Answer:
The correct option is option (D)
The initial investment is $10,600 and the growth rate of the investment is 3.85%.
Step-by-step explanation:
The formula of compound interest:
[tex]A=P(1+r)^n[/tex]
A= Total amount after n years
P= Initial value of deposit
r= rate of interest compound annually
n= time is in year
Given expression is
[tex]A=10,600(1.0385)^x[/tex]
[tex]A=10,600(1+0.0385)^x[/tex]
Now we compare the given expression with the compound interest formula
So,
P= 10,600
r=0.0385 =3.85%
So, the initial investment is $10,600 and the growth rate of the investment is 3.85%.
You sell tires for $65 each at your automotive service shop. At this price, what does it cost to purchase a set of 4 tires, not including tax?
$69
$105
$260
$280
$325
Answer:
$260
Step-by-step explanation:
you multiply $65 by 4 for the set of four and the product is $260.
Answer:
A set of 4 tires cost $260.
Step-by-step explanation:
It is given that each tire is sold for $65. In order to find a set of 4 tires, you have to multiply it by 4 :
1 tire = $65
4 tires = $65×4
= $260
10
A person is selected randomly. What is the probability that the person was born on a
Sunday? *
14.3%
20%
80%
85.7%
Mark, Chase, and Beatrice are running a 100-meter race. Which list represents the sample space of all the possible ways in which the three runners can win first, second, and third places? If there were four runners and three positions to be won, what would the sample size be?
A.
The sample space is {MBC, BCM, CMB}. If there were four runners, the sample size would be 4.
B.
The sample space is {MBC, MCB, BCM, BMC, CBM, CMB}. If there were four runners, the sample size would be 24.
C.
The sample space is {MBC, BCM, CMB}. If there were four runners, the sample size would be 4.
D.
The sample space is {MBC, MCB, BCM, BMC, CBM, CMB}. If there were four runners, the sample size would be 16.
the answer is B: 24
i know it
I need the answer ASAP !!!!
I hope this helps you
x^2+2.(-3).x+(-3)^2
(x-3).(x-3)
(x-3)^2
Explain the differences between solids that are polyhedra and solids that aren’t polyhedra.
Answer:
A polyhedron is a solid shape with flat sides, while a non polyhedron is a solid shape which has curved sides.
Step-by-step explanation:
A polyhedron, can be seen as a solid shape with many plane figures, forming its sides. Examples of polyhedrons are cuboids, squares and pyramids. As you can see, these solid shapes have flat sides.
On the other hand, a non polyhedron is a solid shape that has curved surfaces. Examples include: cones, spheres and cylinders.
Hence polyhedron: No curved surface
Non polyhedron: curved surface
Final answer:
Polyhedral solids are composed of flat polygonal faces and have geometrically regular shapes, while non-polyhedral solids can have curved surfaces and irregular shapes, such as spheres and cylinders.
Explanation:
Differences Between Polyhedral and Non-Polyhedral Solids:
Solids that are polyhedra have flat faces, straight edges, and sharp vertices. Polyhedral solids are a category of solids composed of polygons that are joined together at their edges and vertices. The most common examples of polyhedra include cubes, pyramids, and prisms. These solids have a geometrically regular shape and are often symmetrical.
In contrast, solids that are not polyhedra may have curved surfaces, and irregular shapes, and do not consist exclusively of flat polygonal faces. Common examples of non-polyhedral solids include spheres, cylinders, and cones. These shapes are not limited by flat surfaces and can have continuous curved surfaces.
While polyhedral solids can be easily mathematically described by the polygons that comprise their faces, non-polyhedral solids often require more complex geometry, such as calculus, to describe their curved surfaces.
8 times the sum of 2 and 15
Answer:
136
Step-by-step explanation:
15 plus 2 is 17,then multiplied by 8
I know why but I can’t explain it and it won’t except my explanation someone help!
In triangle ABC a=8. b=6, and angleC= 60°. Find the measure of angleA
16 degrees
46 degrees
74 degrees
106 degrees
Answer: The correct answer is 74˚
Find the value of X.
