Answer:
21300
Step-by-step explanation:
120∑n=13n−4
Split the summation into smaller summations that fit the summation rules.
120∑n=1 3n−4=3120∑n=1 n+120∑n=1 −4
Evaluate
3120∑n=1 n.
21780
Evaluate
120∑n=1 −4 −480
Add the results of the summations.
21780−480
Subtract 480 from 21780.
21300
A cylindrical can has an 8-cm radius and a height of 11 cm. Find its surface area.
Answer:
955.168 cm²
Step-by-step explanation:
The formula to find the surface area of a cylinder is :
Surface area = 2 π r ( r + h )
Here,
r ⇒ radius ⇒ 8 cm
h ⇒ height ⇒ 11 cm
So, Let us solve now.
Surface area = 2 π r ( r + h )
Surface area = 2 × 3.142 × 8 ( 8 + 11 )
Surface area = 50.272 × 19
Surface area = 955.168 cm²
If f(x) = 3x 2 and g(x) = x2 1, which expression is equivalent to (f circle g) (x)? (3x 2)(x 2 1) 3x 2 1 2 (3x 2)2 1 3(x 2 1) 2
The expression is equivalent to (f circle g) (x) will be (3x+2)²+1. The correct option is D.
What is a factor?A number is obtained by dividing another number by itself without leaving a leftover. To put it another way, if multiplying two whole numbers produces a product,
The given expression is;
[tex]f(x) = 3x + 2 \\\\ g(x) = x_2 + 1[/tex]
[tex](f g)(x) =g(f(x)) =g(3x+2)=(3x+2)^2 +1[/tex]
The expression is equivalent to (f circle g) (x) will be (3x+2)²+1. Option D is correct.
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A rectangular banquet room has an area of 182 square meters and a perimeter of 54 meters. Let l and w represent the dimensions of the room in meters. Which statements describe the dimensions of the banquet room? Select all that apply.
Answer:
Choose all but C
Step-by-step explanation:
Givens
Area = 182 m^2
Perimeter = 54 m
Solution.
B: solves for the length, not the width. Area = L*w. Area / w = L. But to get to the length, you need to solve for the width. So this statement can be used. B is true.
C is not true. The length and width differ by 1 which means one of them is even and the other is odd. See below under A.
D is also true. 2L = 54 - 2w Divide both sides by 2
2L/2 = 54/2 - 2w/2
L = 27 - w
E is true.
L * w = 182 Divide both sides by w
L = 182/w
The only one we don't know about is A. We have to solve the problem to get the answer to A.
P= 2L + 2w = 54
2L + 2w = 54
L + w = 27
L = 27 - w
L*w = 182
(27 - w ) * w = 182 Remove the brackets
27w - w^2 = 182 Subtract 27w - w^2 from both sides.
0 = w^2 - 27w + 182 Notice the sign change. Subtraction does that.
This factors into
(w - 13)(w - 14)
A turns out to be true, because w can be 13 or 14. When W = 13, L = 14.
When w = 14, L = 13
I need help with this please.
Is this triangle acute, right or obtuse?
Triangle
Acute
Obtuse
Right
Answer:
ill say acute
Step-by-step explanation:
if im wrong tell me but if im not pls mark brainllest!
Answer:
This triangle is Acute.
Step-by-step explanation:
To figure this out you add the length of the two smaller sides if the sum is greater than the longest side then the answer is Acute. I really hope this helps have a wonderful day!
Alicia and Bennie have decided to play a game. They each draw as many flowers on paper as they can within one
minute, repeating this game many times. The number of flowers Alicia draws and the number of flowers Bennie
draws are independent. The number of flowers Alicia draws within 1 minute, A, is approximately Normally distributed
with a mean of 38 flowers and a standard deviation of 1. 8 flowers. The number of flowers Bennie draws in 1 minute,
B, is approximately Normally distributed with a mean of 41 and a standard deviation of 2. 6 flowers. Let D represent
the difference, A - B in the number of Alicia's and Bennie's flowers drawn in 1 minute
What is the probability that Alicia draws fewer flowers than Bennie in any 1 minute?
Answer:
0.829
Step-by-step explanation:
Tom is in a diving competition. (a) The score, S, for a dive is 60% of the total mark, m, multiplied by the difficulty
factor of the dive, d.
Write down the formula for calculating S in terms of m and d.
Answer:
S = 0.6md
Step-by-step explanation:
Formula
S = (60% of m) x dConvert 60% to decimal60%/100% = 0.6⇒ S = 0.6md[tex]⟼ \sf \: \blue { \boxed{s \: = 0.6m \times d}}[/tex]
Step-by-step explanation:
To obtain a formula for S which is scoreAs, we know it 60% is equal to 0.6
Therefore,:
[tex]⟼ \sf \: \green { \boxed{s \: = 0.6m \times d}}[/tex]
In conclusion, according to the word problem the score was 60% the total mark multiplied by difficulty as and as we all know it 60% equals 0.6 therefore the score equals 0.6m which is Marks × difficulty factor of the dive
#Study hardIf x2 mx m is a perfect-square trinomial, which equation must be true? x2 mx m = (x – 1)2 x2 mx m = (x 1)2 x2 mx m = (x 2)2 x2 mx m = (x 4)2
An expression has numbers, variables, and mathematical operations. The equation that must be true so that x²+mx+m is a perfect square trinomial is x²+mx+m=(x+2)².
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
A perfect square trinomial is in the form (a+b)²=a²+b²+2ab. If we compare the perfect square trinomial x²+mx+m, we will get that the value of m should be such that it satisfies the equation [tex]m^2+2m[/tex]. Since there is only one value that can satisfy this equation that is 2.
Therefore, the equation that must be true so that x²+mx+m is a perfect square trinomial is x²+mx+m=(x+2)².
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how many kilometers per hour would she have been traveling over the speed limit of 60 if covered a distance of 10 km in 5 minutes
Answer:
60 MPH over the limit
Step-by-step explanation:
5 times 12 - 60
25 points
Jose is in 8th grade, and he is researching his favorite colleges. He notices that the current cost of tuition, books and fees at one 4-year college is $14,500 per year.
What will be the total cost of tuition, books, and fees for Jose if he eventually chooses to attend this college for four years?
Here, we are given the cost of Jose for 1 year for attending college i.e $14500/year, and we need to find the total cost for Jose to attend college for 4 years, so here we can just use unitary method, we can just multiply the whole cost for 1 year by 4, to get the total cost for 4 years, as :
[tex]{:\implies \quad \sf Cost\:\: for\:\: 1\:\: year= \$14500}[/tex]
Now, multiplying by 4 on both sides will yield :
[tex]{:\implies \quad \sf Cost\:\: for\:\: 4\:\: years= \$14500\times 4}[/tex]
[tex]{:\implies \quad \boxed{\bf{Cost\:\: for\:\: 4\:\: years= \$58000}}}[/tex]
This is the required answer
The total cost of tuition, books, and fees for Jose if he eventually chooses to attend this college for four years is $58,000.
Total cost of tuitionUsing this formula
Total cost of tuition=Cost of tuition books and fees×Number of years
Where:
Cost of tuition books and fees=$14,500 per year
Number of years=4 years
Let plug in the formula
Total cost of tuition=$14,500 per year x 4 year
Total cost of tuition=$58,000
Inconclusion the total cost of tuition, books, and fees for Jose if he eventually chooses to attend this college for four years is $58,000.
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An object moves at a speed of 20 yards per second.
What is the object's speed, in feet per second?
(1 yard = 3 feet)
A) 17
B) 23
C) 50
D) 60
Let's see
[tex]\\ \rm\Rrightarrow speed=20yd/s[/tex]
See unit given to change is ft/sSo only numerator we need to change[tex]\\ \rm\Rrightarrow Speed=20(3)=60ft/s[/tex]
Option D
Find the are of the shaded region. Are of a triangle = 1/2 base x height . 2w+2 < height. Width is 3w-1
The formula for the area of a triangle is 1 / 2 × base × height. This formula can be more easily written as Area = 1 / 2 bh. The formula of Area = 1 / 2 bh works for all triangles, no matter what size or shape.
gabriella anwswered 72 questions correctly on her multiple choice history final and earned a grade of 36%. how many total question were on final exam
Answer:
200 questions
Step-by-step explanation:
Here,
total answers Gabriella answered=72
grade = 36%
total number of question = ?(X)
We know,
36% of X = 72
or, 36x/100 = 72
or, 36x = 72*100
or, x = 7200/36
or, x = 200
HELP ME PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
[tex]192cm^{2}[/tex]
Step-by-step explanation:
[tex]A = \frac{1}{2} bh[/tex]
We know that b is the measurement of the base, 12, and h is the height of the cone, 32. Now we can simply insert those numbers into the equation and solve it.
