What is the lateral surface area of a right hexagonal prism whose base is a regular hexagon with sides measuring 8 inches long and altitude measuring 6 inches tall?
Answer:
288 square inches
Step-by-step explanation:
Assuming your "altitude" is the height of the prism--the distance between bases, the lateral area is the sum of the areas of the six rectangular faces. Each of those has an area of ...
(8 in)(6 in) = 48 in^2
so the 6 of them will have an area of ...
lateral area = 6×48 in^2 = 288 in^2
_____
Comment on nomenclature
'Altitude' is usually associated with the height of a triangle. In the case of a regular polygon, the 'altitude' of a triangular section of the polygon is called the 'apothem', and is often designated using the letter 'a'. If the polygon is regular, the apothem can be calculated from the side length and the number of sides, but it is often given in problems involving area, perimeter, and/or volume.
The distance between the parallel bases of a prism is often referred to as the prism height or length. The use of the word 'altitude' is confusing in this case.
Since the lateral area is the product of the perimeter of the base and the distance between bases, we have to assume that your 'altitude' refers to the distance between bases. Otherwise, there is not sufficient information to work the problem.
9/10 - 4/10 = _
PLEASE ANSWER!! :)
Answer:
5/10
Step-by-step explanation:
Answer:0.5
Step-by-step explanatiolos divides ambos y después restarlos 0
g Which of the following is equivalent to P( A|B)? a. P(A and B) b. P(B|A) c. P(A)/P(B) d. None of these choices.
Answer:
The correct option is D.
But option B is correct if P(A) = P(B).
Step-by-step explanation:
P(A|B) is read as "The probability of A given B".
It is different from the options A, B, and C.
It is equal to option B only if the probability of A is equal to the probability of B. That is P(A|B) = P(B|A) if P(A) = P(B).
How many gallons of a 5% bleach solution must be
added to 10 Gallons of a 20% bleach solution to
produce that is 15% bleach
Answer:
Step-by-step explanation:
10 gallons of the 20% solution contain 2 gallons of bleach.
x gallons of the 5% solution contain 0.05x gallons of bleach.
If the two are combined, the resulting 10+x gallons contain 2+0.5x gallons of bleach. The concentration is (2+0.05x)/(10+x).
(2+0.05x)/(10+x) = 15%
2+0.05x = 0.15(10+x)
2+0.05x = 1.5+0.15x
0.5 = 0.10x
x = 5
5 gallons of 5% solution is added to the 10 gallons of 20% solution.
f (x) = x - 5. Find f'(x) and its domain.
Answer:
C
Step-by-step explanation:
f(x) = √x - 5
domain: [0. ∞)
range: [-5, ∞)
Let y = √x - 5
√x = y+5
x = (y+5)²
Switch x and y:
y = (x+5)²
f⁻¹(x) = (x+5)²
domain of f⁻¹(x) is the range of f(x): [-5,∞)
The highest attendance at this stadium was in 2007 when 91,547 people attended. The average cost of a ticket was $57. How much money was made on ticket sales for that game?
Answer:57*91547
Step-by-step explanation:
Three 3.0 g balls are tied to 80-cm-long threads and hung from a single fixed point. Each of the balls is given the same charge q. At equilibrium, the three balls form an equilateral triangle in a horizontal plane with 20 cm sides. What is q?
Answer:
q = 0.105uC
Step-by-step explanation:
We can determine the force on one ball by assuming two balls are stationary, finding the E field at the lower right vertex and calculate q from that.
Considering the horizontal and vertical components.
