Let:
t = time spent as tutor
w = time spent walking dogs
Angel's parents want him to work for no more than 18 hours per week, so:
t + w < 18
Besides, He tutors for $20 per hour and walks dogs for $6 per hour and He wants to make at least $250, so:
20t + 6w ≥ 250
Beatrice invests $100 at 7% per year simple interest. i) Show that after 20 years, Beatrice has $240.
Answer:
P(1+rY) (r=Interest in Decimal Form) (Y=Number of years investing)
Step-by-step explanation:
The expression you want to use for simple interest is P(1 + rY), where r = the interest (in decimal, so 0.07) and Y = the number of years you are investing.
100(1+(0.07)(20))
This turns into
100(1+1.4)
100(2.4)
And with simple multiplication (100 x 2.4) you would receive 240 as an answer.
Hope that helps.
A binomial experiment consists of 18 trials. The probability of success on trial 11 is 0.79. What is theprobability of success on trial 15?0.790.280.610.460.560.72
Answer:
0.79
Explanation:
Given a binomial experiment with 18 trials; and
[tex]P(\text{ success on trial 11\rparen}=0.79[/tex]By the conditions required for a binomial experiment, the probability of success (or failure) remains the same throughout the experiment and for each and every trial.
Therefore:
[tex]P(\text{ success on trial 15\rparen}=0.79[/tex]The answer is 0.79
Find the image of the given point
under the given translation.
P(-8, 2)
T(x, y) = (x - 5, y + 4)
P' = ([?], [])
The image of the given point under the given translation is P' = (-13,6).
Given:
P(-8, 2)
Translation T(x, y) = (x - 5, y + 4).
Translation:
In translation notation, the first number represents how many units in the x direction, the second number, how many in the y direction. Both numbers tell us about how far and in what direction we are going to slide the point.
P'(x,y) = (x - 5 , y + 4)
= (-8-5 , 2+4)
= (-13,2+4)
= (-13,6)
Therefore The image of the given point under the given translation is P' = (-13,6).
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Suppose you are riding in a roller coaster which
follows the curve in the graph and when you reach the point
(1.1) your hat falls off. This curve is defined by the equation
23 + 43
=2y. Find an equation of the line that the hat will
follow if you ignore gravity and air resistance.
x + y = 2 is the equation of the line that the hat will follow if we ignore the gravity and air resistance.
Given, we are riding in a roller coaster which follows the curve in the graph and when we reach the point (1 , 1) our hat falls off.
Now, we have to find the equation of the line that the hat follow,
The slope of the tangent to the curve x³ + y³ = 2xy is given by,
3x² + 3y²y' = 2y + 2xy'
at the point (1 , 1)
3 + 3y' = 2 + 2y'
y' = -1
Now, the slope of the line perpendicular to the tangent of the curve is,
-1
Now, the equation of the line that hat follows is,
(y - 1)/(x - 1) = -1
y -1 = 1 - x
x + y = 2
Hence, x + y = 2 is the equation of the line that the hat will follow if we ignore the gravity and air resistance.
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James deposits $12,500 in a simple interest account with an annual interestrate of 1.5%. After a few years, he notices that he has earned $1,687.50 ininterest. How long has James had this account?
Recall that the simple interest means that you will calculate interest only based on the initial deposit amount. This means that the generated interests do not generate any interests.
To find the number of years James has had this account, we will first find a formula for the amount available in the account each year.
At year 0, James deposits 12500. So, at year 0 the account has 12500
At year 1, James earns 1.5% over the 12500. So we add to what we had at year 0, the interest. That is
[tex]12500+\text{ 12500}\cdot i[/tex]where i is the interest annual rate of 1.5%.
At year 2, James earns 1.5% over 12500 again. So we add this value to what we had at year 1, so at year 2 he has
[tex]12500+12500\cdot i+12500\cdot i\text{ = 12500+12500}\cdot2\cdot i[/tex]Finally, at year 3, James earns another 1.5% over the 12500. So we add this value to what he had at year 2, so he has
[tex]12500+12500\cdot2\cdot i+12500\cdot i\text{ = 12500+12500}\cdot3\cdot i[/tex]In general, from this we can see a pattern. At year n, the amount available would be
[tex]12500+12500\cdot i\cdot n\text{ = 12500}\cdot(1+i\cdot n)[/tex]In this formula the amount of interest is given by the expression
[tex]12500\cdot i\cdot n[/tex]We are told that this amount is 1687.5. So we have the following equation
[tex]12500\cdot i\cdot n=1687.5[/tex]so, if we divide both sides by 12500*i, we get
[tex]n=\frac{1687.5}{12500\cdot i}[/tex]we know that i=1.5%. = 0.015. So we have
[tex]n=\frac{1687.5}{12500\cdot0.015}=9[/tex]so James has had the account for 9 years.
Hi, can you help me answer this question please, thank you!
Given information:
[tex]\begin{gathered} H_0\colon\mu_1=\mu_2 \\ H_a\colon\mu_1<\mu_2 \end{gathered}[/tex]n1=12
Mean x1=75.4
SD1=9.7
n2=19
Mean x2=83.3
SD2=17.8
significance level alfa=0.02
To find the test statistic let's use the formula:
[tex]undefined[/tex]Sebastian used difference of squares to factor the expression x^4– 16. His work is shown below. His teacher says that he did not "factor completely."How would you explain to Sebastianwhat he needs to do to completely factorthis expression?
To factor properly this expression, we need to use the next expression for the product of the difference of two squares as follows:
[tex]a^2-b^2=(a+b)\cdot(a-b)[/tex]Since the squares are:
[tex](x^2)^2-(4)^2=(x^2+4)(x^2-4)[/tex]We can also see that we have another difference of two squares in the last part of the expression:
[tex]undefined[/tex]Three time a number is two times the difference of that number and one
Please help. Write an algebriac expression
Answer:
[tex]3x = 2(x - 1)[/tex]
Instructions: Find the surface area of each figure. Round your answers to the nearest tenth, if necessary. 7.5 km. 9 km. 9 km. km² Surface Area:
We can split this prism into 5 planar figures: 1 square and 4 equal triangles. The area of the square is given by
[tex]\begin{gathered} A_{\text{square}}=L^2 \\ A_{\text{square}}=9^2 \\ A_{\text{square}}=81km^2 \end{gathered}[/tex]On the other hand, the area of one triangle is given by
[tex]\begin{gathered} A_{\text{triangle}}=\frac{1}{2}\text{base}\times height \\ A_{\text{triangle}}=\frac{1}{2}9\times7.5 \\ A_{\text{triangle}}=33.75km^2 \end{gathered}[/tex]Then, the surface area S is given by
[tex]S=A_{\text{square}}+4\cdot A_{\text{triangle}}[/tex]By substituting our last results, we have
[tex]\begin{gathered} S=81+4\times33.75 \\ S=216km^2 \end{gathered}[/tex]then, the answer is 216 square kilometers
Consider the following functions.f(x) = x + 4 and g(x) = x - 7=Step 2 of 4: Find (f - 3)(x). Simplify your answer.Answerf-8)(x) =
Solution
[tex]\begin{gathered} f(x)=x+4 \\ g(x)=x-7 \end{gathered}[/tex]Now
[tex]\begin{gathered} (f-g)(x)=x+4-(x-7) \\ (f-g)(x)=x+4-x+7 \\ (f-g)(x)=11 \\ \end{gathered}[/tex]The final answer
[tex]11[/tex]Lloyd is working a problem on the board in his math class. He needs to simplifythe expression below.(2x-3) + (2x*- 3x) – (3x*- 5).What should he write as his answer?
Answer:
-x² - x + 2
Step-by-step explanation:
We are given the following expression:
(2x-3) + (2x²- 3x) – (3x²- 5).
To simplify, we first need to remove the parenthesis. If there is a negative sign before the parenthesis, we change the signal of everything that is inside(+ goes to -, - goes to +). So
(2x-3) + (2x²- 3x) – (3x²- 5) = 2x - 3 + 2x² - 3x - 3x² + 5
Now we need to combine the like terms:
With x²: 2x² - 3x² = -x²
With x: 2x - 3x = -x
Independent: -3 + 5 = 2
Now adding these terms, we get the simplified expression, which is:
-x² - x + 2
Kyle has 20 gallons of gasoline to use for his snow plowing business. He uses gasoline in his snow plow at a constant rate. Let a represent the
number of driveways plowed and y represent the amount of gas remaining. Look at the graph of the function. Construct a function for this
scenario. Assume he must complete a driveway once he starts it.
