Answer:
It will take 27.19 years
Step-by-step explanation:
Compound continuous interest can be calculated using the formula:
[tex]A=Pe^{rt}[/tex] , where
A = the future value of the investment, including interest P = the principal investment amount (the initial amount) r = the interest rate of interest in decimalt = the time the money is invested for∵ Steve deposits $1250 in an account
∴ P = 1250
∵ The account paying 3.4% annual interest compounded continuously
∴ r = 3.4%
- Change it to decimal by dividing it by 100
∴ r = 3.4 ÷ 100 = 0.034
∵ The account balance will reach to $3150.5
∴ A = 3150.5
- Substitute The values of A, P and r in the formula above to find t
∵ [tex]3150.5=1250e^{0.034t}[/tex]
- Divide both sides by 1250
∴ [tex]2.5204=e^{0.034t}[/tex]
- Insert ㏑ to both sides
∴ [tex]ln(2.5204)=ln[e^{0.034t}][/tex]
- Remember that [tex]ln(e^{n})=n[/tex]
∵ [tex]ln(e^{0.034t})=0.034t[/tex]
∴ ln(2.5204) = 0.034t
- Divide both sides by 0.034
∴ 27.18875 = t
∴ t ≅ 27.19
It will take 27.19 years
f(x)=-x2+1 what’s f(2) ?
Answer:
f(2)= 5
Step-by-step explanation:
Given f(x) = -x² + 1
f(2) = -2² + 1 = 4 + 1 = 5
f(2) means the value of x = 2
Hence we substitute the value of X into f(x) = -x² + 1
what’s 12x12? help me asap
Answer:
144
Step-by-step explanation:
12X12 is also 12+12+12+12+12+12+12+12+12+12+12+12
Lets simplify that though.
12(10)+12(2) (since 10 plus 2 is 12)
120+24
144
The value of the expression 12 * 12 = 144
The meaning of the expression 12 * 12 could also be interpreted as adding 12 in 12 places.
We could rewrite as thus :
12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12Adding the above would give a value of 144.
Hence, 12 * 12 = 144
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Charlie used a regression calculator to generate the
equation f(x) = -0.15x + 20.1 for the ordered pairs (2,
15), (4, 21), (6, 26), (8, 20), and (10, 14).
Is a linear representation the best way to represent the
data? If it is, explain why. If not, explain why and suggest
a better alternative.
Answer:
Answer below, let me know if it didn't make sense.
Step-by-step explanation:
I attached a picture of the scatterplot with a line connecting the points. There is a definite upside down u type shape, and it doesn't look close to a line at all, so linear is not a good choice.
an upside down u shape (or right side up u shape for that matter) is exactly what a quadratic is, or any polynomial if you do it right, but quadratic is the simplest, so let's go with that.
A linear representation is not the best way to represent the data from the equation gotten from the regression calculator.
What is regression?Regression simply means a statistical measurement that is used to determine the strength of the relationship that exists between the dependent and independent variables.
In this case, a linear representation is not the best way to represent the data from the equation. A quadratic equation will have been more appropriate in this case.
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I need the answer if u can’t see the pic let me know if u answer I give u points
Answer:
(4 , 2)
Step-by-step explanation:
The solution of the graph is located where the two lines intersect. Remember, the x (horizontal line), is always first, and then followed by the y (vertical line).
The two lines intersect at (4, 2), making B) your answer.
~
What values of a and b make the equation true? StartRoot 648 EndRoot = StartRoot 2 Superscript a Baseline times 3 Superscript b Baseline EndRoot a = 3, b = 2 a = 2, b = 3 a = 3, b = 4 a = 4, b = 3
Option C: [tex]a=3, b=4[/tex] is the value of a and b
Explanation:
Given that the expression [tex]\sqrt{648}=\sqrt{2^a\times3^b}[/tex]
We need to determine the value of a and b
Let us consider the term [tex]\sqrt{648}[/tex] and take the prime factorization of the term 648
Thus, we have,
648 divides by 2,
[tex]648=2 \cdot 324[/tex]
324 divides by 2,
[tex]648=2 \cdot 2 \cdot 162[/tex]
162 divides by 2,
[tex]648=2 \cdot 2 \cdot 2 \cdot 81[/tex]
81 divides by 3,
[tex]648=2 \cdot 2 \cdot 2 \cdot 3 \cdot 27[/tex]
27 divides by 3,
[tex]648=2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 9[/tex]
9 divides by 3,
[tex]648=2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3 \cdot 3[/tex]
Thus, we have,
[tex]\sqrt{648}=\sqrt{2^{3} \cdot 3^{4}}[/tex]
Therefore, equating the powers of 2 and 3, we get,
[tex]a=3, b=4[/tex]
Hence, the value of a and b is 3 and 4
Thus, Option C is the correct answer.
The values of a and b which make the equation true are; a = 3 and b = 4 respectively.
From the question; the expression given is;
[tex] \sqrt{648} = \sqrt{ {2}^{a} \times {3}^{b} } [/tex]
In essence; we have;
648 = 2^a × 3^bBy expression of of 648 as the product of its lowest factors; we have;
648 = 2 × 2 × 2 × 3 × 3 × 3 × 3.In which case; we have;
648 = 2³ × 3⁴Ultimately, the values of a and b which make the equation true are 3 and 4 respectively.
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Solve
What is 83.2 x 0.19
Answer:15.808
Step-by-step explanation:
you just multiply no need to line up the decimal points tho
which equation can be used to find x the length of the hypotenuse of the right triangle?
Answer:
Explanation:For any right triangle, the longest side is called the hypotenuse. Therefore, by Pythagorean theorem it is true that:
[tex]x^2=a^2+b^2[/tex]
Where:
x: Hypotenuse
a, b: The other two sides.
For instance, if we have a right triangle whose sides measure:
[tex]a=3 \\ \\ b=4[/tex]
Then, the hypotenuse can be found as:
[tex]x=\sqrt{3^2+4^2} \\ \\ c=\sqrt{25} \\ \\ c=5[/tex]
15-7 5/6
i need help
first person is the brainliest
Answer:
7 1/6
Step-by-step explanation:
So first step, you subtract the two regular numbers like any other subtraction. 15-7 is 8. Now u have 8 - 5/6, so you change 8 into 7 6/6 - 5/6, since 6/6 is still 1. Now since you have a common denominator, you just subtract the fractions and get 7 1/6.
The lengths of one triangle are are 2/3 the lengths of the sides of a similar triangle. if a side of the larger triangle is 36 millimeters what is the measure of the matching side of the smaller triangle?
Answer:
24
Step-by-step explanation:
36= 3 equal parts
so: 36/3 =12
One part=12
so 2 parts is 12*2
12*2=24mm is the answer
The measure of the matching side of the smaller triangle is 24 millimeters.
When dealing with similar triangles, the lengths of corresponding sides are proportional. This means that if one triangle has sides that are a constant multiple of the sides of another triangle, we can find the length of a matching side by using that constant multiple. In this case, the sides of the smaller triangle are said to be 2/3 the lengths of the sides of the larger triangle.
To find the matching side of the smaller triangle when a side of the larger triangle is 36 mm, we use the proportionality factor, which is 2/3. Therefore, the length of the corresponding side in the smaller triangle is 2/3 of 36 mm, which can be calculated as:
(2/3) * 36 mm = 24 mm
So, the measure of the matching side of the smaller triangle is 24 millimeters.
What is the prime factorization of 45
Answer:
3^2X5
Step-by-step explanation:
Students learn that the prime factorization of a number is the given number written as the product of its prime factors. For example, to find the prime factorization of 45, use a factor tree to find that 45 is 5 x 9, and 9 is 3 x 3. So the prime factorization of 45 is 5 x 3 x 3, or 5 x 3^2.
Answer:
Option B, 3^2 * 5
Step-by-step explanation:
Step 1: Find the prime factorization of 45
45 = 9 * 5
9 can be simplified as 3^2
5 cannot be simplified because it is a prime number
9 * 5
3^2 * 5
So, 45 = 3^2 * 5
Answer: Option B, 3^2 * 5
the pythagorean theorem is true for all similar triangles
No. It is not true for all similar triangles.
Step-by-step explanation:
Pythagorus theorem is generally used to find the third side by using the other two sides of the right angled triangle. Pythagorus Theorem relates the sides of the right angled triangle and not relating all the sides of the other similar triangles, by equating the square of the hypotenuse to the sum of the squares of the other two sides of a right angled triangle. The hypotenuse is nothing but the side opposite to the right angle and it is related to the other 2 legs of the right angled triangle by this Pythagorus Theorem. So the given statement about the triangles is False.Determine if each root is a rational or irrational number. Explain your reasoning. a.√36 b.√78
Answer:
a) rational
b) irrational
Step-by-step explanation:
a) 36 = 6²
So sqrt(36) = 6
b) 72 = 2 × 36
sqrt(72) = sqrt(2) × sqrt(36)
Since 2 is not a perfect square, sqrt(72) is irrational
Final answer:
√36 is a rational number because 36 is a perfect square, which results in a whole number when square rooted. However, √78 is an irrational number as it is not a perfect square and cannot be simplified to a fraction of two integers.
