Answer: D. p(d) = 3(10000)p
Step-by-step explanation:
The function is p(d) = 3(10000)p, where p is the bacteria population and the number of days, d. The correct answer would be option (D).
What are the functions?The function is defined as a mathematical expression that defines a relationship between one variable and another variable.
As per the given situation, we can write the function would be as:
⇒ p(d) = 3(10000)p
It states that the population of the bacteria, p, is equal to the starting population of 10,000 multiplied by 3 number of days, d. This function correctly represents the idea that the population triples each day.
Hence, the correct answer would be an option (D).
Learn more about the functions here:
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Molly wants to buy a skirt. The original price was $40.The skirt is on sale for 12% off. When she goes to pay for it the cashier tells her she can have an additional 13% discount off the sale price, how much will Molly pay for the skirt?
Answer:
$30.62
Step-by-step explanation:
12% of 40 is 4.8
(10% is 4, 2% is 0.8)
40- 4.8= 35.2
13% of 35.2 is 4.576
(10% is 3.52, 3% is 1.056)
35.2- 4.576= 30.624
then rounded to 2 decimal places
30.62
From a class of 25 students how many group of 4
Answer: Well, 4 groups of four, and roughly 6 student in a group
Step-by-step explanation:
The question is not clear, but 25 divided by 4 is 6.25, but it’s students so 6 or 7.
Given the formula, Sn=a 1-r^n/1-r, what is the sum of the first nine terms of the geometric series: 324, -108, 36, -12...
If necessary, round to the hundredths place. (2 places after the decimal)
Answer:
243.01.
Step-by-step explanation:
The first term (a) = 324.
The common ratio (r) = -108/324 = -1/3.
So sum of 9 terms is:
S(9) = 324 * (1 - (-1/3)^9) / ( 1 - (-1/3)
= 324 ( 1 - (-0.00005076)) / 4/3
= 324 * 1.00005076 / 1.33333
= 243.012.
expand and simplify (2x-1)(x-3)
Answer:
Expand the polynomial using the FOIL method.
2 x 2 − 7 x + 3
Step-by-step explanation:
A technique for distributing two binomials. The letters FOIL stand for First, Outer, Inner, Last. First means multiply the terms which occur first in each binomial, Outer means multiply the outermost terms in the product, Inner means multiply the innermost terms, and Last means multiply the terms which occur last in each binomial.
An algebraic expression consisting of one or more summed terms, each term consisting of a constant multiplier and one or more variables raised to integral powers.
The smallest multiple of 13 is
Answer:
0
Step-by-step explanation:
The smallest (greater or equal to zero) multiple of 13 is 0
to get a positive multiple of 13 you have to multiply 13 by a natural number:
0 = 13×0
13 = 13×1
26 = 13×2
.
.
.
then the smallest one is 0.
Find the height of the cylinder if the volume is 225 yard and diameter is 5 yd
Answer:
2.86 yards
Step-by-step explanation:
Height = volume/parameter
Parameter = 1/2 diameter * pi
Height = 225 / parameter
Height=2.86
ice, as long as it stays in its frozen form, will not lose its shape or its volume. Why?
solid form
Step-by-step explanation:
it will not loose shape because it is in solid form
Answer:
It freezes it self in the solid state
Step-by-step explanation:
if a cube measures 5.3 cm on each side and has a mass of 280 grams how much is its volume
Answer:
8.1 g/cm
Step-by-step explanation:
What is the solution to the equation StartFraction m Over m + 4 EndFraction + StartFraction 4 Over 4 minus m EndFraction = StartFraction m squared Over m squared minus 16 EndFraction?
Answer: m = -2.
The given equation is: [tex]\frac{m}{m+4}+\frac{4}{4-m}=\frac{m^{2}}{m^{2}-16}[/tex].
The LCM of the denominators = [tex]m^{2}-16=(m+4)(m-4)[/tex].
We multiply both sides by LCM.
[tex]\left(m+4\right)\left(m-4\right)\left(\frac{m}{m+4}+\frac{4}{4-m}\right)=\left(m+4\right)\left(m-4\right)\cdot\frac{m^{2}}{m^{2}-16}[/tex]
[tex]m\left(m-4\right)-4\left(m+4\right)=m^{2}[/tex]
[tex]m^{2}-4m-4m-16=m^{2}[/tex]
[tex]8m=-16\\m=-2[/tex]
Learn more: https://brainly.com/question/13769924
Answer:
M=-2 B
Step-by-step explanation:
trust me i took the quiz
What is the approximate area of a circle with diameter 6?
