Answer:
10,219 bacteria
Step-by-step explanation:
In this question, we are asked to calculate the population of bacteria in a culture given the formula for the population increase.
From the question, we know the formula to use is
Pt=Po*2^t/d
From the parameters in the question, we identify that Pt is ?, Po is 8300 bacteria , t is 3 hours and d is 10 hours which is the doubling time. Inserting these figures we have;
Pt = 8300 * 2^(3/10)
Pt = 8300 * 2^0.3
Pt = 10,218.5
Pt = 10,219 bacteria to the nearest whole number
Answer:
10218
Step-by-step explanation:
A culture of bacteria has an initial population of 8300 bacteria and doubles every 10 hours. Using the formula P_t = P_0\cdot 2^{\frac{t}{d}}P
t
=P
0
⋅2
d
t
, where P_tP
t
is the population after t hours, P_0P
0
is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 3 hours, to the nearest whole number?
P_0=8300
P
0
=8300
The initial population
t=3
t=3
Time elapsed
d=10
d=10
The doubling time
P_t = P_0\cdot 2^{\frac{t}{d}}
P
t
=P
0
⋅2
d
t
P_t=8300\cdot 2^\frac{3}{10}
P
t
=8300⋅2
10
3
Plug in
P_t=10218.4986\approx10218
P
t
=10218.4986≈10218
Use parenthesis in the calculator for the exponent
10218
Toby wants a paintbrush that costs $2.70, a set of paints that costs $15.45, and an easel that costs $22.90. Toby already has $1.00. How much more money does Toby need?
Answer:
$40.05
Step-by-step explanation:
You would add up 2.70+15.45+22.90 then, subtract the total by 1.00
Answer:
40.05
Step-by-step explanation:
you basically add up all the prices then subtract the 1 dollar the he has and u get ur answer
If anyone could answer these
What is the next term of the geometric sequence?
72,36, 18,
Answer:
9
Step-by-step explanation:
To find the common ratio, take the second term and divide by the first
36/72 = 1/2
To find the next term, take the last term and multiply by the common ratio
18*1/2 = 9
Answer:
9.
Step-by-step explanation:
The common ratio = 36/72 = 18/36 = 1/2.
So the next term is 18 * 1/2 = 9.
Richard and Linda enjoy visiting Hilton Head Island, South Carolina. The distance from their home to Hilton Head is 813 mi, so the drive takes them days. Richard and Linda travel twice as far the first day as they do the second day. How many miles do they travel each day?
Answer:
distance travelled first day is 542 miles while that travelled on second day = 271 miles.
Step-by-step explanation:
please kindly see the attached files for details
Richard and Linda travel 542 miles on the first day and 271 miles on the second day to reach Hilton Head Island, with the total distance being 813 miles.
Explanation:The student's question pertains to splitting a total distance into two parts, with a given ratio between the two parts. Since Richard and Linda travel twice as far on the first day as the second day, we can let the distance traveled on the second day be x miles. Therefore, the distance they travel on the first day would be 2x miles.
The total distance traveled to Hilton Head is 813 miles, so we can write an equation based on the sum of the distances traveled on both days: 2x (first day) + x (second day) = 813 miles. Simplifying this equation, we have 3x = 813 miles. Dividing both sides of the equation by 3 yields x = 271 miles.
This means that Richard and Linda travel 271 miles on the second day and 2 * 271 miles, which is 542 miles, on the first day. So, the distances Richard and Linda travel to Hilton Head Island on the first and second days are 542 miles and 271 miles, respectively.
The scale on a map reads 1/2 inch = 75 miles. If the distance between two cities on the map is 3 and 1/4 inches, find the actual distance between the cities
Answer:
487.5 miles
Step-by-step explanation:
The actual distance between the cities is 487.5 miles.
What is Proportion?Two or more ratios made to be equivalent to each other is termed as the method of proportion.
That is, if 'a' related to 'b' is proportional to 'p' related to 'q', then,
a : b : : p : q
⇒ a/b = p/q
⇒ aq = bp
Here we have the scale on a map reads 1/2 inch as 75 miles.
