The can is made up of aluminium.
So the area of the can must be equal to the area of the Aluminium sheet.
The can is in the form of a cylinder with diameter (d) 5.3 cm, and height (h) 12 cm.
Then its area is calculated as,
[tex]\begin{gathered} A=\pi d(\frac{d}{2}+h) \\ A=\pi(5.3)(\frac{5.3}{2}+12) \\ A=243.9289 \\ A\approx244 \end{gathered}[/tex]Thus, the area of the Aluminium sheet required is 244 square centimeters.
Determine which is the better investment 3.99% compounded semi annually Lee 3.8% compounded quarterly round your answer 2 decimal places
Remember that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]In the 3.99% compounded semiannually
we have
r=3.99%=0.0399
n=2
substitute
[tex]\begin{gathered} A=P(1+\frac{0.0399}{2})^{2t} \\ \\ A=P(1.01995)^{2t} \end{gathered}[/tex]and
[tex]\begin{gathered} A=P[(1.01995)^2]^t \\ A=P(1.0403)^t \end{gathered}[/tex]the rate is r=1.0403-1=0.0403=4.03%
In the 3.8% compounded quarterly
we have
r=3.8%=0.038
n=4
substitute
[tex]\begin{gathered} A=P(1+\frac{0.038}{4})^{2t} \\ A=P(1.0095)^{2t} \\ A=P[(1.0095)^2]^t \\ A=P(1.0191)^t \end{gathered}[/tex]the rate is r=1.0191-1=0.0191=1.91%
therefore
the 3.99% compounded semiannually is a better investmentThe start of a quadratic
sequence is
8, 18, 30, 44, 60, …
What is the nth term rule for this sequence?
Answer:
The correct option is D
98
The general term of the sequence is n(n+7)
i need help, im confused
Answer:
2
Step-by-step explanation:
Joe bought 8 comic books for $36. How much does 1 comic book cost?
Answer:
1 comic book costs $4.5
Explanation:
Given that 8 comic books cost $36
To know how much 1 comic book costs, let x be the cost of 1 comic book, then, we have:
8 comic books = $36
1 comic book = x
Then we have the equation
8x = 36
where we can solve for x
Divide both sides by 8
8x/8 = 36/8
x = 4.5
Therefore, 1 comic book costs $4.5
an object’s velocity at time t is given by v(t) = –2 sin t. Let s(t) represent the object’s position at time t. If s(0) = 0, then s(t) =
GIVEN
The function of the object's velocity is given as follows:
[tex]v(t)=-2\sin t[/tex]Also given:
[tex]s(0)=0[/tex]SOLUTION
To get the position's function (s(t)), the velocity function needs to be integrated:
[tex]s(t)=\int v(t)dt[/tex]Therefore:
[tex]\begin{gathered} s(t)=\int(-2\sin t)dt \\ \mathrm{Take\:the\:constant\:out}: \\ s(t)=-2\cdot\int\sin\left(t\right)dt \\ \mathrm{Use\:the\:common\:integral}:\quad \int \sin \left(t\right)dt=-\cos \left(t\right) \\ s(t)=-2\left(-\cos\left(t\right)\right) \\ \mathrm{Simplify}\text{ and add a constant to the solution} \\ s(t)=2\cos\left(t\right)+C \end{gathered}[/tex]Recall that s(0) = 0. Therefore:
[tex]\begin{gathered} s(0)=2\cos(0)+C=0 \\ \therefore \\ C=-2 \end{gathered}[/tex]Hence, the position function is:
[tex]s(t)=2\cos t-2[/tex]The THIRD OPTION is correct.
Write a SITUATION that can be represented with this graph. Not an equation.
We need to think of something that will cool down 10 degrees in 5 hours to be more realistic. You may say that this graph describes the temperature profile of a fermentation broth after it is heated to 82 degrees is left on the tank to cool down to room temperature.
