Answer:
it would 4 1/4 inches long because you multiply the length of a side by 1.414
A killer whale has eaten 75 pounds of fish today. It needs to eat at least 140 pounds of fish each day. A bucket holds 15 pounds of fish. Write and solve an inequality that represents how many more buckets of fish the whale needs to eat.
Answer: the whale needs to eat at least, 5 buckets of fish
Step-by-step explanation:
Let x represent the number of additional buckets of fish that the whale needs to eat.
A bucket holds 15 pounds of fish. This means that x buckets will hold 15x pounds of fish
A killer whale has eaten 75 pounds of fish today. If It needs to eat at least 140 pounds of fish each day, then the inequality that represents how many more buckets of fish the whale needs to eat is
15x + 75 ≥ 140
15x ≥ 140 - 75
15x ≥ 65
x ≥ 65/15
x ≥ 4.33
The number of buckets can't be a decimal so,
x ≥ 5
Hong built a large wooden storage box. The box was in the shape of a rectangular prism, as shown below. He covered all the sides of the box with special wallpaper that cost a total of $504. How much did the wallpaper cost per square foot?
Answer:
504/(surface area of all walls)
Step-by-step explanation:
Assuming Length=l, breadth=b and height=h
Surface Area of all walls= 2×l×h+2×b×h
Cost per square ft of wall paper= 504/(surface area of all walls)
Amara needs to tile a square section of a bathroom wall that is v inches on each side, except for a square region that is 1.7 inches on each side where a pipe needs to go through. Which function represents the area, A, in square inches, that Amara needs to tile in terms of v?
Answer:
v²-1.89
Step-by-step explanation:
Area of wall= v²
Area of pipe= 1.7²
= 2.89
Area needs to be tiles= v²-1.89
One concern of a gambler is that she will go broke before achieving her first win. Suppose that she plays a game in which the probability of winning is .1 (and is unknown to her). It costs her $10 to play and she receives $80 for a win. If she commences with $30, what is the probability that she wins exactly once before she loses her initial capital?
Answer:
The probability that she wins exactly once before she loses her initial capital is 0.243.
Step-by-step explanation:
The gambler commences with $30, i.e. she played 3 games.
Let X = number of games won by the gambler.
The probability of winning a game is, p = 0.10.
The random variable X follows a Binomial distribution, with probability mass function:
Compute the probability of exactly one winning as follows:
Thus, the probability that she wins exactly once before she loses her initial capital is 0.243.
Malik’s recipe for 4 servings of a certain dish requires 1/{1}/{2} cups of pasta. According to this recipe, what is the number of cups of pasta that Malik will use the next time he prepares this dish?
Answer:
The answer to the question is
cups
Step-by-step explanation:
According to the recipe number of cups of recipe of past required = cups
A recipe is a predefined steps and directions required to make an item mostly especially something to eat.
Recipe in medicine or Latin means to "take" hence, a doctor usually writes on a prescription with a recipe, Latin for take and abbreviated as Rx or similar symbol.
In the original question, the number of cups of pasta that Malik will use the next time he prepares this dish is cups
A balloon is rising vertically above a level, straight road at a constant rate of 2 ft divided by sec. Just when the balloon is 84 ft above the ground, a bicycle moving at a constant rate of 12 ft divided by sec passes under it. How fast is the distance s (t )between the bicycle and balloon increasing 6 seconds later? A coordinate plane has a horizontal x-axis and a vertical y-axis. The angle between the axes is marked with a small square. The location of a balloon on the vertical axis is labeled y(t). An arrow pointing upward lies on the y-axis just below the point y(t). The location of a bicycle on the horizontal axis is labeled x(t). An arrow pointing to the right lies on the x-axis to the right of the point x(t). A segment falling from left to right begins at the balloon and ends at the bicycle and is labeled s(t).
