The equation for the graph sketched below is \(y=-3 \cdot (-\frac{1}{3} )^x\)
The given graph is an exponential graph and the standard exponential graph is expressed as \(y=ab^x\)
a is the y-intercept of the graph
(x, y) is any point on the graph.
Given the following from the graph;
a = -3
(x, y) = (1, 1)
Substitute the point and the y-intercept into the formula to have
\(1=-3\cdot b^1\\\b = -\frac{1}{3} \\)
Get the required exponential equation:
Recall that \(y=ab^x\)
\(y=-3 \cdot (-\frac{1}{3} )^x\)
Hence the equation for the graph sketched below is \(y=-3 \cdot (-\frac{1}{3} )^x\)
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Could someone help me with this? Been stuck on it for a minute
Part a: Area of habitat - Area of field = Area of mowed portion.
Part b: Area of mowed portion: 4x(b - x)
Explain the term area of the square?The maximum number of unit squares forming a square is referred to as the square's area. In other terms, it is described as the area that the square occupies.For the stated question:
Part a:
The complete area is given as: Area of habitat.
The area kept for birds: Area of mowed portion
Central unmowed portion: area of field
Thus,
Area of habitat - Area of field = Area of mowed portion
Part b: Area of mowed portion: 4x(b - x)
Proof:
b² - (b - 2x)² = [b - (b - 2x)] [b + (b - 2x)]
= [b - b + 2x] [b + b - 2x]
= (2x)(2b - 2x)
= 4x(b - x)
Thus, the Area of mowed portion: 4x(b - x).
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The workers' union at a particular university is quite strong. About 96 of all workers employed by the university belong to the workers' union. Recently, the workers went on strike, and now a local TV station plans to interview 4 workers (chosen at random) at the university to get their opinions on the strike. What is the probability that exactly 2 of the workers interviewed are union members?
The probability that exactly 2 of the workers interviewed are union members is approximately 0.044.
To solve this problem, we can use the binomial probability formula, which is:
\(P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)\)
where:
n is the sample size (number of workers being interviewed)
k is the number of successes we are interested in (in this case, 2 of the workers being union members)
p is the probability of success (in this case, the probability that a worker is a union member)
(n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items (this can be calculated using the formula n! / (k! * (n - k)!))
Plugging in the values, we get:
\(P(X = 2) = (4 choose 2) * (0.96)^2 * (1 - 0.96)^(4 - 2)\)
\(= (6) * (0.96)^2 * (0.04)^2\)
= 0.04403136
Therefore, the probability that exactly 2 of the workers interviewed are union members is approximately 0.044.
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a boy was 28 inches tall. Currently, he is 25% taller. How
tall is the boy now?
Answer:
21 inches
Step-by-step explanation:
If the boy is 25% smaller, that means his current height is 75% of his previous height. 75% of 28 is 0.75 * 28 which is 21.
Hope this helps :)
Answer:
35 inches tall. (This is assuming they want him to be 25% taller. Using the past tense of 28, I assume this is growth.)
Step-by-step explanation:
25% is 25/100 therefore we get 1/4 which gives us 28/4 = 7.
So this makes the boy 7 inches taller than 28.
28 + 7 = 35
Making him 35 inches tall.
A landscape engineer is designing a triangular area.
He wants to place potted trees in the two largest corners. In which corners will he place the two potted trees?
Answer:
25.3
Step-by-step explanation:
Hope this answer helps you :)
Have a great day
Mark brainliest
me pueden ayudar , es urgente
Answer:
Step-by-step explanation:
A.) (2, 8)
B.) (1,6)
C.) (5,6)
D.) (2,3)
E.) (4,2)
F.) (8,2)
Las 2 preguntas no se de que se trata no hay un punto que dice M
....Lo siento
pomieThe measures of three of the exterior angles of a convex quadrilateral are 90°, 76°, and 110°. What is the measure of txterior angle at the fourth vertex?tyne your ansvar
84º
1) Since the sum of the exterior angles of a quadrilateral is equal to 360º
we can write, and considering the four vertices of a quadrialateral. We can write:
90+76+110 +x = 360º Add the measures
276+x=360º
x=360º-276º
x=84º
2) Hence the answer is 84º for the fourth angle.
For the function f(x) = 7x + 6, find f-¹(x).
Inverse of function f(x) = 7x + 6 is
Given,
f(x) = 7x + 6
Now,
Put y in place of f(x)
y = 7x + 6
Now interchange the variables,
x = 7y + 6
Solve for variable y,
y = x/7 - 6/7
Replace y with f-¹(x),
f-¹(x) = x/7 - 6/7
Thus the inverse of the function is obtained to be x/7 - 6/7 .
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please help me with this math assignment
Answer:
1.6 for the mean
3 is the median
Step-by-step explanation:
Question 14 (essay worth 12 points)
(writing two step equations HC)
Given the equation 6x + 18 = 72:
Part A: Write a short word problem about a purchase made to illustrate the equation. (6 points)
Part B: Solve the equation showing all work. (4 points)
Part C: Explain what the value of the variable represents. (2 points)
A. Ram spent $18 on six pens and six books. The grand total is $72.
B. The cost of each pen is $9.
C. The variable is called x.
What is an equation?
A set of variables, constants, and mathematical operations such as addition, subtraction, multiplication, or division balanced by the equal sign is known as an equation. The equation's left-hand side (LHS) is on the left side, and its right-hand side (RHS) is on the right side (RHS).
Here, we have
Given: the equation 6x + 18 = 72:
A. The issue is that Ram spent $18 on six pens and six books. The total amount he paid is $72.
B. The following equation will be used to demonstrate this:
6x + 18 = 72
Compile similar terms.
6x = 72 - 18
6x = 54
On dividing,
x = 54 / 6.
x = $9
Hence, each pen will set you back $9.
C. The variable's value is x = 9.
Hence, the pen's price is 9.
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Marla wants to buy a new tablet that cost $565, including tax. she saves $15 per week for 30 weeks . does Marla have enough money saved by the tablet? Explain.
Step-by-step explanation:
No she won't have enough money saved.
This is so because at the end of 30 weeks she would have saved only $450 and short by 115.
The scale on a map is 3cm=15 miles. Mr.Rollins measures the distance to the next town at 8cm. How many miles away is the next town?
Answer:
50 000 cm (or 500 m or 0.5 km)
Step-by-step explanation:
what is 0.7283 written in standard form
Answer:
0.7283 written
in scientific is: 7.283×10^-1
Step-by-step explanation:
thats what i think but i'm not sure, hope you got it right sweetie!
Answer:
in scientific notation is 7.283×10^-1
What is the circumference of the circle if the radius is 10 cm?
The circumference of the circle is 62.8cm.
The Circumference of the circle is given by the formula,
Circumference = 2*\(\pi\)*r cm.........equation 1
Given, r = 10cm
On substituting the radius value in equation 1
Circumference = 2*\(\pi\)*10
Circumference = 62.8 cm
Therefore, the circumference of the circle is 62.8cm.
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HELP ASAPPP! I WILL GIVE BRAINLIEST! PICTURE BELOW.
Answer:
d.....
Step-by-step explanation:
I'm am almost 100% positive that the answer is d
Answer:
creo que la respuesta podría ser c ..
Step-by-step explanation:
Find the AQR Ten for the following list of numbers: 1, 2, 4, 3, 3, 8, 5, 6
The calculated IQR of the list of numbers is 3
How to calculate the IQR of the list of numbersFrom the question, we have the following parameters that can be used in our computation:
1, 2, 4, 3, 3, 8, 5, 6
Sort the above number in ascending order
So, we have
1, 2, 3, 3, 4, 5, 6, 8
Split the above numbers to 2
So, we have
1, 2, 3, 3
4, 5, 6, 8
In the above, we have
Q1 = (2 + 3)/2 = 2.5
Q3 = (5 + 6)/2 = 5.5
using the above as a guide, we have the following:
IQR = 5.5 - 2.5
Evaluate
IQR = 3
Hence, the IQR of the list of numbers is 3
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a farmer has two types of milk, one that is 28% butterfat and another that is 16% butterfat. how many gallons of each should be combined to create a 60-gallon mixture that is 22.5% butterfat?
30 gallons of 28% butterfat and 30 gallons of 16% butterfat should be combined to create a 60-gallon mixture that is 22 % butterfat.
Let x gallon of 28% butterfat mixed with the y gallon of 16% butterfat to obtain 60 gallons of 22.5% butterfat,
⇒ x + y = 60 ⇒ x = 60 - y ----(1),
Quantity of butterfat in x gallon + quantity of butterfat in y gallon = total quantity of butterfat,
⇒ 28% of x + 16% of y = 22% of 60
⇒ 0.28x + 0.16y = 0.22 × 60
⇒ 0.28x + 0.16y = 13.2
⇒ 28x + 16y = 1320
⇒ 14x + 8y = 660
From equation (1),
14(60-y) + 8y = 660
840 - 14y + 8y = 660
6y = 180
y = 30
Again from equation (1),
x = 60 - y
= 60 - 30
= 30
Hence, 30 gallons of 28% butterfat and 30 gallons of 16% butterfat are combined to create a 60-gallon mixture that is 22%
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Mathwatch question please help
Answer:
before 7 = 10%
after 7 = 90
Step-by-step explanation:
percetanges are part/whole
before 7 there are 15 people (the part) and in total there are 150 (the whole) so divide 15 by 150 and miltiply by 100 to get 10
after 7 there are 135 (the part) and the total is still 150 (the whole) so divide 135 by 150 and multiply by 100 to get 90
12 tenths+9 tenths= how many tenths?