Which form most quickly reveals the vertex? choose one answer: a. m(x)=2(x+4)^2-8 b. m(x)=2(x+6)(x+2)c. m(x)=2x^2+16x+24what is the vertex? vertex=(___,___)
The vertx from of the quadratic function is
[tex]f(x)=a(x-h)^2+k[/tex]Where
(h, k) are the coordinates of the vertex
a is the coefficient of x^2
By comparing this form with the answers
a.
[tex]m(x)=2(x+4)^2-8[/tex]a = 2
h = -4
k = -8
The vertex point is (-4, -8)
The quickly reveals the vertex is answer a
....................
Answer:
oop
Step-by-step explanation:
oh
Determine if the figures below are similar. If they are, identify the similarity statement.E70F50GK5060L
We have the following triangles:
And we need to determine if they are similar by identifying the similarity statement.
To determine that similarity statement, we can proceed as follows:
1. Check the measures of the internal angles of the triangles. We need to remember that the sum of the internal angles of a triangle is 180 degrees. Then we have:
2. We can see that to find the angles in the first triangle, EFG, and in the second triangle, JKL, we have that the sum of the three angles must be 180 degrees, and we obtained the other angles as follows:
[tex]\begin{gathered} \text{ Triangle EFG}\rightarrow50+70+x=180 \\ \\ x=180-(50+70)=180-120=60 \\ \\ \text{ Triangle JKL}\rightarrow50+60+y=180 \\ \\ y=180-(50+60)=180-110=70 \end{gathered}[/tex]3. Then we can redraw the triangles as follows:
4. Now, since we can see that, at least, two of the angles of the triangles are congruent (then the third one is also congruent, that is, has the same measure), we also have that to prove that if two triangles are similar it is sufficient that two of the corresponding angles of one triangle are congruent to the two corresponding angles of the other triangle, and this is known as the Angle-Angle method for proving similar triangles, then we can conclude that:
Triangle EFG is similar to triangle JKL by the Angle-Angle method.
Therefore, in summary, we have that:
Triangle EFG is similar to Triangle JKL by Angle-Angle similarity
[tex]\text{ Triangle EFG \textasciitilde Triangle JKL by Angle-Angle similarity}[/tex]
[Last option]
A store is having a sale to celebrate President’s Day. Every item in the store is advertised as one- fourth off the original price. If an item is marked with a sale price of , what was its original price?
If the discount is one fourth off, it means the discount is 1/4 = 25% of the original price, so the final price will be 75% or 3/4 of the original price.
In order to find the original price, we just need to divide the final price by 3/4, this way we "remove" the discount.
For example, if the sale price is $75, the original price would be:
[tex]\text{original price}=\frac{75}{\frac{3}{4}}=75\cdot\frac{4}{3}=25\cdot4=100[/tex]So for a sale price of $75, the original price would be $100.
In general, for a discount of x%, the original price (given the sale price) can be calculated as:
[tex]\text{original price}=\frac{\text{sale price}}{1-\frac{x}{100}}[/tex]The band is selling T-shirts for $15.00 each. They make $5.00 profit from each shirt sold. Write an equation to represent the profit earned,y,for selling,x,number of shirts.
The equation to represent the profit earned y, for selling x, number of shirts is y = 5x.
Given that:-
Selling Price of T-shirt = $ 15
Profit earned per T-shirt = $ 5
We have to form an equation to represent the profit earned y, for selling x, number of shirts.
We know that,
Profit earned by selling 1 T-shirt = $ 5
Hence, profit earned by selling x T-shirts = 5*x
We know that,
Profit earned by selling x T-shirts = y
Hence, we can write,
y = 5x
Hence, the equation that represents the profit earned y, for selling x, number of shirts is y = 5x.
To learn more about equation, here:-
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Solve the given quadratic inequality. Write the answer in interval notation.
Find angle a in the taper shown,x = 9.342 inchesy = 6.692 inchesz = 2.952 inches
We need to find angle a in the figure.
