By writing an exponential equation, we can conclude that the initial deposit is of $606.22
How much money did you deposit in the account?Here we know that we have an annual rate of 6%, so if you deposit an initial amount of A, the amount of money that the account has after t years is:
M(t) = A*(1 + 6%/100%)^t = A*(1.06)^t
Now, you know that after 8 years you earn (in interest) $360, then we can write:
M(8) - A = 360
A*(1.06)^8 - A = 360
Now we can solve that equation for A.
A*( (1.06)^8 - 1) = 360
A = 360/( (1.06)^8 - 1) = 606.22
The initial deposit is of $606.22
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A student states that a triangle can be formed with side lengths 4 in, 5 in, and 8 in. Is the student correct? Why, or why not?
Its formed an obtuse triangle with side lengths 4 in, 5 in, and 8 in.
What is obtuse triangle?
A triangle is said to have an obtuse angle if one of the inner angles is greater than 90 degrees. If one of the angles of an obtuse triangle is greater than 90°, then the total of the other two angles is also less than 90°.Any two of a triangle's angles that are equal in size are said to be in an isosceles triangle. Furthermore, the length of the two sides that are opposite those equal angles is also equal. A triangle is said to be obtuse if one of the angles is between 90 and 180 degrees, while the other two are acute (less than 90 degrees).When given 3 sides of a triangle, the longest side must be less than the sum of the other 2 sides.
8 < 4 + 5 so a triangle can be formed.
In fact it will be an obtuse triangle.
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I have been stuck on this for the past 10 mins PLS HELP
Answer:
55°
Step-by-step explanation:
m∠D = m∠A + m∠B since for a triangle, the exterior angle = sum of interior angles
We can rewrite this as
m∠A + m∠B = m∠D
Given m∠A = (2x)° , m∠B = (3x + 41)° and m∠D = 124° and substituting in the above equation,
2x + (x + 41.5) = 124
2x + x + 41.5 = 124
3x + 41.5 = 124
3x = 124 - 41.5 = 82.5
x = 82.5/3 = 27.5
But m∠A = (2x) = 2 x 27.5 = 55°
what is the answer for 200-{(7x3) +(10x5)}=
Answer: 129
Step-by-step explanation:
200-{(7x3) +(10x5)}=
200-((7*3)+(10*5))=
200-(21+50)=
200-71=129
Lesson 4 multiplication pattern
70 x 500 =
Answer:
3500
Step-by-step explanation:
An easy way to solve this specific problem would be to multiply 7 and 5 together to get 35 and then add on the two zeros from 500 to get 3500. Or you can do the standard multiplication strategy.
Hope this helps!
A number added to -19 is equal to -21
Answer:
-2
Step-by-step explanation:
Let, the needed number be x;
x-19=-21
x=-21+19
x=-2
20,000 ten thousands equals how many hundred thousands
20,000 ten thousand equals 2000 Hundred thousand.
As per the question statement, we are provided with a value: "20,000 ten thousand".
We are required to calculate how many hundred thousand are equal to 20,000 ten thousand.
To solve this question, let us first write down 20,000 ten thousand into the numerical format, i.e, [tex](20000*10,000)=200000000[/tex].
As we know, a hundred thousand when written down in the numerical format becomes 100,000, let us assume that 20,000 ten thousand equals to "x" number of Hundred thousand.
Therefore, we can form a linear equation in one variable "x" based on the condition, in the above-mentioned statement, which goes as [tex](100,000*x)=200000000[/tex]
[tex]or, (100,000x)=200000000\\or,x=\frac{200000000}{100,000}\\or,x=\frac{2*10^{8} }{10^5\\}or,x=(2*10^3)\\or,x=2000[/tex]
Hence, 20,000 ten thousands equals 2000 Hundred thousands.
Linear Equation: linear equations: In Mathematics, a linear equation is an algebraic equation which when graphed, always results in a straight Line and hence comes the name "Linear". Here, each term has an exponent of 1 and is often denoted as (y = mx + c) where, 'm' is the slope and 'b' is the y-intercept. Occasionally, it is also called as a "linear equation of two variables," where y and x are the variables.Variable: n Mathematics, a variable is a symbol or a representative of a value, which is unknown.To learn more about Linear Equations, click on the link below.brainly.com/question/27664510
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On the weekdays a grocery store has 14239 customers and on the weekends the grocery store has
11634 customers. How many more customers does the grocery store have on weekdays than on
weekends?
Answer: 2605 more on weekdays
Step-by-step explanation:
14239 - 11634 = 2605
Can somebody help me if you know what this is
Answer:
[tex]f^{-1}x=\frac{2x}{x-1}[/tex]
Me wailer has 32 students in his class he wishes to place them into groups of 8 of equal size which of the following represents the number of the students per groups
Answer:
Step-by-step explanation:
8 x 4 = 32
8 + 8 + 8 + 8 = 32
32 ÷ 4 = 8
OSTATISTICS
Choosing the best measure to describe data
Answer the questions below.
(a) The 10 members of the swim team completed the following numbers of laps at today's practice:
76, 77, 78, 79, 82, 83, 86, 87, 89, 91.
Which measure should be used to summarize the data?
Mean
O Median
O Mode
(b) Lucy has recorded the number of miles she has driven for each of the last 9 weeks:
126, 380, 383, 385, 386, 396, 398, 404, 419.
Which measure should be used to summarize the data?
Mean
Median
O Mode
(c) A reporter has recorded the rating (G, PG, PG-13, or R) of each movie played in a theater over the
past year.
Which measure gives the most common rating?
O Mean
Median
O Mode
S
Answer:
a) Mean
b) Median
c) Mode
Step-by-step explanation:
a) The data set has no outliers, therefore taking the average (mean) would be the best.
b) The data has outliers which would skew a mean. None of the numbers repeat, therefore mode would not work, so by process of elimination, one can find that Median is the best.
c) This data set does not have numbers, therefore mean does not make sense. The most common rating would be the rating that occurs most often, which would be mode.
well give u brainliest What is the value of the function when x=−2?
Enter the answer in the box.
The value of the given function when x = -2 is; y = 1
How to interpret Linear Graphs?
We are given a linear graph as seen in the given image. Now, in graphs like these, there are input values which are x-values while there are also output values which are values on the y-axis.
Now, looking at the graph, we can see that;
At x = 5, y = -6
At x = 4, y = -5
At x = 3, y = -4
At x = 2, y = -3
At x = 1, y = -2
At x = 0, y = -1
At x = -1, y = 0
At x = -2, y = 1
Thus, we can conclude that the value of the given function when x = -2 is, y = 1
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Compare and contrast the two dot plots shown
answer:
kids that play basketball are taller than kids that play baseball
Step-by-step explanation:
as we see the average height of baseball players ( the majority) is 68 inches and 70 while basketball is 70 to 74
hope this helped have a good day guv'nor :D
A student claims that 2-4=0 because you cant have less than nothing
Answer: -2
Step-by-step explanation:
What is the image of ( − 4 , 12 ) after a dilation by a scale factor of 1/2 centered at the origin?
The image of ( − 4 , 12 ) after a dilation by a scale factor of 1/2 centered at the origin is ( 2, -6 ).
What is Coordinate plane?
Coordinate plane, is represented as the values on the x-axis and y-axis of the graph.
Given that,
To determine the image of (-4,12) after dilation by a scale factor of 1/2 centered at the origin.
Now, For the point, we have a dilation factor of 1/2,
So, a dilated coordinate,
= (1/2 * - 4 , 1/2 * 12)
= (-2 , 6)
To form the image across the origin,
= - (-2, 6)
= (2, -6)
Therefore, The image of ( − 4 , 12 ) after a dilation by a scale factor of 1/2 centered at the origin is ( 2, -6 ).
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Please help me with this question!
Answer:
A. 0
Step-by-step explanation:
| 1 4 4 |
| 5 2 2 |
| 1 5 5 |
a1 = | b2 b3 | = | 2 2 |
|c2 c3 | | 5 5 |
a2 = | b1 b3 | = | 5 2 |
| c1 c3 | | 1 5 |
a3 = | b1 b2 | = | 5 2 |
| c1 c2 | | 1 5 |
a1 - a2 + a3
| 2 2 | | 5 2 | | 5 2 |
(1) | 5 5 | - (4) | 1 5 | + (4) | 1 5 |
1 [(2)(5) - (2)(5)] - 4 [(5)(5) - (2)(1)] + 4[ (5)(5) - (2)(1)]
1 [10 - 10] - 4 [25 - 2] + 4 [25 - 2]
1 [0] - 4 [23] + 4 [23]
- 92 + 92 = 0
I hope this helps!
Compute 5DBE16-9AF416 using 2’s complement, leave your final answer in octal
5DBE16-9AF416 using 2’s complement is -2635716 octal.
We need to compute 5DBE16-9AF416 using 2’s complement, leave your final answer in octal.
What is two's complement?When two's supplement is utilized to address negative numbers, the main piece (MSB) is used to show the indication of the number. A 1 in the MSB position shows a negative number, and a 0 in the MSB position demonstrates a positive number. In two's supplement, negative numbers are addressed by the converse of the positive number in addition to 1.
To find the backwards of a number, every digit is just upset - 0 changes to 1, and 1 changes to 0. In this way, the converse of 5DBE16 is A2416. One is added to the opposite to find the two's supplements giving us A2417.
2's supplement of a number=the numbers supplement+1
5DBE16-9AF416=464416-9AF416=-54AF416+1=-54AF416
The two's supplement of a number can be determined by deducting the number from 2^n, where n is the number of pieces used to address the number. Along these lines, for this situation, we would take away 5DBE16 from 2^32, which gives us 464416.
Since the 2's complement of a number is equivalent to the negative, we can say that 5DBE16-9AF416=-54AF416.
To change over a two's supplement number to octal, we can involve a similar technique as we would use to switch a paired number over completely to the total. We bunch the pieces into three sets, beginning from the right, and convert each gathering into an octal digit.
In this way, the 2's supplements of 5DBE16-9AF416 would be composed as continues in octal 464416-9AF416=-2635716 octal
Therefore, 5DBE16-9AF416 using 2’s complement is -2635716 octal.
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what is the answer for 1/ 2−6=10
Answer:
-1/10
Step-by-step explanation:
1/2-6/10
5/10-6/10
= -1/10
When Ricardo was 9 years old, he was 56
inches tall. Ricardo is now 12 years old and
he is 62 inches tall. Find the percent of
increase in Ricardo's height to the nearest
centh.
Answer:
10.7%
Step-by-step explanation:
The formula for calculating the percent change in a value between two points in time is:
p
=
N
−
O
O
⋅
100
Where:
p
is the percent change - what we are solving for in this problem.
N
is the New Value - 62 inches in this problem.
O
is the Old Value - 56 inches in this problem.
Substituting and solving for
p
gives:
p
=
62
−
56
56
⋅
100
p
=
6
56
⋅
100
p
=
600
56
p
=
10.7
rounded to the nearest tenth.
Ricardo gres 10.7%
Write the quadratic equation whose roots are 1 and -3, and whose leading coefficient is 1.
(Use the letter X to represent the variable)
Answer:
y = x²+2x-3
Step-by-step explanation:
y = a(x-p)(x-q)
p = 1
q = -3
a = 1
y = 1(x-1)(x-(-3))
y = (x-1)(x+3)
y = x²+2x-3
Kaylee owns a food truck that sells tacos and burritos. She only has enough supplies to make 120 tacos or burritos. She sells each taco for $3 and each burrito for $6. Kaylee must sell at least $480 worth of tacos and burritos each day. If xx represents the number of tacos sold and yy represents the number of burritos sold, write and solve a system of inequalities graphically and determine one possible solution.
The system of inequalities is:
x + y ≤ 120
x*3 + y*6 ≥ 480
And one possible solution to it is x = 20 and y = 80.
How to find the system of inequalities?
First, we need to define two variables, we will be using:
x = number of tacos.y = number of burritos.We know that she can make at most 120 units, then:
x + y ≤ 120
And she wants to win at leastt $480, then:
x*3 + y*6 ≥ 480
So our system of inequalities is:
x + y ≤ 120
x*3 + y*6 ≥ 480
And the graph can be seen in the image below, the solution set of the system is given by the region where both shaded areas intersect.
There we can see that one possible solution is x = 20 and y = 80, in that case the total number of items made is:
20 + 80 = 100, which is less than 120
And the income is:
20*3 + 80*6 = 540.
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What is the greatest common factor of 38 and 30?
The greatest common factor of 38 and 30 is 2
The HCF (Highest Common Factor) of two or more numbers is the largest number among all the common divisors of the given numbers.Simply put, the HCF (Highest Common Factor) of two natural numbers x and y is the largest number that divides both x and y. Let's try to understand this definition using two numbers, 18 and 27. The common divisors of 18 and 27 are 1, 3, and 9. Of these numbers, 9 is the largest (greatest) number. So the HCF of 18 and 27 is 9.
We have given two numbers 38 and 30 .
Prime factorization of 38 is given by
[tex]38=2\times19[/tex]
Prime factorization of 30 is given by
[tex]30=2\times3\times5[/tex]
Prime factorization of 30 and 38 contains 2 as common primes factors so , GCF will be [tex]2[/tex] .
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graph the inequality
y < |x+8| -4
Answer:
Your axis will be _8 and make straight lines to (4.-4)
what is c cubed = -64
The value of the expression is -4
What is cube root?
The cube root of a number can be defined as the factor multiplied by three times by itself to get that number.
Cube root is represented using the formula, '∛'
From the information given,
c³ = -64
Take the cube root of both sides
∛c³ = ∛ - 64
c = - 4
Thus, the value of the expression is -4
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What is the value of this expression?
(5 3)
0512
0 5¹
05-¹
057
Answer:
a
Step-by-step explanation:
Rakeem is constructing a triangle. He knows that one side is 32 cm and another is 20 cm
What is the largest size for the last side of the triangle?
b. What is the smallest size for the last side of the triangle?
Answer:38
Step-by-step explanation:
5 more than three times a number is -7
I need some help with this!
what does 2/5 divied by 3/4 equal
Answer: 8/15
Step-by-step explanation:
2/5 x 4/3 (fraction rule)
2 x 4 / 5 x 3
2 x 4 = 8
8 / 5 x 3
5 x 3 = 15
= 8/15
PLEASE HELP ME I NEED THIS ASAP!!!
Answer: 1. D=(7, 4)
2. D=(-2, -2)
3. D=(6, -4)
Step-by-step explanation:
1. point B goes to point C by moving right 6 units and moving down 2 units.
point A goes to point D by moving right 6 units and moving down 2 units.
A=(1, 6)
D=(1+6, 6-2)
D=(7, 4)
2. point B goes to point C by moving left 4 units and moving down 6 units.
point A goes to point D by moving left 4 units and moving down 6 units.
A=(2, 4)
D=(2-4, 4-6)
D=(-2, -2)
3. point B goes to point C by moving right 8 units and moving down 2 units.
point A goes to point D by moving right 8 units and moving down 2 units. A=(-2, -2)
D=(-2+8, -2-2)
D=(6, -4)
You are building an arc entrance over a roadway. The road under
the arc is 20 feet wide with a 6-foot sidewalk on both sides of
the road. Write an equation to accomplish this task.
The equation of the parabolic arc that accomplishes this task is:
y = (-k/256)(x - 16)² + k.
In which k is the maximum height of the arc.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
For this problem, the arc has these following characteristics:
Parabolic.Concave down.The peak is at half the road.The road under the arc is 20 feet wide with a 6-foot sidewalk on both sides of the road, hence it's total length is of 20 + 2 x 6 = 32 feet, and the peak of the arc will be at h = 16.
Hence:
y = a(x - 16)² + k.
The height is of 0 at x = 0 and x = 32, hence:
0 = 256a + k.
a = -k/256
y = (-k/256)(x - 16)² + k.
In which k is the maximum height of the arc.
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