A grandmother deposited $4,000 in an account that pays 5% per year compounded annually when her granddaughter was born. What will the value of the account be when the granddaughter reaches her 13th birthday?
The value of the account is $7542.59.
What is interest?It is computed by adding the annual interest rate raised to the number of compound periods and subtracting one after multiplying the initial principal amount by one. The resulting value is subsequently deducted from the loan's entire original amount.
Given:
P=4000
r = 5%
t = 13 years
Now, using the formula
[tex]A = P( 1 + r/n)^{nt}[/tex]
A = 4000[tex](1 + 0.05/1)^{(13)(1)[/tex]
A= 4000[tex](1.05)^{13[/tex]
A = 4000 x 1.8856
A = $7542.59
Hence, The value of the account is $7542.59.
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A class contains 3 female and 9 male students. Find the probability that a student chosen at random is a male, and then a second student chosen at random from the remaining students is also male.
a). 9/16
b). none
c). 1/2
d).6/11
e).3/4
HELPP today plzzz!!!
The probability that two student chosen at random is a male is 6/11.
What is the Probability?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.
Here, Class contains 3 females and 9 males it means total 12 students.
Probability for having 1st student male = 9/12 = 3/4
Probability for having 2nd student is also male = 8/11
Overall Probability = [tex]\frac{3}{4} X \frac{8}{11}[/tex]
= 6/11
Thus, the probability that two student chosen at random is a male is 6/11.
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Given: segment AB || segment DE, C is the midpoint of segment DB. Prove: ΔACB ≅ ΔECD Fill in the missing reason for the proof. A) definition of midpoint B) vertical angles are congruent C) all right angles are congruent D) supplementary angles are congruent
Answer:
Given: Segment AB || segment DE, C is the midpoint of segment DB.
Prove: ΔA CB ≅ ΔE CD
Proof: In ΔA CB and ΔE CD
C is the Mid point of B D.
BC=C D→ definition of midpoint
∠A CB= ∠ EC D→→vertical angles are congruent
∠BAC=∠DEC→→[AB║DE,so alternate angles are equal]
→→ΔA CB ≅ ΔE CD[A AS or A SA]
Option B: vertical angles are congruent
Answer:
The answer is A) Definition of midpoint
Step-by-step explanation:
Answer B is wrong. I just did the test
1 What is the solution to the system of equations?
3x-4y=16
2x+3y=5
A (–4, 1)
B(4, –1)
C(–4, –1)
D (4, 1)
2 what is the solution to the system of equations?
7x-2y=-24
5x+5y=15
A (2, –5)
B (–2, 5)
C (–2, –5)
D (2, 5)
Answer:
The answer for the first question would be B: (4, –1)
Step-by-step explanation:
what is the slope of the line represented by the equation below? y=-2/3x+3
Answer:
-2/3
Step-by-step explanation:
The slope is the coefficient of x: -2/3.
___
This tells you how much y changes when x changes by 1 unit. The slope is the change in y divided by the change in x.
What is the better estimate for the height of a desk,1 meter or 1 kilometer
The area of a circle is 225 pie square inches. Find the area of the sector whose central angle is 45°.
The area of the sector of the circle is 28.125π inches²
What is a Circle?
A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the centre for every angle
The total internal angle is 360° about the centre
The area of the sector of the circle = ( θ / 360° )πr²
The perimeter of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
Given data ,
Let the area of the circle be = A
The value of A = 225 inches²
Now , the area of the sector whose central angle is 45° is calculated by
The area of the sector of the circle = ( θ / 360° )πr²
Substituting the value for θ = 45° , we get
Area of the sector of the circle = ( 45/360 ) x 225
= ( 1/8 ) x 225
= 28.125 inches²
Therefore , the area of the sector is 28.125 inches²
Hence , The area of the sector of the circle is 28.125π inches²
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Describe how to solve problems for the area of a reduced or enlarged figure when the scale factor and dimensions of the original figure are given.
To solve problems for the area of a reduced or enlarged figure, determine the scale factor, find the corresponding dimensions, and calculate the area using the appropriate formula.
Explanation:To solve problems for the area of a reduced or enlarged figure when the scale factor and dimensions of the original figure are given, follow these steps:
1. Determine the scale factor by comparing the dimensions of the original figure to the dimensions of the reduced or enlarged figure.
