Answer:
(a) 8000 times 5 times 2 = 800
For a research project on rodents, 41 chipmunks were tagged and released. Later, researchers counted 320 chipmunks in the area. Of the chipmunks they counted, 16 had tags. To the nearest whole number, what is the best estimate for the chipmunk population?
820 rodents in total
------------------------------------
create a proportional equation:
[tex]\sf \dfrac{present \ rodents}{present \ marked \ rodents} = \dfrac{later \ rodents}{later \ marked \ rodents}[/tex]
[tex]\hookrightarrow \sf \dfrac{x}{41} = \dfrac{320}{16}[/tex] ( Let the total population be x )
[tex]\hookrightarrow \sf x= \dfrac{320*41}{16}[/tex]
[tex]\hookrightarrow \sf x= 820[/tex]
Let that be x
[tex]\\ \rm\Rrightarrow \dfrac{41}{x}=\dfrac{16}{320}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{41}{x}=\dfrac{1}{20}[/tex]
[tex]\\ \rm\Rrightarrow x=41(20)=820[/tex]
Hello people ~
Find the area of a rectangular blackboard whose length and breadth are 120 cm and 100 cm, respectively.
Thanks in advance
Answer:
12000 cm²Step-by-step explanation:
Area of rectangle is:
A = lw, where l - length, w - widthSubstitute the values into equation and find the area:
A = 120*100 = 12000 cm²Area
Length ×Breadth120(100)12000cm²
Pearl and Jason are working on homework together when Pearl says, "got x = 6 and x=13 as the solutions, but it looks like you got something different. Which solutions are right?
"I found a mistake," says Jason. Where did Pearl make a mistake? Explain why it is incorrect. Pearl's work is shown below.
The mistake made by pearl from solving the quadratic equation is that he didn't equate the equation to zero(0) before solving
How to solve quadratic equation?x² - 3x - 10 = 8
x² - 3x - 10 - 8 = 0
x² - 3x - 18 = 0
x² - 6x + 3x - 18 = 0
x (x - 6) + 3(x - 6) = 0
(x + 3) (x - 6) = 0
x + 3 = 0. x - 6 = 0
x = -3. x = 6
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My neighbor has both chickens and roosters. He has a total of 31 birds. The number of chickens is ten more than twice the number of roosters. How many chickens does he have?
Answer:
24
Step-by-step explanation:
You can use a simple equation for this:
c=chickens, r=roosters
c=10+2r, as "chickens is TEN MORE than TWICE the number of roosters,"
we can then do;
10+2r+r (the original number of roosters)=31
3r=21
r=7
BUT, WE'RE NOT LOOKING FOR ROOSTERS!
10+2r=24
Please help 3(2x+1)+2(x+4)
Answer: 8x+11
Step-by-step explanation:
Kim works at an airport on the runway. She is standing and watching an airplane take off from the runway as shown below.
When the airplane is 1,100 feet above the ground, the distance to the airplane from where Kim is standing is 3,850 feet. What is the approximate angle of elevation to the airplane?
Suppose a polynomial of degree 4 with rational coefficients has the given numbers as zeros. Find the other zero
-2, square root 5, 10/3
Step-by-step explanation:
The root is
-sqr root of 5.
First, we put these roots in the forn of
[tex](x - a)[/tex]
where a is the root
So we have
[tex](x - ( - 2))(x - \sqrt{5} )(x - \frac{10}{3} )[/tex]
[tex](x + 2)(x - \sqrt{5} )(3x - 10)[/tex]
[tex](3 {x}^{2} - 4x - 20)(x - \sqrt{5} )[/tex]
To get rid of that square root, let have another root that js the conjugate posive root of 5.
[tex](3 {x}^{2} - 4x - 20)(x - \sqrt{5} )(x + \sqrt{5} )[/tex]
[tex](3 {x}^{2} - 4x - 20)(x {}^{2} + 5)[/tex]
Which will gives us a rational coeffeicent of degree 4.
Why we didn't do
[tex](x - \sqrt{5} )[/tex]
?
Because
[tex](x - \sqrt{5} ) {}^{2} = {x}^{2} - 2 \sqrt{5} + 5[/tex]
If we foiled out we will still have a irrational coeffceint.
Write an equivalent expression to 16x + 20 using factoring.
Answer:
4(4x + 5)
Step-by-step explanation:
4 goes into both 16 and 20.
4×4 is 16 and
4×5 is 20.
When factoring you put the nunber you factored out typically, in front. Then the remaining factor goes in a set of parenthesis.
This is like undoing distributive property.
