Answer:
[tex]t \approx 17.690\,min[/tex]
Step-by-step explanation:
This differential equation is a first order linear differential equation with separable variables, whose solution is found as follows:
[tex]\frac{dy}{dt} = - \frac{1}{53} \cdot (y - 17)[/tex]
[tex]\frac{dy}{y-17} = -\frac{1}{53} \, dt[/tex]
[tex]\int\limits^{y}_{y_{o}} {\frac{dy}{y-17} } = -\frac{1}{53} \int\limits^{t}_{0}\, dx[/tex]
[tex]\ln \left |\frac{y-17}{y_{o}-17} \right | = -\frac{1}{53} \cdot t[/tex]
[tex]\frac{y-17}{y_{o}-17} = e^{-\frac{1}{53}\cdot t }[/tex]
[tex]y = 17 + (y_{o} - 17) \cdot e^{-\frac{1}{53}\cdot t }[/tex]
The solution of the differential equation is:
[tex]y = 17 + 74\cdot e^{-\frac{1}{53}\cdot t }[/tex]
Where:
[tex]y[/tex] - Temperature, measured in °C.
[tex]t[/tex] - Time, measured in minutes.
The time when the cup of coffee has the temperature of 70 °C is:
[tex]70 = 17 + 74 \cdot e^{-\frac{1}{53}\cdot t }[/tex]
[tex]53 = 74 \cdot e^{-\frac{1}{53}\cdot t }[/tex]
[tex]\frac{53}{74} = e^{-\frac{1}{53}\cdot t }[/tex]
[tex]\ln \frac{53}{74} = -\frac{1}{53}\cdot t[/tex]
[tex]t = - 53\cdot \ln \frac{53}{74}[/tex]
[tex]t \approx 17.690\,min[/tex]
Felicia walks 3 blocks west, 4 blocks south, 3 more blocks west, then
2 blocks south again. How far is Felicia from her starting point?
blocks
Answer:
What’s the correct answer for this question?
Answer:
B.
Step-by-step explanation:
A cone with a radius of 1-unit will be obtained by rotating the 3-D figure.
Please answer this correctly
Answer:
514 square meters
Step-by-step explanation:
Consider the length of p;
[tex]11 * p * 3 = 528,\\33 * p = 528,\\p = 528 / 33 = 16 meters[/tex]
11, 3, and p act as the length, width, and height of this rectangular prism. We can apply the volume formula length * width * height, and thus made 11 * p * 3 equivalent to the volume 528. Now let us determine the surface area;
[tex]Area of Side 1 = 16 * 11 = 176 square meters,\\Area of Side 2 = 3 * 16 = 48 square meters,\\Area of Side 3 = 11 * 3 = 33 square meters,\\\\Surface Area = 2 * ( 176 ) + 2 * ( 48 ) + 2 * ( 33 ) = 352 + 96 + 66 = 514 square meters[/tex]
Hope that helps!
Answer:
514 square meters
Step-by-step explanation:
Since the volume of a rectangular prism is the product of the width, length, and height, 11*3*p=528. Therefore, p=528/(11*3)=16. Now, you can find the surface area. The surface of a rectangular prism is made up of 3 pairs of rectangles. One pair has dimensions of 11 by 3, one pair has dimensions of 16 by 3, and the last pair has dimensions of 16 by 11. The surface area of this figure is therefore:
[tex]2(11\cdot 3)+2(16\cdot 3) + 2(16\cdot 11)=66+96+352=514 m^2[/tex]
Hope this helps!
A bread machine produces 159 loaves of bread per hour. The machine operates 10 hours per day. How many loaves of bread does it produce per day? _____ loaves
Answer:
It can produce 1590 loaves of bread per day.
