The total amount of interest earned on the account is $1049.15.
What is simple and compound interest?Simple interest is interest that is just based on the principal. It does not account for any interest accrued in prior periods and is determined as a percentage of the principal. If your principal is $1,000 and your yearly interest rate is 5%, for instance, you would make $50 in simple interest after a year ($1,000 0.05).
Contrarily, compound interest is calculated on the principal amount in addition to any prior quarters' interest. This means that interest is calculated on the new amount after the principal and interest earned during each period have been added.
The compound interest is given by the formula:
[tex]A = P(1 + r/n)^{(nt)}[/tex]
Rearranging for P we have:
[tex]P = A / (1 + r/n)^{(nt)}[/tex]
Substituting the value of r = 3.2%, n = 2 and t = 6 we have:
[tex]P = 6049.15 / (1 + 0.032/2)^{(2*6)}[/tex]
P = 5000
Here, P is the initial balance.
Now, for interest we have:
I = A - P
Substituting the values:
I = $6049.15 - $5000
I = $1049.15
Hence, the total amount of interest earned on the account is $1049.15.
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I need help with this ASAP
Answer:
the answer is (HK) Because gj is the only other line that goes across the circle but it is not an option.
What is the distance from home to library?
Check the picture below.
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{7})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~5 - 2~~)^2 + (~~7 - 1~~)^2} \implies d=\sqrt{( 3 )^2 + ( 6 )^2} \\\\\\ d=\sqrt{ 9 + 36 } \implies d=\sqrt{ 45 }\implies d\approx 6.7[/tex]
I NEED HELP PLS WILL MARK BRAINLIEST!!!!!!!
Answer: x= 75.52 deg
Step-by-step explanation:
1) cos x = adjacent/hypotenuse
cos x = 2 / 8
x = cos^-1(2/8)
x= 75.52 deg
What is the value of x?
sin(x+16)°=cos(2x+14)°
Enter your answer in the box.
The value of x for which sin(x+16)°=cos(2x+14)° is 20
How to determine the value?Trigonometry is a branch of mathematics concerned with relationships between angles and ratios of lengths
The given equation says:
sin(x+16)°=cos(2x+14)°
Remember that sin(90-x) = cos x
Applying this formula we have
So comparing we have,
sin(x+16)°=cos(2x+14)°
90 - (x + 16) = 2x +14
distributing - over the bracket
90 -x - 16 = 2x + 14
bringing like terms together,
90-16-14 = 2x +x
60 = 3x
Dividing both sides by 3,
x =20
Therefore the value of sin(x+16)°=cos(2x+14)° is 20⁰
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Graph the solution to 4 - 2 x ≥ 10 on the number line. plot an exclusive point.
The solution to the inequality, 4 - 2x ≥ 10, is x ≤ -3.
The graph is shown below.
How to Graph an Inequality?To graph the solution to the inequality given, we have to first of all solve for the possible values of x in the given inequality.
Given the inequality, 4 - 2x ≥ 10, we have:
4 - 2x ≥ 10
Subtract 4 from both sides:
4 - 4 - 2x ≥ 10 - 4
-2x ≥ 6
Divide both sides by -2:
-2x/-2 ≤ 6/-2
x ≤ -3
This means that the values of x are equal to -3 or less than -3.
The graph below shows the solution.
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The numbered disks shown are placed in a box and one disk is selected at random. Find the probability
The probability of selecting a 2 given that a blue disk is selected is 1/8, or 0.125.
What is the calculation for this?1. Let's calculate the probability of selecting a blue disk
We can select a blue disk with number 2, 6 or 8 out of a total of 8 disks, it means that the probability of selecting a blue disk is = 3/8
2. Let's calculate the probability of selecting the blue disk labeled with number 2 =
We can select the blue disk labeled with number 2 out of three blue disks, it means that the probability of selecting the blue disk labeled with number 2 is = 1 /3
3. These are dependent events because the fact that we select the disk labeled with number 2, depends on selecting a blue disk before, thus:
Probability of selecting a 2 given that a blue disk is selected =
3/8 x 1/3 = 3/24 = 1/8
Thus,it is correct to state that the probability of selecting a 2 given that a blue disk is selected is 1/8, or 0.125.
