You deposit $ 3,508 in an account earning 10 % interest compounded monthly. How much will you have in the account in 4 years?
The amount of money A in an account with an interest rate r compounded 12 times a year, after t years and if a principal P is invested, is given by the formula:
[tex]A=P(1+\frac{r}{12})^{12\times t}[/tex]Replace P=3,508, r=10/100 and t=4 to find the amount of money that the account will be worth after 4 years:
[tex]A=3508(1+\frac{0.1}{12})^{12\times4}=3508(1.489354099\ldots)=5224.654178\ldots[/tex]Therefore, to the nearest cent, the amount of money in the account after 4 years will be:
[tex]5224.65[/tex]What is the mode of the data set? Heart Rate 5/06/0007/008/009/05/0 = 50 beats per minute 6070none0
As you have the next data set:
[tex]\lbrace50,60,60,60,70,70,80,80,90\rbrace[/tex]And the mode is the number that appears the most.
The mode of the given data is 60 (it repeats 3 times)
Is it 1/5 or -8 trying to figure this out for the slope
From the graph it can be observed that line passes through points (0,16) and (2,20).
The formula for the slope of line pasing through points (x_1,y_1) and (x_2,y_2) is,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Determine the slope of line passing through points (0,16) and (2,20).
[tex]\begin{gathered} m=\frac{20-16}{2-0} \\ =\frac{4}{2} \\ =2 \end{gathered}[/tex]So slope of line is 2.
What are the solutions to the quadratic equation below? x² -2x -168=0
Answer:
-12 and 14.
Explanation:
Given the quadratic equation: x² -2x -168=0
First, we factorize the expression on the left-hand side.
[tex]x^2-2x-168=(x\text{ )(x )}[/tex]Next, we multiply the first and last term,
[tex]-168\times x^2=-168x^2[/tex]We then write factors of -168.
[tex]\begin{gathered} -168=12\text{ and -14 } \\ -168=-12\text{ and 14} \\ \text{Add the factors:} \\ \text{12-14=-2} \\ -12+14=2 \end{gathered}[/tex]We pick the factors that add up to the middle term: -2
[tex]\begin{gathered} x^2-2x-168=0 \\ (x+12)(x-14)=0 \\ x+12=0\text{ or }x-14=0 \\ x=-12\text{ or x=14} \end{gathered}[/tex]The solutions to the quadratic equation are -12 and 14.
order each set of integers from leat to greatest15,17,21,6,3
we have the set
15,17,21,6,3
so
from least to greatest
3,6,15,17,21because3<6<15<17<21Problem N 2
we have
-55, 143, 18, -79, 44, 101
from least to greatest
-79, -55, 18, 44, 101, 143Does the equation define y as a function of x ? Y^2=x^2-9x+2
Given the following question:
[tex]y^2=x^2-9x+2[/tex]Y^2 = x^2 - 9x +2
[tex]\begin{gathered} \sqrt[]{y^2}=^{}\pm x^2-9x+2 \\ \text{Plus or minus already lets you know that they're more than one value for y for ever value of x} \end{gathered}[/tex]Your answer is no, the equation does not define y as a function of x.
Ronald used 6 centimeters of tape to wrap 2 presents. How many presents did Ronald wrap ifhe used 12 centimeters of tape? Assume the relationship is directly proportional.presents
Answer:
4 presents
Explanation:
Let x represent the number of presents Ronald will wrap with 12 centimeters of tape.
To find x, let's set up proportions as shown below;
[tex]\frac{6\operatorname{cm}}{2\text{ presents}}=\frac{12\operatorname{cm}}{x\text{ presents}}[/tex]Let's cross-multiply;
[tex]\begin{gathered} 6\times x=12\times2 \\ 6x=24 \\ x=\frac{24}{6} \\ x=4 \end{gathered}[/tex]hey I need help with the question what is 88,000÷66,000
Since 88,000 and 66,000 are both divisible by 1000 and:
[tex]\begin{gathered} \frac{88,000}{1,000}=88 \\ \frac{66,000}{1,000}=66 \end{gathered}[/tex]We can just divide 88 by 66 and get the same quotient. Therefore:
[tex]\frac{88,000}{66,000}=\frac{88}{66}=\frac{4}{3}=1.3333[/tex]So, the answer is 4/3 or 1.3333
In circle C, the inscribed angle DEF measures (4x + 17)" and DF measures (9x + 25)°. What is the value of x? O x=9 x=5 Ox=1.6 x=4
The sketch of the question is given below
Using the principle:
Then
[tex]9x+25=2\times(4x+17)[/tex]Simplifying the expression
[tex]\begin{gathered} 9x+25=8x+34 \\ \text{collect like terms} \\ 9x-8x=34-25 \\ x=9 \end{gathered}[/tex]The value of
Select the correct answer.Sarah owns a flower shop and can model the profits from selling springtime bouquets using this equation, where b is the number of springtimebouquets.P=-582 + 4506 - 1,000Which statement is true if Sarah needs to make a profit of at least $9,000?
SOLUTION
[tex]9000\ge-5b^2+450b-1000[/tex]SOLVING THE INEQUALITY
[tex]\begin{gathered} -5b^2+450b-1000\le \:9000 \\ -b^2+90b-2000\le \:0 \end{gathered}[/tex][tex]-\left(b-40\right)\left(b-50\right)\le \:0[/tex][tex]\left(-\left(b-40\right)\left(b-50\right)\right)\left(-1\right)\ge \:0\cdot \left(-1\right)[/tex][tex]\left(b-40\right)\left(b-50\right)\ge \:0[/tex][tex]b\le \:40\quad \mathrm{or}\quad \:b\ge \:50[/tex]This is the top part which has the information and part A (or the first question)I wasn’t able to fit Part B
The function f(a) represents the cost of a pizza.
The function g(b) represents the delivery charge on the cost.
PART A.Having said that, a represents the cost of a pizza, b represents the cost of a pizza and sales tax, f(a) represents the cost of a pizza and sales tax, g(b) represents the delivery fee. At last, g(f(a)) represents the cost of the pizza, sales tax, and delivery fee.
PART B.Let's find the composition of functions
[tex]g(f(a))=1.06a+5[/tex]Hence, the answer to part B is the last option.
a jar contains five black buttons and three brown buttons. if 5 buttons are picked at random, what is the probability that all of them are blacka jar contains five black buttons the three Brown buttons If 5 buttons are picked at random what is the probability that all of them are black
Determine the total number of buttons in the jar.
[tex]\begin{gathered} T=5+3 \\ =8 \end{gathered}[/tex]Determine the probability for the 5 selected buttons are black.
[tex]\begin{gathered} P(x=5)=\frac{^5C_5}{^8C_5} \\ =\frac{1}{56} \end{gathered}[/tex]So answer is 1/56.
What is the volume of a cylinder that has a radius of 3 and a height of 10? Use 3.14 for pi.
The volume of a cylinder is calculated as follows:
[tex]V=\pi\cdot r^2\cdot h[/tex]where r is the radius, and h is the height of the cylinder
Substituting with r = 3 and h = 10, we get:
[tex]\begin{gathered} V=\pi\cdot3^2\cdot10 \\ V=282.6 \end{gathered}[/tex]27 A basketball has a diameter of 9.5 cm Which of the expressions shows how to determine the volume of air the basketball can hold? has A. (4.753 B. 1957 C. **44.757 D. 420.59
Answer:
Option C
Because the radius is 9.5/2 = 4.75
PLSS HELPBy combining the increase and decrease, find an exponential expression for the total change in organism A’s population after 8 days. Show your work.
The total change in organism A’s population after 8 days would be 4 or 2 to the second power. divided the total by two three times to get this answer.
6 liters to gallons Round your answer to the nearest tenth. gallons
Answer:
1.59 gallons
Step-by-step explanation:
The population of a small town is decreasing at a rate of 15% eachyear.If the population of the small town is currently 12,000 people, howmany years will it take for the population to reach 1,500 people?
For this problem, we know the size of a certain population and the rate of decay on its numbers. We need to determine the time it will take for the population to reach 1500 people.
The population can be modeled with the following equation:
[tex]P(t)=12000\cdot(0.85)^t[/tex]Where "t" is the number of years and P is the population. We want to find how long it will take before the population is equal to 1500, so we need to replace P with 1500 and solve for t. We have:
[tex]\begin{gathered} 1500=12000\cdot(0.85)^t\\ \\ 0.85^t=\frac{1500}{12000}\\ \\ 0.85^t=0.125\\ \\ \ln0.85^t=\ln0.125\\ \\ t=\frac{\ln0.125}{\ln0.85}=\frac{-2.07944}{-0.162519}=12.79505 \end{gathered}[/tex]It will take approximately 12.8 years to reach 1500 people.
A gardener has seven identical-looking tulip
bulbs, of which each will produce a different
color tulip. Four of the colors are unknown,
however one will become white, one will
become yellow, and one will become pink. He
plants them abitrarily in a row. When the
flowers start to bloom, what is the probability
that the yellow one is first in the row, the white
one is second, and the pink one is at the end of
the row?
Solution
Step-by-step explanation:
Given
There are 7 bulbs out of which 1 is Yellow and 1 is Pink and 1 is white
If a gardener randomly select 6 bulbs
Then the Probability of selecting yellow = 1/7
probability of selecting white = 1/7
and the probability of selecting pink = 1
[tex]\text{probability = }\frac{1}{7}\times\frac{1}{6}\times1=\frac{1}{42}=0.0238[/tex]Therefore the correct answer is 0.0238
It took Mr. Sullivan 7 hours to drive a distance of 385 miles on a business trip. The followingweek he drove 165 miles in 3 hours. Is the relationship between the number of miles drivenand the amount of time for the two trips a proportional relationship?