Step-by-step explanation:
Given that the bread machine operates only 10 hours per day. So in order to calculate how many loaves can be produce a day, you have to multiply it by 10 :
[tex]1hour = 159loaves[/tex]
[tex]10hours = 159 \times 10[/tex]
[tex]10hours = 1590loaves[/tex]
2. A manufacturer produces light bulbs at a Poisson rate of 300 per hour. The probability that a light bulb is defective is 0.012. During production, the light bulbs are tested, one by one, and the defective ones are put in a special can that holds up to a maximum of 50 light bulbs. On average, how long does it take until the can is lled
Answer:
On average it will take 13 hrs 53 minutes before the van is filled
Step-by-step explanation:
The first thing we need to do here is to find find the number of defective light bulbs
Using the poisson process, that would be;
λ * p
where λ is the poisson rate of production which is 300 per hour
and p is the probability that the produced bulb is defective = 0.012
So the number of defective bulbs produced within the hour = 0.012 * 300 = 3.6 light bulbs per hour
Now, let X be the time until 50 light bulbs are produced. Then X is a random variable with the parameter (r, λ) = (50, 3.6)
What we need to find however is E(X)
Thus, the expected value of a gamma random variable X with the parameter (x, λ) is;
E(X) = r/λ = 50/3.6 = 13.89
Thus the amount of time it will take before the Can will be filled is 13 hrs 53 minutes
If the mean of 5 positive integers is 15, what is the maximum possible difference between the largest and the smallest of these 5 numbers?
Answer:
64
Step-by-step explanation:
If the mean is 15, the sum of 5 numbers is:
5*15 = 75Minimum value for the first four numbers would be:
1, 2, 3, 4Then the fifth number is:
75 - (1+2+3+4) = 75 - 10 = 65So the maximum difference is:
65 - 1 = 64Shape 1 and shape 2 are plotted on a coordinate plane. Which rigid transformation can you perform on shape 2 to show that shape 2 is congruent to shape 1?
Bernard bought 8gal of paint. Convert the volume to liters. Round to the nearest tenth
Answer:
In one gallon of paint there are about 3.8 liters so 8 gallons is about 30.3 liters.
The base diameter and the height of a cone are both equal to
x units.
Which expression represents the volume of the cone, in
cubic units?
pix2
2pix3
1/3pix2
1/12pix3
Answer:
[tex]\frac{\pi x^3}{3}[/tex]
Step-by-step explanation:
[tex]V=\pi r^2h\frac{1}{3}[/tex]
[tex]V=\pi x^2x\frac{1}{3}[/tex]
[tex]V=\pi x^3\frac{1}{3}[/tex]
[tex]V=\frac{\pi x^3}{3}[/tex]
[tex]V=1.047198x^3[/tex]
Answer:
Step-by-step explanation:
1/12 pi x ^3
While filing your income tax, you report annual contributions of $100 to a public radio station, $300 to PBS (television station), $150 to a woman’s shelter, and $450 to other charitable organizations.
Find your monthly expense.
Hey there! I'm happy to help!
Let's add up all of these contributions.
100+300+150+450=1000
However, this is annual. We want monthly. So, we simply divide by 12.
1000/12≈83.33
Therefore, the monthly expense is $83.33
I hope that this helps! Have a wonderful day!
Which ordered pair is the solution of the system of equations? 3x+2y=4, -2+2y=24
Answer:
x = -7.33 OR x = [tex]\frac{-22}{3}[/tex]
y = 13
Step-by-step explanation:
→You can use the substitution method. First, make y by itself in (-2 + 2y = 24):
-2 + 2y = 24
2y = 26
y = 13
→Then, plug in 13 for y into the other equation:
3x + 2y = 4
3x + 2(13) = 4
3x + 26 = 4
3x = -22
x = -7.33 OR x = [tex]\frac{-22}{3}[/tex]
A tree that is 10 feet tall is growing at a rate of 2 foot each year. A tree that is 14 feet tall is growing at a rate of 2/3 foot each year. What is the number of years it will take for both trees to be the same height, and what will their height be?
Answer:
after three years
Step-by-step explanation:
Answer pls need help
The pressure p(in lbs/in^2) that a 160 pound persons shoe exerts on the ground when walking varies inversely with the area A(in in^2) of the sole of the shoe when the shoes have a sole area of 40 in^2 The pressure is 4 lbs/in^2 find equation that relates these variables
A=
What is X:
3x−22=44
5/6 = 10/2x−3
Answer:
x = 22
x = 4,6
Step-by-step explanation:
3x - 22 = 44
3x = 44 + 22
3x = 66
x = 66/3
x = 22
5/6 = 10/2x - 3
5/6 + 3 = 10/2x
5/6 + 18/6 = 10/2x
23/6 = 10/2x
23/6 * 2 = 10x
46 = 10x
x = 46/10
x = 4,6
I NEED HELP PLEASE HELP ME
Answer:
3
Step-by-step explanation:
Solving the inequality
2x-1>=5
2x>=6
x>=3
The graph should have a shaded circle on 3 and a line pointing to values increasing.
Find the measure of angle x in the figure below: A triangle is shown. At the top vertex of the triangle is a horizontal line aligned to the base of the triangle. The angle formed between the horizontal line and the left edge of the triangle is shown as 56 degrees, the angle formed between the horizontal line and the right edge of the triangle is shown as 51 degrees. The angle at the top vertex of the triangle is labeled as y, and the interior angle on the right is labeled as 72 degrees. The interior angle on the left is labeled as x.
Answer:
[tex]x=35^\circ[/tex]
Step-by-step explanation:
From the diagram which I have drawn and attached below:
[tex]56^\circ+y+51^\circ=180^\circ$ (Sum of Angles on a Straight Line)\\y=180^\circ-(56^\circ+51^\circ)\\y=73^\circ[/tex]
Next, in the triangle, the sum of the three interior angles:
[tex]y+x+72^\circ=180^\circ\\$Since y=73^\circ\\73^\circ+x+72^\circ=180^\circ\\x=180^\circ-(73^\circ+72^\circ)\\x=35^\circ[/tex]
The value of angle x is 35 degrees.
Alice studies the relationship between climate and heart disease around the world. H(t)H(t)H, left parenthesis, t, right parenthesis models the probability for the occurrence of heart disease (in percents relative to the global average) at an area where the temperature is ttt degrees Celsius. According to Alice's model, when the temperature is -5\degree\text{ C}−5° Cminus, 5, degree, start text, space, C, end text (which is the lowest temperature included in the model), the probability is 10\%10%10, percent above average. Then the probability decreases until the temperature reaches 30\degree\text{ C}30° C30, degree, start text, space, C, end text (which is the highest temperature included in the model), where the probability is 20\%20%20, percent below average. Which number type is more appropriate for the domain of HHH?
Answer:
The domain of the function H(t), is [-5, 30].
The range of the function H(t), is [(10% + average), (average - 20%)]
Step-by-step explanation:
The domain of a function is the complete set of possible values of the independent variable.
For this question, the function is H(t), with the temperature, t, serving as the independent variables and H(t) the evidently dependent variable.
The domain of a function refers to all the possible independent variable values that will give corresponding real dependent variable values.
For this question, Alice's model has the probability for the occurrence of heart disease (in percents relative to the global average) at an area, H(t) varying with the temperature of that area in degree Celsius.
At a temperature of -5°C (the lowest temperature in the model), the probability is 10% above the average.
Then, the probability decreases with increase in temperature, taking a value 20% lower than the average when the temperature is at its highest of 30°C in the model.
So, temperature ranges from -5°C to 30°C and the probability for the occurrence of heart disease ranges from 10% above the average to 20% below the average.
The domain of the function H(t), from the definition given above would therefore be [-5, 30]
And the range of the function H(t), is [(10% + average), (average - 20%)]
Hope this Helps!!!
The Real Number type is more appropriate fro the domain of H(t).
