Given:
Increased rate = 15%
One month bill = $130
Find-:
What was the monthly food bill after three months?
Explanation-:
Formula:
[tex]A=P(1+\frac{r}{100})^n[/tex]Where,
[tex]\begin{gathered} A=\text{ Amount after time} \\ \\ P=\text{ Initial amount} \\ \\ r=\text{ Rate} \\ \\ n=\text{ Time period } \end{gathered}[/tex]The given value is:
[tex]\begin{gathered} P=130 \\ \\ r=15 \\ \\ n=3 \end{gathered}[/tex]Amount after 3 months.
[tex]A=P(1+\frac{r}{100})^n[/tex][tex]\begin{gathered} A=130(1+\frac{15}{100})^3 \\ \\ A=130(1+0.15)^3 \\ \\ A=130(1.15)^3 \\ \\ A=130\times1.521 \\ \\ A=197.714 \end{gathered}[/tex]So, the food bill after three months is $197.714
What is the solution to the equation below? Round your answer to two
decimal places.
7x = 77
Answer:
x = 11
Step-by-step explanation:
divide both sides by 7
x = 11
Find the value of 12.56 is multiplied by 8.8 and result is divided by 1.57.
Given:
12.56 is multiplied by 8.8 and the result is divided by 1.57.
To find the final result:
First, we multiply 12.56 by 8.8.
We get,
[tex]12.56\times8.8=110.528[/tex]Next, the result 110.528 is divided by 1.57.
So, we get
[tex]\frac{110.528}{1.57}=70.4[/tex]Hence, the answer is 70.4.
Find the equation of the line whose slope is -3 and which passes through the point (5,-2).
Answer:
y = -3x + 13
Step-by-step explanation:
We can use the the point slope form of an equation for this:
y - y1 = m (x - x1)
Replace the y1, x1, and m variables with what we were given:
y - (-2) = -3 (x - 5)
Distribute
y + 2 = -3x + 15
Combine like terms
y = -3x + 13
A rental car company charges $29 per day to rent a car and $0.05 for every mile driven. Santiago wants to rent a car, knowing that: He plans to drive 400 miles. He has at most $100 to spend. What is the maximum number of days that Santiago can rent the car while staying within his budget?
Answer: He can only go 2 days
Step-by-step explanation:
what is the discriminant of the equation-x^2-9x-9=0
Given data:
The given expression is -x^2-9x-9=0.
The descriminant of the given equation is,
[tex]\begin{gathered} D=(-9)^2-4(-1)(-9) \\ =81-36 \\ =45 \end{gathered}[/tex]Thus, the descriminant of the given equation is 45.
When Andy Green broke the land speed record, his vehicle was traveling across a flat portion of the desert with a forward velocity of 341.11 m/s. How long would it take him at that velocity to travel 4.500 km?
Answer:
13.192 seconds
Step-by-step explanation:
You want to know the time to travel 4.500 km at a speed of 341.11 m/s.
Travel timeThe relation between time, speed, and distance is ...
time = distance/speed
time = (4500 m)/(341.11 m/s) ≈ 13.192 s
It would take Andy about 13.192 seconds to travel 4.500 km.
__
Additional comment
The distance of 4.500 km is rounded to the nearest meter, so may have an error of 0.5 meters. At 342.11 m/s, it takes about 1.47 ms to travel that distance. This suggests that timing to the nearest millisecond is consistent with the precision of the other numbers in the problem.
One could argue that speed is 5 significant figures, but distance is 4 significant figures. That suggests their ratio, time, is only accurate to 4 significant figures: 13.19 s. Analysis of the worst-case error in the ratio suggests that this reported value throws away some accuracy, so a better result is 13.192 s.
find angle y If the opposite side is 12 and the adjacent side is 11mm
Answer:
answer is 47.49 because tan theta is equals to 12 / 11 which is 1.09091.
