If there are initially 5000 bacteria in a culture, and the number of bacteria triple each hour, the number of bacteria after t hours can be found using the formula y = 5000(3)^t. How long will it take the culture to grow to 80,000? Round to the nearest tenths.
Answers
Then it will take approximately 6.3 hours for the culture to grow to 80,000 bacteria
The given formula for the number of bacteria in a culture after t hours is:y = 5000(3)^tWe are required to find the number of hours it will take the culture to grow to 80,000.
This can be done by setting y equal to 80,000 and then solving for t.5000(3)^t = 80,000
Divide both sides by 5000:3^t = 16Now, we need to solve for t by taking the logarithm of both sides.
However, it is easier to use logarithmic properties to simplify the equation first.3^t = 2^4
Raise both sides to the power of (1/log3):log3(3^t) = log3(2^4)t = 4/log3(2)Using a calculator, log3(2) ≈ 0.631, so:t ≈ 4/0.631 ≈ 6.3.
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Related Questions
Rewrite 2/3 : 1/15 as a unit rate
Answers
Answer: 10:1
Step-by-step explanation:
I don’t know. I took my math exam and got the wrong answer, this is the correct one. i hope i helped someone :)
2/3 : 1/15 as a unit rate is \(10:1\) .
What is a unit rate?A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.
According to the question
\(\frac{2}{3} : \frac{1}{15}\) as a unit rate
As, unit rate is having denominator = 1
So,
\(\frac{2}{3} : \frac{1}{15}\)
= \(\frac{2}{1} : \frac{1}{5}\)
= \(10:1\)
Hence, 2/3 : 1/15 as a unit rate is \(10:1\) .
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George is given two circles, circle O and circle X, as shown. If he wants toprove that the two circles are similar, what would be the correct second stepin his proof?Given: The radius of circle O is r, and the radius of circle X is .Prove: Circle Ois similar to circle X.1.C = 2rr and C'= 2rr' by the definition of circumference.2._3. d= 2rand d = 2r by the definition of diameter.d= 2r4. d'= 2r andby the division property of equality.5d=2rby the substitution property.and6. Circle Ois similar to circle Xbecause all the linear dimensions are in thesame proportion.
Answers
Answer: B
The correct second step for the given proof is;
\(\begin{gathered} \frac{C}{C^{\prime}}=\frac{2\pi r}{2\pi r^{\prime}} \\ and\text{;} \\ \frac{C}{C^{\prime}}=\frac{r}{r^{\prime}} \end{gathered}\)by the division property of equality.
Explanation:
We want to find the correct second step for the given proof.
Recall that from division property of equality, when we have;
a=b and c=d, dividing the equations by each other, the equation will still be equal;
\(\frac{a}{c}=\frac{b}{d}\)For the given Prove;
statement 1 states that the circumference circle 1 and 2 can be expressed as;
\(\begin{gathered} C=2\pi r \\ \text{and} \\ C^{\prime}=2\pi r^{\prime} \end{gathered}\)So, for step 2;
Applying the division property of equality, we have;
\(\begin{gathered} \frac{C}{C^{\prime}}=\frac{2\pi r}{2\pi r^{\prime}} \\ \text{which then equals;} \\ \frac{C}{C^{\prime}}=\frac{r}{r^{\prime}} \end{gathered}\)Therefore, the correct second step for the given proof is;
\(\begin{gathered} \frac{C}{C^{\prime}}=\frac{2\pi r}{2\pi r^{\prime}} \\ and\text{;} \\ \frac{C}{C^{\prime}}=\frac{r}{r^{\prime}} \end{gathered}\)by the division property of equality.
Please help worth 10 points is this true that line n is perpendicular to line p? I think the answer is C, is this correct or not?
Answers
Answer: A
because slope are
the price of broccoli is $1.25 per pound. let y be the total cost in dollars of buying x pounds of broccoli
which equation represents this situation
a, x=y+1.25
b. y= 1.25x
c. y= x+1.25
d. x= 1.25y
Answers
Explanation:
If you are trying to find out the total cost you would multiply the number of pounds you bought (x) by the cost per pound (1.25) in order to get ur answer
When you put it into the substitute equation
you’d get
y(total spent)= 1.25(cost per pound) x(number of pounds)
Hope this helped!
PLEASE HELP 50 POINTS!!
The sum of two consecutive numbers is 157. This equation, where n is the first number, represents the situation:
2n + 1 = 157.
What is the first number?
A. 77
B. 78
C. 79
D. 80
Answers
If u add them n+(n+1) you get 157
So,
n+n+1=157
2n=156
n=78
in what time will a sum of rs2000 amounts to rs2240 at 4% pa simple interest
Answers
Answer: The time it takes for a sum of money to amount to a certain amount at a certain interest rate can be calculated using the following formula:
Time = (100 x (Amount - Principal)) / (Principal x Rate)
In this case, the principal is Rs. 2000, the amount is Rs. 2240, and the rate is 4%. Therefore, the time is:
Time = (100 x (2240 - 2000)) / (2000 x 4) = 3 years
Therefore, it will take 3 years for Rs. 2000 to amount to Rs. 2240 at 4% simple interest.
Step-by-step explanation:
Evaluate and match each expression on the left to its value on the right, when x=6 and y=5
12 + x
3x + y
4y -10
(1)/(2)xy
Answers
Answer:
12 + x --> 18
3x + y --> 23
4y - 10 --> 10
(1)/(2)xy --> (1)/(60)
Step-by-step explanation:
Let's evaluate each expression with the given values of x=6 and y=5:
Expression: 12 + x
Substituting x=6 into the expression, we get: 12 + 6 = 18
Expression: 3x + y
Substituting x=6 and y=5 into the expression, we get: 3(6) + 5 = 18 + 5 = 23
Expression: 4y - 10
Substituting y=5 into the expression, we get: 4(5) - 10 = 20 - 10 = 10
Expression: (1)/(2)xy
Substituting x=6 and y=5 into the expression, we get: (1)/(2)(6)(5) = (1)/(2)(30) = (1)/(60)
The value of x, rounded to the nearest tenth is...
Answers
Answer:
67
Step-by-step explanation:
Demi has 221 songs on her phone. The songs take up 884 megabytes of storage. Each song takes up the same amount of space. How many megabytes do 135 of these songs take up?
Answers
Sienna buys a mystery pack of sparkly modeling clay. The pack has 5 colors, and there are 7 possible colors that are all equally likely. Sienna wants to know the probability that at least 2 of the colors will be the same. Which of the following is the best simulation? Explain your reason for your answer.
A. Roll a standard number cube 5 times for each trial. Let each number represent a different color. Run 50 trials and find the fraction of times that at least two of the same number are rolled.
B. Create a spinner with 5 equal sections. Label each section with a different color. Spin the spinner 7 times to see if it lands on the same color two or more times.
C. Create a spinner with 7 equal sections. Label each section with a different color. Spin the spinner 5 times for each trial. Run 50 trials and find the fraction of times the spinner lands on the same color two or more times.
D. Put 5 pieces of paper in a bag, each labeled with a different color. For each trial, randomly select and replace a paper 7 times. Run 50 trials and find the fraction of times that at least two of the same color appear.
Answers
The probability that at least 2 of the colors will be the same, the following is the best simulation is Option D Put 5 pieces of paper in a bag, each labeled with a different color. For each trial, randomly select and replace a paper 7 times. Run 50 trials and find the fraction of times that at least two of the same color appear.
Given, Sienna buys a mystery pack of sparkly modeling clay. The pack has 5 colors, and there are 7 possible colors that are all equally likely. We have to find the probability that at least 2 of the colors will be the same. There are 5 colors in the pack of clay, and 7 colors are possible in total.
So, the probability of picking any color at random is
P(picking a color) = 5/7 = 0.7143Let P(X = 2) be the probability that exactly 2 of the colors are the same.
Then, the probability that at least 2 of the colors are the same can be calculated by using the formula:
P(X ≥ 2) = 1 - P(X < 2).
The simulation method that can be used to find the probability of at least 2 of the colors will be the same in the mystery pack is option D.
Put 5 pieces of paper in a bag, each labeled with a different color. For each trial, randomly select and replace a paper 7 times. Run 50 trials and find the fraction of times that at least two of the same color appear.
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3x+25 what would x be
Answers
Answer:
8.3
Step-by-step explanation:
25/3= 8.3
so yes
Maggie wants to pack 20 cookies equally in boxes each box holds 5 cookies how many boxes does she need
Answers
Answer:
4 boxes
Step-by-step explanation:
20/5 is 4 therefore 4 boxes with 5 in each
Answer:
20/5 = 4
Step-by-step explanation:
She needs 4 boxes
What are the solutions to the equation 0=|3x+3|+3
Answers
Therefore, the solutions to the equation 0 = |3x + 3| + 3 are x = -2 and x = 0.
To solve the equation 0 = |3x + 3| + 3, we need to eliminate the absolute value. Remember that the absolute value of a number is always non-negative.
First, let's isolate the absolute value term on one side of the equation:
|3x + 3| = -3
Since the absolute value cannot be negative, there are no solutions to the equation as it stands. However, if we modify the equation to make the right side positive, we can find a solution.
To eliminate the absolute value, we can rewrite the equation as two separate equations, considering both the positive and negative cases:
3x + 3 = -3
-(3x + 3) = -3
Solving equation 1:
3x + 3 = -3
3x = -6
x = -2
Solving equation 2:
-(3x + 3) = -3
-3x - 3 = -3
-3x = 0
x = 0
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Of the delegates at a convention, 60% attended the breakfast forum, 70% attended the dinner speech and 40% attended both events. If a randomly selected delegate is known to have attended the dinner speech, the probability that he also attended the breakfast forum is
Answers
Answer:
The probability that he also attended the breakfast forum is is 0.5714 = 57.14%.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)
In which
P(B|A) is the probability of event B happening, given that A happened.
\(P(A \cap B)\) is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Attended the dinner speech.
Event B: Attended the breakfast forum.
70% attended the dinner speech
This means that \(P(A) = 0.7\)
40% attended both events.
This means that \(P(A \cap B) = 0.4\)
The probability that he also attended the breakfast forum is
\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.4}{0.7} = 0.5714\)
The probability that he also attended the breakfast forum is is 0.5714 = 57.14%.
If g(x) = 2x - 4), find the value of xf g(x) = 20. 12 points)
Answers
Answer:
x = 12
Step-by-step explanation:
g(x)= 2x-4
g(x)= 20
Therefore,
2x-4 = 20
Bringing -4 to the other side it becomes positive,so..
2x= 20+4
= 24
x =24/2
= 12
WILL GIVE BRAINLIEST! FAST!! Which expression represents 7y(8y)?
15y
56y
56y2
15y2
Answers
Answer:
56y²
Step-by-step explanation:
Given expression:
\(7y(8y)\)
Remove the parentheses:
\(\implies 7y \cdot 8y\)
Multiply the numbers:
\(\implies 56 \cdot y \cdot y\)
Apply the exponent rule: a = a¹
\(\implies 56 \cdot y^1 \cdot y^1\)
\(\textsf{Apply exponent rule}: \quad a^b \cdot a^c=a^{b+c}\)
\(\implies 56 \cdot y^{1+1}\)
Simplify:
\(\implies 56 \cdot y^{2}\)
\(\implies 56 y^{2}\)
A book is 9 inches wide and 13.5 inches tall.
What will the area of the front of the book?
Answers
Answer:
121.5
Step-by-step explanation: so what u are supost to do is multiply the sides which will give you your answer of 121.5.
Answer:
\(area = (l \times w) \\ = (13.5 \times 9) \\ = 121.5 \: {inches}^{2} \)
Classify the polynomial by degree and number of terms: 3x ^ 4 - 3x ^ 2 - 7x
Cubic Binomial
Quintic Trinomial
Cubic Trinomial
Quartic Trinomial
Answers
The polynomial 3x^4 - 3x^2 - 7x is classified as a Cubic Trinomial.
The polynomial 3x^4 - 3x^2 - 7x can be classified as a Cubic Trinomial.
Here's the breakdown of the classification:
Degree: The highest power of the variable x is 4, so the degree of the polynomial is 4. Since the degree is 4, the polynomial is not cubic (which would have a degree of 3) or quintic (which would have a degree of 5).
Number of terms: The polynomial consists of three terms: 3x^4, -3x^2, and -7x. A polynomial with three terms is called a trinomial.
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Answer:Quartic trinomial
Step-by-step explanation:
Don't listen to the other guy, I put cubic and I got the answer wrong thanks to the other guy.
What is the fraction equivalent to 488%? on edge help due soon
Answers
Answer:
122/25
Step-by-step explanation:
488/100 percent means out of 100
find the lowest common multiple for 488 and 100 which is 4
divide numerator(488) and denominator(100) by 4
488÷4=122
100÷4=25
How would I solve this problem?
Answers
Answer:
\(2x^2\\\\\)
Step by step explanation:
\(y=\displaystyle \int_{0}^x 2t^2 dt=\dfrac 23\left[t^3\right]^{x}_0=\dfrac 23 x^3\\\\\ y'= \dfrac 23 \cdot 3x^2 = 2x^2\)
Help me pleaseeeeee
Question:
1. Describe a situation or a case btw 2 people then rephrase it to show empathy
Answers
According to the information, It's important to acknowledge both of their perspectives and try to find a way to resolve the situation and move forward positively.
What is the situation?The situation is: two friends are having an argument because one of them forgot to invite the other to a party.
Situation with empathyI can imagine that it must be really difficult for both of your friends right now. One of them might be feeling hurt and left out because they didn't get an invitation to the party, while the other might be feeling guilty and regretful for forgetting to invite them. It's important to acknowledge both of their perspectives and try to find a way to resolve the situation and move forward positively.
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50 POINTS !!
PLEASE HELP !! ILL GIVE BRAINLIEST TO THE RIGHT ANSWERS.
Answers
Answer:
sqrt41
Step-by-step explanation:
a^2+b^2=c^2
25+16=41
sqrt41
Answer:
6.40312
Step-by-step explanation:
need as soon a posible within 2 minutes enjoy your points
Answers
Answer:
(x+6)^2+(y-7)^2= 29
Step-by-step explanation:
general exqn-> (x-h)^2+(y-k)^2=(r)^2
here, h= -6 and k=7
r= √ 29
Therefore, exqn of circle=
(x+6)^2+(y-7)^2= 29
Answer:
(x + 6)² + (y - 7)² = 29
Step-by-step explanation:
the equation of a circle in standard form is
(x - h )² + (y - k )² = r²
where (h, k ) are the coordinates of the centre and r is the radius
here (h, k ) = (- 6, 7 ) and r = \(\sqrt{29}\) , then
(x - (- 6) )² + (y - 7)² = (\(\sqrt{29}\) )² , that is
(x + 6 )² + (y - 7 )² = 29
A certain field is a rectangle with a perimeter of 858 feet. The length is 187 feet more than the width. Find the width and length of the rectangular field.
Answers
Width:242
I’m 75% sure in my answer
What is the area of triangle ABC? pls help i need to pass this test!!
Answers
Answer:
Step-by-step explanation:
A distribution with three or more peaks is said to be
Answers
When a distribution has three or more peaks then it is said to be a multimodal distribution .
What are the types of distributions ?In histograms, there are often three types of distributions which are classified according to the number of peaks that they have . A unimodal distribution would be a histogram that has a single peak in its distribution .
Then there are binomial distributions which boast of having two peaks , Then finally, there is the multimodal distribution which is for all distributions with either three peaks, or more than that .
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The tables show proportional relationships. Find the constant of
proportionality, k. Write an equation to represent the relationship
between the two quantities. Tell what each variable represents. PLS HELP. 16 points
Answers
Answer:
If the ratio of one variable to the other is constant, then the two variables have a proportional relationship,
If x and y have a proportional relationship, the constant of proportionality is the ratio of y to x.
In this section, you will learn, how to find the constant of proportionality from a table which contains the values of x and y.
Step-by-step explanation:
I hope that helps, I'm so sorry if it doesn't
Kurt is running for student senate. He designed the t-shirt logo for his campaign. The logo is made up of a square with 14 cm sides and four half circles. Use 3.14 for pi to approximate the area of the logo.
Answers
Answer:
......
Step-by-step explanation:
A rectangle has a perimeter of 14 cm and length x cm. show that the width of the rectangle is (7-x)cm and hence that the area A of the rectangle is given by the formula A= x(7-x). Draw the graph, plotting x on the horizontal axis with a scale of 2cm to 1 unit, and A on the vertical axis with a scale of 1cm to 1 unit
take x from 0 to 7. From the graph find:
a) the area of the rectangle when x = 2.25cm
b) the dimensions of the rectangle when its area is 9cm^2
c) the maximum area of the rectangle
d) the length and width of the rectangle corresponding to the maximum area
e) what shape of the rectangle has the largest area
Answers
Answer:
B
Step-by-step explanation:
the dimensions of the rectangle when its area is 9cm^2
n the figure at the right UV || BJ || QL, BQ = 6, UL = 3y - 1 , VB = y + 2 and UJ = y + 5 then y =
Answers
Answer:
s
Step-by-step explanation: