Answer:
(a) $556 billion
(b) $581 billion
(c) $693 billion
Step-by-step explanation:
The given function is:
\(\boxed{A(x)=314e^{0.044x}}\)
where A(x) is the assets (in billions of dollars) for a financial firm .
If x = 7 corresponds to the year 2007 then:
x = 13 corresponds to the year 2013.x = 14 corresponds to the year 2014.x = 18 corresponds to the year 2018.Therefore, to find the assets for each of the given years, substitute the corresponding value of x into the function.
\(\begin{aligned}A(13)&=314e^{0.044 \cdot 13}\\&=314e^{0.572}\\&=314(1.77180712...)\\&=556.34743707...\\&=556\; \sf (nearest\;billion)\end{aligned}\)
\(\begin{aligned}A(14)&=314e^{0.044 \cdot 14}\\&=314e^{0.616}\\&=314(1.851507181...)\\&=581.3732549...\\&=581\; \sf (nearest\;billion)\end{aligned}\)
\(\begin{aligned}A(18)&=314e^{0.044 \cdot 18}\\&=314e^{0.792}\\&=314(2.20780762...\\&=693.2515954...\\&=693\; \sf (nearest\;billion)\end{aligned}\)
Use the Distributive Property to expand 3(6x-4y)-8
Answer:
\(18x - 12y -8\)
Step-by-step explanation:
Distribute property means that \(a(b+c)=ab+ac\)
Meaning that you will have to multiply 3(6x) and 3(-4y)
3(6x) = 18x and 3(-4y) = -12y and because -8 isn't inside the parenthasis we don't multiply 3 and -8
It has taken me 32 minutes to drive 48 km. If the total length of my journey is 146 km and I maintain the same speed, estimate how much longer I will be driving for?
It has taken me 32 minutes to drive 48 km. If the total length of my journey is 146 km and I maintain the same speed, then you can estimate that you will be driving for approximately 65.344 minutes longer to complete the remaining 98 km of your journey.
To estimate how much longer you will be driving for, we can use the concept of proportionality. We know that the time taken to drive 48 km is 32 minutes. Let's use this information to find the time it would take to drive 146 km.
We can set up a proportion to find the time:
(time taken for 48 km) / (48 km) = (time taken for 146 km) / (146 km)
Let's solve for the time taken for 146 km:
(time taken for 146 km) = (time taken for 48 km) * (146 km / 48 km)
Substituting the given values:
(time taken for 146 km) = 32 minutes * (146 km / 48 km)
Calculating the value:
(time taken for 146 km) ≈ 32 minutes * 3.042
(time taken for 146 km) ≈ 97.344 minutes
Therefore, it would take approximately 97.344 minutes to drive 146 km at the same speed.
To estimate how much longer you will be driving for, we can subtract the initial time of 32 minutes from the estimated time of 97.344 minutes:
Additional time = 97.344 minutes - 32 minutes
Additional time ≈ 65.344 minutes
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THIS IS A GCF PROBLEM FOR A2 HELP!!!
Can someone help me out?
Answer:
Step-by-step explanation:
you will need to use proportions
MN/SR=18/30=3/5
X=NP
NP/ST=3/5
NP=X=ST*3/5=25*3/5=75/5=15
The diagram shows a shape made from a solid cube and a solid cylinder.
The cube has sides of length 8.7 cm.
The cylinder has a radius of 2.7 cm and a height of 4.9 cm.
Calculate the total surface area of the solid shape.
Give your answer correct to 3 significant figures.
The total surface area of the solid shape made from the cube and cylinder is approximately 583.31 cm².
How to calculate the areaThe side length of the cube is 8.7 cm, so the surface area of one face is A = 8.7²
= 75.69 cm²
Since there are six faces, the total surface area of the cube is 6 * 75.69 = 454.14 cm²
Since there are two circular bases, the total surface area of the bases is 2 * 22.91 = 45.82 cm².
In this case, the radius of the cylinder is 2.7 cm and the height is 4.9 cm, so the curved surface area is A_curved = 2 * π * 2.7 * 4.9 ≈ 83.35 cm².
Total surface area = surface area of the cube + surface area of the cylinder
Total surface area = 454.14 cm² + 45.82 cm² + 83.35 cm²
Total surface area ≈ 583.31 cm²
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3m+3(m+6)
answer fast please.
Answer: 18
-3m + 3(m + 6)
= -3m + 3m + 18
= 18
Step-by-step explanation:
Toby has $65 to buy tshirts for his bowling team each tshirt costs $7 how many tshirts can he buy
A lab technician has to fill the tank given below.
