Answer:
[tex]A\simeq3250.83[/tex]
Step-by-step explanation:
The amount formula in compound interest is:
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
where:
P = principal amount
r = annual interest
n = number of compounding periods
t = number of years
We already know that:
P = $2000
[tex]r = 7\% = \frac{7\%}{100\%}=0.07[/tex]
t = 7 (number of years from 6th to 13th bday)
n = 4 (quarterly in a year)
Then,
[tex]A=2000(1+\frac{0.07}{4} )^{(4)(7)}\\\\A=2000(1+\frac{0.07}{4} )^{28}\\\\A=3250.825792\\\\A\simeq3250.83[/tex]
Select the correct answer.
What is the slope of the line that goes through the points (-1,4) and (14,-2)?
A. -15/6
B. -6/13
C. -5/2
D. -6/15
Slope = (-2 - 4)/(14 - (-1)) = -6/15
The value of y varies directly with x. If x = 3, then y = 4. What is the value of x when y = 120 ?
Answer:
x = 90
Step-by-step explanation:
If x = 3 and y = 4 then when y = 120 just find out what times 4 = 120
which is 30.
so just multiply 30 for x = 3, then the answer will be 90
x = 90
Answer:
x=90
Step-by-step explanation:
x is directly proportional to y
Therefore, if the initial y value was 4 and the final y value is 120. This means that y initial had been multiplied 120/4 times, which is 30.
Same goes for x. If x initial is 3, then the final x value would be x/3=30. This means that x=3×30, which is equal to 90.
Stefan sells Jin a bicycle for $146 and a helmet for $19. The total cost for Jin is 150% of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin?
Stefan spend price $110 and made price $60 by selling bicycle and helmet to Jin.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100.
Here, given that,
Selling price of bicycle = $146
Selling price of helmet = $19
Total = 146+19= $165
Let,
x represents the original cost Stefan to buy the bike and helmet.
150% of x = $165
1.5x=$165
Dividing both sides by 1.5
we get ,
x=$110
Stefan bought bicycle and helmet for $110.
Profit made by Stefan = Selling price - buying price
Profit made by Stefan = 165-110= 55
Hence, Stefan spend price $110 and, made $55 by selling bicycle and helmet to Jin.
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Please help Polynomial
The degree of the given polynomial is 4.
What is the polynomial?A polynomial is a type of algebraic expression in which the exponents of all variables should be a whole number. The exponents of the variables in any polynomial have to be a non-negative integer. A polynomial comprises constants and variables, but we cannot perform division operations by a variable in polynomials.
The given polynomial is y=3x²-7x⁴+5-9x.
a) The polynomial in standard form is -7x⁴+3x²-9x+5.
b) The degree of the polynomial is 4.
c) The number of terms in the polynomial are 4.
d) Use the degree and the leading coefficient to determine the behavior.
Falls to the left and falls to the right
e) Use the derivative to find the maximum and minimum.
(−0.78859507, 11.25584002) is a local maxima
f) Here the y-intercept is (0, 5)
g) The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for x. x≈−1.33755842,0.5797309.
h) Find the domain by finding where the equation is defined. The range is the set of values that correspond with the domain.
Domain: (−∞,∞),{x|x∈R}
i) Range: (−∞,11.25584002],{y|y≤11.25584002}
Therefore, the degree of the given polynomial is 4.
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Evaluate the expression. Write your answer in scientific notation.
1. 4.1x10^3) + (3.7x10^2)
2. (1.2x10^(3))*(4x10^(5))
Please enter the missing number: 4, 8, 14, 22, ?
A. 26
B. 28
C. 32
D. 36
E. 40
Answer:
C) 32
Explanation:
it's adding by 4, 6, 8, and then 10; 22 + 10 = 32, so C will be the answer.
Hope this helps!
Find the surface area of the prism
Answer:
330
Step-by-step explanation:
The prism is a triangular prism
9 * (12 + 5 + 13) + (2 * 30)= 330
30 being the base area
Answer:
330
Step-by-step explanation:
We can break each surface area into it pieces.
For the squares:
9x13=117
9x5=45
9x12=108
For the triangles:
12x5÷2=30
12x5÷2=30
Add all of those together to get the total square area, which is
330
What is the area of the first triangle?