Answer:
Step-by-step explanation:
At time t seconds after the bike passed, the distance z between the balloon and the bike is
z^2 = (84+2t)^2 + (12t)^2
So, at t=6,
z^2 = (84+2*6)^2 + (12*6)^2 = 14400
So, z = 120
2z dz/dt = 2(84+2t)*2 + 2(12t)*12
At time t=6,
240 dz/dt = 2(84+2*6)*2 + 2(12*6)*12 = 2112
dz/dt = 2112/240 = 44/5 ft/s
A coffee shop sells a ceramic refill mug for $8.95. Each refill cost $1.50. Last month rose spent $26.95 on a mug and refills. How many refills did she buy?
Answer:
12 refills
Step-by-step explanation:
$26.95-$8.98=$18 left after buying a refill mug
18/1.5=12 the refills she can buy
Neil has 3 partially full cans of white paint. They contain 1/3 of a gallon and 1/5 and 1/2 of a gallon of paint. About how much paint does Neil have left?
Answer:
1¹/₃₀
Step-by-step explanation:
The 3 gallons were partially full
They contain 1/3 of a gallon and 1/5 and 1/2 of a gallon of paint.
the first is 1/3 of the gallon
the second is 1/5 of galloon
the third is 1/2 of gallon adding them together
1/3 +1/5 +1/2 = (10+6+15)/30 = 31/30 = 1¹/₃₀
Of the 46 cities seven have a lake and 20 want to have a river running through them what fraction of these 46 cities have a lake or river running through them
Answer: The fraction of these 46 cities that have a lake or river running through them is 7/46.
Step-by-step explanation:
Hi, to solve this problem we have to analyze the information given:
The cities that have a lake or river running through them are 7 (the 20 that only want it don´t count).
So, we have to divide the number of cities that have a lake or river running through them (7) by the total number of cities (46).
Mathematically speaking:
7/46
The fraction of these 46 cities that have a lake or river running through them is 7/46.
A particle moves along the parabola y equals x squared in the first quadrant in such a way that its x-coordinate (measured in meters) increases at a steady 10 StartFraction m Over sec EndFraction . How fast is the angle of inclination theta of the line joining the particle to the origin changing when x equals 1 m question mark
Answer:
(dθ/dt) = 1 rad / s = 57.3° /s
Step-by-step explanation:
- A particle moves along curve with function:
y = x^2
- The rate of change of x-coordinate is given by dx/dt = 10 m/s
Find:
How fast is the angle of inclination theta of the line joining the particle to the origin changing when x equals 1 m
Solution:
- The gradient of the line from origin to particle at position ( x , y ) is given by:
tan ( θ ) = y / x
Where, θ is the angle between x-axis and line from origin
x & y are coordinate of the point on given graph.
- To develop a rate of change expression we will derivate the above expression by time t:
d / dt (tan ( θ )) = d/dt (y / x )
(dθ/dt) / cos^2(θ) = (dy/dt) / (dx/dt)
(dθ/dt) = cos^2(θ) * (dy/dt) / (dx/dt)
- The rate of change of angle (dθ/dt) is given by above expression.
- We will apply the following chain rule to evaluate (dy/dt):
(dy/dt) = (dy/dx) * (dx/dt)
(dy/dt) = 2x * (10)
(dy/dt) = 20*x
@ x = 1, (dy/dt) = 20 m/s
@ x = 1, y = (1)^2 = 1
tan (θ) = 1
θ = 45°
- Now use the derived rate of change of angle expression we get:
(dθ/dt) = cos^2(45) * 20 / 10
(dθ/dt) = 0.5 * 20 / 10
(dθ/dt) = 1 rad / s = 57.3° /s
A pediatrician wishes to study how the average weight Y (in kilograms) of children changes during the first year of life. He plots these averages versus the age X (in months) and decides to fit a least-squares regression line to the data with X as the explanatory variable and Y as the response variable. He computes the following quantities: r = correlation between X and Y= 0.84 x = mean of the values of X = 5.69 y = mean of the values of Y = 6.26 S_x = standard deviation of the values of X = 3.23 s_y = standard deviation of the values of Y = 2.04 The slope of the least-squares line is: A) 0.53.B) 0.64. C) 0.84. D) 2.04.
Answer:
Answer is option a ) 0.53
Step-by-step explanation:
slope =
Given that a pediatrician wishes to study how the average weight Y (in kilograms) of children changes during the first year of life. He plots these averages versus the age X (in months) and decides to fit a least-squares regression line to the data with X as the explanatory variable and Y as the response variable.
He finds the following quantities:
r = correlation between X and Y= 0.84
x = mean of the values of X = 5.69
y = mean of the values of Y = 6.26
S_x = standard deviation of the values of X = 3.23
s_y = standard deviation of the values of Y = 2.04
Using the formula for slope given above substitute to get
round off to 0.53
Answer is option a ) 0.53
Meghan also wants to walk to get some exercise, rather than going to the gym. She decides to walk along arc AB. How far will she walk? Round to 3 decimal places.
Answer:
π*AB
Step-by-step explanation:
I m not quite sure about your question because it is lack of details.
However, as my per understanding, Meghan decides to walk along arc AB it means she walks an interval equal to the circumference of the circle AB.
So, apply the formula in caculating the circumference of the circle, we have:
π*d = π*AB
So, she walk a π*AB distance.
Edward bikes the same route to and from school each day. After 28 school says, he bikes a total distance of 389.2 miles. How many miles does he bike each day
Answer:
13.9
Step-by-step explanation:
Bradley has 64 1-inch cubic blocks.He uses all the blocks to build a rectangular prism that is 2 inches high and 2 inches wide.How long is the rectangular prism?
Answer:
The rectangular prism is 16 inches long.
Step-by-step explanation:
Given:
Bradley has 64 1-inch cubic blocks.He uses all the blocks to build a rectangular prism that is 2 inches high and 2 inches wide.
Now, to find the length of rectangular prism.
Volume of rectangular prism = 64 cubic inches.
Height of rectangular prism = 2 inches.
Width of rectangular prism = 2 inches.
Now, to get the length we put formula:
Dividing both sides by 4 we get:
Therefore, the rectangular prism is 16 inches long.
How many different ways can the letters of "referred" be arranged? The number of different ways that the letters of"referred" can be arranged is__________.
Answer:
560 ways
Step-by-step explanation:
Given is a word
referred
We have to find the number of different ways that the letters of"referred" can be arranged
Let us analyse the given word
It contains totally 8 letters
r is repeated 3 times
e is repeated 3 times
f one time and d one time
Using the permutations rule for repeated objects we get
The number of different ways that the letters of"referred" can be arranged
=
560 ways
A random sample of 200 lightbulbs has a mean life of 600 hours and a standard deviation of 53 hours.(a) A histogram of the data indicates the sample data follow a bell-shaped distribution. According to theEmpirical Rule, 99.7% of lightbulbs have lifetimes between _____ and _____ hours.(b) Assuming the data are bell shaped, determine the percentage of lightbulbs that will have a life between494 and 706 hours.(c) Assuming the data are bell shaped, what percentage of lightbulbs will last between 547 and 706 hours?(d) If the company that manufactures the lightbulbs guarantees to replace any bulb that does not last at least 441 hours, what percentage of lightbulbs can the firm expect to have to replace, according to the Empirical Rule?
Given Information:
The average bulb life = μ = 600 hours
standard deviation = σ = 53 hours
Sample follows Bell-Shaped Distribution or Normal Distribution
Step-by-step explanation:
According to the Empirical Rule, 99.7% of the lightbulbs have lifetimes between μ - 3σ and μ + 3σ
600 - 3(53) and 600 + 3(53)
441 and 759 hours
(b) assuming the data are bell shaped, determine the percentage of lightbulbs that will have a life between 494 and 706 hours.