Find its volume.
Use
π=3.14 and round your answer to the nearest hundredth.
Answer:
π(5^2)(8) + (1/2)(4/3)π(5^3)
= 200π + 250π/3 = 850π/3 cubic meters
= about 889.67 cubic meters
point(s) possible
K
Write the standard form of the equation and the general form of the equation of the circle of radius r and center (h,k).
Graph the circle.
r=√√3; (h,k) = (1,-5)
Write the equation for the circle in general form
The standard equation of a circle is \((x-1)^{2} + (y+5)^{2}= (\sqrt{3})^{2}\). The equation of the circle in general form is (x-1)² + (x-1)² = 3.
What is the standard equation of a circle?Standard form of circle equation is (x – a)² + (y – b)² = r²
What is the general form of the equation of a circle?General form of Equation of a Circle.
x² + y² + 2gx + 2fy + c = 0, for all values of g, f and c.
The equation of a circle is
(x-h)²+ (y-k)² = r²
So, it's given that radius,
r = √3
h=1 and k=-5
So, by substituting all values to the standard equation of a circle is :
\((x-1)^{2} + (y+5)^{2}= (\sqrt{3})^{2}\)
The equation of the circle in the general form is written as :
(x-1)² + (x-1)² = 3
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The blue dot is at what value on the number line?
Answer:
the blue dot is at -19 on the number line
Step-by-step explanation:
In a certain video game, there is a mini-game where the main character can choose from a selection of twenty
presents. The presents are wrapped, so the character does not know what is in them. If 7 presents contain money, 3
presents contain gems, 6 presents contain ore, and 4 presents contain fish, what is the probability that the main
character does not choose a present that contains a gem?
Your answer should be an exact decimal value.
The probability of randomly selecting a present that does not contain a gem is
Answer:
There are a total of 20 presents, and 3 of them contain gems. Therefore, there are 20 - 3 = 17 presents that do not contain gems.
The probability of randomly selecting a present that does not contain a gem is 17/20 = 0.85 or 85%.
hope it helps you...
Use the hundredth grids to answer the question.
Which equation is shown by the model?
See picture below
Based on the information we can infer that the equation shown in the image is 1.23 - 0.35 = 0.88 (option B).
How to identify the correct equation?To identify the correct equation we must look at the graph and identify the information it provides. In this case we have two squares divided into 100 squares each. Additionally, the square on the left has 88 squares painted in red and 12 squares with an X inside. In the case of the square on the right, it has 23 squares colored in red with an X inside.
In total we have 123 squares painted in red, which in decimal number is equivalent to 1.23. On the other hand, the number of squares painted red and with an X inside is 35, this value would be 0.35.
On the other hand, the squares painted only in red are 88, so the equivalent in decimal numbers would be 0.88. Therefore, the correct way to express this relationship through an equation would be:
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Rewrite as an exponential equation.
Log3 1/81 = -4
Answer:
3`⁴ = 1/81
Step-by-step explanation:
________________
on a highway there are billboards located every 1 1/2 km there are 14 billboards in that highway how long is the highway
Answer:
1 1/2 = 3/2
3/2 x 14
= 42/2
=21
Step-by-step explanation:
Determine whether the following events are mutually exclusive. Choosing a student who is a French major or a chemistry major from a nearby university to participate in a research study. (Assume that each student only has one major.)
A. Mutually Exclusive
B. Not Mutually Exclusive
Answer:
A. Mutually Exclusive
Step-by-step explanation:
Mutually exclusive events:
Two events are mutually exclusive if they cannot happen together, that is, supposing the events are A and B:
\(P(A \cap B) = 0\)
Choosing a student who is a French major or a chemistry major
Since each student only has one major, the student cannot be both a French and a Chemistry major, that is, \(P(A \cap B) = 0\), so they are mutually exclusive and the correct answer is given by option A.
Amadi has jar with one dollar and two dollar coins in it.
There are coins in total.
A jar of one and two dollar coins.
The ratio of one dollar coins to two dollar coins is .
How many coins are two dollar coins
Without knowing the total number of coins or the ratio between one dollar and two dollar coins in the jar, we cannot accurately determine the number of two dollar coins.
Amadi has a jar with both one dollar and two dollar coins. The question is asking how many of the coins in the jar are two dollar coins.
To determine the number of two dollar coins, we need more information. The question does not provide any details about the total number of coins or the ratio between one dollar and two dollar coins in the jar. Without this information, it is not possible to give an accurate answer.
If we assume that the jar contains a total of 100 coins, we can use algebra to solve for the number of two dollar coins.
