$14587.5 should be deposited today
What is Compound interest?Compound interest, also called "compounding interest," is the interest on the initial investment as well as the accrued interest on that investment.
We would apply the formula for determining compound interest which is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited.
From the information given,
A = 25000
r = 8% = 8/100 = 0.08
n = 1 because it was compounded once in a year.
t = year
Therefore, substituting the values into the formula
25000 = P(1 + 0.08/1)^1 × 7
25000 = P(1.08)^7
25000 = 1.7138P
P = 25000/1.7138
P = $14587.5
Hence, the amount that should be deposited is $14587.5
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Is it true that 5 2/3 - 3 3/4 = 1+ 2/3 + 3/4?
The fraction 5 2/3 - 3 3/4 is not equal to 1+ 2/3 + 3/4.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, 5 2/3 - 3 3/4 will be:
= 5 2/3 - 3 3/4
= 5 8/12 - 3 9/12
= 1 11/12
Therefore 1 + 2/3 + 3/4
= 1 + 2/3 + 3/4
= 1 + 8/12 + 9/12
= 2 5/12
They are not the same.
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A certain forest covers an area of 2,000 square kilometers. Suppose that each year, this area decreases by 6%. What is the equation that best represents the area of the forest each year?
Hint: Use the formula y = P(1 + r)x.
y = 2,000(0.94)x
y = 2,000(1.06)x
y = 2,000(0.06)x
y = 2,000(1.94)x
The equation that best represents the area of the forest each year is A. y = 2,000(0.94)^x.
What is an equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Since the certain forest covers an area of 2,000 square kilometers and each year, this area decreases by 6%.
The equation will be:
= 2000(1 - 6%)^x
= 2000(0.94)^x
In conclusion, the correct option is A.
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Help? and explanation
We can rewrite the circle equation as:
(x - 2)^2 + (y +4)^2 = 3^2
Then the correct option is the first one, the radius is 3 units and the center is (2, -4)
How to find the center and radius of the circle?
The equation for a circle of radius R and center (a, b) is written as:
(x - a)^2 + (y - b)^2 = R^2
Here the equation is:
x^2 + y^2 - 4x + 8y + 11 = 0
We need to complete squares, we can rewrite:
(x^2 - 4x) + (y^2 + 8y) + 11 = 0
(x^2 - 2*2x) + (y^2 + 2*4y) +11 = 0
Now we can add and subtract 2^2 and 4^2 in each parenthesis, so we get:
(x^2 - 2*2x + 2^2) - 2^2 + (y^2 + 2*4y + 4^2) - 4^2 + 11 = 0
(x - 2)^2 + (y + 4)^2 - 4 - 16 + 11 = 0
(x - 2)^2 + (y + 4)^2 = 9 = 3^2
(x - 2)^2 + (y +4)^2 = 3^2
So, the radius of the circle is 3 units, and the center of the circle is the point (2, -4)
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What are the 5 ways triangles are congruent?
The correct answer is the 5 ways to find if two triangles are congruent are SSS, SAS, ASA, AAS and HL.
Two triangles are congruent if and only if they have the same three sides and angles.
SSS (side, side, side): SSS, which stands for "side, side, side," denotes that there are two triangles with identical angles on all three sides. The triangles are congruent if their third sides are the same as those of another triangle.
SAS (side, angle, side): "Side, Angle, Side" stands for two triangles whose two sides and one included angle are known to be equal. The triangles are congruent if two sides and the included angle of one triangle equals the corresponding sides and angle of another triangle.
ASA (angle, side, angle): ASA, which stands for "angle, side, angle," denotes the existence of two triangles whose included side and two known angles are equal. The triangles are congruent if two angles and the included side of one triangle match the corresponding angles and side of another triangle.
AAS (angle, angle, side): AAS, which stands for "angle, angle, side," denotes the equality of the non-included side and two angles in two triangles. The triangles are congruent if two of one triangle's angles and its excluded side are equal to the corresponding angles and sides of another triangle.
HL (hypotenuse, leg): The two triangles are congruent if one right-angled triangle's hypotenuse and one of its legs are equal to its corresponding hypotenuse and leg in another right-angled triangle.
