Using the given function, it is found that:
a) 20 insects were discovered.
b) The population after 5 years will be of 417 insects.
What is the function for the number of insects after t months?As stated in the exercise, it is given by:
[tex]P(t) = \frac{60(1 + 0.4t)}{0.01t + 3}[/tex]
Item a:
[tex]P(0) = \frac{60[1 + 0.4(0)]}{0.01(0) + 3} = \frac{60}{3} = 20[/tex]
20 insects were discovered.
Item b:
5 years = 60 months, hence:
[tex]P(60) = \frac{60[1 + 0.4(60)]}{0.01(60) + 3} \approx 417[/tex]
The population after 5 years will be of 417 insects.
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wait hihfedhsdkfsffsdf
One-fourth of the sum of a number and 10 is 2 less
than twice the number?
Answer:
The number is 2
Step-by-step explanation:
The equation is: 1/4 (x + 10) = 2x - 1
1/4x + 2.5 = 2x - 1
Multiply everything by 4 to get rid of the fraction
x + 10 = 8x - 4
Subtract x from both sides
10 = 7x - 4
Add 4 to both sides
14 = 7x
Divide both sides by 7
x = 2
The equation w = 20n models the total weight of honey, w, in
pounds that a beekeeper expects to collect from n hives.
a. Graph the relationship modeled by the equation. Include a
title on each axis.
b. How does the graph show the expected rate of pounds of
honey per hive? How is this rate related to the equation?
The graph of the weight function w = 20n is an illustration of linear equations
The expected weight of honey per hive is 20 pounds
The graph of the modelThe equation of the model is given as:
w = 20n
To plot the graph, we use the following representations
n is plotted on the horizontal axisw is plotted on the vertical axisSee attachment for the graph of w = 20n
Interpret the graphThe graph shows that:
As the number of hives increases, the weight of honey increasesThe expected weight of honey per hive is 20 poundsRead more about linear equations at:
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Which number does NOT round to 880?
893
883
882
878
Answer:
893
Step-by-step explanation:
893 is too far away to round to 880. It would actually round to 890.
The last digits of 883 and 882 are small enough to round to 880.
The last digit of 878 is large enough to round to 880.
Answer:
893
Step-by-step explanation:
We round down if the digit is less than 5
We round up if the digit is 5 or more
Rounding to the nearest 10:
893 → 890 (round down as 3 is less than 5)
883 → 880 (round down as 3 is less than 5)
882 → 880 (round down as 2 is less than 5)
878 → 880 (round up as 8 is more than 5)
So the only number that does NOT round to 880 is 893.
An archer releases an arrow with an initial velocity of 20 feet per second at a height of 12 feet. The path the arrow takes can be modeled using the function f(x)=−16x^2+20x+12, where f(x) represents the height, in feet, of the arrow and x represents the time the arrow travels in seconds. What is the maximum height, in feet, reached by the arrow? Round your answer to the nearest hundredth if necessary. Do not include units in your answer.
Answer:
18.25 feetStep-by-step explanation:
The given function is quadratic.
The maximum of the quadratic function is its vertex.
The x-coordinate is determined by x = - b/(2a)
x = - 20/(-16*2) = 5/8Apply the x-value and find the value of f:
f(x) = - 16(5/8)² + 20(5/8) + 12 = 18.25 feetAnswer:
18.25
Step-by-step explanation:
we are given a quadratic function
[tex] f(x) = - 16 {x}^{2} + 20x + 12[/tex]
where:
f(x) represents the heightx represents the timeTo find the maximum value of f(x) in other words, the maximum height, in feet, reached by the arrow.
