Answer:
29.7°
Step-by-step explanation:
In a right triangle representing the geometry of the problem, the side opposite the angle is the height of your observation (400 ft). The side adjacent to the angle is the distance from shore (700 ft).
You know the tangent ratio is ...
Tan = Opposite/Adjacent
so your angle of depression satisfies ...
tan(angle of depression) = (400 ft)/(700 ft)
Using the inverse function, we find ...
angle of depression = arctan(4/7) ≈ 29.745°
The angle of depression is about 29.7°.
Write the number 6 x 10-5 in standard form.
Answer:
Step-by-step explanation:
[tex]6*10^{-5}= \frac{6}{100000}\\\\=0.00006[/tex]
A baseball stadium holds 15,002 seats. The lower level has 50 fewer than three times as many seats as the upper
level. The middle level has 40 more than twice as many seats as the upper level.
x+ (2x + 40) + (3x - 50) = 15,002
Answer:
Upper level = 2502 seats
Middle level = 5044 seats
Lower level = 7456 seats
Step-by-step explanation: given that
A baseball stadium holds 15,002 seats.
Let the Upper, middle and lower levels be represented as U, M and L respectively. And x = number of seat at the upper level
The lower level has 50 fewer than three times as many seats as the upper. That is
L = 3x - 50 .... (1)
The middle level has 40 more than twice as many seats as the upper level. That is
M = 2x + 40
Where L = x
x+ (2x + 40) + (3x - 50) = 15,002
You solved for x and found out the upper level has 2,502 seats . How many seats are in the lower level and how many seats are in the middle ?
That is x = 2502
Substitute x into equation 1
L = 3(2502) - 50
L = 7456 seats
Substitutes x into equation 2
M = 2(2502) + 40
M = 5044 seats
Estimate the square root to the nearest (a) integer and (b) tenth. Square root of 685
Final answer:
The square root of 685 lies between 26 and 27. To the nearest integer, the estimate is 26, and to the nearest tenth, the estimate is 26.2, given that it is roughly 9/53 of the way from 26 to 27.
Explanation:
To estimate the square root of 685 to the nearest integer and tenth, we have to determine which two perfect squares it lies between. The perfect square closer to 685 without going over is 676 (√676 is 26), and the next perfect square is 729 (√729 is 27). Thus, the square root of 685 lies between 26 and 27.
To estimate to the nearest integer, we would round √685 to 26, as it's closer to 676. For the nearest tenth, we need to see how much 685 exceeds 676. It exceeds by 9, and since 729-676 is 53, 685 is roughly 9/53 of the way from 26 to 27. So, a quick estimation for √685 to the nearest tenth could be 26 + (9/53)*1 which is approximately 26.2. Therefore, the estimated value of the surd √685 to the nearest tenth would be 26.2.
A zoo keeper published the following stem-and-leaf plot showing the number of lizard at each major zoo in the country. How many zoos have exactly 42 lizards
This question is incomplete because it lacks the diagram showing the leaf and stem plots
Find attached to this answer the diagram showing the Stem and leaf plots
Answer:
Only one Zoo has exactly 42 lizards
Step-by-step explanation:
If you check out the attached diagram , you will observe that there is a separation using a vertical line
In the diagram also we have been provided with a key which was explained as :
2|0 = 20 lizards
On the left hand side, we have number ranging from 0 - 6 arranged in a vertical form. On the right hand side we almost have numbers that are arranged in front of each number horizontally
Let me further explain the attached diagram
It is important to note that the numbers arranged vertically on the left are in the units of tens. Hence, using the given key :2l0
0|
1|
2| 0 6 8 8 8
This means , we have 20 lizards in one zoo, 26 lizards in one zoo, 28 lizards in 3 zoos
3| 0 2 6 6 7 8
30 lizards in one zoo, 32 lizards in one zoo, 36 lizards in 2 zoos , 37 lizards in one zoo and 38 lizards in one zoo
4| 1 2 6 6
We have 41 lizards in one zoo, 42 lizards in one zoo, and 46 lizards in two zoos
5l
6|
Based on the explanation given above, we can see that only one Zoo has exactly 42 lizards
Answer:20
Step-by-step explanation:
KHAN
Periodically a bottling company gets complaints that their bottles are not holding enough liquid. To test this claim the bottling company randomly samples 70 bottles and finds the average amount of liquid held by the bottles is 9.896 ounces with a standard deviation of .46 ounce. Suppose the p-value of this test is .054. State the proper conclusion.
Answer:
The null hypothesis was not rejected at 1% and 5% level of significance, but was rejected at 10% level of significance.
Step-by-step explanation:
The complaints made by the customers of a bottling company is that their bottles are not holding enough liquid.
The company wants to test the claim.
Let the mean amount of liquid that the bottles are said to hold be, μ₀.
The hypothesis for this test can be defined as follows:
H₀: The mean amount of liquid that the bottles can hold is μ₀, i.e. μ = μ₀.
Hₐ: The mean amount of liquid that the bottles can hold is less than μ₀, i.e. μ < μ₀.
The p-value of the test is, p = 0.054.
Decision rule:
The null hypothesis will be rejected if the p-value of the test is less than the significance level. And vice-versa.
Assume that the significance level of the test is, α = 0.01.The p-value = 0.054 > α = 0.01.
The null hypothesis was failed to be rejected at 1% level of
significance. Concluding that the mean amount of liquid that the
bottles can hold is μ₀.
Assume that the significance level of the test is, α = 0.05.The p-value = 0.054 > α = 0.05.
The null hypothesis was failed to be rejected at 5% level of
significance. Concluding that the mean amount of liquid that the
bottles can hold is μ₀.
Assume that the significance level of the test is, α = 0.10.The p-value = 0.054 < α = 0.10.
The null hypothesis will be rejected at 10% level of
significance. Concluding that the mean amount of liquid that the
bottles can hold is less than μ₀.
3. Bradley cut a square hole out of a block of wood in wood shop. If the block was cube-shaped
with side lengths of 10 inches, and the hole had side lengths of 4 inches, how much wood was
left after the hole was cut out?
Answer:
it would be 40 inche and there be not that much for the hole to left
Answer:
840 cubic squares
Step-by-step explanation:
Emily bought 66 yards of fabric to make curtains How many inches of fabric did Emily buy?
Answer:
2,376
Step-by-step explanation:
Answer:
Step-by-step explanation:
Convert the yards into inches and add a label at the end. You could also find out how many inches are in one yard and times the amount of inches you got from that one yard by 66.
What’s the volume of this triangular prism ?
Answer: 157.5
Step-by-step explanation: To get the volume of an object you must multiply the width x height ÷ it by 2 x length
Therefore 7 x 5 = 35 ÷ 2 = 17.5
17.5 x 9 = 157.5
Answer:
157.5
Step-by-step explanation:
The first step is to find the area of the triangular base. The formula for the area of a triangle is bh/2, or in this case 5×7/2=17.5. Multiplying this by the length of the prism, you get 9×17.5=157.5. Hope this helps!
What is the median of the data set 87,98,106,82,111,120
Answer:
Median = 102
Step-by-step explanation:
To find the median we will following the steps below;
study the numbers, if they are not arrange from ascending to descending order, you try to do that.
87,98,106,82,111,120
82, 87, 98,106, 111, 120
Pick the middle number, if there is just one number that falls in the middle, that number is your median, but if there two numbers that falls in the middle, you add the two numbers and then divide by 2.
In this case, two numbers falls in the middle, so we will add and divide by 2
That is;
Median = 98 + 106 /2
=204 /2
=102
Median = 102
Two cars leave towns 450 kilometers apart at the same time and travel toward each other. One car's rate is 12 kilometers per hour less than the other's. If they meet in 3 hours, what is the rate of the slower car?
Answer:
The rate of the slower car is 69km/hr
Step-by-step explanation:
Please kindly check the attached files for explanation.
95 students at a college were asked whether they had completed their required English 101 course, and 72 students said "yes". Find the best point estimate for the proportion of students at the college who have completed their required English 101 course. Round to four decimal places.
0.7579 is the best point for the proportion of students at the college who have completed their required English 101 course.
Step-by-step explanation:
"The proportion is written in the fraction form as required number in the numerator and the total number in the denominator."
Here, the 95 students at a college were asked whether they had completed their required English 101 course.
So, the total students = 95
It is given that, 72 students said "yes".
So, the number of completed students = 72
To estimate the best point for the proportion of students who completed their English 101 course :
Now, the numerator is the no.of students who have completed their required English 101 course.
Proportion = 72 / 95
⇒ the best point is calculated as 72 divided by 95
⇒ 0.7579 (round to four decimal places).
I believe the answer is A can someone confirm please and thank you, I cant get this answer wrong.
Answer:
A is correct.