Answer: 28.27
Step-by-step explanation:
First, you can turn the diameter into a radius, giving you 3. Since the equation of an area in a circle is A=πr^2, you must square 3, giving you 9. Now you must multiply 9 with Pi, which is 3.14159265358, but just 3.14 for short. With that, you get about 28.27 as area.
The area of Jamie's square backyard is 64 square meters. What is the length of one side of Jamie's backyard? Please Answer this asap bc I have to get this turned in, in about 10 mins please hurry
Answer:
8 meters
Step-by-step explanation:
Since the 4 sides of a square are all equal, the area of a square can be found using:
a=s*s or
a=s^2
We know that the area is 64 square meters, so we can substitute 64 in for a
64=s^2
We are trying to find a side, s, so we have to get s by itself. Since s is being squared, take the square root of both sides. This will cancel out the exponent, and leave s by itself.
[tex]\sqrt{64}=\sqrt{s^2}[/tex]
8=s
So, one side of the backyard is 8 meters
if a sample of 57 swimmers is taken from a population of 135 swimmers, the population mean is the mean of how many swimmers' times?
Answer:
135
Step-by-step explanation:
A P E X
the atlantic ocean is 2.78×10^4 feet deep at it's lowest point. If a scuba diver dives 1/50 of the total depth of the ocean, enter how many feets he dove down?
Answer:
556 feet
Step-by-step explanation:
What you have to do to get the answer is find out what 10^4 is, and then multiply that by 2.78. After that, you just need to divide it by 50.
10^4 = 10,000
2.78 × 10,000 = 27,800
27,800 ÷ 50 = 556
Answer:
556
Step-by-step explanation:
The picture shows a cement bag of weight Fg hanging from a rope which itself is supported by two other ropes attached to a ceiling. The latter two ropes make an angle θ1 and θ2 with the ceiling. Determine the tension in each rope. Use the angle addition identity to simplify your result: sin(α ± β) = sin α cos β ± cos α sin β
Answer:
[tex]T_1= \dfrac{F_gcos \theta_2}{sin (\theta_1+\theta_2)}[/tex]
Step-by-step explanation:
From the free body diagram attached below; we will see that
T₃ = Fg ------ (1)
Thus; as the system is in equilibrium, the net force in the x and y direction shows to be zero
Then;
[tex]\sum F_x= 0 \to T_2 Cos \theta _2 - T_1 cos \theta _1[/tex]
[tex]T_2 Cos \theta _2 = T_1 cos \theta _1 \ \ \ \ \ - - - (2)[/tex]
Also;
[tex]\sum F_y =0 \to T_2sin \theta_2+T_1sin \theta_1 - T_3 = 0[/tex]
[tex]T_3 = T_2sin \theta_2+T_1sin \theta_1[/tex] ---- (3)
From equation (2):
[tex]T_2 = \dfrac{T_1cos \theta_1}{cos \theta_2}[/tex]
Replacing the above value for T₂ into equation 3; we have
[tex]T_3 = \dfrac{T_1cos \theta_1}{cos \theta_2}sin \theta_2+T_1sin \theta_1[/tex]
[tex]T_3 cos \theta_2 = {T_1cos \theta_1}{}sin \theta_2+T_1sin \theta_1 cos \theta_2[/tex]
[tex]T_3 cos \theta_2 = T_1(cos \theta_1 sin \theta_2+sin \theta_1 cos \theta_2)[/tex] ---- (4)
Using trigonometric identity Sin (A+B) = SIn A cos B + Cos A sin B
So ; equation 4 can now be:
[tex]T_3 cos \theta_2 = T_1sin(\theta _1 + \theta_2)[/tex] --- (5)
replacing equation (1) into equation (5) ; we have:
[tex]F_g}cos \theta_2 =T_1 sin (\theta_1+\theta_2)[/tex]
Hence; the tension in the string is:
[tex]T_1= \dfrac{F_gcos \theta_2}{sin (\theta_1+\theta_2)}[/tex]
evaluate one third of the sum of 15 and 6
Answer:
7
Step-by-step explanation:
15 plus 6 equals 21
21 divided by 3 is 7
Answer:7
Step-by-step explanation:
sum of 15 and 6
15+6=21
1/3 Of The sum
1/3 of 21
1/3 x 21
(1x21)/3
21/3=7
Please help.
Thank you.
