Answer:
Step-by-step explanation:
a hexagonal prism is made up of two bases that are hexagons and six faces that are rectangles.
Lateral surface area, LA = Perimeter × height
Perimeter = number of sides × length of each side
Perimeter, P = 6 × 10 = 60
LA = 60 × 12 = 720 units squared
Area of each base, B = 1/2a × perimeter
Where
a = apotherm
We would determine the length of the apotherm of each base of the prism by applying the formula,
a = s/[2tan(180/n)]
Where
s = length of each side = 10
n = 6 sides
a = 10/[2tan(180/6) = 10/[2tan30)
a = 8.66
B = 1/2 × 8.66 × 60 = 259.8
Total surface area = LA + 2B
Total surface area = 720 + 2 × 259.8 = 1239.6 units squared
An author published a book which was being sold online. The first month the author
sold 15800 books, but the sales were declining steadily at 5% each month. If this
trend continues, how many total books would the author have sold over the first 11
months, to the nearest whole number?
Answer:
7110 books
Step-by-step explanation:
5%*15800=0.05*15800=790
790*11=8690
15800-8690=7110
Therefore, 7110 books
Answer: 86,900
Step-by-step explanation:
I changed the 5% into decimal form and made it 0.5. Next, I multiplied 0.5 by 11, which gave me 5.5.
15,800 x 5.5 = 86,900
So, the author would’ve sold 86,900 books in the first 11 months.
(Sorry if wrong. Yeah I think I’m wrong now because I’m not even in high school. Just ignore this lol)
Two terms of an arithmetic sequence are a12=70 and a30=124. Write an explicit rule for the nth term.
An = ?
Answer:
The explicit formula is Tn = 34 + 3n
Step-by-step explanation:
The nth term of an arithmetic sequence can be represented using the formula
Tn = a + (n-1)d
where a is the first term , n is the number of terms and d is the common difference
For the 12 term(a12), n = 12
70 = a + (12-1)d
70 = a + 11d •••••••(i)
For the 30th term, n = 30
124 = a + (30-1)d
124 = a + 29d •••••••(ii)
Now, directly subtract equation i from ii, we have;
124-70 = (a-a) + (29d-11d)
54 = 18d
d = 54/18
d = 3
To get a , we substitute the value of d in any of the equations
let’s use the first
70 = a + 11d
substituting d = 3
70 = a + 11(3)
70 = a + 33
a = 70-33
a = 37
Thus the explicit formula for the nth term will be
Tn = a + (n-1)d
where a = 37 and d = 3
Tn = 37 + (n-1)3
Tn = 37 + 3n -3
Tn = 34 + 3n
Please help, and thanks in advance!
Answer:
c i believe sorry if its wrong
Step-by-step explanation:
Answer:
3. A.
4. 136
Step-by-step explanation:
3. Find the surface area:
2 * 1 = 2
3 * 2.2 = 6.6
2 * 3 = 6
3 * 1 = 3
2 + 6.6 + 6 + 3 = 17.6
4. Find the surface area:
5 * 7 * 2 = 70
6 * 4 = 24
7 * 6 = 42
70 + 24 + 42 = 136
A collar of Styrofoam is made to insulate a pipe. Find it's volume. That large R is to the outer rim. The smaller r us to the edge of the insulation. Use pi=3.14
Answer:
the volume of the pipe is 649.98 cubic inches.
Step-by-step explanation:
We have been given that a collar of Styrofoam is made to insulate a pipe. We are asked to find the volume of the given pipe.
We will use volume of hollow cylinder formula to solve our given problem.
[tex]\text{Volume of hollow cylinder}=\pi R^2h-\pi r^2h[/tex]
where,
R = Radius of external cylinder,
r = Radius of internal cylinder.
h = Height of cylinder.
substituting our given values in above formula, we will get:
[tex]\text{Volume of hollow cylinder}=\pi (5\text{ in})^2(\text{23 in})-\pi (4\text{ in})^2(\text{23 in})\text{Volume of hollow cylinder}=\text{23 in}\cdot 3.14 ((5\text{ in})^2-(4\text{ in})^2)\text{Volume of hollow cylinder}=\text{23 in}\cdot 3.14 (25\text{ in}^2-16\text{ in}^2)\text{Volume of hollow cylinder}=\text{23 in}\cdot 3.14 (9\text{ in}^2)\text{Volume of hollow cylinder}=649.98\text{ in}^3[/tex]
Therefore, the volume of the pipe is 649.98 cubic inches.