Step-by-step explanation:
18. A coin is flipped eight times where each flip comes up either heads or tails. Howmany possible outcomesa) are there in total?b) contains exactly three heads?c) contains at least three heads?d) contains the same number of heads and tail
Answer:
16
Step-by-step explanation:
a coin is 2 sided thus has 2 out comes so doing it 8 times = 16 outcomes
HELP!!!!for the given situation identify the independent and dependent variables and then find a reasonable domain and range of values. Listed below will be four statements that relate to the given situation. She’s the statement that would have to be false given the situation and it’s parameters.
Jimmy earns eight dollars an hour at his job. He can work up to 40 hours per week
here are the statements
1)The range will be from zero to $400
2) there a dependent variable will be the amount of money he earns
3) The independent variable will be the number of hours he works
4) The domain will be from 0 to 40 hours
Answer:
1
Step-by-step explanation:
he cant earn 400 dollars because 8*40 is 320. if he cant work more than eight hours, theres no possible way he can earn 400 dollars ('least in a math equation).
A grocery store has a small bag of apples for $5 and a large bag for $8. If you bought 6 bags and spent $45, how many of each size of bags did you buy?
Answer:
1 small bags and 5 large bags
Step-by-step explanation:
In this case we can solve it using a 2x2 system of equations, like this:
let x: number of small bag
let y: number of large bag
So:
5 * x + 8 * y = 45
x + y = 6 => x = 6 - y
Replacing, we are left with that:
5 * ( 6 - y) + 8 * y = 45
30 - 5 * y + 8 * y = 45
- 5 * y + 8 * y = 45 - 30
3 * y = 15
y = 15/3
y = 5
Now to calculate x:
x = 6 - 5
x = 1
this means that 1 small bag and 5 large bags
Answer:
he bought 1 bag of small apple and 5 bags of Large apple
Step-by-step explanation: given that A small bag of apples = $5 and
A large bag = $8.
If you bought 6 bags and spent $45,
Let number of small apple be S
And large Apple be L
L + S = 6 ....... (1) ×8
8L + 5S = 45 .......(2)
Solve equation 1 and 2 simultaneously
8L + 8S = 48
8L + 5S = 45
Eliminate L
3S = 3
S = 1
Substitute S in equation 1
L = 6 - 1 = 5
Therefore, he bought 1 bag of small apple and 5 bags of Large apple
Ariel and her family are going to order one large circular pizza that has a diameter of 20 inches and one small circular pizza that has a diameter of 12 inches. Which measurement is closest to the difference between the area of the large pizza and the area of the small pizza in square inches? *
5 points
804 in. squared
427 in. squared
314 in. squared
201 in. squared
To calculate the difference in area between two circular pizzas, first compute the area of each using the formula A = πr². After finding the areas, subtract the smaller area from the larger one to find the difference. The result is approximately 201 square inches.
Explanation:The question involves calculating the area of two circles and finding the difference between the two. First, we need to find the radius of each pizza. Since the diameter is twice the radius, the large pizza has a radius of 10 inches (20 inches divided by 2), and the small pizza has a radius of 6 inches (12 inches divided by 2). The area of a circle is calculated using the formula A = πr², where π is approximately 3.14159, and r is the radius.
The area of the large pizza is A = π(10 inches)² = π * 100 inches² = 314.16 inches² (rounded to two decimal places). The area of the small pizza is A = π(6 inches)² = π * 36 inches² = 113.10 inches² (rounded to two decimal places). To find the difference, we subtract the area of the small pizza from the area of the large pizza, which gives us 314.16 inches² - 113.10 inches² = 201.06 inches², which is closest to 201 inches².
1 2 3 4 5 6 7 8 9 10 David has $90 to spend on sneakers. The sales tax in his state is 6%. Vincent has $95 to spend on sneakers. The sales tax in his state is 9%. Both boys are interested in a pair of sneakers that costs $86. Who will be able to buy the sneakers?
Vincent will be able to buy the sneakers.
1. David: $90
- David's total cost: $91.16
- David cannot afford the sneakers.
2. Vincent: $95
- Vincent's total cost: $93.74
- Vincent can afford the sneakers.
