A company invests $10,000 in a mutual fund account that earns a fixed
interest per year. The account balance, Alt), in dollars, after t years is shown
in the table below.
t
1
2
3
Alt)
10,800.00
11,664.00
12,597.12
Which of the following equations represents Aſt)?
A(t) = 10,000 + 1.08t
A(t) = 10,000(1.08) - 1
A(t) = 10,800(1.08)
A(t) = 10,800(1.08) - 1
You
Answer:
a(t)=10000+1.08t
Step-by-step explanation:
t
1
2
3
Alt)
10,800.00
11,664.00
12,597.12
2.
Scientists estimate that the distribution of the life span of the Galápagos Islands giant tortoise is
approximately normal with mean 100 years and standard deviation 15 years. Based on the estimate, which
of the following is closest to the age of a Galápagos Islands giant tortoise at the 90th percentile of the
distribution?
Answer:
119.2
Step-by-step explanation:
Given the following :
Mean (m) = 100 years
Standard deviation (sd) = 15 years
closest to the age of a Galápagos Islands giant tortoise at the 90th percentile of the
distribution?
Obtain the Zscore for 90th percentile (0.90) on the z table = 1.28
Zscore = (X - mean) / standard deviation
1.28 = (X - 100) / 15
1.28 × 15 = X - 100
19.2 = X - 100
19.2 + 100 = X
X = 119.2
Using the normal distribution, it is found that an age of 119 years is closest to the 90th percentile.
-------------------
Normal Probability Distribution
The z-score formula is used, which, in a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. Each z-score has a p-value associated, which represents the percentile of X.-------------------
Mean of 100 means that [tex]\mu = 100[/tex]Standard deviation of 15 means that [tex]\sigma = 15[/tex]The 90th percentile is X when Z has a p-value of 0.9, so X when Z = 1.28.Thus:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 100}{15}[/tex]
[tex]X - 100 = 15(1.28)[/tex]
[tex]X = 119.2[/tex]
An age of 119 years is closest to the 90th percentile.
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The area of a rectangle is 136 square centimeters. The
rectangle is 8 centimeters wide how long is the rectangle
Answer:17
Step-by-step explanation: count 8, 17 times and that is how you get your answer
The length of the rectangle is 17 cm if the area of a rectangle is 136 square centimeters.
What is the area of the rectangle?It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.
It is given that:
The area of a rectangle is 136 square centimeters.
A = 136 square cm
w = 8 cm
A = lw
136 = 8l
l = 17 cm
Thus, the length of the rectangle is 17 cm.
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which is longer, 12m or 13yd?
Answer:
13 yards
Step-by-step explanation:
Answer:
12m
Step-by-step explanation:
12 meters . a meter is approx. 4" longer than a yard, x 12 =48 inches (or thereabouts). a yard is 36 inches long therefore 12 meters is longer
what is the solution of 2 - 3i and 2 + 3i?
Answer:
Step-by-step explanation:
Multiplying
(2 + 3i)(2 - 3i)
4 - 6i + 6i - 9i^2
4 - 12i + 9
13 - 12i
Add/subtract
2 - 3i + 2 + 3i = 2
2 - 3i - (2 + 3i) = 2 - 3i - 2 - 3i = -6i
HELP ME PLEASE <33 I NEED THIS
The measure of DE = 90 degrees because its corresponding central angle = 90 degrees.
What is the product of 2x - 5 and 3x² + 5x - 7? Write your answer in standard form.
(a) Show your work.
(b) Is the product of 2x - 5 and 3x² + 5x - 7 equal to the product of 5x - 2 and 3x² + 5x - 7? Explain your answer.
Answer:
see below
Step-by-step explanation:
(a)
[tex]( 2x - 5 )(3x^{2} + 5x - 7)\\\\=2x(3x^2+5x-7)-5(3x^2+5x-7)\\\\=6x^3+10x^2-14x-15x^2-25x+35\\\\=6x^3+(10x^2-15x^2)+(-14x-25x)+35\\\\=6x^3-5x^2-39x+35[/tex]
(b)
[tex](2x-5)(3x^2+5x-7)=(5x-2)(3x^2+5x-7)\\\\\frac{1}{(3x^2+5x-7)}(2x-5)(3x^2+5x-7)= \frac{1}{(3x^2+5x-7)}(5x-2)(3x^2+5x-7)\\\\2x-5=5x-2\\\\2x-5x=-2+5\\\\-3x=3\\\\x=-1[/tex]
only happens when x=-1, not always
What output corresponds with I2?
Answer:
Solve for the input that corresponds to the given output value. (Round answers to three decimal places when appropriate. Enter your answers as a comma-separated list. Note: Even though the question may be completed without the use of technology, the authors intend for you to complete the activity using the technology you will be using.
Step-by-step explanation:
What is the value of x?
1/4x + 17 = x - 4
Please explain:
Answer:
x=28
Step-by-step explanation:
The sum of 20.7 and a number is 50.5.
Answer:
x = 29.8
Step-by-step explanation:
x represents the unknown number
20.7 + x = 50.5
x + 20.7 - 20.7 = 50.5 - 20.7
x = 50.5 - 20.7
x = 29.8
Ax^2+bx+c=(x+p)(x+q) What you know about p and q if c is less than 0. WILL MAKE BRAINLIEST!! If u provide EXPLANATION :)
Answer:
From what I know there is no q.
p=0 I put a slight explanation below.Hope it helps
Step-by-step explanation:
Ax^2+bx+c-p=x
Ax^2+bx+c-p-x=x-x
Ax^2+(b-1)x+c-p=0
why is the following conditional logically true? If 20 is a multiple of 3, then 101 is a perfect square
Answer: A number is a perfect square only if it has a odd number
Step-by-step explanation:
As an example of the use of the prime factorization of an integer, we have the following result. Theorem. If n > 1 is a positive integer, then n is a perfect square if and only if n has an odd number of divisiors.
Since 20 is not a multiple of 3 it means the given statement is wrong so 101 is a perfect square that will be correct.
What is the reasoning?The procedure of utilizing logical reasoning to analyze a condition to determine the best problem-solving approach for a particular issue, then using this approach to create and explain a resolution.
In another word, reasoning is a tricky but interesting problem in mathematics that required relations of variables to solve.
Given the first statement
20 is multiple of 3
Since 20/3 given remainder of 3 so it is not multiple.
So the first statement is wrong.
So if the question is saying this it means the question will consider all correct statements as wrong.
Now,
101 is a perfect square is wrong but the question will consider it correct.
Hence "Since 20 is not a multiple of 3 it means the given statement is wrong so 101 is a perfect square".
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Help!! Me!! Please!!
Answer:
13 and 14
Step-by-step explanation:
the square root of 182 is 13.49 which would lie between 13 and 14
A factory produced 150 tons of steel in one year. The next year, the output increased to 180 tons. What is the percentage increase in the output?
A.
17%
B.
20%
C.
30%
D.
50%
E.
75%
Answer:
It would be 17%
Step-by-step explanation:
Answer:
B: 20%
Step-by-step explanation:
What is the measure of angle TRV? 20° 50° 60° 130°
Answer: 130
Step-by-step explanation:
Answer: 130 (D)
What is the measure of angle TRV?
Given the midpoint and one endpoint. Find the other endpoint. B) Endpoint (-3,7), Midpoint (-1,-1)
Answer:
Step-by-step explanation:
(x - 3)/2 = -1
x - 3 = -2
x = 1
(y + 7)/2 = -1
y + 7 = -2
y = -9
(1, -9) the other endpoint
If M is the midpoint of segment AB, then which of the following statements is/are true? AB=MB AM=MB Segment AM is congruent to segment MB.
AB is the large segment.
AM is half of the large segment.
MB is the second half of the large segment.
AM = MB is true.
Segment AM is congruent to segment MB is true.
AB = MB is false.
The statements that are true.
-Segment AM is congruent to segment MB.
- AM = MB.
What is a midpoint of a line segment?The midpoint of a line segment is given as,
x = (a + c)/2
y = (b + d) / 2
Where (x, y) is the midpoint and (a, b) and (c, d) are the two endpoints.
We have,
If M is the midpoint of segment AB, then the following statements are true.
- AB = 2MB
Since M is the midpoint of AB, MB is half the length of AB.
Therefore,
AB is twice as long as MB.
- AM = MB
Since M is the midpoint of AB, AM, and MB are equal in length.
This is a property of the midpoint of a segment.
Now,
Segment AM is congruent to segment MB.
Since AM and MB are equal in length (as stated in statement 2), they are congruent to each other.
Therefore,
Segment AM is congruent to segment MB with AM = MB statement being true.
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Sherry has a package in the shape of a rectangular prism. What is the volume, in cubic inches (in.), of the rectangular prism? (use cubic inches as your unit) *
Answer:
See Explanation
Step-by-step explanation:
The question is incomplete as the dimension of the prism is not given. However, the following steps can serve as a guide for you.
The volume of a rectangular prism is calculated as thus:
[tex]Volume = Length * Width * Height[/tex]
So, Take for instance
[tex]Length = 2\ in[/tex]
[tex]Width = 3\ in[/tex]
[tex]Height = 4\ in[/tex]
The Volume would be:
[tex]Volume = 2\ in * 3\ in * 4\ in[/tex]
[tex]Volume = 24\ in^3[/tex]
Solve the equation.
t + 25 = 26
Answer: t = 1
Step-by-step explanation:
Subtract 25 on both sides. t = 1The solution to the equation t + 25 = 26 is t = 1.
The given equation is,
t + 25 = 26
To solve this equation,
Isolate the variable t,
Which means we need to get rid of the 25 on the left side of the equation.
To do that, Subtract 25 from both sides of the equation,
since what we do to one side, we must do to the other to keep the equation balanced.
So,
t + 25 - 25 = 26 - 25.
Simplifying this, we have t = 1.
Therefore, the solution to the equation t + 25 = 26 is t = 1.
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What is the place value of 6 in the number 6,029?
Answer:
six thousand
Step-by-step explanation
it lies in place of thousand and value is 6
6* 1000=6000
The place value is thousand.
What is place value?Place value is the value of each digit in a number. For example, the 5 in 350 represents 5 tens, or 50; however, the 5 in 5,006 represents 5 thousands, or 5,000. It is important that children understand that whilst a digit can be the same, its value depends on where it is in the number.
given number:
6,029
So, place values are as follows:
9- ones
2- tens
0- hundred
6 - thousand
Hence, the place of 6 is thousand
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4 ft 5 Ft what is the area
Answer:
20 ft²Step-by-step explanation:
4 x 5 = 20 ft²
3) Sue and Jim are driving on the highway. Sue takes 24 minutes to drive 40 km. If Jim drives
at the same rate, how long will it take for him to drive 115 km?
69 minutes
Answer:
69min
Step-by-step explanation:
sue: 24min 40km
.6 min per 1km
×115
115 km = 69 min
C is between B and D
BC = 8x +13
CD= 12x -73
BD =320
find the value of x
Answer:
..
...
Step-by-step explanation:
..
Answer:
x = 19
Step-by-step explanation:
Since C is between B and D , then
BC + CD = BD , substitute values
8x + 13 + 12x - 73 = 320 , that is
20x - 60 = 320 ( add 60 to both sides )
20x = 380 ( divide both sides by 20 )
x = 19
what property does this equation use.
If LM = NP , then NP = LM
-distributive
-substitution
-division
-subtraction
-multiplication
-transitive
-reflexive
-symmetric
Answer:
reflexive
Step-by-step explanation:
memorize it as the equal sign is a mirror that reflects so its the same!
Please help me!! What is the value of???
-4×3
12÷(-6)???
Answer:
-4x3=12
12÷-6=-2
hope this helps
Which represents where f(x) = g(x)?
f(2) = g(2) and fo) = g(0)
f(2) = g(0) and f(0) = g(4)
f(2) = g(0) and f(4) = g(2)
f(2) = g(4) and f(1) = g(1)
Answer:
2
Step-by-step explanation:
hjjjjjjjiygiciyfcifycitytyx
Answer:
it would be letter c
Step-by-step explanation:
In expanded form, log(1,000a^3/b) is equivalent to...
Answer:
Option (4)
Step-by-step explanation:
Given expression is,
[tex]\text{log}(\frac{1000a^3}{b})[/tex]
To solve this expression we will use the logarithmic properties.
[tex]\text{log}(\frac{1000a^3}{b})=\text{log}1000a^3-\text{log}(b)[/tex] [Since, [tex]\text{log}\frac{p}{q}=\text{log}p-\text{log}q[/tex]]
= log(1000) + log(a³) - log(b) [Since, log(pq) = log(p) + log(q)]
= 3 + 3log(a) - log(b)
= 3[1 + log(a)] - log(b)
Therefore, Option (4) will be the correct option.
Jess is painting his car. He's created a purple color that uses red paint and blue paint in a ratio of 6:5. Jess uses 15
pints of blue paint. How many pints of paint does he use in total?
A
18
B
33
С
11
D
26
Answer:
B.) 33
Step-by-step explanation:
15/5=3
6x3=18
18+15=33
The ratio shows how many times one value is contained in another value.
If the ratio of Red and blue is 6:5 and uses 5 pints of blue color.
The total pints of paint used in total is 33 pints.
What is a ratio?The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
The ratio of minutes and minutes in 1 hour is 60 : 3600
We have,
Purple color:
Red : Blue = 6 : 5
Let,
Red colour = 6x
Blue color = 5x
Now,
Blue color = 15 pints
5x = 15 pints
x = 15/3
x = 3 pints _______(1)
Now,
Total color.
= Red + Blue
= 6x + 5x
= 11x
Now,
From (1) we get,
= 11x
= 11 x 3
= 33
Thus,
If the ratio of Red and blue is 6:5 and uses 5 pints of blue color.
The total pints of paint used in total is 33 pints.
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rewrite 1/4 books over 1/3 hour as a unit rate. A. 1 1/3 bookss/hour B. 1/12 books/hour C. 3/4 books/hour D. 12 books/hour
Answer:
The Answer would be option C. 3/4 books per hour
Step-by-step explanation:
You would flip 1/3 to 3/1 which makes it a whole number. then multiply
1/4 and 3.
Therefore your answer is 3/4
I hope this helped you,
If f(x) = 6x – 1 and g (x) = StartFraction x + 1 Over 6 EndFraction, which expressions can be used to verify g(x) is the inverse of f(x)? Check all that apply.
Answer:
B and C
Step-by-step explanation:
Answer: B and C
Step-by-step explanation: