The amount that Ethan pays for the video game is 47.988.
How to calculate the value?From the information illustrated, it should be noted that it was stated that Ethan buys video games for 39.99 sale on 20% tax.
In this case, the amount that he will pay will be:
= Original amount + Tax
= 39.99 + (20% × 39.99)
= 39.99 + 7.998
= 47.988
The amount is 47.988.
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Complete question
Ethan buys vidio games for 39.99 sale on 20% tax how much ethan payed
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
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.
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
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
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
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
There is a population of 2,363 bacteria in a colony. If the number of bacteria doubles every 157 minutes, what will the population be 314 minutes from now?
9452
Explanation
an exponential function is given by:
[tex]\begin{gathered} y=a(b)^x \\ \text{where a is the initial amount} \\ b\text{ is the rate of change} \\ x\text{ is the time} \end{gathered}[/tex]so
Step 1
Set the equations
a) initial population = 2363
time=0
replace
[tex]\begin{gathered} y=a(b)^x \\ 2363=a(b^0) \\ 2363=a\cdot1 \\ 2363=a \end{gathered}[/tex]b) If the number of bacteria doubles every 157 minutes
[tex]\begin{gathered} (2363\cdot2)=2363(b^{157}) \\ (2363\cdot2)=2363(b^{157}) \\ 4726=2363b^{157} \\ \text{divide both sides by }2363 \\ \frac{4726}{2363}=\frac{2363b^{157}}{2363} \\ 2=b^{157} \\ 2^{(\frac{1}{157})}=(b^{157})^{\frac{1}{157}} \\ 1.00442471045\text{ =b} \end{gathered}[/tex]so, the function is
[tex]y=2363(1.00442471045)^x[/tex]Step 2
what will the population be 314 minutes from now?
Let
time=x =314
replace
[tex]\begin{gathered} y=2363(1.00442471045)^x \\ y=2363(1.00442471045)^{314} \\ y=2363\cdot4 \\ y=9452 \end{gathered}[/tex]therefore, the answer is
9452
I hope this helps you
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]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.
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
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
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.
Find the absolute change and the relative change in the following cases.The number of refugees in the world increased from 8.7 million in 2005 to 16.1 million in 2015.
absolute change is determined by the absolute value of the subtraction of the number of refugees in both years:
absolute change = | 16.1 million - 8.7 million | = 7.4 million
Relative change is given by the quotient between final value and initial value, just as follow:
relative change = final value / initial value
= 16.1 million / 8.7 million
= 1.85
Hence, the absolute change is 7.4 million and relative change is of 1.85
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.
20.Dilate Point B by a scale factor of 1/2Va) (1.5,-4)c) (-1,-1.5)b) (-1.5,1)d) (-2,-2)
the coordinate of point B is (-3,2)
In order to dilate the point with a scale factor of 1/2 we need to multiplicate the scale factor by the coordinate-x and the coordinate-y
coordinate x
[tex]-3\cdot\frac{1}{2}=-1.5[/tex]coordinate y
[tex]2\cdot\frac{1}{2}=1[/tex]the coordinate dilate is
B'(-1.5,1)
the correct answer is b
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
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
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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Given ST is tangent to circle Q, find the value of r
Given the figure of the circle Q
As shown, ST is tangent to circle Q
So, ST is perpendicular to the radius QS
So, the triangle QST is a right-angle triangle
We can apply the Pythagorean theorem where the legs are QS and ST
And the hypotenuse is QT
The side lengths of the triangle are as follows:
QS = r
ST = 48
QT = r + 36
So, we can write the following equation:
[tex]\begin{gathered} QT^2=QS^2+ST^2 \\ (r+36)^2=r^2+48^2 \end{gathered}[/tex]Expand then simplify the last expression:
[tex]\begin{gathered} r^2+2*36r+36^2=r^2+48^2 \\ r^2+72r+1296=r^2+2304 \end{gathered}[/tex]Combine the like terms then solve for (r):
[tex]\begin{gathered} r^2+72r-r^2=2304-1296 \\ 72r=1008 \\ \\ r=\frac{1008}{72}=14 \end{gathered}[/tex]So, the answer will be r = 14
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.
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]
What is the solution to -4y=28 please explain
You have the equation -4y=28
To solve this equation you need to clear the value of the unknown variable y, meaning, you have to simplfy the equation until you reach y=
For this, since y is multiplied by -4 you have to divide it by -4 to leave y alone, and what you do in one side of the equation must be done to the other side to keep the equality:
[tex]\begin{gathered} -4y=28 \\ \frac{-4y}{-4}=\frac{28}{-4} \\ y=-7 \end{gathered}[/tex]The value of y=-7
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]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
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.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]Gordon works for a graphic design firm and is creating a label for a food truck vendor. The vendor specializes in finger food and wants to sell food in right conical containers so that they are easy for people to hold. To complete his label, Gordon needs to collect several different measurements to ensure that the label he designs will fit the surface of the container. Gordon has been told that the containers have a diameter of 4 inches and a height of 6 inches.
Part A
Find out the slant height of the cone
Applying the Pythagorean Theorem
AC^2=AB^2+BC^2
we have
AC ----> slant height
AB=4/2=2 in
BC=6 in
substitute given values
AC^2=2^2+6^2
AC^2=40
AC=2√10 in
Part B
Find out the measure of the angle formed between the base and the slant height
we have that
tan( by opposite side divided by adjacent side
tan(mm
Part C
see the figure below to better understand the problem
we have that
AC and DC are slant height
triangle ADC is an isosceles triangle
because AC=DC
that means
mmmmthe answer part C is 36.86 degrees
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.
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.
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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