that can accommodate at least 2100 sailors.
Given that:
Required quantities
[tex]Wood = 40\ tons[/tex]
[tex]Sailors = 300[/tex] per ship
Available quantities
[tex]Wood = 4\ tons[/tex] daily
[tex]Days = 100[/tex] at most
First, we calculate the total tons of woods Astrid can receive.
[tex]Total = Days \times Wood\ Available[/tex]
[tex]Total = 100 \times 4[/tex]
[tex]Total = 400\ tons[/tex] ---- in 100 days
Next, we calculate the number of ships that can be made from the 400 tons.
[tex]Ships = \frac{Total\ tons}{Wood\ Required}[/tex]
So, we have:
[tex]Ships = \frac{400}{40}[/tex]
[tex]Ships = 10[/tex]
This means that Astrid can build up to 10 ships
The number of sailors the ship can accommodate is:
[tex]Sailors = Ships \times Sailors\ per\ ship[/tex]
So, we have:
[tex]Sailors = 10 \times 300[/tex]
[tex]Sailors = 3000[/tex]
It means the 10 ships can accommodate 3000 sailors.
3000 sailors is greater than 2100 sailors.
So, we can conclude that she can build enough ship for the 2100 sailors.
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Answer:
280 tons
Step-by-step explanation:
:)
Help please!! Thanks
Answer:
B
Step-by-step explanation:
area of the full piece of pie. π(8)²*60/360 (we know 60°, because it's an equilateral triangle)
32π/3
now subtract the area of the triangle
1/2(8)(4√3) = 16√3
32π/3 - 16√3
which one represents translation
Answer:
The third one
Step-by-step explanation:
Translation is when it moves
the number ten is raised to a power between 0 and 1. The answer has to be between which two numbers?
Value of [tex]10^x[/tex] will be between 1 and 10.
Given in the question,
A number [tex]10^x[/tex] where, 0 < x < 1If we have to find the range of the value of the number, substitute x = 0 and 1
[tex]10^0=1[/tex]
[tex]10^1=10[/tex]
Therefore, value of [tex]10^x[/tex] will vary between 1 and 10.
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Nandini makes 'halwa' one evening and divides it into four equal portions for her family of four. However, just as they are about to eat it, an unexpected guest arrives and Nandini has to now re-divide the halwa into five equal portions. By what percentage has each family member's share reduced due to this? A. 5% B. 10% C. 20% D. 25%
Answer:
5%
Step-by-step explanation:
Total 'halwa' made = 1
Divided into four equal portion = 1/4
Arrival of an unexpected guest = 1/5
By what percentage has each family member's share been reduced:
Change in the sharing proportion:
Previous share ratio - new sharing ratio
(1/4 - 1/5) = (5 - 4) / 20 = 1/20
That means total reduction in the sharing = 1/ 20
Since each member comes contributed equally:
Reduction in each family member's share ;
(1 / 20) ÷ 4
(1 / 20) * 1/4 = 1/ 80
Percentage reduction:
(Reduction / original share) * 100%
[(1/80) ÷ (1/4)] * 100
(1/80 * 4/1) * 100%
(1/20) * 100%
= 5%
Reduction in each family members share = 5%
Select the answer choice that is equivalent to the expression given belon.
9(2x - 3) + 5y + 17
0) O-4% - 10
O 23% - 10
0 0 -4% + 17
0 0 -49% + 17
O 16% + 23
Answer:
[tex] 23x - 10 [/tex]
Step-by-step explanation:
To the find the equivalent of [tex] 9(2x - 3) + 5x + 17 [/tex], evaluate the expression. Start by opening the bracket.
[tex] 9*2x - 9*3 + 5x + 17 [/tex]
[tex] 18x - 27 + 5x + 17 [/tex]
Pair like terms
[tex] 18x + 5x - 27 + 17 [/tex]
[tex] 23x - 10 [/tex]
The equivalent of [tex] 9(2x - 3) + 5x + 17 [/tex] is [tex] 23x - 10 [/tex]
What is the volume of this rectangular prism?
Answer:
1
Step-by-step explanation:
rectangular prism volume = Width * Height * Length
Width = 1.33
Height = .6
Length = 1.25
volume = 1
Listed below are numbers of internet users per 100 people and numbers of scientific award winners per 10 million people for different countries. construct aâ scatterplot, find the value of the linear correlation coefficientâ r, and find theâ p-value of r. determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. use a significance level of alpha α equals = 0.05 0.05. internet users 78.0 78.0 79.0 79.0 56.2 56.2 68.3 68.3 77.9 77.9 38.2 38.2 award winners 5.5 5.5 8.8 8.8 3.3 3.3 1.7 1.7 10.8 10.8 0.1 0.1
Answer:
There is not sufficient evidence to support a claim of linear correlation between the two variables.
Step-by-step explanation:
The data provided is as follows:
X Y
78 5.5
79 8.8
56.2 3.3
68.3 1.7
77.9 10.8
38.2 0.1
(a)
The scatter plot is attached below.
(b)
Use the Excel function: =CORREL(array1, array2) to compute the correlation coefficient, r.
The correlation coefficient between the number of internet users and the award winners is,
r = 0.797.
(c)
The test statistic value is:
[tex]t=r\sqrt{\frac{n-2}{1-r^{2}}}[/tex]
[tex]=0.797\times\sqrt{\frac{6-2}{1-(0.797)^{2}}}\\\\=0.797\times 3.311372\\\\=2.639163484\\\\\approx 2.64[/tex]
The degrees of freedom is,
df = n - 2
= 6 - 2
= 4
Compute the p-value as follows:
[tex]p-value=P(t_{n-2}<2.64)=0.057[/tex]
*Use a t-table.
p-value = 0.057 > α = 0.05
The null hypothesis will not be rejected.
Thus, it can be concluded that there is not sufficient evidence to support a claim of linear correlation between the two variables.
The triangle shown below has an area of 4 units
Find the missing side.
Answer:
[tex]\boxed{4 units}[/tex]
Step-by-step explanation:
Hey there!
Well if the base is 4 and we use the formula,
b*h / 2
4*4 = 16
16/2 = 8
So x is 4.
Hope this helps :)
Answer:
x = 2 unitsStep-by-step explanation:
Area of a triangle is given by
base × height
[tex] A = \frac{1}{2} base × height[/tex]
From the question
Area = 4 units²
height = 4 units
let x represent the base
We have
[tex]4 = \frac{1}{2} \times x \times 4[/tex]
4 = 2x
Divide both sides by 2
x = 2 unitsHope this helps you
What is the length of BC?
Answer:
The answer is option B2.1Step-by-step explanation:
To find the length of a we use the cosine rule
That's
a² = b² + c² - 2bc cos A
We have
a² = AB ² + AC ² - 2(AB)(AC) cos A
From the question
AB = 6
AC = 5
A = 20°
Substituting the values into the above formula we have
a² = 6² + 5² - 2(6)(5) cos 20
a² = 36 + 25 - 60cos 20
a² = 61 - 56.38
a² = 4.62
Find square root of both sides
a = √4.62
We have the final answer as
a = 2.1Hope this helps you
Please help me solve this. With Reasoning
6 2/5 - 4 2/3
Answer:
1 and 11/15.
Step-by-step explanation:
To solve, we can separate the integers from the fractions.
(6 - 4) + (2/5 - 2/3)
= 2 + (6/15 - 10/15)
= 2 + (-4/15)
= 1 + 15/15 - 4/15
= 1 + 11/15
= 1 and 11/15
Hope this helps!
URGENT WILL GIVE BRAINLIEST TO FIRST RESPONDER You are visiting a Redwood tree forest and want to verify the height of one of the trees. You measure its shadow along the ground and use trig to calculate the height. The shadow measures 500 feet and you calculate the angle of elevation to be 35 degrees. This forms a right triangle. a. What is the measure of the other acute angle? b. What is the height of the tree? c. You are standing at the end of the tree's shadow and want to take a picture of the tree but your camera can only focus at distance less than 500 feet. When you hold the camera to take the picture it is 5 feet above the ground. What is the distance from the end of the shadow to the top of the tree? d. Can you take a clear picture of the top of the tree from where you are standing?
Answer:
a) 55 degrees
b) 350 ft.
Step-by-step explanation:
a- the sum of angles of triangle=180
( since it is right angle , one angle is 90 degrees), x be the acute angle
x+35+90=180
x=180-125
x=55 degrees
b) tan 35= height of a tree/ length of a shadow
height of a tree=tan35*500=350.103≅350 ft ( rounded to nearest tens)
c) hypotenuse²=350.1²+500²
c=√350.1²+500²
c=610.385 ft
d) no because the distance is more than 500
if y is directly proportional to x and y=5 when x=2, find the value of y when x =7
Answer:
y = 17.5
Step-by-step explanation:
y = kx
→ Substitute in the values
5 = 2k
→ Divide both sides by 2 to isolate k
k = 2.5
⇒ y = 2.5x
→ Substitute in x = 7
y = 2.5x ⇔ y = 2.5 × 7 ⇔ y = 17.5
what is the radical of 5√72 PLZ HELP!
Answer: Exact Form: 30√2
Decimal Form:42.42640687…
Step-by-step explanation: Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
I hope this helped :)
Answer:
30√2
Step-by-step explanation:
The radical portion of the given expression is √72.
__
Perhaps you want the simplest form of your expression. Factor out the perfect squares from under the radical.
[tex]5\sqrt{72}=5\sqrt{36}\sqrt{2}=5\cdot 6\sqrt{2}=\boxed{30\sqrt{2}}[/tex]
$10,000 for 20 years at 5% compounded annually
Answer:
$26532.98
Step-by-step explanation:
Given:
Principal = $10000Profit rate = 5% PA compoundedTime = 20 yearsCompounds = 20*1 = 20Sum is:
10000*(1 + 5/100)²⁰ ≈ 26532.98WILL GIVE BRAINLIEST PLEASE ANSWER
Answer:
D) 972
Step-by-step explanation:
2160*9/20 = 19440/20
= 972
15. Paul is scuba diving and is 3.5 feet below
sea level. He is descending at a rate of 0.5
feet per minute. If Paul is now at 12 feet
below sea level, how many minutes has he
been diving?
Answer:
24min.
Step-by-step explanation:
he descends 0.5 feet per min. Its just like counting by 2's. I hope this helped!!
Answer:
17 minutes
Step-by-step explanation:
This equation can be expressed as .5m+3.5=12 where m = minutes. I put this in a graphing calculator but to solve this you can
12-3.5=8.5
8.5/.5 = 17
Complete the statement to describe the expression abc + defabc+defa, b, c, plus, d, e, f. The expression consists of terms, and each term contains factors.
Answer:
The expression consists of 2 terms and each terms contains 3 factors.
Step-by-step explanation:
Given the expression (abc)+(def), the description of the expression is as shown:
The expression consists of 2 terms and each terms contains 2 factors.
Terms are expressions connected by mathematical signs such as addition and subtraction sign. As we can see from (abc)+(def), 'abc' and 'def' are separated by addition signs therefore both abc and def are the "terms" of the expression.
Factors are variables connected using the multiplication or bracket signs. As we can see, each term contains 3 factors. Looking at the first term 'abc', we can see that there are 3 variables/factors (a, b and c) multiplied together. This shows that they are connected by multiplication signs and same goes with 'def'.
Hence, the expression consists of 2 terms and each terms contains 3 factors.
The statements of expression.
As per the question, the statement which tells us about expression consists of 2 terms, and each term is 3 factors. As per the expression of the ABC and DEF describes expression of 2 terms and each term contains 2 factors.
Hence the answer is 2 terms and 3 factors.
The terms of the expressions are linked by mathematical signs such as addition and the subtraction signs. The factor is variables joined using the multiplication signs. In each term contains the 3 factors are found. Looking at the first term ABC, we can see that there are 3 variables like a, b, and c that are multiplied together.Learn more about the statement to describe.
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