Answer: 10 min
Step-by-step explanation:
Final answer:
The bacterial culture that triples every 2 minutes will surpass 9500 cells just after 10 minutes. Since we cannot have a fraction of a minute in this context, the answer is 11 minutes (Option C).
Explanation:
The student is asking about exponential growth, specifically in a bacterial culture that triples every 2 minutes. To find out how many minutes it will take for the initial 40 cells to grow to more than 9500, we can use the formula for exponential growth:
N = N0 × 3t/2
Where N is the final number of cells, N0 is the initial number of cells (40 in this case), and t is the time in minutes.
We want N to be greater than 9500, so we solve the inequality:
9500 < 40 × 3t/2
Dividing both sides by 40 gives:
237.5 < 3t/2
Next, we find the smallest t for which the inequality holds by applying logarithms and solving:
t > 2 × (log3(237.5))
Calculating the right side, we get:
t > 10.096
So, the culture will have more than 9500 cells just after 10 minutes. The smallest whole number of minutes greater than 10.096 is 11, hence the answer is: C) 11 min
Suppose you draw a card from a well-shuffled pack of playing cards. What is the probability the card you draw will be an ace? A. 4/50 B. 1/13 C. 4/13 D. 1/52
a(1)=20
a(n)=a(n−1)−17
Find the 3rd term in the sequence
Answer:
-14
Step-by-step explanation:
khan academy
Bella made a drawing of her rectangular bedroom with the scale of 1 inch = 3 feet. The drawing was 6 inches long by 4 inches wide. What are the dimensions of Bella's room? What is the actual area? Show your work.
Bella's actual room dimensions are 18 feet by 12 feet, resulting in an actual area of 216 square feet. This was determined by applying the scale factor from the drawing to the actual room size.
To determine the actual dimensions of Bella's room based on her drawing, we first need to use the provided scale factor. According to the scale, 1 inch on the drawing is equal to 3 feet in actual size. We can calculate the actual dimensions by multiplying the length and width of the drawing by the scale factor.
The drawing is 6 inches long by 4 inches wide.
Actual length: 6 inches × 3 feet/inch = 18 feet
Actual width: 4 inches × 3 feet/inch = 12 feet
Now, to determine the actual area of Bella's room, we multiply the actual length by the actual width:
Actual area = actual length × actual width
Actual area = 18 feet × 12 feet = 216 square feet
A stock can go up, go down, or stay unchanged. how many possibilities are there if you own 66 stocks?
What is the distance between the points (3,8) (-9,8)
A)5
B)10
C)15
D)20
The distance between the points (3,8) and (-9,8) is 12. The correct answer is option B) 10.
Explanation:The distance between two points can be found using the distance formula: d = √((x2 - x1)^2 + (y2 - y1)^2). In this case, the coordinates of the two points are (3,8) and (-9,8). Plugging these values into the formula, we get:
d = √((-9 - 3)^2 + (8 - 8)^2)
d = √((-12)^2 + (0)^2)
d = √(144 + 0)
d = √144
d = 12
Therefore, the distance between the points (3,8) and (-9,8) is 12. The correct answer is option B) 10
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What is the degree of each monomial -9
The degree of a monomial is the sum of the exponents of the variables.
For example:
monomial: 257 x^3 y^5 z^21.
The degree is the sum of the exponents of x, y and z, this is 3 + 5 + 21 = 29.
When a monomial is just a number, it means that the exponents of the variables are zero. For example:
- 9 x^0 y^0 z^0 = - 9 * 1 * 1 * 1 = - 9.
This is your case, the monomial -9 has degree 0, which is the option B.
una pizzeria hace pizzas de varios tamaños y las vende en cajas hexagonales de 39 cm de lado y 4.7 cm de alto ¿que cantidad de cartón se anestesia para cada caja teniendo en cuenta q la caja esta formado por dos partes compuestas de una base lateral ?
Final answer:
To calculate the amount of cardboard used for each box, we need to find the surface area of the hexagonal base and the lateral surface area. We can use the formula for the surface area of a hexagon to find the base area. Then, we multiply it by the height of the box and add the two areas together.
