three night guard A, B and C blow their whistles at intervals of 8, 15 and 18 mins respectively, if they blow at 11.00pm, when next are they expected to blow together

Answer: The surface area of the rectangular prism is approximately 4 square yards.

Step-by-step explanation: Given that the volume of the rectangular prism is 160 cubic yards, we can find the dimensions of the prism using the formula:

V = lwh

where V is the volume, l is the length, w is the width, and h is the height.

So, we have:

160 = lwh

Now, we need to find two other measurements in order to calculate the surface area of the rectangular prism. However, we do not have enough information to find all three dimensions. Therefore, we will assume one dimension and find the other two.

Let's assume that the height of the rectangular prism is 10 yards. Then, we can rearrange the formula for the volume to solve for the product of the length and width:

lw = V/h = 160/10 = 16

Now, we have two equations:

lw = 16

wh = 160/10 = 16

Solving for w in the first equation, we get:

w = 16/l

Substituting this expression for w in the second equation, we get:

l(16/l)h = 16

Simplifying, we get:

h = 1

Therefore, the dimensions of the rectangular prism are:

length = l

width = 16/l

height = 10

Now, we can calculate the surface area of the rectangular prism using the formula:

SA = 2lw + 2lh + 2wh

Substituting the values we found, we get:

SA = 2(l(16/l)) + 2(l(10)) + 2((16/l)(10))

SA = 32/l + 20l + 160/l

To find the minimum value of this expression, we can take its derivative with respect to l and set it equal to zero:

dSA/dl = -32/l^2 + 20 + (-160/l^2)

0 = -32/l^2 + 20 - 160/l^2

52/l^2 = 20

l^2 = 52/20

l ≈ 1.44

Substituting this value of l back into the expression for SA, we get:

SA ≈ 4 square yards

Therefore, the surface area of the rectangular prism is approximately 4 square yards.

Answer:

B

Step-by-step explanation:

The \(y\)-intercept is \((0,27)\), eliminating all the options except for B.

Answer: 60% of the usual price.

Step-by-step explanation: To figure out the price, we can divide 150 by 250 to get the percentage of the usual price. When we do so, we get 0.6. We can convert 0.6 to a percentage giving us 60%, which is the answer.

Answer: The vertical line on a graph representing the vertical coordinate points.

Answer:

In analytic geometry, using the common convention that the horizontal axis represents a variable x and the vertical axis represents a variable y, a y-intercept or vertical intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system. As such, these points satisfy x = 0. Hope this helps.

Step-by-step explanation:

The area of the circle circumscribed about the right triangle with legs 6 and 8 is approximately 78.54 square units.

To find the area of the circle circumscribed about a right triangle, we can use the fact that the diameter of the circle is equal to the hypotenuse of the right triangle. In this case, the legs of the right triangle are given as 6 and 8.

Using the Pythagorean theorem, we can find the length of the hypotenuse:

\(c^2 = a^2 + b^2\)

where c is the length of the hypotenuse, and a and b are the lengths of the legs.

Substituting the values:

\(c^2 = 6^2 + 8^2\)

\(c^2 = 36 + 64\\ c^2 = 100\)

Taking the square root of both sides:

\(c = \sqrt{100} \\ c = 10\)

Therefore, the length of the hypotenuse is 10 units.

Since the diameter of the circumscribed circle is equal to the hypotenuse, the radius of the circle is half the length of the hypotenuse, which is 10/2 = 5 units.

Now we can calculate the area of the circle using the formula:

Area = π \(r^2\)

where r is the radius of the circle.

Area = π \(5^2\)

Area = π × 25

Area = 78.54 square units

Hence, the area of the circle circumscribed about the right triangle with legs 6 and 8 is approximately 78.54 square units.

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Answer:

9a-2=7

Step-by-step explanation:

4a+ 5a-2=5+3-1

To simplify each side, combine like terms.

4a+5a = 9a

5+3-1 = 7

The equation becomes:

9a-2=7

Based on the plot, the number of practice puzzles per week that members solve if they finish the contest puzzle

in one hour is c 4

The line of best fit for the scatter plot shows that there is a positive correlation between the number of practice puzzles solved per week and the time it takes to solve a contest puzzle. This means that as the number of practice puzzles solved per week increases, the time it takes to solve a contest puzzle decreases.