20
10
0
Part A
10
20
30
What is the equation of the line?
The required equation of the line is y = -(1/2)x + 20 which represents the given function in the shown graph.
Let a represent the number of driveways plowed and y represent the amount of gas remaining.
The graph of the function is given in the question
As per the given function, we take two points (0,20), and (40,0)
The required equation of the line will be as:
y - 20 = [(0 -20)/40-0)](a-0)
y - 20 = -(20/40)a
y - 20 = -(1/2)a
y = -(1/2)a + 20
Therefore, the required equation of the line is y = -(1/2)x + 20.
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The five‐number summary of a distribution consists of(a) mean, median, standard deviation, and two quartiles.(b) minimum, maximum, mean, median, and standard deviation. (c) minimum, maximum, median, and two quartiles(d) mean, standard deviation, correlation, and two quartiles
The five-number summary of a distribution consists of
1)The minimum(smallest observation)
2)The maximum ( Largest observation)
3)median
4)Two quartiles( The first quartile and the third quartile)
That is option C
How do you graph y= -1/2x
Step-by-step explanation: move down 1 and right 2 because it has to be a negative slope.
Answer: See attached, or read below.
Step-by-step explanation:
First, we see there is no b value, so there is no y-intercept. The line will intercept the graph at (0, 0), also known as the origin.
Next, we see a negative slope of -1/2. This means, starting at the origin, we will move down one unit and right two. Then repeat. Lastly, draw a straight line through all three points for our graph.
5x+4=x+44 solve for x
5x + 4 = x + 44
x is adding on the right, then it will subtract on the left
4 is adding on the left, then it will subtract on the right
5x - x = 44 - 4
4x = 40
4 is multiplying on the left, then it will divide on the right
x = 40/4
x = 10
A rectangle has a perimeter of 14 cm what’s the dimensions of the rectangle
The formula for determining the perimeter of a rectangle is expressed as
Perimeter = 2(lengthe + width)
Given that the perimeter = 14, it means that
2(lenght + width) must be equal to 14
Looking at the options,
2(1 + 6) = 14
2(2 + 5) = 14
2(3 + 4) = 14
2(4 + 3) = 14
2(5 + 2) = 14
2(6 + 1) = 14
Thus, the correct options are A, B, C, D, E, F
Which choices are equations for the line shown below? Check all that apply.(-2,5) 51(2-3)A. y + 3 = -2(x-2)B. y-5= -2(x + 2)O C. y = 2x + 1I D. y=-0.5x + 1E. y-5--2(x-2)OF. y=-2x + 1
Solution
For this case we have two points given :
(-2,5) and (2,-3)
We can find the slope on this way:
[tex]m=\frac{-3-5}{2-(-2)}=-2[/tex]And the intercept would be:
5 = -2(-2)+b
5 = 4 +b
b= 1
Then the original equation is:
y= -2x+1
And we need to find equivalent equations so we can analyze one by one the options like this:
A. y+3 = -2(x-2)
y+3 = -2x+4
y =-2x+1
B. y-5 = -2(x+2)
y-5 =-2x-4
y = -2x +1
C. y=2x+1
D. y= -0.5x +1
E. y-5 = -2(x-2)
y-5 = -2x +4
y= -2x+9
Then the correct options are A and B
This one is simple But I dont exactly know whats a function
ANSWER
B. False
EXPLANATION
We want to identify if the statement is true or false.
A function is a type of relation in which each input value is mapped directly to only one output value. In other words, each value of x has only one value of y.
To identify the graph of a function, if a vertical line can be drawn at any value of x such that it connects more than one point on the graph, then, the graph does not represent a function.
From the given graph, we see that a vertical line can be drawn to touch more than one point at several values of x.
This implies that the graph does not represent a function, hence, the statement is false.
The answer is option B.
Perimeter of a plecewise rectangular figureFind the perimeter of the figure below. Notice that one side length is not givenAssume that all intersecting sides meet right angles,Be sure to include the correct unit in your answer.6 yd8 ydydyd13 yd9 ydx515 yd
The perimeter is the sum of all sides.
