Find the circumference of a circle whose radius is 7 in.
Answer:
43.96
Step-by-step explanation:
you get pi which is 3.14 times 7 and then times 2
Answer:
43.98 inches
Step-by-step explanation:
The circumference of a circle can be found using:
[tex]c=2r\pi[/tex]
We know r, or the radius is 7, so we can substitute that in
[tex]c=2*7(\pi )[/tex]
[tex]c=14\pi[/tex]
c=43.9822972
or, about
43.98 inches
3(x+2)^2=48
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If a given line has a slope of 2/7, what is the slope of a parallel line?
Answer:
2/7
Step-by-step explanation:
Parallel lines have the same slopes but different y-intercepts. That way they go infinity without touching so are perfectly parallel
c=1 when a randomly chosen card out of a standard deck of 52 playing cards is a heart and c=2 otherwise. draw a histogram showing probibility distribution for the random variable
Answer:
The possible values of c are 1 or 2. There are 13 hearts in a deck of cards and 52-13 = 39 cards that are not. There are a total of 52 cards to choose from, so the possibilities for each value of c are found by dividing the number of results for that value by 52. (Image 1)
Histogram is attached for your reference.
You are ordering a burrito with two main ingredients and three toppings. The menu below shows the possible choices. How many different burritos are possible?
(the number of combinations)
Answer:
840
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one. Please have a look at the attached photo.
My answer:
In the menu, there are 6 main ingredients and we take 2 at the same time, so the possible outcomes is:
[tex]C^{6} _{2}[/tex] = [tex]\frac{6!}{(6-2)!*2!}[/tex] = 15
In the menu, there are 8 toppings and we take 3 at the same time, so the possible outcomes is:
[tex]C^{8} _{3}[/tex] = [tex]\frac{8!}{(8-3)!*3!}[/tex] = 56
=> the total number of combinations :
=[tex]C^{6} _{2}[/tex]*[tex]C^{8} _{3}[/tex]
=15 * 56 = 840
You bike 1 mile the first day of your training, 1.5 miles the second day, 2.5 miles the third day, and 4.5 miles the fourth day. If you continue this pattern, how many miles do you bike the seventh day?
Answer:
32.5 miles on the 7th day
Step-by-step explanation:
1, 1.5, 2.5, 4.5
We need to determine the pattern
We are adding .5 + 1/4(2^n)
Lets check
n=1 .5+ 1/4(2) = .5+ .5 =1
n =2 .5 + 1/4*2^2 = .5 +1 = 1.5
n=3 .5 + 1/4 ( 2^3) = .5 + 8/4 = 2.5
n=4 .5 + 1/4 (2^4) = .5 + 16/4 = 4.5
n = 5 .5 + 1/4 (2^5) = .5 +32/4 = 8.5
n = 6 .5 + 1/4 (2^6) = .5 + 64/4 =16.5
n=7 .5 + 1/4(2^7)= .5 + 1/4(128) = 32.5
They bike 32.5 miles
Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 1.5 m/s, how fast is the area of the spill increasing when the radius is 30 m?
Answer:
The area of the oil spill is increasing at a rate 180 π m²/s, when the radius is 30 m.
Step-by-step explanation:
Derivative Rule:
[tex]\frac{d}{dx}x^n=nx^{n-1}[/tex] [tex]\frac{d}{dx}(y^n)=ny^{n-1}\frac{dy}{dx}[/tex]Given that
The radius of the oil spill increases at a rate 1.5 m/s.
i.e [tex]\frac{dr}{dt}= 1.5\ m/s[/tex]
We need to find the rate of area increase i.e [tex]\frac{dA}{dt}[/tex] .
We know,
The area of the oil spills A = [tex]\pi r^2[/tex] ( since it spreads in circular pattern)
[tex]\therefore A=\pi r^2[/tex]
Differentiating with respect to t
[tex]\frac{dA}{dt}=\pi. 2r\frac{dr}{dt}[/tex]
Plug the value of [tex]\frac{dr}{dt} =1.5 \ m/s[/tex]
[tex]\frac{dA}{dt}=\pi. 2r(3\ m/s)[/tex]
[tex]\Rightarrow \frac{dA}{dt}=6\pi r \ m/s[/tex]
Plug r= 30 m
[tex]\Rightarrow \frac{dA}{dt}=6\pi (30\ m) \ m/s[/tex]
=180 π m²/s
The area of the oil spill is increasing at a rate 180 π m²/s, when the radius is 30 m.