We have to find the actual distance of two cities if the distance between the cities in the map is 3 and 1/4 inches.
3 and 1/4 inches = (3 × 4 + 1) / 4 = 13/4 inches.
Let x be the actual distance between the cities.
Using proportion,
1/2 : 75 : : 13/4 : x
[tex]\frac{1/2}{75}[/tex] = [tex]\frac{13/4}{x}[/tex]
1/2 × x = 13/4 × 75
1/2 × x = 243.75
x = 487.5
Hence the actual distance between the cities is 487.5 miles.
To learn more about Proportions, click:
https://brainly.com/question/29774220
#SPJ5
help pls!!!!!!!!!!! i don't know how to attempt
Answer:16
Step-by-step explanation:AC is half of ED
Evaluate 4 - 2f when f = 1.
Answer:
2
Step-by-step explanation:
4 -2f
Let f =1
4 - 2(1)
Multiply and divide first
4 -2
2
Country A has a growth rate of 4.9% per year. The population is currently 4 comma 151,000, and the land area of Country A is 14,000,000,000 square yards. Assuming this growth rate continues and is exponential, after how long will there be one person for every square yard of land?
Answer:
There will be one person on 1 square yard of land after 1,892,147.588 years.
Step-by-step explanation:
Continuous exponential growth formula:
[tex]P(t)=Pe^{rt}[/tex]
P(t)= Population after t years.
P= Initial population
r=rate of growth.
t= time in year
Given that,
Growth rate of country A (r)= 4.9% per year=0.049 per year.
Initial population (P)= 151,000.
Land area of country area= 14,000,000,000 square yards.
There will be one person on one square yard of land.
So, there will be 14,000,000,000 person for 14,000,000,000 square yard of land in country A.
P(t)=14,000,000,000 person
[tex]\therefore 14,000,000,000= 151,000 e^{0.049t}[/tex]
[tex]\Rightarrow e^{0.049t}=\frac{ 14,000,000,000}{ 151,000}[/tex]
Taking ln both sides
[tex]\Rightarrow ln|e^{0.049t}|=ln|\frac{ 14,000,000,000}{ 151,000}|[/tex]
[tex]\Rightarrow {0.049t}=ln|\frac{ 14,000,000,000}{ 151,000}|[/tex]
[tex]\Rightarrow t}=\frac{ln|\frac{ 14,000,000,000}{ 151,000}|}{0.049}[/tex]
[tex]\Rightarrow t}=1,892,147.588[/tex] years
There will be one person for every square yard of land after 1,892,147.588 years.
Un triángulo isósceles ,la altura al lado desigual mide 1 cm mas que longitud de ese lado . Calcula el valor de dicha altura sabiendo que el area es de 6 cm²
Answer:
Hence the required dimension is 4cm.
Step-by-step explanation:
Given:
An Isosceles triangle with uneven side=l+1 cm
Area= 6 sq cm
To Find:
Height of Triangle.
Solution:
We know that area of triangle given by,
Area=1/2*base*height.
Here height =1+base
6=1/2((b+1)*b
12=(b+1)*b.
b^2+b-12=0
(b-3)(b+4)=0
b=3 or b=-4
So length never be negative
so b=3 cm
And height=b+1=3+1=4 cm.
Find the slope of the line through (–9, –10) and (–2, –5). A. –five-sevenths B. seven-fifths C. five-sevenths D. –negative seven-fifths (please help much aprecciated)
Answer:
C 5/7
Step-by-step explanation:
We can find the slope of a line using
m = (y2-y1)/(x2-x1)
= (-5 - -10) /(-2 - -9)
= (-5 +10)/(-2+9)
5/7
The table displays the scores of students on a recent exam. Find
the mean of the scores to the nearest 10th.
Score Number of Students
80
85
6
90
95
100
6
8
Summary:
pls I need a summary asap
The mean is 59
Add all the scores together, then divide by the number of test scores
The mean of the scores to the nearest 10th Score Number of Students is 59.
We have given a data,
80,85,6,90,95,100,6,8
What is the meaning of mean?