2. Use the scale factor to find the corresponding dimensions of the reduced or enlarged figure.
3. Calculate the area of the reduced or enlarged figure using the appropriate formula for the shape (e.g., length * width for a rectangle).
For example, if the original figure is a rectangle with dimensions of 4 inches by 6 inches, and the scale factor is 2, the corresponding dimensions of the reduced or enlarged figure would be 8 inches by 12 inches. The area of the reduced or enlarged figure would then be calculated as 8 inches * 12 inches = 96 square inches.
Sample Response: To solve problems for the area of a reduced or enlarged figure, first square the scale factor. Then use the given dimensions to find the area of the original figure. Multiply the square of the scale factor by the area of the original to get the reduced or enlarged figure.
Last year, 120 new houses were built in a neighborhood. So far this year, 56 of them have been sold. How many new houses have been sold this year?
Katherine practices skiing for 1 1/2 hours every day except Saturday and Sunday. She practices for four hours on Saturday and three hours on Sunday. How many hours does she practice in a week?
1 1/2 hours x 5 days = 7 1/2 hours
4+3 +7 1/2 = 14 1/2 hours per week
You bought the meat for Saturdays cookout. A package of hot dogs cost $1.60 and a package of hamburgers cost $5. You bought a total of 8 packages of meat and you spent $23. How many packages of hamburger meat did you buy?
The number of hamburger meat he bought is 3.
How to find the number of hamburger meat bought?A package of hot dogs cost $1.60 and a package of hamburgers cost $5.
You bought a total of 8 packages of meat and you spent $23.
Therefore,
let
x = number of package of hot dogs
y = number of package of hamburger
Hence,
x + y = 8
1.60x + 5y = 23
multiply equation(i) by 5
5x + 5y = 40
1.60x + 5y = 23
Subtract equation(ii) from equation(i)
3.4x = 17
x = 17 / 3.4
x = 5
y = 8 - 5
y = 3
Therefore, the number of hamburger meat he bought is 3.
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The formula for the area, A, of a circle is A = πr2 , where r is the circle’s radius, and the formula for the circumference, C, of a circle is C = πd , where d is the circle’s diameter. Which statement is correct?
Answer:
The formula for the circumference, C, of a circle is C = πd , where d is the circle’s diameter.
Step-by-step explanation:
For a circulus with radius r, we have that:
The area of the circulus is:
[tex]A = \pi r^{2}[/tex]
That is, the radius is squared, not multiplied by 2, so the first statement is incorrect.
The circumference of the circulus is:
The derivative of the area, so
[tex]C = 2\pi r[/tex]
However
The radius if half the diameter. So
[tex]C = 2\pi \frac{d}{2}[/tex]
[tex]C = \pi d[/tex]
So the correct statement is:
The formula for the circumference, C, of a circle is C = πd , where d is the circle’s diameter.
Both statements are correct. The formula for the area of a circle is A = πr², where r is the radius, and the formula for the circumference of a circle is C = πd, where d is the diameter.
The formula for the area of a circle is given by A = πr², where A represents the area and r represents the radius of the circle. In this formula, the radius is squared and then multiplied by the mathematical constant π (pi) to calculate the area enclosed by the circle.
On the other hand, the formula for the circumference of a circle is given by C = πd, where C represents the circumference and d represents the diameter of the circle. In this formula, the diameter is multiplied by the mathematical constant π to calculate the total distance around the circle.
These formulas are derived from the properties of circles. The radius is the distance from the center of the circle to any point on its edge, while the diameter is the distance across the circle passing through its center. The circumference represents the boundary or perimeter of the circle, while the area represents the space enclosed by the circle.
It's important to note that the relationship between the radius and diameter is given by the equation d = 2r, where d represents the diameter and r represents the radius. This relationship allows us to interchangeably use the radius or diameter in the formulas for the area and circumference of a circle.
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Complete Question:
1. The formula for the area, A, of a circle is A = [tex]\pi r^2[/tex] , where r is the circle’s radius.
2. The formula for the circumference, C, of a circle is C = πd , where d is the circle’s diameter.
Which of the above statements is correct?