The domain of H(t) is given as [tex]-5 \leq t \leq 30[/tex]
Given that:
The lowest temperature included in the model is -5° C
The highest temperature included in the model is 30° C
The domain of H includes the values of the temperature. Since the temperature can be non integer too, sometimes rational too, thus we use Real Number type for the domain of H(t).
The domain of H(t) will be given by the following interval on real number line:
[tex]\begin{aligned} Domain(H(t)) = [-5, 30]\\\end{aligned}[/tex]
or [tex]-5 \leq t \leq 30[/tex].
Hence, the Real Number type is more appropriate fro the domain of H(t).
The domain of H(t) is given as [tex]-5 \leq t \leq 30[/tex].
Learn more here:
https://brainly.com/question/9463453
The table shows ordered pairs of the function y=8-2x What is the value of y when x = 8?
Answer:-8
Step-by-step explanation:
8 - 2 × 8
8 - 16
-8
What is the solution to this equation?
10x - 3(x- 6) = x + 30
O A. x = 8
O B. x = 2
C. X= 4
[tex]answer \\ 2\\ solution \\ 10x - 3(x - 6) = x + 30 \\ or \: 10x - 3x + 18 = x + 30 \\ or \: 10x - 3x - x = 30 - 18 \\ or \: 7x - x = 12 \\ or \: 6x = 12 \\ or \: x = \frac{12}{6} \\ x = 2 \\ hope \: it \: helps[/tex]
Answer:
x=2
Step-by-step explanation:
10x - 3(x- 6) = x + 30
Distribute
10x -3x+18 = x+30
Combine like terms
7x + 18 = x+30
Subtract x from each side
6x+18 = 30
Subtract 18 from each side
6x = 30-18
6x = 12
Divide by 6
6x/6 = 12/6
x =2
HELP PLEASE
Find the solution set.
(x - 11)(x - 11) = 0
Answer:
x = 11
Step-by-step explanation:
You are solving for the solution of the variable given (x). Set each parenthesis equal to 0 and simplify:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Add 11 to both sides:
x - 11 = 0
x - 11 (+11) = 0 (+11)
x = 0 + 11
x = 11
Do the same for the other set:
x - 11 = 0
x - 11 (+11) = 0 (+11)
x = 0 + 11
x = 11
~
Can anybody please help me with this one??
Answer:
[tex]the \: answer \: is \: d.(x + 4) {}^{2} = 8(y + 4)[/tex]
Can someone help me with this I don’t know if I’m right so
Answer 5x + 8 − 3x = −10
Answer:
-9
Step-by-step explanation:
5x+8-3x = -10
Combine like terms
2x+8 = -10
Subtract 8 to both sides
2x = -18
Divide both sides by 2
x = -9
Answer:
-9
Step-by-step explanation:
5x + 8 - 3x = -10
Combine like terms
2x + 8 = -10
Subtract 8 to both sides
2x = -18
Divide both sides by 2
x = -9
The length and with of a rectangle are consecutive odd integers . The perimeter is 104 meters .find the length and with
Answer:
25 m, 27 m
Step-by-step explanation:
The perimeter is twice the sum of length and width, so that sum is 52 m. Half that is the average of length and width, so will be the even integer between the two consecutive odd integers.
52/2 = 26
The length and width are 25 m and 27 m.
URGENT!! EASY IM DUMB MY LAST QUESTION WILL FOREVER BE GRATEFUL PLS HELP WILL GIVE BRANLIEST!! AT LEAST TAKE A LOOK!!!! PLS I AM BEGGING!!!
18. Using the diagram below as reference, write a paragraph proof to prove that the symmetric property of congruence exists for any two angles. (IMAGE BELOW)
Given: ∠A is congruent to ∠B
Prove: ∠B is congruent to ∠A
Plan: Show that ∠A and ∠B have the same measure, thus ∠B and ∠A have the same measure under symmetry for equality. Conclude with ∠B being congruent to ∠A.
Answer:
Below.