16x + 20
= 4(4x+5)
Take 2 common
2(8x+10)Again take two common
2(2(4x+5)Simplify
4(4x+5)Done
An equation is shown below: 2(7x − 3) = 9 Which of the following correctly shows the beginning steps to solve this equation? (4 points)
Answer:
2(7x-3)=9
14x-6=9
14x=9+6
14x=15
x=15/14
Hey there!
Let's solve this equation!
We have
2(7x-3)=9
Use the Distributive Property & distribute 2:
14x-6=9
Now, add 6 to both sides:
14x=15
Divide both sides by 14:
x=15/14
Hope everything is clear.
Let me know if you have any questions!
#ILoveLearning
:-)
(4, 6) (-3, -2) Find the slope
Answer:
The value of the slope would be:
8/7
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
Answer:
[tex] slope = \dfrac{8}{7} [/tex]
Step-by-step explanation:
(4, 6) and (-3, -2)
[tex] slope = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]
[tex] slope = \dfrac{-2 - 6}{-3 - 4} [/tex]
[tex] slope = \dfrac{-8}{-7} [/tex]
[tex] slope = \dfrac{8}{7} [/tex]
Consider a sequence whose first five terms are: 4, 8, 16, 32, 64.
Which function (with domain all integers n 2 1) could be used to define and continue this sequence?
A f(n) = 4(n-1)
® f(n) = 4(2)"-1
f(n) = 4n2
f(n) = 4n
Answer:
Considere una secuencia cuyos primeros cinco términos son: 4, 8, 16, 32, 64.
¿Qué función (con dominio todos los enteros n 2 1) podría usarse para definir y continuar esta secuencia?
A f(n) = 4(n-1)
® f(n) = 4(2)"-1
f(n) = 4n2
f(n) = 4n
Step-by-step explanation:
Ginger and Caleb each have 0.77 of a dollar. Ginger does not have any quarters. Caleb does not have any dimes. Explain how many of each type of coin each of them might have.
Ginger can have 7 dimes and 7 pennies while Caleb can have 3 quarters and 2 pennies.
What is an equation?An equation is an expression used to show the relationship between two or more numbers and variables.
Ginger and Caleb each have $0.75
Ginger does not have any quarters. He might have 7 dimes and 7 pennies.
Caleb does not have any dimes. He can have 3 quarters and 2 pennies.
Ginger can have 7 dimes and 7 pennies while Caleb can have 3 quarters and 2 pennies.
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Answer number 10 please. Thank you.
Assume that f(x) = 2x^2 + 4. The function f(x) + k, where k is a constant, is represented by the graph below. what effect did adding k have on the graph of f(x)‽
The effect of adding k on the graph of f(x) will shift the curve upward by k units on the xy-plane.
Shifting of quadratic graph is the vertical directionGiven the parent function of the given graph expressed as f(x) = 2x^2 + 4.
If this function is represented as f(x)+k, the addition of the constant "k" shows hat the function f(x) has been shifted vertically upwards by a factors of 'k'
Hence the effect of adding k on the graph of f(x) will shift the curve upward by k units on the xy-plane.
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Find the volume of a cone with a base diameter of 12 m and a height of 11 m.
Step-by-step explanation:
the volume of a cone is
ground area × height / 3
and the ground area is a circle.
so,
pi×r²×h/3
with r being the radius (half the diameter) and h being the height.
therefore, we get
pi×(12/2)²×11/3 = pi×6²×11/3 = pi×12×11 = 132pi =
= 414.6902303... m³
The volume,V, of any cube with a side length,s, can be determined using the formula V= as to the third power. what is the volume, in cubic centimeters, of a cube with a side length of 2.3 cm.
A.5.29
B.6.9
C.8.026
D.12.167
Answer:
D
Step-by-step explanation:
Volume of cube = s^3
volume = 2.3^3 = 12.167 cm^3
true or false are these lines are intersecting
Answer: True.
Step-by-step explanation: Lines that don't intersect are parallel lines, and those are not parallel. Parallel lines look like the image below. The point of intersection in your image is where K is.
Hope this helps! :)
Can someone help me with this. Please I beg you.
Answer:
180 cm
Step-by-step explanation:
Please answer this order of operations question
-8 - (-2 + 7)2
Answer:
-18
Step-by-step explanation:
= -8 - (-2 +7) x 2
= -8 - 5 x 2
= -8 - 10
= -18
What is the value of the expression below?
4. 8 x 108
-x (2. 2 x 10-6)
1. 2 x 104
Answer:
I'm not sure I understand the formatting. I don't know what the x is supposed to be for the middle term (-x(2.2x10^6)), so I dropped the x for the calculation. I also assumed all terms are to be added. If these assumptioons are correct, the answer is:
4.58012 x 10^8 or 4.6x10^8 (see below)
Step-by-step explanation:
(4.8x10^8) - (2.2x10^6) + 1.2x10^4
(4.8x10^8) - (0.022x10^8) + (0.00012x10^8)
4.8
-0.22
+0.00012
4.58012
4.58012 x 10^8
There are only 2 significant digits (2.8x10^8) so if this is an answer relating to a scientific measurement, it would need to rounded to simply 4.6x10^8.