To determine who will be able to buy the sneakers, let's calculate the total cost including sales tax for each boy:
1. David:
- Sneaker cost: $86
- Sales tax rate: 6%
- Total cost [tex]\(= 86 + 0.06 \times 86\)[/tex]
- Total cost [tex]\(= 86 + 5.16\)[/tex]
- Total cost [tex]\(= 91.16\)[/tex]
2. Vincent:
- Sneaker cost: $86
- Sales tax rate: 9%
- Total cost [tex]\(= 86 + 0.09 \times 86\)[/tex]
- Total cost [tex]\(= 86 + 7.74\)[/tex]
- Total cost [tex]\(= 93.74\)[/tex]
Let X be an exponential random variable with parameter Λ, which is itself a random variable with distribution Exponential(β). Find a formula for the conditional density of Λ given X = x, and identify its type (i.e. its name and parameter(s)).
Answer:
Step-by-step explanation: solution solved below
Final answer:
To find the conditional density of Λ given X = x, calculate the joint density function of X and Λ and apply the formula for conditional density.
Explanation:
The conditional density of Λ given X = x when Λ is a random variable with distribution Exponential(β) can be found as follows:
Calculate the joint density function of X and Λ.
Use the formula for conditional density: f(Λ|X=x) = f(X,Λ) / f(X=x).
Identify the type of the conditional density based on the distribution it follows.
A yearbook company was investigating whether there is a significant difference between two states in the percents of high school students who order yearbooks. From a random sample of 150 students selected from one state, 70 had ordered a yearbook. From a random sample of 100 students selected from the other state, 65 had ordered a yearbook. Which of the following is the most appropriate method for analyzing the results?
A. A one-sample zz-test for a sample proportion
B. A one-sample zz-test for a population proportion
C. A two-sample zz-test for a difference in sample proportions
D. A two-sample zz-test for a difference in population proportions
E. A two-sample zz-test for a population proportion
Answer:
Null hypothesis: [tex] p_1 = p_2[/tex]
Alternative hypothesis: [tex] p_1 \neq p_2 [/tex]
So we need to conduct a:
D. A two-sample z-test for a difference in population proportions
Because the idea is to check if the population proportions in the states are similar or not.
Step-by-step explanation:
For this case they are trying two proof if there is a significant difference between two states in the percents of high school students who order yearbooks, and we chan check this with the difference of proportions.
Lets say that [tex]p_1,p_2[/tex] are the two proportions of interest and we want to check the following hypothesis:
We have the following info given:
[tex]\hat p_1 = \frac{70}{150}= 0.47[/tex] proportion of students that had ordered a yearbook from one state
[tex]\hat p_2= \frac{65}{100}= 0.65[/tex] proportion of students that had ordered a yearbook from another state
[tex]n_1 = 150[/tex] sample size from one state
[tex]n_2=100[/tex] sample size from another state
Null hypothesis: [tex] p_1 = p_2[/tex]
Alternative hypothesis: [tex] p_1 \neq p_2 [/tex]
So we need to conduct a:
D. A two-sample z-test for a difference in population proportions
Because the idea is to check if the population proportions in the states are similar or not.
Name three uses for mercury
Answer:
Sample Response:
Mercury is used for making thermometers, barometers, diffusion pumps, and other laboratory instruments. It can also be used to make mercury-vapor lamps, advertising signs, and mercury switches as well as pesticides, dental preparations, batteries, and catalysts.
Mercury is used for making thermometers, barometers and mercury switches
Mercury is used for making thermometers, barometers, diffusion pumps, and other laboratory instruments.
It can also be used to make mercury-vapor lamps, advertising signs, and mercury switches as well as pesticides, dental preparations, batteries, and catalysts.
Therefore, the three uses of mercury are making thermometers, barometers and mercury switches
Learn more about Mercury here;
https://brainly.com/question/31856953
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Which mark on the tape measure is closest to 2.23607 inches?
Answer:
5.7 cm or 2 1/4 in
Step-by-step explanation:
Your tape measure is not shown.
On my tape measure, 5.7 cm is the closest mark. On the inch scale, 2 1/4 inches is the next-closest mark.
_____
On a tape measure graduated in 1/32 inch between 2 and 3 inches, you can find the closest mark by rounding to the nearest 32nd:
2.23607 × 32 ≈ 71.55 ≈ 72 --- 32nds of an inch
72/32 = 2 1/4 . . . . the closest mark on an inch ruler graduated in 32nds
__
For a ruler graduated in millimeters, you can find the closest millimeter in the same way. There are 25.4 mm to the inch.
2.23607 in × 25.4 mm/in ≈ 56.80 mm ≈ 57 mm
57 mm = 5.7 cm . . . closest mark on metric scale
__
When we check the error, we find the metric mark is closer than the inch mark.