[tex]A = \frac{1}{2} (12*32)\\\\A = \frac{1}{2} (384)\\\\A = \frac{384}{2} \\\\A = 192[/tex]
651 x 5 porfavor ayudenme SIN CALCULADORA - please help me NO CALCULATOR
Answer:
3,255
Step-by-step explanation:
,
A right rectangular prism has a length of 2 1/2 feet, a width of 3 feet, and a height of 1 1/2
feet. Unit cubes with side lengths of 1/2 foot are added to completely fill the prism with no space remaining. What is the volume, in cubic feet, of the right rectangular prism?
Answer: 11.25 ft³
Step-by-step explanation:
We can use the volume formula to solve. I will turn the halves into 0.5 for calculation purposes.
V = L * W * H
V = 2.5 * 3 * 1.5
V = 11.25 ft³
The volume of the rectangular prism is 11.25 ft³.
Please help me I can’t figure it out
Answer:
Your answer is 4
Step-by-step explanation:
(52 - 2(2)) / (9 + 3)
(52 - 4) / (9 + 3)
48 / 12 = 4
rachel bought an equal number of bowls and plates for$96. each plate cost $2 and each bowl cost $4 more than each plate. how much did she spend on all the plates
Answer:
$24
Step-by-step explanation:
Cost per plate: $2
Cost per Bowl: $2 + $4 = $6
Cost of 1 Plate and 1 Bowl: $2 + $6 = $8
Total cost of $96 divided by Cost of 1 Plate and 1 Bowl $8 = 12 sets of 1 Plate and 1 Bowl
12 plates x $2 Cost per Plate = $24
Answer:
$24
Step-by-step explanation:
Let [tex]b[/tex] = bowl
Let [tex]p[/tex] = plate
Given:
Equal number of bowls and plates for $961 plate = $2 1 bowl = $4 + $2 = $61) We can translate these into algebra. Since Rachel has equal number of bowls and plates, [tex]b=p[/tex], totaling to $96.
[tex]b=p\\2p + 6b = 96[/tex]
2) We can solve for [tex]p[/tex] these two equations simultaneously using the substitution ot elimination method. I will demonstrate using the substitution method here.
[tex]2p + 6(p) = 96\\2p+ 6p = 96\\8p = 96\\p = \frac{96}{8} \\p = 12[/tex]
So, Rachel bought 12 plates and 12 bowls since plates are equivalent to bowls.
3) Use ratio to find the the cost of the plates.
[tex]1p[/tex] = $2
[tex]12p[/tex] = $24
Estimate 6 divided by 253 please show the work
0.023...
hope it helps...!!!
Doesn’t it tell you the hight of the base I do not understand.
Answer:
Height of base (x) is 9cm exact
Step-by-step explanation:
Please help me with this question. Thank you
Answer:
9.
Step-by-step explanation:
6 9 12 15:- multiplying by 3.
Answer:
B) 9
Step-by-step explanation:
When looking in both the horizontal and vertical direction of the missing space, we can see that the difference between the two numbers, 12 and 15, is 3.
15 - 12 = 3
Using this, we can see that each space on the second row and second column change by 3. Therefore, when looking at the missing space in the sequence, we can figure out that it is 9 by adding 3 to 6.
Dana just finished paying off the $15,400 loan she took out four years ago. the loan had 6.68% interest, compounded monthly. if dana paid a total of $18,321.60, how much did she pay in service charges? a. $730.08 b. $366.49 c. $1,028.72 d. $266.76 please select the best answer from the choices provided a b c d
If Dana paid a total of $18,321.60, then the amount that she paid for in service charges will be $730.08
What is Compound interest?Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.
For service charge
[tex]\rm Pv = PMT[(1 - (1 + (r/k))^{-kn}) / (r/k)][/tex]
Where;
Pv is the amount of the loan = $15400
PMT is monthly payment
R is interest rate = 6.68% = 0.0668
K is number of times compounded monthly = 12
N is time = 4years
PMT the subject of the formula gives
[tex]PMT = Pv/ [(1 - (1 + (r/k))^{-kn}) /(r/k)][/tex]
PMT = 15,400 ÷ ((1 − (1 + 0.0668 ÷ 12)^(−12 × 4)) ÷ (0.0668 ÷ 12))
PMT = 366.49
Thus, the total amount paid
A = 366.49 × 12months × 4years
A = $17,591.52
Thus, the Service charge is
S.C = 18,321.60 − 17,591.52
S.C = $730.08
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From the top of a building 37 feet high, the angle of depression to a car stopped on the ground is 19 degrees. What is the distance from the car to the base of the building?