Answer:
12 + 9 = 21 if thats what ur asking
The measure of one angle of a right triangle is 26°. Find the measure of the other angle.
Enter an integer or decimal number [more...]
Question Help:
Post to forum
Calculator
Answer:
64°
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180°
let the third angle be x , then
x + 90° + 26° = 180°
x + 116° = 180° ( subtract 116° from both sides )
x = 64°
the other angle is 64°
Question 4Mple Choice Worth 2 points)
Ares of Polygons and Composite Figures MC)
A composte figure is shown
024413
028.445²
1.15 in
Which of the following represents the total area of the figure?
010 663 ²
034.335 ²
4.6 in.
3h 563
P
The total area of the composite figure which has triangle and rectangle is 24.41 square inches
The given composite figure has two triangles and one rectangle
Area of rectangle =length × width
=4.6×3.15
=14.49 square inches
Area of left side triangle, it has base of 3.3 in and height 3.15 inches
Area of triangle = 1/2×3.3×3.15
=5.1975 square inches
Area of triangle on right side
Base = 3 in
Height = 6.3-3.15=3.15 in
Area of triangle = 1/2×3×3.15
=4.725 square inches
Total area = 14.49 + 5.1975 + 4.725
=24.41 square inches
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Which is the best buy?
12 tins of fish at K7.80 or 6 tins of fish at K4.20?
the och price and the initia
Answer:
12 tins of fish at K7.80
Step-by-step explanation:
The first quote is the best buy.
If we evaluate both quotes we would see that.
For the first one, we have:
12 tins of fish at K7.80
Therefore the cost of one tin would be; K7.80/12= K0.65
For the second;
6 tins of fish at K4.20, one tin cost
K4.20/6=K0.70
So we see we are paying less for the cost of one tin of fish in the first quote.
While preparing his budget sheet, John Drake noticed that his annual
expenses were $17,700 while his monthly living expenses were $300 more than
his monthly fixed expenses. If John's total monthly expenses were $3,250, find his
monthly fixed expenses and his monthly living expenses.
Answer:
Step-by-step explanation:
I might need help on this.
Answer:
90 because 3/4 of 120 is 90 hope this helps :)
Step-by-step explanation:
Answer:
I'm only answering if you definatley need halp on it.
Step-by-step explanation:
What is 56 divided by 89?
Answer:
0 or 0.62921348314 (if done by the calculator)
Step-by-step explanation:
Step 1:
Start by setting it up with the divisor 89 on the left side and the dividend 56 on the right side like this:
8 9 ⟌ 5 6
Step 2:
The divisor (89) goes into the first digit of the dividend (5), 0 time(s). Therefore, put 0 on top:
0
8 9 ⟌ 5 6
Step 3:
Multiply the divisor by the result in the previous step (89 x 0 = 0) and write that answer below the dividend.
0
8 9 ⟌ 5 6
0
Step 4:
Subtract the result in the previous step from the first digit of the dividend (5 - 0 = 5) and write the answer below.
0
8 9 ⟌ 5 6
- 0
5
Step 5:
Move down the 2nd digit of the dividend (6) like this:
0
8 9 ⟌ 5 6
- 0
5 6
Step 6:
The divisor (89) goes into the bottom number (56), 0 time(s). Therefore, put 0 on top:
0 0
8 9 ⟌ 5 6
- 0
5 6
Step 7:
Multiply the divisor by the result in the previous step (89 x 0 = 0) and write that answer at the bottom:
0 0
8 9 ⟌ 5 6
- 0
5 6
0
Step 8:
Subtract the result in the previous step from the number written above it. (56 - 0 = 56) and write the answer at the bottom.
0 0
8 9 ⟌ 5 6
- 0
5 6
- 0
5 6
A convex lens with focal length f centimeters will project the image of an object on a
point behind the lens. If an object is placed a distance of p centimeters from the lens,
then the distance q centimeters of the image from the lens is related to p and f by the
lens equation: 1/p+1/q=1/f
A. If the focal length of the convex lens is supposed to be 5 cm, and if the image is
formed 7 cm from the lens, find the distance from the lens to the object, p. (It’s not necessary to simplify your answer.)