Answer:
x = 109
Step-by-step explanation:
In pentagons, the total degrees for the interior angles is always 540 degrees.
540 = 91 + 160 + 100 + 80 + x
540 = 431 + x
109 = x
I hope this helped!
You miss 6 out of 25 questions on an science quiz 5 out of 20 questions on an math quiz. Which Quiz has an higher percent of correct answers.
The science quiz has a higher percentage of correct answers.
To determine which quiz has a higher percent of correct answers, we need to calculate the percentage of correct answers for each quiz.
Science Quiz:
You missed 6 out of 25 questions. Therefore, you answered 25 - 6 = 19 questions correctly.To find the percentage of correct answers, use the formula:Math Quiz:
You missed 5 out of 20 questions. Therefore, you answered 20 - 5 = 15 questions correctly.For the math quiz:[tex]Percentage = \frac{15}{20}*100 = 75\%[/tex]Comparison
The science quiz has a higher percentage of correct answers (76%) compared to the math quiz (75%).
A system of equations is shown below.
Equation A: 5x +9y = 12
Equation B: 4x – 3y = 8
Which method eliminates one of the variables?
1) Multiply equation A by and add the result
to equation B.
2) Multiply equation B by 3 and add the result to
equation A.
3) Multiply equation A by 2 and equation B by - 6
and add the results together.
4) Multiply equation B by 5 and equation A by 4
and add the results together.
1on
Multiply equation B by 3 and add the result to
equation A.
Option 2 is correct
Multiply equation B by 3 and add the result to A
How to Solve linear equations?When we are given two equations we can solve them by eliminating one variable, and equating the value of one variable to another or by using a matrix.
How to Eliminate One Variable?Let us assume two-equation ax+by = c and px+qy = d, now suppose we want to eliminate x from this two-equation, then we cross-multiply the x coefficients and then subtract them or add them considering the final coefficients of x, we multiply the equation by a multiple of their LCM So multiplying equation ax+by= c by p we get: apx+bpy=pc similarly we mulitply (-a) in equation px+qy=d we get -apx-aqy= -ad If we add the new equation we get y(bp-aq) = pc-ad and we have eliminated x successfully. for eliminating y we would have used coefficients of y.Solving the questionIf we want to eliminate y in the given equation we will, LCM of (9,3) is 9 we can multiply B by 3 and add to A.
Hence Option 2 is correct.
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Are you winning or losing?
Answer:
You are winning
Step-by-step explanation: If you drop in $2 a day for 10 weeks you have spent $20. You have won $75 from the slots which leaves you with a gain of $55.
Solve the system of equations below by graphing both equations with a
pencil and paper. What is the solution?
y = 2x - 3
y = -2x + 5
A.) (-2,5)
B.) (-2,-7)
C.) (2,1)
D.) (2,-3)
Answer:
4
Step-by-step explanation:
Answer:
The answer is C. (2,1)
Step-by-step explanation:
The partial factorization of x2 – 3x – 10 is modeled with algebra tiles.
Factoring out in algebra simplifies expressions such as quadratic equations into products of binomials or linear factors, sometimes using complex coefficients to achieve this if necessary.
The process of factoring out involves finding the numbers or expressions that divide evenly into the original expression. In the case of quadratic expressions like [tex]x^2 - 3x - 10[/tex], we look for two binomials that multiply together to give us the original quadratic. In algebra, a common method of factoring is looking for two numbers that multiply to give the constant term (in this case -10) and add up to the coefficient of the middle term (in this case -3). These two numbers are the factors of -10 that we use to split the middle term.
For example, the factors of -10 that add up to -3 are -5 and 2. Using these numbers, we can write [tex]x^2 - 3x - 10[/tex] as (x - 5)(x + 2). This is called factoring by grouping, wherein we factor common terms out of pairs of terms and then factor further if possible.
In the context of complex numbers, all second-order polynomials can be factored into linear factors. For instance, [tex]x^2 + 1[/tex] can be factored as (x - i)(x + i), utilizing complex roots i and -i. The fundamental theorem of algebra assures us that any polynomial can be factored completely into linear factors using the complex number system.
pls help i’ll give u a brainlest
Answer:
(13×14×6)/3= 364 centimeter cube
I answered wrongly cuz forgot to divide by 3
my mistake
Answer:
4263m^3
Step-by-step explanation:
So for number 2, that is a right rectangular pyramid. The formula is lwh/3.
The length is 21, the width is 21, and the height is 29. So the volume is 4263.
Heather has a bag with 16 red blocks, 11 bile blocks, 9 purple blocks, 15 green blocks, 8 yellow blocks, and 20 orange blocks. If she
was to draw a block out of the bag, record the color and replace the block back in the bag, repeating 500 times, what would most
likely be the probability of drawing a green block (round to the nearest hundredth)?
Answer:0.19
Answer:
it would be 0.25
Step-by-step explanation:
I think the answer would be 0.19
(Hope this helps!)
simplify 3 square root of 4/ 3 square root of 5
The final simplified expression is 2 over the square root of 5, represented as [tex]\( \frac{2}{\sqrt{5}} \).[/tex]
Let's break it down step by step:
1. Simplify the square roots:
[tex]- \(\sqrt{4}\) equals 2 because \(2 \times 2 = 4\). So, \(\sqrt{4} = 2\).[/tex]
- We have [tex]\(\sqrt{5}\)[/tex] in the denominator, which cannot be simplified further because 5 is a prime number and doesn't have any perfect square factors.
2. Substitute the simplified square roots:
- After simplifying [tex]\(\sqrt{4}\)[/tex] to 2, the expression becomes [tex]\(\frac{3 \times 2}{3\sqrt{5}}\).[/tex]
3. Cancel out the common factor:
- Both the numerator and the denominator have a factor of 3. So, we can cancel out 3 from both sides:
[tex]\[\frac{3 \times 2}{3\sqrt{5}} = \frac{2}{\sqrt{5}}\][/tex]
4. Final simplification:
- The expression [tex]\(\frac{2}{\sqrt{5}}\)[/tex] is simplified as far as it can go because the square root of 5 cannot be simplified further.
So, the simplified expression is [tex]\(\frac{2}{\sqrt{5}}\).[/tex]
Let p be a prime number such that p>2. Use the proof by contradiction to show that at least one of numbers p−1 and p+1 is divisible by 4.
Suppose that Marvin rolls a pair of fair six-sided dice. Let A be the event that the first die lands on a 4 and B be the event that rolls doubles
P(A), the probability that the first die lands on 4?
P(B), the probability that Marvin rolls doubles?
P(A and B) the probability that the first die lands on 4 and Marvinv rolls doubles?
DEPENDENT OR INDEPENDENT?
Answer:
1/6
1/6
1/36
Independent
Step-by-step explanation:
Make a chart with 36 outcomes of a pair of six sided dice.
Count the amount that starts with 4, which is 6. 6/36 = 1/6
Doubles. Count the pairs, basically both numbers are the same. 6 outcomes out of total is 1/6.
Last one.
(1/6)^2 = 1/36
These are independent, because the first die landing on 4 doesn't have anything to do with making the die becoming doubles.
What is side Bc round to nearest hundredth
Answer:
BC = 15.01
Step-by-step explanation:
Solve this question using a trigonometry ratio, which you can remember them all with SohCahToa, which says:
sinθ = opp / hyp
cosθ = adj / hyp
tanθ = opp / adj
θ means the "angle of reference" (angle we are talking about).
In this problem, θ is A = 65°,
To decide which trig. ratio to use, find out which sides we want to use. We will use AC = 7 because we know it.
We also use BC because we need to find it.
In relation to ∠A or θ, AC is adjacent and BC is opposite.