The distance from the car to the base of the building is 107.46 feet
Angle of elevation and depressionFrom the question We are given the following information
Angle of depression
Height of the building H = 37 feet
Required
distance from the car to the base of the building
Using the SOH CAH TOA identity
tan 19 = opp/hyp
tan 19 = 37/B
B = 37/tan 19
B = 37/0.34432
B = 107.46
Hence the distance from the car to the base of the building is 107.46 feet
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Which statement is true? the equation –3|2x 1.2| = –1 has no solution. the equation 3.5|6x – 2| = 3.5 has one solution. the equation 5|–3.1x 6.9| = –3.5 has two solutions. the equation –0.3|3 8x| = 0.9 has no solution.
The statement which is true for the provided reason is the equation 3.5|6x – 2| = 3.5 has one solution.
How to find one solution of equation?If the equation is given a unique and single value of variable after solving then the equation is said one solution equation. Such equation gives exactly one solution.
The three types of solution of an equation are-
One solution-When the provides the singe value of the given variable, we get one or unique solution.No solution-When the graph of equations is equal than it provides the no solution. When the value, does not equate for the expression, then the expression has no solution.Infinite many solution-For the same line, the equation has the infinite many solutions.
The first equation given in the problem is,
[tex]-3|2x+ 1.2| = -1[/tex]
This equation has one solution. This in not correct option.
The second equation given in the problem is,
[tex]3.5|6x - 2| = 3.5 \\|6x-2|=0\\6x=2\\x=\dfrac{2}{6}\\x=\dfrac{1}{3}[/tex]
This equation has one solution. This in correct option.
Hence, the statement which is true for the provided reason is the equation 3.5|6x – 2| = 3.5 has one solution.
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Can someone help me with this please
y – 6 ≥ 12
What is mZRST in degrees? O 78° O 84° O 120° O 156°
Answer:
rst = ust + usr
6x+12 = 78 + 3x - 12
3x = 54
3x+66 = 54 + 66
3x +66= 120
thus rst = 120
The measure of angle ∠RST in degree is 156°
What is measure of an angle?The measure of angle is the amount of rotation performed by initial side to get the terminal side. A complete angle is divided by 360 equal parts we get 360 number of small angles. Each of these small angle has measure 1 degree.
Given that, ∠RSU=78° , ∠UST=(3x - 11)° and ∠RST=(6x + 12)°
Now, ∠RSU+UST=∠RST
Putting the values of ∠RST and ∠UST we get,
78 + (3x - 12) = 6x + 12
78 + 3x - 12 - 6x - 12 = 0
54 - 3x = 0
3x = 54
So, x = 54/3=18
Therefore, (6x + 12)°=(6×18 + 12)°
=(144 + 12)°
=156°
Hence the measure of angle ∠RST is 156°
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#SPJ5
Amira is planning to plant a new food forest with papaya guava and banana trees she wants to plant a total of 36 trees in the forest and select 18 of them to be the buyer none of them to be guava she says that they're made in 25% of the forest will be banana trees is she correct? Explain.
Answer:
No
Step-by-step explanation:
If 18 are papaya or banana and none are guava then the remaining two trees would split the 36 50-50
if two dice are thrown together , what is the probability of getting an even number on one die and odd number on the other die ?
Answer:
1/2
Step-by-step explanation:
the probability of the die rolling an even number = the probability of the die rolling an odd number =1/2
Let us name these 2 dice as A and B
One die can roll an even and the other can roll an odd, in the following cases
A rolls even and B rolls odd. The probability of this happening =1/2×1/2
A rolls odd and B rolls even. The probability of this happening =1/2×1/2
∴ The required probability
=1/2×1/2+1/2×1/2
=1/4+1/4
=1/2
8
5.1
What is the area of the parallelogram?
(Please my geometry is due tomorrow an I haven’t even started yet)
Answer:
s the answer is 40
n
Step-by-step explanation:
a the formula is A=bh
p so 8*5=40
dsan168
What is 5/8 times 1/2
Answer:
5/16
Step-by-step explanation:
When multiplying fractions, you multiply the numerator by the numerator & the denominator by the denominator.
So 5/8 x 1/2 = 5 x 1/8 x 2 = 5/16