Let's define the next variables
x: amount of money invested in one account
y: amount of money invested in the other account
Milan had $10,000 to invest, then
x + y = 10000 (eq. 1)
The interest Milan gets after one year are: 0.06x and 0.09y. He received a total of $840 in interest, then
0.06x + 0.09y = 840 (eq. 2)
Isolating x from equation 1:
x = 10000 - y
Replacing this result into equation 2,
0.06(10000 - y) + 0.09y = 840
0.06(10000) - 0.06(y) + 0.09y = 840
600 + 0.03y = 840
0.03y = 840 -600
0.03y = 240
y = 240/0.03
y = 8000
Then,
x = 10000 - y
x = 10000 - 8000
x = 2000
He invested $2000 in the account that paid 6% simple interests per year and $8000 in the account that paid 9% simple interests per year
3 parts!!! Suppose that on January 1 you have a balance of $4500 on a credit card whose APR is 12%, which you want to pay off in 1 year. Assume that you make no additional charges to the card after January 1.a. Calculate your monthly payments.b. When the card is paid off, how much will you have paid since January 1?c. What percentage of your total payment from part(b) is interest?Part A: The monthly payment is ?(Do not round until the final answer. Then round to the nearest cont as needed.)
Given,
P=$4500
r=12%
For 1 month the rate is 12/12%=1%
So interest for one month is
[tex]I=\frac{4500\times1\times1}{100}=45[/tex]a. The monthly payment is:
[tex]\begin{gathered} A=\frac{4500\times0.01\times(1+0.01)^{12}}{(1+0.01)^{12}-1} \\ \Rightarrow A=\frac{50.70}{0.12} \\ \Rightarrow A=422.5 \end{gathered}[/tex]The monthly payment is $422.5
b. Total payment for a year is:
A=4500+(12x45)=$5040
Total amount paid since January is $5040
c. The percentage of interest is:
[tex]\frac{45\times12}{5040}\times100\%=10.71[/tex]The percentage interest is 10.71%
a cube has a volume of seven units. what is the edge length of a cube?
Given:
The volume of the cube = seven units.
Let a be the edge length of the cube.
Consider the formula for the volume of the cube.
[tex]V=a^3[/tex]Substitute V=7 in the formula, we get
[tex]7=a^3[/tex]Taking cubic root on both sides, we get
[tex]\sqrt[3]{7}=a[/tex][tex]T\text{he edge length of the given cube is }\sqrt[3]{7}\text{ units.}[/tex]or
[tex]T\text{he edge length of the given cube is }1.91\text{ units.}[/tex]What is the value of sin C? a) 15/17b) 15/8c) 8/15d) 8/17
Answer:
d) 8/17
Explanation:
From trigonometry, we know that in a right triangle:
[tex]\sin \theta=\frac{Opposite}{\text{Hypotenuse}}[/tex]From the diagram:
• The side, opposite C, is 8.
,• The ,hypotenuse, is 17.
Therefore:
[tex]\sin C=\frac{8}{17}[/tex]Solve the triangle: Q=60", B = 60", y = 60". If it is not possible, say so.a= 1, b = 1,0 = 1a== 13,6 = 13,0 = 3a = 100,6 = 100,c = 100This triangle is not solvable.
Solution:
this triangle is not solvable because to solve this triangle we need one of the sides to find the missing sides.
part A Jasmine ran 5 miles in 42 minutes at what rate did Jasmine run Jasmine ran at a rate of ? minutes per mile
We will find the rate as follows:
[tex]r=\frac{5}{42}[/tex]So the rate is the distance divided by the time it took to traverse.
what is 13 divided by 113.1
The number of dogs per household in a neighborhood is given in the probabilitydistribution. Find the mean and the standard deviation. Round to 1 decimal.# of Dogs0123stP(x)0.620.240.070.05.02a) What is the mean rounded to 2 decimal place?b) What is the standard deviation rounded to 2 decimal place?
A Labrador retriever weighs 50kg. After a diet and exercise program the dog weighs 41kg. What is the percentage loss in weight.
inital weight = 50 kg
Final weight = 41 kg
loss = 50 - 41 = 9 kg
[tex]\begin{gathered} \text{percentage loss=}\frac{9}{50}\times100 \\ \text{percentage loss=}\frac{900}{50} \\ \text{percentage loss = }18\text{\%} \end{gathered}[/tex]If Lydia invests $3000 in a certificate of deposit and d dollars in a stock, write an expression for the total amount she invested.
ANSWER:
[tex]\text{ total amount }=3000+d[/tex]STEP-BY-STEP EXPLANATION:
The total invested is equal to 3000 investment and the previous money in stock, therefore, the expression would be:
[tex]\text{ total amount }=3000+d[/tex]Find the equation of the line with the given properties. Sketch the graph of the line. Passes through (1, -6) and (8,3)
A line equation can be written in slope-intercept form, which is
[tex]y=mx+b[/tex]Where m represents the slope and b the y-intercept.
If we evaluate our points on this form, we're going to have a linear system where the solutions are those coefficients.
[tex]\begin{cases}3=8m+b \\ -6=m+b\end{cases}[/tex]If we subtract the second equation from the first, we're going to have a new equation only for the slope.
[tex]\begin{gathered} 3-(-6)=8m+b-(m+b) \\ 3+6=8m+b-m-b \\ 9=7m \\ m=\frac{9}{7} \end{gathered}[/tex]Now that we have the slope, we can use any of the equations to find the b value.
[tex]\begin{gathered} -6=(\frac{9}{7})+b \\ -6-\frac{9}{7}=b \\ b=-\frac{51}{7} \end{gathered}[/tex]Then, our line equation is
[tex]y=\frac{9}{7}x-\frac{51}{7}[/tex]And this is the graph
A basketball team has 13 Active players, in how many ways can 5 players be selected to start the game??
Answer:
1287
Explanation:
The number of distinct ways n objects can b selected from N total objects is given by
[tex]\frac{N!}{n!(N-n)!}[/tex]Now in our case, we have a total of 13 basketball players. N = 13 and 5 players to choose n = 5. Therefore, the above formula gives
[tex]\frac{13!}{5!(13-5)!}[/tex][tex]-\frac{13!}{5!8!}[/tex][tex]=\frac{13\cdot12\cdot11\cdot10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{5!\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}[/tex][tex]=\frac{13\cdot12\cdot11\cdot10}{5!}[/tex][tex]=\frac{13\cdot12\cdot11\cdot10}{5\cdot4\cdot3\cdot2\cdot1}[/tex][tex]=1287[/tex]Hence, there are 1287 ways 5 different players can be selected from 13 players.
Total blood cholesterol level was measured for each of 10 adults. Here are the 10 measurements (in mg/dL).176, 251, 247, 262, 150, 214, 192, 194, 154, 255Send data to calculator(a) What is the mean of this data set? If your answer is not aninteger, round your answer to one decimal place.00(b) What is the median of this data set? If your answer is notan integer, round your answer to one decimal place.(c) How many modes does the data set have, and what aretheir values? Indicate the number of modes by clicking in theappropriate circle, and then indicate the value(s) of themode(s), if applicable.zero modesone mode:two modes: andXS
a) 209.5mg/dL
b) 204mg/dL
c) zero modes
Explanations:Mean is also known as average of a dataset. Given the data expressed below;
[tex]Mean=\frac{sum\text{ of data}}{sample\text{ size}}[/tex]Given the following parameters
Sum of data = 176 + 251 + 247 + 262 + 150 + 214 + 192 + 194 + 154 + 255
Sum of data = 2095
Sample size = 10 (Total measurement)
Determine the mean of the data
[tex]\begin{gathered} Mean=\frac{2095}{10} \\ Mean=209.5 \end{gathered}[/tex]Therefore the mean of the data is 209.5mg/dL
b) The median of the dataset is the value in the middle after rearrangement. On rearranging in ascending order;
150, 154, 176,192, (194, 214), 247, 251, 255, 262
The two values at the middle are 194 and 214.
[tex]\begin{gathered} Median=\frac{194+214}{2} \\ Median=\frac{408}{2} \\ Median=204 \end{gathered}[/tex]c) The mode of the data is the value that occur the most in the dataset. SInce all the data only appear once in the dataset, hence there are ZERO MODES
Could you explain the following:Use s=rwt to find the value of the missing variable.S=pi/5m, r=7m, t=2sec
Answer:
[tex]0.0449[/tex]Explanation:
Here, we want to find the value of the missing variable w
We start by substituting the individually given values as follows:
[tex]\begin{gathered} \frac{\pi}{5}\text{ = 7}\times w\times2 \\ \\ w\text{ = }\frac{\pi}{5\times7\times2}\text{ = 0.0449} \end{gathered}[/tex]
Based on the density graph below, what is the probability of a valuein the sample space being anywhere from 0 to 20?
Answer
Option A is correct.
Probability of a value in the sample space being anywhere from 0 to 20 = 80%
Explanation
The probability of an event is calculated as the number of elements in the event divided by the total number of elements in the sample space.
For this question,
Number of boxes from 0 to 20 = 20
Total number of boxes in the density graph = 25
Probability of a value in the sample space being anywhere from 0 to 20 = (20/25) = 0.8 = 80%
Hope this Helps!!!
a sphere has radius 3xcm. write down an expression for the surface area of the sphere in terms of x.give your answer in the simplest form
The expression to obtain the surface area of a sphere is
[tex]A=4\cdot\pi\cdot r^2[/tex]If the radius is equal to 3x cm then the expression is
[tex]A=4\cdot\pi\cdot(3x)^2[/tex]square the 3x
[tex]\begin{gathered} A=4\cdot\pi\cdot(3^2)\cdot x^2 \\ A=4\cdot\pi\cdot9\cdot x^2 \end{gathered}[/tex]Simplify the expression
[tex]A=36\pi\cdot x^2[/tex]The expression for the surface area of a sphere of radius 3x cm is:
[tex]A=36\cdot\pi\cdot x^2[/tex]1.Find the quotient of 1/2and 3/4.2. Divide 4by2/33.If 5/9is divided by3, what is the quotient4. Mrs. Dolentebuys 5 1/2kilograms of rice. If she cooks 1/4kilogram for every meal, how many meals will it last?5.Marita needs 2/3meter of lace for each pillowcaseshe makes. How many pillowcasescan she make with 7 1 3meters of lace
1) We can find the quotient between two fractions by multiplying the first one by the reciprocal of the second one this way:
[tex]\frac{\frac{1}{2}}{\frac{3}{4}}=\frac{1}{2}\times\frac{4}{3}=\frac{4}{6}=\frac{2}{3}[/tex]2) Let's now divide 4 by 2/3 following the same principle:
[tex]\frac{4}{\frac{2}{3}}=4\times\frac{3}{2}=\frac{12}{2}=6[/tex]Notice that we have simplified as well as the previous item (1).
3) Proceeding with that we have:
[tex]\frac{\frac{5}{9}}{3}=\frac{5}{9}\times\frac{1}{3}=\frac{5}{27}[/tex]4) To find this out, we need to convert that Mixed Number to Improper Fraction:
[tex]\begin{gathered} 5\frac{1}{2}=\frac{2\times5+1}{2}=\frac{11}{2} \\ \frac{\frac{11}{2}}{\frac{1}{4}}=\frac{11}{2}\times4=\frac{44}{2}=22 \end{gathered}[/tex]We kept the denominator then multiplied it by the whole number and added it to 1. So it will last 22 meals.
5) To find it out we are going to divide 7 1/3 by 2/3 meter, after converting that Mixe Number into an Improper Fraction:
[tex]\begin{gathered} 7\frac{1}{3}=\frac{3\times7+1}{3}=\frac{22}{3} \\ \frac{\frac{22}{3}}{\frac{2}{3}}=\frac{22}{3}\times\frac{3}{2}=\frac{66}{6}=11 \end{gathered}[/tex]Notice, that we have used the same procedure to convert from Mixed Numbers to an Improper fraction. Marita can make 11 pillowcases.
And those are the answers.
what is the area of a triangle with a base of 5ft and a height of 8.4ft?
To answer this question, we need to remember the formula for finding the area of a triangle:
[tex]A_{\text{triangle}}=\frac{b\cdot h}{2}[/tex]Where
• b is the base of the triangle
,• h is the height of the triangle
Then, we have that:
b = 5ft
h = 8.4ft
Then, we have:
[tex]A_{\text{triangle}}=\frac{5ft\cdot8.4ft}{2}=\frac{42ft^2}{2}\Rightarrow A_{triangle}=21ft^2[/tex]Therefore, the area of this triangle is equal to 21 sq. feet.
I need help fast thanks it looks kinda hard and I can’t figure it out
Looking at the figure, we see that there are 6 identical squares of side 26 yd.
We know that the area of a square of side L can be calculated using the formula:
[tex]A=L^2[/tex]Now, if there are 6 squares, the total area is:
[tex]A_{\text{Total}}=6\cdot L^2[/tex]From the problem, L = 26 yd, then:
[tex]\begin{gathered} A_{\text{total}}=6\cdot26^2 \\ \therefore A_{Total}=4056yd^2 \end{gathered}[/tex]Jennifer. Leigh Anne, and Karyn went out to eat. Jennifer bought an entrée for $12.95 and split a $4.95 dessert with Karyn, who bought a sandwich for $7.95. Leigh Anne bought soup for $3.95, a salad for $6.95, and coffee for $1.70. Determine the total amount each should pay if tax is 6% and each one tips 15% of her individual bill rounded up to the next quarter.
The total amount Leigh Anne spent is $3.95 plus $6.95 plus $1.7, that is $12.6. Since they pay a tax of 6% and a tip of 15%, she pays a total of 21% extra; this 21% can be obtained by the tule of three:
[tex]\begin{gathered} 12.6\rightarrow100 \\ x\rightarrow21 \end{gathered}[/tex]then:
[tex]x=\frac{21\cdot12.6}{100}=2.65[/tex]Therefore, Leigh Anne spent a total of $15.25.
Assuming the dessert was split in half, then Jennifer spent a total of $15.43. To this amount we have to add the tax and tip. By the same logic as before we have:
[tex]\begin{gathered} 15.43\rightarrow100 \\ x\rightarrow21 \end{gathered}[/tex]then:
[tex]x=\frac{21\cdot15.43}{100}=3.24[/tex]Therefore, Jennifer spent $18.75
Finally Karyn spent $10.43, obtaining the extra amount we have:
[tex]\begin{gathered} 10.43\rightarrow100 \\ x\rightarrow21 \end{gathered}[/tex]Then:
[tex]x=\frac{21\cdot10.43}{100}=2.19[/tex]Therefore, Karyn spent $12.75.
Please help ASAP *image imported*
Describe the transformations made on this function:(stretch/compression, reflect, left/right, up/down)
The function we have is:
[tex]f(x)=\frac{1}{2}(x-7)^3+6[/tex]Since this is a cubic function, we start with the parent cubic function (the simplest form of the cubic function):
[tex]f(x)=x^3[/tex]And compare it to the given function.
The first thing we can note is that there was a subtraction of 7 to the value of x:
[tex]x\longrightarrow x-7[/tex]When we add a number to the x value, the graph moves to the left, and when we subtract a number to the x value, the graph moves to the right.
So the first transformation is moving to the right 7 units.
Next, we have that there was +6 added to the expression --> When you add a number to the function, the graph moves up, and when you subtract a number to the function, the graph moves down.
In this case, since we added a constant value of 6, the graph is translated 6 units up.
The second transformation is moving up 6 units.
Finally, let's analyze the effect that the 1/2 has on the function.
We can compress or stretch the graph of a function by multiplying the x by a constant (a number). If the number of between 0 and 1, there is a stretch, and if the number is greater than 1 there is compression.
In this case, the number next to the x is:
[tex]\frac{1}{2}=0.5[/tex]Since the number is between 0 and 1 there is a stretch of the function.
In summary:
Answer:
Translation of 7 units to the right
Translation of 6 units up
Stretch of the function of 0.5
A radar gun measured the speed of a baseball at 103 miles per hour. If the baseball was actually going 102.8 miles per hour, what was the percent error in this measurement? Round to the nearest hundredth percent
Answer
Percent Error = 0.195%
Explanation
Percent error is given as
[tex]\text{Percent Error = }\frac{Error}{True\text{ value}}\times100\text{ percent}[/tex]Error = | (Incorrect value) - (True value) |
Incorrect value = 103 miles per hour
True value = 102.8 miles per hour
Error = | (Incorrect value) - (True value) |
Error = | 103 - 102.8 |
Error = 0.2 miles per hour
[tex]\begin{gathered} \text{Percent Error = }\frac{Error}{True\text{ value}}\times100\text{ percent} \\ \text{Percent Error = }\frac{0.2}{102.8}\times100\text{ percent} \\ \text{Percent Error = 0.195 percent} \end{gathered}[/tex]
Hope this Helps!!!
Give the name of the parent function and describe the transformation represented.
5 units to the left and 2 units downwards
Explanation:[tex]f(x)\text{ = |x + 5| - 2}[/tex]The parent function:
f(x) = |x|
Name of parent function is absolute value function
The transformtion from parent function to the new function:
[tex]\begin{gathered} \text{from f(x) = |x| to f(x) = |x + 5| - 2} \\ \text{For translation:} \\ f(x)\text{ = |x + a| (translation to the left)} \\ f(x)\text{ = |x - a| (translation to the right)} \\ \\ So\text{ f(x) = |x + 5| is a translation of 5 units to the left} \end{gathered}[/tex][tex]\begin{gathered} For\text{ translation: } \\ f(x)\text{ = |x| + a (translation upwards)} \\ f(x)\text{ = |x| }-\text{ a (translation downwards)} \\ \\ So\text{ f(x) = |x| - 2 is a translation downwards} \end{gathered}[/tex]Combining both transformation:
f(x) = |x + 5| - 2 is a translation of 5 units to the left and 2 units downwards
The Reyes family is going to the mall. When they leave home,
What is the problem about?
Average speed
What information is given?
Starting odometer reading, ending odometer reading, time taken
What do you need to find?
The average speed of the car
An odometer measures the distance traveled by a wheeled vehicle
The starting odometer reading was 54,362 miles
The ending odometer reading was 54,372 miles
It took 15 minutes to get to the mall
Step 1: Find how far Reyes traveled in 15 minutes
54372 - 54362 = 10 miles
At this speed, the car will travel 10 miles in 15 minutes
Step 2: How far the Reyes would travel in 60 minutes?
The Reyes would travel 40 miles in 60 minutes
I need help solving this problem. My answer isn’t coming out right. I have to find the missing length.
From the given diagram we get that the lines marked with the arrow are parallel, then the two triangles are similar.
To answer this question we will use the following diagram as a reference:
Therefore:
[tex]\frac{?}{18}=\frac{9-4}{9}.[/tex]Simplifying the above result we get:
[tex]\frac{?}{18}=\frac{5}{9}.[/tex]Multiplying the above result by 18 we get:
[tex]\frac{?}{18}\times18=\frac{5}{9}\times18.[/tex]Simplifying the above result we get:
[tex]\begin{gathered} ?=\frac{90}{9}, \\ ?=10. \end{gathered}[/tex]Answer:
[tex]?=10.[/tex]Find the number of distinct arrangements of 12 letters in REENGINEERED. Two of the same letter are considered identical
We have to find the number of distinct arrangements of 12 letters in REENGINEERED.
First, we list the number of unique letters we have and its frequency. We have:
• R: 2
,• E: 5
,• N: 2
,• G: 1
,• I: 1
,• D: 1
for a total of 12 letters.
We can then calculate the number of distinct arrangements as the the total number of arrangements divided by the permutations that are repeated.
This can be expressed as the factorial of 12 divided by the product of the factorial of the frequencies of each letter (the letters that have a frequency of 1 will not affect the result so they are ignored for the denominator):
[tex]n=\frac{12!}{2!5!2!}=\frac{479001600}{2*120*2}=\frac{479001600}{480}=997920[/tex]Answer: there are 997,920 distinct arrangements.
Answer below due to inability to type out the following question.
ANSWER
[tex]11.04\text{ or }\frac{-2+\sqrt{580}}{2}[/tex]EXPLANATION
Given that:
In the figure provided, the triangle EFG is similar to the triangle is ECD
FE = 12
CD = 12
FG = CF + 2
To find the length CF, apply the similarity triangle theorem
[tex]\frac{\text{ FE}}{\text{ CF}}\text{ }=\frac{\text{ FG}}{CD}[/tex]Substitute the given data into the above equation
[tex]\begin{gathered} \text{ }\frac{12}{CF}=\frac{CF+2}{12} \\ \text{ cross multiply} \\ \text{ 12}\times12\text{ }=\text{ CF\lparen CF + 2\rparen} \\ \text{ 144 }=\text{ CF}^2\text{ }+\text{ 2CF} \\ CF^2\text{ }+\text{ 2CF -144 =0} \\ \text{ Find CF using the general formula} \\ x\text{ }=\text{ }\frac{-b\pm\sqrt{b^2-\text{ 4ac}}}{\placeholder{⬚}} \\ \text{ a }=1,\text{ b}=2,\text{ c}=-144 \\ \text{ x }=\frac{-2\text{ }\pm\sqrt{2^2-4\times1\times(-144)}}{2} \\ \text{ x}=\text{ }\frac{-2\pm\sqrt{4+576}}{2} \\ \text{ x }=\text{ }\frac{-2\pm\sqrt{580}}{2} \\ \text{ x }=\text{ }\frac{-2+\sqrt{580}}{2} \\ \text{ x }=\text{ }\frac{-2+24.083}{2} \\ \text{ x }=\frac{22.083}{2} \\ \text{ x }=11.04 \\ \text{ Therefore, CF is 11.04 or }\frac{-2+\sqrt{580}}{2} \end{gathered}[/tex]Clara likes the buffet option of chicken, swordfish, roasted potatoes, and brussels sprouts
for $23 per person. She does not think everyone will eat the swordfish, so she decides to
only do a half portion of swordfish per guest, which means half the price. If the original
price of the swordfish was $7 per guest, what will the new overall price of the buffet be
per person?
The unitary method is used to find the unit value of the quantity. The price for the buffet after taking half portion of swordfish will be $19.5.
What is Unitary method?In order to solve a problem for two different values of a quantity, its unit value is first derived. This method is known as unitary method.
Given that,
The price for complete buffet is $23 per person.
The price for swordfish per guest is $7.
Then, the price for half portion swordfish is $7 / 2 = $3.5.
Now, the price of buffet without swordfish is $23 - $7 = $16.
Thus, after taking only half portion of swordfish the new price becomes,
$16 + $3.5 = $19.5
Hence, the new price of the buffet for each person will be $19.5.
To know more about unitary method click on,
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y=-2x + 4 3y + 6x = 12 O One Solution O No Solutions o Infinitely Many Solutions
To find the number of solutions of a system of linear equations you need to identify the slope (m) of each equation
[tex]y=mx+b[/tex]If the slope is the same in both lines the system has no solution.
If the slope is different in the lines the system has one solution.
If the equation are the same (incluided the value of b) the system has infinitely many solutions.
In the given equations the slope is:
First equation:
[tex]y=-2x+4[/tex]Slope: m=-2Second equation:
[tex]3y+6x=12[/tex]Write the equation in slope-intercept form by solving for y:
[tex]\begin{gathered} 3y+6x-6x=-6x+12 \\ 3y=-6x+12 \\ \\ y=-\frac{6}{3}x+\frac{12}{3} \\ \\ y=-2x+4 \end{gathered}[/tex]Slope: m= -2In this case as the equatinos are the same the system has infinitely many solutionsIf a board 9 feet 6 inches in length is cut into 2 equal parts, what will be the length of each part?
5 feet 2 inches
4 feet 8 inches
4 feet 5 inches
4 feet 9 inches
3 feet 8 inches
Answer:
4 feet and 9 inches
Step-by-step explanation:
First, we shall convert 9 feet and 6 inches into just inches.
9 x 12 = 108
108 + 6 = 114 inches.
114 divided by 2 = 57 inches.
Then, we divide 57 by 12:
57 divided by 12 = 4.75.
So, we have 4 feet.
0.75 x 12 = 9 inches.
In conclusion, we have 4 feet and 9 inches.
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