Step-by-step explanation:
Since A is congruent to B, you can conclude that B is congruent to A by the Reflexive Property of Congruence.
write this small number in standard form. 0.00078
Answer:
78/100000
Hope it helps you
An eight-sided die, which may or may not be a fair die, has four colors on it; you have been tossing the die for an hour and have recorded the color rolled for each toss. What is the probability you will roll a green on your next toss of the die? Express your answer as a simplified fraction or a decimal rounded to four decimal places.
The complete question is;
An eight-sided die, which may or may not be a fair die, has four colors on it; you have been tossing the die for an hour and have recorded the color rolled for each toss. What is the probability you will roll a green on your next toss of the die? Express your answer as a simplified fraction or a decimal rounded to four decimal places.
orange brown green yellow
46 23 32 19
Answer:
probability of rolling green on the next toss of the die = 4/15
Step-by-step explanation:
We are given how many times each of the colours appeared for each toss and they are;
Orange - 46
Brown - 23
Green - 32
Yellow - 19
Thus,
Total number of tosses = 46 + 23 + 32 + 19 = 120 rolls
Thus, probability of rolling green on the next toss of die will be = number of times green appeared/total number of rolls = 32/120 = 4/15
You wake up one morning, and find yourself wearing a toga and scarab ring. Always a logical person, you conclude that you must have become an Egyptian pharoah. You decide to honor yourself with a pyramid of your own design. You decide it should have height h = 130 and a square base with side s = 870
To impress your Egyptian subjects, find the volume of the pyramid.
Answer:
32799000 cubic units
Step-by-step Explanation:
Height if the Pyramid=130 Units
Side Length of square base=870 Units
Volume of a Pyramid=[tex]\frac{1}{3}[/tex]* Base Area*Height
Since the base is a square,
Area of a Square of side length s[tex]=s^2[/tex]
Therefore:
Volume[tex]=\frac{1}{3}*870^2*130[/tex]
=32799000 cubic units
The volume of your pyramid is 32799000 cubic units.
Answer:
V = 3.28x10⁷
Step-by-step explanation:
The volume of a pyramid is given by:
[tex] V = \frac{1}{3}bh [/tex]
Where:
b: is the base of the pyramid
h: is the height of the pyramid = 130
The base of the square base of the pyramid is given by:
[tex] b = s^{2} [/tex]
Where:
s: is the side of the square base = 870
Thus, the base of the square base of the pyramid is:
[tex] b = s^{2} = (870)^{2} = 7.56 \cdot 10^{5} [/tex]
Now, the volume of a pyramid is:
[tex] V = \frac{1}{3}bh = \frac{1}{3}(7.56 \cdot 10^{5})*130 = 3.28 \cdot 10^{7} [/tex]
Therefore, the volume of the pyramid is 3.28x10⁷.
I hope it helps you!
When planning road development, the road commission estimates the future population using the function represented in the table, where x is the time in years and f(x) is the total population. What is the significance of 160,000 in the function . Graph is x: 0, 1, 2, 3, 4, 5 f(x):160,000, 163,200, 166,464, 169,793, 173,189, 176,653
Answer:C
Step-by-step explanation:
Answer:
The answer is C
Step-by-step explanation:
Source: Dude trust me
A machine part consist of a half sphere and a cylinder, as shown in the figure.the total volume of the part is blank pi c
Answer:
Volume of the machine part = 114π inches³
Step-by-step explanation:
Volume of the machine part = Volume of cylinder + Volume of hemisphere
Volume of cylinder = [tex]\pi r^{2}h[/tex]
Where r = radius of the cylinder
h = height of the cylinder
Volume of the cylinder = [tex]\pi(\frac{6}{2})^{2}(12)[/tex]
= 108π inches³
Volume of the hemisphere = [tex]\frac{2}{3}\pi r^{3}[/tex]
= [tex]\frac{2}{3}\pi (3)^{3}[/tex]
= 6π inches³
Total area of the machine part = 108π + 6π
= 114π inches³