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When a transversal cuts parallel lines, how can one angle measurement be used to determine all of the other measurements?
Answer: If two parallel lines are cut by a transversal, then corresponding angles are congruent.
Step-by-step explanation:
The table shows that the total cost of a ride-sharing trip, y, is a function of the distance traveled, a.
What is the rate of change and what does it mean?
2; the ride costs $2 per mile.
43; the ride costs $3 per mile.
2; it costs $2 as soon as you start the ride.
4) 3; it costs $3 as soon as you start the ride.
Distance (mi), Total Cost ($). y
2
5
8
11
14
0
1
2
3
4
Answer:3; the ride costs $3 per mile
Step-by-step explanation:
Rate of Change of the function is 3. then the ride costs $3 per mile.
What is the average rate of change?The average Rate of Change of the function f(x) can be calculated as;
[tex]f(x) = \dfrac{f(b) - f(a)}{b-a}[/tex]
We are given the total cost of a ride-sharing trip, y, is a function of the distance traveled,
Distance (mi), Total Cost ($). y
2 0
5 1
8 2
11 3
14 4
Therefore,
Rate of Change of the function
(5 - 2) / (1- 0)
= 3 / 1
Hence, we can conclude that the ride costs $3 per mile.
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Please help I need part A and B
Formula for the mass m = Dv and the mass of gasoline is 9520 gm. The formula for volume is v = m/D and the volume of the syrup is 52.63 cm³.
What is the meaning of mass?
A measure of the amount of matter contained in or constituting a physical body.
Given that, D = m/v
Multiply both sides by v
Dv = m
Rearrange the above equation:
m = Dv
Putting D = 0.680 gm/cm³ and v = 14000 cm³ in the above equation:
m = (0.680 gm/cm³) × (14000 cm³)
m = 9520 gm
Given that, D = m/v
Multiply both sides by v
Dv = m
Divide both sides by D
v = m/D
Putting D = 0.950 gm/cm³ and m = 50.0 gm in the above equation:
v = (50.0 gm) / (0.950 gm/cm³)
m = 52.63 cm³
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Eight workers are hired to harvest strawberries from a field. Each is given a plot with an area of 72 ft² What is the total area
strawberry field?
Answer:
576 ft squared
Step-by-step explanation:
8 x 72 ft= 576 total area
Hope this helps!
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 circular spinner has seven sections of equal size, each of which is colored either red or blue. Two colorings are considered the same if one can be rotated to yield the other. In how many ways can the spinner be colored?
The number of ways that the spinner can be colored is 21 ways.
How to calculate the number of ways?Combinations are also referred to as selections. Combinations implies the selection of things from a given set of things. In this case, we intend to select the objects.
Combination formula
nCr = n! / ((n – r)! r!)
n = the number of items.
r = how many items are taken at a time.
Based on the information given, the number of ways will be to select 2 out of 7. This will be:
= 7! / (7 - 2)!2!
= 7! /5!2!
= (7 × 6) / 2
= 42/2
= 21
There'll be 21 ways.
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1. The unit price of an item is how much it costs for one item. It's useful to know the unit price when buying in bulk. If we're buying 100 items, then you'll save quite a bit of money if you buy the unit priced item that costs $10 per item compared to the unit price of $12 per item!
You can calculate a unit price by dividing the total amount of money you spent for items by the number of items you purchased. For instance: $7.99 per oz of goldfish is $ 7.99 / 30= 0.26$ per ounce.
Which purchase has the lower unit price - $\$ 200$ for 15 flower arrangements, or $70 for 5 flower arrangements?
What is division?
Division is the process by which value of single unit can be calculated from the value of multiple unit.
The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.
There is a well known formula for division
Divisor x Quotient + Remainder = Dividend.
This is a problem sum of division
Cost of 15 flowers = $200
Cost of 1 flower = $200 [tex]\div[/tex] 15 = $13.33
Cost of 5 flowers = $70
Cost of 1 flower = $70 [tex]\div[/tex] 5 = $14
So unit price of 15 flower arrangement of $200 is lower than unit price of 5 flower arrangement of $70
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"Even in winter, the roadsides were places of beauty, where countless birds came to feedon the
berries and on the seed heads of the dried weeds rising above the snow. The countryside was, in
fact, famous for the abundance and variety of its bird life, and when the flood of migrants was
pouring through in spring and fall, people came from great distances to observe them"
(paragraph 5).