You can observe in the figure that one side length is missing, but we can find it by subtraction.
[tex]13yd-8yd=5yd[/tex]Once we have all side lengths, we can sum them.
[tex]\begin{gathered} P=13yd+6yd+8yd+9yd+5yd+15yd \\ P=56yd \end{gathered}[/tex]Therefore, the perimeter of the figure is 56 yards.3) Mary made 1/5 of a batch of cookies in 1/10 of an hour. How many batches of cookies can she make in one hour?
Given in the scenario:
a.) Mary made 1/5 of a batch of cookies in 1/10 of an hour.
Let's determine how many batches of cookies can she make in one hour.
Step 1: Let's convert the given into a ratio and proportion.
Mary made 1/5 of a batch of cookies in 1/10 of an hour = 1/5 : 1/10
At x = number of batches of cookies in one hour, we get = x : 1
Step 2: Let's determine the value of x.
[tex]\frac{\frac{1}{5}}{\frac{1}{10}}\text{ = }\frac{x}{1}[/tex][tex](1)(\frac{1}{5})\text{ = (x)(}\frac{1}{10})[/tex][tex]\frac{1}{5}\text{ = }\frac{1}{10}x[/tex][tex](1)(10)\text{ = (1)(5)(x) }\rightarrow\text{ 10 = 5x}[/tex][tex]\frac{5}{5}x\text{ = }\frac{10}{5}[/tex][tex]\text{ x = 2}[/tex]Therefore, Mary can make 2 batches of cookies in one hour.
Which of the following functions shows the quadratic parent function,
Given the function f(x);
[tex]f(x)=x[/tex]When the function is flipped across the x-axis, we'll have the sign reversed.
So, the new function formed is;
[tex]undefined[/tex]Suppose you invested $4,500 and it grew by 4% every year for 30 years. How much would this investment be worth after 30 years?
Answer:
a) 14,595.29
Explanation:
We'll use the below compound interest formula to solve the given problem;
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where A = future amount
P = initial amount = $4500
r = interest rate in decimal = 4/100 = 0.04
n = number of compounding periods = 1
t = time period = 30 years
Let's go ahead and substitute the above values into our formula and solve for A;
[tex]\begin{gathered} A=4500(1+\frac{0.04}{1})^{1\times30} \\ A=4500(3.24339751003) \\ A=14,595.29 \end{gathered}[/tex]We can see from the above that the investment would be worth $14,595.29 after 30 years.
which choice represents the best rational approximation for 15 ?es)A)2B)2.2C)2.5D)2.7
ANSWER:
STEP-BY-STEP EXPLANATION:
[tex]undefined[/tex]Hello, I am currently very stuck with this problem and I am unsure as to how I would solve it.
We have the equation
[tex]20y=x^2-10-15[/tex]Let's complete the square, to do it let's add and subtract 25 on the right side
[tex]\begin{gathered} 20y=x^2-10-15+25-25 \\ \\ 20y=(x-5)^2-15-25_{} \\ \\ 20y=(x-5)^2-40 \\ \\ \end{gathered}[/tex]Now we can have y in function of x
[tex]\begin{gathered} y=\frac{1}{20}(x-5)^2-2 \\ \\ \end{gathered}[/tex]Now we can already identify the vertex because it's in the vertex form:
[tex]y=a(x-h)+k[/tex]Where the vertex is
[tex](h,k)[/tex]As we can see, h = 5 and k = -2, then the vertex is
[tex](5,-2)[/tex]Now we can continue and find the focus, the focus is
[tex]\mleft(h,k+\frac{1}{4a}\mright)[/tex]We have a = 1/20, therefore
[tex]\begin{gathered} \mleft(5,-2+5\mright) \\ \\ (5,3) \end{gathered}[/tex]The focus is
[tex](5,3)[/tex]And the last one, the directrix, it's
[tex]y=k-\frac{1}{4a}[/tex]Then
[tex]\begin{gathered} y=-2-5 \\ \\ y=-7 \end{gathered}[/tex]Hence the correct answer is: vertex (5, -2); focus (5, 3); directrix y = -7
write an equation for the n th term of the arithmetic sequence 23, 16, 9, 2, ... .Then find a25?
