a_n=224(1/2)^n-1
Aiden has $6,000 in an account. The interest rate is 5% compounded annually. To the nearest cent, how much will he have in 5 years?
Answer:
$7,657.69
Step-by-step explanation:
To find this, use the interest formula:
[tex]A = P(1+r)^{t}[/tex]
A = final amount
P = principal amount ($6,000)
r = interest rate (5% or 0.05)
t = time (5 years)
Given this formula, we can plug in the information and find how much Aiden has after 5 years:
[tex]A = 6000(1+0.05)^{5}[/tex]
[tex]A = 6000(1.05)^{5}[/tex]
[tex]A = 7657.69[/tex]
Therefore, after 5 years Aiden will have $7,657.69.
I hope this helps! Good luck!
A researcher wanted to see if different breeds of dogs preferred toys of certain colors. The researcher presented each dog with 3 toys, identical except that each was a different color, and recorded which toy the dog played with the most in a set time period. Here are the outcomes and partial results of a chi-square test (expected counts appear below observed counts):
The value for the test statistic and the p value on the test when the researcher wanted to see if different breeds of dogs will be x² = 0.9421 and 0.05 < p value < 0.10.
How to illustrate the research?From the information given, the null hypothesis is that the variables have no difference while the alternative hypothesis is that they have a difference.
The degree of freedom will be:
= (3 - 1) × (3 - 1)
= 4
The critical value is 9.4877. In this case, the p value is greater than the significance level. Therefore, we fail to reject the null hypothesis.
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Answer:
Step-by-step explanation:
From Khan
Please please I need help. What is the value of X
Answer:
x = 25
Step-by-step explanation:
Solving
∠CAD = 1/2 ∡ CD180° - 90° - (2x)° = 1/2 (80°)2x = 90° - 40° = 50°x = 25Gasoline cost $0.60 a gallon if a car makes 25 miles to the gallon what is will gasoline for an 800 mile trip cost
Answer:
$19.29
Step-by-step explanation:
800 ÷ 25 = 3232 x 0,60 = $19.20there you have it
find the mode of the following data set.
help please
Answer:
Step-by-step explanation:
The most repeated number is 1,
Therefore, 1 is the anser
Need help please thanks
Answer: There is no zeros for this equation.
Step-by-step explanation: First, we use the quadratic formula and plug in values. -2 plus or minus the square root of 2^2 - 4*5*8.
The square root will be -39 (negative 39.) This is impossible without using complex numbers (you cannot use complex numbers to get a zero.) Negative square roots are not real. Thus, this equation has no real solution.
is 3/2 = to square of 2
Answer:
No, it will not
Step-by-step explanation:
as square of 2 is 4
In an in-text citation, direct quotes go in_______.
A. between parenthesis
B. between double quotation marks
C. at the end of the paragraph
D. between commas
(06.01 LC) A scatter plot is shown. 10 9 8 7 6 5 4 3 2. 0 1 2 3 4 5 6 7 8 9 10 How many outliers does the graph show? (1 point) 01 02 03 4
Answer:
2 outliers
Step-by-step explanation:
(1,9) and (10,7) both are outliers.
There are 2 outliers in the given scatter plot. Therefore, option B is the correct answer.
What does outliers mean in scatter plots?An outlier is a data point that does not fit the rest of the data. It lies outside of a cluster and does not follow the same pattern. Scatter plots can have many outliers, just one outlier, or no outliers.
From the given graph, we can see that coordinates (1, 9) and (10, 7) are not in the cluster.
These two points lies out side the cluster, so these points are outliers.
Therefore, option B is the correct answer.
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You send an email with a file size of 4 kilobytes. One kilobyte is 2^{10} bytes. What is the file size of your email in bytes? Write your answer as a power.
Answer:
2¹² Bytes
Step-by-step explanation:
One kilobyte is 2¹⁰ bytes.
File size of the email is 4 kilobytes. That is 4 times 1 kilobyte. Therefore multiply with 4.
4 KB = 4 × 2¹⁰ B
Now notice that you can rewrite 4 like 2².
4 KB = 2² × 2¹⁰ B
Use exponental rule (Product Rule):
[tex]a^x + a^y = a^{x+y}[/tex]
4 KB = 2²⁺¹⁰ B = 2¹² B
Pa help po (yung buo sana sagot)
what are you saying?
Step-by-step explanation:
i dont kno if you are a thailander or not???
Which is an example of an isosceles right triangle?
Answer:
D.