First find the directions of the fields at the lower right vertex. From the lower left vertex the field will be at 0° and from the top vertex, the field will be at -60° or 300° because + charge fields point radially outward in all directions. The distances from both charges are the same since this is an equilateral triangle. The fields have the same magnitude:
E=kq/r²
Where r = 20cm
= 20/100
= 0.2m
K = 9.0×10^9
9.0×10^9 × q /0.2²
9.0×10^9/0.04
2.25×10^11 q
These are vector fields of course
Sum the horizontal components
Ecos0 + Ecos300 = E+0.5E
= 1.5E
Sum the vertical components
Esin0 + Esin300 = -E√3/2
Resultant = √3E at -30° or 330°
So the force on q at the lower right corner is q√3×E
The balls have two forces, horizontal = √3×E×q
and vertical = mg, therefore if θ is the angle the string makes with the vertical tanθ = q√3E/mg
mg×tanθ = q√3E.
..1
Then θ will be...
Since the hypotenuse = 80cm
80cm/100
= 0.8m
The distance from the centroid to the lower right vertex is 0.1/cos30 =
0.1/0.866
= 0.1155m
Hence,
0.8×sinθ = 0.1155
Sinθ = 0.1155/0.8
Sin θ = 0.144375
θ = arch sin 0.144375
θ = 8.3°
From equation 1
mg×tanθ = q√3E
g = 9.8m/s^2
m = 3.0g = 0.003kg
0.003×9.8×tan(8.3)
0.00428 = q√3E
0.00428 = q×1.7320×E
Where E=kq/r²
Where r = 0.2m
0.0428 = kq^2/r² × 1.7320
K = 9.0×10^9
0.0428/1.7320 = 9.0×10^9 × q² / 0.2²
0.02471×0.04 = 9.0×10^9 × q²
0.0009884 = 9.0×10^9 × q²
0.0009884/9.0×10^9 = q²
q² = 109822.223
q = √109822.223
q = 0.105uC
What is the constant of variation, k, of the direct variation, y = kx, through (–3, 2)?
k = –k equals negative StartFraction 3 Over 2 EndFraction.
k = –k equals StartFraction 2 Over 3 EndFraction.
k = k equals StartFraction 2 Over 3 EndFraction.
k = k equals StartFraction 3 Over 2 EndFraction.
Answer: k = 2/-3
Step-by-step explanation: Option (B)
Taking the test as we speak
Divide. Write the quotient in lowest terms. 3 3/4 ÷ 5/7
Rewrite 3 3/4 as an improper fraction
3 3/4 = 15/4
Now you have
15/5 / 5/7
When you divide fractions, change the division to multiplication and flip the second fraction over:
15/4 x 7/5
Now multiply the top numbers together and the bottom numbers together:
( 15 x 7) / (4 x 5) = 105/20
Write as a proper fraction:
105/20 = 5 1/4
7 10/3 x 3 1/10= Can you explain step by step to me
Thanks
Answer:
710/3×31/10
[tex]reduce \: fraction \: to \: the \: lowest \\ term \: by \: canceling \: the \: greatest \\ common \: factor \: \\ = \frac{71 \times 31}{3} \\ calculate \: the \: first \: two \: terms \\ = \frac{2201}{3} \: is \: the \: answer[/tex]
Find the measure of a.
A. 20
B. 70
C. 80
D. 40
A circle is a curve sketched out by a point moving in a plane. The measure of a is 70°. The correct option is B.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
In the given circle, the line AC is the diameter of the circle, therefore, the measure of ∠ABC will be 90°.
∠ABC = 90°
This is because a triangle formed on the diameter of the circle such that all the vertices of the triangle intersect the circle, then the angle opposite to the diameter is a right angle.
Now, in ΔABC, the sum of all the angles of the triangle can be written as,
∠ABC + ∠BCA + ∠BAC = 180°
90° + a + 20° = 180°
110° + a = 180°
a = 180° - 110°
a = 70°
Hence, the measure of a is 70°.
Learn more about Circle:
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A recent survey asked 1200 randomly selected U.S. adults if they believe that the U.S. federal government is doing enough to keep U.S. elections safe from outside interference. After analyzing the results, the researchers were able to state that they are 95% confident that between 52.5% and 59.5% of all U.S. adults believe that the U.S. federal government is not doing enough to keep U.S. elections safe. Which statement BEST describes how to interpret these results
Complete Question
The complete question is shown on the first uploaded image
Answer:
The correct option is D
Step-by-step explanation:
From the question the question we are told that
The researchers were able to state that they are 95% confident that between 52.5% and 59.5% of all U.S. adults believe that the U.S. federal government is not doing enough to keep U.S. elections safe.
Generally a confidence interval states to what extent the chances of the true population is within the a given range
So the 95% confidence interval given in the question as 52.5% and 59.5% means that the chances of the true population mean being with this given range is 95%
So given that the the true population mean is within this range then it means that the population mean will be greater than 50%
So the statement that best describe and interprets this result is
The results show significant statistical support that most U.S. adults (over 50%) believe that the U. S. Federal government is not doing enough to keep U.S. election safe.
Please help asap, will mark Brainliest xoxo
Answer/Step-by-step explanation:
Given, [tex] b(x) = (\frac{6}{7})^{x} [/tex]
The table for the function are:
When x = -2
[tex] b(-2) = (\frac{6}{7})^{-2} [/tex]
[tex] b(-2) = \frac{1}{(\frac{6}{7})^{2}} [/tex]
[tex] b(-2) = \frac{1}{(\frac{36}{49})} [/tex]
[tex] b(-2) = 1*\frac{49}{36} [/tex]
[tex] b(-2) = \frac{49}{36} [/tex]
When x = -1
[tex] b(-1) = (\frac{6}{7})^{-1} [/tex]
[tex] b(-1) = \frac{1}{(\frac{6}{7})} [/tex]
[tex] b(-1) = 1*\frac{7}{6} [/tex]
[tex] b(-2) = \frac{7}{6} [/tex]
When x = 0
[tex] b(0) = (\frac{6}{7})^{0} [/tex]
[tex] b(0) = \frac{6^0}{7^0} [/tex]
[tex] b(0) = \frac{1}{1} [/tex]
[tex] b(0) = 1 [/tex]
When x = 1
[tex] b(1) = (\frac{6}{7})^{1} [/tex]
[tex] b(1) = \frac{6}{7} [/tex]
When x = 2
[tex] b(2) = (\frac{6}{7})^{2} [/tex]
[tex] b(2) = \frac{6^2}{7^2} [/tex]
[tex] b(2) = \frac{36}{49} [/tex]
Find n for the arithmetic sequence for which sn=345, u1=12 and d = 5 .
Answer:
n = 10
Step-by-step explanation:
The sum to n terms of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
Here a₁ = 12 and d = 5 and [tex]S_{n}[/tex] = 345, thus
[tex]\frac{n}{2}[/tex] [ (2 × 12) + 5(n - 1) ] = 345 ( multiply both sides by 2 )
n( 24 + 5n - 5) = 690 ← distribute and simplify left side
n(19 + 5n) = 690
19n + 5n² = 690 ( subtract 690 from both sides )
5n² + 19n - 690 = 0 ← in standard form
(5n + 69)(n - 10) = 0 ← in factored form
Equate each factor to zero and solve for n
5n + 69 = 0 ⇒ 5n = - 69 ⇒ n = - [tex]\frac{69}{5}[/tex]
n - 10 = 0 ⇒ n = 10
However, n > 0 , thus n = 10
How dose this input and output table work?
Aswer:I am sure of the answer it is 6 and 42
Step-by-step explanation:
5+30=3512+30=4230+30=6036+30=6640+30=60Given g(x) = -x - 2, find g(3).
Answer:
g(3) = -5
Step-by-step explanation:
g(3) is basically the value of g(x) when x = 3. Therefore, g(3) = -3 - 2 = -5.