Why most likely does the author give a detailed description of a healthy ecology (the
study of organisms and how they interact to the environment around them) as noted in
paragraph 5?
A. To promote birdwatching to people visiting the town
B. To give the natural history of a specific region
C. To describe different tourist activities of people pouring through the town
D. To contrast how the town changed once the ecology was compromised with the use of
harmful pesticides
The author gives a detailed description of a healthy ecology D. To contrast how the town changed once the ecology was compromised with the use of harmful pesticides.
What is the ecology about?
Ecology also teaches us about the benefits of ecosystems and how to use the Earth's resources in a way that protects the environment for future generations. We can learn more about our surroundings thanks to the various fields of ecology, which include statistical ecology, marine ecology, and vegetation ecology.
With the help of this information, we can manage our natural resources, protect human health, and improve the environment. In this case, the author give a detailed description of a healthy ecology.
The correct option is D.
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Question 3 of 10
If r^n = a, then which of the following are true statements?
Check all that apply.
A. Va=r
B. a¹/n=r
C. n¹/r= a
D. a = n
Answer:
Option B is the correct option
Step-by-step explanation:
What is a prime multiple?
The multiples of a number are numbers found by multiplying the original number by any whole number. Prime multiples are number which multiply each other and form a prime
What are Prime Numbers ?
A prime number is a number that is only divisible by 1 and itself. So, prime numbers have only two factors, 1 and the number itself.
This means these numbers cannot be divided by any number other than 1 and the number itself without leaving a remainder.
Numbers that have more than 2 factors are known as composite numbers.
For example :
The factors of 3 are 1 and 3.
Therefore, the prime multiples of 3 are 1 and 3.
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The floor of a rectangular banquet hall has an area of 3,600 3 m 3 (cubic meters). The length is 90 meters. A. What is the width of the banquet hall?
The width of the rectangular banquet hall is 40 meters
Calculating the width of a rectangular floorFrom the question, we are to determine the width of the rectangular banquet hall.
From the given information,
"The floor of a rectangular banquet hall has an area of 3,600 m² (square meters)"
From the formula for calculating the area of a rectangle, we have that
A = L × W
Where A is the area of the rectangle
L is the length
and W is the width
From the given information,
The length of the hall is 90 meters.
Thus,
3600 = 90 × W
W = 3600 / 90
W = 40 meters
Hence, the width is 40 meters
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What is the variable in this expression?
4b + 2b + 1⁄4
The variable in this expression 4b + 2b + 1⁄4 is b
How to determine the variable?From the question. we have the following expression
4b + 2b + 1⁄4
Take for instance, we have an expression
Ax
Where A is a number
It means that the expression x is a variable
This is so because the value of x can change
Similarly, the variable in 4b + 2b + 1⁄4 is b
This is so because the value of b can change
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When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle it means that we are going to use what postulate?
The used postulate is explained below.
What is congruent triangles?
Two triangles are stated to be congruent if the 3 facets and the 3 angles of each the angles are same in any orientation.
When angles and facet blanketed in among those angles of 1 triangle are identical as any other one, each those triangle are Congruent.
This standards of congruency is is aware of as ASA criterion as a facet blanketed among angles are all identical.
Two triangles are congruent, if angles and the facet blanketed among them in a single triangle is same to the 2 angles and the facet blanketed among them of the alternative triangle.
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Complete the sentence.
The intersection of two regular pentagons can be _____.
a point a line
a ray a hexagon
The intersection of two regular pentagons can be a hexagon.
What are regular pentagons?It is a regular pentagon if all of its sides and angles are equal in size. and it is an irregular pentagon if it is not. Each angle inside the regular pentagon is 108° , that is all internal angles of a regular pentagon has 108 degrees for each internal angle. Every side of a regular pentagon has an equal length and an equal angle. Equiangular shapes are those with angles that are exactly equal. It is due to the fact that the internal angles of a polygon add up to 360 degrees. Additionally, the length of every side is the same.A pentagon's centre is at an angle of 72 degrees produced by two lines connecting its two adjacent corners in other words, each angle outside or the exterior angle is 72°. The intersection of two regular pentagons can be a hexagon.To learn more about regular pentagons ,refer:
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I need help bxbcbcbcbcbcbcbcbcbcb
The shape of Keisha's rectangular shaped planter would be the shape with the dimensions shown in the image below.