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Full Question:
See attached image.
If the common ratio is 0.6, what is the percent change?
Include the percentage symbol with your answer.
Answer:
If the common ratio is 0.6, then the percent change is a decrease of 40%.
If the common ratio is 0.6 then the percent change is 40%
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
The percent change for a geometric sequence with common ratio r is given by the formula:
percent change = (r - 1) × 100%
In this case, the common ratio is 0.6, so the percent change is:
percent change = (0.6 - 1) × 100% = -0.4 × 100% = -40%
The percent change is negative, which means the sequence is decreasing.
Hence, If the common ratio is 0.6 then the percent change is 40%
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AsAp need helllpppppppp
The value of x is 31/64 or 0.484375 and the value of 61/64 is given by adding the value of 29/64 and 31/64 which is 0.9375.
How to convert a fraction to a decimal?To convert a fraction to a decimal, you need to divide the top number by the bottom number. Here are the steps to follow:
1. Fraction should be written as numerator (top) divided by denominator (bottom).
2. Divide the numerator by the denominator using long division or a calculator.
3. Keep dividing until you get a decimal that terminates or repeats.
a) The given equation is
[tex]\frac{61}{64} = \frac{29}{64} + x[/tex]
[tex]\frac{61}{64} - \frac{29}{64} = x[/tex]
[tex]x = \frac{31}{64}[/tex]
b) Now 31/64 = 0.484375 and given that 29/64 = 0.453125
Hence from the equation 61/64 = 29/64 + 31/64 = 0.453125 + 0.484375
= 0.9375.
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Suppose 128 ounces of a radioactive substance exponentially decays to 28 ounces in 6 hours. What is the half-life of the substance? The half-life is:
Answer:
half-life ≈ 2.74
Step-by-step explanation:
One formula we can use for half life is,
N(t) = No * (1/2)^(t / t_1/2), where
N(t) is the amount remaining, No is the initial amount,1/2 is the base t is the time, and t_1/2 is the half lifeWe already know that N(t) = 28, No = 128, the base is 1/2, and t is 6. Thus, we must solve for t_1/2 using the following equation:
28 = 128 * (1/2) ^ (6 / t_1/2)
Step 1: Divide both sides by 128 to clear 128 on the right-hand side of the equation:(28 = 128 * (1/2) ^ (6 / t_1/2) / 128
0.21875 = (1/2) ^ (6 / t_1/2)
Step 2: Take the natural log (ln) of both sides:ln (0.21875) = ln (1/2 ^ (6 / t_1/2))
Step 3: According to the rules of logs, since we're taking the natural log of ln (1/2 ^ 6 / t_1/2, we can bring down the 6 / t_1/2 and it will now act like a coefficient:ln (0.21875) = 6 / t_1/2 * ln (1/2)
Step 4: Divide both sides by ln (1/2) to clear ln (1/2) on the right-hand side of the equation:(ln ( 0.21875) = 6 / t_1/2 * ln (1/2)) / ln (1/2)
ln (0.21875) / ln (1/2) = 6 / t_1/2
Step 5: You can cross multiply, which appears easier when you use the vertical fraction form instead of the horizontal fraction form.[tex]\frac{ln(0.21875)}{ln(1/2)}=\frac{6}{t_{1/2} }\\ \\ t_{1/2}*ln(0.21875)=6*ln(1/2)[/tex]
Step 6: Finally, you can now divide both sides by ln (0.21875) to isolate t_1/2 and to find the half-life. I simply rounded to the nearest hundredth, but I'll provide the entire half-life number so you can round as liberally as much as you need or would like(t_1/2 * ln (0.21875) = 6 * ln (1/2)) / ln (0.21875)
t_1/2 = (6 * ln (1/2) / ln (0.21875)
t_1/2 = 2.736420983 hours
t_1/2 = 2.74 hours
The only real difference between the longer number and the rounded number is that the longer answer gives a more exact answer when you plug it in, but the rounded answer seems to make more sense to write:
Result when plugging in exact answer for t_1/2:
N (2.736420983) = 128 (1/2) ^ (6 / 2.736420983) = 28
Result when plugging in rounded answer for t_1/2:
N (2.74) = 128 (1/2) ^ (6 / 2.74) = 28.05564116
A rocket is launched in the air. Its height in feet is given by h(t)=−16t^2 +24t where
t represents the time in seconds after launch. How long is the rocket in the air?