If a member finishes a contest puzzle in one hour, they are on the line of best fit. This means that they solve approximately 4 practice puzzles per week.

The other options are incorrect. Option a is too high, option b is too low, and option d is not on the line of best fit.

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Answer:

d. t ≈ 5m

e. y ≈ 44°

f. x = 36°

Step-by-step explanation:

We'd apply the trigonometry function to solve for all missing sides and angles as follows:

d. Adjacent length = t

Hypothenuse = 11.1m

θ = 62°

Use Cos θ = adjacent/hypothenuse

Cos(62) = t/11.1

Multiply both sides by 11.1

11.1*cos(62) = t

11.1*0.4695 = t

t = 5.21 ≈ 5 m

e. Opposite = 7m

Hypotenuse = 10m

θ = y°

Use sine θ = opposite/hypotenuse

Thus,

sine θ = 7/10

sine θ = 0.7

θ = sin-¹(0.7) = 44.4

y ≈ 44° (nearest whole number)

f. Opposite = 4.2cm

Adjacent = 5.8cm

θ = x°

Use tan θ = opposite/adjacent

tan θ = 4.2/5.8

tan θ = 0.7241

θ = tan-¹(0.7241) = 35.91

θ = x ≈ 36°

Simple answer.

-1 x 3 = -3

3 is your x and -3 is your y.

Using the uniform distribution, it is found that:

a) There is a 0.3333 = 33.33% probability that the friend is between 10 and 20 minutes late.

b) Within 9 minutes.

It is a distribution with two bounds, a and b, in which each outcome is equally as likely.

The probability of finding a value of at lower than x is:

\(P(X < x) = \frac{x - a}{b - a}\)

The probability of finding a value between c and d is:

\(P(c \leq X \leq d) = \frac{d - c}{b - a}\)

Researching the problem on the internet, it is found that the variable is uniform with a = 0 and b = 30.

Item a:

\(P(10 \leq X \leq 20) = \frac{20 - 10}{30 - 0} = 0.3333\)

There is a 0.3333 = 33.33% probability that the friend is between 10 and 20 minutes late.

Item b:

This is x for which P(X < x) = 0.3, hence:

\(P(X < x) = \frac{x - a}{b - a}\)

\(0.3 = \frac{x}{30}\)

\(x = 9\)

Within 9 minutes.

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We are given two curves on a graph paper and we have to find the y values for the given x.

From the graph we can check for a value of x, what is the value of y from the curve.

x     -3     -2     -1    0      1         2        3

Exp  8      4      2    1      0.5  0.25  0.125

Lin.   7.5   6    4.5   3      1.5     0     -1.5

We find that the two have the same values where the two curves intersect.

From the graph we find that near to -3 and near to 2 both have the same values.

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The missing graph is attached below.

The inverse function:  \(f^{-1} (x) =\) \((\frac{x -5}{5} )^{2} -13\)

The inverse is defined on the domain x < 5 and x ≥ -13 for the original function, which means that the range of the original function is y ≥ 5.

A function is a relationship that exists between two sets of numbers, with each input from the first set, known as the domain, corresponding to only one output from the second set, known as the range.

Given function is;   \(f(x) = 5\sqrt{(x + 13)} + 5\)

To find the inverse of the given function, we first replace f(x) with y:

⇒  \(y = 5\sqrt{(x + 13)} + 5\)

Subtract 5 from both sides:

⇒ \(y -5 = 5\sqrt{(x + 13)}\)

⇒ \(\frac{(y -5)}{5} = \sqrt{(x + 13)}\)

⇒ \((\frac{y -5}{5} )^{2} = x + 13\)

⇒ \((\frac{y -5}{5} )^{2} -13 = x\)

Now we have x in terms of y, so we can replace x with f⁻¹(x) and y with x to get the inverse function:

f⁻¹(x) = \((\frac{x -5}{5} )^{2} -13\)

The domain of the inverse function is x ≥ 5, because this is the range of the original function, and we were given that the inverse is defined on the domain x < 5. However, we must also exclude the value x = 5, because the denominator of the fraction \((\frac{x -5}{5} )^{2}\) becomes zero at this value. Therefore, the domain of f⁻¹(x) is x > 5.

We were given that x ≥ -13 for the original function, which means that the range of the original function is y ≥ 5. Therefore, the domain of the inverse function becomes the range of the original function, and the range of the inverse function becomes the domain of the original function.

