a ladder ft long leans against a vertical wall. if the lower end is being moved away from the wall at the rate of ​ft/sec, how fast is the height of the top changing​ (this will be a negative​ rate) when the lower end is feet from the​ wall?

The formula that represents the volume of water in the tank in terms of the number of minutes since the water began draining is v = 40 - 1.5t.

This can be seen by realizing that the volume of water in the tank decreases by 1.5 gallons per minute, so after t minutes the volume will be 40 - 1.5t. The graph of this formula is a straight line with a slope of -1.5 and an intercept of 40. This means that the graph starts at the point (0,40), which represents a tank that is full of water, and decreases linearly as the number of minutes increases.

The statement "The graph of v in terms of t represents all possible values of v and t" is true. This is because the formula v = 40 - 1.5t is defined for all possible values of t, and the graph of this formula includes all possible pairs of (v, t) values that satisfy the formula.

The statement "The point (7.5,35.75) conveys that when the tank has been draining for 7.5 minutes, it has 35.75 gallons of water remaining" is false. This is because the point (7.5,35.75) does not lie on the graph of the equation v = 40 - 1.5t. The correct point on the graph that represents the volume of water in the tank after 7.5 minutes would be (7.5,26.25), which can be found by substituting t = 7.5 into the equation v = 40 - 1.5t.

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The least amount of extra cash Lilianna requires is $126 and the inequality is [tex]x+$68\geq 194[/tex]

What justifies an inequality?

The relationship between two values in an imbalanced algebraic statement is represented by an inequality in mathematics. One of the two variables can be larger than, more than or equal to, smaller than, or equal to another value by using a sign of inequality.

Let

The least amount of extra money is x.

The fact that

[tex]x+$68\geq 194[/tex]

The problem is represented by inequality.

Solve for x.

[tex]x+$68\geq 194\\x\geq $126[/tex]

The least amount of money Lilianna requires is $126

and inequality is [tex]x+$68\geq 194[/tex]

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The points (-10, 0) and (0, 5), on the path of the first boat that can be modeled by a quadratic function and the point (10, 4) on the path of the linear function modelling the second boat, indicates that besides the common starting location, the solution for the point at which the paths of the  boats cross again at (6, 3.2)

The solution to a system of equation is the value of the input variable at which the output of the equations in the system of equations are the same.

Location of the port = (-10, 0)

The vertex of the path of the first boat that can be modeled by a quadratic function = (0, 5)

Point through which the boat that follows a path that can be modeled as a linear function passes = (10, 4)

The vertex form of the equation of a parabola is; y = a·(x - h)² + k

Where;'

(h, k) = The coordinates of the vertex

(h, k) = (0, 5)

Therefore;

y = a·(x - 0)² + 5 = a·x² + 5

When x = -10, y = 0, therefore;

y = 0 = a·(-10)² + 5 = 100·a + 5

0 = 100·a + 5

a = -5/100 = -1/20

a = -0.05

The equation is therefore; y = -0.05·x² + 5

The slope of the straight line path of the other boat is; m = (4 - 0)/(10 - (-10)) = 1/5 = 0.2

The equation is therefore; y - 0 = 0.2·(x - (-10)) = 0.2·x + 2

y = 0.2·x + 2

The point where the two paths cross is therefore;

-0.05·x² + 5 = 0.2·x + 2

-0.05·x² - 0.2·x + 5 - 2

-0.05·x² - 0.2·x + 3 = 0

x = (0.2 ± √((-0.2)² - 4 × (-0.05) × 3))/(2×(-0.05))

Therefore;

x = -10 and x = 6

The x-coordinate of the point the two paths cross, besides the starting location is x = 6

Therefore;

y = 0.2 × 6 + 2 = 3.2

The point besides the common starting location, the paths of the boats cross is; (6, 3.2)

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Answer:

(–6, 3.2)

Step-by-step explanation:

The answer above is correct.

When evaluating an exercise, evaluators record their observations in the exercise evaluation guide (eeg). observations that should be recorded include d.) a and b

When analyzing an activity, evaluators record their observations in the Exercise Evaluation Guide (EEG) (EEG). Actual time needed by exercise participants to perform the necessary tasks and resources used are among the observations that should be recorded.

EEGs (Exercise Evaluation Guides) offer a reliable instrument to direct exercise monitoring and data gathering. EEGs list capability aims and crucial tasks that are in line with exercise objectives and core capabilities.

EEGs achieve a number of objectives:

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The probability the game lasts less than 4.5 hours is 0.2877.

μ = mean population = 5

σ = standard deviation = 0.9

The probability for the game lasts less than 4.5 hours can be calculated using z test formula.

P(x < 4.5) = P(z < [tex]\frac{x-\mu}{\sigma}[/tex] )

= P(z < [tex]\frac{4.5-5}{0.9}[/tex])

= P(z < -0.56)

Using z table for P(z < -0.56). So,

= 0.2877

Thus, the probability is 0.2877 for the game lasts less than 4.5 hours.

Your question is incomplete, but most probably your full question was

on average, an american professional football game lasts about five hours, even though the ball is actually in play only 11 minutes. assume that game times are normally distributed with a standard deviation of 0.9 hour. 1. Find the probability that a game lasts less than 4.5 hours.

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Answer:

I hope this helps for you

If 5 out of 200 things were flawed, the population's estimated defect percent would be 2.5%.

Percent, which is a relative figure used to denote hundredths of any amount. Since one percent (symbolized as 1%) is equal to one tenth of anything, 100 percent stands for everything, while 200 percent refers to double the amount specified. The word "percent" simply refers to "per hundred," and the sign for percentage is %. By multiplying the total or whole number by 100, one percent (or 1%) is equal to one hundredth of the whole or whole.

Here,

Total number of items=200

number of defective items=5

Percentage of defective items,

=5/200*100

=2.5%

Therefore, if 5 out of 200 things were defective, the population's estimated percentage of defective items is 2.5%.

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Answer:

Step-by-step explanation:

ANSWER: 40x^2+10xy-15y^2

Lenth * Width * Height:

(4x+3y)*(2x-y)*5

Distribute 5 through the parentheses :

(20x+15y)*(2x-y)

Simplify:

40x^2-20xy+30xy-15y^2

Collect like terms:

40x^2+10xy-15y^2

As per the dimensions, the volume of rectangular-shaped glass is equal to 40x² + 10xy - 15y².

Every three-dimensional item takes up space in some way. The volume of this area is what is used to describe it. The area covered within an entity's three-dimensional bounds is referred to as its volume. The object's size is another name for it.

As per the given information in the question,

Use the formula of volume:

Length × Width × Height:

(4x+3y) × (2x-y) × 5

5 should be distributed through parenthesis:

(20x+15y) × (2x-y)

Now, simplify the above equation,

40x² - 20xy + 30xy - 15y²

Now, keep all like terms together,

40x² + 10xy - 15y²

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Answer:

60

Step-by-step explanation:

she read 60 pages in just 2 days

The type of sample that the sample taken by Marlene represents is a Convenience sample.

Researchers who use convenience sampling obtain market research data from a pool of respondents who are conveniently accessible. Because it is so rapid, easy, and economical, it is the sampling procedure that is used the most frequently. If members choose to be part of the sample, they are frequently simple to get in touch with.

Therefore, Marlene employed a convenience sampling technique by going to the park, which was close by, and taking a sample of the people present.

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The value of z-stat is -0.6721.

What is z stat?

The relationship between a value and the mean of a group of values is quantified by a Z-stat. The Z-stat is calculated using standard deviations from the mean. When a data point's Z-stat is 0, it means that it has the same score as the mean.

One standard deviation from the mean would be indicated by a Z-stat of 1.0. Z-stats can be positive or negative; a positive value means the score is above the mean, while a negative value means it is below the mean.