Explanation:
We are tasked with determining whether each given root, √36 and √78, is a rational or irrational number. First, we observe that √36 is the square root of 36. Since 36 is a perfect square (6 x 6), √36 equals 6, which is a rational number because it can be expressed as the quotient of two integers (6/1).
On the other hand, √78 is not a perfect square; its square root cannot be simplified to a whole number or a simple fraction of two integers. Therefore, √78 is an irrational number because it cannot be written exactly as a simple fraction or repeating or terminating decimal.
In a survey, 250 shoppers were asked whether they have access to a computer at home and if they have a personal e-mail account. Their responses are summarized in the following table.
E-Mail account/ No e-mail account
Computer access at home--------- 73------------------32
No computer access at home----22------------------123
(a) What percentage of the shoppers do not have computer access at home?
(b) What percentage of the shoppers do not have an e-mail account?
Answer:
a) 42%
b) 62%
Step-by-step explanation:
a) (73+32)/250 × 100 = 42
b) (32+123)/250 × 100 = 62
58% of shoppers do not have access to a computer at home, and 62% of shoppers do not have an e-mail account.
Explanation:Let's first calculate the total number of shoppers. From the survey, 250 people were interviewed. We want to find (a) The percentage of shoppers who do not have computer access at home and (b) the percentage of shoppers who do not have an e-mail account.
(a) According to the table, the number of shoppers who do not have computer access at home is 22 + 123 = 145. The percentage can be calculated as 145/250 * 100 = 58%. Therefore, 58% of shoppers do not have computer access at home.
(b) The number of shoppers who do not have an e-mail account equals 32 + 123 = 155. The percentage is calculated in the same way, 155/250 * 100 = 62%. Therefore, the percentage of shoppers who do not have an e-mail account is 62%.
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A townhouse in San Francisco was purchased for $80,000 in 1975. The appreciation of the building is modeled by the equation: A=80000(1.12)^t, where t represents time in years.
In what year was the building worth double it’s value in 1975?
Year:
Answer:
In 1981 was the building worth double it’s value.
Step-by-step explanation:
Given : A townhouse in San Francisco was purchased for $80,000 in 1975. The appreciation of the building is modeled by the equation : [tex]A=80000(1.12)^t[/tex], where t represents time in years.
To find : In what year was the building worth double it’s value in 1975?
Solution :
The amount is $80,000.
The building worth double it’s value in 1975.
i.e. amount became A=2(80000).
Substitute in the model,
[tex]2(80000)=80000(1.12)^t[/tex]
[tex](1.12)^t=\frac{2(80000)}{80000}[/tex]
[tex](1.12)^t=2[/tex]
Taking log both side,
[tex]t\log (1.12)=\log 2[/tex]
[tex]t=\frac{\log 2}{\log (1.12)}[/tex]
[tex]t=6.11[/tex]
i.e. Approx in 6 years.
So, 1975+6=1981
Therefore, in 1981 was the building worth double it’s value.
The building was worth double its value in [tex]1975[/tex] around the year [tex]1981[/tex]
To determine in what year the building was worth double its value in [tex]1975[/tex], we need to set up the equation based on the appreciation model given:
[tex]\[ A = 80000 \times (1.12)^t \][/tex]
Here, [tex]\( A \)[/tex] represents the current value of the townhouse in dollars, and [tex]\( t \)[/tex] represents the time in years since [tex]1975.[/tex]
We want to find the year [tex]\( t \)[/tex] when the value [tex]\( A \)[/tex] is double the initial value of [tex]\$80,000[/tex]
[tex]\[ A = 2 \times 80000 = 160000 \][/tex]
Now, substitute [tex]\( A = 160000 \)[/tex] into the equation:
[tex]\[ 160000 = 80000 \times (1.12)^t \][/tex]
Divide both sides by [tex]80000[/tex] to solve for [tex]\( (1.12)^t \)[/tex]
[tex]\[ 2 = (1.12)^t \][/tex]
To solve for [tex]\( t \)[/tex], take the natural logarithm ([tex]ln[/tex]) of both sides:
[tex]\[ \ln(2) = \ln((1.12)^t) \][/tex]
[tex]\[ \ln(2) = t \times \ln(1.12) \][/tex]
Now, divide both sides by [tex]\( \ln(1.12) \)[/tex] to solve for [tex]\( t \)[/tex]:
[tex]\[ t = \frac{\ln(2)}{\ln(1.12)} \][/tex]
Using a calculator to find the approximate value:
[tex]\[ t = \frac{0.6931}{0.1178} = 5.88 \][/tex]
Since [tex]\( t \)[/tex] represents years after [tex]1975[/tex], we add this to [tex]1975[/tex] to find the year when the building was worth double its value in [tex]1975[/tex]:
[tex]\[ \text{Year} = 1975 + 5.88 = 1980.88 \][/tex]
In [tex]1981[/tex], the building was worth double its value in [tex]1975.[/tex]
Which table of values is correct for the equation y = - x + 3.
x y
-3 0
0 3
3 6
x y
-3 -6
0 -3
3 0
x y
-3 0
0 -3
3 -6
x y
-3 6
0 3
3 0
Answer:
x y
-3 6
0 3
3 0
Step-by-step explanation:
The correct table of values for the equation y = -x + 3 is x; y; -3; 6; 0; 3; 3; 0.
Let's go through the steps to find the values of y for the given equation y = -x + 3 for the specified values of x:
1. For x = -3:
y = -(-3) + 3 = 6
2. For x = 0:
y = -(0) + 3 = 3
3. For x = 3:
y = -3 + 3 = 0
Therefore, the correct table of values is:
x y
-3 6
0 3
3 0
The correct values are [tex]\(x \; y \; -3 \; 6 \; 0 \; 3 \; 3 \; 0\)[/tex].
What’s the vertical and horizontal line?
Answer:
Part 1) Vertical line : [tex]x=1[/tex]
Part 2) Horizontal line : [tex]y=-4[/tex]
Step-by-step explanation:
Part 1) Write the equation for the vertical line passing through the point (1,-4)
we know that
The equation of a vertical line (parallel to the y-axis) is equal to the x-coordinate of the point that passes through it
so
The x-coordinate is 1
therefore
The equation of the line is
[tex]x=1[/tex]
Part 2) Write the equation for the horizontal line passing through the point (1,-4)
we know that
The equation of a horizontal line (parallel to the x-axis) is equal to the y-coordinate of the point that passes through it
so
The y-coordinate is -4
therefore
The equation of the line is
[tex]y=-4[/tex]
Find the sum 6y sqrt a +7y sqrt a
For this case we must add the terms of the following expression:
[tex]6y \sqrt {a} + 7y \sqrt {a}[/tex]
It is noted that the terms are similar, so we can add:
We take common factor [tex]\sqrt {a}:[/tex]
[tex]\sqrt {a} (6y + 7y) =[/tex]
We add the terms within the parenthesis:
[tex]\sqrt {a} (13y) =[/tex]
finally we have:
[tex]13y \sqrt {a}[/tex]
Answer:
[tex]13y \sqrt {a}[/tex]
Answer:
D.) 13y sqrt a
Step-by-step explanation:
If x = 2 and y = 4, then xy =
Answer:
8
Step-by-step explanation:
XY = X times Y
If you substitute them its 2 X 4
a baseball player lost 20% of the games he pitched. If he pitched 40 ball games how many games dis he win?
Answe idk
Answer:
32
Step-by-step explanation:
When you multiply 40 by 20% or 0.20, the product will be the amount of games he lost. When you subtract 40-8 you get how many games he won.
System of equations
2x+1=5
x=2 :)
2x+1-1=5-1
2x=4
2/2x=4/2
x=2
if you do the opposite on one side you gotta do it on the other :)))
Answer:
x=2
Step-by-step explanation:
2x+1+5 move constant to right-hand side and change its sing
2x+5-1 subtract the numbers
2x+4 Divide both sides of the equation by 2
c = 5/9 (f-32)
if f = 68
Answer:
5
Step-by-step explanation:
Answer: 20
Step-by-step explanation:
C = 5/9 (f - 32)
since f = 68 and substitute it into the equation above
C = 5/9 ( 68 - 32)
C = 5/9 (36)
opening the bracket
C = 5/9 x 36
C = 180/9
C = 20
What are dot plots best used for?
Dot plots are best used to show a distribution of data.
Dot plots are best used to show answers to a non-statistical question.
Dot plots are best used to help you ask questions.
Dot plots are best used to help you tally data.
Answer:
dot plots are best used to show a distribution of data
Answer:
Dot plots are best used for a.Dot plots are best used to show a distribution of data.