Step-by-step explanation:
An isosceles triangle is a triangle with 2 equal sides (2 sides with the same length)
Let $a_1, a_2, a_3, \dots$ be a non-constant arithmetic sequence. Suppose that $a_4, a_7, a_{12}$ form a geometric sequence. If $a_7 = 30$, what is $a_1$?
The terms a1, a2 and a3 do not have a common difference, and the value of a1 in the geometric sequence is 10/9
How to determine the value of the first term?The arithmetic sequence is given as:
a₁, a₂ and a₃
The geometric sequence is given as:
a₄, a₇ and a₁₂
The common ratio of a geometric sequence is:
[tex]r = \frac{T_2}{T_1}[/tex]
So,we have:
[tex]\frac{a_7}{a_4} = \frac{a_{12}}{a_7}[/tex]
Cross multiply
[tex]a_{12} * a_4 = a_7 * a_7[/tex]
Given that a7 = 30, the equation becomes
[tex]a_{12} * a_4 = 30 * 30[/tex]
Evaluate the product
[tex]a_{12} * a_4 = 900[/tex]
Rewrite as:
[tex]a_{4} * a_{12} = 900[/tex]
Express 900 as 10 * 90
[tex]a_{4} * a_{12} = 10 * 90[/tex]
By comparison, we have:
a₄ = 10 and a₁₂ = 90
This means that the geometric sequence is:
10, 30, 90 ---- it has a common ratio of 3
The nth term of a geometric sequence is:
[tex]a_n = ar^{n-1}[/tex]
So, we have:
[tex]a_7 = ar^6[/tex]
[tex]a_4 = ar^3[/tex]
Substitute values for a7 and 14
[tex]ar^6 = 30[/tex]
[tex]ar^4 = 10[/tex]
Divide both equations
[tex]r^2 = 3[/tex]
Take the cube of both sides
[tex]r^6 = 27[/tex]
Substitute [tex]r^6 = 27[/tex] in [tex]ar^6 = 30[/tex]
[tex]a * 27 = 30[/tex]
Divide both sides by 27
[tex]a = \frac{10}{9}[/tex]
Hence, the value of a1 in the geometric sequence is 10/9
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By cross multiplication find x and y if
ax + by = a² + b² and bx - ay = 0
[tex] \bold{\underline{\underline{\underbrace{Answer}}}} [/tex]
x = a and y = b
Step-by-step explanation:
To findThe value of x and y
⠀
Givenax + by = a² + b² (equation 1)
bx - ay = 0 (equation 2)
⠀
Solution{Taking equation 2}
[tex] \sf bx - ay = 0 [/tex]
{Taking ay on RHS}
[tex] \sf bx = ay[/tex]
{Dividing both sides by a}
[tex] \sf \frac{bx}{a} = y(equation \: 3)[/tex]
{Now substituting the equation 3 in equation 1}
[tex] \sf ax + b( \frac{bx}{a} ) = {a}^{2} + {b}^{2} \\ \\ \sf ax + \frac{ {b}^{2} x}{a} = {a}^{2} + {b}^{2} [/tex]
{Taking LCM on LHS}
[tex] \sf \frac{ {a}^{2}x + {b}^{2} x }{a} = {a}^{2} + {b}^{2} \\ \\ \sf \frac{x( {a}^{2} + {b}^{2}) }{a} = ( {a}^{2} + {b}^{2} )[/tex]
{Dividing by (a² + b²) both sides}
[tex] \sf \frac{x}{a} = 1 \\ \\ \green{\boxed {\tt{x = a} } }[/tex]
{Now substituting the value of x in equation 3}
[tex] \sf \frac{ba}{a} = y \\ \\ \green {\boxed{ \tt{y = b}} }[/tex]
Which is the closest to the area that is painted blue? A 308 units B. 116 units C. 463 units? D 124 units
Step-by-step explanation:
first of all, all answer options are basically wrong, because an area is always measured in units² (and not just in units).
the blue colored area is the area of the whole square minus the area of the circle.
the side length of the square is 2 times the radius of the circle (the diameter) : 2×12 = 24 units.
so, the area of the square is
24² = 576 units²
the are of the circle is
pi×r² = pi×12² = 144pi units²
so, the blue area is
576 - 144pi = 123.6106579... ≈ 124 units²
therefore, D is the right answer.
In a bag there are 3 blue marbles, 2 green marbles, 4 red marbles, 1 white marble, and 5 yellow marbles. What is the probability of drawing a green marble then drawing a blue marble from the bag? (With Replacement)
Answer:
So, you must NOT draw a yellow marble on the first draw, a probability of 8/12. Then, you must NOT draw a yellow marble on the second draw, a probability of 7/11. Then you MUST draw a yellow marble on the third draw, a probability of 4/10. So, the three required events, taken together, look like this in lowest terms:
2/3 * 7/11 * 2/5 = 28/165
HOPE IT HELPS!!