Answer:
[tex] \boxed{\sf g(3) = -5} [/tex]
Given:
g(x) = -x - 2
To Find:
g(3) i.e. g(x) where x = 3
Step-by-step explanation:
[tex]\sf Evaluate \ -x - 2 \ where \ x = 3:[/tex]
[tex] \sf \implies - x - 2 = - 3 - 2[/tex]
[tex] \sf - 3 - 2 = - (3 + 2) : [/tex]
[tex] \sf \implies - (3 + 2)[/tex]
[tex] \sf 3 + 2 = 5 : [/tex]
[tex] \sf \implies - 5[/tex]
a theater has (2x+1) rows of seats, with (x-3) seats in each row. how many seats are in the theater?
A. 2x^2- 5x- 3
B. 2x^2+ 5x- 3
C. 2x^2- 7x+ 3
D. 2x^2- 7x- 3
(2x+1)(x-3)
y(x-3) .... let y = 2x+1
y*x+y(-3) .... distribute
xy - 3y
x( y ) - 3( y )
x( 2x+1 ) - 3( 2x+1) ... replace y with 2x+1
2x^2 + x - 6x - 3 ..... distribute
2x^2 - 5x - 3
Answer is choice A
find the missing side. round your answer to the nearest tenth. PLEASE HURRY!
Answer:
44.8
Step-by-step explanation:
Using the Cosine formula, we first have Cos 48 = 30/x. So then we just solve for x and get 44.8342965, which rounds to 44.8
I hope this helped! :D
What is the value of x to the nearest tenth?
Answer:
x=9.6
Step-by-step explanation:
The dot in the middle represents the center of the circle, so therefore, the line that is represented by 16 is the radius. Since that is the radius, the side that is the hypotenuse of the small triangle is also 16, since they have the same distance.
The line represented by 25.6 with x as its bisector shows that when we divide it by 2, the other side of the triangle besides the hypotenuse is 12.8.
Now that we have the two sides of the triangle, we can find the last side (represented by x). Use pythagorean theorem:
[tex]a^2 +b^2=c^2\\x^2+(12.8)^2=16^2\\x^2+163.84=256\\x^2=92.16\\x=9.6[/tex]
Someone help me understand
Answer:
f¯¹(x) = 23/ (6x + 3)
Step-by-step explanation:
f(x) = (23 – 3x)/6x
The inverse, f¯¹, for the above function can be obtained as follow:
f(x) = (23 – 3x)/6x
Let y be equal to f(x)
Therefore, f(x) = (23 – 3x)/6x will be written as:
y = (23 – 3x)/6x
Next, interchange x and y.
This is illustrated below:
y = (23 – 3x)/6x
x = (23 – 3y)/6y
Next, make y the subject of the above expression. This is illustrated below:
x = (23 – 3y)/6y
Cross multiply
6xy = 23 – 3y
Collect like terms
6xy + 3y = 23
Factorise
y(6x + 3) = 23
Divide both side by (6x + 3)
y = 23/ (6x + 3)
Finally, replace y with f¯¹(x)
y = 23/ (6x + 3)
f¯¹(x) = 23/ (6x + 3)
Therefore, the inverse, f¯¹, for the function f(x) = (23 – 3x)/6x is
f¯¹(x) = 23/ (6x + 3)
You flip two coins. What is the probability
that you flip at least one head?
Answer:
[tex]\boxed{Probability=\frac{1}{2} }[/tex]
Step-by-step explanation:
The probability of flipping at least 1 head from flipping 2 coins is:
=> Total sides of the coins = 4
=> Sides which are head = 2
=> Probability = 2/4 = 1/2
Factor of
x2 – 14x + 24
A. (x - 6)(x - 4)
B. (x - 8)(x - 3)
C. (x - 12)(x - 2)
D. (x - 24)(x - 1)
Answer: The answer is C.
Step-by-step explanation:
Hi, there!!!
The answer is option C.
The solution is in picture.
I hope it helps....