The ratio with adjacent and opposite is tangent.
tanθ = opp / adj Substitute the variables for this question
tanA = BC / AC Substitute the values you know
tan65° = BC / 7 Rearrange this and isolate C
BC = 7tan65° Multiply 7 and tan65 to find the missing side
BC = 15.011548...... Exact answer on your calculator
BC ≈ 15.01 Round to nearest hundredth
Sophia invests $12,500 in an account that earns 4% annual simple interest. Assuming she makes no additional deposits or withdrawals, how much interest will Sophia earn after 3 years?
[tex]\text{Simple interest formula:}\\\\A=P(1+rt)\\\\\text{Plug in your given values:}\\\\A=12,500(1+0.04(3))\\\\\text{Solve:}\\\\A=12,500(1+0.04(3))\\\\A=12,500(1+0.12)\\\\A=12,500(1.12)\\\\A=14,000\\\\\boxed{\$14,000}[/tex]
Sophia will earn $14, 000 in interests after 3 years.
What is Interest?The fee you pay to borrow money or the fee you charge to lend money is called interest. The most common way to represent interest is as a yearly percentage of the loan amount. The interest rate on the loan is known as this percentage.
We have,
Sophia invests $12,500 in an account.
R= 4%
Time= 3 years
So, Amount = P(1+ rt)
A = 12500 (1 + 0.04(3))
A = 12500 ( 1 + 0.12)
A = 12500 + 1.12
A = $14, 000
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A bag contains 5 blue marbles, 2 blavk marbles, and 3 red marbles. A marble is randomly drawn from the bag. The probability of not drawing a black marble is ___. The probability of drawing a red marble is ___.
Answer:
20% black marble 30% red marble
Final answer:
The probability of not drawing a black marble is 4/5. The probability of drawing a red marble is 3/10.
Explanation:
To find the probability of not drawing a black marble, we need to find the ratio of the number of marbles that are not black to the total number of marbles. In this case, there are 5 blue marbles and 3 red marbles, so the total number of marbles is 5 + 2 + 3 = 10. The number of marbles that are not black is 5 + 3 = 8. Therefore, the probability of not drawing a black marble is 8/10 or 4/5.
To find the probability of drawing a red marble, we need to find the ratio of the number of red marbles to the total number of marbles. In this case, there are 3 red marbles out of a total of 10 marbles. Therefore, the probability of drawing a red marble is 3/10.
What is the value of x 4 + 0:5y 3 when x = 2 and y = 4?
Answer:
Step-by-step explanation:
x^4+0.5y^3=2^4+0.5x4^3
=16+0.5x64
=16+32
=48
Solve the following system via substitution.
m = 2n + 30
2m - n = 39
Answer:
m=16
n=-7
Step-by-step explanation:
Answer: n=-7, m=16
Step-by-step explanation:
I need help please. Solve by the method of substitution, and could you please show/explain how? Im stumped. Thanks
Answer:
D x+9 = 2x+1
Step-by-step explanation:
y = x+9
y = 2x+1
Substitute x+9 for y in the second equation
y = 2x+1
x+9 = 2x+1
This answers the question
To finish the problem
Subtract x from each side
x+9-x =2x-x+1
9 = x+1
Subtract 1 from each side
9-1 =x+1-1
8=x
Now find y
y = x+9
y = 8+9
y=17
PLEASE HELP!!!!!!
Look at the figure. Find the value of x.
A.) 90
B.) 30
C.) 15
D.) 45
Answer:
15
Step-by-step explanation:
An isosceles triangle has equal base angles.
Hence,
[tex] 3x=5x-30\\
\implies 30=2x\\
\implies x=15[/tex]
Answer:
C
Step-by-step explanation:
Well all triangles need to be equal to 180°. When you substitute a, b, and d in for x, the result are bigger than 180 not including the 3rd angle. With C the angles equal 45° and 45° angle which leave the appropriate sized angle for the 3rd angle at 90°. So x is equal to 15.
Ariel and her family are going to order one large circular pizza that has a diameter of
20 inches and one small circular pizza that has a diameter of 12 inches.