5.7 cm ≈ 2.24409 in . . . . error of 0.00802 in
2 1/2 in = 2.25000 in . . . error of 0.01393 in
Final answer:
The mark on the tape measure closest to 2.23607 inches is just above 2 3/16 inches, which can be more precisely measured with a tape measure that features millimeter or half-millimeter markings.
Explanation:
The student has asked which mark on the tape measure is closest to 2.23607 inches. To answer this question, we must consider the precision of the measuring device. When using a ruler without millimeter markings, such as the bottom ruler mentioned, the measurement can be understood in tenths of a centimeter. This would make it difficult to conclusively measure and report on the hundredths digit for a length.
Conversely, using a tape measure with millimeter or even half-millimeter markings (akin to the top ruler), the user can measure more precisely. Given that 1 inch equals 2.54 centimeters, 2.23607 inches would be approximately 5.679818 centimeters. This would be between the 2.5 cm and 2.6 cm marks on a metric tape measure or between 2 3/16 inches and 2 1/4 inches on an imperial tape measure; 2.23607 inches is very close to, but slightly above, 2 3/16 inches, so this would be the mark on an imperial tape measure that is closest to 2.23607 inches.
Jamal has a pair of shoes that have a total mass of 960 grams and four identical books that have a total mass of 2 kilograms. Which has the greater mass : one shoe or one book use the drop down Menus to explain
One shoe has a mass of 950 divided _____ = _____ grams . One book has a mass of _____ divided 4 = _____ grams . So one _____ has a greater mass
Answer: One book has a greater mass.
Step-by-step explanation:
Jamal has a pair of shoes with a total mass of 960 grams. This means that each shoe has a mass of:
960 grams ÷ 2= 480 grams per shoe.
Jamal also has four identical books with a total mass of 2 kilograms. Note that 1000 grams make a kilograms. Therefore 2 kilograms will be (2 × 1000 grams) = 2000 grams.
Each book will have a mass of:
2000 ÷ 4 = 500 grams per book.
One shoe has a mass of 960 divided 2 = 480 grams . One book has a mass of 2000 divided 4 = 500 grams . So one book has a greater mass.
Fill in the blank...
Answer:
Positive
Step-by-step explanation:
If a is positive, the parabola opens up or to the right. If it's negative it does the opposite.
Which equation is the correct translation of the following statement?
Four less than a number is nine.
4 - x = 9
9 - 4 = x
9 - x = 4
x - 4 = 9
Answer: x - 4 = 9 (x will equal 13)
What I did was since 4 is less than 13 we could use 13-4 since 4 is less than 13.
13-4 will get u 9 so that x will equal 13
13-4=9
Answer:
Answer: x - 4 = 9
Step-by-step explanation:
Which graph represents this system? y = 2 x + 1. y = negative 4 x + 7. On a coordinate plane, a line goes through (0, 7) and (1, 3) and another goes through (1, 3) and (2, 5). On a coordinate plane, a line goes through (negative 4, 0) and (0, 7) and another line goes through (negative 4, 3) and (0, 1). On a coordinate plane, a line goes through (0, negative 4) and (1, 3) and another goes through (0, 2) and (1, 3). On a coordinate plane, a line goes through (0, 7) and (8, 5) and another line goes through (0, 1) and (8, 5).
Answer:
It is the first choice. (A)
Step-by-step explanation:
Red line: y = 2x + 1
Blue line: y = -4x + 7
The city limits of Las Pythagoras form a perfect shape of an isosceles right triangle whose legs are both 25 kilometers long. The population in Las Pythagoras is 100,000,000 people. What is the population density of Las Pythagoras?
Answer:
320,000 people / km²
Step-by-step explanation:
We need to find the area of the city first.
The area of a triangle is: [tex]A=\frac{1}{2} bh[/tex], where b is the base and h is the height.
Here, both b and h are the legs of the right triangle and they're equal to 25 km. So:
[tex]A=\frac{1}{2} bh[/tex]
[tex]A=\frac{1}{2} *25*25=312.5[/tex] km²
Population density is simply (population) ÷ (area). Here, the population is 100,000,000 people and the area is 312.5 km², so:
100,000,000 ÷ 312.5 = 320,000 people / km²
Answer:
320,000 people per km²
Step-by-step explanation:
Since two angles are equal, their opposite lengths are also equal
Assuming it's a right ankle triangle,
Area = ½ × 25 × 25 = 312.5 km²
Population density:
100,000,000/312.5
320,000
Shane is measuring a shelf. It is 24 inches long. He measures again to find the number of feet. Will the length of the shelf be less than, greater than, or the same length in feet?