Differentiate both sides:
[tex] f'(x) = \dfrac{d}{dx}( - 16 {x}^{2} + 20x + 12)[/tex]
with sum differentiation rule, we acquire:
[tex] \displaystyle f'(x) = \frac{d}{dx}( - 16 {x}^{2} )+ \frac{d}{dx} 20x + \frac{d}{dx} 12[/tex]
recall that,
differentiation of a constant is equal to 0[tex] \dfrac{d}{dx} {x}^{n} = n {x}^{n - 1} [/tex]utilizing the rules we acquire:
[tex] \displaystyle f'(x) = - 32 {x}^{} + 20 [/tex]
now equate f'(x) to 0:
[tex] \displaystyle - 32 {x}^{} + 20 = 0[/tex]
solving the equation for x yields:
[tex]x _{max}= \dfrac{5}{8} [/tex]
plug in the maximum value of x into the quadratic function:
[tex]f(x )_{max}= - 16 {( \frac{5}{8} )}^{2} + 20( \frac{5}{8} ) + 12[/tex]
simplify:
[tex]f(x )_{max} = 18.25[/tex]
hence,
The maximum height reached by the arrow is 18.25 feet
please answer the following mcqs with proper explanation
Answer:
(iv) b
(v) c
(vi) d
Step-by-step explanation:
The first two questions have to with understanding the meaning of the English words. (It's reading comprehension.)
__
(iv) "no larger than 10" means "less than or equal to 10"
(b) x ≤ 10
__
(v) "at most 1600" means "less than or equal to 1600"
(c) c ≤ 1600
__
(vi) A value of x will be a solution to the inequality if substituting it into the inequality results in a true statement. Here, using x=0 effectively eliminates the x-term from the inequality.
(a) 0 > 0 . . . false
(b) 5 < 0 . . . false
(c) 2 < 0 . . . false
(d) -2 < 0 . . . true
What is the volume of this right prism?
96 in³
60 in³
48 in³
44 in³
Answer:
96 in³
Step-by-step explanation:
Volume = 2(BHD) / 2
The 2s cancel out
Volume = 3(8)4
Volume = 96
It takes 7 hours and 12 minutes to fly
from Singapore to Tokyo, Japan. You have
to arrive at the airport 45 minutes before
departure. It is a 17 minute taxi ride from
your hotel. By what time would you need
to leave the hotel if the flight lands
at 3:23 p.m.?
The time I would need to leave the hotel if the flight lands at 3:23 p.m is 7 : 09 am
What time should I leave the hotel?The first step is to add the total hours of the flight to the time of the tax ride and the time you need to get to the airport.
7h + 12 min + 45 + 17 = 8 hours 14 minutes
Now subtact 8 hours 14 minutes form 3: 23
(12 + 3:23) - 8 hours 14 minutes =7 : 09 am
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simplificar la radicacion 18
Answer:
441
Step-by-step explanation:
Figure ABCD is a parallelogram.
Parallelogram A B C D is shown. A diagonal is drawn from point A to point C.
Which sequence could be used to prove that AD = BC?
First prove TriangleABC is congruent to TriangleCDA, and then state AD and BC are corresponding sides of the triangles.
First prove TriangleABC is similar to TriangleCDA, and then state AD and BC are opposite sides of the parallelograms.
First prove ParallelogramABCD is congruent to ParallelogramCDAB, and then state AD and BC are corresponding sides of two parallelograms.
First prove ParallelogramABCD is similar to ParallelogramCDAB, and then state AD and BC are opposite sides of the parallelograms.
Answer:
A
First prove Triangle ABC is congruent to Triangle CDA, and then state AD and BC are corresponding sides of the triangles.
Hope this helps!
Please Mark Brainleast!!!
The sequence to prove that AD = BC is; First prove ABC is similar to CDA, and then state AD and BC are opposite sides of the parallelograms.
How to prove Quadrilateral Theorems?From the question, we see that the parallelogram ABCD has a diagonal AC. Thus; AB║ CD and AD║BC.
Now, the parallelogram is divided into two triangles ΔABC and ΔADC by its diagonal AC.
Thus;
∠ACB = ∠DAC and ∠CAB = ∠ACD because they are alternate interior angles.
Also, AC = AC (Reflexive property)
Thus; by ASA congruence postulate, we can say that; ΔABC ≅ ΔADC
Also, by corresponding sides of the congruent triangles are congruent we can say that AD = BC.
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Erica has a rectangular living room that is 9.78 meters long from front to back and 11.85 meters long from side to side. Draw a sketch of Erica's living room, labeling the lengths, and estimate how many square meters of carpet Erica would need to cover her living room floor.
Answer:
-> See attached
115.893 meters²
Step-by-step explanation:
See attached for my sketch.
Area for a rectangle is A = L * W:
9.78 meters * 11.85 meters = 115.893 meters²
What is the Area of this shape?