So tan-¹(1.09091) = 47.49
please help. what are the x and y values here
Answer:
(6,0)
(-2,0)
2,-3
-3,-2
7,7
Step-by-step explanation:
Solve .graph the solution, state the interval notation and state the solution & set. 14x-6]
Starting with the inequality:
[tex]\lvert4x-6\rvert\le4[/tex]We have two cases:
Case 1: 4x-6≥0
Since 4x-6≥0, then |4x-6| = 4x-6. Then:
[tex]\begin{gathered} 4x-6\le4 \\ \Rightarrow4x\le10 \\ \Rightarrow x\le\frac{10}{4} \\ \therefore x\le\frac{5}{2} \end{gathered}[/tex]Case 2: 4x-6<0
Since 4x-6<0, then |4x-6| = -4x+6. Then:
[tex]\begin{gathered} -4x+6\le4 \\ \Rightarrow-4x\le-2 \\ \Rightarrow x\ge\frac{-2}{-4} \\ \Rightarrow x\ge\frac{1}{2} \end{gathered}[/tex]The solution set of the inequality is all the numbers x which are greater or equal to 1/2 AND lower or equal to 5/2:
[tex]\frac{1}{2}\le x\le\frac{5}{2}[/tex]The graph of the solution is a number line from 1/2 to 5/2 including the endpoints:
The interval notation of the solution, is:
[tex]x\in\lbrack\frac{1}{2},\frac{5}{2}\rbrack[/tex]The solution set S is:
[tex]S=\lbrace x\in\R|\frac{1}{2}\le x\le\frac{5}{2}\rbrace[/tex]If students recieve a whole numberof pointson every exam item. Can the exam be worth 80 points
Each response includes a thorough explanation of how it was arrived at. The student seemed to have been unsure of which approach to utilize so they hedged their chances by trying both in the hopes that one of them would work. (I don't think it was rewriting that they forgot to cross out; the student presented their response as "it is either X or Y," then in subsequent questions supplied parallel replies depending on whether X or Y was accurate.)
How can I give this question a grade?
Full points given that they provided the correct response
partial marks for being "half-right"?
Or perhaps they didn't get any points since they didn't fully comprehend the issue?
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Solve the system. Check the solution.x + y = 8(x=y-3
Answer:
[tex]\begin{gathered} \text{Solution:} \\ (2.5,5.5) \end{gathered}[/tex]Step-by-step explanation:
Given the following system of equations:
[tex]\begin{gathered} x+y=8\text{ (1)} \\ x=y-3\text{ (2)} \end{gathered}[/tex]Since on equation 2, x is already isolated, substitute it into equation 1:
[tex]\begin{gathered} (y-3)+y=8 \\ \end{gathered}[/tex]Solve for y.
[tex]\begin{gathered} 2y=8+3 \\ y=\frac{11}{2}=5.5 \end{gathered}[/tex]Knowing the value of y, plug it into equation (2) and solve for x:
[tex]\begin{gathered} x=y-3 \\ x=5.5-3 \\ x=2.5 \end{gathered}[/tex]Graph the function. Then state the domain and range. f(x) = 1/4x-2
The domain and the range of the function f(x) = 1/4x - 2 is the all set of real values
What is the domain of a function?The domain of the function is the set of input values of the graph
What is the range of a function?The range of a function is the set of output values of the graph.
This in other words mean the range of a function is the set of y values of the graph.
How to determine the domain and the range?The function is given as
f(x) = 1/4x - 2
Next, we plot the graph of the function (see attachment)
From the graph, we can see that the graph is a linear graph
This means that the function has a domain and a range of all set of real values
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2 printing machines of a printing house can complete the printing work of the required number of Excel in Mathematics textbooks in 20 days. After printing the books for 8 days, if 1 more machine was added, in how many days would the remaining work be completed?
The remaining work can be completed in if 2 printing machines of a printing house can complete the printing work in 20 days, After printing the books for 8 days, if 1 more machine was added, is 8 days.