Mean is the adding all the scores together, then divide by the number of test scores.
So we have given a data,
80,85,6,90,95,100,6,8
80+85+6+90+95+100+6+8=470
The number of of test scores=8
[tex]mean=\frac{470}{8}=58.75[/tex]
Mean≈59
To learn more about the mean visit:
https://brainly.com/question/1136789
A container contains a large unspecified number of ping-pong balls. A student takes 80 balls from the container, marks them with a blue dot, returns the marked balls to the container, and thoroughly mixes the balls. She then takes 80 balls again from the container. Of these, 16 have blue dots. She now wants to use this data to estimate the total number of ping-pong balls in the container. What is an estimate for the number of ping-pong balls in the container?
Answer:
400 ping pong balls
Step-by-step explanation:
Let the total number of ping pong balls =x
Out of x ping pong balls, 80 are marked with a blue dot
Out of 80 ping pong balls, 16 are marked with a blue dot.
Expressing it as a ratio:
x:80=80:16
[tex]\frac{x}{80}=\frac{80}{16}\\ 16x=80X80\\x=6400 \div 16\\x=400[/tex]
There are an estimate of 400 ping pong balls in the container.
A dot plot titled seventh grade test score. There are 0 dots above 5, 6, 7, 8 and 9, 1 dot above 10, 1 dot above 11, 2 dots above 12, 1 dot above 13, 1 dot above 14, 2 dots above 15, 3 dots above 16, 3 dots above 17, 2 dots above 18, 2 dots above 19, 3 dots above 20. A dot plot titled 5th grade test score. There are 0 dots above 5, 6, and 7, 1 dot above 8, 2 dots above 9, 10, 11, 12, and 13, 1 dot above 14, 3 dots above 15, 2 dots above 16, 1 dot above 17, 2 dots above 18, 1 dot above 19, and 1 dot above 20.
Students in 7th grade took a standardized math test that they also had taken in 5th grade. The results are shown on the dot plot, with the most recent data shown first.
Which statement is true?
Both data sets have a gap.
Both data sets have the same median.
Both plots have the same mode.
Both data sets have the same number of data points.
Answer:
D. Both data sets have the same number of data points.
Step-by-step explanation:
Answer:
itd d on egeunity
Step-by-step explanation:
A tree grows 6 feet per year. Which rates are equivalent to 6 feet per year? Select all that apply. A. 2 inches per year B. 18 inches per year C. 12 feet in 4 years D. 72 inches per year E. 2 yards per year F.18 feet in 3 years
Answer:
D is correct E is correct F is correct
Step-by-step explanation:
72/12=6 ft per year
2 yards= 6 ft per year
18/3=6 ft per year
The equivalent rates to 6 feet per year are 18 inches per year, 12 feet in 4 years, 72 inches per year, 2 yards per year, and 18 feet in 3 years.
Explanation:The student is asking about equivalent rates. To determine which rates are equivalent to 6 feet per year, we need to compare each option against the given rate. The conversion factors needed for this problem are:
1 foot = 12 inches1 yard = 3 feetOption A: 2 inches per year is not equivalent to 6 feet per year.
Option B: 18 inches per year is equivalent to 6 feet per year because 18 inches is 1.5 feet, and thus, 1.5 feet multiplied by 4 would give us 6 feet in 4 years.
Option C: 12 feet in 4 years is equivalent to 6 feet per year because dividing 12 feet by 4 years gives us 3 feet per year, which is half of the given rate.
Option D: 72 inches per year is equivalent to 6 feet per year because 72 divided by 12 is 6.
Option E: 2 yards per year is equivalent to 6 feet per year because 2 multiplied by 3 is 6.
Option F: 18 feet in 3 years is equivalent to 6 feet per year because dividing 18 feet by 3 years gives us 6 feet per year.
Thus, the equivalent rates to 6 feet per year from the options given are 18 inches per year, 12 feet in 4 years, 72 inches per year, 2 yards per year, and 18 feet in 3 years.
Learn more about Equivalent Rates here:
https://brainly.com/question/14248389
#SPJ2
Consider the graph below.
