you invest $2000 in an account that pays simple interest of 2% for twenty years. what amount of money will you have in 20 years
Answer:
$2971.9
Step-by-step explanation:
2000*(1+2%)^20 = 2971.895
What is the volume of the following rectangular prism? 3 1/3 1 2/5
Area of rectangular prism: Base x Height.
so 3x1/3x2/5=0.4 0r 2/5
Give a recursive definition for the following set of ordered pairs of positive integers (\(a|b\) means that a is a factor of b): \(S=\){\((a,b)|a \in Z^+, b \in Z^+, a|b\)}
A recursive definition for the set S can be given as follows:
What is recursion?
Recursion is a programming technique where a function calls itself to solve a problem.
Base case: (1, n) is in S for all positive integers n, since 1 is a factor of all positive integers.
Recursive case: If (a, b) is in S, then (a', b) is in S for all positive integers a' that are factors of a, and (a, b') is in S for all positive integers b' that are multiples of b.
In other words, the set S contains all pairs (a,b) where a is a positive integer that divides b, and b can be obtained by multiplying any such a with another positive integer. The base case includes all pairs where a=1 and b is any positive integer.
The recursive case states that if (a,b) is in S, then all pairs where a' is a factor of a and b is a positive integer such that b=a'b are also in S, as well as all pairs where b' is a multiple of b and a is a positive integer that divides b'.
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You will get 60 points!!!!
What is 1 whole as a fraction, decimal and percentage?
Fraction = 1/1
decimal = 1.0 or 1
percentage = 100%
A random sample of elementary school children in New York state is to be selected to estimate the proportion p who have received a medical examination during the past year. A random sample of 200 elementary school children indicated that 18 of them had received a medical examination in the past year.
a)Find point estimate for p and also construct a 95% confidence interval for p.
95 % of confidence interval of p = {0.0503372, 0.129663}
Point estimation
A single price estimate of a parameter is stated as a degree estimate.
A sample mean, for instance, could be a single purpose estimate of the population mean.
confidence interval
This is the vary of values you expect your estimate to fall between if you redo your take a look at at a given level of confidence.
p = 18 /200
95% means using 1.96
18/200 + 1.96*\(\sqrt{\frac{18 * 182}{200^{3} } }\)
18/200 - 1.96 *\(\sqrt{\frac{18 * 182}{200^{3} } }\)
18/200 + 1.96 *\(\sqrt{\frac{18 * 182}{200^{3} } }\)
{0.0503372, 0.129663}
Therefore, the 95% of confidence interval is {0.0503372, 0.129663}
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Find the 87th term in the following
arithmetic sequence:
-2, 6, 14, 22, ...
Hint: Write a formula to help you.
1st term + common difference (desired term - 1)
Answer:
first term (a)=-2
common difference (d)=8
Now,
87th term=a+(n-1)d
=-2+(87-1)×8
=-2+86×8
=-2+688
=686
A system of equations is created by using the line represented by 2 x + 4 y = 0 and the line represented by the data in the table below.
x
y
–1
8
3
–4
5
–10
6
–13
What is the x-value of the solution to the system?
A specific X-value for the solution ,-4 is not equal to -3/2.
The x-value of the solution to the system of equations, we need to solve the given equation and the line represented by the data in the table. Let's begin by examining the first equation, 2x + 4y = 0.
We can rewrite this equation in terms of y:
4y = -2x
y = (-2/4)x
y = (-1/2)x
Now, let's use the data from the table to create a system of equations:
For the first data point (-1, 8):
y = (-1/2)x
8 = (-1/2)(-1)
8 = 1/2
Since 8 is not equal to 1/2, the first data point does not satisfy the equation.
For the second data point (3, -4):
y = (-1/2)x
-4 = (-1/2)(3)
-4 = -3/2
Again, -4 is not equal to -3/2, so the second data point does not satisfy the equation.
We can continue this process for the remaining data points, but from the information given, it seems that none of the data points satisfy the equation. Therefore, there is no solution to the system of equations.
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-3x + 6 = 4 - 6x
I kept getting 1.5 But it's not correct. ???