Which measurement is closest to the difference between the area of the large pizza and the
area of the small pizza in square inches?
The difference between the area of the large pizza (20-inch diameter) and the small pizza (12-inch diameter) is about 201.06 square inches. We calculated this by finding the area of each pizza using the formula for the area of a circle, and then subtracted the smaller area from the larger.
Explanation:The subject of this question is Mathematics, specifically the concept of area for circles. To calculate the difference between the areas of the two pizzas, we first have to find the area of each pizza individually.
The formula for the area of a circle is A = πr^2, where r is the radius of the circle. For the large pizza with a diameter of 20 inches, the radius is 20/2=10 inches, so its area would be A = π * (10^2) = 314.16 square inches.
For the smaller pizza with diameter of 12 inches, the radius is 12/2 = 6 inches. So, the area of the small pizza is A = π * (6^2) = 113.10 square inch.
Now, to get the difference between the two areas, we subtract the smaller area from the larger area: 314.16 square inches - 113.10 square inches = 201.06 square inches. This is the difference between the area of the large pizza and the small pizza.
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find the mode of the following data: 9,15,17,18,6,20,8,5,18,18,10,5,14,12,10,7
Answer:
18
Step-by-step explanation:
mode is the number that occurs the most
Answer:
18
Step-by-step explanation:
I just identified the numbers and saw 18 the most
what is the cost of a new trampoline cover that needs to cover a trampoline with a diameter of 8 feet if the material cost 6.75 per square foot?
Answer: The cost of the trampoline cover would be $339.12
Step-by-step explanation: The radius of the trampoline is 4 feet (Diameter divided by 2 equals radius).
The trampoline cover will effectively cover the entire area of the trampoline and the area is given as
Area of circle = πr²
Area of circle = 3.14 x 4²
Area of circle = 3.14 x 16
Area of circle = 50.24 square foot
However the material costs $6.75 per square foot, which means the total cost of the trampoline cover would be derived as
Total area x cost per square foot = cost of trampoline cover
50.24 x 6.75 = Cost of trampoline cover
$339.12 = Cost of trampoline cover
Answer: The cost of the new trampoline cover is $339.29
Step-by-step explanation:
Hi, we have to calculate the area of the trampoline cover.
Since it has a circle form with a 8 ft diameter.
Area of a circle = π r^2
Since the radius (r) is equal to the diameter (d) divided by 2
R = d/2 = 8/2 =4
Replacing in the formula:
A = π 4^2 = 50.26 square ft
Since the material cost 6.75 per square foot
Cost = 6.75 x 50.26 = $339.29
A bacterial culture starts with 400 bacteria and grows at a rate proportional to its size. After 2 hours there will be 800 bacteria.
1) Express the population, P(t) after t hours as a function of t
2) Using your equation from above, what will the population be after 8 hours?
3) Using your equation from above, after how many hours will the population reach 2270 bacteria?
Answer:
P(t) = 400×2^(t/2)64005.0Step-by-step explanation:
The wording "a rate proportional to its size" is an indication that growth (or decay) is exponential.
1) For many problems involving exponential growth, I like to use the numbers given in the problem statement as follows.
population = (initial population) × (growth factor)^(t/(growth period))
where the "growth period" is the period of time in which the population is multiplied by the "growth factor".
Here, we're given ...
(initial population) = 400
(growth factor) = 800/400 = 2
(growth period) = 2 . . . . hours
So, our population function can be written as ...
P(t) = 400×2^(t/2)
__
2) Putting t=8 into the formula, we get ...
P(8) = 400×2^(8/2) = 400×16 = 6400
After 8 hours, the population will be 6400.
__
3) Fill in the given number and solve for t.
2270 = 400×2^(t/2)
2270/400 = 2^(t/2)
Taking logs, we have ...
log(227/40) = (t/2)log(2)
t = 2×log(227/40)/log(2) ≈ 5.009
After 5.0 hours, the population will reach 2270.