Ratio 1: 385 miles in 7 hours.
• Ratio 2: 165 miles in 3 hours.
Now, a proportion is defined as the equality between two ratios, that means we need to put these two given ratios in an equation and see if they are equivalent.
[tex]\frac{385}{7}=\frac{165}{3}[/tex]Then, we divide each fraction
[tex]55=55[/tex]As you can observe both of them are equal to 55. That means they are in the same proportion.
Therefore, these two ratios have a proportional relationship.In a poll, 50 residents in Greenville and Fairfield were asked whether they prefer swimming or jogging for exercise. This table shows the relative frequencies from the survey.The graph is in the pictureBased on the data in the table, which statements are true? Select all that apply.The questions are in a separate picture
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given probabilities
STEP 2: Check if option A is correct
[tex]\begin{gathered} Greenvile\text{ that likes swimming}\Rightarrow0.18 \\ Greenvile\text{ that likes jogging}\Rightarrow0.38 \\ 0.38>0.18 \end{gathered}[/tex]Hence, Most residents of Greenville prefer jogging to swimming
STEP 3: Check if option B is correct
[tex]\begin{gathered} People\text{ who prefer jogging from Greenville}\Rightarrow0.38 \\ People\text{ who prefer jogg}\imaginaryI\text{ng from Fairfield}\operatorname{\Rightarrow}0.20 \\ 0.38>0.20 \\ People\text{ who prefer jogging are more likely from Greenville} \end{gathered}[/tex]Hence, Option B is not true
STEP 4: Check if option C is correct
Since more people from Greenville prefers jogging to swimming and more people people from Fairfield prefers swimming to jogging, therefore "There is an association between the town a person lives in and their exercise preference"
Hence, Option D is wrong.
Answer:
Options A and C are true
I want to know the correct equation by the synthetic division problem
When using synthetic division the numbers on top represent the coefficients of the polynomial that represents the dividend. The coefficients are arranged in descending order of exponents, therefore, the dividend of the synthetic division shown is:
[tex]x^3+8x^2+14x-8[/tex]In the synthetic division, the number on the left is the root of the divisor, therefore, we have:
[tex]\begin{gathered} x=-4 \\ x+4=0 \end{gathered}[/tex]Therefore, the divisor is "x + 4".
Finally, the numbers at the bottom are the coefficient of the result of the division but we subtract 1 from the exponents of the polynomial. We write each of the coefficients with its corresponding polynomial from left to right and the last number is the remainder of the division, therefore, we have that the result is:
[tex]x^2+4x-2[/tex]Therefore, the correct equation is:
[tex](x^3+8x^2+14x-8)\div(x-4)=x^2+4x-2[/tex]Condense the following expression using exponent properties.p5 k.p10 k:12HTML EdiBI U AA - IITT: 12ptPar
If two terms have the same base (the letter or number below the exponent), then their multiplication is equal to the number with the same base but with the exponent given by the sum of both exponents. So, in this case we have
[tex]\begin{gathered} r^5k\cdot r^{10^{}}k^{12}=r^{5+10}k^{1+12}=r^{15}k^{13} \\ (\text{if procedure is needed)} \end{gathered}[/tex]So, the condensed expression is
[tex]\begin{gathered} r^{15}k^{13} \\ (\text{ correct answer)} \end{gathered}[/tex]The radius of a circle is 2 miles. What is the circumference?Give the exact answer in simplest form. ____ miles (pi/fraction)
The formula for the circumference of a circle is :
[tex]C=2\pi r[/tex]Where r is the radius of the circle which is equal to 2 miles
The circumference will be :
[tex]C=2\pi(2)[/tex][tex]C=4\pi[/tex]The answer is 4π miles or 12.56 miles in decimal
austin is paid a salary of $250 weekly. find austins earnings per year
the graph show the amount of money Sheila has in her saving account as she adds money to it each week
Given data:
The given graph of the function.
In the given graph the dependent variable is the amount in saving.
Thus, the correct option is (C).
5. Caleb earns points on his credit card that he can use towards future purchases. He earns fourpoints per dollar spent on flights, two points per dollar spent at hotels, and one point perdollar spent on all other purchases. Last year, he charged a total of $9,480 and earned14,660 points. The amount of money spent on flights was $140 more than twice the amountof money spent on hotels. Find the amount of money spent on each type of purchase.can you solve it as matrix
This problem can be seen as the next equation
[tex]\begin{gathered} 4F+2H+1O=T \\ F\text{ = dollars spent on flights} \\ H\text{ = dollars spent at hotels} \\ O\text{ = dollars spent in other stuff} \\ T\text{ = total of points} \end{gathered}[/tex]Since he have charged 9480 dollars in total then we also have the next equation.
[tex]F+H+O=9480[/tex]With the rest of the information, we conclude the next system of equations
[tex]\begin{gathered} 4F+2H+O=14660 \\ F+H+O=9480 \\ F-2H=140 \end{gathered}[/tex]From the first two equations, we can substract them to obtain
[tex]\begin{gathered} 4F+2H+O=14660 \\ - \\ F+H+O=9480 \\ = \\ 3F+H=5180 \end{gathered}[/tex]If we multiply this last equation by 2 and add it to the last equation in the system we have
[tex]\begin{gathered} 6F+2H=10360 \\ + \\ F-2H=140 \\ = \\ 7F\text{ = }10500 \\ \end{gathered}[/tex]So
[tex]\begin{gathered} F=\frac{10500}{7}=1500 \\ H=\frac{1500-140}{2}=680 \\ O=9480-1500-680=7300 \end{gathered}[/tex]Then, he spent 1500 dlls. on flights, 680 dlls. at hotels and 7300 dlls. on others
[tex]\begin{gathered} 4\text{ 2 1 14660 } \\ 1\text{ 1 1 9480} \\ 1\text{ -2 0 140 }\approx \\ 4\text{ 2 1 14660 } \\ 3\text{ 1 0 5180} \\ 1\text{ -2 0 140 }\approx \\ 4\text{ 2 1 14660 } \\ 3\text{ 1 0 5180} \\ 7\text{ 0 0 }10500 \\ \end{gathered}[/tex]the steps to solve 9x - 2c= k solving for x
The given equation is
9x - 2c = k
We would solve for x by making x the subject of the formula. The first step is to add 2c to both sides of the equation. It becomes
9x - 2c + 2c = k + 2c
9x = k + 2c
We would divide both sides of the equation by 9. It becomes
9x/9 = (k + 2c)/9
x = (k + 2c)/9
find the difference and simplify your answer (5t^2 + 2t - 4 ) - (5t^2 - 2t - 3 )
To find the difference, you can follow the steps above:
1) Evaluate if you can solve the expressions inside the parentheses.
Since there is nothing to solve inside the parentheses, we can move in.
2) Remove the parentheses (do not forget the external signs).
[tex]5t^2+2t-4-5t^2+2t+3[/tex]3) Organize the variables putting the same variables together.
[tex]5t^2-5t^2+2t+2t-4+3[/tex]4) Sum the corresponding variables.
[tex]\begin{gathered} 0+4t+1 \\ 4t+1 \end{gathered}[/tex]So, the answer is:
[tex]4t+1[/tex]
Flynn bought 3 cheeseburgers and 4 sodas for $24.50. Catherine bought one cheeseburger and two sodas for $9.00. Set up you what the cost of one cheeseburgers is? *Do not include $ signs in your answer Type your answer... Previous
Flynn bought 3 cheeseburgers and 4 sodas for $24.50.
3 b + 4 s = 24.50
Where:
b= price of a cheeseburger
s= price of a soda
Catherine bought one cheeseburger and two sodas for $9.00
b + 2s = 9
We have the system of equations:
3 b + 4 s = 24.50
b + 2s = 9
Solve the second equation for s:
b+2s=9
2s= 9 -b
s= (9-b)/2
s= 4.5-0.5b
Replace s on the first equation and solve for b
3b+ 4 (4.5-0.5b) = 24.50
3b + 18 - 2b = 24.50
3b -2b = 24.50-18
b= 6.5
Cost of one cheeseburger 6.5
Find the value of x in the triangle shown below.73CChoose 1 answer:= 21* = 582 = 10C=58
SOLUTION
The question provides us with a right-angled triangle and we know the adjacent to be 3 and the oppoisite to be 7.
With this set of values, it is clear that the best way to solve this question is using PYTHAGORAS THEOREM
The Pythagoras theorem is shown below:
Given the below right-triangle
The Pythagoras theorem is given as
[tex]\begin{gathered} A^2+B^2=C^2 \\ \text{where,} \\ C=\text{longest side} \end{gathered}[/tex]Thus, using the Pythagoras theorem described above, we can solve the problem, with the longest side, in this case, being x.
This is done below:
[tex]3^2+7^2=x^2[/tex]Let us solve the above equation by finding the value of x
[tex]\begin{gathered} 3^2+7^2=x^2 \\ 9+49=x^2 \\ 58=x^2 \\ \text{ Find the square root of both sides} \\ \sqrt[]{58}=\sqrt[]{x^2} \\ \sqrt[]{58}=x \\ \\ \therefore x=\sqrt[]{58}\text{ } \\ \\ \text{Thus, the final answer is OPTION B} \end{gathered}[/tex]