Designer Dolls found that its number of Dress-Up Dolls sold, N, varies directly with their advertising budget, A, and inversely proportional with the price of each doll, P. When $54,000 was spent on advertising and the price of the doll is $90, then 9,600 units are sold. Determine the number of dolls sold if the amount of advertising budget is increased to $144,000.
Answer:
25,600
Step-by-step explanation:
You can use the rule of three considering that the number of dolls sold varies directly with the advertising budget:
$54,000 → 9,600
$144,000 → x
[tex]x=\frac{144,000*9,600}{54,000}[/tex]
x=25,600
According to this, the number of dolls sold if the amount of advertising budget is increased to $144,000 is 25,600.
The number of dolls sold should be 25,600.
Given that,
When $54,000 was spent on advertising and the price of the doll is $90, then 9,600 units are sold.Based on the above information, the calculation is as follows:
[tex]= \$144,000 \times 9,600 \div \$54,000[/tex]
= 25,600
Therefore we can conclude that The number of dolls sold should be 25,600.
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At a restaurant, 40% of customers order tacos and 60% order fajitas. Of the customers that order tacos, 50% order a chicken tacos. Of the customers that order fajitas, 30% order chicken fajitas. What is the percentage of customers that order a chicken dinner (either chicken tacos or chicken fajitas)?
Answer:
38% order a chicken dinner
Step-by-step explanation:
40% order tacos. 50% of 40% order chicken tacos. 50% of 40% = 0.5 * 0.4 = 0.2 = 20% order chicken tacos.
60% order fajitas. 30% of 60% order chicken fajitas. 30% of 60% = 0.3 * 0.6 = 0.18 = 18% order chicken fajitas.
20% + 18% = 38% order a chicken dinner.
Correct answers only please!
To the nearest cent, how much interest will she earn in 2 years?
Use the formula B = p(1 + r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Answer:
$915.92
Step-by-step explanation:
i = p(1 + r)^t
i = $800(1 +.07)^2
i = $800(1.07)^2
$915.92
What are the domain and points of discontinuity of y= x-4/x^2+8x-20? What are the x and y intercepts?
Step-by-step explanation: To find the x-intercept, substitute in 0 for y and solve for x.
x-intercept(s): (2.30581496,0)
y-intercept(s): None
b) Write 25 x 10° in standard form.
Answer:
2.5x10^1
Step-by-step explanation:
When the first number goes down, add one to the 10's power
Answer:
2.5x10∧1
Step-by-step explanation:
Seventeen more than the product of a number and -3 is less than -29 plz answer
Answer:
-3x + 17 < -29
Step-by-step explanation:
Need help pls have no idea how to this
Answer:
The local minimum point of f(x) is at the point (-2,-2)
Step-by-step explanation:
the minimum point is located on the very bottom of the parabola!
so its cut off but its (-2,-2)
sorry I didnt see the 6,-2
so I am gussing the y-value is the minimum point so it should be -2....tell me if I am wrong but if your looking for a points it (-2,-2) if your looking for the value it would be -2
pls mark me brainliest
Teri has a bag of colored marbles. Five marbles are red, four are green, ten are blue, and one is white. Marbles are randomly selected out of the bag.
What is the probability of selecting a red marble and then a white marble without replacement?
Answer:
1/76
Step-by-step explanation:
Five marbles are red,
four are green,
ten are blue, and
one is white.
Sample space S= 5+4+10+1= 20
Probability of selecting a red Mable
Pr(red) = 5/20= 1/4
Probability of selecting a white Mable without replacement after the first selection
Pr(white) = 1/19= 1/19
the probability of selecting a red marble and then a white marble without replacement?
= 1/4*1/19= 1/76
A student is deriving the quadratic formula. Her first two steps are shown.
Step 1: –c = ax2 + bx
Step 2:
Which best explains or justifies Step 2?
Please consider the complete question.
A student is deriving the quadratic formula. Her first two steps are shown. Step 1: [tex]-c = ax^2 + bx[/tex]
Step 2: [tex]-c = a[x^2+\frac{b}{a}x][/tex]
Which best explains or justifies Step 2?
A. division property of equality
B. factoring the binomial
C. completing the square
D. subtraction property of equality
We can see that in step 2 student has factored the right side of equation.
The student factored our a from the right side of equation. To factor our a from right side, student has divide the bx term by a.
We can multiply and divide by same quantity in an equation.
[tex]-c = ax^2+a\cdot \frac{b}{a}x[/tex]
Now we can factor out a as:
[tex]-c = a(x^2+\frac{b}{a}x)[/tex]
Therefore, the 2nd step is known as factoring of binomial and option B is the correct choice.
Answer:
it b factoring a binomial on
Step-by-step explanation:
thats on edge
Find the parallelogram.