What situation could the
integer - 5 represent?
Answer:
What is the average temperature in degrees Celcius of Alaska in the winter?
The integer -5 can represent a loss or debt of 5 in real-world situations like owing someone 5 dollars, or a temperature drop 5 degrees below zero. Another example could be temperature. If the temperature drops 5 degrees below zero, it can be represented as -5 degrees.
Explanation:
In Mathematics, an integer can represent various scenarios. The integer -5 could symbiotically stand for a loss or debt of 5 in real-world situations. For example, if you owe someone 5 dollars, your net balance would be -5 dollars. Another example could be temperature. If the temperature drops 5 degrees below zero, it can be represented as -5 degrees.
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Find the value of 5w-1 given that 3w-4=8
Simplify your answer as much as possible
Answer:
19
Step-by-step explanation:
Solve for the value of w.
3w - 4 = 8
Isolate the variable, w. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
First, add 4 to both sides:
3w - 4 (+4) = 8 (+4)
3w = 8 + 4
3w = 12
Divide 3 from both sides to fully isolate the variable, w:
(3w)/3 = (12)/3
w = 12/3
w = 4
Plug in 4 for w in the first expression & solve:
5w - 1
5(4) - 1
20 - 1
19
19 is your value.
~
Answer:
19
Step-by-step explanation:
First, we need to solve for w by isolating it
3w-4=8
Add 4 to both sides
3w=12
Divide both sides by 3
w=4
Now we know w and can plug 4 in for w and solve
5w-1
5(4)-1
20-1
19
What percent of 80 is 32?
Answer:
40%
Step-by-step explanation:
multiply 80 by.40 you will get 32 hope this helps god bless
The number of hours of daylight y for day x (x = 1 to 365) in Anchorage, Alaska, can be modeled by y=7.0sin(2π365x−1.4)+12.4. What is the minimum number of hours of daylight in Anchorage?
Answer:
5.4 hours
Step-by-step explanation:
As the number of hours of daylight y is modeled as a function of sin, and sin has the minimum value of -1. Therefore
[tex]sin(2\pi 365x-1.4) \geq -1[/tex]
[tex]7sin(2\pi 365x-1.4) \geq -7[/tex]
[tex]7.0sin(2\pi 365x-1.4)+12.4 \geq 5.4[/tex]
[tex]y \geq 5.4[/tex]
So the minimum number of hours of daylight in Anchorage is 5.4 hours
Final answer:
The minimum number of hours of daylight in Anchorage, Alaska, can be found using the equation provided. By considering the minimum value of the sine function, we determine that Anchorage experiences a minimum of 5.4 hours of daylight.
Explanation:
The minimum number of hours of daylight in Anchorage, Alaska, can be determined by examining the mathematical model y=7.0sin(2ω⁄365x−1.4)+12.4.
The amplitude of the sine function in this equation is 7.0, which determines the maximum variation above or below the average value.
Since the sine function oscillates between -1 and 1, the minimum value of the sine part of the equation will be -1.
Therefore, the minimum number of hours of daylight, y, occurs when the sine function is at its minimum value. By substituting -1 into the equation, we get y=7.0×(-1)+12.4, which simplifies to y=5.4.
This means that the minimum number of hours of daylight in Anchorage is 5.4 hours.
The radius of the base of a cone is decreasing at a rate of 2 22 centimeters per minute. The height of the cone is fixed at 9 99 centimeters. At a certain instant, the radius is 13 1313 centimeters. What is the rate of change of the volume of the cone at that instant (in cubic centimeters per minute)?
Answer:
The Volume is decreasing at a rate of [tex]156\pi[/tex] [tex]cm^3[/tex] per minute.
Step-by-step explanation:
Given a cone of radius r and perpendicular height h
Volume of the cone, [tex]V=\frac{1}{3}\pi r^2 h[/tex]
Since the height of the cone is fixed, the rate of change of the volume of the Cone, [tex]\frac{dV}{dt}[/tex] is given as:
[tex]V=\frac{1}{3}\pi r^2 h \\\frac{dV}{dt}=\frac{h\pi}{3} \frac{d}{dt} r^2\\\frac{dV}{dt}=\frac{2rh\pi}{3} \frac{dr}{dt}[/tex]
We are to determine the rate of change of the Volume, V when:
The radius is decreasing at a rate of 2 cm per minute, [tex]\frac{dr}{dt} = -2 cm/min[/tex]
Height, h=9 cm
Radius = 13cm
[tex]\frac{dV}{dt}=\frac{2rh\pi}{3} \frac{dr}{dt}\\=\frac{2*13*9\pi}{3}* ( -2)\\\frac{dV}{dt}=-156\pi \:cm^3/min[/tex]
The Volume is decreasing at a rate of [tex]156\pi[/tex] [tex]cm^3[/tex] per minute.
