Answer:
-4x (1-3) - (2x + 2)
-4(5)(1-3) - (2(5) + 2)
-20(1-3) - (10 + 2)
-20(-2) - (12)
40 - (12)
28
Step-by-step explanation:
Graded Assignment Unit Test, Part 2: More Math Models Answer the questions. When you have finished, submit this assignment to your teacher by the due date for full credit. Total score: ____ of 18 points (Score for Question 1: ___ of 10 points) 1. There are 400 rice weevils at the beginning of an insect study. The population is expected to grow at a rate of 150% each week. (a) Write and simplify a formula that can be used to predict the rice weevil population for any week after the beginning of the study. (b) Use the formula to predict the rice weevil population 10 weeks after the beginning of the study. Show your work. (c) Use the formula to predict when the rice weevil population will reach 1,000,000,000. Show your work. Answer:
Answer:
Y(n) = 400(2.5)^n
Y = 3,814,697 rice weevils
16.1 weeks
Step-by-step explanation:
To predict the population of rice weevil for any week after the start of the study ; wwe use an exponential function for this purpose :
y(n) = A(1 + r)^n
Where;
Y(n) = population at week n
r = growth rate ; n = number of weeks
A = initial population at the start of the study
r = 150% = 1.5
Hence, we have the equation :
Y(n) = 400(1 + 1.5)^n
Y(n) = 400(2.5)^n
B.)
Population after 10 weeks
n = 10
Y(10) = 400(2.5)^10
Y = 400 * 9536.7431640625
Y = 3814697.265625
Y = 3,814,697 rice weevils
C)
When population will reach 1,000,000,000
We have :
1,000,000,000 = 400(2.5)^n
1000000000 / 400 = 2.5^n
2500000 = 2.5^n
Take the log of both sides :
log(2500000) = nlog(2.5)
6.3979400 = n * 0.3979400
n = 6.3979400 / 0.3979400
n = 16.077649
n = 16.1 weeks approximately
Find the missing terms.
3, _____, _____, 21 (arithmetic)
Answer:
3, 9, 15, 21
Step-by-step explanation:
3x1=3 v
3x2=6
3x3=9 v
3x4=12
3x5=15 v
3x6=18
3x7=21 v
Skip one each time, 3, 9, 15, 21
Pls Help! I will give Brainliest!
Answer:
45 = 3z
Step-by-step explanation:
On the left we have 45
On the right we have 3 z's
45 = 3z
Answer:
45 = 3 z
Step-by-step explanation:
LHS = 45RHS = z + z + z = 3 zLHS = RHS.
45 = 3 z
Which set of side lengths forms a right triangle?
O 2,3, 13
O 4,6, 10
O 9, 12, 18
O 15, 36, 39
Awnser:
9,12,18
Step-by-step explanation:
you have to add the smallest numbers together and it has to be greater that the greatest number.
9+12= 21
21>18
A 10 meter ladder was placed on an angle. The base of the ladder is 5 meters away from the
building along the ground.
Write an equation to determine the height, h, of the building.
Answer:
5^2 + h^2 = 10^2
Step-by-step explanation:
This is a clear example of the Pythagorean Theorem, a relation of all sides in a right triangle. The equation itself is a^2 + b^2 = c^2. By simply plugging in the given values into the triangle, you would get the answer.
Answer:
To determine the height we will use a² = b²+c²
(10m)²= (5m)²+(h)²
<=> 100m²=25m²+h²
<=> 100m²-25m²=75m²=h²
<=> √ 75m² = h = 8,660m
Which equation can be used to solve for x?
A. sin (x) =
30
18
B. cos (x)
30
24
C. cos (x)
24
30
D.
tan (x)
24
18
NÉED HELP ASAP PLEASE check the picture
Answer:
[tex] \cos(x) = \frac{24}{30} [/tex]
OPTION C
What is the value of Y if x=1
Answer:
y=6
the first equation:
3(1)+y=9
3+y=9
y=6
the second equation:
y= -4(1)+10
y= -4+10
y=6
I hope this helped! :)
Help pls, the question is in the picture. I'm to lazy to do the math today. I hate math.
Answer:
C
Step-by-step explanation:
Both models represent half of the gymnasium, its just that one is vertical and one is horizontal. Both are basically correct. C is the right answer since it says both models are correct. Each class also does occupy 1/12 of the gymnasium since they get 1/6 of 1/2 of the gymnasium. Of means multiply so 1/6 * 1/2 = 1/12.
Please help with imaginary numbers worksheet!
Problem 5
Answer: 6i------------------
Explanation:
We have these four identities
i^0 = 1i^1 = ii^2 = -1i^3 = -iNotice how computing i^4 leads us back to 1. So i^4 = i^0. The pattern repeats every 4 terms. So we divide the exponent by 4 and look at the remainder. We ignore the quotient entirely. We can see that 28/4 = 7 remainder 0. Meaning that i^28 = i^0 = 1.
We can think of it like this if you wanted
i^28 = (i^4)^7 = 1^7 = 1
Then the sqrt(-36) becomes 6i
So overall, we end up with the final answer of 6i
=============================================
Problem 6
Answer: -3i------------------
Explanation:
We'll use the ideas mentioned in problem 5
46/4 = 11 remainder 2
i^46 = i^2 = -1
sqrt(-9) = 3i
The two outside negative signs cancel out, but there's still a negative from -1 we found earlier. So we end up with -3i
In other words, here is one way you could write out the steps
[tex]-i^{46}*-\sqrt{-9}\\\\-i^{2}*-3i\\\\i^{2}*3i\\\\-1*3i\\\\-3i\\\\[/tex]
=============================================
Problem 7
Answer: -1------------------
Work Shown:
i^10 = i^2 because 10/4 = 2 remainder 2
i^19 = i^3 because 19/4 = 4 remainder 3
i^7 = i^3 because 7/4 = 1 remainder 3
Again, all we care about are the remainders.
[tex]i^{10}+i^{19} - i^{7}\\\\i^{2}+i^{3} - i^{3}\\\\i^{2}\\\\-1[/tex]
=============================================
Problem 8
Answer: -1 + i------------------
Work Shown:
i^22*i^6 = i^(22+6) = i^28
Earlier in problem 5, we found that i^28 = i^0 = 1
So,
[tex]i^1 - \left(i^{22}*i^{6}\right)\\\\i^1 - i^{28}\\\\i^1 - i^{0}\\\\i - 1\\\\-1+i[/tex]
Which expression is equivalent to 30 (1/2 x-2)+40(3/4y-4)
Answer:
15x+30y-220
Step-by-step explanation:
Carl worked 15 hours and Derrick worked 20 hours their combined pay is $640
How much an hour did Carl get paid
Answer:
he got payed 5 dollars an hour
Hurry plz what is the following prouduct?
Answer:
2nd one
Step-by-step explanation:
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
Answer:
A
Step-by-step explanation:
An altitude is drawn from the vertex of an isosceles triangle, forming a right angle and two congruent triangles. As a result, the altitude cuts the base into two equal segments. The length of the altitude is 26 inches, and the length of the base is 9 inches. Find the triangle’s perimeter. Round to the nearest tenth of an inch.
Answer:
The triangle's perimeter is 61.77 inches.
Step-by-step explanation:
Since an altitude is drawn from the vertex of an isosceles triangle, forming a right angle and two congruent triangles, and as a result, the altitude cuts the base into two equal segments, and the length of the altitude is 26 inches, and the length of the base is 9 inches, to find the triangle's perimeter the following calculation must be performed:
Isosceles triangle = 2 equal sides
To obtain the value of the sides, the Pythagorean theorem must be applied on the right triangle formed with the altitude.