Solution Explained:

We use the formula,

[tex]z = \frac{P - \pi }{\sqrt{\frac{\pi (1-\pi )}{200} }}[/tex], where P is the observed proportion, π is the hypothesized proportion

Therefore, P = 42/200 = 0.21 & π = 23/100 = 0.23

Putting the values in

[tex]z = \frac{0.21 - 0.23 }{\sqrt{\frac{0.23 (1-0.23)}{200} }}[/tex]

After calculating, z-stat is therefore equal to -0.6721

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The inequality and the maximum possible width are 12w  ≥ 132 and 11 feet respectively

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g 2x > 4

If the room is 12 feet long and  Tom had enough paint to cover an area of 132 square feet. This implies Tom had paint that can cover greater or equal to 132 square feet of area. Thus:

L x w ≥ A

where l = 12 feet, A = 132 square feet

12w  ≥ 132    (This is the inequality)

To solve for width:

12w  ≥ 132

w ≥ 132 /12

w ≥ 11 feet

Therefore, the inequality is 12w  ≥ 132 and the maximum possible width is  11 feet

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Answer:

Step-by-step explanation:

You want to know the x- and y-intercepts of a function described by a data table.

The x-intercept is the x-value where y = 0. There is no y=0 entry in the table, and the entries there are not regular enough to support any speculation as to how the function might be extrapolated.

There is no x-intercept.

The y-intercept is shown in the table where x=0.

The y-intercept is (0, 7).

The probability that he hits a target at most 13 times is 0.5031 when a marksman has a 0.89 percent chance of hitting the target each time he fires.

Given that,

A marksman has a 0.89 percent chance of hitting the target each time he fires.

We have to find what is the probability that he will only hit the target 13 times out of 15 shots.

We know that,

The probability of getting exactly k successes in n trials is given by the probability mass function that is,

P(X=k)=[tex](\frac{n}{k} )p^{k}(1-p)^{n-k}[/tex]

Where [tex](\frac{n}{k})= n!/k!(n-k)![/tex]

The probability that he hits the target at most 13 times is,

1-[P(he hits 14 times)+P(he hits 15 times)]

So, calculate the probability that he hits a target 14 times as follows:

P(X=14)=[tex](\frac{15}{14} )0.89^{14}(1-0.89)^{1}[/tex]

P(X=14)=15×(0.89)¹⁴×(0.11)

P(X=14)=0.3228

And the probability that he hits a target 15 times is

P(X=15)=[tex](\frac{15}{15} )0.89^{15}(1-0.89)^{0}[/tex]

P(X=15)=1×(0.89)¹⁵×(1)

P(X=15)=0.1741

And the required probability is

=1-[P(he hits 14 times)+P(he hits 15 times)]

=1-[0.3228+0.1741]

=0.5031

Therefore, The probability that he hits a target at most 13 times is 0.5031 when a marksman has a 0.89 percent chance of hitting the target each time he fires.

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Step-by-step explanation:

0.5×3×4= 6cm^2

6×8

=48cm^3

After evaluation, the resultant value of the function f(2009) is 1.9021.

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X.

The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

Any input for x results in a single output for y.

Considering that x is the input value, we would state that y is a function of x.

So, evaluate f(2009) as follows:

Given that f(x) is a function with all positive real numbers satisfying the requirement that f(x) > 0 and for all x > 0 and also:

[tex]\begin{aligned}&f(x-y)=\sqrt{f(x y)+1} \\&x > 0, y > 0 \\&\text { for, } x=1, \text { and } y=\frac{1}{2} \\&f\left(1-\frac{1}{2}\right)=\sqrt{f\left(1 \times \frac{1}{2}\right)+1} \\&f\left(\frac{1}{2}\right)^2=f\left(\frac{1}{2}\right)+1 \\&f\left(\frac{1}{2}\right)=\frac{1+\sqrt{5}}{2}\end{aligned}[/tex]