Let's say the number of two dollar coins is x. Then, the number of one dollar coins would be 100 - x.
Since the value of the two dollar coins is double the value of the one dollar coins, we can set up the equation 2x + 1(100 - x) = total value of coins.
Simplifying the equation, we get 2x + 100 - x = total value of coins.
Combining like terms, we have x + 100 = total value of coins.
Since we don't know the total value of coins, we cannot solve for x. Therefore, we cannot determine the number of two dollar coins without additional information.
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Four less than the product of ten and a number is eleven. is
Answer:
If written in algebraic form it is, 10x - 4 = 11
Step-by-step explanation:
Four less ( minus 4 ) than the product of ten and a number ( 10 times x ) is eleven ( equal to 11 ).
Hopefully this helps!
Brainliest please?
please help me with my online classwork!
Answer:
840 cm²---------------------------
There are two triangular faces with base of 16 cm and height of 15 cm and three rectangular faces.
Find the sum of areas of all five faces:
S = 2*(1/2)*16*15 + (17*2 + 16)*12 = 240 + 600 = 840What is the difference in volume between a sphere with radius r and a sphere with radius 0.3r?
Answer:
\(d = 1.2973\pi r^3\)
Step-by-step explanation:
Given
\(R_1 = r\)
\(R_2 = 0.3\)
Required
The difference in their volumes
The volume of a sphere is:
\(V = \frac{4}{3}\pi r^3\)
So, the difference d is:
\(d = \frac{4}{3}\pi [R_1^3 - R_2^3]\)
\(d = \frac{4}{3}\pi [r^3 - (0.3r)^3]\)
\(d = \frac{4}{3}\pi [r^3 - 0.027r^3]\)
\(d = \frac{4}{3}\pi *0.973r^3\)
\(d = \frac{3.892}{3}\pi r^3\)
\(d = 1.2973\pi r^3\)
Volume is a three-dimensional scalar quantity. The difference in the volume between a sphere with radius r and a sphere with radius 0.3r is 4.0757r³ unit³.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
The volume of the sphere with radius(r) is,
Volume = (4/3)×π×r³
The volume of the sphere with radius (0.3r) is,
Volume = (4/3)×π×(0.3r)³
The difference in the volume between a sphere with radius r and a sphere with radius 0.3r is,
Difference = [(4/3)×π×r³] - [(4/3)×π×(0.3r)³]
= (4/3)πr³[1-0.027]
= (4/3)πr³(0.973)
= 4.0757r³ unit³
Hence, The difference in the volume between a sphere with radius r and a sphere with radius 0.3r is 4.0757r³ unit³.
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May you please help me with this I tried and tried to answer and still stuck
Answer:
Point E
Step-by-step explanation:
Consider the polynomial
(4mn^2n - 2mn + 6) + (6mn^2 - 1) - (mn^2 - 2 + 9mn)
Combine all like terms and enter the coefficients for each term into the blanks below
The required coefficients are:4, -1, -11, and 7.
Coefficients refer to the numerical values that are assigned to variables in mathematical equations, models, or formulas. They indicate the relative importance or contribution of each variable in the equation. Coefficients are used to determine the relationship between variables and are often estimated through statistical analysis or optimization techniques.
In algebraic equations, coefficients are the numbers multiplied by variables. For example, in the equation 2x + 3y = 5, the coefficients are 2 and 3.
In statistical models, such as linear regression, coefficients represent the slopes or weights assigned to the predictor variables. These coefficients indicate how much the response variable is expected to change for a unit change in the corresponding predictor variable, assuming all other variables are held constant.
We need to consider the polynomial:
(4mn^2n - 2mn + 6) + (6mn^2 - 1) - (mn^2 - 2 + 9mn)
To combine the like terms and find the coefficients of each term, we can write the polynomial in the following form:
4mn^2n - 2mn + 6 + 6mn^2 - 1 - mn^2 + 2 - 9mn
Taking the coefficients of the terms with "mn^2"4mn^2n - mn^2
Taking the coefficients of the terms with "mn"-2mn - 9mn = -11mn
Taking the coefficients of the constant terms6 + 2 - 1 = 7
Therefore, the required coefficients are:4, -1, -11, and 7.
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In ΔNOP, OP = 7, PN = 13, and NO = 19. Which statement about the angles of ΔNOP must be true?
The angles must be acute and all the measured angles must be different.