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Answer:

see below

Step-by-step explanation:

Using the Pythagorean Theorem:

a^2+ b^2 = c^2

5^2+ 9^2 = 13^2

25+81 = 169

106 = 169

This is not true so it is not a right triangle

Answer:

\(\boxed{\sf Not \ a \ right \ triangle}\)

Step-by-step explanation:

Apply Pythagorean theorem to check if the triangle is a right triangle.

\(a^2+ b^2 = c^2\)

\(5^2+ 9^2 = 13^2\)

\(25+81=169\)

\(106=109\)

False statement.

The triangle is not a right triangle.

The better prediction for y, when x = 74, based on the scatter plot, can be found to be 57.

Looking at the scatter plot, the better prediction of y when the value of x is 74 can be found by looking for the values of y that have a value of x that is around 74.

From the scatter plot, we see that the value of x of 74, would correspond with the value of y of 57. We can therefore infer that y = 57 is the better prediction for x = 74.

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let's firstly convert the mixed fractions to improper fractions and then multiply.

\(\stackrel{mixed}{1\frac{2}{3}}\implies \cfrac{1\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{5}{3}}~\hfill \stackrel{mixed}{2\frac{2}{3}}\implies \cfrac{2\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{8}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{5}{3}\cdot \cfrac{8}{3}\implies \cfrac{40}{9}\implies 4\frac{4}{9}\)

Using linear approximation, the expression √125.2 can be approximated as approximately 10.02.

To find the equation of the tangent line to the function f(x) = √x at x = 125, determine the slope (m) and the y-intercept (b) of the tangent line.

First, find the slope (m) using the derivative of the function f(x) = √x:

f'(x) = 1 / (2√x)

Evaluate the derivative at x = 125:

f'(125) = 1 / (2√125) = 1 / (2 × 5) = 1/10

Now, find the y-coordinate of the point on the function f(x) at x = 125:

f(125) = √125 = 5

So, the tangent line at x = 125 passes through the point (125, 5) and has a slope of 1/10.

Using the point-slope form of a linear equation, the equation of the tangent line can be written as:

y - 5 = (1/10)(x - 125)

To simplify, multiply through by 10:

10y - 50 = x - 125

Rearranging the equation, express it in the form y = mx + b:

y = (1/10)x - 75/10 + 5

Simplifying further:

y = (1/10)x - 75/10 + 50/10

Combining the terms:

y = (1/10)x - 25/10

Therefore, the equation of the tangent line to f(x) = √x at x = 125 is y = (1/10)x - 25/10.

Now, use this tangent line to approximate the value of √125.2:

Substitute x = 125.2 into the equation:

y = (1/10)(125.2) - 25/10

y = 12.52 - 2.5

y ≈ 10.02

So, using linear approximation, approximate √125.2 as approximately 10.02.

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S={-1,3/4}

1) Let's solve this quadratic equation

4x²+x -3=0

Let's solve that using the traditional way. Applying the Resolutive Formula for Quadratic Equations. First, we find the discriminant Delta:

2) So the Solution set is S={-1, 3/4} the roots for that quadratic equation, where y=0 at x=-1, and x=3/4

Answer:

\(\frac{1}{5}\)

Step-by-step explanation:

Given the expression;

\(\lim_{x \to \infty} \dfrac{x+x^2}{5x^2}\)

To find the limit of the function, we need to first divide through by the highest degree if x i.e x² as shown;

\(\lim_{x \to \infty} \dfrac{\frac{x}{x^2} +\frac{x^2}{x2}}{\frac{5x^2}{x^2} }\\ \lim_{x \to \infty} \frac{\frac{1}{x}+ 1 }{5}\\As \ x \ tends \ to \ \infty, \ \frac{1}{x} \ tends \ to \ zero. \ Hence;\\ \lim_{x \to \infty} \frac{\frac{1}{x}+ 1 }{5} = \frac{0+1}{5}\\= \dfrac{1}{5}\)

Hence the limit of the function as x tends to infinity is \(\frac{1}{5}\)

Answer:

B=70

Step-by-step explanation:

A+B=180

5x+25+3x+19=180

8x+44=180

8x=136

x=17

B=3(17)+19

B=51+19

B=70

Answer:

The answer is 140!!!

