Given:
The initial money = $3000
Rate = 4.7% = 0.047
Frederick doesn't want to pay more than $423 in interest.
So, we need to find the number of years
Assume simple interest rate:
[tex]\begin{gathered} I=P\cdot r\cdot t \\ I=423 \\ P=3000 \\ r=0.047 \\ \\ 423=3000\cdot0.047\cdot t \\ 423=141\cdot t \\ \\ t=\frac{423}{141}=3 \end{gathered}[/tex]so, the number of years = 3 years
Two sprinters, Nick and Ryan, want to find out who has the faster time when compared to each of their teams. Nick has a time of 10.8 seconds, and his team has a mean time of 11.4 seconds and a standard deviation of 0.4 seconds. Ryan has a time of 11.2 seconds, and his team has a mean of 11.5 seconds and a standard deviation of 0.1 seconds. Who has the faster time when compared to each of their teams?a) Nick b) Ryan c) The times are equal when compared to each of their teams.d) There is not enough information
Given data:
The time taken by Nick is 10.8 seconds.
The mean time taken by Nick is 11.4 seconds.
The given standard deviation of Nick is 0.4 seconds.
The time taken by Ryan is 11.2 seconds.
The mean time taken by Ryan is 11.5 seconds.
The given standard deviation of Ryan is 0.1 seconds.
The z-score of Nick is,
[tex]\begin{gathered} z=\frac{10.8-11.4}{0.4} \\ =\text{ -1.5} \end{gathered}[/tex]The z-score of Ryan is,
[tex]\begin{gathered} z=\frac{11.2-11.5}{0.1} \\ =\text{ -3} \end{gathered}[/tex]Thus, Ryan z-score is lower, so Ryan has the faster time when compared to each of their teams, option (b) is correct.
-2/5 divide (-3) multiply and reduce to lowest terms.
Answer:
2/15
Explanation:
Given the expression:
[tex]-\frac{2}{5}\div(-3)[/tex]First, change the division sign to times by taking the reciprocal of the number after the sign:
[tex]=-\frac{2}{5}\times-\frac{1}{3}[/tex]Next, multiply the numerators and denominators:
[tex]\begin{gathered} =\frac{(-2)\times(-1)}{5\times3} \\ =\frac{2}{15} \end{gathered}[/tex]The fraction is already in its lowest form as required.
Raul works at a movie theatre. The function f(x) represents the amount of money Raul earns per ticket, where x is the number of tickets he sells. The function g(x) represents the number of tickets Raul sells per hour, where x is the number of hours he works. Show all work to find f(g(x))f(x) = 2x2 + 16g(x) = /5x^3
Given the functions
[tex]\begin{gathered} f(x)=2x^2+16 \\ g(x)=\sqrt[]{5x^3} \end{gathered}[/tex]First, we get the composite function
[tex]f(g(x))=f(\sqrt[]{5x^3})[/tex]To get f(√5x³), we will substitute x in f(x) with √5x³ as shown:
[tex]f(g(x))=2(\sqrt[]{5x^3})^2+16[/tex]The square root and power 2 cancel each other
[tex]\begin{gathered} f(g(x))=2(5x^3)+16 \\ \text{Simplify} \\ f(g(x))=10x^3+16 \end{gathered}[/tex]Answer:
[tex]f(g(x))=10x^3+16[/tex]Nina and Nathan are creating a budget so they can afford paying all their billsand save to move to a nicer apartment. They decide that the ratio of spendingto saving needs to be 7:3. Last month their bills totaled $3975.20. Theymanaged to save $1,248.00. What was their actual spending ratio? At thisrate, will they meet their goal?
The ratio of spending to savings needs to be 7:3.
The actual spending ratio is 3,975.20 : 1,248.00.
In order to reach the goal, the actual spending ratio must the lower than the decided spending ratio.
3,975.20 : 1,248.00 < 7:3.
Dividing the ratios:
3.18 < 2.33
Since 2.33 is not greater than 3.18, they will not reach their goal at this rate.
Alice fills up the gas tank of her car before going for a long drive . The equation below models the amount of gas , g , in gallons , in Alice's car when she has driven m miles . What is the meaning of 32 in the equation ?
Solution
For this case we have the following equation given:
[tex]g=15-\frac{m}{32}[/tex]We want to know what represent the 32 value
So then the answer is:
Total of miles that can cover the car with 15 gallons of gas
simplify 2(w+3)-(w-1)
we have
2(w+3)-(w-1)
apply distributive property first term and remove the parenthesis
2w+6-w+1
combine like terms
w+7The ratio of the number of adults to the number of students at a field trip has to be 3:8. During a current field trip, there are 190 more students on the trip than there are adults. How many students are attending the field trip? How many adults?
Please put this answer in a easy way (no algebra) use ratios and basic opreations.
The number of students attending the field trip is 304 and the number of adults is 114.
Calculating number of students and adults attending a field tripFrom the question, we are to determine the number of students and adults attending the field trip.
From the given information,
"The ratio of the number of adults to the number of students at a field trip has to be 3:8"
Let the number of students be x and the number of adults be y
Thus,
y/x = 3/8
8y = 3x ------------- (1)
Also,
There are 190 more students on the trip than there are adults
That is,
x - y = 190
Therefore,
x = 190 + y -------------- (2)
Substitute into equation
8y = 3x
8y = 3(190 + y)
8y = 570 + 3y
8y - 3y = 570
5y = 570
y = 570/5
y = 114
Thus, the number of adults is 114
Substitute the value of y into equation (2)
x = 190 + y
x = 190 + 114
x = 304
Hence, the number of students is 304
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We consider the sets D = {m, n, p, q} E = {3,6,8} and the relation from D to E.R = {(m, 3), (m, 8), (n, 6), (n, 8) (p, 3), (q, 3), (q, 6)a) List the pairs of D × Eb)R is it a proper subset of D × E? Why ?c)Represent the relation R using a Cartesian network
D= {m, n, p, q}
E= {3,6,8}
a) D x E = { (m, 3), (m, 6), (m, 8), (n, 3), (n,6), (n,8), (p, 3), (p, 6), (p, 8), (q, 3), (q, 6),
(q, 8) }
b) We need to know what a proper subset is.
Proper subset
A proper subset of a set A is a subset of A that is not equal to A. In other words, if B is a proper subset of A, then all elements of B are in A but A contains at least one element that is not in B.
From the above definition, we can say R is a proper subset of D x E because there are element in D x E that is NOT in R.
Suppose f(x) = x. Find the graph of f(x + 2).graph 1, 2, 3, or 4
Find the area, to the nearest thousandth, of the standard normal distribution between the given z-scores.z = 1 and z = 1.81
Since this is a normal distribution, the area between the z-scores z₁ = 1 and z₂ = 1.81 is just the probability that the random variable Z is between z₁ and z₂:
[tex]P(z_1\leq Z\leq z_2)=P(z_1\leq Z)-P(z_2\leq Z_{})=P(1\leq Z)-P(1.81\leq Z)[/tex]Using the values reported on tables for the standardized normal distribution, we know that:
[tex]\begin{gathered} P(1\leq Z)=0.158655 \\ P(1.81\leq Z)=0.035148 \end{gathered}[/tex]Now, using these results:
[tex]P(z_1\leq Z\leq z_2)=0.158655-0.035148=0.123507[/tex]24. Which point is part of the solution for the system of inequalities graphed below? A. (-1,-2) B. (3,1) C. (1,-2) D. (-3,1)
The solution must be insige the red grind so we can see that the only point inside this area is the coordinate (-3, 1) so the answer is D
The height of the object at 1 second is what amount of feet?
If t= 1s. Then let's replace t-value in the equation:
[tex]\begin{gathered} \text{ -16t}^2\text{ + 1130= } \\ \text{ -16 \lparen1\rparen + 1130= } \\ \text{ -16 + 1130= } \\ 1,114\text{ feet. } \end{gathered}[/tex]The height of the object at 1 second is 1,114 feet.
-ExerciseActivity 1Please see the image above & use table NOTE: HELP ME ASAP
Given:
Required:
To complete the table.
Explanation:
[tex]\begin{gathered} 1\text{ pinch = }\frac{1}{16}\text{ teaspoon} \\ 2pinch\text{ = }\frac{2}{16\text{ }}tps \\ 2p\imaginaryI nch=\frac{1}{8}\text{ tps} \end{gathered}[/tex][tex]\begin{gathered} 1\text{ teaspoon = 76.0012} \\ 3\text{ teaspoons = 1 tablespoon} \end{gathered}[/tex]Since
[tex]\begin{gathered} 16\text{ tablespoon = 1 cup} \\ \end{gathered}[/tex]Divide by 8 into both sides.
[tex]\begin{gathered} 2\text{ tablespoon = }\frac{1}{8}\text{ cup} \\ 4\text{ tablespoon=}\frac{\text{1}}{4}\text{{\text{cup}}} \end{gathered}[/tex][tex]\begin{gathered} 16\text{ tablespoon = 1 cup} \\ 8\text{ tablespoon=}\frac{1}{2}\text{cup} \end{gathered}[/tex][tex]\begin{gathered} 2\text{ cups = 1 pint} \\ 4\text{ cups = 2 pint} \end{gathered}[/tex][tex]4\text{ quarts = 1 gallon}[/tex]Final Answer:
Explain in explanation parts.
Creating and solving equationstwo-thirds a number plus 4 is 7
Given:
two-thirds a number plus 4 is 7
First Part: Converting the statement into equation
Let x be the number in the given statement.
The phrase "two-thirds a number" can be expressed as
[tex]\frac{2}{3}x[/tex]Pair it with "... plus 4" and we get
[tex]\frac{2}{3}x+4[/tex]Finally, it is stated it is equal to 7, and we complete the equation
[tex]\frac{2}{3}x+4=7[/tex]Second Part: Solving for the number
Now, that we have the equation, we can now solve for the missing number x.
Subtract both sides by 4, to remove the constant 4 on the left side of the equation
[tex]\begin{gathered} \frac{2}{3}x+4=7 \\ \frac{2}{3}x+4-4=7-4 \\ \frac{2}{3}x\cancel{+4-4}=3 \\ \frac{2}{3}x=3 \end{gathered}[/tex]Multiply both sides by 3/2, and we get
[tex]\begin{gathered} \frac{2}{3}x=3 \\ \frac{2}{3}x\cdot\frac{3}{2}=3\cdot\frac{3}{2} \\ \frac{\cancel{2}}{\cancel{3}}x\cdot\frac{\cancel{3}}{\cancel{2}}=\frac{9}{2} \\ x=\frac{9}{2} \end{gathered}[/tex]Therefore, the number is 9/2 or nine-halves.
Rearrange the equation so r is the independent variable q-10=6(r+1)
can someone help me with this question explain
Given expression [tex]\frac{2x^3+11x^2-21x}{x^2+3x}[/tex] is equivalent to [tex]2x+5 -\frac{36}{x+3}[/tex].
What do you mean by algebraic expression?
The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables.
Variables and constants can both be used in an algebraic expression.
There are 3 main types of algebraic expressions which include:
Monomial Expression
Binomial Expression
Polynomial Expression
Given expression:
[tex]\frac{2x^3+11x^2-21x}{x^2+3x}[/tex] for [tex]x[/tex] ≠ -3 or 0.
Using long division method and euclid lemma
On dividing [tex]2x^3+11x^2-21x[/tex] by [tex]x^2+3x[/tex] we get, (given in the snip)
As we know division can be written as
dividend = divisor × quotient + remainder
[tex]2x^3+11x^2-21x = (2x+5)(x^2+3x)-36x[/tex]
⇒ [tex]2x^3+11x^2-21x = 2x+5 -\frac{36x}{x^2+3x}[/tex]
⇒ [tex]2x^3+11x^2-21x = 2x+5 -\frac{36}{x+3}[/tex]
Therefore, given expression [tex]\frac{2x^3+11x^2-21x}{x^2+3x}[/tex] is equivalent to [tex]2x+5 -\frac{36}{x+3}[/tex].
To learn more about the algebraic expression from the given link.
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5. If the area of a parallelogram is 456 cm2 and the base is 24 cm. Find the height. Height = 1.
The area of a parallelogram is computed as follows:
A = base*height
Substituting with A = 456, and base = 24,
456 = 24*height
456/24 = height
19 cm = height
Write the polynomial in factored form as a product of linear factors:g(t)=t^3+2t^2−10t−8
Okay, here we have this:
We need to write the following polynomial in factored form as a product of linear factors:
[tex]\begin{gathered} g\mleft(t\mright)=t^3+2t^2-10t-8 \\ =\mleft(t+4\mright)\mleft(t^2-2t-2\mright) \end{gathered}[/tex]Now, let's solve the following polynomial using the general formula for equations of the second degree:
[tex]\begin{gathered} (t^2-2t-2)=0 \\ t_{1,\: 2}=\frac{-\left(-2\right)\pm\sqrt{\left(-2\right)^2-4\cdot\:1\cdot\left(-2\right)}}{2\cdot\:1} \\ t_{1,\: 2}=\frac{-\left(-2\right)\pm\:2\sqrt{3}}{2\cdot\:1} \\ t_1=\frac{-\left(-2\right)+2\sqrt{3}}{2\cdot\:1},\: t_2=\frac{-\left(-2\right)-2\sqrt{3}}{2\cdot\:1} \\ t=1+\sqrt{3},\: t=1-\sqrt{3} \end{gathered}[/tex]Finally, we obtain the following polynomial:
[tex]g(t)=(t+4)(t-1-\sqrt{3})(t-1+\sqrt{3})[/tex]10. A glass jar contains 8 red, 6 green, 12 blue, and 10 yellow marbles. If a single marble is chosen at random from the jar, what is the probability of choosing a(a) red marble? (b) green marble? (c) blue marble?
Let:
• A ,be the event of getting a red marble
,• B ,be the event of getting a green marble
,• C ,be the event of getting a blue marble
We'll have that:
[tex]\begin{gathered} P(A)=\frac{8}{36} \\ \\ P(B)=\frac{6}{36} \\ \\ P(C)=\frac{12}{36} \end{gathered}[/tex]Determine if the table is linear or exponential. Tables 2 , 3 and 4 are the same
Exponential and linear relations differ in the way the y-values change when the x-values increase by a constant amount, that is, in a linear relationship, the y-values have equal differences and in an exponential relationship, the y-values have equal ratios.
In our first table, when the x-values increase one unit, the y-values decreses 2 units. Similarly, when the x-values increase 2 units, the y-values decrease 4 units and so on:
. Therefore, the first table shows a linear behavior.
On the other hand, table 2,3 and 4 are the same. In those cases, when the x-values increase one unit the, the y-values have a ratio of 2. Similarly, when the x-values increase 2 units the corresponding ratio for the y-values in 4 and so on.
This means that tables 2, 3 and 4 denote an exponential relationship.
Solve the following exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 4^-x=2.6What is the exact answer? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.A. The solution set { } (simplify your answer. type an exact answer)B. There is no solution
Given:
[tex]4^{-x}=2.6[/tex]To solve for x:
Taking log on both sides
[tex]\begin{gathered} \log 4^{-x}=\log 2.6 \\ -x\log 4=\log 2.6 \\ -x=\frac{\log 2.6}{\log 4} \\ -x=0.689255811 \\ x=-0.689255811 \\ x\approx-0.689 \end{gathered}[/tex]Hence, the value of x is -0.689 (rounded to three decimal places).
Complex numbers are used to describe current. I voltage, E, and impedance, Z. These three quantities are related by the equation E = IZ. Given two ofthese quantities, solve the equation E = IZ for the missing variable.I = 4 + 4i, Z= 7+3iE=(Simplify your answer. Type your answer in the form a+b/. Use integers or fractions for any numbers in the expression.)
We have the following equation to solve
[tex]E=I\cdot Z[/tex]Where E, I, and Z are complex numbers, therefore let's put it in numbers
[tex]E=(4+4i)(7+3i)[/tex]We can solve it directly into the rectangular form by doing the distrutive
Then
[tex](4+4i)(7+3i)=28+12i+28i+12i^2[/tex]Remember that
[tex]i^2=-1[/tex]Then
[tex]\begin{gathered} (4+4\imaginaryI)(7+3\imaginaryI)=28+12i+28i-12 \\ \\ (4+4\imaginaryI)(7+3\imaginaryI)=16+40i \end{gathered}[/tex]Now we have completely solved the problem!
[tex]E=16+40i[/tex]______________________
The second solution (usual)
When we have real engineering problems, we like to do multiplication and division with the polar form, then let's convert Z and I to the polar form
[tex]\begin{gathered} I=4+4i=4\sqrt{2}\angle45° \\ \\ Z=7+3i=\sqrt{58}\angle23.2° \end{gathered}[/tex]Now to do the multiplication we multiple the magnitude and sum the phases (angles)
[tex]\begin{gathered} ZI=4\sqrt{2}\cdot\sqrt{58}\angle45°+23.2° \\ \\ ZI=4\sqrt{116}\operatorname{\angle}68.2° \end{gathered}[/tex]We already have the result, now just put it in the rectangular form
[tex]\begin{gathered} ZI=4\sqrt{116}\cdot\cos(68.2)+i4\sqrt{116}\sin(68.2) \\ \\ E=16+40i \end{gathered}[/tex]Write T for true or F for false. 6. The number 14 is a multiple of 4. 7. The Identity Property says that any number times 1 equals the number itself. 8. A bar diagram can be used to show 3 X 6.
In the number 6, it says the number 14 is a multiple of 4. It means there would be an integer number X which when multiplied by 4 would result in the number 14. To check it, we can perform the following calculation.
[tex]14=X\times4\to X=\frac{14}{4}=3.5[/tex]Because the value of X found is not an integer, 6. is FALSE
In the number 7, it says the Identity Property rays that any number times 1 equals the number itself. This property says that there is a number that, when multiplied by any number will always equal the number itself, and this is the number 1. From this, 7 is TRUE
Number 8 says a bar diagram can be used to show 3X6. This technique can be used to show any multiplication by an integer number. Because both. 3 and 6, are integer, 8 is TRUE
To pay for a 15,300 car, Tony made a down payment of $3900 and took out a loan for the rest. On the loan , he paid monthly payment payment of $252.34 for 4 years.A:what was the total amount Tony end up paying for the car.(including the down payment and monthly payment.B: how much interest did Tony pay on the loan.
Down Payment = 3900
Loan Amount - 15,300 - 3900 = $11,400
Total Paid on Loan = $252.34 (monthly) for 4 years (4 x 12 = 48 months).
So, he paid
[tex]252.34\times48=\$12,112.32[/tex]So, total amount Tony paid for the car is "downpayment (3900) + loan amount with interest (12,112.32)".
So,
[tex]3900+12,112.32=\$16,012.32[/tex]Answer: $16,012.32
B)The interest is the excess amount on the loan.
Loan amount = $11,400
Loan + Interest amount = $12,112.32
Thus, the interest amount is 12,112.32 - 11,400 = $712.32
Answer: $712.32
You flip a coin 100 times and record each outcome.You find that you land on heads 47 times and land ontails 53 times. What is the theoretical probability oflanding on heads?
If we were asked the "experimental probability", the answer would have been
[tex]\frac{47}{100}\text{ that is number of outcomes/total outcomes. }[/tex]But we were asked the "theoretical probability". And in theory, we can get either a head or a tail if a coin is flipped. So that makes it
[tex]\frac{1\text{ outcome }}{total\text{ outcomes of 2 }}\text{ = }\frac{1}{2}[/tex]Therefore, the answer is
[tex]\frac{1}{2}[/tex][tex] \sqrt[3]{80} [/tex]simplify in simplest radical form
Start by decomposing the number inside the root into primes
Then group the terms into cubes if possible
[tex]\begin{gathered} 80=2\cdot2\cdot2\cdot2\cdot5 \\ 80=2^3\cdot2\cdot5 \\ 80=10\cdot2^3 \end{gathered}[/tex]rewrite the root
[tex]\sqrt[3]{80}=\sqrt[3]{10\cdot2^3}[/tex]then cancel the terms that are cubes and bring them out of the root
[tex]\sqrt[3]{80}=2\sqrt[3]{10}[/tex]Our university consists of three colleges: business, engineering, and fine arts. There are 2,900 students in the business college, 1,500 students in the engineering college, and 1,000 students in the fine arts college. What percent of the total number of students are in the fine arts college. Round your answer to the nearest percent.
Given data:
The numbers of students in business college is B=2,900.
The numbers of students in engineering college is E=1,500.
The numbers of students in fine arts is A=1,000.
The percentage of total number of students in fine arts is,
[tex]\begin{gathered} P=\frac{A}{B+E+A}\times100 \\ =\frac{1,000}{2,900+1,500+1,000}\times100 \\ =18.52\text{ percent} \\ \approx18\text{ percent} \end{gathered}[/tex]Thus, the percentage of the students in fine arts is 18 %.
.1.2_Updated_FY21 Question: 1-3 The elevation of the Vander's home is -108 feet. The elevation of the Gail's home is exactly of that depth below sea level. What is the elevation of the Gail's home in feet? -36 -72 -162 -180
Given:
Elevation of Vander's home = -108 feet
Elevation of Gali's home is ⅔ of that depth below sea level.
Thus, the elevation of Gali's home is:
⅔ of -108 feet =
[tex]\frac{2}{3}(-108)\text{ = }\frac{2(-108)}{3}=\frac{-216}{3}=\text{ -72 f}eet[/tex]We know that the elevation of Vander's home is already below sea level since it's a negative value.
Therefore, since the elevation of Gali's home is ⅔ of the depth of Vander's home below sea level, the elevation of Gali's home is:
-72 feet
ANSWER:
-72 feet
Can you please help me out with a question
In the figure, the value of angle inscribed, m[tex]\text{Inscribed angle=}\frac{1}{2}\times Intercepted\text{ arc}[/tex]In the figure, Hence,
[tex]\begin{gathered} mTherefore, m ZWX= 230º.What is 3ln5x=10? I have a test
Answer:
x=e^10/3
————
5
Step-by-step explanation:
Decimal Form:x=5.60632497
