A light bulb consumes 600 watt hours per day. How many Watt hours? Does it consume in 3 days and 12 hours?

We have been given that a new kind of rocket takes off along an exponential trajectory, with height, in miles, represented by [tex]3^x[/tex], where x is the time, in seconds. We are asked to find the time when the height of the rocket id 8 miles.

To find the time, we will equate height function with 8 and solve for x as:

[tex]3^x=8[/tex]

To solve for x, we will take natural log on both sides as:

[tex]\ln(3^x)=\ln (8)[/tex]

We can rewrite 8 as [tex]2^3[/tex].

[tex]\ln(3^x)=\ln (2^3)[/tex]

Using natural log property [tex]\ln(a^b)=b\cdot \ln(a)[/tex], we will get:

[tex]x\cdot \ln(3)=3\cdot\ln (2)[/tex]

[tex]\frac{x\cdot \ln(3)}{ \ln(3)}=\frac{3\cdot\ln (2)}{ \ln(3)}[/tex]

[tex]x=\frac{3\cdot\ln (2)}{ \ln(3)}[/tex]

Therefore, exact solution will be [tex]\frac{3\cdot\ln (2)}{ \ln(3)}[/tex].

[tex]x=\frac{2.0794415416798359}{1.0986122886681097}[/tex]

[tex]x=1.892789260714[/tex]

Upon rounding to nearest thousandth, we will get:

[tex]x\approx 1.89[/tex]

Therefore, the height of the rocket will be 8 miles after approximately 1.89 seconds.

Answer:

8223 cubic meter

Step-by-step explanation:

Louvre Pyramid

Vertical Height =21.6 meters

Side Length of Square Base =35 m

Volume of a Pyramid [tex]=\frac{1}{3}*$Base Area X Height[/tex]

Therefore, Volume of Louvre Pyramid[tex]=\frac{1}{3}*35^2 X 21.6[/tex]

=8820 cubic meter.

Inverted Pyramid

Vertical Height =7 meters

Side Length of Square Base =16 m

Volume of a Pyramid [tex]=\frac{1}{3}*$Base Area X Height[/tex]

Therefore, Volume of Louvre Pyramid[tex]=\frac{1}{3}*16^2 X 7[/tex]

=597.33 cubic meter.

Difference in Volume

Difference=Volume of Louvre Pyramid-Volume of Inverted Pyramid

=8820-597.33

=8222.67

=8223 cubic meter (to the nearest cubic meter)

Answer:

  B.  4 bags

Step-by-step explanation:

The number of bags that will have the same quantities of the different gifts is the Greatest Common Divisor of the numbers of gifts.

  GCD(24, 32, 44) = 4

Mrs. Dupree can make at most 4 identical bags.

___

How to find the GCD

The GCD can be found by looking at factors:

4 is the largest common factor of these numbers.

__

The GCD can also be found using Euclid's algorithm. In that algorithm, the larger number is divided by the smaller, with the remainder replacing the larger number after each step. If the remainder is zero, the smaller number is the GCD.

The GCD of several numbers can be found by finding the GCD of a pair, then of that value and the next number:

  GCD(24, 32, 44) = GCD(GCD(24, 32), 44) = GCD(8, 44) = 4

_

  32/24 = 1 r 8 . . . . first step in Euclid's algorithm for GCD(24, 32)

  24/8 = 3 r 0   ⇒   GCD(24, 32) = 8

Then

  44/8 = 5 r 4

  8/4 = 2 r 0   ⇒   GCD(8, 44) = 4 = GCD(24, 32, 44)

The domain and range of each function y = 3.52 is All real numbers and {3.52}.

The domain of a function is defined as the set of all the possible input values that are valid for the given function.

The range of a function is defined as the set of all the possible output values that are valid for the given function.

We are given that;

The function y=3.52

Now,

For the function y = 3.52, the output (y-value) is always the same, regardless of the input (x-value). Therefore, the domain of this function is all real numbers, and the range of this function is the single value 3.52.

