We have in this question a case of Annual Compound Interest. The formula for this case is as follows:
[tex]A=P(1+r)^n_{}_{}[/tex]Where:
A = accrued amount.
P = Principal (starting amount).
r = interest rate.
n = number of years.
We have from the question:
r = 6%
n = 3 years.
P = $4,000.00
A = it is the unknown amount.
We can determine A to then find the interest he earned. Thus, we can proceed as follows:
[tex]A=4000(1+0.06)^3\Rightarrow A=4000(1.06)^3\Rightarrow A=4764.064[/tex]This previous amount is the accrued amount (the starting amount plus the interest after 3 years annually compounded).
Therefore, the amount Vijay earned in interests (after 3 years) is:
[tex]4764.064-4000=764.064[/tex]And, rounding this amount to the nearest cent, we have that, finally, the earned interest (after 3 years) is $764.06.
please help me solve. blank I have 9 and blank 2 I have 5. blank 2 is correct but not blank 1.
We have that
[tex]\begin{gathered} 3\cdot\sqrt[]{45}=3\cdot(\sqrt[]{9\cdot5}) \\ =\text{ 3(}\sqrt[]{9}\cdot\sqrt[]{5}\text{)} \\ =\text{ 3(3 }\cdot\sqrt[]{5}) \\ =9\cdot\sqrt[]{5} \end{gathered}[/tex]So the answer is
[tex]9\cdot\sqrt[]{5}[/tex]A train is traveling at a constant speed of 105 mph how many feet does a travel in three seconds remember that 1 mile is 5280 feet
We are given that a train is traveling at the following constant speed:
[tex]v=\frac{105\text{ miles}}{hour}[/tex]We are asked to determine the distance after 3 seconds. To do that, let's remember that speed is the ratio between distance and time, that is:
[tex]v=\frac{d}{t}[/tex]Where:
[tex]\begin{gathered} d=\text{ distance} \\ t=\text{ time} \end{gathered}[/tex]Since we want to determine the distance we will multiply both sides of the equation by "t":
[tex]vt=d[/tex]Now, we substitute the values:
[tex]\frac{105\text{ miles}}{hour}\times(3s)=d[/tex]Since the velocity is given per unit of hour, we need to convert the 3 seconds into hours. We do that using the following conversion factor:
[tex]1\text{hour}=3600s[/tex]Now we multiply the time by the conversion factor:
[tex]3s\times\frac{1h}{3600s}=\frac{1}{1200}h[/tex]Now we substitute in the formula for the distance:
[tex]\frac{105\text{ miles}}{hour}\times(\frac{1}{1200}hour)=d[/tex]Solving the operations:
[tex]\frac{7}{80}miles=d[/tex]Now, we convert the miles into feet using the given conversion factor:
[tex]1\text{mile}=5280\text{feet}[/tex]Now, we multiply by the conversion factor:
[tex]d=\frac{7}{80}\text{miles}\times\frac{5280feet}{1mile}[/tex]Solving the operations:
[tex]d=462feet[/tex]Therefore, the distance is 462 feet.
8 pounds of bananas cost $24. How much would 31 pounds cost
31 pounds cost $93
Explanation
you can easily solve this by using a rule of three.
Step 1
Let x represents the cost for 31 pounds,the proportion is
[tex]\frac{x}{31}[/tex]Now
[tex]\begin{gathered} 24\text{ usd}\rightarrow8\text{ Pounds} \\ \text{the proportion must be the same, then} \\ \frac{24}{8}=\frac{x}{31} \\ 3=\frac{x}{31} \\ \end{gathered}[/tex]Step 2
solve for x
[tex]\begin{gathered} 3=\frac{x}{31} \\ x=3\cdot31 \\ x=93 \end{gathered}[/tex]Hence, 31 pounds cost $93
I hope this helps you
Find the probability of getting a 1, 5, or 6 when you roll a standard six-sided die.Select the correct answer below:1/61/31/22/35/6
Step 1
Write out the expression for the probability of an event occurring
[tex]Pr(\text{event occurring) = }\frac{number\text{ of required outcomes}}{\text{Total number of outcomes}}[/tex]Where,
Total of required outcomes= 6
Step 2
Find the probability of getting a 1
[tex]Pr(1)=\text{ }\frac{1}{6}[/tex]Step 3
Find the probability of getting a 5
[tex]Pr(5)\text{ =}\frac{1}{6}[/tex]Step 4
Find the probability of getting a 6
[tex]Pr(6)=\frac{1}{6}[/tex]Step 4
Find the probability of getting a 1,5 or 6
[tex]Pr(1,5\text{ or 6)=Pr}(1)+Pr(5)+Pr(6)_{}[/tex][tex]\begin{gathered} Pr(1,5\text{ or 6) = }\frac{1}{6}+\frac{1}{6}+\frac{1}{6} \\ Pr(1,5\text{ or 6) = }\frac{1}{2} \end{gathered}[/tex]Hence, the probability of getting a 1, 5 or 6 when you roll a standard six-sided die = 1/2
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Click on an item at the bottom of the problem. Click again to drop each statement in the appropriate spot in the flow chart for adding fractions.
Let's say we want to add 1/2 and 1/3. Since they both have different denominators, first we find the LCD:
[tex]\text{LCD}(2,3)=2\cdot3=6[/tex]Now that we have the LCD, we express the fractions with a common denominator:
[tex]\frac{1}{2}+\frac{1}{3}=\frac{3}{6}+\frac{2}{6}[/tex]Now that we have both fractions with the same denominator, we can add directly the numerators and keep the denominator:
[tex]\frac{3}{6}+\frac{2}{6}=\frac{5}{6}[/tex]We have that 1/2+1/3=5/6. Since 5/6 can't be reduced anymore, we have found the result.
To summarize, the algorithm to solve addition of fraction would be like this:
Are The Ratios 1:2 and 18:16 equivalent?
The ratios given are;
1: 2 and 18: 16
To know it the ratios are equivalent , simplify the second pair until you can nologer express it in its simplest form then compare it with the he
x - y + z = - 3x - y - z = - 35x - 5y + z = - 15Solution: _, _, _
Given -
x - y + z = -3
x - y - z = -3
5x - 5y + z = -15
To Find -
Solution =?
Step-by-Step Explanation -
x - y + z = -3 ........(1)
x - y - z = -3 ..........(2)
5x - 5y + z = -15 .........(3)
So, from equation 1:
z = -3 -x + y
Now, put the value of z in equation 2 and 3:
x - y - (-3 -x + y) = -3
2x - 2y = -6
x - y = -3 ........(4)
5x - 5y + (-3 -x + y) = -15
4x - 4y = -12
x - y = -3 ......(5)
Now, on subtracting equations (5) and (6):
x - y -(x - y) = -3 - (-3)
x - x + y - y = 3 - 3
0 = 0
So, The System of equations has infinitely many solutions
Final Answer -
Solution: infinitely many solutions
Keishas teacher gives her the following information: • m,n,p, and q are all integers and p =/ 0 and q =/ 0 • A= m/q and B = n/pAnswer: A+B = mp + nq / pq, so the sum of a rational number and an irrational number is an irrational number A•B = mp + nq / pq, so the product of two rational number is a rational number A + B = mp + nq / pq, so the sum of two rational number is a rational number. A•B = mp + nq / pq , so the product of two irrational number is an irrational number
Let A and B be the following fractions:
[tex]\begin{gathered} A=\frac{m}{q} \\ B=\frac{n}{p} \\ p,q\ne0 \end{gathered}[/tex]if we add A and B, we get:
[tex]A+B=\frac{m}{q}+\frac{n}{p}=\frac{mp+nq}{pq}[/tex]therefore, the sum of two rational numbers is a rational number
need answer with steps[tex](7 + 9i) + ( - 5i)[/tex]
Gy, this is the solution:
(7 + 9i) + ( - 5i)
Solving the parenthesis:
7 + 9i - 5i
7 + 4i
Nathan and Tony hiked in the woods yesterday and came home with poison ivy. Tony has 5 times as many spots as Nathan. How many spots does Nathan have, x? Which table represents this situation?