Given the sequence:
23, 16, 9, 2
Use the arithmetic sequence formula:
[tex]a_n=a_1+(n-1)d[/tex]Where
an = nth term
a1 = first term
n = number of terms
d = common difference
d = a2 - a1 = 16-23 = -7
Since d = -7, let's find the equation for the nth term.
[tex]\begin{gathered} a_n=23+(n-1)-7 \\ a_n=23+n(-7)-1(-7) \\ a_n=23-7n+7 \\ \text{Combine like terms} \\ a_n=-7n\text{ +23}+7 \\ \\ a_n=-7n+30 \end{gathered}[/tex]The equation for the nth term is:
[tex]a_n=-7n+30[/tex]Let's find the 25th term, a25:
Substitute n for 25 and evaluate
[tex]\begin{gathered} a_{25}=-7(25)+20 \\ \\ a_{25}=-175+30 \\ \\ a_{25}=-145 \end{gathered}[/tex]ANSWER:
[tex]\begin{gathered} a_n=-7n+30 \\ \\ \\ a_{25}=-145 \end{gathered}[/tex]Using the function f(x)=-x+7, find f(1).
For this type of questions you just have to substitute x by the given number ( in this case 1) anywhere x shows in the equation
f(1)= -1+7 = 6
Jamal works as a computer network technician and last year they paid $4061 in social security tax. what was their annual income last year? Take the tax percentage as 6.2%
We know that Jamal paid 4061 of taxes and
[tex]4061=P\cdot(0.062)[/tex]where P is Jamal's income and 6.2% correspond to 0.062. Now, we must isolate P. It yields,
[tex]\begin{gathered} P=\frac{4061}{0.062} \\ P=65500 \end{gathered}[/tex]this means that Jamal's income was $65500 last year
write an equation for a parabola opening upward, shifted 6 units right, and three units down
y = (x-6)²-3
1) Let's write a transformation described as it is, algebraically speaking.
• opening upward, (a >0)
,• shifted 6 units right, (-6)
,• and three units down -3
2) Starting from the parent function y=x², then we can write:
y = (x-6)²-3
Notice that the horizontal shift is within the parentheses with a swapped sign. And outside that -3 indicating the vertical shift.
I have started number 7 but am not so sure about my answer just wanted to see if I was doing the problem right way.
To get a probability in a given set, we need to count the events we want to happen and divide by the total possibilities.
a) Here, we have a set that goes from 1 to 12, so there is 12 possibilities. We want to pick a prime number, so we need to count how many primes we have in this set.
1 is not prime.
Also, 4, 6, 8, 9, 10 and 12 are not primes.
So, we have the primes: 2, 3, 5, 7 and 11. There are 5.
So, the probability will be:
[tex]P=\frac{5}{12}\approx0.42[/tex]b) Assuming the die are 6-sided going from 1 to 6, we can obtain the numbers from 1 + 1 = 2 until 6 + 6 = 12. However, there are differento number of possibilities. We still are looking for 2, 3, 5, 7 and 11, however now we have a total of 6 times 6 possibilities:
[tex]C_T=6\cdot6=36[/tex]And we have to calculate the combinations for each prime and add them.
2: there is only 1 + 1, so:
[tex]C_2=1[/tex]3: We can do 1 + 2 and 2 + 1, so there are 2:
[tex]C_3=2[/tex]5: We have 1 + 4, 2 + 3, 3 + 2 and 4 + 1, so 4 possibilities:
[tex]C_5=4[/tex]7: We have 1 + 6, 2 + 5, 3 + 4, 4 + 3, 5 + 2 and 6 + 1, 6 possibilities:
[tex]C_7=6[/tex]11: We have 5 + 6 and 6 + 5 only. 2 possitilities:
[tex]C_{11}=2[/tex]In total, we have:
[tex]C_2+C_3+C_5+C_7+C_{11}=1+2+4+6+2=15_{}[/tex]So, the probability will be:
[tex]P=\frac{15}{36}\approx0.42[/tex]It ended up being the same.
Given the figure above, determine the angle that is an alternate interior angle with respect to
Explanation
When two lines are crossed by another line (called the Transversal): Alternate Interior Angles are a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal.
so, the angle is
[tex]\measuredangle3[/tex]I hope this helps you