Which of the following is the function represented
by the graph?
y=(x+3)-5
2
*5
*
x
+
5
DONE
ONANODOTTI
Answer:
y=−259x+8
Step-by-step explanation:
i think this might be the answer but not sure
Answer:D
Step-by-step explanation:
Given that segment US and segment RU are equidistant from the center, determine the value of m in the circle below.
Leave your answer in fraction form.
m = _____
Answer:
7/4
Step-by-step explanation:
We know that US = RU, so we can just set those expressions equal to each other.
US = 3m + 2
RU = -m + 9
US = RU ⇒ 3m + 2 = -m + 9 ⇒ 4m = 7 ⇒ m = 7/4
Hope this helps!
Answer:
7/4 or 1¾
Step-by-step explanation:
Since US = UR
3m + 2 = -m + 9
4m = 7
m = 7/4
m = 1¾
7. A travel website wants to gauge the perceived quality of a major airport. The maximum possible rating is 10, and the results of a random sample of 50 travelers can be found in the Airport.xlsx file. Develop a 95% confidence interval estimate of the population mean rating for the airport based upon this data.
Answer:
The 95% confidence interval has Minimum = 6.053 and Maximum = 7.467
Step-by-step explanation:
Here we have
Data as
1 5 6 7 8 8 8 9 9 9 9 10 3 4 5 5 7 6 8 9 10 5 4 6 5 7 3 1 9 8 8 9 9 10 7 6 4 8 10 2 5 1 8 6 9 6 8 8 10 10
The sum is 338
∴ Mean, [tex]\bar x[/tex] = 6.76, Standard Deviation, s = 2.55
Sample size, n = 50
For a 95% confidence interval, we have
[tex]CI=\bar{x}\pm z\frac{s}{\sqrt{n}}[/tex]
Where z is;
z at 95% z = [tex]\pm[/tex]1.96
Therefore, we have
95% confidence interval as Minimum = 6.053 to Maximum = 7.467.
I will give you all my points and mark you the brainliest! Please help
Answer and Step-by-step explanation:
Since this is a quadrilateral, we know that all the angles will add up to 360 degrees (by definition). We are given that angle A is 90 degrees and that the ratio of A to B is 5 to 3. This means that we can set up a proportion and solve for B:
A/B = 5/3 ⇒ 90/B = 5/3 ⇒ 5B = 270 ⇒ B = 54
So, we know that angle B is 54 degrees.
Now that we know angle B is 54 and A is 90, we can find the sum of the remaining two angles X and Y because A + B + X + Y = 360:
90 + 54 + X + Y = 360
X + Y = 216 degrees
We also know that the ratio of X to Y is 1 to 3, so we can set up another proportion:
X/Y = 1/3 ⇒ Y = 3X
Substitute 3X in for Y in X + Y = 216:
X + 3X = 216
4X = 216
X = 54
Thus, we see that both angles B and X equal 54, so B = X.
Hope this helps!
Answer:
[tex]\frac{a}{b}=\frac{5}{3}=>b=\frac{3a}{5}=\frac{270}{5}=54 \\\\x+y=360-(90+54)=360-144=216\\\\\frac{x}{y}=\frac{1}{3}=>y=3x\\ \\x+3x=216\\\\4x=216\\\\x=216:4\\\\x=54\\\\x=b\\[/tex]
Convert 30 to radians. Leave answer as a reduced fraction in terms of pi
Answer:
[tex]\frac{\pi }{6}[/tex]
Step-by-step explanation:
[tex]\frac{\pi}{180}[/tex] = [tex]\frac{x}{30}[/tex]
180x = 30π
x = [tex]\frac{30\pi }{180}[/tex]
x = [tex]\frac{3\pi }{18}[/tex]
x= [tex]\frac{\pi}{6}[/tex]
Complete the division. The remainder is 0. The quotient is
X^2 - X - 12
-X^2 + x + 12
12x^2 - X-1
12x^2 + x + 1
Answer:
The first option....x^2-x-12
Step-by-step explanation:
Answer: x^2-x-12
Step-by-step explanation: correct answer
A fountain in the park has two circular pools that are the same size. What is the total area of the pools if the radius is 3 yards? Use 3.14 for Pi and round the approximate area to the nearest tenth, if necessary. Check all that apply.