Here, we want to get the correct equation and select the correct table
From the question, we have it that Tony has 5 times what Nathan had
Hence, given that Nathan has x, Tony has 5 times this and we have it as;
[tex]5\times x\text{ = 5x}[/tex]What this mean is that the right column of the table will be 5 times what is on the left column
Hence, the correct table here is the table with the heading 5x
15 is 20% of what numberOA 3O B. 60O C 75O D. 300
c)75
Explanation
to figure out this, we can use a rule of three
so,
let x represents the unknown value(
[tex]\begin{gathered} if \\ 15\Rightarrow20\text{ \%} \\ \text{then} \\ x\Rightarrow100\text{ \%} \end{gathered}[/tex]make the proportion and solve for x
[tex]\begin{gathered} \frac{15}{20}=\frac{x}{100} \\ \text{cross multiply} \\ 15\cdot100=20\cdot x \\ 1500=20x \\ \frac{1500}{20}=x \\ 75=x \end{gathered}[/tex]so, the answer is
C)75
I hope this helps you
A store sells packages of candy for $52. Each packet cost $4 to make and contains $48 flavored gum and candy.Rolando knows how much each candy cost per pound and knows how many pounds of each candy are packed in each package. Let x represent the amount of gum per pound in each package and y represent the amount of candy per pound in each package.Use the following equation to complete the questions: x+y=180.75x+5.25y+4=52how many pounds of candy are in a box?what is the price per pound for a piece of candy?what does the term 0.75x represents in the second equation?
Let:
x be the amount of gum in pounds in each package.
y be the amount of candy in pounds in each package.
Each box or package cost $52: a packaging that cost $4 and $48 in gum and candy.
The amount of candy (in pounds) in each package is shown in the equation:
[tex]x+y=18[/tex]As this is the sum of the amount of gum x and the amount of candy y, we can say that each package has 18 pounds of candy and gum.
Then, the following equation,
[tex]0.75x+5.25y+4=52[/tex]seems to be the total cost, as it results in 52, that is the total cost of the box. There is also a term with value 4, that corresponds to the packaginf cost.
The other terms represent the cost of the gum (0.75 * x) and the candy (5.25 * y).
We can read from this equation that the price per pound of the gum is 0.75, because it is the factor that multiply the amount x to calculate the cost.
In the same way, we can say that 5.25 is the price per pound of the candy, as it is the factor that multiplies y.
Answers
How many pounds of candy are in a box? 18 pounds
What is the price per pound for a piece of candy? 5.25 $/lb
What does the term 0.75x represents in the second equation? The second equation represents the sum of all the costs (gum, candy and packaging cost). The term 0.75x represents the cost of the gum, as it multiplies the price of the gum per pound (0.74 $/lb) and the amount of gum (x, in lb/package).
3. A business account was opened with $225,000earning 6.25% interest compounded yearly. Whatis the balance in the account after 3 years? Howmuch interest is earned after 3 years?
Answer:
Balance = 269,897.15
Interest earned 44,879.15
Explanation:
The compound interest formula is
[tex]A=P(1+r)^t[/tex]where P is the principal amount, is the interest rate, and t is the time interval.
Now in our case, we have
P = $225,000
r = 6.25%/100
t = 3 years
therefore, the final amount is
[tex]A=225,000(1+\frac{6.25}{100})^3[/tex][tex]\boxed{A=\$269,879.15}[/tex]which is the balance earned in 3 years.
The interest earned is the final amount minus the initial amount
[tex]\begin{gathered} I=A-P \\ I=\$269,879.15-\$225,000 \end{gathered}[/tex][tex]\boxed{I=\$44,879.15}[/tex]which is the interest earned in 3 years.
b Exit Ticket COS 28 = C 12 tan 28 = b с 12 28 b Download image X
Answer
b = 22.6 units
c = 25.6 units
Explanation
In a right angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.
For this question,
Hypotenuse = c
Opposite = 12
Adjacent = b
Trignometric ratios can then be used to find b and c.