Answer:
-2/3 or -0.6666
Step-by-step explanation:
-3x + 6 = 4 -6x
Let's move the x to one side
-3x +6x=4-6
Combine like terms
3x = -2
Divide both sides by 3
-2/3=x
or -0.666666
can 10/12 be simplified
Answer:
5/6
Step-by-step explanation:
10/12
Divide the top and bottom by 2
10/2 = 5
12/2 =6
the fraction becomes 5/6
Answer :
10/12
Reduce the fraction
= 5/6
Solve these 2 Question. 50 Points + Brainelist
using simultaneous equation:
2x + 3y = 190
3x + y = 180 * 3
Then:
2x + 3y = 190
9x + 3y = 540
--------------------
-7x = -350
x = 50
Insert this in equation 1 to find value of y:
2x + 3y = 190
2(50) + 3y = 190
3y = 190 - 100
3y = 90
y = 30
expanding the following:
→ (x + 2)³
\(\sf apply \ cubic \ formula : \bold{\left(a+b\right)^3=a^3+3a^2b+3ab^2+b^3}\)
\(\rightarrow \sf x^3+3x^2\cdot \:2+3x\cdot \:2^2+2^3\)
\(\rightarrow \sf x^3+6x^2+12x+8\)
Justify for x = 5
\(\rightarrow \sf (5)^3+6(5)^2+12(5)+8\)
\(\rightarrow \sf 125+150+60+8\)
\(\rightarrow \sf 343\)
Answer:
(a) x=50 y=30Step-by-step explanation for (a):
First use system of equations. Isolate a variable and substitute.
2x + 3y = 190
3x + y = 180
Isolate
subtract 3x from both sides of the second equation
y = 180 - 3x
since 180 - 3x = y, you can substitute this into the first equation for y
Substitute
2x + 3y = 190
2x + 3(180 - 3x) = 190
Distribute the 3
2x + (540 - 9x) = 190
Solve for x
subtract 540 from both sides
2x - 9x = -350
simplify
-7x = -350
divide each side by -7
x = 50
But you still need to solve for y, so substitute the x back into the first equation.(But really you could use either equation)
2(50) + 3y = 190
subtract 100 (2 * 50) from both sides
3y = 90
y = 30
Check your work by resubstituting.
3(50) + 30 = 180.
(b) This one is weird.
(x + 2)^3 expands to (x + 2)(x + 2)(x + 2).(Remember, it is NOT (x^3 + 8), you don't "distribute" the exponent)
It then simplifies to x^3 + 6x^2 + 12x + 8, and x = 5 is NOT an answer here. Maybe there is something more that you might not have screenshotted?
*edit its not asking to prove x is a solution(which i thought lolllll) its asking to plug x = 5 into the equation*
Identify the values of the variables. Give your answers in simplest radical form. HELP!
The value of the variables in the right triangle are as follows;
\(v = \frac{3\sqrt{2} }{2}\)\(w=\frac{3\sqrt{6} }{2}\)How to find the side of a right tringle?A right triangle is a triangle that has one of its angles as 90 degrees.
The side of a right triangle can be found by using trigonometric ratios.
Therefore, let's find the variable length of the right triangle as follows;
sin 30 = opposite / hypotenuse
sin 30 = v / 3√2
1 / 2 = v / 3√2
cross multiply
3√2 = 2v
divide both sides by 2
v = 3√2 / 2
Let's find the variable w.
cos 30 = adjacent / hypotenuse
cos 30 = w / 3√2
√3 / 2 = w / 3√2
cross multiply
√3 × 3√2 = 2w
3√6 = 2w
divide both sides by 2
w = 3√6 / 2
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What is the total surface area of the triangle prism shown
Answer:
Total surface area = 468 in.²
Step-by-step explanation:
Total surface area of triangular prism = 2BA + PH
Base area (BA) = ½*bh
b = 9 in.
h = 12 in.
2BA = 2(½*9*12) = 108 in.²
Perimeter of base (P) = 9 + 12 + 15 = 36 in.
Height of prism (H) = 10 in.
Plug in the values
Total Surface area of triangular prism = 108 + 36*10 = 468 in.²
Select the correct answer. Consider the function below. x -1 0 1 2 f(x) -2 3 8 13 Which of the following functions could be the inverse of function f? A. x -2 3 8 13 q(x) -1 0 1 2 B. x -2 -3 -8 -13 r(x) 1 0 -1 -2 C. x 1 0 -1 -2 s(x) -2 3 8 13 D. x -1 0 1 2 p(x) 2 -3 -8 -13
The function s(x) = -2, 3, 8, 13 could be the inverse of function f(x).
The correct option is C.
To determine the inverse of the given function f(x), we need to find a function that, when applied to the output of f(x), returns the input value.
Let's analyze the given function f(x):
x -1 0 1 2
f(x) -2 3 8 13
To find the inverse function, we need to swap the input and output values.
So, the input values of f(x) become the output values of the inverse function, and vice versa.
Let's examine the options:
A. x -2 3 8 13
q(x) -1 0 1 2
B. x -2 -3 -8 -13
r(x) 1 0 -1 -2
C. x 1 0 -1 -2
s(x) -2 3 8 13
D. x -1 0 1 2
p(x) 2 -3 -8 -13
By comparing the input and output values of the inverse functions with the original function f(x), we can see that option C (x and s(x)) matches the inverse function.
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determine what integer makes the inequality 6 ( n- 5 ) < ( n+ 4) true
The value of the integer n used to make the inequality true is n < 34/5.
What is inequality?In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using the inequality symbols.
The give inequality is:
6(n- 5) < (n+ 4)
Multiply the parentheses:
6n - 30 < n + 4
Regroup the variables such that n is on the same side of the equation:
6n - n < 4 + 30
5n < 34
Divide both sides of the equation with 5:
n < 34/ 5
Hence, the value of the integer n used to make the inequality true is n < 34/5.
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you sailed 0.032 units to the left and found treasure at 0.248 units find where the ship started
x + (-4) = -12 what is x?
Answer:
x=-8
Step-by-step explanation:
x+(-4)=-12
x-4=-12
x=-12+4
x=-8
UVT equals what?....
Answer:
m<UVT = 114°
Step-by-step explanation:
½(sum of intercepted arcs) = measure of vertex of an angle inside a circle
Thus:
½(FS + UT) = m<UVT
Substitute
½(53 + 175) = m<UVT
½(228) = m<UVT
114 = m<UVT
m<UVT = 114°
Kemone has a trunk that measures 3 feet wide, 4 feet long, and 2 feet high. What is the volume of the trunk? *
Answer:
24 ft cubed
Step-by-step explanation:
V=l*w*h
V= 4 x 3 x 2
4 x 3=12 and 12 x 2= 24
A random sample of 100 adults aged 18 years or older were given a list of ice cream flavors and were asked to list which flavors they liked. The responses are given below. Chocolate 45 Strawberry 42 Vanilla 23 Mocha 19 Which of the following graphs would be most appropriate for visually displaying the results? Pie Chart Frequency Bar Graph Relative Frequency Bar Graph
The most appropriate graph to visualize the information is a PIE CHART. The frequency bar graph makes an independent bar of each fruit each, while it is ideal, it is not easy to identify the total or percentage of each.
Both charts could be used to make a display of the information given.
The frequency bar graph makes an independent bar of each fruit each, while it is ideal, it is not easy to identify the total or percentage of each.
The pie chart could be used to represent a whole of the 100 fruits as a single circle and divides the circle into parts based on the number of fruit belonging to each type including their respective percentages.
Also, since the number of fruits/types are just 5, using a pie chart gives a more accurate and readable visual representation of the information.
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four numbers 43 and 44, write an equation for the parabola in standard form
Answer: 43) y = -x² - 2x + 3
44) y = (1/2)x² + 2x + 3
Step-by-step explanation:
43) Since the x-intercepts and another point are given, use the Intercept form:
y = a(x - p)(x - q) where
p and q are the x-intercepts"a" is the vertical stretch(x, y) is another point on the curveGiven: p = -3, q = 1 (x, y) = (-1, 4)
y = a(x - p)(x - q)
y = a(x + 3)(x - 1)
4 = a(-1 + 3)(-1 - 1)
4 = a(2)(-2)
4 = -4a
-1 = a
Equation: y = -1(x + 3)(x - 1)
Expand: y = -(x² - x + 3x - 3)
= -(x² + 2x - 3)
= -x² - 2x + 3
***********************************************************************************
Since the vertex and another point are given, use the Vertex form:
y = a(x - h)² + k where
(h, k) is the vertex"a" is the vertical stretch(x, y) is another point on the curveGiven: (h, k) = (-2, 1) and (x, y) = (0, 3)
y = a(x - h)² + k
y = a(x + 2)² + 1
3 = a(0 + 2)² + 1
3 = 4a + 1
2 = 4a
1/2 = a
Equation: y = (1/2)(x + 2)² + 1
Expand: y = (1/2)(x² + 4x + 4) + 1
= (1/2)x² + 2x + 2 + 1
= (1/2)x² + 2x + 3
Please answer this correctly
Answer:
Surface Area is 56π cm²
Step-by-step explanation:
The area for a cylinder's surface area is
a=2πrh+2πr²
The cylinder base's radius is 4 cm
The cylinder's height is 3 cm
Putting into the equation:
a=2×π×4×3+2×π×4²
a=2π×4×3+2×π×4²
a=8π×3+2×π×4²
a=24π+2×π×4²
a=24π+2×π×16
a=24π+2π×16
a=24π+32π
a=56π
The surface area of the cylinder is 56π cm².
which relation is a function? PLEASE HELPPPPP
Step-by-step explanation:
in the first
x =2y
actually I don't think that I can get the last two relations
A board that is 17/20
inch thick is run through a surfacing machine to reduce its thickness by 3/20
inch. What is the thickness of the board after this process?
Answer:
7/10
Step-by-step explanation:
17/20 - 3/20
14/20
7/10
find the area of the shaded region please
The area of the shaded region is 24x² - 78x + 33.
What is a square?A square is a two-dimensional figure that has four sides and all four sides are equal.
The area of a square is side².
We have,
Two squares:
Smaller square:
Side = x + 4
Larger square:
Side = 5x - 7
Now,
Area of the shaded region.
= Area of the bigger square - Area of the smaller square
= (5x - 7)² - (x + 4)²
= 25x² - 70x + 49 - x² - 8x - 16
= 24x² - 78x + 33
Thus,
24x² - 78x + 33 is the area of the shaded region.
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What is the third part of the process of investigating a question using data?
A. Making an inference
B. Rephrasing the question
C. Collecting the data
D. Describing the data
The third part of the process of investigating is describing the data.
It is required to find the third part of the process of investigating a question using data.
What is a statement?A statement is a declarative sentence that is either true or false but not both. A statement is sometimes called a proposition. The key is that there must be no ambiguity. To be a statement, a sentence must be true or false, and it cannot be both.
Given:
A. Making an inference
B. Describing the data
C. Rephrasing the question
D. Collecting the data
We have to determine which option is correct for
The third part of the process of investigating a question using
data.
What is the third part of the process of investigating?
The investigative process is a progression of activities or steps moving from evidence-describing tasks.
Therefore in this case third part of the process of investigating is describing the data.
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Brainliest If correct
what is −4/5+40/75+100%=
-0.8+1.875+100%
1.05+100%
0.1
Lines that appear to be tangent are tangent. O is the center of each circle.
What is the value of x? Show all work to receive full credit.
Note that in the prompt above, the value of x is given as: 16°
To answer the issue, we will first name all of the points supplied to us on the isosceles triangle, then identify O, and last discover the value of x. See the attached image.
What is an isosceles triangle?As a result, an isosceles triangle has two equal sides and two equal angles. The term is derived from the Greek words iso (same) and skelos (skull) (leg). An equilateral triangle has all of its sides equal, whereas a scalene triangle has none of its sides equal.
In ΔAOB
OA = OB = R, the radius of the circle O,
therefore, the ΔAOB is an isosceles triangle, with OA, OB as the congruent sides and AB as the base of the triangle.
Thus, ∠OAB = ∠OBA = 53°
Sum of all the angles of a triangle = 180°
∠O + ∠AOB + ∠OBA = 180°
We know ∠AOB = ∠OBA, therefore,
∠O + 2(∠AOB) = 180°
∠O + 2(53°) = 180°
∠O = 180 - 106
∠O = 74°
In ΔOBC,
BC is the tangent to the circle O, therefore,
∠OBC = 90°
Sum of all the angles of a triangle = 180°
∠O + ∠OBC + ∠OCB = 180°
74° + 90° + ∠OCB = 180°
∠OCB = 180° - 74° - 90°
∠OCB = 16°
Hence, the value of x is 16°.
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Graph the solution to this inequality on the number line.
−3x<4.2
Answer:
\(3x < 4 .2\)
\(huge/pink/answer[text]
Answer:
draw the 4th arrow from -1.4 to full right until 3 or more
Step-by-step explanation:
Open circles are used for numbers that are less than or greater.
Closed circles are used for numbers that are equal to and less than or equal to and greater than.
im not sure how to solve this can somebody help
The population of organisms is described by the following exponential equation:
P(t) = 18,000*(0.9966)^t
How to get the exponential equation?
The general exponential equation is:
P(t) = A*(b)^t
Where A is the initial value, b depends on the percentage that changes, and t is the variable.
In this case, the population decreases by 3.4%, then we have:
B = 1 - 3.4%/100% = 0.9966
And the initial value is 18,000 organisms, replacing that in the general equation we get:
P(t) = 18,000*(0.9966)^t
This is the equation that represents the population.
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