We know that:
x = 9.342 inches
y = 6.692 inches
z = 2.952 inches
We can do so by finding the legs in the following triangle:
The adjacent leg is x. And the opposite leg is found by subtracting z from y, and then dividing the result by two (assuming the figure is symmetric):
[tex]\frac{y-z}{2}[/tex]Thus, we have:
[tex]\begin{gathered} \sin a=\frac{\text{ opposite leg}}{\text{ adjacent leg}} \\ \\ \sin a=\frac{\frac{y-z}{2}}{x} \\ \\ \sin a=\frac{\frac{6.692-2.952}{2}}{9.342} \\ \\ \sin a=\frac{1.87}{9.342} \\ \\ a=\arcsin\left(\frac{1.87}{9.342}\right) \\ \\ a\cong11.55\degree \end{gathered}[/tex]B 961 m Solve the triangle 40° 41 С b B= degrees minutes m (Round to the nearest whole number.) b = m (Round to the nearest whole number.)
To find the angle B we can use the propertie that sya that the sum of the internal angles of a triangle is equal to 180º so:
[tex]\measuredangle b+90º+40º,41^{\prime}=180[/tex]and we solve for angle b so:
[tex]\begin{gathered} \measuredangle b=180º-90º-40º,41^{\prime} \\ \measuredangle b=49º,19^{\prime} \end{gathered}[/tex]So B is equal to: 49 degrees and 19 minutes
So now to find a we can use the trigonometric identitie of sin so:
[tex]\begin{gathered} \sin (40.68)=\frac{a}{961} \\ a=961\cdot\sin (40.68) \\ a\approx626 \end{gathered}[/tex]and to find b we use the trigonometryc identitie of cos so:
[tex]\begin{gathered} \cos (40.68)=\frac{b}{961} \\ b=961\cdot\cos (40.68) \\ b\approx729 \end{gathered}[/tex]The histogram below shows the number of hurricanes making landfall in the United States for a period of 108 years. On average, there have been 1.72 hurricanes per year with a standard deviation of 1.4 hurricanes per year. Is the distribution approximately normal?
(A) No, the distribution is skewed to the right.
(B) No, the distribution is skewed to the left.
(C) Yes, the distribution has a single peak.
(D) Yes, the percentage of values that fall within 1, 2, and 3 standard deviations of the mean are close to 68%, 95%, and 99.7%, respectively.
Using the Empirical Rule, the correct option regarding the skewness of the distribution is given as follows:
(A) No, the distribution is skewed to the right.
What does the Empirical Rule state?The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is given as follows:
The percentage of scores within one standard deviation of the mean of the distribution is of 68%.The percentage of scores within two standard deviations of the mean of the distribution is of 95%.The percentage of scores within three standard deviations of the mean off the distribution is of 99.7%.In the context of this problem, the mean and the standard deviation are given as follows:
Mean: 1.72.Standard deviation: 1.4.A huge percentage is within one standard deviation of the mean, and the distribution is not symmetric, hence it is not normal.
Since most values are at the lower bounds of the histogram, the distribution is right skewed and option a is correct.
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Find the AreaA. 314.2 IN2B. 1256.6 IN2C. 31.4 IN2D. 62.8 IN2
Given:
Diameter = 20 in
Find-:
Area of circle
Explanation-:
The area of circle is:
[tex]A=\pi r^2[/tex]The radius of circle is:
[tex]r=\frac{D}{2}[/tex]Where,
[tex]\begin{gathered} r=\text{ Radius} \\ \\ D=\text{ Diameter} \end{gathered}[/tex]So the radius of given circle is:
[tex]\begin{gathered} D=20\text{ in} \\ \\ r=\frac{D}{2}\text{ in} \\ \\ r=\frac{20}{2}\text{ in} \\ \\ r=10\text{ in} \end{gathered}[/tex]The area of circle is:
[tex]\begin{gathered} A=\pi r^2 \\ \\ A=\pi(10)^2 \\ \\ A=100\pi \\ \\ A=314.159 \\ \\ A=314.2\text{ in}^2 \end{gathered}[/tex]So, the area of a circle is 314.2
Factor the quadratic expression2x²+x-62x+ +x-6= (Factor completely.)
