A storage tank is completely empty. At 12:00 noon, oil is poured into the top of the tank and a valve is opened at the bottom. Oil is poured into the tank at a rate of 2.1 gallons per minute and the valve at the bottom empties at a rate of 1.9 gallons per minute. If the tank does not fill until 12:00 the next day, how many gallons does the tank hold?

Answer: The height of the ball (in meters) after t seconds is given by the equation h = 2 + 5t - 5t^2. We can use this equation to find the values of t for which the ball's height is 3 meters.

We need to find the values of t that make h = 3, so we can substitute 3 for h in the equation:

3 = 2 + 5t - 5t^2

Then we can solve for t by moving all the terms to one side of the equation and factoring it:

-5t^2 + 5t - 1 = 0

And we can use the quadratic formula to find the solutions of this equation:

t = (5 +/- sqrt(5^2 - 4*(-1)(-1)))/ 2(-1)

t = (5 +/- sqrt(25 + 4))/ -2

t = (5 +/- sqrt(29))/ -2

The solutions of this equation are t = (5 +/- sqrt(29))/ -2

Since the time, t, is a real value the square root of 29 should be positive.

The values of t for which the ball's height is 3 meters are not real values, so there's no time when the ball's height is 3 meters.

Step-by-step explanation:

The number of​ 18-inch wreaths is 7, and

the number of 22-inch wreaths is 18.

When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."

There are both one-variable and two-variable linear equations.

Given the cost of an 18-inch wreath = $15

cost of a 22-inch wreath = $30

let the number of 18-inch wreaths be x and the number of  22-inch wreaths is y,

the total cost of both wreaths = $645

cost of x 18-inch wreaths = $15x

cost of y  22-inch wreaths = $30y

equation is,

$15x + $30y = $654

and the number of​ 22-inch wreaths sold was four more than twice the number of​ 18-inch wreaths,

y = 4 + 2x

substitute the value of y in the equation

15x + 30y = 645

15x + 30(4 + 2x) = 645

15x + 60x = 645 - 120

75x = 525

x = 525/75

x = 7

and y = 4 + 2x

y = 4 + 2*7

y = 18

Hence store sells 18  22-inch wreaths and 7  18-inch wreaths.

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Answer:

(x^2 - 7)(4x - 3)

Step-by-step explanation:

first, we split the expression by grouping the first two terms in parentheses and the last two terms in parentheses. this gives us:

[tex](4x^{3}-3x^{2})(-28x+21)[/tex]

next, we factor out the GCF of each group. this gives us:

[tex]x^{2}(4x-3)-7(4x-3)[/tex]

finally, all you have to do is take each factored-out term and put them together into a group/expression. the leftover expression from both groups is the same value, so you get:

[tex](x^{2}-7)(4x-3)[/tex]

hope this helped, good luck!

Answer:

m∠ABD = 111

Step-by-step explanation:

69 + x = 180

x = 111

Answer:

< ABD  = 111 °

Step-by-step explanation:

< ABD and < DBE form a straight line which is 180 degrees

< ABD + < DBE = 180

< ABD + 69= 180

< ABD  = 180 -69

< ABD  = 111

The equation which represents the graph function is g ( x ) = f ( x - 3 ) + 3

Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.

Identify the even and odd multiplicities of the polynomial functions' zeros.

Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.

The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities

Given data ,

Let the function be represented as A

Now , the value of A is

f ( x ) = x³   be equation (1)

Now , the graph of the function f ( x ) is plotted with the exponent value meeting closely at ( 0 , 0 )

And , the function which describes the function g ( x ) is given by

g ( x ) = f ( x - 3 ) + 3

Hence , the function is g ( x ) = f ( x - 3 ) + 3

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By performing a change of units, we will see that the caterer should purchase 107.8 lb

First, let's find how many kilograms are needed. We know that the recipe recomends using 0.7kg per person, and there are 70 guests, so an estimate of the mass needed is:

M = 70*0.7kg = 49 kg

Now weneedto do a change of units, we know that:

1 kg =  2.2 lb

Then we can rewrite:

49 kg = 49*(2.2 lb) = 107.8 lb

The caterer should purchase 107.8 pounds

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The required  initial and final amounts of water contained in the pool are 46 ans 26 gallons of water.

A graph is made up of vertices, or points, and edges, or lines connecting those vertices. In addition to linked and disconnected graphs, weighted graphs, bipartite graphs, directed and uncorrected graphs, and simple graphs, there are many other forms of graphs.

As graph says

The initial amount of water contained in the pool is

at t = 0

= 46 gallons of water

And at t = 5, is final amount of water in pool

= 26 gallon of water

Thus, there are 46 ans 26 gallons of water.

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Answer:

Answer in attached photo.

Step-by-step explanation:

Solution in attached photo, do take note the standard form of an equation is:

y = mx + c,

where m is the gradient and c is the y-intercept.

Answer: (x– 8)2= 4(1)(y+ 3); vertex: (8, –3); opens upward

(a) The average rate of change over the interval [2, 5] is given by (f(5) - f(2)) / (5 - 2), which is equal to (24 - 16) / (5 - 2) = 8 / 3 = 2.67.

(b) The average rate of change over the interval [3.8, 4] is given by (f(4) - f(3.8)) / (4 - 3.8), which is equal to (19 - 19.6) / (4 - 3.8) = -0.6 / 0.2 = -3.

The average rate of change over a given interval [a, b] is a measure of how much the value of a function changes on average as the input changes over that interval. It is calculated as the difference between the value of the function at the endpoints of the interval divided by the difference of the corresponding inputs.

Formally, the average rate of change over the interval [a, b] is given by:

f_avg = (f(b) - f(a)) / (b - a)

where f is the function being evaluated and f_avg represents the average rate of change.

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The chance of exactly one of population members A, B, and C being in a sample of 100, drawn randomly from a population of 100,000 is 0.0003%.

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Answer:

Step-by-step explanation:

[tex]-63y^2+27y[/tex]

[tex]-63yy+27y[/tex]

[tex]-9\cdot \:7yy+9\cdot \:3y[/tex]

[tex]9y\left(-7y+3\right)[/tex]

divide the lateral height in half, Height squared lateral height squared is subtracted from height squared, the answer from step three, and find its square root. The radius of the cone is the outcome.

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Therefore , the solution of the given problem of volume comes out to be 9,003.75π cubic cm.

The following are the conical Frustum formulas in terms of r and h: V = (1/3) * * h * (r12 + r22 + (r1 + r2)) is the formula for a conical frustum's volume. The base's radius is the same as the cylinder's radius. The cylinder's height is equal to the length of the altitude, which is a segment running perpendicular to the planes of each of its bases.

Here,

Given :

=> 15 cm is the AB

=> radius = 49/2 = 24.5 cm

The radius of base is 24.5 cm

and

the volume of frustrum:

=> π(24.5)(24.5)(15)

=> 9,003.75π cubic cm

Therefore , the solution of the given problem of volume comes out to be

9,003.75π cubic cm.

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Reducing the completion average  time for Jobs J and K by one day will shorten the overall project completion time by one day, allowing the project to finish one day early.

In order to finish the project one day early, the completion time for Jobs J and K should be reduced by one day. This is because these two jobs are part of the three critical paths of the project. By reducing the completion time for these two jobs by one day, the entire project will be completed one day early. This is because the critical paths are the paths that will determine the overall project completion time. By reducing the completion time for these two jobs, the overall project completion time will be shortened. This will allow the project to be finished one day earlier than expected.

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Answer: In the figure above, clearly the line L is perpendicular to x-axis and passing through the value 'c' on x- axis. So, the equation of a line perpendicular to x axis is x = c

After the raise, Tyler's brother will make $14 x 1.05 = $14.70 per hour.

Answer:

14 x 1.05 = 14.70

Step-by-step explanation:

The type of sampling used in this example is Convenience sampling.

Convenience sampling is a type of non-probability sampling in which the sample is selected based on the ease of access or availability of the subjects. The sample is selected based on the researcher's convenience, and it does not use a random selection process.

In this case, the reporter chose to interview people in his own apartment building because it was convenient for him and he had easy access to them.

The other options you listed are:

a) Cluster sampling, which is a form of probability sampling in which the sample is selected by first dividing the population into smaller groups or clusters, and then selecting a random sample of those clusters.

b) Voluntary response sampling, which is a type of non-probability sampling where individuals choose to participate in the study.

c) Systematic sampling, which is a form of probability sampling in which the sample is selected by choosing a random starting point and then selecting every nth subject from the population.

d) Attempted census, which is when the researcher tries to include all members of a population in the sample.

Therefore, The type of sampling used in this example is Convenience sampling.

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it would take 29.5 hours the second airplane to overtake the first.

speed is described as. the pace at which an object's location changes in any direction. Speed is defined as the distance traveled divided by the travel time. Speed is a scalar quantity because it just has a direction and no magnitude.

Given, Two airplanes leave Philadelphia for Rochester. The first airplane to leave travels at an average speed of 590 kilometers per hour. The second airplane, which leaves 3 hours later, travels at an average speed of 650 kilometers per hour.

So, in 3 hours first airplane will reach at;

Distance = speed *time

Distance = 590 * 3

Distance travels by first airplane in 3 hours will be = 1770 km

Since, Relative speed of given two planes = 650 - 590

Relative speed of given two planes = 60 km/hour

To reach 1770 km it would take  = 1770/60 hours

Thus,

To reach 1770 km it would take  = 29.5 hours

therefore, it would take 29.5 hours the second airplane to overtake the first.

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Answer:

1.478 x 10^2 AU

Step-by-step explanation:

To convert this distance to astronomical units (AU), we can use the fact that 1 AU is approximately equal to 93 million miles.

So, 13.8 billion miles is approximately:

13.8 billion miles / 93 million miles/AU = 147.8 AU

In scientific notation, this distance would be written as: 1.478 x 10^2 AU

Probability of less than 50 % democrats for the example based on sample proportion is equal to 0.1562.