Step-by-step explanation:

Answer:

4/33

Step-by-step explanation:

Multiply 3x4 across which equals 12

Multiply 11x9 across which equals 99

Simplify to equal 4/33

Hope this helps!! :)

Answer:

Exact Form:

433

Decimal Form:

0.¯¯12¯¯

Step-by-step explanation:

Answer:

B) \(4i\sqrt{2}\)

Step-by-step explanation:

\(\sqrt{-2}=i\sqrt{2}\\\sqrt{-18}=i\sqrt{18}=i\sqrt{9*2}=3i\sqrt{2}\\\\\sqrt{-2}+\sqrt{-18}=i\sqrt{2}+3i\sqrt{2}=4i\sqrt{2}\)

Answer:

Question 1:

As the pollster used the telephone directory, they will get the numbers of listed people in that community. Cellphones are not listed along with households with telephones so these will be underrepresented.

Question 2:

Question 3:

Households with unlisted numbers will still be called because the person is using random dialling which means that even if the number is not listed, it can still be called. Households with landlines will most definitely be reachable as well.

Answer:

See below

Step-by-step explanation:

Starting with 42, there would be two branches of 2 and 21 connected to 42. Since 2 is prime, there are no more branches. Since 21 is composite, then two more branches are drawn of 3 and 7 connected to 21. Since 3 and 7 are prime, there are no more branches.

Therefore, the prime factorization of 42 is 2*3*7, and its factors would be 1,2,3,6,7,14,21,42.

Answer:

i = right angle

ii = obtuse angle

iii = straight angle

iv = obtuse angle

v = acute angle

Step-by-step explanation:

an acute angle is an angle less than 90 degrees

an obtuse angle is an angle more than 90 degrees

a right angle is an angle equivalent to 90 degrees (looks like two straight lines perpendicular)

a straight angle is an angle equivalent to 180 degrees (looks like a straight line)

a reflex angle is an angle greater than 180 degrees

so, ...

i = right angle

ii = obtuse angle

iii = straight angle

iv = obtuse angle

v = acute angle

The volume of the cardboard box is approximately 13197.402 cubic inches.

The volume of a cardboard box is 216 dm³, we can convert it to the English system of measurements.

1 dm (cubic decimeter) is equivalent to 1 liter.

To convert dm³ to cubic inches, we can use the following conversion factors:

1 dm³ = 61.0237 cubic inches

Using this conversion factor, we can calculate the volume of the box in cubic inches:

The cube carton volume is 216 dm3 and the cube edge value is 6 dm.

The volume of the cube is calculated by dividing the edge values. In other words, volume = edge 3.

To find the edge (side) value, you can solve for the volume formula as follows:

edge 3 = volume.

edge = ∛ volume,

Where ∛ is the cube root.

Applying this formula to the given problem gives edge = ∛(216 dm³).

Edge = 6dm. Therefore, the side (edge) value of the cube is 6dm.

Volume (cubic inches) = 216 dm³ * 61.0237 cubic inches/dm³

= 13197.402 cubic inches

Question :- If the volume of a cubic cardboard box is 216 dm³

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Answer: Done-

Step-by-step explanation:

The pairs of numbers that have HCF 4 and LCM 60 are : 4 and 60 , 12 and 20.

In this case, we must use the following relationship between HCF and LCM:

Number 1 + Number 2 = HCF x LCM

In other words, multiplying both factors equals multiplying the given numbers that we are looking for. We don't know the numbers yet, but we can get an idea of what they could be by calculating the product of the factors:

4 x 60 = 240

We know that the products should be 240 and that if the HCF is 4 , then both numbers can be divided by 4 as the highest factor, so let's write the multiple of 7:

4-digit multiples:

4, 8, 12, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60

By using, we can get an idea: if 60 x 4 = 240, all we need to do is find the other two numbers that result in 240:

So the pairs of numbers are 4 and 60 , 12 and 20.

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Answer:

answer is 18096.

Step-by-step explanation:

12,4×10=124

124-(4+4)=124-8=116

(1,5×104)=156

116×156=18096

Answer: 8

Step-by-step explanation:

I do not understand the question. But if my interpretation is correct, then:

If there are 64 players and 3 rounds, 32 will get out in the first round. 16 will get out in the second, and 8 will get out on the third. Thus, the answer is 64-(32+16+8) or just simply 8.