Therefore, the domain and range will be All real numbers and {3.52}

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Answer:

Paul is the youngest at 17 years old. Fiona is 20 years old, Sara is 23 years old

Step-by-step explanation:

Assign variables to the ages.

S = sara's age

F = Fiona's age

P = Paul's age.

S + F + P = 60

S = 3 + F

P = F - 3

(3 + F) + F + (F - 3) = 60

3 + 3F - 3 = 60

3F = 60

F = 20

S = 23

P = 17

Answer:

x=46 gives us the minimum value

Step-by-step explanation:

Let us have the height of the box to be y. Since the box has a square base, let us call the side of the base as x. So, the volume of the box is given by

[tex]x^2\cdot y = 48668[/tex]. From here, we know that [tex]y=\frac{48668}{x^2}[/tex]

Now, we will find the area of the box. Since the box has an open top, then we only have the 4 sides of the box and the base. The base is a square of side x, so its area is [tex]x^2[/tex]. Recall that each side is a rectangle of base x and height y. So, the are of one side is [tex]x\cdot y[/tex]. Then, the area of the box is given by the function

[tex]A(x,y) = x^2+4xy[/tex]. Since we can relate y to x through the volume, this can be a function of one variable. Namely

[tex]A(x) = x^2+4x\cdot \frac{48668}{x^2}= x^2+4\cdot \frac{48668}{x} = x^2+48668x^{-1}[/tex]

If we want to find the mininum value, we should derive the function A and find the value of x for which A'(x) is zero. REcall that the derivative of a function of the form [tex]x^n[/tex] is [tex]nx^{n-1}[/tex]. Then, applying the properties of derivatives, we have

[tex] A'(x) = 2x-4\cdot \frac{48668}{x^2} = \frac{2x^3-4\cdot 48668}{x^2}[/tex]

So, we want to solve the following equation

[tex]2x^3-4\cdot 48668 =0[/tex]

which implies [tex]x^3 = 97336[/tex]. Using a calculator we get the value [tex] x= 46[/tex]

REcall that to check if the point is a minimum, we use the second derivative criteri. It states that the point x is a mininimum if f'(x) =0 and f''(x)>0

Note that [tex]A''(x) = 2+8\cdot\cdot 48668}{x^3}[/tex], note that A''(46) = 6>0, so x=46 is the minimum value of the area.

To find the formula for the surface area of the box in terms of only the length of one side of the square base, express the height of the box in terms of x. The formula for the surface area is S = 194672 / x + x².

To find the formula for the surface area of the box in terms of only the length of one side of the square base, we need to express the height of the box in terms of x. The volume of the box is given as 48668 cm³, which is equal to the base area (x²) multiplied by the height (h). So, we have the equation x² * h = 48668. Solving for h, we get h = 48668 / x².

The surface area of the box consists of the area of the four sides of the box (4 * x * h) and the area of the square base (x²). We can substitute the value of h in terms of x into this expression to get the simplified formula for the surface area: S = 4 * x * (48668 / x²) + x². Simplifying further, we get S = 194672 / x + x².

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The correct answer is that the probability of the random variable having an outcome of 3 is 0.

To solve this problem, we need to understand that the random variable assigns the number of blue marbles drawn to each outcome of the experiment. Since the experiment consists of two independent draws with replacement, there are four possible outcomes:

1. Draw a blue marble, then draw another blue marble.

2. Draw a blue marble, then draw a red marble.

3. Draw a red marble, then draw a blue marble.

4. Draw a red marble, then draw another red marble.

The probability of drawing a blue marble in a single draw is given as 3/8. Therefore, the probability of drawing a red marble is the complement of this, which is 1 - 3/8 = 5/8.

Now, let's calculate the probability of each of the four outcomes:

1. The probability of drawing two blue marbles (BB) is (3/8) * (3/8), because the draws are independent.

2. The probability of drawing a blue marble followed by a red marble (BR) is (3/8) * (5/8).

3. The probability of drawing a red marble followed by a blue marble (RB) is (5/8) * (3/8).

4. The probability of drawing two red marbles (RR) is (5/8) * (5/8).

Since the random variable assigns the number of blue marbles to each outcome, the only way to have an outcome of 3 is to draw a blue marble, then draw another blue marble. This is the first outcome listed above.

The probability of drawing two blue marbles (BB) is (3/8) * (3/8) = 9/64.

However, the question asks for the probability of the random variable having an outcome of 3. Since the maximum number of blue marbles that can be drawn in two draws is 2, it is impossible to have an outcome of 3. Therefore, the probability of the random variable having an outcome of 3 is 0.

In conclusion, the probability that the random variable has an outcome of 3 is 0, because it is not possible to draw more than 2 blue marbles in two independent draws with replacement from a bag where the probability of drawing a blue marble is 3/8.

Answer: 42

Step-by-step explanation:

convert 5 1/4 to an improper fraction=21/4

then multiply 21/4 • 8 = 42!

hope this helps (:

The volume of the rectangular prism is, 42 units³

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

For a rectangular prism,

Base area = 5 1/4 units

Height = 8 units

We know that;

The volume of the rectangular prism = Base area x Height

Substitute given values, we get;

The volume of the rectangular prism = Base area x Height

The volume of the rectangular prism = 5 1/4 x 8

The volume of the rectangular prism = 21/4 x 8

The volume of the rectangular prism = 42 units³

Thus, The volume of the rectangular prism is, 42 units³

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Answer:

  no

Step-by-step explanation:

Look at the first numbers of each ordered pair:

  4, 8, 4, 20, 12

If any are repeated, the relation is NOT a function. Here, 4 is repeated.

The relation is not a function.

Answer:

282.7431 cm^2 (Lateral Surface Area)

Step-by-step explanation:

If you didn't need Lateral Surface Area let me know and I'll see what I can do :3

Answer:

The probability that the first drop of rain will be felt between 9:10 AM and 3:30 PM on at least one of the next two days is 0.2639.

Step-by-step explanation:

The random variable X is defined as the time a new thunderstorm begins to produce rain.

The random variable X is uniformly distributed throughout the day, i.e. between the 24 hours a day or 1440 minutes.

[tex]X\sim Uniform\ [0, 1440][/tex]

The probability density function of X is:

[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b,\ a<b[/tex]

It is provided that it will rain at some point both of the next two days.

Compute the probability that the first drop of rain will be felt between 9:10 AM and 3:30 PM as follows:

9:10 AM = (9 × 60) + 10 = 550 minutes.

3:30 PM = 15:30 = (15 × 60) + 30 = 930 minutes.

Compute the value of P (550 < X < 930) as follows:

[tex]P(550<X<930)=\int\limits^{930}_{550}{\frac{1}{1440-0}}\, dx\\\\=\frac{1}{1440}\times \int\limits^{930}_{550}{1}\, dx\\\\=\frac{1}{1440}\times [x]^{930}_{550}\\\\=\frac{930-550}{1440}\\\\=0.2639[/tex]

The probability that the first drop of rain will be felt between 9:10 AM and 3:30 PM is 0.2639.

Then the complement of this event is:

The probability that the first drop of rain will not be felt between 9:10 AM and 3:30 PM is:

P (Not between 9:10 AM and 3:30 PM) = 1 - 0.2639 = 0.7361

Compute the probability that the first drop of rain will be felt between 9:10 AM and 3:30 PM on at least one of the next two days as follows:

P (At least 1) = 1 - P (Less than 1)

                    = 1 - P (None)

                    = 1 - P (Not between 9:10 AM and 3:30 PM)

                    = 1 - 0.7361

                    = 0.2639

Thus, the probability that the first drop of rain will be felt between 9:10 AM and 3:30 PM on at least one of the next two days is 0.2639.

Answer:

1) The most common salary is $460.

2) The salary that half of the employees surpassed is $475

3) The percentage of employees with salaries below $485 is 75%

4) 75% of the employees have a salary above $450.

5) The salary that stands 3 standard deviations below the mean is $380

6) 33% of the employees have a salary above $483.

7) The salary that stands 2 standard deviations above the mean is $530

Step-by-step explanation:

Hello!

1. What is the most common salary?______________

The measure that allows you to know which one is the most common value (i.e. the most frequent/observed number) in a data set is the mode. According to the given statistics, the most common salary is $460.

2. What salary did half the employees surpass?_________________

The measure that divides the sample in exactly a half (bottom 50% from the top 50%) is the median. In this example the salary that half of the employees surpassed is $475.

3. About what percent of employee's salaries is below $485?__________________

As you can see in the descriptive statistics, the third quartile (Q₃) is $485.

The Q₃ is the value that divides the bottom 75% of the sample from the top 25%. So the percentage of employees with salaries below $485 is 75%

4. What percent of the employees are above $450?___________________

The first quartile (Q₁) is the value that separates the bottom 25% of the sample from the top 75%. In this case Q₁= $450, which means that 75% of the employees have a salary above $450.

5. What salary is 3 standard deviations below the mean?____________________

The mean is $ 470 and the standard deviation is $30, the salary that stands 3 standard deviations below the mean is

X[bar]-3S= $470-3*$30= $380

6. About what percent of employee's salaries is above $483?__________________

P₆₇= $483, this value is the 67th percentile and means that 67% of the employees have a salary below $483.

If 67% are below $483, then 100 - 67= 33% of the employees have a salary above $483.

7. What salary is 2 standard deviations above the mean?______________________

The mean is $ 470 and the standard deviation is $30, the salary that stands 2 standard deviations above the mean is

X[bar]+2S= $470+2*$30= $530

I hope you have a SUPER day!

Answer:

121

Step-by-step explanation:

Answer:

if the 1/4 is supposed to be small and above the 12, the answer should be 12

Step-by-step explanation:

test

The answer is D.) (13,0)

I remember seeing this question somewhere before... Along with the graph.

Additionally, make sure to add the graph to the question next time!

The coordinates of focus are ( 13, 0)

The hyperbola can be defined as the difference of distances between a set of points, which are present in a plane to two fixed points is a positive constant.

A hyperbola is a set of points whose difference of distances from two foci is a constant value. This difference is taken from the distance from the farther focus and then the distance from the nearer focus. For a point P(x, y) on the hyperbola and for two foci F, F', the locus of the hyperbola is PF - PF' = 2a.

We know,

Foci for hyperbola is : (c,0) and (−c,0)

As, from the attached graph below the focus is:

Focus : ( 13, 0)

Hence, the Focus is: ( 13, 0).

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Answer:

The correct answer is A

Step-by-step explanation:

1,260 divided by 180 = 7

180 times 6 = 1,080

180 times 7 = 1,260

If the car traveled 1260 miles, then 42 gallons of gas would be used.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

y = mx also represents direct proportionality. We can write [m] as -

m = y/x

OR

y₁/x₁ = y₂/x₂

We have the amount of gas consumed by a car varies directly with the miles driven.

Using the formula for direct proportionality -

y₁/x₁ = y₂/x₂

180/6 = 1260/x₂

x₂ = (1260 x 6)/180

x₂ = (126 x 6)/18

x₂ = (21 x 2)

x₂ = 42

Therefore, If the car traveled 1260 miles, then 42 gallons of gas would be used.

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Answer:

Step-by-step explanation:

34

Answer:

552.78

Step-by-step explanation:

45 x 6 =270

2πr = r x 2 x 3.142 = 45 x 2 x 3.142 = 282.78

270 + 282.78

The total length of the steel when both the circular section is added would be = 552.6cm.