What is addition?In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation.
Given:
2 printing machines of a printing house can complete the printing work in 20 days,
After printing the books for 8 days, if 1 more machine was added,
Assume the total work is x,
Calculate the amount of work done in 8 days by both machines as shown below,
The amount of work done in 8 days = x / 20 × 8
The amount of work done in 8 days = 2x / 5
Calculate the remaining work = x - 2x / 5
The remaining work = 3x / 5
Calculate the time taken to complete the remaining work,
Time = (3x / 5) / (3x / 40) = 8 days
Thus, the total time is 16 days.
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Can anyone help me with this?
Determine whether the statement is true or false. If false, correct the right-hand side of the statement. 0 Question content area bottom Part 1 Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The statement is true. B. The statement is false. The correct statement is enter your response here. (Simplify your answer.)
Based on the given statement of hy⁰ = 0, the answer is B. The statement is false. The correct statement is hy⁰ = 1.
Why is the mathematical statement wrong?The statement given is that hy⁰ = 0. This is false because of the mathematical rule that whenever a number or figure is raised to the power of 0, the result would be that the answer is 1.
For instance:
2 ⁰ = 1
56 ⁰ = 1
8676⁰ = 1
From hy ⁰ = 0, we take the value of y⁰:
y ⁰ = 1
If y ⁰ = 1, then it means that on the right hand side of the statement, we would have the expression h(1).
This therefore means that the equation hy⁰ = 0 is false because h(1) is h and so the correct statement is:
hy ⁰ = 1
Rest of the question is:
Determine whether the statement is true or false. If false, correct the right-hand side of the statement. hyº = 0
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John Baxley borrowed $25,000 for one year. He borrowed some at 13% interest and the rest at 50% interest. At the end of the year, he owed $36,000 in interest how much did he borrow at each rate?
The amount borrowed at 13% interest is $20,945.95.
The amount borrowed at 50% interest is $4,054.05.
How much is borrowed at each rate?The first step is to formulate a system of equations:
a + b = $25,000 equation 1
0.13a + 0.5b = (36,000 - 25,000
0.13a + 0.5b =11,000 equation 2
Where:
a = amount borrowed at 13% interest
b = amount borrowed at 50% interest
Take the following steps to determine the value of b:
Multiply equation 1 by 0.13
0.13a + 0.13b = 3,250 equation 3
Subtract equation 3 from equation 2
7,750 = 0.37b
b = $20,945.95
a = $25,000 - $20,945.95 = $4,054.05
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Find a polynomial function of degree 5 with -2 as a zero of multiplicity 3,0 as a zero of multiplicity 1, and 2 as a zero of multiplicity 1.
The zeros and their multiplicities are:
-2 with multiplicity 3
0 with multiplicity 1
2 with multiplicity 1
The polynomial function is therefore given as:
[tex]\begin{gathered} f(x)=(x+2)^3(x-0)^1(x-2)^1 \\ f(x)=x(x-2)(x+2)^3 \\ f(x)=(x^2-2x)(x^3+6x^2+12x+8) \\ f(x)=x^5+6x^4+12x^3+8x^2-2x^4-12x^3-24x^2-16x \\ f(x)=x^5+4x^4-16x^2-16x \end{gathered}[/tex]Therefore, the polynomial function of degree 5 is:
[tex]f(x)=x^5+4x^4-16x^2-16x[/tex]State the adjacent side for the angle marked as x in the picture.
Answer:
Explanation:
In
help meeeeeeeeeeeeeee
Answer:
Rose.
Step-by-step explanation:
Because the number is positive, it does not symbolize a withdrawal, it shows. deposit.
I hope this helps!
P.S, Brainliest if correct, thanks!
True or false?
Barriers that keep a business from entering a market can lead to perfect competition.
