A 8 1/4 inch candle burns down in 11 hours how far has it burns after 8 1/2 hours

Step-by-step explanation:

G=2m

m+G=30

m +2m =30

3m=30

m=10

The highest point for the quadratic function for the height of the object, h(t) = -16·t² + 224·t + 816, indicates that the interval over which the height of the object is increasing is; (-∞, 7]

The shape of the graph of a quadratic function is a parabola.

The function for the height of the object in question 3 is; h(t) = -16·t² + 224·t + 816

Where;

t = The time in seconds

The height of the object is increasing in the interval to the left of the highest point, which can be found as follows;

The x-coordinate of the highest point of the quadratic function, f(x) = a·x² + b·x + c is; x = -b/(2·a)

Therefore, the x-coordinates of the highest point of the object is; -224/(2 × (-16)) = 7

Therefore, the height of the object is increasing in the interval; -∞ < t ≤ 7

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The interest earned and the future value of an annuity with monthly payments of $200 for two years that pays 6% interest per year compounded monthly is $25.43 and $225.43

Principal,P = $200

Time, t = 6%

Number of periods, n = 12

Interest rate, r = 6%

= 6/100

= 0.06 rate per year,

FV = P(1 + r/n)^nt

FV = 200.00(1 + 0.06/12)^(12)(2)

FV = 200.00(1 + 0.005)^(24)

FV = $225.43

Therefore,

Principal = $200.00

Interest = $25.43

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Answer:

The roots of this function are at -4 and -1.

f(x) = (2x + 8)(-2x - 2)

= (2x + 8)(-2x + (-2))

The volume of the cylindrical silo is 6,431 cubic feet.

For a cylinder with a height H and a radius R, the volume is given by the formula:

V = pi*R^2*H

Where pi = 3.14

In this case, we know that the height is 32 feet, then:

H = 32ft

We also know that the diameter is 16 ft, and the radius is half of that, so:

R = 16ft/2 = 8ft

Replacing all of that in the volume formula we get:

V = 3.14*(8ft)^2*32ft = 6,430.72 ft²

Rounding to the next whole number in this case means that we need to round up, so the volume is  6,431 ft²

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Answer:

33m

Step-by-step explanation:

add up all of the sides

9+9=18

18+15=33

Answer:

9+9+15 = the perimeter.

Step-by-step explanation:

The perimeter is the length of the outside lines of the triangle.

9+9+15 = 33

Answer:

7.4

Step-by-step explanation:

10% of 74 is 7.4 by moving the decimal over one place. This will save them $7.40

The derivative of the function g(x) as given in the task content by virtue of the Fundamental theorem of calculus is; g'(x) = √2 ln(t) dt = 1.

g(x) = Integral; √2 ln(t) dt (with the upper and lower limits e^x and 1 respectively).

Since, it follows from the Fundamental theorem of calculus that given an integral where;

Now, g(x) = Integral f(t) dt with limits a and x, it follows that the differential of g(x);

g'(x) = f(x).

Consequently, the function g'(x) which is to be evaluated in this scenario can be determined as:

g'(x) = \(\int\limits^{e^x}_1 2 ln(t) dt\) = 1

The derivative of the function g(x) as given in the task content by virtue of the Fundamental theorem of calculus is; g'(x) = √2 ln(t) dt = 1.

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Answer:

25g/4 - 2/3

Is what I got

Answer:

The answer is x = 5

Step-by-step explanation:

1) Remove parentheses.

\(x - 4 - 1\)

2) Add 4 to both sides.

\(x = 1 + 4\)

3) Simplify 1 + 4 to 5.

\(x = 5\)

Therefor, the answer is x = 5.

Answer:

X = 5

Step-by-step explanation:

This is an example of a basic algebraic equation! The explanation is below

\((x-4)=1\\x-4=1\\x-4+4=1+4\\x=5\)

Above, we simply removed the parenthesis, added four to both sides in order to cancel out "-4", and ended up with 5 = x. We know we are correct because 5 minus 4, really does equal one!

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Answer:

10, -5+5i*sqrt(3), -5-5i*sqrt(3).

Step-by-step explanation:

x^3=1000

x=10, -5+5i*sqrt(3), -5-5i*sqrt(3).

An irrational number is a number that cannot be expressed as a fraction or a ratio of two integers. Let's examine each option:

1. The number pi: Pi (π) is an irrational number. It is a mathematical constant representing the ratio of a circle's circumference to its diameter. Pi cannot be expressed as a fraction or a terminating decimal. It is an infinite, non-repeating decimal (approximately 3.14159...).

2. A whole number: Whole numbers are integers without any fractional or decimal parts. They include positive numbers (0, 1, 2, 3, ...) and their negatives (-1, -2, -3, ...). Whole numbers can always be expressed as fractions by setting the denominator as 1, making them rational numbers.

3. Fractions: Fractions are numbers expressed as the ratio of two integers. They can be written in the form a/b, where a and b are integers and b is not zero. All fractions are rational numbers because they can be expressed as the division of two integers.

4. A decimal that terminates: A terminating decimal is a decimal number that has a finite number of digits after the decimal point. Terminating decimals can always be expressed as fractions, making them rational numbers. For example, 0.25 can be written as 1/4.

Based on the explanations above, the only option that represents an irrational number is "The number pi."

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Answer:

x ≈ 20.0

Step-by-step explanation:

using the cosine ratio in the right triangle

cos26° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{18}{x}\) ( multiply both sides by x )

x × cos26° = 18 ( divide both sides by cos26° )

x = \(\frac{18}{cos26}\) ≈ 20.0 ( to the nearest tenth )

Answer:

\({ \tt{f(x) = - 10x - 18}} \\ { \tt{g(x) = - 3x}} \\ \\ { \tt{(f - g)(x) = ( - 10x - 18) -( - 3x) }} \\ \\ { \tt{(f - g)(x) = ( - 10x + 3) - 18}} \\ \\ { \tt{(f - g)(x) = - 7x + (3 - 18)}} \\ \\ { \tt{(f - g)(x) = - 7x - 15}}\)

Answer: 5575 Marbles

Step-by-step explanation:

This can be solved simply by subtracting and adding.

3409-1290=2119

2119+3456=5575

The intercepts of the parabola are A ( 6 , 0 ) and B ( -2 , 0 ) and the y intercept of the parabola is ( 0 , -12 )

A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line

The equation of the parabola is given by

( x - h )² = 4p ( y - k )

y = a ( x - h )² + k

where ( h , k ) is the vertex and ( h , k + p ) is the focus

y is the directrix and y = k – p

The equation of the parabola is also given by the equation

y = ax² + bx + c

where a , b , and c are the three coefficients and the parabola is uniquely identified

Given data ,

Let the equation of the parabola be represented as A

Now , the value of A is

y = x² - 4x - 12   be equation (1)

On simplifying , we get

when y = 0

x² - 4x - 12 = 0

On factorizing the quadratic equation , we get

x² - 6x + 2x - 12 = 0

( x + 2 ) ( x - 6 ) = 0

So , the two values of x are

when ( x + 2 ) = 0

x = -2

And , when ( x - 6 ) = 0

x = 6

So , the x intercepts of the parabola are A ( 6 , 0 ) and B ( -2 , 0 )

The y intercept is when x = 0

So , y = 0 - 0 - 12

y = -12

And , the y intercepts of the parabola are ( 0 , -12 )

Hence , the intercepts of the parabola are solved

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By considering these rules and properties of integers, the correct result of 6 was obtained.

When writing the response, I considered the following information:

The product or quotient of two integers with different signs is negative. This rule was used to determine that 2(-12) equals -24, not 24.

To subtract an integer, add its opposite. This rule was applied when subtracting -30 from -24, resulting in -24 - (-30) = -24 + 30.

To add integers with opposite signs, subtract the absolute values. The sum has the same sign as the integer with the greater absolute value.

This rule was used to calculate -24 + 30 = 6, where the absolute value of 30 is greater than the absolute value of -24.

By considering these rules and properties of integers, the correct result of 6 was obtained.

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The formula for perimeter is 2(Length) + 2(width)

Fill in the known information:

22 = 2(6.5)+ 2(width)

Simplify:

22 = 13 + 2(width)

Subtract 13 from both sides:

9 = 2(width)

Divide both sides by 2:

Width = 4.5m

Answer:

  a. {1, 2, 3, 4, 5, 6, 7}

  b. {1, 2, 3, 4, 5, 6, 8}

  c. {4, 5, 7}

  d. {1, 4, 5}

Step-by-step explanation:

The union of two sets is the list of elements in either set. The intersection of two sets is the list of elements in both sets. The complement of a set is the list of elements in the universal set that are not in the set being complemented. The complement of a set can be indicated with an apostrophe: A' is the complement of set A, for example.

B∪C = {2, 5, 6, 7} ∪ {3, 4, 6, 7} = {2, 3, 4, 5, 6, 7}

A∪(B∪C) = {1, 4, 5, 7} ∪ {2, 3, 4, 5, 6, 7} = {1, 2, 3, 4, 5, 6, 7}

B∩C = {2, 5, 6, 7} ∩ {3, 4, 6, 7} = {6, 7}

A ∩ (B∩C) = {1, 4, 5, 7} ∩ {6, 7} = {7}

(A∩(B∩C))' = {7}' = {1, 2, 3, 4, 5, 6, 8}

A∩Β = {1, 4, 5, 7} ∩ {2, 5, 6, 7} = {5, 7}

Α∩C = {1, 4, 5, 7} ∩ {3, 4, 6, 7} = {4, 7}

(A∩B)∪(A∩C) = {5, 7} ∪ {4, 7} = {4, 5, 7}

(A∩B')∪(A∩C') = A∩(B'∪C') = A∩(B∩C)'

(B∩C)' = {6, 7}' = {1, 2, 3, 4, 5, 8}

A∩(B∩C)' = {1, 4, 5, 7} ∩ {1, 2, 3, 4, 5, 8} = {1, 4, 5}

__

Additional comment

In part (d) we made use of De Morgan's law for sets:

  B'∪C' = (B∩C)'

We also made use of the distributive property for sets:

  A∩(B∪C) = (A∩B)∪(A∩C)

Answer:

a) f(1) = 3

b) f(-1) = -0.25

c) x = 0, 3

d) x = -0.75

e) domain   [-2, 4]

    range   [-1, 3]

Step-by-step explanation:

In this graph, f(x) is represented by the y-axis.

a) We can see that f(1) (the y-value when x = 1) is 3.

b) Looking at the graph, we can estimate f(-1) as about -0.25.

c) We need to find the x-values when the y-axis is at 1. We can see that there are two points at x = 0, 3.

d) Looking at the graph, we can estimate that f(x) = 0 around when x = -0.75.

e) The domain of a function is its set of x-values. We can see that f(x) spans from x = -2 to x = 4. That range in interval notation is: [-2, 4]

The range of a function is its set of y-values. We can see that f(x) spans from y = -1 to y = 3. That range in interval notation is: [-1, 3].

Answer: Yes

Step-by-step explanation:

The statement that describes the distribution based on the given information is:

A) The distribution is approximately Normal, with a mean of 128 messages and a standard deviation of 98 messages.

The graph shows a normal distribution, as indicated by the shape of the curve. The highest point of the curve (the peak) is at 128, which represents the mean of the distribution.

The standard deviation measures the spread of the data, and based on the information given, it is 98. Therefore, option A accurately describes the distribution.

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Answer:

59.3 °

Step-by-step explanation:

its trigonometry

so you have the

opposite side= 43.5

and the adjacent side = 24.8

if you use SOH CAH TOA you will find that to find y you need to use TOA as tou have the opposite and adjacent.

to find the angle (tan) you need to do tue opposite / adjacent

tan^-1 (43.5/25.8)

= 59.3 to 1 d.p.

you need to use tan^-1 as you are finding the missing angle

a) To find the average life of the ten batteries, we need to calculate the mean, which is the sum of all the values divided by the number of values.Sum of all values = 10.8 + 10.6 + 11.4 + 8.9 + 10.1 + 10.6 + 9.9 + 12.6 + 10.5 + 11.9 = 106.2

Number of values = 10

Average life = Sum of all values / Number of values = 106.3 / 10 ≈ 10.63

Therefore, the average life of the ten batteries, rounded to the nearest tenth of an hour, is approximately 10.6 hours.

b) Comparing the two advertisements:

i) The first advertisement claims that Atlas batteries are guaranteed to last 10 hours. This means that all Atlas batteries are expected to last at least 10 hours. However, based on the data provided, we can see that the average life of the batteries is approximately 10.6 hours, which is higher than the guaranteed 10-hour minimum

ii) The second advertisement claims that Atlas batteries have an average life of over 10 hours. This statement aligns with the data we have, as the average life of the batteries is indeed over 10 hours.

Based on the information provided, the second advertisement claiming that Atlas batteries have an average life of over 10 hours is more accurate, as the average life calculated from the given data is 10.6 hours.

In summary, the average life of the ten batteries is approximately 10.6 hours, and the second advertisement stating an average life of over 10 hours is more accurate based on the data provided.

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Answer:

\(-8(y+4) =(x-6)^{2}\)  

Step-by-step explanation:

The standard form of a parabola is given by the following equation:

\((x-h)^{2} =4p(y-k)\)

Where the focus is given by:

\(F(h,k+p)\)

The vertex is:

\(V=(h,k)\)

And the directrix is:

\(y-k+p=0\)

Now, using the previous equations and the information provided by the problem, let's find the equation of the parabola.

If the focus is (-6,6):

\(F=(h,k+p)=(6,-6)\)

Hence:

\(h=6\\\\k+p=-6\hspace{10}(1)\)

And if the directrix is \(y=-2\) :

\(-2-k+p=0\\\\k-p=-2\hspace{10}(2)\)

Using (1) and (2) we can build a 2x2 system of equations:

\(k+p=-6\hspace{10}(1)\\k-p=-2\hspace{10}(2)\)

Using elimination method:

(1)+(2)

\(k+p+k-p=-6+(-2)\\\\2k=-8\\\\k=-\frac{8}{2}=-4\hspace{10}(3)\)

Replacing (3) into (1):

\(-4+p=-6\\\\p=-6+4\\\\p=-2\)

Therefore:

\((x-6)^{2} =4(-2)(y-(-4)) \\\\(x-6)^{2} =-8(y+4)\)

So, the correct answer is:

Option 3

Answer:

0.75 g ≤ 35

Step-by-step explanation:

if each games costs $0.75, then the answer of g will be given by 35/0.75.

he can go up to exactly $35 but not over

so, the inequality is given by 0.75 g ≤ 35