Answer:
1/2 foot
Step-by-step explanation:
1 x 1 = 1
1/2 = 1/2
An approximate solution to an equation is found using this iterative process.
(x, Jº-1
X,+1
and x, = -1
4
The values of X1, X2 , X3 could be -1 , -0.6 , -0.041600 using the iterative process.
What is iteration ?
iteration can be defined as the repeating itself to perform a particular task.
Given
X2 is when n=1
X2 = X1+1 = X1 ^ 3 - 5/10
because X1 = -1
so X2 = -1-5/10 = -6/10 = -0.6
X3 is when n=2
X3 = X2+1
= X2 ^ 3 -5/10
because X2 = -3/5
so X3 could be
X3 = (-0.6*-0.6*-0.6) - 5 / 10
X3 = -0.041600
Hence, The values of X1, X2 , X3 could be -1 , -0.6 , -0.041600 using the iterative process.
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Which body part is approximately 3 "heads" down from the top of the head
O Shoulder
B Belly Button
O Knees
O Ankles
B. Belly button
Step-by-step explanation:
It can't be knees or ankles because they are too far down, and shoulders are at head level
Just do the second one…
The L.C.M. defines the least number that is exactly divisible by two or more numbers, whereas the G.C.F. defines the greatest factor present between any given pair of two or more numbers.
What is the difference between LCM and GCF?LCM is also known as the Least Common Multiple (LCM), and HCF is also known as the Greatest Common Factor (GCF).
The highest common factor (HCF) between two or more numbers is two or more. The LCM, on the other hand, is the lowest common multiple that exactly divides these two figures. The greatest common factor between any two numbers is also known as HCF. Between two or more numbers, LCM is also known as Least Common Divisor.
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2. A Grade 12 student is taking Biology, English, Math, and Physics in her first term. If a student timetable has room for five courses (meaning the student has a spare), how many ways can she schedule her courses
The schedule of her course in 120 ways.
How to calculate how many ways can she schedule her courses?A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression. Operations include addition, subtraction, multiplication, and division.
A mathematical expression is the collection of mathematical symbols that results from the proper combination of numbers and variables using operations like addition, subtraction, multiplication, division, exponentiation, and other as-yet-unlearned operations and functions.
The three different types of algebraic expressions are monomial, binomial, and polynomial.
According to the question there are five spaces for different subjects which are arranged in different order so the number of ways are
2(5,4)
= 5 * 4 * 3 * 2
=120 ways
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Write the explicit formula for the sequence below:
The explicit formula for the sequence will be an = 10 + 5n. The correct option is C.
What is arithmetic progression?The sequence in which every next number is the addition of the constant quantity in the series is termed as the arithmetic progression.
A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15.
Given series is 15,20,25,30,...,
The common difference is d = 20 - 15 = 5
First term is, 15
The formula can be written as,
an = a₁ + d(n-1)
an = 15 + 5 ( n - 1 )
an = 15 + 5n - 5
an = 10 + 5n
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Help i got some more math
x = 5
AB = 6
BC = 13
What is a line?A line can be defined as a straight set of points that extend in opposite directions, It has no ends in both directions(infinite). It has no thickness. It is one-dimensional.
Given,
AB = 2x - 4
BC = 3x - 2
AC = 19
By the figure
AB + BC = AC
2x - 4 + 3x - 2 = 19
5x - 6 = 19
5x = 25
x = 5
AB = 2 × 5 - 4 = 10 - 4 = 6
BC = 3 × 5 - 2 = 15 - 2 = 13
Hence the value of x, AB and BC is 5, 6, 13 respectively.
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Given that K is the midpoint of segments RM and JL, and prove Δ RKJ ≅ Δ MKL.
Statements
Reasons
1. K is the midpoint of segments RM and JL
1. Given
2.
2.
3. and
3.
4. RK = MK and JK = LK
4. Definition of Congruent Segments
5. Δ EGF ≅ Δ EGH
5.
What is Reason #3?
a
Given
b
Definition of Midpoint
c
CPCTC
d
SSS Congruence Postulate
The complate table is,
Statement Reasons
1) K is the midpoint of segments Given
RM and JL.
2) RJ ≅ ML SSS Congruence Postulate
3) RK ≅ MK , JK ≅ LK Definition of Midpoint
4) RK = MK , JK = KL Definition of Congruence
Segments
5) Δ EGF ≅ Δ EGH CPCTC
What is Line segment?A line segment is a part of line having two endpoints and it is bounded by two distinct end points and contain every point on the line that is between its endpoint.
Given that;
K is the midpoint of segments RM and JL.
Now,
Since, K is the midpoint of segments RM and JL.
Hence, We get;
Statement Reasons
1) K is the midpoint of segments Given
RM and JL.
2) RJ ≅ ML SSS Congruence Postulate
3) RK ≅ MK , JK ≅ LK Definition of Midpoint
4) RK = MK , JK = KL Definition of Congruence
Segments
5) Δ EGF ≅ Δ EGH CPCTC
Thus, The complete table is shown above.
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2. A jet travels 540 miles in 4.5 hours. At this
rate, how far could the jet travel in 11 hours?
a. 1,320 miles
b. 1,500 miles
c. 1,450 miles
de none of the above
Answer:
a
Step-by-step explanation:
Divide distance by time for speed per hour, that is
speed = 540 ÷ 4.5 = 120 mph
Then distance travelled in 11 hours
= 11 × 120 = 1320 miles → a
A school plans to spend twice the amount it did last year on its winter dance, less the cost of the disco ball which was $150, since they have it from last year. A total of $1,500 is being spent this year. Fill in the blanks to write an equation that will determine the amount of last year’s budget, a.(2 points)
__(a −__) = __
Equation that will determine the amount of last year’s budget
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that a school plans to spend twice the amount it did last year on its winter dance , less the cost of the disco ball which was $150 since they have it from last year
A total of $1,500 is being spent this year.
We need to find the equation which determine the amount of last year’s budget
2a-150=1500
When a is the amount of last year’s budget
Hence, 2a-150=1500 is the equation that will determine the amount of last year’s budget
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Solve 84=3u^2, where u is a real number.Round your answer to the nearest hundredth.
3u^2-84 = 0 then u=5.29 is the nearest hundredth
What are real numbers?The union of both rational and irrational numbers is known as a real number. They are represented by the letter "R" and can be either positive or negative.
This category includes all natural integers, decimals, and fractions.
In the number system, real numbers are only the fusion of rational and irrational numbers.
These numbers can generally be used for all arithmetic operations and can also be expressed on a number line.
Imaginary numbers, which are often known as unreal numbers since they cannot be stated on a number line, are frequently used to symbolize complex numbers. Examples of actual numbers include 23, -12, 6.99, 5/2, and so forth.
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A cylindrical tank contains 172.48 litres of water. If its
height is 0.7 m then find the radius of the base.
Answer:
Radius= 8.86 m
Step-by-step explanation:
Pie x r^2 x 0.7= 172.48
Pie x r^2= 246.4
r^2= 78.43
R= square root of 78.43
Radius= 8.86m
PLEASE HELP ME ASAP!!!!!!!
At a carnival, Diana sees a balloon shooter game. The ticket cost is $3. The rule is that the first person to shoot 10 balloons from a total 30 balloons wins $10. What is the expected payoff for the winner?
Answer:
$13
Step-by-step explanation:
The expected payoff for the winner would be the ticket cost, $3, plus the prize money, $10, which totals $13. This is the expected value of playing the game. However, it's important to note that this does not guarantee that the winner will receive exactly $13, as the outcome of the game is dependent on chance and the player's skill. There is always a chance that the player could win more or less than the expected value.
Pls help
(3 x 8 x 5)⁷
To evaluate (3 x 8 x 5)⁷, you need to first multiply 3, 8, and 5 together to get the base, then raise that result to the seventh power.
What does a math exponent mean?
The number of times a number has been multiplied by itself is referred to as an exponent. For instance, the expression 2 to the third (written as 23) signifies 2 x 2 x 2 = 8. 23 and 2 x 3 = 6 are not equivalent. Keep in mind that any number is itself when raised to the power of 1.
So,
(3 x 8 x 5)⁷ = (120)⁷ = 120 x 120 x 120 x 120 x 120 x 120 x 120
= (1.2 x 10^2)^7 = 1.2 x 10^2 x 1.2 x 10^2 x 1.2 x 10^2 x 1.2 x 10^2 x 1.2 x 10^2 x 1.2 x 10^2
=1.2^7 x 10^14 = 1.2^7 x 10^14
=4096 x 10^14
=4.096 x 10^17
Therefore (3 x 8 x 5)⁷ = 4.096 x 10^17
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PLS HELP ASAP, given angle m ABD is a straight angle.
Answer:
measure of CBD is 125 degrees
Step-by-step explanation:
ABC + CBD is equal to 180 degrees
8x - 41 + 9x + 17 = 180
combine like terms
17x - 24 = 180
add 24 to both sides
17x = 204
divide both sides by 17
x = 12
then plug in to find CBD
9 (12) + 17
108 + 17 = 125 degrees
Answer:
angle CBD = 125°
Step-by-step explanation:
Because ABD is a straight angle we know it is equal to 180°
because we have this information we can create the equation
(8x-41) + (9x+17) = 180
17x - 24 = 180
(here you would add 24 to both sides)
17x = 204
(divide both sides by 17)
x = 12
Then you would plug in 12 for x in the equation for CBD which will then get you 125°
PLEASE HELP I AM BEGGIN YOU EXTRA POINTS AND BRAINLIEST PLEASE !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Karsik borrowed $8,500 from a bank. During a period of five years, he paid a total of $2,125 in interest. What was the simple annual interest rate that the bank charged Karsik for his loan?
0.05%
0.5%
5%
7.7%
Answer:
5%
Step-by-step explanation:
2,125 interest/5 years=425 interest/year
425/8500=.05 or 5%
Answer:
the real answer is 4.25
Step-by-step explanation:
hope this helps
by the way to calculate the interest you have to divide the total interest by how many days or years then put in percent form example 2.125 divided by 5 wich equals 4.25
Find the area of a circle with diameter 12 cm.
Use the value 3.14 for it, and do not round your answer.
Be sure to include the correct unit in your answer.
PLZZ HELP I WILL MARK BRAINLIEST!!
Answer:
113.04 cm.
Step-by-step explanation:
Step 1: Formula/explain
To find the area of a circle, multiply the radius by itself twice, then multiply the product pi.
[tex]a=\pi r^2(3.14*radius*radius)[/tex]
Step 2: Solve
According to the word problem, the circle has a diameter of 12. This means it has a radius of 6.
Now, we plug the numbers into formula.
[tex]\pi 6^2 (3.14*6*6)=113.04[/tex]
Step 3: Conclude
Therefore, the area of this circle is 113.04 cm.
Activity 1.1 Simplify Me Simplify by removing perfect nth powers: 1. √20 2. √300 3. √128 3 4. √ 5 3 5. √50 3
Answer:
[tex](a)\ \sqrt{20}=2\sqrt{5}[/tex]
[tex](b)\ \sqrt{300} = 10 \sqrt{3}[/tex]
[tex](c)\ \sqrt{128} = 8 \sqrt{2}[/tex]
Step-by-step explanation:
Required
Simplify
[tex](a)\ \sqrt{20}[/tex]
Express 20 as 4 * 5
[tex]\sqrt{20}=\sqrt{4 * 5}[/tex]
Split
[tex]\sqrt{20}=\sqrt{4} * \sqrt{5}[/tex]
This gives:
[tex]\sqrt{20}=2 * \sqrt{5}[/tex]
[tex]\sqrt{20}=2\sqrt{5}[/tex]
[tex](b)\ \sqrt{300[/tex]
Express as 100 * 3
[tex]\sqrt{300} = \sqrt{100} * \sqrt{3}[/tex]
This gives:
[tex]\sqrt{300} = 10 * \sqrt{3}[/tex]
[tex]\sqrt{300} = 10 \sqrt{3}[/tex]
[tex](c)\ \sqrt{128}[/tex]
Express as 64 * 2
[tex]\sqrt{128} = \sqrt{64*2}[/tex]
Split
[tex]\sqrt{128} = \sqrt{64} * \sqrt{2}[/tex]
[tex]\sqrt{128} = 8 * \sqrt{2}[/tex]
[tex]\sqrt{128} = 8 \sqrt{2}[/tex]
Questions 4 and 5 are not clear
Follow the steps in 1 - 3 to solve 4 and 5
The brain volumes ?( cm cubed cm3?) of 20 brains have a mean of 1083. 9 1083. 9 cm cubed cm3 and a standard deviation of 122. 2 122. 2 cm cubed cm3. Use the given standard deviation and the range rule of thumb to identify the limits separating values that are significantly low or significantly high. For such? data, would a brain volume of 1348. 3 1348. 3 cm cubed cm3 be significantly? high?
Therefore , the solution of standard deviation is because the value of 1452.2 cm3 does not fall between the range of 917.4 cm3 and 1422.2 cm3.
what is the standard deviation?Standard deviation, often known as variance in a set of data, is a statistical measure of variation. A low standard deviation indicates that the values are more likely to be near the mean of the collection, whereas a high standard deviation indicates that the values are widely distributed. How far the data depart from the mean is expressed by the standard deviation, abbreviated as.
Here,
Considering the details here,
The average brain volume is 1169.8 cm3, while the standard deviation is 126.2 cm3.
The much lower results are u-2 = 11169.8-2(126.2) => 917.4.
Reason: According to the range rule of thumb, the required incredibly low values are 91.7 cm3 or less.
Hint: Use the algorithm to identify values that are at least considerably high.
Step: 2
Considering the data supplied,
The average brain volume is 1169.8 cm3, while the standard deviation is 126.2 cm3.
Significantly higher values include,
u-2α = 11169.8+ 2(126.2)
=> 1422.2
Justification: According to the range rule of thumb, the necessary significantly high values must be 1422.2 cm3 or higher.
Hint: To determine whether the value 1452.2 cm3 is very high, use the findings of steps (1) and (2).
Step: 3
Using step 1 and step (4),
917.4 is among the significantly low numbers or less.
The significantly high values are 1422.2 or higher.
Yes, 1452.2 cm3 is a noticeably high value.
The apt response is choice (B).
Reason: The value is much higher than expected based on the range rule of thumb because the value of 1452.2 cm3 does not fall between the range of 917.4 cm3 and 1422.2 cm3.
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What is the measure, in degrees, of ZA?
Answer:
28
Step-by-step explanation:
2x + 3x + 40 =180
5x= 180 - 140
5x=140
x= 28
Answer:
Step-by-step explanation:
We know that the sum of interior angles of a triangle is 180° so we can say:
40 + 2x + 3x = 180°
40 + 5x = 180°
5x = 140°
x = 28°
Now substitute in 28 for the value of x in Angle A:
=> 2x would become 2(28)
=> 56° = ∠A
Hope this helps!
For what value of a the system of equations Ax Y 2 and 6x 2y 3 has a unique solution?
A = 1, y = -2/3, The value of a for which the system of equations has a unique solution is a = -3.
1. Set the first equation equal to 0:
2x + ay = 2
2. Subtract 2x from both sides of the equation to get:
ay = -2
3. Divide both sides of the equation by a to get:
y = -2/a
4. Substitute this value of y into the second equation to get:
6x + 3(-2/a) = 3
5. Multiply both sides of the equation by a and simplify to get:
6ax - 6 = 3a
6. Add 6 to both sides of the equation to get:
6ax = 3a + 6
7. Divide both sides of the equation by 6 to get:
x = (3a + 6)/6
8. The value of a for which the system of equations has a unique solution is a = -3.
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Isabella has already baked 4 pies, and she can bake 2 pies with each additional cup of sugar she buys. Write an equation that shows the relationship between the additional cups of sugar x and the number of pies y.
Answer:
It would be y = 2x+4
Step-by-step explanation:
This is because Isabella has started with 4 baked pies and is gaining additional pies with in amounts of 2 pies.
With this, 4 would be by itself and 2 would be attached to the variable x for the unknown amount of additional pies.
Lastly, you would have this all equaling y, as y is the total amount of pies.
Mila cuts a sphere with a 13-inch radius in half. Whats the area of the cross section of the sphere in square inches in terms of pi
The area of the cross-section of the sphere in square inches in terms of pi will be 169π inch^2.
The area of a two-dimensional shape created when a three-dimensional object, like a cylinder, is cut perpendicular to a predetermined axis at a point is known as the cross-sectional area.
An area is projected onto the plane when a plane slices through a solid object. The axis of symmetry is then perpendicular to that plane. The cross-sectional area refers to its projection.
The cross-section of a sphere is a circle. Hence the area of the cross-section is the area of a circle with a radius of 13, which is given by π*r^2
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