Taking into account the zeros of a quadratic function, the time of the rocket when it is in the air is equal to 1.5 seconds.
Zeros of a functionThe points where a polynomial function crosses the axis of the independent term (x) represent the so-called zeros of the function.
The zeros represent the roots of the polynomial equation that is obtained by making f(x)=0.
In a quadratic function that has the form:
f(x)= ax² + bx + c
the zeros or roots are calculated by:
[tex]x1,x2=\frac{-b+-\sqrt{b^{2} -4ac} }{2a}[/tex]
Time of he rocket in the airA rocket launched with height function h(t)= -16t²+ 24t
where
't' represents the time in seconds'h' is the height of rocket.Time for which rocket is in the air given by h(t) = 0, so:
0= -16t²+ 24t
where:
a= -16b= 24c= 0Solving:
[tex]x1=\frac{-24+\sqrt{24^{2} -4x(-16)x0} }{2x(-16)}[/tex]
[tex]x1=\frac{-24+\sqrt{24^{2}} }{2x(-16)}[/tex]
[tex]x1=\frac{-24+24 }{2x(-16)}[/tex]
[tex]x1=\frac{0 }{-32}[/tex]
x₁= 0
and
[tex]x2=\frac{-24-\sqrt{24^{2} -4x(-16)x0} }{2x(-16)}[/tex]
[tex]x2=\frac{-24-\sqrt{24^{2} } }{2x(-16)}[/tex]
[tex]x2=\frac{-24-24}{2x(-16)}[/tex]
[tex]x2=\frac{-48}{-32}[/tex]
x₂= 1.5
Therefore, the time of the rocket in the air is 1.5 seconds.
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Use the frequency distribution to complete parts (a) through (e)
For the frequency distribution table;
1. The total number of observation is 24.
2. The width of each class is 11
3. The midpoint of the second class is 26
4. The model class is 65-75
5. The class limits of the next class is 76-86
How do we find the width, model, midpoint and next class limit for the frequency distribution table?For the frequency distribution table,
1. Total observation is the sum of the frequency:
2 + 3 + 5 + 6 + 0 + 8 = 24
2. The width is the first limit lower class - first limit of upper class.
21-10 = 11 or 32-21 = 11
3. The midpoint of class 2 is 21 + 31 = 52/2 = 26
4. The class with the highest frequency is the model class
5. Next class lower limit = 75 + 1 = 76
Next class upper limit = 75 + 11 = 86
Use the frequency distribution to complete parts (a) through (e).
Class Frequency
a) Determine the total number of observations. 10-20 2
b) Determine the width of each class. 21-31 3
c) Determine the midpoint of the second class. 32-42 5
d) Determine the modal class (or classes). 43-53 6
e) Determine the class limits of the next class 54-64 0
if an additional class were to be added. 65-75 8
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Jackson invested $52,000 in an interest rate of 2.1% compounded continuously assuming no deposits or withdraws are made how much money to the nearest dollar would be in the account after 17 years
The amount of money in the account after 17 years, to the nearest dollar, would be $76,956.
What is the formula for the future value?
The formula for the future value of an investment with continuous compounding is [tex]A = Pe^{(rt)}[/tex] where A is the future value, P is the principal (initial investment), e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate as a decimal, and t is the number of years.
Putting in the given values,
[tex]A = 52000 \times e^{(0.021 \times 17) }\\ A ≈ 76,956.18[/tex]
Therefore, the amount of money in the account after 17 years, to the nearest dollar, would be $76,956.
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For the following polynomial [tex]f(x) = 2x^3 - 4x^2 - 3x + C[/tex] find a real number [tex]C[/tex], so that the polynomial has the indicated root of [tex]x= -1[/tex]
x = -1 is a root of the polynomial only if C = 3.
