Answer:
9:16
Step-by-step explanation:
The ratio of sides of the lengths of rectangles is 3:4.
Now since the scale is constant. So the scale ratio of area will be square of the side ratio .That is :-
→ Ratio of Area = ( 3 : 4)²
→ Ratio of Area = (3/4)²
→ Ratio of Area = 9/16
→ Ratio of Area = 9:16
Hence the ratio of areas is 9:16 .A ship captain looks up at the top of a lighthouse at a 7 degree angle of elevation and calculates that he is 1221 feet from its base. How tall is
the lighthouse, rounded to two decimal places?
123.01 feet
134.78 feet
149.92 feet
148.80 feet
What are the solutions of this quadratic equation?
Please help
Answer:
B
Step-by-step explanation:
Use quadratic formula
Carlos plays college soccer, and will attempt two goals in a row.
A = the event Carlos is successful on his first attempt. P(A) = 0.60.
B = the event Carlos is successful on his second attempt. P(B) = 0.55.
The probability that he makes the second goal GIVEN that he made the first goal is
0.35
What is the probability that he makes both goals?
Which pair of functions are inverses of each other?
Answer:
D.f(x)=2x-9and g(x)=X+9/2
A storage tank contains a liquid radioactive element with a half-life of 96 years. It will be relatively safe for the contents to leak from the tank when 0.02% of the
radioactive element remains. How long must the tank remain intact for this storage procedure to be safe?
The tank must remain intact for years.
(Round the base of the exponential function to four decimal places. Then round the final answer to the nearest year as needed.)
Answer:
The tank must remain intact for 1183 years.
Step-by-step explanation:
Exponential equation for decay:
The amount of a substance after t years is given by:
[tex]A(t) = A(0)e^{rt}[/tex]
In which A(0) is the initial amount and r is the decay rate.
A storage tank contains a liquid radioactive element with a half-life of 96 years.
This means that [tex]A(96) = 0.5A(0)[/tex], and we use this to find r.
[tex]A(t) = A(0)e^{rt}[/tex]
[tex]0.5A(0) = A(0)e^{96r}[/tex]
[tex]e^{96r} = 0.5[/tex]
[tex]\ln{e^{96r}} = \ln{0.5}[/tex]
[tex]96r = \ln{0.5}[/tex]
[tex]r = \frac{\ln{0.5}}{96}[/tex]
[tex]r = -0.0072[/tex]
So
[tex]A(t) = A(0)e^{-0.0072t}[/tex]
It will be relatively safe for the contents to leak from the tank when 0.02% of the radioactive element remains. How long must the tank remain intact for this storage procedure to be safe?
This is t for which [tex]A(t) = 0.0002A(0)[/tex]. So
[tex]A(t) = A(0)e^{-0.0072t}[/tex]
[tex]0.0002A(0) = A(0)e^{-0.0072t}[/tex]
[tex]e^{-0.0072t} = 0.0002[/tex]
[tex]\ln{e^{-0.0072t}} = \ln{0.0002}[/tex]
[tex]-0.0072t = \ln{0.0002}[/tex]
[tex]t = -\frac{\ln{0.0002}}{0.0072}[/tex]
[tex]t = 1183[/tex]
The tank must remain intact for 1183 years.
HELP
Which Trig ratio should be used to find the missing side?
A.Sin
B.Cos
C.Tan
Answer:
It's Sin.
Thumbs-up (^_-)
Step-by-step explanation:
the answer is A ,since the unknown side is opposite while the known side is the hypotenuse
Which of the statements below are true? Select all that apply. A) The table shows a proportional relationship B) The table does not show a proportional relationship C) With $3.00, you could buy 10 bananas D) Each banana costs $0.30
Answer:
go to school, do your work, you are only cheating yourself, not the school, or end up homeless
Step-by-step explanation:
click image to see it all:))))
9514 1404 393
Answer:
16 miles
Step-by-step explanation:
The problem can be modeled by a right triangle with one angle of 7° and the side opposite being 10,000 ft. The distance needed is the hypotenuse of the triangle, so the relevant trig relation is ...
Sin = Opposite/Hypotenuse
Hypotenuse = Opposite/Sin
air distance = (10,000 ft)/sin(7°) ≈ 82,055 ft
At 5,280 ft per mile, that is ...
(82,055 ft)/(5,280 ft/mi) ≈ 15.54 mi
The plane's air distance to the airport is about 16 miles.
Describe the end behavior of the graph of the function.
hx()=−3x4+4x3+10x2−8x+7
a.hx()→−∞as x→−∞and hx()→−∞as x→∞
b.hx()→−∞as x→−∞and hx()→∞as x→∞
c.hx()→∞as x→−∞and hx()→−∞as x→∞
d.hx()→∞as x→−∞and hx()→∞as x→∞
9514 1404 393
Answer:
a.hx()→−∞as x→−∞and hx()→−∞as x→∞
Step-by-step explanation:
The negative leading coefficient tells you the function tends toward -∞ as x gets large. The even degree tells you it goes the same direction as x tends toward -∞.
h(x) → -∞ for x large or small . . . . matches A
Point D is located at (-2,-4) on a coordinate plane.
Part A
What are the coordinates of the point that is 5 units to the left of point D?
Part B
What are the coordinates of the point that is 5 units to the right of point D?
Answer:
Part A: (-7,-4)
Part B: (3,-4)
Step-by-step explanation:
Four customers came into a bakery. The first one said, "give me half of all the donuts you have left, plus half a donut more." The second customer said, "give me half of all the donuts you have left, plus half a donut more." The third customer said, "give me three donuts." The last customer said, "give me half of all the donuts you have left, plus half a donut more." This last transaction emptied the display case of donuts. How many donuts were there to start with?
Step-by-step explanation:
A bag of M&Ms contains 13 blue, 5 brown, 10 orange, 8 yellow, 8 red, and 4
green. Reaching into the bag, a person grabs 5 M&Ms.
What is the probability of getting no browns? Round to 3 decimal places.
Answer:
0.5622 = 56.22% probability of getting no browns.
Step-by-step explanation:
The M&Ms are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
13 + 5 + 10 + 8 + 8 + 4 = 48 total M&Ms, which means that [tex]N = 48[/tex]
Sample of 5 means that [tex]n = 5[/tex]
5 browns means that [tex]k = 5[/tex]
What is the probability of getting no browns?
This is P(X = 0).
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,48,5,5) = \frac{C_{5,0}*C_{43,5}}{C_{48,5}} = 0.5622[/tex]
0.5622 = 56.22% probability of getting no browns.
Find cotθ if θ terminates in Quadrant III and secθ = 2
a. - (sqrt 3)/3
b. (sqrt 3)/3
c. - sqrt 3
d. sqrt 3
Answer:
we have
secθ = 2
[tex] \frac{1}{cos θ} [/tex]=2
Cosθ =[tex] \frac{1}{2 }[/tex]
[tex] \frac{b}{h }=\frac{1}{2 }[/tex]
b=1
h=2
p=[tex] \sqrt{2²-1} = \sqrt{3} [/tex]
again
Cot θ=[tex] \frac{b}{p }[/tex]
Cot θ=[tex] \frac{1}{ \sqrt{3}} [/tex]
Cot θ=[tex] \frac{\sqrt{3}}{3} [/tex]
It lies in Quadrant III cot is positive
Cot θ=[tex] \frac{\sqrt{3}}{3} [/tex]
b. (sqrt 3)/3
PLEASEEEEEEEEE HELPPPPPP FASTT!!
How do I simplify 8 - 4(x - 7x) + 3
Answer:
11 + 24x
Step-by-step explanation:
8 - 4(x - 7x) + 3
8 - 4x + 28x + 3
11 - 4x + 28x
11 + 24x
Answer:
8-4x+28x+3 = 24x+11
Step-by-step explanation:
brainliest?
Twelve times of a number decreased by lo is equal to 14. write this in a mathematical sentence and find the number
Answer:
12n-10=14, n=2
Step-by-step explanation:
( Twelve times of a number decreased by 10 is equal to 14 ) This sentence can be written mathematically to be: 12n-10=14
The answer: Add 10 to both sides: 12n-10=14 > 12n-10+10=14+10 > 12n=24
Divide both sides by 12: 12n=24 > [tex]\frac{12n}{12} =\frac{24}{12}[/tex] > n=2
The area of a rectangle is 93.6 square inches. If the length of one of its sides is 5.2 in. what is its perimeter?
the area of a rectangle is the product of its length and width.
Help please! I think I wrote the rectangle right but I do not get the questions!
Step-by-step explanation:
perimeter = 2×(7+5) = 2×12= 24 units
area = 7×5 = 35 sq. units
Students set a goal of collecting 900 cans for the canned food drive. The number of cans they have collected so far is 82% of their goal. How many more cans do the students need to collect to reach their goal?
Answer:
162 cans
Step-by-step explanation:
100 - 82 = 18
18% of 900 =
0.18 * 900 =
162
You want to invest $300 in stock QRS. How many more shares of QRS will
you own at the end of the year if you use the DCA strategy instead of
investing all of your money at the start of the year?
Answer:
3 shares
Step-by-step explanation
HELP PLZ MATH IM FAILING
Answer:
Hello! In this picture I marked the new dot for that point and reflected it across the x axis!
The original coordinates are: 5, -3
and the new coordinates are: 5, 3
Hope that helps!
Find the area of the triangle in the picture.
Answer:
A =16.25 cm^2
Step-by-step explanation:
The area of a triangle is given by 1/2 bh where b is the base and h is the height
A = 1/2 (5) * 6.5
A =16.25 cm^2
What is the y-intercept of y= 2/3x+2
1.(2,3)
2.(3,2)
3.(0,2)
4.(-3,0)
Mr. Harris ran 2 miles in 14.5 minutes. Ms. Mullen ran 2.5 miles in 16 minutes. Ms. Hubbard ran 3.5 miles in 24 minutes.
A. Ms. Mullen was the fastest.
B. Ms. Hubbard was the fastest.
C. Mr. Harris was the fastest.
Answer:
A. Ms harris was the fastest considering she finished 2.5 miles under 14.5 minutes
Step-by-step explanation:
The baseball field is 9/10 of a mile from Benson’s house. Benson runs 3/10 of a mile and walks 4/10 of a mile on his way to the field. How much farther does Benson need to go to get to the baseball field?
Answer:
2/10 I believe
Step-by-step explanation:
3/10 + 4/10= 7/10
9/10 - 7/10 = 2/10
For each of the following variables, identify the type of variable (categorical vs. numerical).
(I) Fuel economy (miles per gallon) of used car
(II) Number of auto insurance claims in a month
1) (I) Categorical , and (II) Categorical
2) (I) Categorical , and (II) Numeric
3) (I) Numeric , and (II) Numeric
4) There is no correct match.
5) (I) Numeric , and (II) Categorical
Answer:
3) (I) Numeric , and (II) Numeric
Step-by-step explanation:
Numeric variable:
The variable assume number values.
Categorical values:
The variable assumes labels. Examples are yes/no, good/bad.
(I) Fuel economy (miles per gallon) of used car
(II) Number of auto insurance claims in a month
Both of these variables are numbers, none have labels, so they are both numeric. The correct answer is given by option 3).
which best describe one-way to show 1/3 shaded?
Answer:
A
Step-by-step explanation:
Draw a circle and cut it into 3 equal parts. shade 1 part
hope this helps please mark as brainliest
Draw a circle and cut it into 3 equal parts best describe to show 1/3 shaded, option A is correct
Since 1/3 represents one out of three equal parts, drawing a circle and dividing it into 3 equal parts allows you to shade one of those parts to accurately represent 1/3.
This method ensures that each part represents an equal fraction of the whole, which is necessary to accurately show 1/3 shaded.
Hence, one-way to show 1/3 shaded is draw a circle and cut it into 3 equal parts. shade 1 part.
To learn more on Fractions click:
https://brainly.com/question/10354322
The complete question is:
which best describe one-way to show 1/3 shaded?
(A) Draw a circle and cut it into 3 equal parts. shade 1 part
(B) Draw a circle and cut it into 3 unequal parts. shade 1 part
1. Match the polygons with their appropriate clouds. A polygon can match to more than 1 cloud
PLEASE HELP THIS IS VERY IMPORTANT I'LL GIVE YOU BRAIN THING IF ITS CORRECT!! <3 NO LINKS PLEASEE.
Answer:
Options A, C, E
hope it helps
please mark brainliest
Weather balloons are filled with hydrogen and released at various sites to measure and transmit data about conditions such as air pressure and temperature. A weather balloon is filled with hydrogen at the rate of 0.5 ft^3/s. Initially, the balloon has 4 ft^3 of hydrogen. Initially, the balloon has 2 ft^3 of hydrogen.
Required:
a. Find a linear function V that models the volume of hydrogen in the balloon at any time t.
b. If the balloon has a capacity of 15 ft^3, how long does it take to completely fill the balloon?
Answer:
a) The linear function that models the volume of hydrogen in the balloon at any time [tex]t[/tex] is [tex]V(t) = 2 + 0.5\cdot t[/tex].
b) 26 seconds are needed to completely fill the balloon.
Step-by-step explanation:
The statement has a mistake, the correct form is described below:
Weather balloons are filled with hydrogen and released at various sites to measure and transmit data about conditions such as air pressure and temperature. A weather balloon is filled with hydrogen at the rate of [tex]0.5\,\frac{ft^{3}}{s}[/tex]. Initially, the balloon has [tex]2\,ft^{3}[/tex] of hydrogen.
a) The volume of weather balloons is increasing linearly in time ([tex]t[/tex]), in seconds, since the rate of change of volume ([tex]\dot V[/tex]), in cubic feet per second, is stable. The linear function of the volume of the weather balloon in terms of time is:
[tex]V(t) = V_{o} + \dot V\cdot t[/tex] (1)
Where:
[tex]V(t)[/tex] - Current volume, in cubic feet.
[tex]V_{o}[/tex] - Initial volume, in cubic feet.
If we know that [tex]V_{o} = 2\,ft^{3}[/tex] and [tex]\dot V = 0.5\,\frac{ft^{3}}{s}[/tex], then the volume as a function of time is:
[tex]V(t) = 2 + 0.5\cdot t[/tex]
b) If we know that [tex]V(t) = 2 + 0.5\cdot t[/tex] and [tex]V(t) = 15\,ft^{3}[/tex], then the time taken to fill the balloon is:
[tex]V(t) = 2 + 0.5\cdot t[/tex]
[tex]V(t) - 2 = 0.5\cdot t[/tex]
[tex]t = \frac{V(t) - 2}{0.5}[/tex]
[tex]t = \frac{15-2}{0.5}[/tex]
[tex]t = 26\,s[/tex]
26 seconds are needed to completely fill the balloon.