Answer:
56.6 square yards.
Step-by-step explanation:
Given:
A fountain in the park has two circular pools that are the same size.
Question asked:
What is the total area of the pools if the radius is 3 yards ?
Solution:
First of all we will calculate the area of a circular pool.
As we know:
[tex]Area\ of\ circle=\pi r^{2}[/tex]
[tex]=\frac{22}{7} \times(3)^{2} \\ \\ =\frac{22}{7}\times9\\ \\ =\frac{198}{7} \\ \\ =28.28\ square\ yards[/tex]
Area of circular pool nearest tenth = 28.3 square yards
Now, as given that both pools are of same size.
Total area of the pools = 28.3 square yards + 28.3 square yards
= 56.6 square yards.
Thus, the total area of the pools are 56.6 square yards.
Answer:
ur answer is 56.5 and 18
Step-by-step explanation:
y= 0.216 x + 32.575
what is the slope
Given:
The given equation of the line is [tex]y=0.216x+32.575[/tex]
We need to determine the slope of the equation.
Slope:
Let us determine the slope of the equation.
The general form of the equation of the line is given by
[tex]y=mx+b[/tex]
where m is the slope of the equation and b is the y - intercept.
Now, we shall compare the general form of the equation of the line with the given equation, we have;
[tex]m= 0.216[/tex] and [tex]b=32.575[/tex]
Thus, the slope of the equation of the line is [tex]m= 0.216[/tex]
the slope is 0.216
And just in case you need it the y-intercept is 32.575
I hope this was helpful :)
Find the volume of this prism
Answer:
840cm cubed
Step-by-step explanation:
720+120
A backyard pool has a concrete walkway around it that is 3 feet wide on all sides. The total area of the pool and the walkway is 950 ft2. If the length of the pool is 8 feet longer than the width, find the dimensions of the pool.
Answer:
[tex]x \approx 21.080\,ft[/tex], [tex]y = 29.080\,ft[/tex]
Step-by-step explanation:
The total area of the pool and the walkway is:
[tex](x + 6\,ft)\cdot (y + 6\,ft) = 950\,ft^{2}[/tex]
[tex](x + 6\,ft)\cdot (x + 14\,ft) = 950\,ft^{2}[/tex]
[tex]x^{2} + 20\cdot x + 84\,ft^{2} = 950\,ft^{2}[/tex]
[tex]x^{2} + 20\cdot x - 866\,ft^{2} = 0[/tex]
The roots of the second-order polynomial is:
[tex]x_{1} \approx 21.080\,ft[/tex] and [tex]x_{2} \approx -41.081\,ft[/tex]
The only possible root is:
[tex]x \approx 21.080\,ft[/tex]
The other dimension of the pool is:
[tex]y = x + 8\,ft[/tex]
[tex]y = 21.080\,ft + 8\,ft[/tex]
[tex]y = 29.080\,ft[/tex]
This is due, in part, to damage from the first episode. The performance of a new drug designed to prevent a second episode is to be tested for its effectiveness in preventing a second episode. In order to do this two groups of people suffering a first episode are selected. There are 163 people in the first group and this group will be administered the new drug. There are 160 people in the second group and this group wil be administered a placebo. After one year, 13% of the first group has a second episode and 14% of the second group has a second episode. Select a 90% confidence interval for the difference in true proportion of the two groups.
Answer:
Δπ Min = -0.0709
Δπ Max = -0.0535
Step-by-step explanation:
Here we have
[tex]z=\frac{(\hat{p_{1}}-\hat{p_{2}})-(\mu_{1}-\mu _{2} )}{\sqrt{\frac{\hat{p_{1}}(1-\hat{p_{1}}) }{n_{1}}-\frac{\hat{p_{2}}(1-\hat{p_{2}})}{n_{2}}}}[/tex]
Where:
[tex]{\hat{p_{1}}[/tex] = 13% = 0.13
[tex]\hat p_{2}[/tex] = 14% = 0.14
n₁ = 163
n₂ = 160
Therefore, we have;
[tex]z=\frac{(\hat{p_{1}}-\hat{p_{2}})}{\sqrt{\frac{\hat{p_{1}}(1-\hat{p_{1}}) }{n_{1}}-\frac{\hat{p_{2}}(1-\hat{p_{2}})}{n_{2}}}}[/tex]
Plugging the values gives
z = -0.263
CI 90% = critical z = [tex]\pm[/tex]1.644
The minimum difference in true proportion = -0.0709
The maximum difference in true proportion = 0.0535.
READ CAREFULLY! :)
John is putting a fence around his garden that is shaped like a half circle and a rectangle
Answer:
46 feet
Step-by-step explanation:
Perimeter of rectangle needed =
[tex]14+14+7= 35\\[/tex]
Half of the circumference of a circle needed =
[tex]\frac{1}{2} \pi d = \frac{1}{2} * \frac{22}{7} * 7= 11[/tex]
Total perimeter needed =
[tex]35 + 11=46[/tex]
Answer:
46 ft
Step-by-step explanation:
John will need to put a fence along 3 sides of the rectangle: 14 ft, 7 ft, 14 ft
He also needs to put a fence along the half circle:
C (circumference) = 2×π×r = π×d
⇒C÷2 = π×d÷2 = 22/7×7÷2 = 22÷2 = 11 ft
Together: 14 + 7 + 14 + 11 = 46 ft
An isosceles triangle has an angle that measures 70°. Which other angles could be in that isosceles triangle? Choose all that apply. 40 55 70 1-
Answer:
This depends on the way the triangle
Step-by-step explanation:
Anyway angles that apply includes: 55 and 70
Select the expression that represents the additive inverse of 6. A. 1/6 B. -1/6 C. -(-6) D. -6
Answer:
D. -6.
Step-by-step explanation:
The inverse is the number when added to 6 results in 0.
So it is 0 - 6 = -6. (6 + -6 = 0)
Answer:
C
Step-by-step explanation: I big brain
A square pizza box has a width of 24”. What it the area of the largest circular pizza that could fit in the box?
Answer:
452.16 inches squared
Step-by-step explanation:
Answer:
452.39 in.^2
Step-by-step explanation:
since the width of the box is 24, the diameter of the circles is also 24.
using 12 as the radius, we plug it into the equation pi(12)^2 and we get 452.39 in^2
In a recent survey of monetary donations made by 489 college graduates, the following information was obtained. 95 has donated to a political campaign, 76 had donated to assist medical research, 133 had donated to preserve the environment, 25 had donated to all three, 38 had donated to a political campaign and to medical research, 46 had donated to medical research and to preserve the environment, and 54 donated to a political campaign and to preserve the environment.
(a) How many college graduates donated to none of the listed causes?
(b) What percent of the college graduates donated to exactly one of the three listed causes?
Answer:
Step-by-step explanation:
The Venn diagram representing this situation is shown in the attached photo.
P represents the set of college graduates that donated to a political campaign.
M represents the set of college graduates that donated to assist medical research.
E represents the set of college graduates that donated to preserve the environment.
From the diagram,
The number of college graduates that donated to all three is 25
The number of college graduates that donated to a political campaign and medical research only is
38 - 25 = 13
The number of college graduates that donated to a political campaign and preserve the environment only is
54 - 25 = 29
The number of college graduates that donated to medical research and to preserve the environment only is 46 - 25 = 21
The number of college graduates that donated to a political campaign only is
95 - (29 + 25 + 13) = 28
The number of college graduates that donated to medical research only is
76 - (13 + 25 + 21) = 17
The number of college graduates that donated to preserve the environment only is
133 - (29 + 25 + 21) = 58
a) the number of college graduates that donated to none is
489 - (28 + 17 + 58 + 13 + 21 + 29 + 25)
= 298 college graduates
b) the number of college graduates that donated to exactly one of the three listed causes is
28 + 17 + 58 = 103
The percentage would be
103/489 × 100 = 21.1%