Imagine that you are pouring cement into cinder blocks to build a very sturdy wall. Each cinder block is 1.3 feet long, 0.67 feet high, and 0.67 feet wide. If 1 bag of cement is equivalent to 5 cubic feet, what is the number of bags of cement that you will need to fill the entire wall? Show the work
To find out how many cement bags are needed, calculate the volume of one cinder block and see how many such blocks fit in a cement bag. Then, divide the total number of cinder blocks by the number of blocks one bag can fill and round up to the nearest whole number.
To determine the number of cement bags needed to fill a cinder block wall with the given measurements, first calculate the volume of one cinder block. Then, figure out how many cinder blocks fit into one bag of cement.
The volume of one cinder block is:
V = length × height × width
V = 1.3 ft × 0.67 ft × 0.67 ft
V [tex]\approx[/tex] 0.5809 cubic feet
Now, since one bag of cement is equivalent to 5 cubic feet, determine how many cinder blocks one bag can fill:
Number of blocks per bag = 5 cubic feet / 0.5809 cubic feet per block
Number of blocks per bag [tex]\approx[/tex] 8.61 blocks
We need the total number of cinder blocks for the entire wall. Assuming we know the total wall dimensions, let's say we have a total of 100 blocks (for example purposes).
Total number of bags = Total number of blocks / Number of blocks per bag
Total number of bags = 100 / 8.61
Total number of bags [tex]\approx[/tex] 11.62
Since you can't buy a fraction of a bag, you would need to round up to the next whole number, so you would need 12 bags of cement to fill the wall.
Which type of deposit is paid in advance to protect landlords against nonpayment?
a.security deposit
b.special deposit
c.surity deposit
20 POINTS!! pleasee help!
Example: y = -2x and y = x + 3
does the point (0,4) make either equation true? substitute it in and find out
There are 50 identical apples that need to be distributed among alice, bob, and cathy. determine the numberof ways that this can be done such that each one of them gets at least 2 apples. as examples, possible distributions ofthe identical apples among alice, bob and cathy include (a, b,
c.= (46, 2, 2); (10, 10, 30); (9, 2, 39), etc., where a,b and c denote the number of apples allocated to alice, bob and cathy respectively.
The first class had a kids in it, the second had b kids in it, and the third class had c kids in it. Kids from all three classes were equally divided between two buses. How many kids were on each bus?
(30 points)
What are genes?
A. The ovservable characteristic.
B. The expressed trait.
C. The basic unit of inheritance.
D. The measurable factor.
Gets Brainliest and 11 pts!
The table below shows the number of marbles of different colors in a bag: Color of Marbles Number of Marbles Pink 5 Blue 2 Green 3 Ursula draws a marble from the bag randomly without looking. She then draws another marble from the bag without replacing the first one. Which expression shows the probability of drawing green marbles in both the trials? 3 over 10 multiplied by 2 over 9 3 over 10 multiplied by 2 over 10 3 over 10 added to 2 over 9 3 over 10 added to 2 over 10
Answer:
3/10 * 2/9
Step-by-step explanation:
5a - {3b - 5[a - (b + -4a)]}
I need help I would really thank wheeler answers this for me
5 is one-fourth of a number c.
The value of number c is 20
5 as one-fourth of a number c is represented using the following equation
[tex]5 = \frac 14 \times c[/tex]Multiply both sides of the above equation by 4
[tex]4\times 5 = \frac 14 \times c \times 4[/tex]Evaluate the products
[tex]20 = c[/tex]Rewrite the above equation as
[tex]c = 20[/tex]Hence, the value of number c is 20
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If given f(x) = x + 4 and g(x) = –2x2 + 3x – 1, what is (f – g)(x)?
A.
(f – g)(x) = –2x2 + 4x – 3
B.
(f – g)(x) = –2x2 – 2x + 5
C.
(f – g)(x) = 2x2 + 2x + 5
D.
(f – g)(x) = 2x2 – 2x + 5
For the graph x = -3 find the slope of a line that is parallel to it.
-3
-1/3
0
undefined
Answer:
undefined
Step-by-step explanation:
Meis mothers is 4 times as old as mei. Mei’s mother is twice as old as mei’s mother.the sum of the three ages of 117. How old is mei, her mother, and her grandmother?