B. Find an expression that gives q as a function of p, assuming that the focal length is a constant of 5 centimeters.
C. Sketch a graph of q as a function of p (i.e., q(p)), assuming that the focal length is a
constant of 5 centimeters. Show any important features of the graph.
D. Find limq(p) as p approaches infinity and limq(p) as p approaches 5from the positive side. What do these limits represent physically? What must
happen to the distance of the image and the object?
Answer:
A. Using the lens equation, 1/p + 1/q = 1/f, and substituting f = 5 cm and q = 7 cm, we can solve for p:
1/p + 1/7 = 1/5
Multiplying both sides by 35p, we get:
35 + 5p = 7p
Simplifying and rearranging, we get:
2p = 35
Therefore, the distance from the lens to the object, p, is:
p = 35/2 cm
B. Solving the lens equation, 1/p + 1/q = 1/f, for q, we get:
1/q = 1/f - 1/p
Substituting f = 5 cm, we get:
1/q = 1/5 - 1/p
Multiplying both sides by 5qp, we get:
5p = qp - 5q
Simplifying and rearranging, we get:
q = 5p / (p - 5)
Therefore, the expression that gives q as a function of p is:
q = 5p / (p - 5)
C. Here is a sketch of the graph of q(p):
The graph is a hyperbola with vertical asymptote at p = 5 and horizontal asymptote at q = 5. The image distance q is positive for object distances p greater than 5, which corresponds to a real image. The image distance q is negative for object distances p less than 5, which corresponds to a virtual image.
D. Taking the limit of q as p approaches infinity, we get:
lim q(p) = 5
This represents the horizontal asymptote of the graph. As the object distance becomes very large, the image distance approaches the focal length of the lens, which is 5 cm.
Taking the limit of q as p approaches 5 from the positive side, we get:
lim q(p) = -infinity
This represents the vertical asymptote of the graph. As the object distance approaches the focal length of the lens, the image distance becomes infinitely large, indicating that the lens is no longer able to form a real image.
In order for the lens to form a real image, the object distance p must be greater than the focal length f. When the object distance is less than the focal length, the lens forms a virtual image.
NEED FAST HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
3rd
Step-by-step explanation:
i got a 100
I will give brainiest to whoever answers correctly !!
Please do not steal my points I'm tired of it put a legit answer or leave!! I will give brainiest to whoever answers correctly!!
Answer:
15450
Step-by-step explanation:
Given two sides of a triangle, find a range of possible side lengths for the third side.
9 and 32
Answer: Two sides of a triangle have lengths 2 and 7. Find all possible lengths of the third side. Show Answer. difference $$< x <$$ sum $$7 -2 < x < 7+2$$ Answer: $$5 < x < 9$$ Problem 7. Two sides of a triangle have lengths 12 and 5. Find all possible lengths of the third side
Step-by-step explanation: i hope i helped
I need to know how to do this problem please
Answer: Total expenses if 3 widgets are produced is $11,018.00
Step-by-step explanation: The variable cost per unit is given by the coefficient of q in the expense function. In this case, the variable cost is $6.00 per widget. To find the variable costs to produce 2 widgets, we simply multiply the variable cost per unit by the number of units produced: Variable costs for 2 widgets = 2 x $6.00 = $12.00 Therefore, the variable costs to produce 2 widgets is $12.00. To find the variable costs to produce q widgets, we simply multiply the variable cost per unit by the number of units produced: Variable costs for q widgets = q x $6.00 = $6q Therefore, the variable costs to produce q widgets is $6q. To find the total expenses if 3 widgets are produced, we can use the expense function and substitute q = 3:E = 6.00 q + 11,000
E = 6.00 (3) + 11,000
E = 18.00 + 11,000
E = 11,018.00 Therefore, the total expenses if 3 widgets are produced is $11,018.00.
Of the last 20 trains to pull into Lakeside
Station, 14 were full. What is the
experimental probability that the next
train to pull in will be full?
Write your answer as a fraction or whole
number.
P(full) =
The experimental probability that the next train to pull into Lakeside Station will be full is 7/10.
The experimental probability of the next train to pull into Lakeside Station being full can be calculated by dividing the number of times a full train occurred by the total number of trains observed.
Given that out of the last 20 trains, 14 were full, we can express the experimental probability as a fraction:
P(full) = Number of full trains / Total number of trains observed
P(full) = 14 / 20
Simplifying the fraction, we get:
P(full) = 7 / 10
Therefore, the experimental probability that the next train to pull into Lakeside Station will be full is 7/10.
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