The total length of the steel can be calculated following the steps below:

The total length of the 6 stems with 45cm = 45×6 = 270cm

The length of circular section = 2πr

where r = 45cm

C = 2× 3.14×45

= 282.6

The total length = 270+ 282.6

= 552.6cm

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Answer:

Check the explanation

Step-by-step explanation:

First define the below events

Delayt : Traffic delay in current period

Delayt-1 : Traffic delay in preceding period

No-Delayt : No traffic delay in current period

No-Delayt-1 : No traffic delay in preceding period

Based on above definitions, define below given probabilities

P(No-Delayt/No-Delayt-1) = Probability of "no delay" in current period given that "no delay" in preceding period

= 0.85

P(Delayt/Delayt-1) = Probability of "delay" in current period given that "delay" in preceding period

= 0.75

and given that one period = 30 minutes

a) Given that motorist already knows that there is a traffic delay, probability of delay in next 60 minutes will be possible if both the consecutive periods is in "delay" state.

Period A Period B

---------------- -----------------

Delay -------> Delay ------> Delay

Since both the delay events should occur together(consecutive) to get the required probability, hence

Probability that next 60 minutes(two consecutive periods) will be in delay state

= P(Delayt/Delayt-1) * P(Delayt/Delayt-1)

= 0.75 * 0.75

= 0.5625 [ANSWER]

b) probability that in the long run the traffic will not be in the delay state is equivalent to proability that all the time in No-delay state.

First calculate the probability of currren period in delay state given that preceding period in No-delay state

 P(Delayt/No-Delayt-1) = 1 - P(No-Delayt/No-Delayt-1)

= 1 - 0.85

= 0.15

Now the required probability,

  P(All the time No-Delay state) = 1 - P( one period in delay state)

= 1 - ( P(Delayt/Delayt-1) + P(Delayt/No-Delayt-1) )

= 1 - (0.75 + 0.15)

= 0.10 [ANSWER]

c) Yes. Because this assumption assumes that for the 30 minutes traffic will be in delay state and just after 30 minutes, there will be No-delay state which is a hypothetical situation. In general scenario, traffic doesn't behave like this. To make the model more realistic, the probabilities might have been modeled as a function of time, instead of being constant for 30 minutes.

Cutting off one corner of a rectangular prism creates a bicapped trigonal prismatic shape.

When you cut off one of the corners of a rectangular prism, you would get a shape known as a bicapped trigonal prismatic. This shape is formed by twisting one face of a cube relative to another, folding opposing faces towards one another, and distorting the original rectangular prism.

Answer:

The answer is A

Step-by-step explanation:

When doing an equation you always have to follow this order: exponents, parentheses, multiply/divide, then addtion/subtraction

Answer:

327

Step-by-step explanation:

7 ones = 7*1 = 7

2 tens = 2*10 = 20

3 hundreds = 3 * 100 = 300

300 +20 +7 = 327

Answer:

A

Step-by-step explanation:

the solid figure that has the shape like a cereal box is a rectangular prism

listen yeah

plot the points on the graph and join up dots

then draw a line x = 4 so 4 on x axis draw a vertical line as its line of symmetry

then reflect the shape

for the x co ordinates, say that they are different because the x values are not the same

for the y co ordinates, say thay they are the same because the y values did not change

plot points on 2nd graph and join up dots

then draw a line y = 2 so 2 on y axis draw a horizontal line as its line of symmetry

then reflect shape

for the x co ordinates, say that they are the same because the x values did not change

for the y co ordinates, say that they are different because the y values are not the same

Answer:

Step-by-step explanation:

The growth factor is 1 added to the growth rate of 1.5%, so is 1.015. This factor is applied each year. So the number of students will be the original number multiplied by this factor as many times as there are years (after 2002).