494 = 600 - 106 = 600 - 2(53) = μ - 2σ
706 = 600 + 106 = 600 + 2(53) = μ + 2σ
Therefore, according to the Empirical Rule, 95% of the lightbulbs have lifetimes between μ - 2σ and μ + 2σ
(c) Assuming the data are bell shaped, what percentage of lightbulbs will last between 547 and 706 hours?
547 = 600 - 53 = 600 - 1(53) = μ - σ
653 = 600 + 53 = 600 + 1(53) = μ + σ
Therefore, according to the Empirical Rule, 68% of the lightbulbs have lifetimes between μ - σ and μ + σ
(d) If the company that manufactures the lightbulbs guarantees to replace any bulb that does not last at least 441 hours, what percentage of lightbulbs can the firm expect to have to replace, according to the Empirical Rule?
441 = 600 - 159 = 600 - 3(53) = μ - 3σ
99.7% of the lightbulbs have lifetimes between μ - 3σ and μ + 3σ
100 - 99.7 = 0.3/2 = 0.15 %
According to the Empirical rule, 0.15% lightbulbs will last less than 441 hours.
Martha makes an investment of $500 in an account that pays 6% interest compounded monthly. Write an equation you could use to determine the interest she earns in t years
Answer:
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited.
t represents the number of years.
From the information given,
P = $500
r = 6% = 6/100 = 0.06
n = 12 because it was compounded 12 times in a year.
An equation that could be used to determine the interest she earns in t years is
A = 500(1+0.06/12)^12 × t
A = 500(1+0.005)^12t
A = 500(1.005)^12t
100 POINTS!!!! The Johnsons want to cover their backyard with new grass. Their backyard is rectangular, with a length of 3x – 5 feet and a width of 4x – 10 feet. However, their rectangular swimming pool, along with its surrounding patio, has dimensions of x + 8 by x – 2 feet. What is the area of the region of the yard that they want to cover with new grass?
The area of whole backyard:
a = 3x - 5
b = 4x - 10
a · b = (3x - 5) · (4x - 10) = 3x · 4x + 3x · (-10) - 5 · 4x - 5 · (-10) =
= 12x² - 30x - 20x + 50 = 12x² - 50x + 50
The area of swimming pool with patio:
a = x + 8
b = x - 2
a · b = (x + 8) · (x - 2) = x · x + x · (-2) + 8 · x + 8 · (-2) =
= x² - 2x + 8x - 16 = x² + 6x - 16
Then the area of the region they want ot cover with new grass is:
12x² - 50x + 50 - (x² + 6x - 16) = 12x² - 50x + 50 - x² - 6x + 16 =
= 11x² - 56x + 66
Answer:
11x² - 56x + 6 is your answer
Step-by-step explanation:
The price of gold is often reported per ounce at the end of 2005 this price was 513 at the end of 2015 it was 1060 by what percentage did the price per ounce of gold increase
Answer:
206.63 %
Step-by-step explanation:
Hello, I can help you with this.
you can easily solve this by using a rule of three
Step one
define the data to use
year:2005
price:513
this is our initial value, the 100 percent (100%)
513⇔100%
then, in 2015 the price was 1060
year:2015
price:1060
%=x( the unknown number)
Step two
do the relation
so, the percentage that the price per ounce of gold increase was 206.63%
I really hope it helps, Have a great day.
You $5,000 in a simple interest bearing account. If the annual interest rate is 3.5% , what will your account balance be in 10 years if you do not make any additional deposits
Answer:
Therefore my account balance will be in 10 year=$6,750
Step-by-step explanation:
Simple interest: Simple interest is calculated on the same principal each year.
I= simple interest.
r = rate of interest per annum.
t= time
Compound interest: The principal is not same each year. The principal will change from the second year.
The principal of 2nd year = Principal+ interest of 1st year.
The principal of 3rd year = Principal of 2nd year+ interest of 2nd year.
and so on
The Amount
Here P= $5,000
r=3.5%
and t=10 years
=$1750
Therefore my account balance will be in 10 year=$(5,000+1750)=$6,750.