Answer: true
Step-by-step explanation:
leads to a monopoly
The city is issuing bonds to raise money for a building project. You obtain a $6700 bond that pays 6% interest annually that matures in 8 years. How much interest will you earn?
The interest will earn is 3216
Interest Earned = Amount * Rate of Interest * Time
Interest Earned = 6700*6%*8 = [tex]6700*\frac{6}{100}*8[/tex]
Interest Earned = 3216
Interest Calculator
The term "interest" refers to the additional revenue received by the investor over and above the investment or the additional debt owed by the borrower over and above the amount borrowed. Simple interest and compound interest are the two different kinds of interest. The sorts of interests are covered in further detail in the interest formula. Let's explore the interest formula in further detail and go through several cases.
Interest Formula: What is it?
Simple interest and compound interest are both included in the interest formula. Interest is the cost a borrower pays a lender for a loan. This additional sum, or the interest, must be paid in addition to the loan itself. The Simple Interest Formula and the Compound Interest Formula are both discussed in the interest formula Compound Interest Formula. The interest formula for both is
Simple Interest = P × R × T
Compound Interest = [tex]P(1 + r/n)^{nt}- P[/tex]
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Two friends are both pregnant, and find out they are each expecting twins!
Let A be the event that one friend is pregnant with identical twins, and note that P(A)=0.0045.
Let B be the event that the other friend is pregnant with fraternal twins, and note that P(B)=0.01.
A and B are independent events. What is the probability that one friend is pregnant with identical twins, and one friend is pregnant with fraternal twins?
Give your answer as a percent, rounded to four decimal places if necessary.
The probability that one friend is pregnant with identical twins, and one friend is pregnant with fraternal twins is 0.000045.
What is the probability?From the information illustrated,
Let A = event that one friend is pregnant with identical twins, and note that P(A)=0.0045.
Let B = event that the other friend is pregnant with fraternal twins, and note that P(B)=0.01.
Therefore, the probability will be gotten by using the multiplication for two independent events. This will be:
= P(A) × P(B)
= 0.0045 × 0.01
= 0.000045
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A store and a bank would both charge fees for
Answer:A returned check
Step-by-step explanation:
Answer: D. bouncing a check
Bouncing a check
When a check is deposited in a bank, or when it is written out to a store teller to ultimately deposit in the store bank, the funds are tracing back from an origin bank account. When the check bounces a fee is then charges by both the bank out of which the check is written (for non-sufficient funds) and by the payee. If the payee is a store they will often charge fees that are charged back to them by their bank of deposit."
ANSWERS ASAP PLEASEEE
A bag has six balls labeled A, B, C, D, E, and F.
One ball will be randomly picked, and its letter will be recorded as the outcome.
Give the sample space describing all possible outcomes.
Then give all of the outcomes for the event of choosing the letter A or C.
If there is more than one element in the set, separate them with commas.
Sample space:
Event of choosing the letter A or C:
Sample space={ A,B,C,D,E,F}
Event of choosing A or C = {A,C}
What is sample space?
A sample space is a set which contains the set of all the possible outcomes or results that could occur while performing an experiment.
i.e. the sample space while flipping a coin is: {H,T}
The sample space while tossing a six-sided die is: {1,2,3,4,5,6}
Here it is given that:
A bag has six balls labeled: A,B,C,D,E,F
One ball will be randomly picked, and its letter will be recorded as the outcome.
This means that the sample space is given by:
Sample space={ A,B,C,D,E,F}
Now, when the event is choosing a letter from A or C.
Then the sample space is:
Sample space= {A,C}
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After many studies, a researcher finds thatthe probability that a word-recognitionprogram correctly interprets a hand-writtenword is 10. How many words out of40 would the researcher expect theprogram to correctly interpret?
Given:
The probability that a word-recognition the program correctly interprets a hand-written word is:
[tex]=\frac{9}{10}[/tex]Find-:
How many words out of 40 would the researcher expect the program to correctly interpret?