National League Hockey play-off games go into overtime if the score is tied at the end of a game. Overtime lasts until one of the teams scores a goal. From years of experience we know that the distribution of the lengths of the overtime periods is right skewed with a mean of 9.8 minutes and a standard deviation of 12 minutes. What is the (approximate) probability that a random sample of 30 overtime periods would have a (sample) mean length of more than 13 minutes? Give your answer to 3 decimal places, e.g, 0.123.
Answer:
0.07215 = 0.072 to 3 d.p.
Step-by-step explanation:
Central limit theorem explains that the sampling distribution obtained from this distribution will be approximately a normal distribution with
Mean = population mean
μₓ = μ = 9.8 minutes
Standard deviation of the distribution of sample means = σₓ = (σ/√n)
σ = 12 minutes
n = sample size = 30
σₓ = (12/√30) = 2.191
Probability that a random sample of 30 overtime periods would have a (sample) mean length of more than 13 minutes
Required probability = P(x > 13)
Since we've established that this distribution of sample means approximates a normal distribution
We first standardize 13 minutes.
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ = (13 - 9.8)/2.191 = 1.46
Required probability
P(x > 13) = P(z > 1.46)
We'll use data from the normal probability table for these probabilities
P(x > 13) = P(z > 1.46) = 1 - P(z ≤ 1.46)
= 1 - 0.92785 = 0.07215
Hope this Helps!!!
The life in hours of a biomedical device under development in the laboratory is known to be approximately normally distributed. A random sample of 15 devices is selected and found to have an average life of 5617.8 hours and a sample standard deviation of 234.5 hours.
a) Test the hypothesis that the true mean life of a biomedical device is greater than 500 using the P - value approach.
b) Construct a 95% lower confidence bound on the mean.
c) Use the confidence bound found in part (b) to test the hypothesis.
Answer:
a) The evidence suggest the true mean life of a biomedical device > 5500
b) (5487.94, +∞)
c) There is evidence to support that the mean is equal to 5500
Step-by-step explanation:
Here we have
(a) To test the hypothesis we have the claim that the mean life of biomedical devices > 5500
Therefore, we put the null Hypothesis which is the proposition that a difference does not exist. That is
H₀: μ = 5500
Therefore, the alternative hypothesis will be
Hₐ: μ > 5500
The test statistic is then found by;
[tex]t=\frac{\bar{x}-\mu }{\frac{s }{\sqrt{n}}} =\frac{5617.8-5500 }{\frac{234.5 }{\sqrt{15}}} \approx 1.95[/tex]
The P value from the T table at df = n - 1 = 15 - 1 = 14 is
0.025 < P < 0.05
The P value is given as 0.036 from the T distribution at 14 derees of freedom df
Therefore, since P < α or 0.05, we reject the null hypothesis. That is we fail to reject Hₐ: μ > 5500. The evidence suggest the true mean life of a biomedical device > 5500
(b) The 95% confidence interval is given as
[tex]CI=\bar{x}\pm t_\alpha \frac{s}{\sqrt{n}}[/tex]
Which gives t[tex]_\alpha[/tex] = [tex]\pm[/tex]2.145
[tex]CI=5617.8\pm 2.145 \times \frac{234.5}{\sqrt{15}}[/tex]
The confidence interval of the lower bound on the mean is then
(5487.94, +∞)
c) From the above result, we find that the mean of 5500 is contained in the range of the lower confidence on the mean. We can therefore, accept the null hypothesis. That is there is evidence to support that the mean is equal to 5500.
A certain triangle has a 30° angle in a 60° angle. Which must be a true statement about the triangle
Answer:
It is a right triangle.
Step-by-step explanation:
A right triangle is a triangle with at least one angle with 90 degrees.
We know that every triangle has 180 degrees. The other unknown angle is 180 - (30+60) = 180 - 90 = 90. That means that the other angle is 90 degrees. Therefore, it is a right triangle
We also know that in this triangle, that the square of one side plus the square of another is side is equal to the square of the hypotenuse of the triangle. (According to Pythagorean theorem)
Answer:
The second-longest side is the square root of 3 times as long as the shortest side.
If the rate, in gallons per minute continues, how many gallons of water will flow from the hose in 45 minutes
Answer:
Step-by-step explanation:
45 gallons but your questtion doesnt make sense because you dont give us the number in gallons per minute
What is the value of 4/15 divided 2/3
Answer:
⅖
Step-by-step explanation:
4/15 ÷ 2/3
4/15 × 3/2
2/5
Answer: 2/5 or 0.4
Step-by-step explanation: When dividing a fraction by another fraction you will always find the reciprocal of the second fraction and then multiply to get your answer.
4/15 divided by 2/3
4/15 multiplied by 3/2
0.4 or 4/10 or 2/5 is the value of 4/15 divided by 2/3
Solve the equation. 8 – 2x = –8x + 14 x = –1 x = x equals negative StartFraction 3 Over 5 EndFraction x = x equals StartFraction 3 Over 5 EndFraction x = 1
Answer:
x =1
Step-by-step explanation:
Solve the equation:
8 - 2x = -8x + 14
Collect like terms
8 - 14 = -8x + 2x
-6 = -6x
x = -6/-6
x = 1
Answer:
x=1
Step-by-step explanation:
i did the quiz
The tile backslash will be a mixture of colors of five-inch square tiles. One quarter of the tiles will be "Indian Red" one sixth will be "Tuscan Blue", one fifth will be "Eucalyptus", and the rest will be the color "Sand". What fraction of the tiles will be the color of "Sand"
Answer:
The fraction of tiles that will be the color of "sand" is 23/60
Step-by-step explanation:
we know that
The sum of the fractions of the tiles must be equal to 1
Let
x ----> the fraction of tiles that will be the color of "sand"
we have that
[tex]\frac{1}{4}+\frac{1}{6}+\frac{1}{5}+x=1[/tex]
solve for x
Find the Least Common Multiple of denominators
[tex]LCM=(2^2)((3)(5)=60[/tex]
Multiply both sides by 60
[tex]\frac{60}{4}+\frac{60}{6}+\frac{60}{5}+60x=60[/tex]
simplify
[tex]15+10+12+60x=60[/tex]
[tex]60x=60-37\\60x=23\\x=\frac{23}{60}[/tex]
therefore
The fraction of tiles that will be the color of "sand" is 23/60
Can someone please help me on this
Answer:
28.4 miles less
Step-by-step explanation:
1. Find the length of the third side of the triangle with the pythagoream theroum
2. Pythagorean theroum= a^2+b^2=c^2
3. 45^2+ 55^2=c^2
4. 2025+3025=c^2
5. 5050=c^2
6. 71.06=c
7. Instead of driving 100 miles to work, Evelyn will now drive only 71.06 miles to work
7. That is 28.4 miles less than before
Answer:30 miles you save 30 miles
Step-by-step explanation: if you go around its 48+55=103 miles
Do formula a^2+ b^2= c^2
48^2+ 55^2=c^2
2304+3025= c^2
5329=c ^2
Sq rt of 5329 is 73
103-73=30
I need help on this quick
Answer:
The hypotenuse to the nearest tenth is 8.1
Step-by-step explanation:
We can use the Pythagorean theorem to solve
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
Let a be the x leg and b be the y leg
a = 7 units
b= 4 units
7^2 + 4^2 = c^2
49+ 16 = c^2
65 = c^2
Take the square root of each side
sqrt(65) = sqrt(c^2)
8.062257748 =c
To the nearest tenth
8.1 =c
Which is the solution to the inequality? y minus 27 greater-than-or-equal-to negative 13
Answer:
y is greater than or equal to 14
Step-by-step explanation:
Answer:
y ≥ 14
Step-by-step explanation:
y - 27 ≥ -13
you manipulate this inequality like it is an equation. Only take care that the inequality swaps if you multiply by a negative. In this case, that is not needed.
y - 27 +27 ≥ -13+27
y ≥ 14
What is the difference between the measure of an arc and the arc length? Explain.
The measure of an arc is the degree/radian measure. You measure the central angle to find the measure of an arc.