Repeated multiplication is signified using an exponent. The function can be written as ...

  n(t) = 972×1.015^t

In 12 years after 2002, the number of students is modeled as ...

  n(12) = 972×1.015^12 ≈ 1162 . . . students in 2014

__

When the change is described as "increased by ...", it means the function is modeling growth. If the population were to decrease, it would be considered decay. That is, the "growth factor" is greater than 1 for growth, and less than 1 for decay. 1.015 is greater than 1, so this is considered growth.

Answer:

The volume of the hemisphere is 496741.6 m³

Step-by-step explanation:

The volume of an sphere is given by:

[tex]V_{s} = \frac{4\pi r^{3}}{3}[/tex]

In which [tex]\pi = 3.14[/tex] and r is the radius.

An hemisphere is half of an sphere, so it's volume is half the sphere's volume. So

[tex]V_{h} = \frac{V_{s}}{2} = \frac{2\pi r^{3}}{3}[/tex]

In this question:

[tex]r = 61.9[/tex]. So

[tex]V_{h} = \frac{2\pi (61.9)^{3}}{3} = 496741.6[/tex]

The volume of the hemisphere is 496741.6 m³

Answer:

The volume of the hemisphere = 496741.6 m³

Step-by-step explanation:

Volume of a sphere is= (4/3) × π × r³

r is the radius

π is 22/7

hemisphere is half of an sphere,

so the volume of henisphere is  (2/3) × π × r³

Given that ;

r = 61.9 m

[tex]V = \frac{2\pi (61.9)^{3}}{3} = 496741.6[/tex]

therefore, the volume of the hemisphere is 496741.6 m³

Answer:

Red-5-0.1

Blue-0.26

White-10

Green-22

Step-by-step explanation:

In the experiment, Alexis drew colored balls and you need to organize the results in a frequency table. The numbers given represent frequency counts for each color. Keep in mind that the total draws were 50, so no frequency count should exceed this number.

The question is about Alexis' experiment involving drawing colored balls from a box. The results of the 50 trials are recorded in a frequency table. As the student, you are expected to correctly assign certain numbers to their respective places in this table. These numbers represent the total counts per color across the 50 trials.

To accomplish this, you must first understand what a frequency table is. A frequency table is a method of organizing raw data in a compact form by displaying a series of data values in ascending order, along with their corresponding frequencies.

In this scenario, the frequencies are the number of times Alexis drew a ball of a specific color. For example, if she drew a red ball 15 times, we would put 'Red' in the color column and '15' in the frequency column.

Please note that not all the provided numbers will be used, and there should be no number in the table higher than 50 since that was the maximum number of trials Alexis performed.

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Answer:

143°

Step-by-step explanation:

We know that the two lines are parallel, which means that since ∠A and ∠B are same-side angles, they are equal. That means we can set the expressions equal:

7x + 24 = 3x + 92

4x = 68

x = 17

Plug this into the expression for A:

∠A = 7x + 24 = 7 * 17 + 24 = 143

The answer is 143°.

Since both lines are parallel, both equations are equal.

7x + 24 = 3x + 92

Solve for x.

~Subtract 24 to both sides

7x + 24 - 24 = 3x + 92 - 24

~Simplify

7x = 3x + 68

~Subtract 3x to both sides

7x - 3x = 3x - 3x + 68

~Simplify

4x = 68

~Divide 4 to both sides

4x/4 = 68/4

~Simplify

x = 17

Substitute 17 with x in ∠A

∠A = 7x + 24

∠A = 7(17) + 24

∠A = 119 + 24

∠A = 143

Best of Luck!

Answer:

(C)18 Units

Step-by-step explanation:

Volume of a Triangular Prism =Base Area X Height

The base is a right triangle of base 8 Units and Height 15 Units.

Area of the Triangle =0.5 x 8 x 15 =60 Square Units

Base Area, B=60 Square Units

Since Volume of the Triangular Prism=1080

1080=60h

Divide both sides by 60

Height of the Prism=18 Units