Question 19 of 20:
Select the best swer for the question
19. The distance from the center of a round table top to the edge of the table top is 4 ft what is the area of the table top
Answer:
50.26 ft^2
Step-by-step explanation:
Area=pi*r^2
Area=pi*(4)^2=pi*16=50.26
what is a 200% increase of 50
Answer:
150
Step-by-step explanation:
Increase = New Number - Original Number.
divide the increase by the original number and multiply the answer by 100.
I hope this helped! :)In a random sample of 380 cars driven at low altitudes, 42 of them exceeded a standard of 10 grams of particulate pollution per gallon of fuel consumed. In an independent random sample of 90 cars driven at high altitudes, 24 of them exceeded the standard. Compute the test statistic for testing if the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard.
Answer:
The test statistic for testing if the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard is 3.234.
Step-by-step explanation:
We are given that in a random sample of 380 cars driven at low altitudes, 42 of them exceeded a standard of 10 grams of particulate pollution per gallon of fuel consumed.
In an independent random sample of 90 cars driven at high altitudes, 24 of them exceeded the standard.
Let [tex]p_1[/tex] = population proportion of cars driven at high altitudes who exceeded a standard of 10 grams.
[tex]p_2[/tex] = population proportion of cars driven at low altitudes who exceeded a standard of 10 grams.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]p_1\leq p_2[/tex] {means that the proportion of high-altitude vehicles exceeding the standard is smaller than or equal to the proportion of low-altitude vehicles exceeding the standard}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]p_1>p_2[/tex] {means that the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard}
The test statistics that will be used here is Two-sample z-test statistics for proportions;
T.S. = [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex] ~ N(0,1)
where, [tex]\hat p_1[/tex] = sample proportion of cars driven at high altitudes who exceeded a standard of 10 grams = [tex]\frac{24}{90}[/tex] = 0.27
[tex]\hat p_2[/tex] = sample proportion of cars driven at low altitudes who exceeded a standard of 10 grams = [tex]\frac{42}{380}[/tex] = 0.11
[tex]n_1[/tex] = sample of cars driven at high altitudes = 90
[tex]n_2[/tex] = sample of cars driven at low altitudes = 380
So, the test statistics = [tex]\frac{(0.27-0.11)-(0)}{\sqrt{\frac{0.27(1-0.27)}{90}+\frac{0.11(1-0.11)}{380} } }[/tex]
= 3.234
The value of z-test statistics is 3.234.
Yuko added a 15 percent tip when she paid her cab driver. If the fare was $25.50, what was the total amount she paid? A. $28 B. $30 C. $31
Answer:
B. $30
Step-by-step explanation:
First, find the amount of the tip.
Multiply the tip rate and taxi fare.
tip rate * taxi fare
The tip rate is 15% and the taxi fare is $25.50
15% * 25.50
Convert 15% to a decimal. Divide 15 by 100 or move the decimal place two spots to the left.
15/100=0.15
15.0 ---> 1.5 ---> 0.15
0.15 * 25.50
3.825
The tip amount is $3.825
Next, find the total amount she paid.
Add the taxi fare and the tip amount.
taxi fare + tip amount
The taxi fare is $25.50 and the tip amount is $3.825
$25.50 + $3.825
$29.325
Round to the nearest dollar. Typically, this would round down to $29, but that is not an answer choice. So, if we round up, the next best answer is $30.
Therefore, the best answer choice is B. $30
find the HCF of 72,108 and 180
Answer:
36 is the answer
Step-by-step explanation:
Answer:
36
Step-by-step explanation:
72: 2×2×2×3×3
108: 2×2×3×3×3
180: 2×2×3×3×5
here, common factors are 2,2,3 and 3 ..
so.. HCF: 2×2×3×3
•°•HCF=36 ..
Simplify 3m2 (−6m3 )
Answer:
3m2(-6m3)
since it's a term you have to multiply it by the number in bracket
6m(-6m3)
6m(-18m)
-108m²
the bold answer is incorrect. what is the right answer?
How to solve this question
hopefully this answer can help you to answer the next question. can you choose this answer as the brainliest answer and give five stars