Explanation:
To find the amount of cardboard used for each box, we need to calculate the surface area of the hexagonal base and the lateral surface area. The surface area of a hexagon can be found using the formula:
Surface Area = 3 x √3 x s^2
where s is the length of the side of the hexagon. Given that the side length is 39 cm, we can substitute this into the formula to find the surface area of the hexagonal base. Once we have the surface area, we can calculate the lateral surface area by multiplying it by the height of the box, which is 4.7 cm. Adding the two areas together will give us the total amount of cardboard used for each box.
A coin is tossed 72 times. Find the standard deviation for the number of heads that will be tossed
The standard deviation for the number of heads that will be tossed is [tex]\boxed{4.24}.[/tex]
Further Explanation:
The random variable X follows binomial distribution.
[tex]\boxed{X \sim {\text{Bin}}\left( {n,p} \right)}[/tex]
Here, n represents the total number of experiments and p denotes the probability of the event.
Apply central limit theorem.
[tex]\boxed{X \sim {\text{Normal}}\left( {np,np\left( {1 - p} \right)} \right)}[/tex]
The mean of the binomial distribution can be calculated as follows,
[tex]\boxed{{\text{Mean}} = n \times p}[/tex]
The standard deviation of binomial distribution can be calculated as follows,
[tex]\boxed{{\text{Standard deviation}} = \sqrt {np\left( {1 - p} \right)} }[/tex]
Given:
Coin is tossed 72 times.
Explanation:
Consider X is the random variable that head will occur.
The probability of head occur is [tex]p = \dfrac{1}{2}.[/tex]
The mean can be calculated as follows,
[tex]\begin{aligned}{\text{Mean}}&= 72\times \frac{1}{2}\\&= 36\\\end{aligned}[/tex]
The standard deviation of the number of heads can be calculated as follows,
[tex]\begin{aligned}{\text{Standard deviation}}&= \sqrt {72 \times \frac{1}{2}\left( {1 - \frac{1}{2}} \right)} \\&= \sqrt {72 \times\frac{1}{2} \times \frac{1}{2}}\\&=\sqrt{\frac{{72}}{4}}\\&= \sqrt {18}\\&= 4.24\\\end{aligned}[/tex]
Hence, the standard deviation for the number of heads that will be tossed is [tex]\boxed{4.24}.[/tex]
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Answer details:
Grade: College
Subject: Statistics
Chapter: Binomial Distribution
Keywords: coin, tossed 72 times, number of heads, binomial distribution, standard normal distribution, standard deviation, test, measure, probability, low score, mean, repeating, indicated, normal distribution, percentile, percentage, proportion, empirical rule.
Write the set of points greater than or equal to −5−5 but strictly less than 44, excluding 00, as a union of two intervals (if you're having trouble with this, try drawing a number line):
solve The quantity 2 x minus 10 divided by 4 = 3x
To solve the equation 2x - 10 / 4 = 3x, multiply both sides by 4, simplify, and solve for x to find its value as -1.
Step 1: Multiply both sides of the equation by 4 to get rid of the fraction:
4 * (2x - 10) / 4 = 4 * 3x
Step 2: Simplify the equation:
2x - 10 = 12x
Step 3: Rearrange the equation to solve for x:
2x - 12x = 10
-10x = 10
x = -1
Daniella wrote the equation shown to represent “four less than – 3.7 times a number is –11.9.” 4n – (–3.7) = 11.9 Explain her error, include the correct equation in your response.
Answer:
The correct equation is [tex]-3.7n-4=-11.9[/tex]
Step-by-step explanation:
Let
n-------> the number
we know that
The equation that represent the expression “four less than [tex]-3.7[/tex] times a number is [tex]-11.9[/tex] " is equal to
[tex]-3.7n-4=-11.9[/tex]
The equation that Daniella wrote represents the expression "[tex]-3.7[/tex] less than four times a number is [tex]11.9[/tex] "
Answer:
The coefficient of the variable should be -3.7 because of the word “times.” The words “four less than” mean that 4 will be subtracted from 3.7n. “Is” represents the equals sign, and “-11.9” is the second expression. The correct equation is -3.7n – 4 = -11.9.
Step-by-step explanation:
Edg math
Use cavalieri's principle to a circular pillar candle is 2.8 inches wide & 6 inches tall. find the volume of the candle.
The sides of a triangle are in the ratio 5:12:13. what is the length of each side of the triangle if the perimeter of the triangke is 15 inches
Each triangle is a 30-60-90 triangle, and the hypotenuse of one triangle is the longer leg of an adjacent triangle. the hypotenuse of the larger triangle is 16 centimeters. what is the number of centimeters in the length of the longer leg of the smaller triangle?
The length of the longer leg of the smaller triangle is 8[tex]\sqrt{3}[/tex] centimeters.
In a 30-60-90 triangle, the ratio of the lengths of the sides is as follows:
- The length of the shorter leg is x.
- The length of the longer leg is x[tex]\sqrt{3}[/tex].
- The length of the hypotenuse is 2x.
Given that the hypotenuse of the larger triangle is 16 centimeters, we can set up the equation:
2x = 16
Solving for x:
x = [tex]\frac{16}{2}[/tex] = 8
Now, we know that the length of the longer leg of the larger triangle is x[tex]\sqrt{3}[/tex] = 8[tex]\sqrt{3}[/tex] centimeters.
Since the hypotenuse of the larger triangle becomes the longer leg of the smaller triangle, the longer leg of the smaller triangle is 8[tex]\sqrt{3}[/tex] centimeters.
The question is:
There are two triangles. Each triangle is a 30-60-90 triangle, and the hypotenuse of one triangle is the longer leg of an adjacent triangle. the hypotenuse of the larger triangle is 16 centimeters. What is the number of centimeters in the length of the longer leg of the smaller triangle?
Jane Marko buys a car for $43,900. In three years, the car depreciates 48% in value. How much is the car worth in 3 years
Jorge bought a car for $41,902 . He paid for the car with a check. Round the price to the nearest:
For a daily airline flight between two cities, the number of pieces of checked luggage has a mean of 380 and a standard deviation of 20. What number of pieces of checked luggage is 3 standard deviations above the mean?
Answer:
The answer is 440 pieces of checked luggage
Step-by-step explanation:
Mean = 380
Standard deviation = 20
No. of pieces of checked luggage for 1 standard deviation = 20 pieces
Therefore, Mean for 3 standard deviations above the mean = 3 × 20 = 60
Now, number of pieces of checked luggage 3 standard deviations above the mean = Mean for 1 standard deviation + Mean for 3 standard deviations above the mean
⇒ 380 + 60 = 440 pieces
What is the area of the triangle?
Because the car that has a terrible oil leak not only as a new battery for the van but also slows him down because he needs the Atwell after every hundred miles of driving he drives 100 miles every two hours it takes him 15 minutes to add oil how long should it take him to drive 500 miles
To drive 500 miles, taking into account both driving time and oil stop time, it would take 11 hours and 15 minutes.
He drives 100 miles every 2 hours, so to drive 500 miles he would take 10 hours (5 segments of 100 miles each).He needs to add oil every 100 miles, which takes 15 minutes each time. Therefore, for the 500-mile trip, he would spend an additional 75 minutes (5 segments x 15 minutes each).Adding the driving time and oil stop time, he would take 10 hours (driving) + 1 hour 15 minutes (oil stops) = 11 hours 15 minutes to drive 500 miles.The variable Z is inversely proportional to X. When X is 6, Z has the value 2. What is the value of z . When x = 13
Round to at least the thousandths place if needed.
Z= k/x
when x is 6, Z= 2
2=k/6
k=2*6
k=12
Z=12/X
when x = 13
Z=12/13
Z=0.923
If today is tuesday what day will it be in 100 days
What does 6× mean in math
You have 12 balloons to blow up for a party. You blow up 1313 of them, and your friend blows up 5 of them. What fraction of the balloons still need blowing up?
Answer:
The Answer Is 1/4
Step-by-step explanation:
Ur brain xd
Use the distributive property to expand the following expression. -3(6.3x + 7y - 2.5)
The expression -3(6.3x + 7y - 2.5) expands to -18.9x - 21y + 7.5 using the distributive property by multiplying each term inside the parentheses by -3.