Step-by-step explanation:
a rectangle has a width of 8m and length of 7m how does the area change when each dimension is multiplied by 5
Answer:
The first thing we need to do is find the area of the rectangle...
l x w = A
7 x 8 = 56
So the area of the first rectangle is 56m.
Now we multiply each dimension by 5...
8 x 5 = 40
7 x 5 = 35
So, now the width is 40m and the length is 35m,
Then, find the area of the new rectangle...
35 x 40 = 1400
The area of this rectangle is 1,400m!
1,400 / 56 = 25
So, by multiplying each dimension by 5, the area is now multiplied by 25!
A floor plan of a house was drawn using a scale of 1 cm = 1.5 m. The family room in the plan is pictured as 5 cm by 4 cm. What is the area, in square meters, of the actual family room. (please see picture below)
A: 20
B: 27
C: 30
D: 45
2. Liz chose C as the correct answer. How did she get that answer?
Answer in complete sentences.
In circle V, angle WXZ measures 30°. Line segments WV, XV, ZV, and YV are radii of circle V.
Circle V is shown. Line segments W V, X V, Z V, and Y V are radii. Lines are drawn from point W to point X and from point Z to point Y to form secants. Point U is on the circle between points W and X.
What is the measure of Arc W U X in circle V?
60°
90°
120°
150°
The measure of arcWUX in circle V of the given diagram with the circle geometry is; C: 120°
How to solve Circle geometry?From the complete image as seen online, we can say that;
The measure of ∠WUX is similar to the measure of vertex ∠V.
To get the measure of angle V (∠V), we will use the sum of angles in a triangle theorem to get;
30 + ∠V + ∠X = 180
60 + ∠V = 180
∠V = 180 - 60
∠V = 120°
Since ∠V = arcWUX
Then, measure of arcWUX is 120°
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Answer: C. 120
Step-by-step explanation: First guy wrote out the math cause he's smart like that.
the weight of 72 books is 9kg . what will be the weight of 40 such books?
Answer: 5kg
Step-by-step explanation:
If 72 books weigh 9kg
Then, 1 book weighs 9/72 = 1/8 kg
Therefore, 40 books will weigh
40 times 1/8 = 5kg
A green number cube and a red number cube are rolled. An outcome is the pair of numbers rolled on the two different cubes. Which of the following are true? Select all that apply.
Each result is equally likely.
The sample space has 36 different outcomes.
The sample space has 11 different outcomes.
A total roll of 7 is very likely.
Answer:
Each result is equally likely
The sample space has 36 different outcomes
Step-by-step explanation:
A number cube has 6 sides, and there are 2 number cubes so there are 36 possible outcomes because 6²=36
Remind me if im wrong
The statements which are true are each result is equally likely , the sample space has 36 different outcomes and the total roll of 7 is very likely.
When a green number cube and a red number cube are rolled, the outcomes indeed have specific characteristics. Here's a breakdown based on the selections provided in the question:
Each result is equally likely is true, because when rolling two fair six-sided dice (or in this case, cubes), each side of each cube has an equal chance of landing face up, making each combination of the two cubes equally likely
The sample space has 36 different outcomes is true, as each cube has 6 faces, and when two are rolled together, the total number of possible outcomes (or the sample space) is 6 times 6, equating to 36
The sample space has 11 different outcomes is false, because as previously stated, there are 36 possible outcomes based on the combination of two six-sided dice.
A total roll of 7 is very likely is true, not because it will happen every time, but because there are more combinations (6 in total) that sum to 7 than any other number. These are (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1).
Find the product of (x - 3)^2
Answer:x^2-6x+9
Step-by-step explanation:
An above ground pool in the shape of a cylinder has a diameter of 18 feet and a height of 4.5 feet. if the pool is filled with water to 6 inches from the top of the pool what is the volume
Answer:
r = 9ft
h = 4ft
Step-by-step explanation:
I have this math homework and I don’t know how to simplify this equation 4x-8-3
Answer:
4x-11(simplified)
x=2.75(solved, if needed)
Step-by-step explanation:
Simplify like terms
4x(-8-3)
4x-11
If you wanted it solved,
4x=11 (adding 11 to both sides)
x=2.75 (divide by 4)
Answer: x=2.75 or without simplifying 4x-11
hope it helps please give brainliest!
Step-by-step explanation:
[tex]4x-8-3\\4x-11\\[/tex]
This is the farthest you can go but you can simplify to...
[tex]4x-11\\x-\frac{11}{4}\\ x-2.75\\-x=-2.75\\/-1 /-1\\x=2.75[/tex]