Answer:
area - 120 cm
Step-by-step explanation:
Answer:
A = 120 cm^2
P = 54 cm
Step-by-step explanation:
Area of parallelogram: = base * height
A = 15 cm * 8 cm = 120 cm^2
Perimeter of parallelogram = sum of lengths of sides
P = 15 cm + 15 cm + 12 cm + 12 cm = 54 cm
Gary needs to solve 120 problems by a certain day. He calculated, that to finish all the problems in time, he needs to solve 5 problems every day. But Gary's family is going on a trip, and for 4 days Gary will simply have no time to do math. How many problems will he need to be solving every day when he is not on a trip to still be done in time?
Answer:
To be done in time, he would need to solve 6 questions per day on the days that he is not on trip
Step-by-step explanation:
If he solves the problems 5 per day, the total number of days that would be required to finish solving the problem would be 120/5 = 24 days
Now, he has 4 free days which would be for a family trip. The number of questions that he would miss during those trip days will be 4 * 5 = 20 questions
Now since he wants to still finish on time, what is needed to be done is to share the 20 left overs amongst the 20 days which he has to work
This makes a total of 1 question per day
Adding this to the 5 questions per day he has before will be = 6 questions per day
Answer:
6 problems
Step-by-step explanation:
Suppose that 15 years ago, a benefactor set up an account for your education. This benefactor made a single deposit of $20,000 that has been earning 6% interest compounded monthly. Since the deposit 15 years ago, no money has been added to or taken from the account. Will this account be sufficient to cover tuition for all four years that you will be in school? (Answer this question using the school that you chose for parts C and D and the formula given below.) Make sure that the "time in years" that you use is 15 years + the number of years you will be at school.
Answer:
No it wont
Step-by-step explanation:
find the sum of the first 15 terms of the goemetric series 3+9+27
Answer:
Step-by-step explanation:
hello : here is an solution
write an equation that represents the points (2,6)(0,3) but a linear kind of an equation in any form
Answer:
y=[tex]\frac{3}{2} x+3[/tex]
Step-by-step explanation:
(-3 x 10 to the 4th power) x (2 x 10 to the power of -3) RESPOND QUICK PLEASE
Answer:
-60
Step-by-step explanation:
(-3 x [tex]10^{4}[/tex]) x (2 x [tex]10^{-3}[/tex])
(-30,000) x (.002) = -60
Sean tossed a coin off a bridge into the stream below. The path of the coin can be represented by the equation 2 h tt = − 16t^2+ 72t+ 100 (where t is time in seconds and h is height in feet) How long will it take the coin to reach the stream?
Answer:
It will take 5.61 seconds for the coin to reach the stream.
Step-by-step explanation:
The height of the coin, after t seconds, is given by the following equation:
[tex]h(t) = -16t^{2} + 72t + 100[/tex]
How long will it take the coin to reach the stream?
The stream is the ground level.
So the coin reaches the stream when h(t) = 0.
[tex]h(t) = -16t^{2} + 72t + 100[/tex]
[tex]-16t^{2} + 72t + 100 = 0[/tex]
Multiplying by (-1)
[tex]16t^{2} - 72t - 100 = 0[/tex]
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]\bigtriangleup = b^{2} - 4ac[/tex]
In this question:
[tex]16t^{2} - 72t - 100 = 0[/tex]
So
[tex]a = 16, b = -72, c = -100[/tex]
[tex]\bigtriangleup = (-72)^{2} - 4*16*(-100) = 11584[/tex]
[tex]t_{1} = \frac{-(-72) + \sqrt{11584}}{2*16} = 5.61[/tex]
[tex]t_{2} = \frac{-(-72) - \sqrt{11584}}{2*16} = -1.11[/tex]
Time is a positive measure, so we take the positive value.
It will take 5.61 seconds for the coin to reach the stream.
can someone help me plzzzzzzzzzzzzzzzzzzzzzzzzz it's for 10 poits
Answer:
Step-by-step explanation:
3^2 + 4^2 = 5 ^2
in right triangle. c is always the longest
Answer:
[tex]3^{2} +4^{2}+ 5^{2}[/tex]
Step-by-step explanation:
Find the surface area and volume of the triangular prism. Remember to show your work on scratch paper.
10 cm
6 cm
5 cm
8 cm
Answer:
27cm
Step-by-step explanation:
so you are dumb for not nowing it
How did mendeleev arrange the elements ?
PLSSS HELP!! WILL GIVE BRAINLIEST!
Answer:
Although it's blurry, I believe y is equal to 3.
Step-by-step explanation:
You can see where x (the horizontal line) = 7, then go up to where the diagonal line meets that point, which is at y (the vertical line) = 3.