To use the distributive property to expand the expression -3(6.3x + 7y - 2.5), you multiply each term inside the parentheses by -3. The distributive property lets you reverse the distributive law and turn it into factors (multiples).
-3 × 6.3x = -18.9x
-3 × 7y = -21y
-3 ×-2.5 = 7.5
Once each term is multiplied, the expanded expression is: -18.9x - 21y + 7.5
I REALLY NEED HELP ON THESE EQUATIONS THE LAST PIC AND THIS ONE PLEASEEE IM IN DANGER OF FAILING
An acute angle θ is in a right triangle with sin θ = two thirds . What is the value of cot θ?
Answer:
six divided by the square root of thirteen
Step-by-step explanation:
hey there,
< sin θ = [tex]\frac{O}{H}[/tex]
So that means O = 2 and H = 3. In order to find cot θ, first let's find tan θ.
tan θ = [tex]\frac{O}{B}[/tex]
We only know what O is equal to, not B. So let's draw out a triangle.
7
◢ 6
B
As you can see (sorry for the poor triangle), this is a right triangle. In order to find an unknown part, use [tex]a^2 + b^2 = c^2[/tex]!
[tex]6^2 + B^2 = 7^2[/tex]
B = ±√13
Obviously, a side of a triangle can't be negative, so it stays positive. Now we can find tangent!
tanθ = [tex]\frac{6}{\sqrt{13} }[/tex]
But, we're not done here. We're trying to find cotθ.
cotθ = [tex]\frac{1}{tan}[/tex]θ
[tex]\frac{1}{\frac{6}{\sqrt{13} } }[/tex] = [tex]\frac{\sqrt{13} }{6}[/tex]
That's your final answer! >
Hope this helped! Feel free to ask anything else.
Your teacher is giving you a test worth 100 points containing 40 questions. there are two-point and four-point questions on the test. let the number of two-point questions be x and the number of four-point questions be y. how many of each type of question are on the test?
Answer:
t=30 f=10
Step-by-step explanation:
t= 100*1 - 40*4 = 30
2*1 - 1*4
f= 2*40 - 1*100 = 10
2*1 - 1*4
t=30 f=10
A personal identification code consists of five digits (0 through 9). how many codes are possible?
a. 50
b. 252
c. 100,000
d. 30,240
There are 30,240 codes that are possible which consist of five digits (0 through 9).
What is a permutation?A permutation is defined as a mathematical process that determines the number of different arrangements in a set of objects when the order of the sequential arrangements.
There are 10 options for each of the 5 digits in the personal identification code (0 through 9). Since the order of the digits matters, we can use the formula for the number of permutations of n items taken r at a time, which is:
n!/(n-r)!
In this case, n is the number of options (10) and r is the number of items (5). Plugging these values into the formula gives us:
10!/(10-5)! = 10!/(5!) = 109876 = 30,240
Therefore, the correct answer is (d) 30,240.
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an arc that lies between the two sides of a cental angle is called a_____.
A. minor arc
B. major arc
C. semicircle
Sasha sets a goal to read 5 minutes longer than each previous day for 30 days. On the first day, Sasha reads for 20 minutes. The expression mc018-1.jpg represents the total number of minutes Sasha reads during the 30 days. How many total minutes does she read?
Final answer:
Sasha reads a total of 2775 minutes over 30 days, calculated using the formula for the sum of an arithmetic sequence.
Explanation:
To calculate the total number of minutes Sasha reads over 30 days, we note that she starts with 20 minutes on the first day and reads 5 minutes more each subsequent day. This is an arithmetic sequence where the first term (a1) is 20 minutes, the common difference (d) is 5 minutes, and the number of terms (n) is 30.
We can use the formula for the sum of an arithmetic sequence: Sn = n/2 (2a1 + (n - 1)d).
Plugging in the given values gives us S30 = 30/2 (2(20) + (30 - 1)(5)).
Now we calculate: S30 = 15(40 + 29(5)) = 15(40 + 145) = 15(185) = 2775 minutes.
Therefore, Sasha reads a total of 2775 minutes over the course of 30 days.