Sample size 'n' = 100

Registered voters  'p' = 55%

                                    = 0.55

σ = √ p( 1- p )/ n

  = √0.55( 0.45)/ 100

  = 0.04975

Mean 'μ' = 55%

               = 0.55

Probability of getting less than 50% democrats in a sample size of 100 voters

X = 0.5

Z = ( X - μ ) / σ

  = ( 0.5 - 0.55) / 0.4975

 = -1. 005

 = -1.01

p-value pf -1.01 is equal to 0.156248

Therefore, the probability of getting 50% democrats for the given sample size id equal to 0.1562. The given example represents sample proportion.

The above question is incomplete , the complete question is :

In a congressional district, 55% of the registered voters are Democrats. Which of the following is closest to the probability of getting less than 50% Democrats in a random sample of size 100?

Is this an example of a sample proportion OR a sample mean?

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There is a difference in average systolic blood pressure between smokers and non-smokers.

To evaluate if average systolic blood pressure differs by smoking status, we need to calculate the mean systolic blood pressure for both smokers and non-smokers. We can calculate the mean systolic blood pressure for smokers by taking the sum of systolic blood pressure values for all smokers in the sample, divided by the number of smokers in the sample. This formula can be written as:

Mean Systolic Blood Pressure for Smokers = (Sum of Systolic Blood Pressure Values for all Smokers) / (Number of Smokers)

Similarly, we can calculate the mean systolic blood pressure for non-smokers by taking the sum of systolic blood pressure values for all non-smokers in the sample, divided by the number of non-smokers in the sample. This formula can be written as:

Mean Systolic Blood Pressure for Non-Smokers = (Sum of Systolic Blood Pressure Values for all Non-Smokers) / (Number of Non-Smokers)

Once we have calculated the mean systolic blood pressure for both smokers and non-smokers, we can compare the two means to evaluate if there is a difference in average systolic blood pressure between smokers and non-smokers.

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the fourth one. I know it is correct, you may look it up on the desmos graphing calculator if you have suspicion it is not.

The amount Jacob has to pay in a month where he used x GB over the limit is  y=25+20x.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Jacob has a smart phone data plan that costs $25 per month that includes 5 GB of data, but will charge an extra $20 per GB over the included amount.

Amount Jacob has to pay in a month where he used 4 GB over the limit is

25+4×20

= $105

Amount Jacob has to pay in a month where he used x GB over the limit is

y=25+20x

Where, y is total amount of money

Hence, the amount Jacob has to pay in a month where he used x GB over the limit is  y=25+20x.

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Answer:

Step-by-step explanation:

I don’t know just 5 point

Differentiating the expression [tex]\frac{d}{dx} [(4x-7)^4(7x+8)^5 ][/tex] with respect to x will be [tex]16(4x-7)^3(7x+8)^5 + 35(4x-7)^4(7x+8)^4[/tex]

We are given with

[tex]\frac{d}{dx} [(4x-7)^4(7x+8)^5 ][/tex]

Here we will be using the chain rule. According to the chain rule, we will first have to solve the parentheses as a variable. Then we will have to solve the expression within the parenthesis

First, we will differentiate [tex](4x-7)^4[/tex] keeping [tex](7x+8)^5[/tex] constant. Here we will first assume [tex](4x-7)[/tex] as one variable and differentiate using the formula d/dx[x^n] then we will differentiate 4x - 7 to get just 4. They would be multiplied by one another

Hence we get

[tex]4 X4(4x-7)^3(7x+8)^5[/tex]

[tex]16(4x-7)^3(7x+8)^5[/tex]

Now, we will keep [tex](4x-7)^4[/tex] constant and differentiate [tex](7x+8)^5[/tex] and adding it up we get

[tex]16(4x-7)^3(7x+8)^5 + 5X7(4x-7)^4(7x+8)^4[/tex]

[tex]= 16(4x-7)^3(7x+8)^5 + 35(4x-7)^4(7x+8)^4[/tex]

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Complete Question

[tex]\frac{d}{dx} [(4x-7)^4(7x+8)^5 ][/tex]

Answer:

20,45 kg,

Step-by-step explanation:

45  Lb * (1 kg / 2,2 Lb) + (12 Austrália * (1 kg / 35 ,2 Austrália)) = 20,45 kg

Um resposta é 20,45 kg.

The required value of exponential function for the given values of x are 1.43, 1 , 0.7.

Calculating the exponential growth or decay of a given collection of data is done using an exponential function, which is a mathematical function. Exponential functions, for instance, can be used to estimate population changes, loan interest rates, bacterial growth, radioactive decay, and disease spread. ​

We have,

f(x) = [tex](0.7)^{x}[/tex]

So, at x = -1

f(x) = (0.7)^-1

f(x) = 1.43

At x = 0

f(x) = (0.7)^0

f(x) = 1

At x = 1

f(x) = (0.7)^1

f(x) = (0.7)

Thus, required value of function are 1.43, 1, 0.7

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Answer:

Yes, one gallon is enough

Step-by-step explanation:

16ft x 12ft = 192ft

If one gallon covers 250 square feet then she will have enough for another 58ft remaining

Answer: Anything that has the same two numbers

Step-by-step explanation:

You don't have a picture, so I'm basing this off of what I know. A number over another number that is the same is equivalent to one.