Final answer:
Mei is 9 years old, her mother is 36 years old, and her grandmother is 72 years old, determined by defining variables for their ages and solving the equation based on their age relationships and the given total sum of their ages.
Explanation:
To solve the problem regarding the ages of Mei, her mother, and her grandmother, we can use a system of equations based on the information given. Let's define Mei's age as m, her mother's age as 4m (since her mother is 4 times Mei's age), and her grandmother's age as 8m (since the grandmother is twice as old as Mei's mother).
According to the problem, the sum of their ages is 117 years:
m + 4m + 8m = 117
Simplifying this equation gives us:
13m = 117
Next, we divide both sides by 13 to find m:
m = 117 / 13
m = 9
Now that we have Mei's age, we can easily calculate her mother's and grandmother's ages:
Mei's mother: 4m = 4(9) = 36 years oldMei's grandmother: 8m = 8(9) = 72 years oldTherefore, Mei is 9 years old, her mother is 36 years old, and her grandmother is 72 years old.
Asha and Jamal are selling plants to raise money for their soccer team. They started out with 45 plants. They sold some plants and now they have 21 plants left. Asha wrote the equation 45 – p = 21 to find the number of plants they sold. Jamal wrote the equation 21 + p = 45 to find the number of plants sold. Whose equation will find the number of plants sold? A. Asha’s equation. B. Jamal’s equation. C. Both equations will find the correct solution. D. Neither equation will find the correct solution.
Answer:
C. Both equations will find the correct solution.
Step-by-step explanation:
A square is ____ a parallelogram. always sometimes never submit
Angles C and D are complementary. The measure of angle D is 25 degrees greater than the measure of angle C. What is the measure of each angle?
Angle C measures 32.5 degrees and angle D measures 57.5 degrees.
Explanation:Let's represent the measure of angle C as x. Angle D is 25 degrees greater than angle C, so we can represent the measure of angle D as x + 25.
We know that angles C and D are complementary, so their measures must add up to 90 degrees.
Therefore, we can set up the equation:
x + (x + 25) = 90
Combining like terms, we get:
2x + 25 = 90
Subtracting 25 from both sides, we get:
2x = 65
Dividing both sides by 2, we get:
x = 32.5
So, the measure of angle C is 32.5 degrees, and the measure of angle D is 57.5 degrees.
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Describe the vector as an ordered pair. Round the coordinates to the nearest tenth. The diagram is not drawn to scale.
ANSWER
[tex]
\angle19.4,50.4 \: > [/tex]
EXPLANATION
The given vector has magnitude 54 units.
The vector is making an angle of 69° with the x-axis.
The horizontal component of the vector is
[tex] = 54 \cos(69) [/tex]
[tex] = 19.35[/tex]
To the nearest tenth, we have,
[tex] = 19.4[/tex]
The vertical component is
[tex] = 54 \sin(69 \degree) [/tex]
[tex] = 50.41[/tex]
[tex] = 50.4[/tex]
to the nearest tenth.
The required vector is
[tex]
\angle19.4,50.4 \: > [/tex]
The components of the vector with magnitude 54 and the angle of 69° from the horizontal can be written as <19.3519, 50.4133>.
What is a vector?A vector is a quantity that has both magnitude and direction. It has two components a vertical component(Sine) and a horizontal component(Cosine). The component of a vector can be written as,
Vertical component, [tex]V_y = \vec V\ Sin(\theta)[/tex]
Horizontal component, [tex]V_x = \vec V\ Cos(\theta)[/tex]
We know that a vector can be divided into two components a horizontal component and a vertical component, therefore, the vector components can be written as,
[tex]V_y = \vec V Sin\theta\\\\V_y = 54\ Sin(69^o)\\\\V_y = 50.4133[/tex]
[tex]V_x = \vec V Cos\theta\\\\V_x = 54\ Cos(69^o)\\\\V_x = 19.3519[/tex]
Hence, the components of the vector with magnitude 54 and the angle of 69° from the horizontal can be written as <19.3519, 50.4133>.
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The cone in the diagram has the same height and base area as the prism. What is the ratio of the volume of the cone to the volume of the prism?
Answer:
B. 1/3
I had this question on Plato this is the answer.