Answer:
y = [tex]2 \frac{11}{12}[/tex] gallonsStep-by-step explanation:
The water run at a constant speed with the slope of 5/12.
Slope-intercept form would be y = 5/12x.
So if we were to plug it in the equation,
y = 5/12 (7) = 35/12 or 2 11/12.
Hope this helps ;D
A day of the week is randomly chosen What is the probability of choosing Monday or a day that starts with the letter
S?
P(Monday)
P(starts with 5)
P(Monday or starts with )
Answer:
Well, P(Monday)= 1/7 = 14.3%
P(starts with S)= 2/7 = 28.6%
P(Monday or starts with S)= 3/7 = 42.9%
Step-by-step explanation:
Have a good day!!!
The probability of choosing Monday is,
P = 1 / 7
And, the probability of choosing starts with S is,
P = 2/7
And, the probability of choosing Monday or starts with S is,
P = 3/7
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Given that;
A day of the week is randomly chosen.
Since, Number of days in a week = 7
Hence, the probability of choosing Monday is,
P = 1 / 7
And, the probability of choosing starts with S is,
P = 2/7
So, the probability of choosing Monday or starts with S is,
P = 2/7 + 1/7
P = 3/7
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[8 + (24 x 3)] divided by 7
Use PEMDAS &’ show work .
Answer:
11.43
Step-by-step explanation:
[8 + (24 x 3)] divided by 7
[8 + (72)] divided by 7
80/7
11.42857142857143
11.43 (I rounded it)
Answer:
11.42
My explanation:
P( )
E *
M x
D /
A +
S -
the first step is to multiply 24x3 because parenthesses go first
the second step is that get the 72 form multiplying and add 8 to it becasue its inside the lines
third step is to divide by 7 and then you get 11.42
Feel free to ask for more help :)
Can someone please help with these 4 questions?
Answer:
Q4. 2144 Q5. -16 Q6. Downwards Q7. 0 seconds
Step-by-step explanation:
Q4. h(t) = -16t² + 2400 Substitute 4 for t
h(4) = -16(4)² + 2400 Simplify the exponent
h(4) = -16(16) + 2400 Multiply
h(4) = -256 + 2400 Add
h(4) = 2144
Q5. I graphed the equation on the graph below to find the instantaneous velocity. The instantaneous velocity is -16.
Q6. At 4.5 seconds, the water rocket is traveling down because the highest point the rocket goes is at 2.8, so 4.5 is traveling downwards.
Q7. 0 seconds because the rocket goes 0 feet in 0 seconds.
If these answers are correct, please make me Brainliest!
The property taxes on a home varies directly with the value of the home. Jack currently lives in a home worth $172,000 and pays $13,760 in taxes.
You have money in an account at 6% interest, compounded monthly. To the nearest year, how long
will it take for your money to double.
Answer:
Step-by-step explanation:
Let amount now be x , meaning principal is x
and the amount later A is 2x
A = P(1+r/n)^nt
n = 12
2x = x (1 + 0.06/12)^12t
divide through by x
2 = (1+ 0.005)^12t
2 = (1.005)^12t
Take log of both sides
log 2 = 12t log 1.005
12t = log2/log 1.005
12t = 138.975721610697
t = 138.975721610697/12
t = 11.58
t = 12 years
Fiona draws a circle with a diameter of 14 meters. What is the area of Fiona’s circle?
Answer:
The area of the circle is [tex]153.94meters^2[/tex]
Step-by-step explanation:
The formula for the area of a circle is : [tex]\pi *radius^{2}[/tex]
To work this out you would first need to divide the diameter of 14 by 2, this gives you 7. This is in order for us to calculate the radius. The radius of a circle is the length from one side to the centre.
Now that we know the radius the next step is to multiply pi by the radius of 7 squared, this gives you 153.94. This is because in order for you to calculate the area you would substitute the values into the formula.
1) Divide 14 by 2.
[tex]14/2=7[/tex]
2) Multiply pi by 7 squared.
[tex]\pi *7^2=153.94 meters^2[/tex]
153.94 square meters is the area of the triangle.
What is Area?The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.
The formula to calculate the area of a circle is A = πr², where A is the area and r is the radius of the circle.
Since the diameter is given as 14 meters, the radius can be calculated by dividing the diameter by 2:
r = d/2 = 14/2 = 7 meters
Now, we can substitute this value of radius into the formula for the area of a circle:
A = πr² = π(7)² = 49π square meters
Therefore, the area of Fiona's circle is 49π square meters (or approximately 153.94 square meters if π is approximated to 3.14).
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