Answer:
Same length
24 ÷ 2=12
There is 12 inches in a foot
1 + 1= 2 ft
24 inches = 2 feet
Answer:
The length of the shelf will be less than 24 in feet. It will be 2 feet long.
Step-by-step explanation:
Inches are a smaller unit than feet, meaning that when something is measured in inches, the numerical amount of inches will be higher than the numerical amount of feet. The ratio is 12 inches to 1 foot, meaning that even though the length may be the exact same, inches represents the length with a higher numerical value and feet represent the length with a lower numerical value.
How many solutions does this system have?
2x-4y=8
x+y=7
The system has ______
solution(s)
Answer:
The solution for the system is the pair (6,1).
Step-by-step explanation:
The system has two equations and two variables, therefore i has only one solution. To solve it we will multiply the second equation by "-2". So we have:
2x-4y = 8
x + y = 7 *(-2)
2x - 4y = 8
-2x -2y = -14
We now sum boh equations:
2x -2x -4y -2y = 8 -14
-6y = -6
y = -6/-6 = 1
2x - 4(1) = 8
2x - 4 = 8
2x = 8 + 4
2x = 12
x = 12/2 = 6
The solution is the pair (6,1).
Answer:
The system has 2 solution .
Step-by-step explanation:
The equation is a simultaneous equation
2x - 4y=8 ............(i)
x + y=7................(ii)
make x the subject of the formula in equation (ii)
x = 7 - y
Substitute the value of x in equation(i)
2(7 - y) - 4y = 8
14 - 2y - 4y = 8
14 - 6y = 8
-6y = 8 - 14
-6y = -6
divide both sides by -6
y = 1
insert the value of in equation (ii)
x + y = 7
x + 1 = 7
x = 7 - 1
x = 6
The system has 2 solution .
A potter forms a piece of clay into a cylinder. As he rolls it, the length, L, of the cylinder increases and the radius, r, decreases. If the length of the cylinder is increasing by 0.7 cm per second, find the rate at which the radius is changing when the radius is 2 cm and the length is 9 cm.
Answer:
The radius is decreatsing at a rate 0.78 cm per second.
Step-by-step explanation:
We are given the following in the question:
[tex]\dfrac{dl}{dt} = 0.7\text{ cm per second}[/tex]
Instant radius,r = 2 cm
Instant length,l = 9cm
The radius of the cylinder decreases.
Volume of cylinder =
[tex]V =\pi r^2l[/tex]
Since the volume of the cylinder does not changes, we can write:
[tex]\dfrac{dV}{dt}=0[/tex]
Rate of change of volume:
[tex]\dfrac{dV}{dt} = \pi(2r\dfrac{dr}{dt}l + r^2\dfrac{dl}{dt})[/tex]
Puttiung values, we get
[tex]0 = \pi(2(2)\dfrac{dr}{dt}(9) + (2)^2(0.7))\\\\\dfrac{dr}{dt}=-\dfrac{4\times 0.7}{4\times 9} \approx -0.78[/tex]
Thus, the radius is decreatsing at a rate 0.78 cm per second.
Using differentiation, it is found that the radius is increasing at a rate of 0.35 cm/second.
The length of a cylinder is the diameter, which is double the radius, hence:
[tex]l = 2r \rightarrow r = \frac{l}{2}[/tex]
Applying differentiation, the rate of change of the radius is given by:
[tex]\frac{dr}{dt} = \frac{1}{2}\frac{dl}{dt}[/tex]
We are given that the rate of change of the length is [tex]\frac{dl}{dt} = 0.7[/tex], hence:
[tex]\frac{dr}{dt} = \frac{1}{2}\frac{dl}{dt} = \frac{1}{2}(0.7) = 0.35[/tex]
The radius is increasing at a rate of 0.35 cm/second.
A similar problem is given at https://brainly.com/question/9543179
Ramon earns $1,600 each month and pays $53.60 on electricity. To the nearest tenth of a percent, what percent of Ramon's earnings are spent on electricity each month?
Answer:
3.4%
Step-by-step explanation:
Ramons monthly salary is $1600
The electricity is $53.60
So, to find the percentage of his earnings spent on electrcity, we´re going to divide:
[tex]\frac{53.60}{1600} = 0.0335[/tex]
multiply that by 100 to get the percent
0.0335 x 100 = 3.35%
rounded to the nearest tenth would be 3.4%
i hope this helps!