How to find the value of C?We want to have x = -1 as a root of the polynomial, then we just need to solve:
f(-1) = 0
this is:
2(-1)³ - 4(-1)² - 3(-1) + C =0
-2 - 4 + 3 + C = 0
-3 + C = 0
C = 3
Tha must be the value of C.
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what is the constant of proportionally in th equation 2y= 2x
Answer:
The constant of proportionality in the equation 2y = 2x is 1.
Note that this equation is actually the same as y = x, which is a linear equation with a slope of 1 and a y-intercept of 0. In this case, the coefficient of x (which is 2) is not the constant of proportionality because it does not represent a proportional relationship between x and y. Instead, the constant of proportionality is the ratio of the change in y to the change in x, which is 1.
Which of the following options correctly describes the given statement?
Mark all that apply. (There is more than 1 answer.)
r
r
r
r
Г
The statement can be written as a biconditional: Two angles are complementary if
and only if the sum of their measures is 90.
The converse of the statement is false.
The statement is false.
The converse of the statement is true.
Ev
A
counter-example to prove the converse is false is: a Linear pair of angles are not
complementary, they add up to 180.
The statement is true.
The answers are given below:
The statement can be written as a biconditionalThe converse of the statement is falseA counter-example to prove the converse is false is: a Linear pair of angles are not complementary, they add up to 180.What is a Conditional Statement?A conditional statement is a form of logical statement that consists of two parts: a conclusion and an antecedent (sometimes known as a "if-clause")
If p, then q is a common way to represent the link between the hypothesis and the conclusion, where p stands for the hypothesis and q for the conclusion.
Therefore, the correct options are:
The statement can be written as a biconditional: Two angles are complementary if and only if the sum of their measures is 90.
The converse of the statement is false.
A counter-example to prove the converse is false is: a Linear pair of angles are not complementary, they add up to 180.
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Find the area of parallelogram VW XY. Round your answer to the nearest tenth if necessary.
Answer:
Step-by-step explanation
A=bh for a parallelogram. The diagram is flipped(turn your paper)
b=9
h=6.7
A=(9)(6.7)=60.3 in²
Select the correct answer from each drop-down menu.
Consider right triangle ABC.
A
sin(A) =
cos(A) =
Reset
40
41
11
=
Next
B
9
C
Answer:
sinA =9/41. CosA=40/41
Step-by-step explanation:
in right triangles, the sine, cosine and tangent represent ratios of the sides of a triangle. Sine of an angle is the ratio of the side opposite the angle divided by the hypotenuse and the cosine of the angle is side adjacent (touching) the angle divided by the hypotenuse.
The value of Sin A = 9 / 41 and the value of Cos A = ( 40 / 41).
What is trigonometry?The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
here, we have,
The values of the angels will be calculated by using the trigonometry property.
Sin A = Perpendicular / Hypotenuse
Sin A = 9 /41
Cos A = Base / Hypotenuse
Cos A = 40 / 41
Therefore the value of Sin A = 9 / 41 and the value of Cos A = ( 40 / 41).
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amber and bethan tries a number of sweets and shares them in the ratio 2:1
The ratio of the number of sweets that Amber has to the number of sweets that Callum has is 16:9.
What is ratio?A quantitative comparison of two or more quantities that shows their relative sizes is called a ratio.
In terms of how many times one is greater or less than the other, it describes the relationship between the two quantities.
Let's assume that Amber and Bethan bought x number of sweets, then Callum and David also bought x number of sweets.
According to the problem, Amber and Bethan share the sweets in the ratio 2:1. Therefore, Amber has (2/3)(x) sweets and Bethan has (1/3)(x) sweets.
Also, Callum and David share the sweets in the ratio 3:5. Therefore, Callum has (3/8)(x) sweets and David has (5/8)(x) sweets.