CAH and TOA
Cos 28° = (Adj/Hyp)
Cos 28° = (b/c)
Tan 28° = (Opp/Adj)
Tan 28° = (12/b)
Cross multiply
b = 12/(Tan 28°)
b = 12/0.5317
b = 22.57
We can then solve for c
Cos 28° = (b/c)
Cos 28° = (22.57/c)
Cross multiply
c = (22.57/Cos 28°)
c = (22.57/0.8829)
c = 25.56 units
Hope this Helps!!!
What is the volume of the triangular prism?3.2 cm length 6 cm height5.4 cm width A: 8.64 cmB: 17.28 cmC: 51.84 cmD: 103.68 cm
The volume of a prism can be calculated by multiplying the area of the base of the prism times its height:
[tex]V=A\cdot h[/tex]On the other hand, the area of the base of a triangle can be found by multiplying 1/2 times its base times its height (don't confuse the height of the triangle with the height of the prism):
[tex]A=\frac{1}{2}b\times h[/tex]Substitute the values for the base of the triangle and its height to find the area of the base. Then, substitute the result for the area and the value of the height of the prism to find the volume of the triangular prism.
If the base of the triangle has a length of 5.4cm, and its height is 3.2cm, then:
[tex]\begin{gathered} A=\frac{1}{2}\times5.4\operatorname{cm}\times3.2\operatorname{cm} \\ =8.64cm^2 \end{gathered}[/tex]If the height of the prism is 6cm, then its volume is:
[tex]\begin{gathered} V=8.64cm^2\times6\operatorname{cm} \\ =51.84cm^3 \end{gathered}[/tex]Therefore, the volume of the triangular prism, is:
[tex]51.84cm^3[/tex]part 1- Selected Response
Which of the following linear equations
have a negative y- intercept? Circle all that
apply.
A. y = 6x
Cy=
-3x +2
2
E. y=
• X
3
B.y=-5 + 2x
D.y=-x+8
F.y=-5
Answer: B, C, D and F
Step-by-step explanation: The y-intercept of a linear equation is the point at which the line crosses the y-axis. The y-axis is the vertical axis on a graph, and it is the axis where the x-coordinate is always 0. To find the y-intercept of a linear equation, we can set the x-coordinate to 0 and solve for the y-coordinate.
For example, consider the linear equation y = 6x. If we set the x-coordinate to 0, we get the equation 0 = 6 * 0, which simplifies to 0 = 0. Therefore, the y-intercept of this equation is (0, 0).
On the other hand, consider the linear equation y = -3x + 2. If we set the x-coordinate to 0, we get the equation 0 = -3 * 0 + 2, which simplifies to 0 = 2. Therefore, the y-intercept of this equation is (0, -2).
In general, a linear equation will have a negative y-intercept if the constant term in the equation is negative. In this case, the linear equations that have a negative y-intercept are B, C, D, and F. Therefore, the correct answer is B, C, D, and F.
A bag contains 31 coins, some dimes and some quarters. The total amount of money in the bag is $4.45. How many dimes and how many quarters are in the bag?_____dimes_____quarters
A bag contains 31 coins, some dimes and some quarters. The total amount of money in the bag is $4.45. How many dimes and how many quarters are in the bag?
_____dimes
_____quarters
we know that
1 quarter=$0.25
1 dime=$0.10
Let
x -----> the number of quarters
y ----> the number of dimes
we have that
x+y=31 ------> equation A
0.25x+0.10y=4.45 -----> equation B
Solve the system of equations
Isolate the variable x in equation A
x=31-y ------> equation C
Substitute equation C in equation B
so
0.25(31-y)+0.10y=4.45
solve for y
7.75-0.25y+0.10y=4.45
0.25y-0.10y=7.75-4.45
0.15y=3.30
y=22 dimes
Find the value of x
x=31-22
x=9 quarters
therefore
the answer is
22 dimes9 quartersWhat is the correct answer to 9+(-3)= ?
To solve the question given, we will follow the steps below:
Open the parenthesis
9+(-3)
= 9 - 3
=6
The correct answer is 6
What would be the angles for K, J, and L?