Answer:
448 ft ^2
Step-by-step explanation:
[tex]A = \frac{b_{1} + b_{2}}{2} * h\\A = \frac{17 + 39}{2} * 16\\A = \frac{56}{2} * 16\\\\A = 28 * 16\\\\A = 448 ft^{2}[/tex]
Hope this helps,
If best, mark brainliest, if not, hope it helps anyway.
Marco has two number cubes. The faces of each number cube are numbered from 1 to 6. Marco rolled the number cubes and recorded the number showing on the top face of each number cube. The results are shown in the table.
4, 2 5, 2 3, 1 3, 4 2, 6
1, 1 4, 2 2, 3 3, 3 5, 1
1, 5 5, 2 1, 5 1, 2 1, 5
2, 4 4, 2 2, 4 5, 3 2, 4
Based on these results, what is the experimental probability that the next time the number cubes are rolled, they will land with a 2 showing on the top face of one number cube and a 4 showing on the top face of the other number cube?
A.
3
10
B.
9
20
C.
11
20
D.
1
36
Using it's concept, it is found that the probability that the next trial will result in a 2 and 4 is given by:
A. [tex]\frac{3}{10}[/tex].
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In an experimental probability, the number of outcomes are taken from previous trials.
In this problem, the table states that of 20 trials, 6 resulted in either (2,4) or (4,2), hence the probability is given by:
p = 6/20 = 3/10.
Which means that option A is correct.
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Please help
Suppose Troy conducted a statistical study by asking 12 math teachers the following question:
"How many students are in your first period dass this year?"
Explain why this is or is not a statistical question.
The question asked by Troy is a statistical question because there would be variability in the answers he get fro the 12 maths teachers.
What is a statistical question?A statisical question is a question that can only be answered through the collection of data. Thhere would be variablility in the results gotten from the data.
A non- statistical question is a question that has only one answer. For example, how old are you? is a non-statistical question.
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Sam watched 10 cars drive past
him. 6 of those cars were white.
Write a fraction to describe the
fraction of white cars.
Answer:
3/5
Step-by-step explanation:
6 white cars out of 10 cars would be written as 6/10.
You then would simplify this fraction to 3/5.
So your answer is 6/10 or 3/5.
if g = 6x-9 and x = 15 what is g
Answer:
g= 81
Step-by-step explanation:
Replace X with 15
g = 6x -9
g = 6(15) - 9
g = 90 - 9
g = 81
Step-by-step explanation:
g=6x-9
putting the value of x
g=6×15-9
g=81
Jeremiah has a mailing cylinder for posters that measures 12 inches long and 8 inches in diameter. What approximate volume can it hold? Use 3.14 for pi. Do not round. SHOW YOUR WORK.
Answer:
The cylinder can hold 508.68 in³
Explanation:
The volume of a cylinder can be calculated using the following rule:
Volume of cylinder = πr²h cubic units
where r is the radius of the cylinder and h is its height
Now, we are given that:
height of cylinder = 18 in
diameter of cylinder = 6 in which means that the radius of the cylinder is 3 in
π is 3.14
Substitute with the givens in the above equation to get the volume of the cylinder as follows:
Volume of cylinder = πr²h
Volume of cylinder = 3.14 * (3)² * 18
Volume of cylinder = 508.68 in³
Our school’s girls volleyball team has 14 players, including a set of
3 triplets: Alicia, Amanda, and Anna. In how many ways can we
choose 6 starters if at most one of the triplets is in the starting lineup? There can't be 2 or more triplets and there can be none.
Answer:
[tex]1,\!848[/tex].
Step-by-step explanation:
There are two disjoint sets of ways to choose a lineup as required:
Include none of Alicia, Amanda, or Anna, orInclude exactly one of Alicia, Amanda, and Anna.Assume that none of Alicia, Amanda, or Anna is to be selected. This lineup of [tex]6[/tex] would then need to be selected from a set of [tex]14 - 3 = 11[/tex] players (which excludes Alicia, Amanda, and Anna.)
The number of ways of selecting (without order) [tex]6[/tex] items out of a set of [tex]11[/tex] (distinct) items is equal to the combination:
[tex]\begin{aligned}\begin{pmatrix}11 \\ 6\end{pmatrix} &= \frac{11!}{(6!)\, (11 - 6)!} \\ &= \frac{11!}{6! \times 5!}\end{aligned}[/tex].
Assume that Alicia is selected, but neither Amanda nor Anna is selected. The other [tex]6 - 1 = 5[/tex] players in this lineup would then need to be selected from a set of [tex]14 - 1 - 2 = 11[/tex] players. (This set of [tex]11[/tex] excludes Alicia, Amanda, and Anna.)
The number of ways to select [tex]5[/tex] items from a set of [tex]11[/tex] items is:
[tex]\begin{aligned}\begin{pmatrix}11 \\ 5\end{pmatrix} &= \frac{11!}{(5!)\, (11 - 5)!} \\ &= \frac{11!}{5! \times 6!} \\ &= \frac{11!}{6! \times 5!}\end{aligned}[/tex].
Similarly, there would be another set of [tex](11!) / (6! \times 5!)[/tex] distinct ways to select the lineup if Amanda is selected, but neither Alicia nor Anna is.
Likewise, the number of ways to select the lineup with Anna but neither Amanda nor Alicia would also be [tex](11!) / (6! \times 5!)[/tex].
These sets of configurations for the lineup are pairwise disjoint from one another. Thus, the total number of ways to select this lineup would be:
[tex]\begin{aligned}& \begin{pmatrix}11 \\ 6 \end{pmatrix} + 3 \times \begin{pmatrix}11 \\ 5 \end{pmatrix} \\ =\; & \frac{11!}{6! \times 5!} + 3 \times \frac{11!}{6! \times 5!} \\ =\; & \frac{4 \times 11!}{6! \times 5!} \\ =\; & \frac{4 \times 11 \times 10 \times 9 \times 8 \times 7}{5 \times 4 \times 3 \times 2} \\ =\; & \frac{11 \times 10 \times 9 \times 8 \times 7}{5 \times 3 \times 2} \\ =\; & 1,\!848\end{aligned}[/tex].
A rectangle has a length of 32 yards less than 10 times its width. If the area of the rectangle is 384 square yards, find the length of the rectangle.
The length of the rectangle is 48 yards.
Let's denote the width of the rectangle as "w" yards.
According to the information given, the length of the rectangle is 32 yards less than 10 times its width. So, the length can be represented as: 10w - 32 yards.
The formula for the area of a rectangle is length times width: Area = length × width.
Given that the area of the rectangle is 384 square yards, we can set up an equation:
Area = length × width
384 = (10w - 32) × w
Now, let's solve for the width (w):
384 = 10w² - 32w
0 = 10w² - 32w - 384
Dividing the equation by 2 to simplify:
0 = 5w² - 16w - 192
Now we have a quadratic equation. We can either factor it or use the quadratic formula to solve for "w." Let's use the quadratic formula:
w = (-b ± √(b² - 4ac)) / 2a
For our equation, a = 5, b = -16, and c = -192. Plugging these values into the formula:
w = (16 ± √((-16)² - 4 × 5 × (-192))) / (2 × 5)
w = (16 ± √(256 + 3840)) / 10
w = (16 ± √4096) / 10
w = (16 ± 64) / 10
This gives us two possible solutions for the width:
w = (16 + 64) / 10 = 8 yards
w = (16 - 64) / 10 = -4.8 yards
Since width can't be negative, we'll ignore the second solution.
So, the width of the rectangle is 8 yards. Now, let's find the length using the earlier expression:
Length = 10w - 32
Length = 10 × 8 - 32
Length = 80 - 32
Length = 48 yards
Therefore, the length of the rectangle is 48 yards.
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what is the percentage of this
Answer:
69%
Step-by-step explanation:
10×10 table, 69 cells are orange. Therefore the fraction 69/100 as a percentage is 69%.
Help picture below problem 10
Answer:
180-52=128
Do mark BRAINLIEST
Cassie wants to buy carpet to cover her whole living room, except for the tiled floor. The tiled floor is 4
5
6
ft by 2
1
3
ft. Find the area the carpet needs to cover.
Answer:
1456
Step-by-step explanation:
56x2x13
56x26
1456
Translate this phrase into an algebraic expression. 73 less than twice Jose's height Use the variable to represent Jose's height.