Answer:
The first option is not a function
Explanation:
A function is where there is no repeated x values
Just a reminder
Lola has h hats. Polly has triple as many hats as Lola. Darla has eight less hats than Polly.
a. Write an expression for how many hats each person has in terms of h.
Answer:
number of Lola hats = h
number of Polly hats = 3h
number of Darla hats = 3h - 8
Step-by-step explanation:
Lola has h number of hats . Polly has triple as many as Lola . Then Darla has eight number of hat less than Polly. The expression for how many hat each person has in terms of h can be express below.
Let
number of Lola hats = h
number of Polly hats = 3h (recall Polly has triple as many as Lola)
number of Darla hats = 3h - 8(Note Darla has 8 number less of hats than Polly who already have 3h number of hats)
The simplest way to explain this is that Lola has h number of hats. This means she has h number of hats .Polly has triple of Lola hats, this implies that 3 times h of Lola hats is Polly hats. Then finally Darla hats is 8 less than Polly hats. This simply means if you subtract 8 from Polly's hats you have gotten Darla's hats.
This object is made with five identical cubes. each cube edge if 4 centimeters long, What is the surface area of this object in square centimeters.
Answer:
480 cm ^ 2
Step-by-step explanation:
To calculate the surface area of the figure, we must calculate the surface area of the cube, we know that they are identical, therefore, calculating the area of one is sufficient.
We have that the surface area of a cube is:
A = 6 * a ^ 2
where a is the edge, we know that if it is a cube all its sides are equal, in this case it is 4 centimeters, if we replace we have:
A = 6 * (4 ^ 2)
A = 96
96 square centimeters is the area of a cube, but since the area of the object would be the sum of the area of all the cubes, then:
AT = 96 * 5
AT = 480 cm ^ 2
The surface area of the object formed with the cubes is 480 cm ^ 2
If the graph of f(x) = x is shifted up 13 units, what would be the equation of the new graph?
Answer:
f(x) = x + 13
Step-by-step explanation:
f(x) = x
when x = 0, y = 0
f(x) = x + 13
when x = 0, y = 13
A wheel with radius 1 foot makes 1 revolution in 4 seconds. What is the linear velocity, in feet per second, of a point on the edge of the wheel?
In one revolution of the wheel, a point on the edge travels a distance equal to the circumference of the wheel.
The wheel has radius 1 ft, so its circumference is 2π (1 ft) = 2π ft.
Then the point has a linear speed of
(1/4 rev/s) * (2π ft/rev) = 2π/4 ft/s = π/2 ft/s
The linear velocity of a point on the edge of the wheel is π/2 feet per second.
In this case, the wheel has a radius of 1 foot and makes 1 revolution in 4 seconds.
The circumference of a circle is given by the formula
C = 2πr, where r is the radius of the circle.
So, the circumference of the wheel is 2π(1) = 2π feet.
Now, the linear velocity of the point on the edge of the wheel is the distance traveled (circumference) divided by the time taken, which is:
Linear velocity = Circumference / Time = 2π feet / 4 seconds
Linear velocity = π/2 feet per second
So, the linear velocity of a point on the edge of the wheel is π/2 feet per second.
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what is the sum of 21 and 5 times a number f is 61
Answer:
f = 8
Step-by-step explanation:
21 + 5f = 61
5f = 61 - 21
f = (61 - 21) / 5
f = 8
Answer:
f = 8
Step-by-step explanation:
"Sum" = addition
"Times" = multiplication
Write an equation to represent this scenario
21 + 5 * f = 61
Multiply 5 by f
21 + 5f = 61
Subtract 21 from both sides of the equation
5f = 40
Divide both sides of the equation by 5
f = 8
Hope this helps :)
Jessica bought the ingredients to make chicken soup, and wanted to make a double batch, which would be 18 cups of soup. A quick Google search told her that this was 259.9 cubic inches. She hoped the soup pot below would be big enough. The soup pot is 9 inches tall with a radius of 3.5 inches. What is the volume of the soup pot? Answer choices are rounded to the nearest tenth cubic inch. 169.6 cubic inches 890.6 cubic inches 197.9 cubic inches 346.4 cubic inches
Answer: 346.4 in^3
Step-by-step explanation:
The pot can be thinked as a cylinder:
The volume of a cylinder is equal to:
V = (pi*r^2)*h
where h is the height, r is the radius and pi = 3.1416
Here we have that: r = 3.5in, h = 9in.