(9/2) ^ 2 + 26 ^ 2 = X ^ 2
4.5 ^ 2 + 26 ^ 2 = X ^ 2
20.25 + 676 = X ^ 2
√ (20.25 + 676) = X
√696.25 = X
26.38 = X
26.3865 x 2 + 9 = X
52.77 + 9 = X
61.77 = X
Therefore, the triangle's perimeter is 61.77 inches.
Twice the sum of a certain number and 26 is 72
Answer:
The unknown number is 12
Step-by-step explanation:
2(x+26)=76
or,x+26=76÷2
or,x=38-26
Therefore,x=12.
Undefined geometric term that is described as two dimensional set of points that has no beginning or end
Answer:
Plane
Step-by-step explanation:
There are three undefined geometric terms:
1. Point: A point is just a location. It has no size.
2. Line: A line has no width and extends infinitely in one dimension.
3. Plane: A plane extends infinitely in two dimensions.
So the answer is plane.
I’ll give brainliest
Answer:
6
Step-by-step explanation:
We need to find the slope
We have 2 points
(0,0) and (1,6)
m = (y2-y1)/(x2-x1)
= (6-0)/(1-0)
= 6/1
= 6
y = 6x
The constant of proportionality is 6
Answer:
The constant of proportionality is 6.
Step-by-step explanation:
(0,0) and (1,6)
m = (y2-y1)/(x2-x1)
→ (6-0)/(1-0)
→ 6/1
So, y = 6x.
Patrick is keeping track of how far he jogs each morning.
Use a ratio in lowest terms
to represent how much
farther he ran today
The ratio of
420 m to 1 km =
Answer:
21:50
Step-by-step explanation:
We need to find the ratio of 420 m to 1 km.
We know that,
1 km = 1000 m
So,
The ratio becomes,
[tex]\dfrac{420\ m}{1\ km}=\dfrac{420\ m}{1000\ m}\\\\=\dfrac{42\ m}{100\ m}\\\\=\dfrac{21}{50}[/tex]
So, the required ratio is 21:50.
Let f(x)= -5x+6. Find and simplify f(3b-5).
Answer:
-15b+31
Step-by-step explanation:
f(x)=-5x+6
f(3b-5)=-5(3b-5)+6=-15b+25+6=-15b+31
how do i solve 2/7v-1/7+14=20
Answer: 1: Combine multiplied terms into a single fraction
2: Multiply the numbers
3: Add the numbers
4: Solution
= 43/2
Step-by-step explanation:
Answer:
v = 43/2.
Step-by-step explanation:
2/7v - 1/7 + 14 = 20
2/7 v = 20 - 14 + 1/7
2/7 v = 6 1/7
2/7 v = 43/7
v = 43/7 / 2/7
v = 43/7 * 7/2
v = 43/2
If t is time in hours, what does this function represent?
f(t) = 2.0.3^t
A. a 30-percent increase every hour
B. a 30-percent decrease every hour
C. a 70-percent decrease every hour
D. a 100-percent increase every hour
Answer:
C. a 70-percent decrease every hourStep-by-step explanation:
Given function:
f(t) = 2.0*(0.3)^tThis is exponential decay because:
0.3 = 1 - 0.7 = 100% - 70%and it represents 70% decrease every hour (if it is time in hours)
Correct choice is C
can a circular tabletop with diameter 2.7 meters long fit through a doorway 2.5 meters high and 1 meter wide why or why not
What's X in the diagram??
========================================================
Explanation:
Angles EGD and BGF are vertical angles. Both are unknown and equal to x.
Notice how angle AGD is adjacent to angle CGD. These two angles form a straight angle (180 degrees) and angle CGD is a right angle. That must mean AGD is also a right angle.
Angles AGE and EGD must add to 90 degrees since AGD is 90
----------
(angleAGE)+(angleEGD) = (angle AGD)
(30) + (x) = 90
x = 90-30
x = 60
The figure below shows a circle with segment AB as it's diameter. The center of the circle is NOT known. A square needs to be inscribed in the circle with A and B as a pair of opposite vertices.
