SOLUTION
From the question, we want to find the value in dollars of the account after 2 years.
We will usethe formula
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ Where\text{ A = value of the account, amount in dollars = ?} \\ P=principal\text{ money invested = 40,000 dollars } \\ r=annual\text{ interest rate = 4.25\% = }\frac{4.25}{100}=0.0425 \\ n=number\text{ of times compounded = daily = 365} \\ t=time\text{ in years = 2 years } \end{gathered}[/tex]Applying this, we have
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=40,000(1+\frac{0.0425}{365})^{365\times2} \\ A=40,000(1.000116438)^{730} \\ A=40,000\times1.0887116 \\ A=43,548.467179 \\ A=43,548.47\text{ dollars } \end{gathered}[/tex]Hence the answer is 43,548.47 to the nearest cent
Is the following relation a function? Justify your answer.
No, because there is an input value with more than one output value
No, because there is an output value with more than one input value
Yes, because each input value has only one output value
Yes, because each output value has only one input value
Answer:
A
Step-by-step explanation:
There are two inputs for one output, which means the relation is not a function.
Answer:
A
Step-by-step explanation:
a normal distribution with u= 40 with o=4 what is the probability of selecting a score greater than x=44?
We have the following information:'
[tex]\begin{gathered} \mu=40 \\ \sigma=4 \\ x=44 \end{gathered}[/tex]We want to calculate the following probability:
[tex]P(X>44)[/tex]then, using the information that we are given, we havE:
[tex]P(X>44)=P(X-\mu>44-40)=P(\frac{X-\mu}{\sigma}>\frac{44-40}{4})=P(\frac{X-\mu}{\sigma}>1)[/tex]since:
[tex]Z=\frac{X-\mu}{\sigma}[/tex]we have the following:
[tex]P(X>44)=P(Z>1)=0.1587[/tex]therefore, the probability of selecting a score greater than 44 is 15.87%
I need help with homework . BC=5, angle A=25 degree.
AC = 2.332
AB = 5.517
Explanation:
Given:
BC = 5.
Angle B = 25 degree.
Angle C = 90 degree.
The objective is to find AC and AB.
By the trigonometric functions, Consider AB as hypotenuse, AC as opposite and BC as adjacent.
Then, the relationship between opposite (AC) and adjacent (BC) cnbe calculated by trigonometric ratio of tan theta.
[tex]\begin{gathered} \tan \theta=\frac{opposite}{adjacent} \\ \tan 25^0=\frac{AC}{5} \\ AC=\tan 25^0\cdot5 \\ AC=2.332 \end{gathered}[/tex]Now, the length AB can be calculated by Pythagorean theorem,
[tex]\begin{gathered} AB^2=AC^2+BC^2 \\ AB^2=2.332^2+5^2 \\ AB^2=5.436+25 \\ AB^2=30.436 \\ AB=\sqrt[]{30.436} \\ AB=5.517 \end{gathered}[/tex]Let's check the value using trigonometric ratios.
For the relationship of opposite and hypotenuse use sin theta.
[tex]\begin{gathered} \sin \theta=\frac{opposite}{hypotenuse} \\ \sin 25^0=\frac{2.332}{y} \\ y=\frac{2.332}{\sin 25^0} \\ y=5.517 \end{gathered}[/tex]Thus both the answers are matched.
Hence, the length of the side AC = 2.332 and the length of the side AB = 5.517.
Which ocean animal is closest to a depth of -0.7km?
Answer:
whales, walruses, porpoises, dolphins, seals, dugongs, manatees, and sea otters
Step-by-step explanation:
have good day
e costs 7 dollars. Lamar buys p pounds. Write an equation to represent the total00XХ$?
Given:
A pound of chocolate costs 7 dollars.
To find:
The equation represents the total cost c for buying p pounds of chocolate.
Solution:
It is given that a pound of chocolate costs 7 dollars. So,
[tex]\begin{gathered} 1\text{ pound}=7\text{ dollars} \\ 1\times p\text{ pounds}=7\times p\text{ dollars} \\ p\text{ pounds}=7p\text{ dollars} \end{gathered}[/tex]Since the cost of p pounds of chocolate is c. So,
[tex]c=7p[/tex]Thus, the answer is c = 7p.