Explanation-:
the probability that a word-recognition the program correctly interprets a hand-written word is:
[tex]=\frac{9}{10}[/tex]For 40 world is:
[tex]\begin{gathered} =\frac{9}{10}\times40 \\ \\ =9\times4 \\ \\ =36 \end{gathered}[/tex]So, there are 36 words.
If Jenna saves $20 buying an item for 40 percent off the regular price, then what were the regular price and the sales price?
Solution
For this case we can create the following proportional rule:
[tex]\frac{20}{100-40}=\frac{x}{100}[/tex]For this case x = original price
Then solving for x we have:
[tex]x=100\cdot\frac{20}{60}=33.33[/tex]Then the original price is 33.33$
use the graph to determine which the ordered pair is a solution of the equation y equals negative X over 3 - 1
(3, - 2)
1) As the rule of the function has been given to us. Let's find out which point fits in the Solution for:
y=-x/3 -1
As we can see, the y-intercept is b=-1
3) So, (3, - 2) is the solution. Since (3, -2) belongs to the blue line
Checking algebraically
y=-x/3 -1
-2= -3/3 -1
-2 = -2 TRUE!
-
=
Let y² = x² + sin(xy). Find using implicit differentiation.
By using implicit differentiation, we get dy/dx=(2x+cos(xy)y)/(-xcos(xy)+2y)
What is implicit differentiation?
Implicit differentiation is the process to finding the derivative of the implicit function.
We have given,
y^2=x^2+sin(xy)
Differentiate with respect to x, and using product rule
2y dy/dx=d/dx(x^2+sin(xy))
2y dy/dx=(dx^2)/dx+(dsin(xy))/dx
2y dy/dx=2x+cos(xy)(d(xy))/dx
2y dy/dx=2x+cos(xy)[y+x dy/dx]
2y dy/dx=2x+ycos(xy)+xcos(xy)dy/dx
2y dy/dx-xcos(xy) dy/dx=2x+ycos(xy)
On simplification, we get
dy/dx=(2x+xcos(xy))/(-xcos(xy)+2y)
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The telephone company offers two billing plans for local calls. Plan 1 charges $30 per month for unlimited calls and Plan 2 charges $15 per month plus $0.03 per call.
a. Use an inequality to find the number of monthly calls for which Plan 1 is more economical than Plan 2 .
b. Explain the meaning of the answer to part a.
The fixed $30 unlimited calls charge for Plan 1 and the initial charge as well as a charge per call of $0.03 calls in Plan 2 gives;
a. The inequality that indicates the number of calls for which Plan 1 is more economical than Plan 2 is presented as follows;
30 > 15 + 0.03•x
Which gives;
x > 500
b. The meaning of the inequality, in part a. is that Plan 1 is more economical than Plan 2 when more than 500 calls are made
What is an inequality?An inequality makes a comparison between two values that are not equal.
The given parameters are;
The billing plan for Plan 1 is presented as follows;
Charges, C = $30
The charges of the billing plan for Plan 2 is presented as follows;
C = $15 + $0.03×xWhere;
x = The number of calls made per month
a. The inequality that can be used to find the number of monthly calls for which Plan 1 is more economical than Plan 2 is found as follows;
At the start of registration for each plan, we have;
Cost of Plan 1 = $30
Cost of Plan 2 = $15 + $0.03 × 0 = $15
Therefore, Plan 2 is initially more economical than Plan 1
At the point (or number of calls) at which the expenses for both plans are the same, we have;
30 = 15 + 0.03 × x
Which gives;
x = (30 - 15)/0.03 = 500From the above equation, we have that after 500 calls, the expenses of both plans will be the same
The inequality that gives the number of calls for which Plan 1 is more economical than Plan 2 is therefore;
30 > 15 + 0.03•x
Which gives;
x > 500b. The meaning of the inequality, x > 500 is that Plan 1 is becomes more economical than Plan 2 when a person makes more than 500 calls in a month
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