Which step will be used in the construction? PLEASE HELP
A. constructing four arcs on the circles circumference with the compass width as the radius
B. constructing a segment that is tangent to the circle at point A
C. constructing a perpendicular to a line segment through a point not lying on it.
D. constructing a perpendicular bisector of a line segment.
Answer:
its b i took the test
Step-by-step explanation:
What is f(0)?
12 only
2 and 3 only
–2, –1, 1, and 2 only
–2, –1, 1, 2 and 12
Answer:
The expression f(0) represents the y-intercept on the graph of f(x). The y-intercept of a graph is the point where the graph crosses the y-axis.
Step-by-step explanation:
HOPE IT HELPS ❤
Answer:
12
Step-by-step explanation:
Doing the test rn
How many line segments are shown?
A.8
B.12
C.6
D.10
Answer:
B. 12
Step-by-step explanation:
A to E = 1 1
C to G = 1 2
D to H = 1 3
B to F = 1 4
A to B = 1 5
E to F = 1 6
C to D = 1 7
G to H = 1 8
A to C = 1 9
E to G = 1 10
B to D = 1 11
F to H = 1 12
12 line segments
A transport company is greatly reducing the amount of oil it uses—but by how much? What number should be below the final barrel?
Answer:
2
Step-by-step explanation:
first nomber,
19247
second nomber,
7429
third nomber,
924
fourth nomber,
42
fifth nomber,
2
Answer:
2
Step-by-step explanation:
no. 1 is 19247
no. 2 is 7429 ,so the last four number of 19247 are reply
no. 3 is 924 ,so the last three number of 7429 are reply
no. 4 is 42 ,so the last two number of 924 are reply
no. 5 is 2,so, the last number of 42 are reply
Identify a rational number among the following numbers.
3.3535535553 √5 6.3
Find the pressure in N/m2 exerted by a force of 40 N on an area of 5 m2
N/m2
Answer:
[tex]pressure = \frac{force}{area} \\ = \frac{40}{5} \\ = 8 \: N {m}^{ - 2} [/tex]
F(x) = -3x-3 g(x) =2x^3+2
Find f(6) and g(-3)
Answer:
[tex]f(6)=-21\\\\g(-3)=-52[/tex]
Step-by-step explanation:
When given the following two functions,
[tex]f(x) =-3x-3\\g(x)=2x^3+2[/tex]
One is asked to evaluate the functions for, (f(6)) and (g(-3)). One can do this by substituting the values (6) into the function (f) and (-3) into the function (g). These values will replace the parameter (x).
[tex]f(6)=-3(6)-3\\[/tex]
Simplify,
[tex]f(6)=-18-3\\f(6)=-21[/tex]
Now repeat this process for the guncion (g(x)) to evaluate for (g(-3))
[tex]g(-3)=2(-3)^3+2[/tex]
Simplify,
[tex]g(-3)=2(-27)+2\\g(-3)=-54+2\\g(-3)=-52[/tex]
Drink coffee Do not drink coffee Total Drink water 0.3 0.24 0.54
Do not drink water 0.25 0.21 0.46 Total 0.55 0.45 1.00
Let A represent drinking coffee and B represent drinking water.
Which statement is true?
Drinking coffee and drinking water are not independent events because P(A|B)≠P(A)and P(B|A)≠P(B).
Drinking coffee and drinking water are not independent events because P(A|B)=P(A) and P(B|A)=P(B).
Drinking coffee and drinking water are independent events because P(A|B)≠P(A) and P(B|A)≠P(B) .
Drinking coffee and drinking water are independent events because P(A|B)=P(A)and P(B|A)=P(B).
Answer:
Drinking coffee and drinking water are independent events because
P(A|B)=P(A)and P(B|A)=P(B)
Step-by-step explanation:
Drinking coffee and water are independent events. People can choose to have both, none or any one. It is on their own will. Those who drink coffee can also drink water. The total of people who drink coffee may include those who drink water also.