Then the volume is:
V = 3.1416*(3.5in)^2*9in = 346.4in^3
A large trucking company wants to estimate the proportion of its tracker truck population with refrigerated carrier capacity. A random sample of 200 tracker trucks is taken and 30% of the sample have refrigerated carrier capacity. The 95% confidence interval to estimate the population proportion is _______.
Answer:
The 95% confidence interval to estimate the population proportion is (0.2365, 0.3635).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 200, \pi = 0.3[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3 - 1.96\sqrt{\frac{0.3*0.7}{200}} = 0.2365[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3 + 1.96\sqrt{\frac{0.3*0.7}{200}} = 0.3635[/tex]
The 95% confidence interval to estimate the population proportion is (0.2365, 0.3635).
The answer plz hurryyy
Answer:
The answer is that the y-coordinate should be -3 1/2.
Step-by-step explanation:
First, look at the graph. On the x-axis, the dot is at -5, since it is 5 units to the left of the origin. On the y-axis, the dot is at -3 1/2. It is between -3 and -4, not -4 and -5. Therefore, the answer is that the y-coordinate should be -3 1/2, not -4 1/2. You can also check by seeing if -4 1/2 is reasonable. -4 1/2 would mean the dot would be more than 4 units below the origin. On the graph, the dot is clearly above the -4 mark, so the -4 1/2 must not be correct.
Find the constant of proportionality (r)(r)left parenthesis, r, right parenthesis in the equation y=rxy=rxy, equals, r, x.The quantities xxx and yyy are proportional.
xxx yyy
777 353535
121212 606060
202020 100100100
Find the constant of proportionality (r)(r)left parenthesis, r, right parenthesis in the equation y=rxy=rxy, equals, r, x.
Answer:
5
Step-by-step explanation:
Solving the given equation for r, we get ...
y = rx
y/x = r
Then we can find r from any pair in the table:
r = 35/7 = 5
The constant of proportionality is 5.
Answer:
y=3
Step-by-step explanation:
i did it in khan academy :)
PLZ HELP
Figure ABCD is reflected across the x-axis.
What are the coordinates of A' , B' , C' , and D' ?
Enter your answer in each box.
A' (
,
)
B' (
,
)
C' (
,
)
D' (
,
)
A graph with a quadrilateral on it formed between points A begin ordered pair 2, 3 end ordered pair, B begin ordered pair 5, 5 end ordered pair, C begin ordered pair 7, 3 end ordered pair, and D begin ordered pair 5, 2 end ordered pair
Answer:
A' (2,-3)
B' (5,-5)
C' (5,-2)
D' (7,-3)
Step-by-step explanation:
I used desmos graphing calculator to help me solve
Answer: The answers would be A= 2,-3 B= 5,-5 C=-5-2 and D= 7,-3
Two trains leave stations 390 miles apart at the same time and travel toward each other. One train travels at 70 miles per hour while the other travels at 80 miles per hour. How long will it take for the two trains to meet?
Do not do any rounding.
Answer:
Let's denote:
x: the time both trains traveled.
Then, we have:
70x + 80x = 390
=> 150x = 390
=> x = 390/150 = 2.6 hour
Answer:
2.6 hours ( or 2 hours 36 minutes).
Step-by-step explanation:
The combined speed is 70+80 = 150 mph.
Speed = distance / time, so time = distance / speed.
So the time when they will meet
= 390 / 150
= 2.6 hours.
Tony wants to estimate the number of bees in a beehive. He catches 100 bees from the hive and marks each one with a dye. He then lets the bees go. The next day, tony catches 60 bees from the hive. 15 of these bees have been marked with dye. A) using this information what is a good estimate for the number of bees in the beehive.
Answer:
Number of total bees = 400
Step-by-step explanation:
He catches 100 bees from the hive and marks each one with a dye.
He later catches 60 and 15 were marked with the dye.
Its very to estimate from the data given.
I'll answer it with ratio.
We'll ratio number of bees with dye to total he caught the second day.
I.e 15:60 = 1:4
We'll multiply this ratio with the number he caught the first day to know the total.
1/4x =100
X = 100*4
X= 400
Where x is the total number of bees in the bee hive.
what is the equation of the line in slope-intercept form?
Answer:
y = 5x
Step-by-step explanation:
Slope intercept form is y = mx + b
m is the slope
m = 5 on this graph
b is the y intercept which is 0 on this graph
What’s the correct answer for this?
Answer:
A.
Step-by-step explanation:
We would reflect the point P so that another point would be made of the same length from the line.