2x² + x - 6
The coefficient of x² is 2 and the constant term is -6. The product of 2 and -6 is -12. The factors of -12 which sum 1 are -3 and 4 so:
2(2x - 3) + x(2x - 3)
Factor 2x - 3 from 2(2x - 3) + x(2x - 3):
(2x - 3)(x + 2)
What will be the coordinates of the vertex s of this parallelogram? Which answer choice should I pick A B C or D?
Answer:
A
Step-by-step explanation:
the opposite sides of a parallelogram are parallel
then QT is parallel to RS
Q → T has the translation
(x, y ) → (x + 2, y- 7 ) , so
R → S has the same translation from R (0, 3 )
S = (0 + 2, 3 - 7 ) → S (2, - 4 )
if 3x +6 = 18 what is 10x -2
38
1) Starting from the first equation
3x +6 = 18 Subtract 6 from both sides
3x = 18 -6
3x = 12 Divide both sides by 3
x =4
2) Since x =4, let's plug that into the second expression 10x -2 to find out "what is 10x -2"
10x -2 Replace x, by 4
10(4) -2 Effectuate the multiplication
40 -2
38
Hence, the answer is 38
can you please find the slope and the y intersept of the graph of the linear equation y= 4x-5
the slope of the linear equation is 4 and the y intercept is -5
Explantion:we apply the equation of line to find the slope and intercept
Equation of line is in the form: y = mx + c
where m = slope and c = y - intercept
comparing the given equation with the equation of line:
linear equation y= 4x-5
y = y
4x - 5 = mx + c
This means m = 4
4x = mx
m = 4
-5 = c
Hence, the slope of the linear equation is 4 and the y intercept is -5
The area of a rectangle is x2 – 8x + 16. The width of therectangle is x – 4. What is the length of the rectangle?-
To answer this question, we need to remember that the area of a rectangle is given by:
[tex]A_{\text{rectangle}}=l\cdot w[/tex]And we have - from the question - that:
[tex]A_{\text{rectangle}}=x^2-8x+16[/tex]And the width of the rectangle is:
[tex]w=x-4[/tex]If we factor the polynomial that represents the area, we need to find two numbers:
• a * b = 16
,• a + b = -8
And both numbers are:
• a = -4
,• b = -4
Since
• -4 * -4 = 16
,• -4 - 4 = -8
Therefore, we can say that:
[tex]x^2-8x+16=(x-4)(x-4)=(x-4)^2[/tex]Therefore:
[tex]l\cdot w=A_{\text{rectangle}}[/tex][tex]l=\frac{A_{rec\tan gle}}{w}[/tex]Then the length of the rectangle is:
[tex]l=\frac{x^2-8x+16}{x-4}=\frac{(x-4)(x-4)}{x-4}\Rightarrow\frac{x-4}{x-4}=1[/tex][tex]l=\frac{(x-4)}{(x-4)}\cdot(x-4)\Rightarrow l=x-4[/tex]In summary, therefore, the length of the rectangle is x - 4.
[tex]l=x-4[/tex][We can check this result if we multiply both values as follows:
[tex]A_{\text{rectangle}}=l\cdot w=(x-4)\cdot(x-4)=(x-4)^2_{}[/tex]And we already know that the area of the rectangle is:
[tex]x^2-8x+16=(x-4)^2[/tex].]
How much will it cost to buy a low fence to put all the way around the bed? The fencing material costs $0.59 per foot and can only be bought in whole numbers of feet.
To find the cost we first need to know how many feet of fence we need. To do this we add all the lengths of the sides:
[tex]6+6+8.5=20.5[/tex]Now, since we can only buy whole numbers of feet we need to buy 21 feets of fence, then the total cost is:
[tex]21\cdot0.59=12.39[/tex]Therefore the cost will be $12.39
Hello, a little confused on this section. Thanks for your help!
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
graph
Step 02:
notation for domain and range:
we must analyze the graph to find the solution.
graph:
The domain is reflected on the x-axis and the range is reflected on the y-axis.
Inequality / Agebraic:
D:
R:
Interval:
D:
R:
Set-Builder:
D:
R:
The graph of F(x), shown below, resembles the graph of G(x) = x^2 but it hasbeen stretched somewhat and shifted. Which of the following could be theequation of F(x)?
Solution
The final answer
Option C
35% of the employees in a company receive an incentive in the month of April. What is theprobability that among 4 employees chosen at random, all 4 do not receive the incentive inApril?
ANSWER :
0.1785
EXPLANATION :
35% will receive an incentive and (100% - 35% = 65%) will NOT receive an incentive.
So an employee has 65% chance of NOT receiving an incentive.
The probability that among 4 employees do not receive the incentive is :
[tex](0.65)^4=0.1785[/tex]What is the mean of 3x, 4x - 5 and 2x - 1?
Pablo Is choosing at random from a bag of colored marbles. The probability he will choose a red marble is1/9What are the odds in favor of him choosing a redmarble?
Given:
[tex]\text{The probability to choose a red marble=}\frac{1}{9}[/tex]The odds in favour of Pablo chosing a re marble is 1 : 8
an 8-foot ladder leaning against a wall makes an angle of elevation of 70 degrees with the ground how far up the wall is the ladder to the nearest Foot
The length of the ladder is L = 8 foot.
The angle of ladder with ground is 70 degree.
The ladder lean on the wall can be expressed as,
Determine height on the wall to which ladder is up on the wall.
[tex]\begin{gathered} \sin 70=\frac{h}{8} \\ h=0.9397\cdot8 \\ =7.51 \\ \approx8 \end{gathered}[/tex]So up the wall is the ladder is 8 foot.
I am trying to solve this equation using Synthetic Division. I got the answer wrong, I would like to see where I made a mistake.
The result for the division is:
[tex]2x^2+43x+865+\frac{17309}{x-20}[/tex]Explanation:Step 1: Write the coefficients of the numerator on the right-hand side, and the opposite of the constant term in the denominator on the left-hand side.
20..............2 || 3 || 5 || 9
..................2
Step 2: Multiply 20 by 2 and add the result to 3
20..............2.......................|| 3 || 5 || 9
..................2*20 = 40
....................2 || 3 + 40 = 43
Step 3: Multiply 43 by 20, and add the result to 5
20..............2 || 3 .........................|| 5 || 9
...................... 40.......20*43 = 860
....................2||43 .......5+860=865
Step 4: Multiply 865 by 20, and add the result to 9
20..............2 || 3 || 5 ..........................|| 9
...................... 40 ||860......20*865=17300
....................2||43||865...9 + 17300=17309
The coefficients are 2, 43, 865, 17309
The quotient is:
[tex]2x^2+43x+865[/tex]and the remainder is 17309
So, we can write:
[tex]2x^2+43x+865+\frac{17309}{x-20}[/tex]Caitlin and her family eat at at a restaurant. They spend $240 before tax. The restaurant charges them an additional 8% tax on their bill. Complete the two expressions that represent the total cost of the bill after the 8% tax is added to the bill. 240+ _______ x240240+_______Which 2 of these go in the blank?A.) 8B.) 0.08C.) 0.80D.) 19.20E.) 192F.) 259.20G.) 24
Answer:
B.) 0.08
D.) 19.20
Explanation:
The cost of the meal before tax = $240
Percentage added as tax = 8%
Therefore, the total cost of the bill after the 8% tax is added to the bill is:
[tex]\begin{gathered} 240+8\%\times240 \\ =240+\frac{8}{100}\times240 \\ =240+0.08\times240 \end{gathered}[/tex]If we simplify further, we have:
[tex]=240+19.20[/tex]