Now, consider: x = 2009 and y = 0

[tex]\begin{aligned}&f(2009-0)=\sqrt{f(2009 * 0)+1} \\&f(2009)=\sqrt{f(0)+1} \\&f(2009)=\sqrt{f\left(\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{2}}\right)+1} \\&f(2009)=\sqrt{\sqrt{f\left(\frac{1}{\sqrt{2}} * \frac{1}{\sqrt{2}}\right)+1}+1} \\&f(2009)=\sqrt{\sqrt{f\left(\frac{1}{2}\right)+1}+1} \\&f(2009)=\sqrt{\sqrt{\frac{1+\sqrt{5}}{2}+1}+1} \\&f(2009)=\sqrt{\sqrt{\frac{3+\sqrt{5}}{2}}+1} \\&f(2009)=\sqrt{\sqrt{5.2362}+1} \\&=\sqrt{3.6180} \\&=1.9021\end{aligned}[/tex]

Therefore, after evaluation, the resultant value of the function f(2009) is 1.9021.

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Answer:

yes y/x = 5/2

Step-by-step explanation:

y/x = 5/2, 10/4=5/2, 15/6=5/2, 20/8=5/2

Answer: 144a^14 b^8

Step-by-step explanation:

(-4a^(5)b^(3))^(2)* (-3a^(2)b)^(2) = 144a^14 b^8

The number line that represents the number 0.7 is number line (B)

From the question, we have the following parameters:

From the dots on each line, we have the following statement

At minus 0.7 on B

This statement means that

B = -0.7

Hence, the number line represented by the statement is the number line B

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We REJECT the null hypothesis that these rats came from a population with a mean of 32 in favour of the alternative that they were selected in a way that the mean was different from 32 because our test statistic is bigger than this (in absolute value).

In the given question,

The population mean is 32g with a st. dev. of 4g.

We collect a sample of n=25 mice with a sample average of 30.4g.

We wish to test the hypothesis that these were drawn randomly from the population.

So our null hypothesis is

H0: mean = 32

Our alternative hypothesis is

HA: mean ≠ 32.

This is a two-sided test.

A sample mean should have the same mean as the population mean, and the sample st. dev. should be (pop st. dev./√n).

In this case, under the null hypothesis, the sample mean should be distributed with an average of 32 and a st. dev. of 4/√25 = 4/5 = 0.8.

To test this hypothesis, we need to calculate a test statistic and compare it to a critical value of the standard normal distribution.

Our test statistic is:

z = (Observed value - hypothesized value) / (st. dev. in sample mean)

z = (30.4-32)/0.8

z = -1.6/0.8

z = -2.

The critical value of the z-distribution with α/2 = 0.05/2 = 0.025 is 1.96.

We REJECT the null hypothesis that these rats came from a population with a mean of 32 in favour of the alternative that they were selected in a way that the mean was different from 32 because our test statistic is bigger than this (in absolute value).

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The right answer is:

A colony of laboratory mice consists of several thousand mice. The average weight of all the mice is 32 grams with a standard deviation of 4 grams. A laboratory assistant was asked by a scientist to select 25 mice for an experiment. However, before performing the experiment the scientist decided to weigh the mice as an indicator of whether the assistant’s selection constituted a random sample or whether it was made with some unconscious bias (perhaps themice selected were the ones that were slowest in avoiding the assistant, which might indicate some inferiority about this group). If the sample mean of the 25 mice was 30.4, would this be significant evidence, at the 5 percent level of significance, against the hypothesis that the selection constituted a random sample?

The  proportion of the total variation in the sample y-values that can be explained by the estimated linear relationship between x and y is 0.48

Given:

SSR = 1.9350

SST = 4.012

we are asked to find the proportion of the total variation in the sample y-values that can be explained by the estimated linear relationship between x and y.

To find the sample proportion we need to divide.

SSR/SST

= 1.9350/4.012

= 0.48

Hence we get the required answer as 0.48

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Considering the number of trials in the data, the binomial distribution only counts the two possible states, which are typically represented as 1 (for a success) or 0 (for a failure).

The probability distribution known as the binomial distribution, which is used in statistics, quantifies the chances that a value will take one of two independent values given a particular set of conditions or hypotheses.