What is the Volume of a Rectangular Box?The volume of a rectangular box = length × width × height.
The shape of the planter is a rectangular box.
Given that the rectangular shaped planter would be filled first by 4 in. of rocks, it means the height of the rectangular shaped planter that the rock will occupy up to would be 4 in.
Find the volume the rock would fill:
Height = 4 in.Length = 10 inWidth = 10 in.Volume occupied by the rocks in the rectangular shaped planter = (10)(10)(4) = 400 in.²
If the soil to be filled must be exactly 800 in.², then the total volume of the shape of the rectangular planter that would be used would be: 400 + 800 = 1,200 in.².
From the options given, the last shape that has a height of 12 in., length of 10 in, and width of 10 in will have a volume = (12)(10)(10) = 1,200 in.².
Therefore, the last shape in the diagram below could be the shape of Keisha's rectangular shaped planter.
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How do you find a polynomial?
Answer:
To find a polynomial, you must identify the terms, coefficients, and degrees. The degree of a polynomial is the highest exponent of the variable in the equation. The coefficients of a polynomial are the values that are multiplied by the variables. The terms of a polynomial are the pieces of the equation, including the coefficients and the variables. After identifying the terms, coefficients, and degree of the polynomial, you can write it in standard form.
Step-by-step explanation:
In Exercises 13-16, find the area of the polygon with the given vertices. (See Example 3.)
13. E(3,1), F(3,-2), G(-2,-2)
14. J(-3,4), K(4,4), L(3,-3)
The area of the polygon EFG with given vertices is, 7.5 units.
What is area of triangle?
The area of a triangle is the area that it completely encloses in a two-dimensional plane. A triangle is a closed shape that, as we all know, has three sides and three vertices. As a result, the total area occupied by a triangle's three sides is known as its area. The general formula for calculating a triangle's area is the product of the triangle's base and height divided by half.
Let the given vertices are,
E(3, 1), F(3, -2), G(-2, -2)
There are three vertices, so the polygon is a triangles.
Since,
Area of triangle = 1/2 x base x height.
If we draw the given vertices on the coordinate plane then the base is FG and the height of the triangle is EF.
Now to find the lengths of side FG and EF.
By using the distance formula,
[tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\EF =\sqrt{(3-3)^2+(-2-1)^2} = \sqrt{9} = 3\\ FG = \sqrt{(-2-3)^2 + (-2-(-2))^2} = \sqrt{25+0} = 5[/tex]
⇒ Area = 1/2 x 5 x 3
= 1/2 x 15
Area = 7.5
Hence, the area of the polygon EFG is 7.5 units.
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Find the length of the hypotenuse, side c, of a right triangle with legs of length a = 6 and b = 12. Use a calculator to estimate
the square root to one decimal place.
6
12
The length of the hypotenuse, c, is approximately
The solution is
Answer:
c=13.4
Step-by-step explanation:
The perimeter of a rectangle is 204 centimeters. Find the length and width if the length is an even integer and the width is 3 times the next consecutive even integer.
Step-by-step explanation:
2×length + 2×width = 204 cm
length = x
width = 3×(x + 2)
as consecutive even integers are always spaced out by 2 (2, 4, 6, ...).
we are using these 2 equations in the first main equation :
2×x + 2×3×(x + 2) = 204
2x + 6x + 12 = 204
8x + 12 = 204
8x = 192
x = 192/8 = 24
length = x = 24 cm
width = 3(x + 2) = 3×26 = 78 cm
What would the answer be? I tried 4 and -4 and a lot more.
Answer:
-2
Step-by-step explanation:
a is -3
d is -1
you subtract the two
-3 - (-1)
when you have two negatives they cancel each other out and become positive
-3 + 1
-3 + 1 = -2
that is your answer
how many sides does a regular polygon have
Answer: a polygon is a shape with at least three straight sides and angles, and typically five or more
Step-by-step explanation:
what is the end behavior of the graph of fx x 5 8x 4 16x 3
The end behavior of the graph of f(x) = x⁵ – 8x⁴ + 16x³ does not cross the x-axis at x = 4 and crosses the x-axis at x = 0. This is about the end behavior of a graph of a function at the end of the x-axis. Also, f(x) => -∞ as x => -∞; f(x) => +∞ as x => +∞.
We are given the function;
f(x) = x⁵ - 8x⁴ + 16x³
A) As x approaches negative infinity -∞, x⁵ will also approach negative infinity -∞. This is because when we raise a negative number to the power of an odd number, the result remains negative.
B) As x approaches positive infinity +∞, x⁵ will also approach positive infinity -∞. This is because when we raise a positive number to the power of an odd number, the result remains positive.
Let's now find the roots of this function;
f(x) = x⁵ - 8x⁴ + 16x³
Let's factorize it first to get;
f(x) = x³(x² – 8x + 16)
(x² – 8x + 16) is a perfect square trinomial and can be expressed as (x – 4)(x - 4).
Thus;
f(x) = x³ (x – 4)(x - 4)
C) Since we have found the factorized form to be;
f(x) = x³ (x – 4)(x - 4)
The roots are at f(x) = 0;
The roots are; x³ = 0; (x – 4) = 0 ; (x - 4) = 0
This means the roots of f(x) are; x=0 and x=4. x = 4
This means the graph has a repeated root and so it will touch the x-axis but not at the repeated root of x=4.
D) Since, 0 is a root and it does not cross at x = 4, the graph will cross at x = 0.
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How do you find the range on a graph?
The range of a graph can be found using the values depicted on the y-axis.
According to the question,
We have the following information:
We have a graph and we need to know how do we find the range of that graph.
We know that the domain of a graph is the collection or in other words set of input values depicted on x -axis and the range of a graph is the set of possible output values portrayed on y-axis of the graph.
In noting down the range of a graph, we first list down the down value and then the up value or in other words we move from down to up in order to find the range of a graph.
Hence, the range of a graph can be found using the values depicted on the y-axis.
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(1 point)
Solve this inequality, and write your answer in interval notation.
|x|>-5
Please type:
- int for oo,
- no solution if there are no real solutions
- U for the union symbol U
You have attempted this problem 8 times.
Your overall recorded score is 0%
You have unlimited attempts remaining.
Answer: [tex](-\infty, \infty)[/tex]
Step-by-step explanation:
Absolute value is always non-negative.
If I have the quadratic parent
function and I move it to the
right 6 units, what is the new
question?
Answer: [tex]y=(x-6)^2[/tex]
Step-by-step explanation:
If the original equation is [tex]y=f(x)[/tex], then the equation after the shift is [tex]y=f(x-6)[/tex].
Directions: Find the value of each variable.
11) x=?
y=?
12) x=?
y=?
13) x=?
y=?
14) x=?
y=?
15) x=?
y=?
z=?
The value of the variables x and y are,
11) x = 13, y = 18.4
12) x = 6.9, y = 8.
What is right angle triangle?
A right triangle is a triangle with one angle at a right angle, meaning that two of its sides are perpendicular. It is also known as a right-angled triangle, an orthogonal triangle, or more commonly as a rectangled triangle. Trigonometry's foundation is the right triangle's relationship between its sides and other angles.
11)Let the given triangle is a right angle triangle.
So we can use trigonometric ratio,
[tex]tan(45) = \frac{x}{13} \\x = 13(tan(45))\\x = 13[/tex]
Using this to find the value of y.
[tex]sin(45) = \frac{x}{y} \\sin(45) = \frac{13}{y} \\y = \frac{13}{sin(45)} \\y = 18.4[/tex]
So, the values of x and y are x = 13 and y = 18.4.
12) The given triangle is a right angle triangle.
So we can use trigonometric ratio,
[tex]tan(30) = \frac{4}{y}\\ y = \frac{4}{tan(30)} \\y = 6.9[/tex]
Now to find the value of x.
[tex]sin(30) = \frac{4}{x} \\x = \frac{4}{sin(30)} \\x = 8[/tex]
Hence, the values of x and y are, x = 6.9 and y = 8.
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