The arc length is the actual length (like 2pi inches or 7 cm, etc.). You find the length of the curved part (the arc), not the straight distance between the 2 points given.
help please! super urgent. simple math problem!! will mark brainliest
Answer:
B
Step-by-step explanation:
Answer:B
Step-by-step explanation:
What is the slope of the line that passes through the points (5,-2) and (1, 10)
Answer:
-3
Step-by-step explanation:
10 - -2 = 12
1 - 5 = -4
12 / -4 = -3
Answer:
m = -3
Step-by-step explanation:
slope formula [tex]\frac{10-(-2)}{1-5} = -\frac{12}{4}[/tex] = -3
Leslie has a rectangular patio. She measures it and finds out it is 2135 feet long by 1115 feet wide. She wants to know how many square feet of tile she will need to completely cover the patio. Draw the patio, and label the measurements. How much tile will Leslie need to cover the patio? If each square foot of tile costs 75 cents, how much will she have to pay to cover her patio?
Answer: (1) Leslie will need 2,380,525 square tiles (1 foot by 1 foot each)
(2) She will have to spend $1,785,393.75 to cover her patio.
Step-by-step explanation: Please refer to the picture attached.
The rectangular patio has been designed and as shown in the diagram has on side measuring 2135 ft and the other side measuring 1115 ft. This means, in order to cover the entire patio, she would have to cover an entire area defined as 2,135 feet into 1,115 feet. If one tile measures 1 foot long by 1 foot wide, the total number of tiles to cover the patio can simply be derived as;
Area = L x W
Where the length is 2135 and the width is 1115,
Area = 2135 x 1115
Area = 2380525
**Having in mind that one tile measures 1 ft by 1 ft, the area of each tile is given as
Area = L x W
Area = 1 x 1
Area = 1 square foot**
(1) The above calculation shows that Leslie would be using up a total of 2,380,525 square tiles to completely cover her patio.
(2) Having been told that each square foot of tile costs 75 cents ($0.75), the total amount spent to cover her patio would be calculated as follows;
Cost = Area x cost per tile
Cost = 2380525 x 0.75
Cost = 1785393.75
The total cost therefore is $1,785,393.75
Leslie needs [tex]\( 2380025 \)[/tex] square feet of tile, and it will cost her [tex]\( \$1785018.75 \)[/tex] to cover her patio.
1. Calculate the area of the patio:
[tex]\[ \text{Area} = 2135 \times 1115 = 2380025 \text{ square feet} \][/tex]
2. Calculate the total cost of tiles:
[tex]\[ \text{Total cost} = 2380025 \text{ square feet} \times \$0.75/\text{sq ft} = \$1785018.75 \][/tex]
Therefore, Leslie needs [tex]\( 2380025 \)[/tex] square feet of tile, and it will cost her [tex]\( \$1785018.75 \)[/tex] to cover her patio.
Que es la mitad de 5
Answer:
2,5
Step-by-step explanation:
es decimal porque es un numero impar
Answer:
2.5
Step-by-step explanation:
básicamente, dividirías 5 y 2. No hagas 2 y 5. Eso te dará un número completamente diferente y no querrás un decimal de la fracción 2/5. Quieres la mitad de 5. ¡Entonces será 2.5! Lo siento, estoy usando el traductor de Google.
What is 6/ 8 equal to
Answer:
1216 is equivalent to 68 because 12 x 8 = 16 x 6 = 96.
Step-by-step explanation:
Help meeeeeeeeeeereeee
Answer:
5
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
1/2( 4^3 - 6 * 3^2)
PEMDAS says parentheses first
( 4^3 - 6 * 3^2)
Exponents
(64 - 6 * 9)
Multiply and divide from left to right
64 - 54
Add and subtract from left to right
10
Substitute back into the expression
1/2(10)
5
The newly elected Chancellor of the Galactic Federation is interested in the opinions of all citizens regarding economic conditions in the galaxy. Unfortunately, she does not have the resources to visit every populated planet or to send delegates to them. Describe how the Chancellor might organize a multi-stage sample to carry out her survey.
The Chancellor can use a multi-stage sampling method to gather citizen opinions by dividing the galaxy into various regions, selecting a sample of these regions, and then selecting a sample of planets within these regions for surveying citizens.
Explanation:The Chancellor could use a multi-stage sampling method to effectively gather data from the galaxy's population. This method involves breaking down the larger population into smaller, manageable subsets in a sequence of levels or 'stages'. Here's an example of how it could work:
First Stage: The Chancellor divides the galaxy into distinct regions (e.g., solar systems, clusters of stars, etc.). This is sometimes called 'clustering'.Second Stage: A random sample of these regions is selected for further study.Third Stage: Within the selected regions, a random sample of planets is chosen.Final Stage: Within the chosen planets, a random sample of citizens is surveyed.This method will make the task feasible and manageable, given the constraint of resources. It also ensures that a diverse range of opinions can be captured from all over the galaxy.
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