What is the radius of the circle with equation (x + StartFraction 1 Over 5 EndFraction) squared + (y minus two-fifths) squared = StartFraction 1 Over 25 EndFraction? StartFraction 1 Over 25 EndFraction unit StartFraction 2 Over 25 EndFraction units One-fifth unit Two-fifths units
Considering the circle of the given equation, and comparing to the standard equation of a circle, it is found that the given circle has radius is of [tex]\frac{1}{5}[/tex].
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
In this problem, the equation is given by:
[tex]\left(x + \frac{1}{5}\right)^2 + \left(y - \frac{2}{5}\right)^2 = \frac{1}{25}[/tex]
Hence, the radius is found as follows.
[tex]r^2 = \frac{1}{25}[/tex]
[tex]r = \sqrt{\frac{1}{25}}[/tex]
[tex]r = \frac{1}{5}[/tex]
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Answer:
c 1/5
Step-by-step explanation:
The ratio 216 : x is equivalent to x^2 : 216. What is the value of x?
if y=5x-3, find the value of y when x=-2
Answer:
y = -13
Step-by-step explanation:
y = 5(-2) - 3
y= -10 -3
y = -13
Step-by-step explanation:
or, y = 5x - 3
or, y = 5 (-2) - 3
or, y = -10 - 3
y = -13
Problem
The garden club earned
$
15
$15dollar sign, 15 per hour by weeding neighborhood gardens for
t
tt hours. A generous donor has agreed to double their earnings.
How much did the garden club earn in all?
Write your answer as an expression.
$
$dollar sign
The radius of a circle is 13 in. Find its circumference in terms of T(pi)
Answer: 40.82
Step-by-step explanation: You have to multiply pi and 13 to get the answer
Post Falls High School in Idaho has 1160 students and is growing by 22 students per year. Richmond High School in Indiana has 1900 students and is shrinking by 15 students per year.
Can someone explain how to simplify radicals? (Please leave an example) Im so confused!!
Answer:
Sure!
Step-by-step explanation:
So a radical(or a root) is the opposite of the exponent(for example square root is the opposite of the square of a number). Graphically it's not but it's more simple to think of it like that. Simplifying integer radicals is simple. For example, the square of 11 is 121, so sqr121 (√121) is equal to 11. Other radicals/powers are similar. cuberoot27= 3 because 3^3 is 27. If you add variables, the same thing happens. You can think of the √ as a funnel where only the numbers "big enough" can leave. If you have √xy^2z^3,
the x would have to stay because it's only to the first power, the √y^2 would be reduced to just y, and one pair of zs can come out resulting in z√z. The final answer to √xy^2z^3 would be yz√xz. Hope that helps :)
What is the end behavior of the function f of x equals negative 4 times the cube root of x?
As x → –∞, f(x) → –∞, and as x → ∞, f(x) → ∞.
As x → –∞, f(x) → ∞, and as x → ∞, f(x) → –∞.
As x → –∞, f(x) → 0, and as x → ∞, f(x) → 0.
As x → 0, f(x) → –∞, and as x → ∞, f(x) → 0.
The function [tex]f(x) = 4\sqrt[3]{x}[/tex] is a cube root function
The function end behavior is:
[tex]\quad \mathrm{as}\:x\to \:+\infty \:,\:f\left(x\right)\to \:+\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:f\left(x\right)\to \:+\infty[/tex]
How to determine the end behavior?The equation of the function is given as:
[tex]f(x) = 4\sqrt[3]{x}[/tex]
To determine the end behavior, we plot the graph of the function f(x).
From the attached graph of the function, we can see that:
As x approaches infinity, the function f(x) approaches infinity, and vice versa
Hence, the function end behavior is:
[tex]\quad \mathrm{as}\:x\to \:+\infty \:,\:f\left(x\right)\to \:+\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:f\left(x\right)\to \:+\infty[/tex]
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Using the data in the scatter plot what is a reasonable slope of a model that fits this data
We can conclude that the reasonable slope of a model that fits the given data is: C. 1.
What is the Slope on a Scatter Plot?Slope = change in y/change in x.
To find the slope of that fits the data, pick any two points on the scatter plot, say, (12, 1985) and (16, 1988)
Slope = (1988 - 1985)/(16 - 12) = 0.75 ≈ 1.
Therefore, we can conclude that the reasonable slope of a model that fits the given data is: C. 1.
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How do i know what's is the number