The high school soccer booster club sells tickets to the varsity matches for $4 for students and $8
for adults. The booster club hopes to earn $200 at each match.
what does the slope mean in terms of the situation?
Perform a DuPont analysis on Healthy Body Nursing Home, Inc. Assume that the industry average ratios are as follows: Total margin: 3.9%
Total asset turnover: 0.5
Equity multiplier: 2.8
Return on equity: %
Using the DuPont analysis the return on equity is 5.46%.
What is the return on equity?
Return on equity is the ratio of net income to average total equity. Return on equity is an example of a profitability ratio. Profitability ratios measure the ability of a firm to generate profits using available resources.
Return on equity = net income / average total equity
Using the Dupont formula, return on equity can be determined using:
Return on equity = total margin x asset turnover x equity multiplier
Return on equity = (Net income / Sales) x (Sales/Total Assets) x (total asset / common equity)
3.9% x 0.5 x 2.8 = 5.46%
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Solve the missing elements for each problem. Use 3.14 for π. Area = πr^2; C=π D
Given,
Diameter = 32 cm
Radius
We know the radius is half of the diameter. Thus,
[tex]\begin{gathered} r=\frac{32}{2} \\ r=16 \end{gathered}[/tex]Radius 16 cm
Circumference
The formula is:
[tex]C=\pi D[/tex]Where
D is the diameter
So,
[tex]\begin{gathered} C=\pi D \\ C=(3.14)(32) \\ C=100.48 \end{gathered}[/tex]Circumference = 100.48 cm
Area
The formula is:
[tex]A=\pi r^2[/tex]Where
r is the radius
So,
[tex]\begin{gathered} A=\pi r^2 \\ A=(3.14)(16)^2 \\ A=(3.14)(256) \\ A=803.84 \end{gathered}[/tex]Area = 803.84 sq. cm.
Chords WP and KZ intersect at point L in the circle shown.Wz*3x - 22KIL5РWhat is the length of KZ?7.5910O 12
For the cicle with intersecting chords the relation between the length of segments of chords is,
[tex]KL\cdot ZL=WL\cdot PL[/tex]Substitute the values in the equation and solve for x.
[tex]\begin{gathered} 2\cdot(3x-2)=x\cdot5 \\ 6x-4=5x \\ 6x-5x=4 \\ x=4 \end{gathered}[/tex]So value of x is 4.
The equation for the length of chord KZ is,
[tex]\begin{gathered} KZ=KL+LZ \\ =2+3x-2 \\ =3x \end{gathered}[/tex]Substitute the value of x in equation to determine the length of KZ.
[tex]\begin{gathered} KZ=3\cdot4 \\ =12 \end{gathered}[/tex]So answer is 12.
Write an addition equation and a subtraction equation
to represent the problem using? for the unknown.
Then solve.
There are 30 actors in a school play. There are
10 actors from second grade. The rest are from third
grade. How many actors are from third grade?
a. Equations:
b. Solve
The Equation is 10 + x= 30 and 20 actors are from third grade.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
There are 30 actors in a school play.
There are 10 actors from second grade.
The rest are from third grade.
let the actors in third grade is x.
Equation is:
Actors from second grade + Actors from third grade = Total actors
10 + x= 30
Now, solving
Subtract 10 from both side
10 +x - 10 = 30 - 10
x = 20
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The time spent waiting in the line is approximately normally distributed. The mean waiting time is 5 minutes and the standard deviation of the waiting time is 3 minutes. Find the probability that a person will wait for more than 1 minute. Round your answer to four decimal places.
We were given the following details:
This is a normal distribution. Normal distributions are solved using the z-score
[tex]\begin{gathered} \mu=5min \\ \sigma=3min \end{gathered}[/tex]The z-score for a value, X is calculated using the formula:
[tex]\begin{gathered} Z=\frac{X-\mu}{\sigma} \\ The\text{ probability that a person will wait more than 1 minute implies that: }X=1 \\ Z=\frac{1-5}{3} \\ Z=-\frac{4}{3} \\ At\text{ Z =}-\frac{4}{3}\text{, pvalue =}0.091759 \\ The\text{ probability that a person waits more than 1 minute is given by:} \\ P=1-0.091759 \\ P=0.908241\approx0.9082 \\ P=0.9082\text{ or }90.82\text{\%} \end{gathered}[/tex]Section 11 - Topic 5Probability and Independence• In your own words, describe what the word independeyou.Now describe dependent..
In probability , there are two events independent events and dependent events.
Independent Events :
Two events A and B are said to be independent if the fact that one event has occurred does not affect the probability that the other event will occur.
Example
. Choosing a marble from a jar AND landing on heads after tossing a coin.
Dependent Events :
If whether or not one event occurs does affect the probability that the other event will occur, then the two events are said to be dependent.
Example
Buying ten lottery tickets and winning the lottery.
Beth Johnson's bank card account charges 1.1% every month on the average daily balance as well as the following special fees:Cash advance fee: 2% ( not less than $2 nor more than $10)Late payment fee: $25Over-the - credit- limit fee $10In the month of June, Beth's average daily balance was $1886. She was on vacation during the month and did not get her account payment in on time, which resulted in a late payment and resulted in charges accumulating to a sum above her credit limit. She also used her card for five Cash advances of$100,while on vacation. Find the special fees charged to the account based on account transactions in that month. The special fees are?
List of special fees paid by Beth:
1.Late payment fee: $25.
2.Cash advance fee: $10.
2% of $100 multiplied by 5 is equal to (2/100)(100)(5) = 10.
3.Over-the - credit- limit fee: $10
The addition of the special fees is equal to $45. (After adding $25+$10+$10)
The answer $45.
Please help me with my Calc hw, it is not outside scope of brainly tutor. I am following along diligently, thanks!
ANSWER
[tex]-2\sqrt[]{1+\cos(x)}+C[/tex]EXPLANATION
To solve this integral we have to use the substitution method. Let u = 1 + cos(x), then du is,
[tex]du=-\sin (x)dx[/tex]Thus, dx is,
[tex]dx=\frac{du}{-\sin (x)}[/tex]Replace the function and the differential in the integral,
[tex]\int \frac{\sin(x)}{\sqrt[]{1+\cos(x)}}dx=\int \frac{\sin(x)}{\sqrt[]{u}}\cdot\frac{du}{-\sin (x)}[/tex]The sin(x) cancels out,
[tex]\int \frac{\sin(x)}{\sqrt[]{u}}\cdot\frac{du}{-\sin(x)}=-\int \frac{1}{\sqrt[]{u}}du[/tex]We have to find a function whose derivative is 1/√u. This function is √u since its derivative is,
[tex]\frac{d}{du}(\sqrt[]{u})=\frac{1}{2\sqrt[]{u}}[/tex]Note that a coefficient 1/2 is missing, so to cancel it out, we have to multiply by 2. Don't forget the constant of integration,
[tex]-\int \frac{1}{\sqrt[]{u}}du=-2\sqrt[]{u}+C[/tex]Finally, we have to replace u with the function we substituted before,
[tex]-2\sqrt[]{u}+C=-2\sqrt[]{1+\cos (x)}+C[/tex]Hence, the result of the integral is,
[tex]-2\sqrt[]{1+\cos(x)}+C[/tex]A flagpole casts a shadow 3.5 meters long, Anita is standing near the pole. Her shadow is 0.75 meters long, Anita's height is 1.5 meters.How tall is the flagpole? Draw a diagram, label, and solve. Type your answer as a whole number or a decimal with no labels. EX5.2
Solution:
The heights and the shadows are in the same ratio because the sun is shining from the same angle, so the triangles formed are similar.
Notice that Anita's height is twice as long as her shadow, so the height of the flagpole will be
[tex]2\text{ x }3.5\text{ = 7m}[/tex]We can also write a direct proportion:
[tex]\frac{x}{3.5}\text{ = }\frac{1.5}{0.75}\text{ }\frac{\leftarrow\text{heights}}{\leftarrow shadows}[/tex]solving for x, we get:
[tex]x\text{ =}\frac{3.5\text{ x }1.5}{0.75}\text{ = 7m}[/tex]then, we can conclude that the correct answer is:
[tex]x\text{ = 7m}[/tex]The graph shows melting points in degrees Celsius of selected elements. Use the graph to answer the question.The melting point of a certain element is -5 times the melting point of the element C. Find the melting point of the certainelement.***The melting point of the certain element is °C.(Simplify your answer.)
The melting point of element C is 41 degrees C
The question states "The melting point of a certain element is -5 times the melting point of the element C."
Multiply the melting point of Element C by -5 to get the melting point of the certain element
-5 * 41
Solution
-205
when his bus arrives Calvin is 40 ft east of the corner the door of the bus is 30 feet north of the corner how far will Calvin run directly across the field to the bus
Since this situation can be represented by a right triangle, we can use the pythagorean theorem. Doing so, we have:
[tex]\begin{gathered} a^2+b^2=c^2\text{ } \\ (30)^2+(40)^2=c^2\text{ (Replacing)} \\ 900+1600=c^2\text{ (Raising both numbers to the power of 2)} \\ 2500=c^2\text{ (Adding)} \\ \sqrt[]{2500}=\sqrt[]{c^2} \\ 50=c\text{ (Taking the square root of both sides)} \\ \text{The answer is 50 ft} \end{gathered}[/tex]convert this number into scientific notation 0.00098
We have to convert the number into scientific notation.
The number is 0.00098.
We start by expressing it as a fraction.
If we divide it by 10, we can express it as:
[tex]\frac{0.00098\cdot10}{10}=\frac{0.0098}{10}[/tex]Dividing by 10 is not enough. In the same way, we have to look a numerator that is multiple of 10 that gives us a numerator that is 9.8.
We would get:
[tex]\frac{0.00098\cdot10000}{10000}=\frac{9.8}{10000}[/tex]Now we have the numerator we need.
We now express the denominator 10,000 as a power of 10 and we get the number in scientific notation as:
[tex]\frac{9.8}{10000}=\frac{9.8}{10^5}=9.8\cdot10^{-5}[/tex]Answer: 0.00098 = 9.8 * 10^(-5)
Equation of line passing thru point -6,-3 and perpindicular to JK -2,7 and 6,5
Equation of the line passing through the point (-6,-3) and perpendicular to the line passing through (-2,7) and (6,5) is y = 4x -19.
First we will find the slope of the line passing through (-2,7) and (6,5).
Slope of the line = (5-7)/(6-(-2)) = -2/8 = -1/4.
We know that,
Product of the slopes of two perpendicular lines = -1.
Let the equation of the line we have to find be y = mx + c.
Slope will be m.
Hence, we can write,
m*(-1/4) = -1
m = -1*(-4/1)
m = 4
Putting (6,5) and m = 4 in y = mx + c , we get
5 = 4*(6) + c
5 = 24 + c
c = 5 - 24 = -19
Hence, the equation of the line is:-
y = 4x -19
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use Pythagoras rule to find the slant height of a cone a height of 8 and base radius of 6cm
The Pythagoras rule states that the square hypotenuse is equal to the sum of the squares of the other two sides
In this case, we are given both sides' measures and are asked about the hypotenuse. We leave the hypotenuse on the left side alone by applying the square root on both sides
L = √64+36
L= √100
L = 10
Simplify.8(10 m)ANSWER CHOICES:80 m18 m810 m80 + m
To simplify this, we need to apply distributive property.
Given: 8(10 m)
Expand the parenthesis:
[tex]\begin{gathered} 8\text{ }\ast\text{ 10m} \\ =\text{ 80m} \end{gathered}[/tex]ANSWER:
[tex]80m[/tex]In the rhombus m<1 = 160 what are m<2 and m<3. This diagram is not drawn to scale. Show all work
We are given a rhombus shape.
The measure of angle ∠1 = 160°
Recall that in a rhombus, the oppsite angles are equal, this means ∠1 = ∠2
So, ∠2 = 160°
Recall that the sum of all four interior angles in a rhombus must be equal to 360°
The diagonal line divides the angles in half.
This means that angle 3 and angle x are equal.
[tex]\begin{gathered} 160\degree+160\degree+2(\angle3+x)=360\degree_{} \\ 320\degree+2(\angle3+x)=360\degree \\ 2(\angle3+x)=360\degree-320\degree \\ 2(\angle3+x)=40\degree \\ \angle3+x=\frac{40\degree}{2} \\ \angle3+x=20\degree \end{gathered}[/tex]Since we know that ∠3 and ∠x are equal then
∠3 = 10° and ∠x = 10°
Therefore,
∠2 = 160°
∠3 = 10°
Given a triangle ABC at points A = ( - 2, 2 ) B = ( 2, 5 ) C = ( 2, 0 ), and a first transformation of right 4 and up 3, and a second transformation of left 2 and down 5, what would be the location of the final point B'' ?
Answer
a. (4, 3)
Step-by-step explanation
The translation of a point (x, y) a units to the right and b units up transforms the point into (x + a, y + b).
Considering point B(2, 5), translating it 4 units to the right and 3 units up, we get:
B(2, 5) → (2+4, 5+3) → B'(6, 8)
The translation of a point (x, y) c units to the left and d units down transforms the point into (x - c, y - d).
Considering point B'(6, 8), translating it 2 units to the left and 5 units down, we get:
B'(6, 8) → (6 - 2, 8 - 5) → B''(4, 3)
Answer: The answer would be (4,3)
Step-by-step explanation: because if you started with (2,5), which would be (x,y) x goes left and right, and y goes up and down, and the questions says that you have to go 4 to the right and 3 up, then add 4 to 2, which is 6, and 3 to 5, which is 8, so now you have the point (6,8), then the second translation would be 2 to the left, and down 5, this is negative so you subtract this time, so subtract 2 from 6, which is 4, and 5 from 8, which is 3, so your final answer is (4,3).
Determine m such that the line through points (2m,4) and (m-3,6) has a slope of -5.
We have to use the formula of the slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where,
[tex]x_1=2m,x_2=m-3,y_1=4,y_2=6,m=-5[/tex]Replacing all these values, we have
[tex]-5=\frac{6-4}{m-3-2m}[/tex]Now, we solve for m
[tex]\begin{gathered} -5=\frac{2}{-m-3} \\ -m-3=\frac{2}{-5} \\ -m=-\frac{2}{5}+3 \\ m=\frac{2}{5}-3=\frac{2-15}{5}=\frac{-13}{5} \end{gathered}[/tex]Therefore, m must be equal to -13/5 in order to meet the given characteristics.Solve this system of linear equations. Separatethe x- and y-values with a comma.6x + 20y = -623x - 9y = -12Enter the correct answerDONE
Given the following systems of linear equations,
6x + 20y = -62 (Equation 1)
3x - 9y = -12 (Equation 2)
Step 1 : Solve 6x+20y=−62 for x:
6x + 20y + (−20y) = −62 + (−20y) (Add -20y to both sides)
6x = −20y −62
6x/6 = (−20y −62)/6 (Divide both sides by 6)
x = (-10y/3) + (-31/3)
Substitute to Equation 2:
3x−9y=−12
3[(-10y/3) + (-31/3)] - 9y = -12
−19y−31=−12 (Simplify both sides of the equation)
−19y−31+31=−12+31 (Add 31 to both sides)
−19y=19
-19y/-19 = 19/-19 (Divide both sides by -19)
y= −1
Step 2: Substitute −1 for y in x =(-10y/3) + (-31/3)
x =(-10(-1)/3) + (-31/3)
x = -7
Answer:
x=−7 and y=−1
Solve the system of linear equations by substitution:x - y = -2 and 3x - y = 2
To solve the system by substitution, isolate one variable from one equation and substitute the expression obtained for that variable into the other equation.
[tex]\begin{gathered} x-y=-2 \\ 3x-y=2 \end{gathered}[/tex]Isolate x from the first equation:
[tex]\begin{gathered} x-y=-2 \\ \Rightarrow x=y-2 \end{gathered}[/tex]Substitute x=y-2 into the second equation:
[tex]\begin{gathered} 3x-y=2 \\ \Rightarrow3(y-2)-y=2 \end{gathered}[/tex]Solve for y:
[tex]\begin{gathered} \Rightarrow3y-6-y=2 \\ \Rightarrow2y-6=2 \\ \Rightarrow2y=2+6 \\ \Rightarrow2y=8 \\ \Rightarrow y=\frac{8}{2} \\ \Rightarrow y=4 \end{gathered}[/tex]Substitute y=4 into the expression of x to find its value:
[tex]\begin{gathered} x=y-2 \\ \Rightarrow x=4-2 \\ \Rightarrow x=2 \end{gathered}[/tex]Therefore, the solution to the given system is:
[tex]\begin{gathered} x=2 \\ y=4 \end{gathered}[/tex]A 128 ounce container of hand lotion is separated into 4 ounce sample packs. How many sample packs are created from the large
container?
Please help will give brainlest!!
Answer:
32
Step-by-step explanation:
Solution
If the total amount of hand lotion is available, then you have 128 ounces of hand lotion.
If 128 oz is put into a number of smaller containers (each one 4 oz) then you have
128/4 containers.
128 / 4 = 32.
You can make 32 containers each one holding 4 ounces. The question uses division to solve.
enter the explicit and recursive equations for sequence 2, 12,72, 432
The explicit and recursive equations of the sequence 2, 12, 72, 432 are f(n) = 2 · 6ⁿ⁻¹ and f(n) = 6 · f(n - 1).
What is the equation behind the sequence?
In this problem we find an example of a geometric progression, whose explicit and recursive forms are defined below:
Explicit form
f(n) = a · rⁿ⁻¹
Recursive form
f(1) = 2, f(n) = r · f(n - 1)
Where:
a - Value of the first element of the series.r - Common ration - Index of the n-th element of the series.If we know that a = 2 and r = 6, then we find the explicit and recursive equations below:
Explicit form
f(n) = 2 · 6ⁿ⁻¹
Recursive form
f(n) = 6 · f(n - 1)
The first four elements of the sequence are 2, 12, 72, 432.
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Hey need your help it’s the one about the %
Answer:
[tex]\text{\$}$219.27$[/tex]Explanation:
We were given that:
Pamela bought an electric drill at 85% off the original price (she bought it at 15% of the original price)
She paid $32.89 for the drill
The regular price is calculated using simple proportion as shown below:
[tex]\begin{gathered} 15\text{\%}=\text{\$}32.89 \\ 100\text{\%}=\text{\$}x \\ \text{Cross multiply, we have:} \\ x\cdot15\text{\%}=\text{\$}32.89\cdot100\text{\%} \\ x=\frac{\text{\$}32.89\cdot100\text{\%}}{15\text{\%}} \\ x=\text{\$}219.27 \\ \\ \therefore x=\text{\$}219.27 \end{gathered}[/tex]Therefore, the regular price was $219.27
Find S13 of the arithmetic sequence below.
1/4, 1/2, 3/4, 1, …
Sum of arithmetic progression is given as 91/4
What is arithmetic progression?
An arithmetic sequence or progression is defined as a sequence of numbers in which for every pair of consecutive terms, the second number is obtained by adding a fixed number to the first one.
What is Sum of arithmetic progression?
The sum of the first n terms can be calculated if the first term, common difference and the total terms are known. The formula for the arithmetic progression sum is explained below:
Consider an AP consisting “n” terms.
Sn = n/2[2a + (n − 1) × d]
Given, a = 1/4, n = 13
d = 1/2-1/4 = 1/4
formula for sum is given by
Sn = n/2[2a+(n-1)d]
Substitute the values, we get
S13 = 13/2[2(1/4)+12(1/4)]
=13/2(1/2+3)
=13/2(7/2)
=91/4
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