Now, we can find the ratio of the number of sweets that Amber has to the number of sweets that Callum has as follows:
Amber/Callum = [(2/3)(x)]/[(3/8)(x)] = (16/9)
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A game has a spinner with 8 equal- sized sections. The results of 450 spins are shown in the table. Part Frequency 1 58 2 52 3 39 4 77 5 50 6 43 7 60 8 71
For Which Number is the number difference between the theoretical probability and experimental probability greatest?Explain
The theoretical probability of each section is 1/8, since there are 8 equal-sized sections on the spinner. To find the theoretical frequency, we multiply the theoretical probability by the total number of spins:
Theoretical frequency = (1/8) x 450 = 56.25
We can then calculate the experimental probability for each section by dividing the frequency by the total number of spins:
Experimental probability = Frequency/Total number of spins
Using this formula, we can calculate the experimental probabilities for each section:
Part 1: Experimental probability = 58/450 ≈ 0.129
Part 2: Experimental probability = 52/450 ≈ 0.116
Part 3: Experimental probability = 39/450 ≈ 0.087
Part 4: Experimental probability = 77/450 ≈ 0.171
Part 5: Experimental probability = 50/450 ≈ 0.111
Part 6: Experimental probability = 43/450 ≈ 0.096
Part 7: Experimental probability = 60/450 ≈ 0.133
Part 8: Experimental probability = 71/450 ≈ 0.158
To find the number with the greatest difference between the theoretical and experimental probability, we can calculate the difference between the two probabilities for each section:
Part 1: |0.125 - 0.129| = 0.004
Part 2: |0.125 - 0.116| = 0.009
Part 3: |0.125 - 0.087| = 0.038
Part 4: |0.125 - 0.171| = 0.046
Part 5: |0.125 - 0.111| = 0.014
Part 6: |0.125 - 0.096| = 0.029
Part 7: |0.125 - 0.133| = 0.008
Part 8: |0.125 - 0.158| = 0.033
As we can see, the greatest difference between the theoretical and experimental probability is for Part 4 with a difference of 0.046. This indicates that the experimental frequency for Part 4 is significantly different from the theoretical frequency, which may suggest that the spinner is biased towards that section.
Find the slope of the line, then write the equation of the line in slope-intercept form.
y = x - 4 is the equation of the line in slope-intercept form.
How do you interpret a slope-intercept form?
The data provided by that form can be used to graph a linear equation in slope-intercept form. As an illustration, the equation y=2x+3 indicates that the line's slope is 2 and that its y-intercept is located at (0,3). This reveals the single point at which the line passes as well as the direction in which we should draw the full line after that.
Point from graph = (2, -2 )
slope (m) = y/x
= -2/2
= 1
slope-intercept form ⇒ y = mx + c
-2 = 1 * 2 + c
- 2 = 2 + c
c = -4
slope-intercept form ⇒ y = x - 4
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Anton must pay a co-pay of $30 for an office visit. His insurance company will then pay 85% of the cost of the visit.
How much will Anton pay for an office visit that costs $270?
Answer: I think the answer is $229.5, or $259.5 since it says he has to pay $30
Step-by-step explanation: Just multiply 270 by the percent as a decimal. 85% is equal to 0.85 and that multiplied by 270 is 229.5
The coordinates of the vertices of DEF are D(2,3), E(4,0), and F(1,−2). The coordinates of the vertices of TVW are T(0,3), V(−2,0), and W(1,−2).
Answer:
To find the equation of the line containing the segment DE, we can use the coordinates of D and E to find the slope:
slope = (change in y) / (change in x) = (0 - 3) / (4 - 2) = -3/2
We can use the point-slope form of the equation of a line, using either D or E as the point:
y - 3 = (-3/2)(x - 2)
Simplifying this equation, we get:
y = (-3/2)x + 6
Similarly, to find the equation of the line containing the segment EF, we can find the slope using the coordinates of E and F:
slope = (change in y) / (change in x) = (-2 - 0) / (1 - 4) = 2/3
Using either E or F as the point, we can write the equation in point-slope form:
y - 0 = (2/3)(x - 4)
Simplifying, we get:
y = (2/3)x - (8/3)
To find the equation of the line containing the segment TV, we can find the slope using the coordinates of T and V:
slope = (change in y) / (change in x) = (0 - 3) / (-2 - 0) = 3/2
Using either T or V as the point, we can write the equation in point-slope form:
y - 3 = (3/2)(x - 0)
Simplifying, we get:
y = (3/2)x + 3
Finally, to find the equation of the line containing the segment VW, we can find the slope using the coordinates of V and W:
slope = (change in y) / (change in x) = (-2 - 0) / (1 - (-2)) = -2/3
Using either V or W as the point, we can write the equation in point-slope form:
y - 0 = (-2/3)(x - (-2))
Simplifying, we get:
y = (-2/3)x + (4/3)
Answer:
are reflection across the y-axis and translation 2 units right.
Step-by-step explanation:
Find the Missing angle and find the missing side.
The solution of given trigonometric Problem by using formula of sine , cosine , tangent is part A 1)cos-1(12/13) 2)∅=cos-1(2/3) 3)sin-1(4/13)
part B 1)13.75 unit 2) 8.112 unit 3) 5.5 unit
What is trigonometric ?Trigonometry is a branch of mathematics that deals with the study of relationships between angles and sides of triangles. It primarily focuses on the properties and functions of angles, and how they can be used to calculate the measurements of sides and angles in a triangle.
According to given informationPart A
1)In the given ΔACB Right angle at ∠C
for find ∅ we use
cos∅=B/H
cos∅=AC/AB
cos∅=12/13
∅=cos-1(12/13)
2) cos∅= AC/AB
∅=cos-1(6/9)
∅=cos-1(2/3)
3) sin∅=CB/AC
∅=sin-1(4/13)
Part-B
1) cos37°=11/x
4/5=11/x
x=55/4
x=13.75 unit
2) tan32°=x/13
0.624=x/13
x= 8.112 unit
3) cos 60°=x/11
1/2= x/11
x=11/2
x=5.5 unit
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What percent larger is 20.49 trillion to 4.00 trillion
20.49 trillion is 412.25% larger than 4.00 trillion.
How to calculate a percentage increase?To calculate the percentage increase of a value from an initial value to a final value, you can use the following formula:
increase in percentage = ((final value - initial value) / initial value) x 100%
Percentage increase is useful in a variety of contexts, including: Finance, Sales, Economics, Science, Education. Percentage increase is a useful tool for measuring growth or change over time and comparing different values.
To find the percentage increase, we first need to calculate the difference between the two numbers:
20.49 trillion - 4.00 trillion = 16.49 trillion
Next, we can divide the difference by the original amount (4.00 trillion) and multiply by 100 to get the percentage increase:
(16.49 trillion / 4.00 trillion) * 100 = 412.25%
Therefore, 20.49 trillion is 412.25% larger than 4.00 trillion.
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Find an expression which represents the difference when (5x + 6y) is subtracted
from (2x + 7y) in simplest terms.
Answer: -3x+y
Step-by-step explanation:
This is a subtraction problem and "from" means it's the 1st number so
(2x+7y) - (5x + 6y) be careful to distribute negative
2x +7y - 5x -6y
-3x+y
To find the simplest expression when (5x + 6y) is subtracted from (2x + 7y), we subtract the coefficients of like terms. This gives us -3x + y as the final result.
Explanation:The expression represents the difference when (5x + 6y) is subtracted from (2x + 7y) can be found using the properties of addition and subtraction for algebraic expressions. We will combine like terms to simplify.
So, Subtract (5x + 6y) from (2x + 7y), it's like saying (2x + 7y) - (5x + 6y) this will give us:
-3x + y is the final expression in the simplest form.
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Anna invested $69,000 in an account paying an interest rate of % compounded 8 1/2 % continuously. Hudson invested $69,000 in an account paying an interest rate of 8 3/8 % compounded daily. After 10 years, how much more money would Anna have in her account than Hudson, to the nearest dollar?
The solution of compound interest problem using formula of amount is
Anna have$2,734 more money than Hudson.
what is compound interest ?Compound interest is a type of interest in which the interest gained is added to the principal sum before the interest for the subsequent period is calculated using the updated total sum. In other words, in addition to the initial principal, the accumulated interest from prior periods is also taken into account for calculating interest. As a result, as time passes, the interest earned increases, increasing the total amount earned or due. Savings accounts, loans, and investments frequently use compound interest.
According to given informationFor continuous compounding, the formula is:
A = Pe^(rt)
Where:
A = the amount after t years
P = the principal amount
r = the annual interest rate (as a decimal)
t = the time in years
For daily compounding, the formula is:
A = P(1 + r/n)^(nt)
Where:
A = the amount after t years
P = the principal amount
r = the annual interest rate (as a decimal)
n = the number of times compounded per year
t = the time in years
Using these formulas, we can calculate the amount that Anna and Hudson will have after 10 years, and then find the difference between them.
For Anna's investment:
r = 8.5% = 0.085 (as a decimal)
t = 10 years
P = $69,000
A = Pe^(rt) = 69000 * e^(0.085*10) = $156,794.63
For Hudson's investment:
r = 8 3/8% = 8.375% = 0.08375 (as a decimal)
n = 365 (daily compounding)
t = 10 years
P = $69,000
A = P(1 + r/n)^(nt) = 69000(1 + 0.08375/365)^(365*10) = $154,060.52
Therefore, the difference between the two amounts is:
$156,794.63 - $154,060.52 = $2,734.11
So Anna will have approximately $2,734 more in her account than Hudson after 10 years.
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CAN SOMEONE IN THE UNIVERSE HELP ME!!!!
Answer:
Step-by-step explanation:
Formula for trapezoid:
A=[tex]\frac{1}{2}[/tex](b1 + b2)h
1. b1=5 b2=23 h=12
A=1/2(5+23)12
=168
Find the value of x needed to make the equation true.
Answer:
x = -3
Step-by-step explanation:
We know that,
[tex]\sf a^x*a^y=a^{x+y}\\\\(a^x)^y=a^{xy}\\\\\frac{a^x}{a^y} =a^{(x-y)}[/tex]
Accordingly,
[tex]\sf \frac{(7^{10})^2}{7^4} =\frac{7^9*7^{10}}{7^x} \\\\\sf \frac{7^{10*2}}{7^4} =\frac{7^{9+10}}{7^x} \\\\\sf \frac{7^{20}}{7^4} =\frac{7^{19}}{7^x}\\\\7^{20-4}=7^{(19-x)}\\\\16=19-x\\\\16-19=x\\\\-3 =x[/tex]
A sequence is represented by the explicit formula an = 14 +9n
What is a 26?
262
14
234
248
Answer:
a₂₆ = 248
Step-by-step explanation:
to find the 26th term substitute n = 26 into the explicit formula
a₂₆ = 14 + 9(26) = 14 + 234 = 248
Data show that men between the ages of 20 and 29 in a general population have a mean height of 69.3 inches, with a standard deviation of 2.7 inches. A baseball analyst wonders whether the standard deviation of heights of major-league baseball players is less than 2.7 inches. The heights (in inches) of 20 randomly selected players are shown in the table.
The crucial t-value is determined to be 1.734 using a t-table with 19 degrees of freedom and a significance threshold of 0.05 for a one-tailed test.
What is null hypothesis?A type of statistical hypothesis known as a null hypothesis claims that a certain collection of observations has no statistical significance. The viability of hypotheses is evaluated using sample data. known as "zero" at times and represented by the letter H0. The assumption made by researchers is that there is a relationship between the variables. The null hypothesis, on the other hand, asserts that such a connection does not exist. Although it might not seem significant, the null hypothesis is an important part of research.
We may run a one-tailed t-test for the standard deviation to test the hypothesis that the standard deviation of heights of major-league baseball players is less than 2.7 inches.
The following formula may be used to get the sample standard deviation of the players' heights among the 20 chosen at random:
where n is[tex]s = 1/(n-1) * \sum(x' - x)^2 = 1/(20-1) * (1.83-1.755)^2 + ... + (1.9-1.755)^2 = 0.0414[/tex] the sample size, xi is the player's height at position i, and x is the average player's height in the sample.
The test statistic may then be calculated as follows:
[tex]t = (n-1) * s^2 / \sigma ^2 = 19 * 0.0414^2 / 2.7^2 = 0.197[/tex]
The crucial t-value is determined to be 1.734 using a t-table with 19 degrees of freedom and a significance threshold of 0.05 for a one-tailed test.
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