The fundamental presumptions of the binomial distribution are that each trial has only one possible outcome, that each trial has the same success probability, and that each trial is independent of the others or mutually exclusive.

The likelihood of success is constant from trial to trial, and subsequent trials are independent. A binomial distribution, which derives from counting successes across a series of trials, has just two possible outcomes on each trial.

Hence, Considering the number of trials in the data, the binomial distribution only counts the two possible states, which are typically represented as 1 (for a success) or 0 (for a failure).

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Both the given expression are equivalent expression as 5m + 4.

Given that,
to determine whether the two given expressions are equivalent ot each other,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression,
5(m + 1 ) - 1 = 2(2m + 2) + m
5m + 5 - 1 = 4m + 4 + m
5m + 4 = 5m + 4

Thus, Both the given expression are equivalent expression as 5m + 4.

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Answer:

Step-by-step explanation:

(attached)

The quadratic equation 15[tex]x^{2}[/tex]-22x -7 = 0 has solution x = 1.7355 or -0.26886

In algebra, a quadratic equation (from Latin quadratus 'square') is any equation that can be rearranged in standard form as

a[tex]x^{2}[/tex] + bx + c =0

where x represents an unknown value, and a, b, and c represent known numbers. One supposes generally that a ≠ 0; those equations with a = 0 are considered degenerate because the equation then becomes linear or even simpler. The numbers a, b, and c are the coefficients of the equation and may be distinguished by calling them, respectively, the quadratic coefficient, the linear coefficient and the constant or free term.

The values of x that satisfy the equation are called solutions of the equation, and roots or zeros of the expression on its left-hand side. A quadratic equation has at most two solutions. If there is only one solution, one says that it is a double root. If all the coefficients are real numbers, there are either two real solutions, or a single real double root, or two complex solutions that are complex conjugates of each other. A quadratic equation always has two roots, if complex roots are included; and a double root is counted for two. A quadratic equation can be factored into an equivalent equation

given that

5(x-1)3x = 7(x+1)

15[tex]x^{2}[/tex]-15x = 7x +7

15[tex]x^{2}[/tex]-22x -7 = 0

x = -b ± [tex]\sqrt{b^{2}-4ac }[/tex]/2a

x = -(-22) ± [tex]\sqrt{(-22)-4(15)(-7)}[/tex] /2(15)

x = 1.7355 or -0.26886

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Answer: x = 12

Step-by-step explanation:  

Distribute the parenthesis on both sides of the equation

5x - 5 + 3x = 7x + 7

8x - 5 = 7x + 7 ( subtract 7x from both sides )

x - 5 = 7 ( add 5 to both sides )

x = 12

Therefore, your answer is: x = 12

The greatest volume of the cone made be 4372.7 m³.

Given, a right triangle whose hypotenuse is 22 m long is revolved about one of its legs to generate a right circular cone.

Let the base of the right triangle be, b

and the height of the right triangle be, h

Using Pythagoras Theorem, we get

22² = b² + h²

484 = b² + h²

Now, the height of the cone be, h and the radius of the cone be, b

Volume of the cone =  1/3πb²h

as, b² = 484 - h²

Volume = 1/3π(484 - h²)h

Volume = 1/3π(484h - h³)

On differentiating, we get

V' = 1/3π(484 - 3h²)

h² = 484/3

h = 22/√3

h = 22√3/3

b = 22√2/√3

Volume = 1/3π(22√2/√3)(22√2/√3)(22√3/3)

Volume = 1/9√3π(22³)(2)

Volume = 4372.7 m³

Hence, the greatest volume of the cone made be 4372.7 m³.

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Answer:

Length=18 feet

Width=7 feet

Hope this helps! :)

Step-by-step explanation:

perimeter=50

length=18

width=w

Rectangle:2l+2w=50           2(18)+2(7)=50

36+2w=50

50-36=14

14/2=7

(36+14+50)

Answer:

33.45 is the price of 11 dog food cans