What is a triangle?This a shape with 3 sides and angke
If in ΔNOP, OP = 7, PN = 13, and NO = 19, then the measure of the angles must be different as well;
Hence the statement that must be true about the angles is that the angles must be acute and all the measured angles must be different. The given triangle must also be a scalene triangle
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A quilt piece is designed with four congruent triangles to form a rhombus so that one of the diagonals is equal to the side length of the rhombus.Which measures are true for the quilt piece? Select three options
Answer:
THE FOLLOWING MEASURES ARE TRUE FOR THE QUILT:
1. a = 60°
3. The perimeter of the rhombus is 16 inches.
5. The length of the longer diagonal is approximately 7 inches
Step-by-step explanation:
I have attached the picture describing the rhombus.
One by one we will check all the options:
As we can see that:
a+30°=90°
a = 90-30
1) a= 60° which is true
Taking the triangle with the perpendicular x, and using pythagoras theorem, we get:
=16-4 = 12
x= =3.46 ≠3
So option 2, is not true.
Find the area of the irregular figure. Use 3.14 for π. Show your work. Round to the nearest tenth
The area of the irregular figure to the nearest tenth is 8.12 sq. ft.
What are irregular figures?Shapes classified as irregular lack both equal sides and equal angles. The entire area occupied by an irregular shape on a two-dimensional plane is referred to as the shape's area. An irregular form can be split into a number of regular shapes, such as triangles, squares, and rectangles, to determine its area. The area of those smaller shapes can then be added to determine the total area.
Given that, the diameter of the semicircle= 2.8 ft.
The radius of the semicircle = 1.4 ft.
The area of the semicircle is:
A = πr² / 2
A = (3.14)(1.4)²/2
A= 3.077 sq. ft
The area of the triangle is given as:
A = 1/2(b)(h)
A = 1/2(2.8)(3.6)
A = 5.04 sq. ft
The area of the irregular figure is:
A = Area of semicircle + area of triangle
A = 3.077 + 5.04
A = 8.117 sq. ft
Hence, the area of the irregular figure to the nearest tenth is 8.12 sq. ft.
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Please show work and thank you.
Answer: \(x=6\sqrt{3}, y=12\)
Step-by-step explanation:
In a 30-60-90 triangle, the length of the side opposite the 60-degree angle is \(\sqrt{3}\) times the length of the side opposite the 30-degree angle, so \(\boxed{x=6\sqrt{3}}\).
Also, the length of the side opposite the 90-degree angle is twice the length of the side opposite the 30-degree angle, so \(\boxed{y=12}\)
You are baking chocolate chip cookies. The recipe asks for 3 3/4 cups of flour and you want to make 2 times the original recipe.
A. 1 1/2 cups
B. 30/4 cups
C. 7 2/4 cups
D. 7 1/2 cups
Factor the expression using the GCF.
22+11=
ANSWER
the factor will
11 is common in both the given term
so, when we take 11 from both term
it will left with
11( 2+1)
this is the final answer
hope it helps and u have a great day
Tell whether the ratios are equivalent: 3 miles to 4 minutes and 9 miles to 12 miles. Show your work.
Answer:
they are
Step-by-step explanation:
divide 12*4=3
9*3=3
same ratio
Which of the following methods would NOT be used to prove that two triangles are congruent?
Two triangles cannot be proven to be congruent using the method: A. Prove all sets of corresponding angles are congruent.
How to Prove that Two Triangles are Congruent?Two triangles are congruent to each other if they have the same shape and the same size, that is, all three sets of corresponding sides and all three sets of corresponding angles of the two triangles are congruent to each other.
Also, the following condition or criteria can be used to determine if two triangles are congruent to each other:
The HL congruence theorem: when two right triangles have corresponding equal hypotenuse and a pair of corresponding congruent legs, then they are congruent triangles by HL theorem.The SSS congruence theorem: two triangles having all three pairs of corresponding sides congruent are proven to be congruent by SSS congruence theorem.The SAS congruence theorem: Two triangles with two pairs of corresponding congruent sides and a pair of non-included congruent angle are congruent by the SAS.Thus, the method that cannot be used is: A. Prove all sets of corresponding angles are congruent.
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Write a two-column proof for the following information. Upload your proof below.
Given: M is the midpoint of CD; CM = 5x – 2; MD = 3x + 2
Prove: x = 2
The required two column proof is explained below.
What is a midpoint?A midpoint is a point which divides a line segment into two equal parts. Thus it can be referred to as the middle point of the line segment.
The two column proof for the information is given as:
M is the midpoint of CD (Given)
CD = CM + MD (addition property of a line segment)
CM = MD (definition of a midpoint)
So that;
5x – 2 = 3x + 2 (Definition of midpoint)#
Then,
5x - 3x = 2 + 2 (collecting like terms)
2x = 4
x = 2
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