Please help, image below. Thank you!
Answer:
10 Inches
Hope it helps, have a fantastic day.
Step-by-step explanation:
The Circumference of a circle can be displayed by this formula:
[tex]C = 2\pi r[/tex]
[tex]C[/tex] is the circumference, and [tex]r[/tex] is the radius.
So just plug in 31 for [tex]C[/tex], and simplify:
[tex]31 = 2\pi r[/tex]
Because the question is asking for the diameter, we only need to divide both sides by pi, as [tex]2r[/tex] is the same thing as diameter.
[tex]9.87 = 2r[/tex] (rounded to the nearest hundredth)
We can even rewrite [tex]2r[/tex] as [tex]d[/tex], which stands for diameter, to make things a little simpler.
[tex]9.87 = d[/tex]
Now we just take 9.87, and round it to the nearest whole number, and we get 10. So your answer is 10 Inches.
Hope it helps, have a fantastic day.
A square pyramid with a side length of 5 cm and a slant height 7 cm has a total surface area of ... square centimeter
20
165
95
25
70
Answer:
95
Step-by-step explanation:
Surface Area :
⇒ Area (4 triangle faces) + Area (square base)
⇒ 4 x 1/2 x 5 x 7 + (5)²
⇒ 2 x 35 + 25
⇒ 70 + 25
⇒ 95 square centimeters
If you use mobile payment and lose your phone, you should NOT:
OA. Cancel your card.
OB. Get a new phone and keep using the same card in the app.
OC. Remotely lock your device.
OD. If possible, clear the data off of your device.
Reason:
Yes you should get a new phone, but you should not keep using the same card. Whoever has your phone (assuming anyone found it or stole it) may be able to gain access to the phone, and use the card fraudulently. You should call the credit card company and cancel that card, and get a new card. This is why choice A is eliminated. Choices C and D are eliminated as well so that you protect your privacy from any potential thieves.
(5x+1)3=15x3 que Propiedad pertenece
Answer:
Step-by-step explanation:
1) Reagrupar términos.
3(5x + 1) = 15x^3
2) Divide ambos lados por tres.
5x + 1 = 5x^3
3) Mueva todos los términos a un lado.
5x + 1 - 5x^3 = 0
4) No se encontró ninguna raíz algebraicamente. Sin embargo, las siguientes raíces se encontraron por métodos numéricos.
x=−0.878886,−0.209148,1.088033
Construct an isosceles triangle ABC in which AB=AC = 9 cm and BÂC = 45°. Measure ABC and BC
Answer:
m∠ABC = 67.5°BC = =6.888301782572 cmStep-by-step explanation:
ABC is an isosceles triangle
Then
m∠ABC = m∠ACB
The sum of the interior angles of a triangle is equal to 180°
Then
m∠ABC + m∠ACB + m∠BAC = 180°
Then
m∠ABC + m∠ACB + 45 = 180°
Then
2 × m∠ABC = 180°
Then
m∠ABC = (180−45)÷ 2 = 67.5°
Law of SIN :
[tex]\frac{9}{\sin \left( 67.5\right) } =\frac{BC}{\sin \left( 45\right) }[/tex]
[tex]BC=\frac{9}{\sin \left( 67.5\right) } \times \sin \left( 45\right) ==6.888301782572[/tex]
which expression is greater than 4
Answer:
all numbers<4
so numbers 5 and up
Step-by-step explanation:
What set of transformations could be applied to rectangle ABCD to create A″B″C″D″?
A composite transformation is the production of the image of a figure through two or more transformation
The set of transformations that could be applied to rectangle ABCD to create rectangle A'B'C'D' is the second option;
Reflected over the y-axis and rotated 180°The reason the above selected option is correct is as follows:
Known parameters:
The given coordinates of the vertices of the preimage of the rectangle ABCD are; A(-4, 2), B(-4, 1), C(-1, 1), and D(-1, 2)
The given coordinates of the vertices of the image of the rectangle ABCD, which is rectangle A'B'C'D' are; A'(-4, -2), B'(-4, -1), C'(-1, -1), and D'(-1, -2)
Solution:
The form of the ordered pair of the vertices of the pre-image is negative value for x, positive value for y, which can be written as (-x, y), where x, and y, are positive numbers
The form of the ordered pair of the vertices of the image is (-x, -y)
The location of a point (-x, y) following a reflection over the y-axis is the point (x, y)
The location of a point (x, y) following a 180° rotation is the point (-x, -y)
Therefore, the set of transformations that can be applied to (-x, y), to create (-x, -y), is a reflection over the y-axis, followed by a rotation of 180
Which gives;
The set of transformations that transforms A(-4, 2) to create A'(-4, -2), B(-4, 1), to create B'(-4, -1), C(-1, 1), to create C'(-1, 1), and D(-1, 2), to create D'(-1, -2) is a reflection over the y-axis followed by a rotation of 180°.Therefore, the correct option is; Reflected over the y-axis and rotated 180°
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Answer: B is your correct answer!
Step-by-step explanation:
Bearing. A is on a bearing of 095° from B. What is the bearing of B from A?
Find the area of the rhombus
Answer:
25
Step-by-step explanation:
area of the rhombus=1/2×d1×d2
1/2×5×10
=25
Shreya has 40 pairs of shoes stacked in boxes.
If a pair is 2 shoes, how many shoes does Shreya have?
Answer:
80 shoes
Step-by-step explanation:
sin e a pair is 2 shoes,
Shreya has 40×2shoes
= 80 shoes
therefore, Shreya has 80 shoes
40 x 2
=80 shoes
(We now have school systems which force students to study maths and, through enough exposure, our brains can learn to think mathematically. But if those skills cease to be used, the human brain will quickly return to factory settings...- Matt Parker )
in a semiconductor company's quality control test, a machine found that 22 out of a sample of 600 computer chips were defective how many of the 36,000 computer chips the company makes each would you expect to be defective?
Answer:
1320 should be expected
Step-by-step explanation:
22 = 600
x10
220 = 6,000
x6
1320=36,000
Yuna grows two varieties of pears—Bosc and Anjou. She took a sample of each variety to test if their average caloric contents were significantly different. Here is a summary of her results:
Calories
Variety nnn Mean StDev SE mean
Bosc 656565 120120120 151515 1.861.861, point, 86
Anjou 656565 116116116 131313 1.611.611, point, 61
99\% \text{ CI for } \mu_\text{B} - \mu_{\text{A}}\text{:}99% CI for μ
B
−μ
A
:99, percent, start text, space, C, I, space, f, o, r, space, end text, mu, start subscript, start text, B, end text, end subscript, minus, mu, start subscript, start text, A, end text, end subscript, start text, colon, end text 4 \pm 6.444±6.444, plus minus, 6, point, 44
Yuna wants to use these results to test \text{H}_0\text{: }\mu_\text{B}=\mu_\text{A}H
0
: μ
B
=μ
A
start text, H, end text, start subscript, 0, end subscript, start text, colon, space, end text, mu, start subscript, start text, B, end text, end subscript, equals, mu, start subscript, start text, A, end text, end subscript versus \text{H}_\text{a}\text{: }\mu_\text{B} \neq \mu_\text{A}H
a
: μ
B
=μ
A
start text, H, end text, start subscript, start text, a, end text, end subscript, start text, colon, space, end text, mu, start subscript, start text, B, end text, end subscript, does not equal, mu, start subscript, start text, A, end text, end subscript. Assume that all conditions for inference have been met.
Based on the interval, what do we know about the corresponding P-value and conclusion at the \alpha=0.01α=0.01alpha, equals, 0, point, 01 level of significance?
Answer:
The P-value is greater than α=0.01 and she cannot conclude that there is a difference between the means.
Step-by-step explanation:
did the khan assignment
The Hiking Club plans to go camping in a State park where the probability of rain on
any given day is 0.68. What is the probability that it will rain on at least three of the
five days they are there? Round your answer to the nearest thousandth.
Answer:
0.3386 = 0.339 (rounded).
Step-by-step explanation:
It is the binomial type probability distribution.
The number of trial n= 3; the probability of the success trial is 0.16, and the number of success trial k = 1.
You are stationary on the ground and are watching a bird fly horizontally towards you at a rate of 3 m/s. The bird is located 60 m above your head. How fast does the angle of elevation of your head change when the horizontal distance between you and the bird is 80 m? (Leave your answer as an exact number.)
Based on the rate the bird is flying and the distance above your head, the speed of change in the angle of elevation is 0.018 rad/sec.
What is the speed of the change in angle of elevation?First use the Pythogoreous theorem to find the distance between you and the bird at 80 m:
= √(60² + 80²)
= √(3,600 + 6,400
= 100 m
Cos² = 80² / 100²
= 16 /25
Differentiate this to get:
= ((-60 x 16/25) / 80²) x (-3)
= 9/500
= 0.018 rad/sec
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