Answer:
x-73
Step-by-step explanation:
Let x=Jose's height. If it says "less than," then that is subtraction. Since Jose's height is not defined, there is no specific number that can be used to describe "73 less than twice Jose's height," so I use the variable x, and then subtract 73.
Write the equation in standard form for the circle with center (0, -3) passing through (15/2 , 1)
Check the picture below, so the green line is really the radius of the circle, and we know its center.
[tex]~~~~~~~~~~~~\textit{distance between 2 points}\\\\(\stackrel{x_1}{0}~,~\stackrel{y_1}{-3})\qquad(\stackrel{x_2}{\frac{15}{2}}~,~\stackrel{y_2}{1})\qquad \qquadd = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}\\\\\\\stackrel{radius}{r}=\sqrt{[\frac{15}{2} - 0]^2 + [1 - (-3)]^2}\implies r=\sqrt{\left( \frac{15}{2} \right)^2 + (1+3)^2}\\\\\\r=\sqrt{\left( \frac{15}{2} \right)^2 +4^2}\implies r=\sqrt{\frac{225}{4} + 16}\implies r=\sqrt{\cfrac{289}{4}}\implies r=\cfrac{17}{2}\\\\[-0.35em]\rule{34em}{0.25pt}[/tex]
[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{0}{ h},\stackrel{-3}{ k})\qquad \qquad radius=\stackrel{\frac{17}{2}}{ r} \\\\\\\ [x-0]^2~~ + ~~[y-(-3)]^2~~ = ~~\left( \cfrac{17}{2} \right)^2\implies x^2+(y+3)^2 = \cfrac{289}{4}[/tex]
write a quadratic function f whose only zero is 11
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Here's the solution ~
To write a quadrilatic function, we have to use its roots, like we have to subtract the roots from x and multiply them ~ then we will get our required function !
Since our only root is 11 here, we have to do t double
[tex]\qquad \sf \dashrightarrow \:(x - 11)(x - 11)[/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} - 11x - 11x + 121 [/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} - 22x + 121[/tex]
That's our required function ~ I hope you understood the whole thing !
A survey of 2,00 registered voters is used to predict by how many percentage points a candidate is leading. Of the 2,00 people, 1,240 planned to vote for Candidate A. By how many percentage points is Candidate A leading.
This might help cross divide and multiply.
Zack went on 6 hikes. The hikes were:
7 miles - 6 miles - 5 miles - 4 miles - 4 miles - 6 miles
What was the range of the lengths of Zack's hikes?
Answer:
3 miles
Step-by-step explanation:
Range is the biggest number minus the smallest number.
First put the distance in order from least to greatest.
4 miles, 4 miles, 5 miles, 6 miles, 6 miles, 7 miles.
Now subtract the greatest and least amounts.
7 - 4 = 3
All of the quadrilaterals in the shape below are squares. Find the area of the shaded region
To find area of square one :-
Given :
side = 9 (unit)To find :
Area of squareWe know :
Area of square = side²
Therefore:-
→Area of square = 9²
→Area of square = 9 × 9
→Area of square = 81 (unit)²
To find area of square two :-
Given :
side = 11 (unit)To find :
Area of squareWe know :
Area of square = side²
Therefore:-
→Area of square = 11²
→Area of square = 11 × 11
→Area of square = 121 (unit)²
Now it's clearly visible that the whole figure is also. a square .
Therefore AE = CP
Which means area of square three = 81 (unit)²
Now area of shaded figure :-
Area of square one + Area of square two + Area of square three81 + 81 + 121283 (unit)²Help with this answer
Answer:
down syndrome
Step-by-step explanation:
Find the value of X. Round your answer to the nearest tenth please
The value of x from the figure is 17.82 units
SOH CAH TOA identity1) From the first figure.
Opposite side = x
Adjacent = 12
Using the SOH CAH TOA identity
tan53 = opp/adj
tan53 = x/12
x = 12tan53
x = 15.92 units
2) Using the SOH CAH TOA identity
cos27 = adj/hyp
cos27 = x/20
x = 20cos27
x = 17.82units
Hence the value of x from the figure is 17.82 units
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