The given is a triangle. As we know that the sum of all the interior angles in a triangle is 180 degrees, we have,
[tex]\begin{gathered} 6x-5+x+8+2x-3=180 \\ 9x=180 \\ x=\frac{180}{9}=20 \end{gathered}[/tex]Therefore, the angles can be calculated as,
[tex]\begin{gathered} K=6\times20-5=115 \\ J=20+8=28 \\ L=2\times20-3=37 \end{gathered}[/tex](-3x² + 6x - 12) + (5x + 9) is equivalent to expression
Use the graph to find the indicated values:line with y intercept at (0,3) and x intercept at (2,0)f(0)=AnswerIf f(x)=0 then x=?Answerf^{-1}(0)=AnswerIf f^{-1}(x)=0 then x=?Answer
From the graph:
[tex]f(0)=3[/tex]If:
[tex]\begin{gathered} f(x)=0 \\ then \\ x=2 \end{gathered}[/tex]For the last ones, we can use this fact:
The domain of the inverse of a function is the same as the range of the original function. Therefore:
[tex]f^{-1}(0)=2[/tex]If:
[tex]\begin{gathered} f^{-1}(x)=0 \\ then \\ x=3 \end{gathered}[/tex]did the teacher go wrong in making the square in the circle?! that’s what the question is asking pls help
Given two arcs, we follow the steps:
1) Label the intersection point of each pair of arcs as U and V:
2) Next, we need to construct the perpendicular bisector of the segment UV and label the intersection points to the circumference as P and Q:
3) Finally, we draw four line segments connecting the successive points on the circumference of the circle:
Looking at the steps given in the problem, the answer is:
The teacher makes a mistake in Step 2
at 3:00 the temperature is 8°C the temperature increases 2 degrees each hour for the next 3 hours. what is the temperature at 6:00?
We know that at 3:00 the temperature is 8°C, and the temperature increases 2°C each hour for the next 3 hours.
This means that after 3 hours, the temperature will increase:
[tex]2^{\circ}C+2^{\circ}C+2^{\circ}C=6^{\circ}C[/tex]Thus, the temperature at 6:00 will be:
[tex]8^{\circ}C+6^{\circ}C=14^{\circ}C[/tex]11. Write ____ as a single radical using the smallest possible root.
Answer:
[tex]\sqrt[6]{n^{23}}[/tex]Explanation:
The given expression is
[tex]\sqrt{n^5}\sqrt[3]{n^4}[/tex]To simplify, we first need to write them in exponent form
[tex]n^{\frac{5}{2}}\cdot n^{\frac{4}{3}}[/tex]Now, we can add the exponents
[tex]\begin{gathered} n^{\frac{5}{2}}\cdot n^{\frac{4}{3}}=n^{\frac{5}{2}+\frac{4}{3}}=n^{\frac{23}{6}} \\ \\ Because \\ \frac{5}{2}+\frac{4}{3}=\frac{5(3)+2(4)}{2(3)}=\frac{15+8}{6}=\frac{23}{6} \end{gathered}[/tex]Finally, we can write the expression in radical form
[tex]n^{\frac{23}{6}}=\sqrt[6]{n^{23}}[/tex]Therefore, the answer is
[tex]\sqrt[6]{n^{23}}[/tex]Solve the equation. -2/3 (x - 7) = 1/6 (x + 1) - 3
Given:
[tex]\frac{-2}{3}(x-7)=\frac{1}{6}(x+1)-3[/tex]Solving it,
[tex]\begin{gathered} \frac{-2}{3}x+\frac{14}{3}=\frac{x}{6}+\frac{1}{6}-3 \\ \end{gathered}[/tex]Solving further,
[tex]\begin{gathered} \frac{-2}{3}x-\frac{x}{6}=\frac{1}{6}-3-\frac{14}{3} \\ \frac{-4x-x}{6}=\frac{1-18-28}{6} \\ \frac{-5x}{6}=\frac{-45}{6} \\ -5x=-45 \\ x=\frac{45}{5} \\ x=9 \end{gathered}[/tex]Therefore, the value of x = 9
Directoins: consider the leading coefficient of each polynomial function. what is the end behavior of the graph? can check using graphing calculator or Desmos.10. F(x) = 4×over 3 - 3x
Concept
We can find the degree of a polynomial by identifying the highest power of the variable that occurs in the polynomial. The term with the highest degree is called the leading term because it is usually written first. The coefficient of the leading term is called the leading coefficient.
From the function
[tex]f(x)=4x^3\text{ - 3x}[/tex]Therefore,
The leading coefficient = 4
The degree = 3
Next, the end behavior of the function
The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity. So, the sign of the leading coefficient is sufficient to predict the end behavior of the function.
Interpretations:
As x tends to positive infinity, f(x) tend to positive infinity
As x tends to negative infinity, f(x) tend to positive infinity
Really need help solving this, having trouble with it. It is trigonometry and it is from my online ACT prep guide
Solution
For this case we have the following:
Statement True False
sin (60º)= sqrt(3)/2 X
cot (pi)= 1 X
cos (-240º)= 1/2 X
csc(3pi/4)= sqrt(2)/2 X
Hi, can you help me answer this question please, thank you!
Given:
Two populations
Sample Size (n₁) = 202
Success (x₁) = 122
Sample size (n₂) = 340
Success (x₂) = 220
Find: test statistic and p-value of this sample
Solution:
Based on the given data, we have two proportions here and its sample size is large. The test statistic that is appropriate for this would be Test of Two Proportions and the formula is:
[tex]z=\frac{p_1-p_2+cont\text{ }}{\sqrt[]{\frac{p(1-p)}{n_1}+\frac{p(1-p)_{}}{n_2}}}[/tex]in which,
[tex]p=\frac{x_1+x_2}{n_1+n_2}[/tex]Let's solve the value of p first. Let's plug in the given data that we have above.
[tex]p=\frac{122+220}{202+340}=\frac{342}{542}=\frac{171}{271}[/tex]Now that we have the value of p, let's calculate p₁ and p₂. Formula is:
[tex]\begin{gathered} p_1=\frac{x_1}{n_1}=\frac{122}{202}=\frac{61}{101} \\ p_2=\frac{x_2}{n_2}=\frac{220}{340}=\frac{11}{17} \end{gathered}[/tex]Lastly, let's calculate the value of cont or continuity correction. Formula is:
[tex]cont=\frac{F}{2}(\frac{1}{n_1}+\frac{1}{n_2})\text{ }[/tex]For our claim p₁ < p₂, our F = 1.
[tex]cont=\frac{1}{2}(\frac{1}{202}+\frac{1}{340})=0.0039458[/tex]Let's plug these values to the test of two proportions formula:
[tex]\begin{gathered} z=\frac{p_1-p_2+cont\text{ }}{\sqrt[]{\frac{p(1-p)}{n_1}+\frac{p(1-p)_{}}{n_2}}} \\ z=\frac{\frac{61}{101}-\frac{11}{17}+0.0039458}{\sqrt[]{\frac{\frac{171}{271}(1-\frac{171}{271})}{202}+\frac{\frac{171}{271}(1-\frac{171}{271})_{}}{340}}} \end{gathered}[/tex][tex]z=\frac{-0.03915259}{\sqrt[]{\frac{0.2328399668}{202}+\frac{0.2328399668}{340}}}=\frac{-0.03915259}{0.04286603008}\approx-0.913[/tex]Hence, the test statistic is -0.913.
The equivalent p-value for this is 0.1805.
The p-value is greater than α = 0.05.
Since p-value is greater than α, we fail to reject the null hypothesis.
IF LA = LB and LB = LC, then LA = LC. What property has been illustrated? a. Transitive b. Substitutionc. Distributived. Reflexive
The transitive property states that if x = y and y = z, then x = z
Considering the given scenario, IF LA = LB and LB = LC, then LA = LC, by comparing this statement with the earlier statement, we can see that
LA = x
LB = y
LC = z
Thus, the property being illustrated is
a. Transitive
help me help me help me help me help me help me help me help me help me help me help me help me help me help me help me help me help me help me help me help me help me help me help me help me help me help me help me help me help me
Given:
Three numbers are 42, 90 and 144.
Required:
What is the highest common factor
Required:
We know the factors of 42
Answer: 42, 90 and 144.
Step-by-step explanation: