Tom takes exactly 30 minutes to rake a lawn and his son Mike takes exactly 60 minutes to rake the same lawn. If Tom and Mike decide to rake the lawn together, and both work at the same rate that they did previously, how many minutes will it take them rake the lawA. 16


b. 20


c. 36


d. 45


e. 90

Statements are sentences that express a fact or proposition that can be either true or false.The statements are a and b.

a. "1,024 is the smallest four-digit number that is a perfect square." - This is a statement because it presents a specific fact that can be verified.

b. "She is a mathematics major." - This is a statement because it describes a person's academic major.

c. "128 = 26" - This is not a statement because it presents an incorrect equation.

d. "x = 26" - This is not a statement unless the value of x is specified. Without knowing the value of x, it is an equation rather than a statement.

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Answer:

See below.

Step-by-step explanation:

x^4+5x-3

The expression is odd. x^4 is also equal to 1x^4. 5 is odd, and 3 is odd.

-hope it helps

Answer:

The following function is f(x) = -9x 4 + 5x+3 is neither even nor odd.

Step-by-step explanation:

Because a function is said to be even if f (-x) = f (x). Then a function is said to be odd if f (-x) = -f (x). And there is your answer to those who need help with their math.

Answer:

y=1x-5

Step-by-step explanation:

Answer:

The equation for line one is y = -2x - 5

Answer:

A. 63

Step-by-step explanation:

Given functions:

    f(x) = 2x² + 5

    g(x) = 8 + x

find:

g o f(-5)

Solution:

Start first by finding f(-5);

       f(x) = 2x² + 5

              = 2(-5)² + 5

              = 50 + 5

              = 55

Now

g o f(-5);

     g(55) = 8 + 55 = 63

Answer:

Look at attachment

Step-by-step explanation:

There is sufficient proof to presume that under 77% of messages are spam.

A statistical hypothesis test  is a technique for measurable induction used to conclude whether the information within reach adequately support a specific theory. Speculation testing permits us to offer probabilistic expressions about populace boundaries.

Given the information in the inquiry;

Test size n = 500

x = 361

p₀ = 77% = 0.77

q₀ = 1 - p₀ = 1 - 0.77 = 0.23

p = x/n = 361/500 = 0.722

Speculation;

Null hypothesis H₀ : p ≥ 77% or 0.77

Alternative hypothesis  Hₐ : p ≥ 77% or 0.77

Test Measurement

z = ( p - p₀ )/√( ( p₀ × q₀ )/n )

so we substitute

z = ( 0.722 - 0.77 )/√( ( 0.77 × 0.23 )/500 )

z = - 0.048/√( 0.1771/500 )

z = - 0.048/√0.0003542

z = - 0.048/0.01882

z = - 2.55

so our p-worth will be;

p-value = p( z < - 2.55 ) {from table }

p-value = 0.0054

at 0.05 degree of importance ∝

p-value ( 0.0054 ) is not as much as importance level ∝ ( 0.05 )

Accordingly we Reject Null hypothesis H₀

Thus, there is sufficient proof to presume that under 77% of messages are spam.

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If a large cube is made up of 27 equal-sized smaller cubes, and all faces of the large cube are painted, then the cubes on the interior of the large cube will not have any paint on any of their faces.

The large cube consists of 27 smaller cubes arranged in a 3x3x3 pattern. The smaller cubes on the exterior faces of the large cube will have some of their faces painted, while the smaller cubes on the interior will not have any of their faces painted.

To calculate the number of smaller cubes that will not have any paint on any of their faces, we need to subtract the smaller cubes on the exterior faces from the total number of smaller cubes in the large cube.

The number of smaller cubes on the exterior faces of the large cube can be calculated as follows:

There are 9 smaller cubes on each of the six faces of the large cube (3x3=9), for a total of 54 smaller cubes on the exterior faces.

So, the total number of smaller cubes in the large cube is 27, and the number of smaller cubes on the exterior faces is 54. Therefore, the number of smaller cubes that will not have any paint on any of their faces is:

27 - 54 = -27

Since we cannot have a negative number of cubes, the correct answer is 0. There will be 0 smaller cubes that will not have any paint on any of their faces.

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Answer:

\(y=-\frac{1}{2}x-3\)

Step-by-step explanation:

Hi there!

Linear equations are typically organized in slope-intercept form: \(y=mx+b\) where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)

1) Determine the slope (m)

\(m=\frac{y_2-y_1}{x_2-x_1}\) where the two given points are \((x_1,y_1)\) and \((x_2,y_2)\)

Plug in the given points (6,-6) and (-2,-2)

\(=\frac{-2-(-6)}{-2-6}\\=\frac{-2+6}{-2-6}\\=\frac{4}{-8}\\=-\frac{1}{2}\)

Therefore, the slope of the line is \(-\frac{1}{2}\). Plug this into \(y=mx+b\):

\(y=-\frac{1}{2}x+b\)

2) Determine the y-intercept (b)

\(y=-\frac{1}{2}x+b\)

Plug in one of the given points and solve for b

\(-6=-\frac{1}{2}(6)+b\\-6=-3+b\)

Add 3 to both sides

\(-6+3=-3+b+3\\-3=b\)

Therefore, the y-intercept of the line is -3. Plug this back into \(y=-\frac{1}{2}x+b\):

\(y=-\frac{1}{2}x-3\)

I hope this helps!

The critical value for the given hypothesis test with a significance level of 0.05 and sample size of 19, testing the alternative hypothesis H1: σ > 4.5, cannot be determined without additional information.

To find the critical value, we need to know the distribution of the data and the desired level of significance (also known as the alpha level) for the hypothesis test. In this case, we are given that the significance level, denoted as alpha (α), is 0.05, but we do not have information about the distribution of the data or the desired level of significance.

The critical value is a value from the distribution that is used as a threshold to determine whether to reject or fail to reject the null hypothesis. If the test statistic (calculated from the sample data) is greater than the critical value, we would reject the null hypothesis in favor of the alternative hypothesis. If the test statistic is less than or equal to the critical value, we would fail to reject the null hypothesis.

However, without knowing the distribution of the data and the desired level of significance, we cannot determine the critical value for this hypothesis test. Therefore, we cannot provide a specific numerical value for the critical value in this case.

Therefore, the critical value for the given hypothesis test with a significance level of 0.05 and sample size of 19, testing the alternative hypothesis H1: σ > 4.5, cannot be determined without additional information.

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Answer:

5x cm

Step-by-step explanation:

Total length of AE = 2x + 3x

= 5x cm

The heart beats normally between 60 and 100 times per minute while at rest. Your heart beats far more quickly than usual if you have ventricular tachycardia, with many individuals reporting heart rates of 170 or more per minute.

64% level: 170 x 0.64 = 109 bpm, and 76% level: 170 x 0.76 = 129 bpm

77% level: 185 x 0.77 = 142 bpm, and 93% level: 185 x 0.93 = 172 bpm

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Answer:

7h+3=-11?

then h=-11-3 divided by 7

Step-by-step explanation:

If the given function is f '(t) = 20/1 + t², the value of the function f will be 20 tant+C.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that the function is,f '(t) = 20/1 + t² f(1) = 0

In order to find f integrate the function,

\(\rm f = \int \frac{20}{1+t^2}dt \\\\ f =20\cdot \int \frac{1}{1+t^2}dt \\\\ f =20\tan \left(t\right) \\\\ f =20\tan \left(t\right)+C\)

f(1) = 0

0=20 tan(1)+C

0=20(1.55)+C

C= -31

Thus, if the given function is f '(t) = 20/1 + t², the value of the function f will be 20 tant+C.

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Answer:(5,4)

Step-by-step explanation:

Answer:

(5,4)

Step-by-step explanation:

Ethernet LANs are usually arranged in a star topology with computers wired to central switching circuitry that is incorporated in modern routers.

Ethernet is a family of computer networking technologies that is used in LAN, metropolitan area networks (MAN), and wide area networks (WAN). It was first introduced in 1980 by Xerox Corporation, and later standardized by the Institute of Electrical and Electronics Engineers (IEEE) as IEEE 802.3.

Ethernet networks can be implemented in different topologies, such as a bus, star, or mesh topology. However, the most common topology for Ethernet LANs is a star topology, in which computers are wired to a central switching circuitry that is incorporated in modern routers. This allows for efficient communication between the computers on the network.In addition to LANs, Ethernet is also used for other networking applications such as Internet access, wireless networking, and broadband access. Overall, Ethernet is a widely used technology that has become an important component of modern computer networking.

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Answer:

(-2,-1)

Step-by-step explanation:

y=4x+7 y=-5/2x-6

Set equal to each other

4x+7=-5/2x-6

add 5/2x

13/2x+7=-6

subtract 7

13/2x=-13

divide by 13/2

x=-2

Plug in -2 for x

4(-2)+7=-1

y=-1

(-2,-1)

Hope this helped!

The percent needed on the final test is 99.6% in order to earn 93% on all 4 tests combined.

Let x be the percentage of the final test in order to earn 93% on all 4 tests combined.

To solve the problem, we will have to use weighted averages.

It is a method used to determine the mean of a set of data, where each observation has a different weight or frequency.

Let's first find the weighted average of the three tests you have already taken.

Given that you earned scores of 88%, 94%, and 90% on the first three tests, and each test was worth 150 points.

88% of 150 points = 132 points

94% of 150 points = 141 points

90% of 150 points = 135 points

The sum of the points you earned = 132 + 141 + 135 = 408 points

The total possible points = 450 points, which is the sum of 150 points for each of the 3 tests.

So, the weighted average of the first three tests = 408/450 × 100% = 90.67%.

To earn a 93% average on all 4 tests combined, the sum of the total points earned must be 93% of the total possible points.

93% of (450 + 250) = 657 points

The total points earned on the first three tests = 408 points

So, the points required on the final test are 657 - 408 = 249 points.

The final test is worth 250 points, so you need to earn 249/250 × 100% = 99.6%.

Therefore, you need to earn 99.6% on the final test to earn a 93% average on all 4 tests combined.

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The claim that the population mean is less than 125 (Option E) would

the interval tends to refute.

The 90% confidence interval for the population mean is 135 to 160. This means that if we were to repeat the process of taking samples from the same population and constructing a 90% confidence interval, we would expect 90% of the intervals to contain the true population mean.

With this in mind, let's consider each claim:

A. The interval does not rule out the possibility that the population mean is more than 110, as 110 is less than the lower bound of the interval.

B. The interval does not rule out the possibility that the population mean is less than 150, as 150 is greater than the upper bound of the interval.

C. The interval does not rule out the possibility that the population mean is between 140 and 150, as both of these values fall within the interval.

D. The interval does not rule out the possibility that the population mean is more than 140, as 140 is less than the upper bound of the interval.

E. The interval refutes the claim that the population mean is less than 125, as 125 is less than the lower bound of the interval.

Therefore, the answer is (E) The population mean is less than than 125.

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The 3 × 3 matrix that translates a point in r 2 by (3, 1) then rotates the result 45 degrees about the origin is

M = | 1/√2    -1/√2    3/√2- 1/√2 |

      | 1/√2    1/√2     1/√2 + 1/√2 |

       | 0           0                1 |

To find the 3x3 matrix that translates a point in R^2 by (3, 1) and then rotates the result 45 degrees about the origin using homogeneous coordinates, we can follow these steps:

Translation Matrix:

The translation matrix for a 2D translation by (3, 1) is:

T = | 1 0 3 |

| 0 1 1 |

| 0 0 1 |

This matrix translates a point (x, y) by adding the translation vector (3, 1) to it.

Rotation Matrix:

The rotation matrix for a 2D rotation by 45 degrees counterclockwise is:

R = | cos(theta) -sin(theta) 0 |

| sin(theta) cos(theta) 0 |

| 0 0 1 |

Since we want to rotate by 45 degrees, theta = 45 degrees = π/4 radians. Therefore, the rotation matrix becomes:

R = | cos(π/4) -sin(π/4) 0 |

| sin(π/4) cos(π/4) 0 |

| 0 0 1 |

Simplifying, we have:

R = | 1/√2 -1/√2 0 |

| 1/√2 1/√2 0 |

| 0 0 1 |

Combine Translation and Rotation:

To obtain the combined transformation matrix, we multiply the translation matrix T by the rotation matrix R:

M = T * R

Performing the matrix multiplication:

M = | 1 0 3 | | 1/√2 -1/√2 0 |

| 0 1 1 | * | 1/√2 1/√2 0 |

| 0 0 1 | | 0 0 1 |

Simplifying, we have:

M = | 1/√2 -1/√2 3/√2 - 1/√2 |

| 1/√2 1/√2 1/√2 + 1/√2 |

| 0 0 1 |

This is the desired 3x3 matrix that translates a point in R^2 by (3, 1) and then rotates the result 45 degrees about the origin using homogeneous coordinates.

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The first three nonzero terms of two linearly independent solutions about x = 0 can be obtained by Taylor expanding the solutions in terms of the exponent r and truncating the series to the desired order.

To determine if x = 0 is a regular singular point of the differential equation xy'' + y = 0, we substitute y = x^r into the equation and solve for the exponent r. Differentiating y twice with respect to x, we have y'' = r(r - 1)x^(r - 2). Substituting these expressions into the differential equation, we get \(x(x^r)(r(r - 1)x^(r - 2)) + x^r = 0\). Simplifying, we obtain r(r - 1) + 1 = 0, which yields r^2 - r + 1 = 0. Solving this quadratic equation, we find that the exponents at the singular point x = 0 are complex and given by r = (1 ± i√3)/2.

To find the first three nonzero terms of two linearly independent solutions about x = 0, we can use the Taylor series expansion. Let's consider the solution y1(x) corresponding to the exponent r = (1 + i√3)/2. Expanding y1(x) as a series around x = 0, we have y1(x) =\(x^r = x^((1 +\)i√3)/2) = x^(1/2) *\(x^(i√3/2\)). Using the binomial series expansion and Euler's formula, we can write \(x^(1/2) and x^(i√3/2)\) as infinite series.

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Answer:

B: \(y=-\frac{1}{3}x+7\)

Step-by-step explanation:

Straight lines are set out in the format of \(y = mx+c\), where \(m\) is the gradient, and \(c\) is the y-intercept.

The gradient between parallel lines remains the same, and this means the gradient of the new line will also be \(-\frac{1}{3}\).

This rules out options C and D.

Going back to the format, so far, we have filled in \(y=-\frac{1}{3}x+c\). We are still looking for the y-intercept.

We can find that using the coordinate you've been given, \((6,5)\).

This coordinate tells us that when \(x=6\), \(y=5\). Therefore we can substitute those in the places of \(x\) and \(y\) in the original equation.

This leaves us with \(5 = -\frac{1}{3}(6)+c\).

We can now rearrange for \(c\).

\(5 = -2 + c\\c=7\)

Now we have all the values we need, we can form the final equation.

\(y=-\frac{1}{3}x+7\)

This indicates the answer is option B. Hope this helps.

Rounding up, the editors will need to contact at least 385 randomly selected employers to estimate the percentage of businesses that plan to hire additional employees in the next 60 days with a margin of error of ​% and a confidence level of ​%.

To calculate the sample size, the editors can use the following formula:
n = (Z^2 * p * q) / E^2
where:
- n is the required sample size
- Z is the Z-score corresponding to the desired confidence level (for example, if the desired confidence level is 95%, the Z-score would be 1.96)
- p is the estimated proportion of businesses that plan to hire additional employees (this value is unknown and will be estimated based on past data or other sources)
- q is 1 - p
- E is the desired margin of error
Assuming the editors want a 95% confidence level and a margin of error of ​%, let's say they estimate that 50% of businesses plan to hire additional employees. Plugging these values into the formula, we get:
n = (1.96^2 * 0.5 * 0.5) / (0.05^2)
Simplifying, we get:
n = 384.16
They have a desired margin of error and a desired confidence level, and you need to determine the number of randomly selected employers they must contact.

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Anton needs 3.75 lbs of sugar and 1.25 lbs of water to make 5 lbs of 75% sugar syrup.

To make a 75% sugar syrup, Anton will need 75% sugar and 25% water by weight. To find out how much sugar and how much water he needs, we can use the following formulas:

Sugar weight = 5lbs x 75% = 3.75lbs

Water weight = 5lbs x 25% = 1.25lbs

So Anton needs 3.75 lbs of sugar and 1.25 lbs of water to make 5 lbs of 75% sugar syrup.

It's important to note that syrup with 75% sugar content is heavy syrup, it is mostly used for preservation and not as a sweetener.

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The probability that none of the three adults get news from the newspaper is 0.378.

To understand why, let's break down the problem step by step.

Step 1: Calculate the total number of ways to choose 3 adults out of the 70 surveyed. This can be done using the combination formula:

C(n, r) = n! / (r!(n - r)!)

In this case, n = 70 (the total number of adults surveyed) and r = 3 (the number of adults being chosen).

C(70, 3) = 70! / (3!(70 - 3)!)

Step 2: Calculate the number of ways to choose 3 adults who don't get news from the newspaper. Since there are 12 adults who get news from the newspaper, we need to choose 3 adults from the remaining 70 - 12 = 58 adults who don't get news from the newspaper.

C(58, 3) = 58! / (3!(58 - 3)!)

Step 3: Calculate the probability by dividing the number of ways to choose 3 adults who don't get news from the newspaper by the total number of ways to choose 3 adults:

P = C(58, 3) / C(70, 3)

Step 4: Substitute the values and calculate the probability:

P = (58! / (3!(58 - 3)!)) / (70! / (3!(70 - 3)!))

P = (58! / (3!55!)) / (70! / (3!67!))

P = (58! * 67! * 3! * 3!) / (3! * 55! * 70!)

Many terms in the numerator and denominator will cancel out, leaving us with:

P = (58 * 57 * 56) / (70 * 69 * 68)

P = 0.378

So, the probability that none of the three adults get news from the newspaper is 0.378.

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Complete Question

A news organization surveyed 70 adults. Each said he or she gets news from only one source. Here is a summary of their sources of news. Source of news Number of adults 22 Radio 12 Newspaper 13 Television 23 Internet Three of the adults from the survey are selected at random, one at a time without replacement. What is the probability that none of the three adults get news from the newspaper? Do not round your intermediate computations. (Round your final answer to three decimal places)

The explicit equation of the sequence is an = 3 + (n-1)*6

First term = 3

Second term = 9

A series of numbers in mathematics whose each term is always expressed as a, a+d, a+2d, or a+3d. An arithmetic progression is defined as a + (n-1)d, where a is the first term,d is the common difference of the series and n is the number of terms in the sequence

Any two continuous terms in the arithmetic sequence differ by the same number.

Arithmetic sequence is given by an = a + (n-1)d

So, the common difference = 9-3 = 6

a = 3

Substituting the values in the formula we get:

For nth term: an = 3 + (n-1)*6

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The walking speed x = (L/t) - (3/65) L + (2/50) L .We can solve this problem using the concept of average speed and the time and distance relationship.

Let's assume the length of the moving sidewalk be L and the speed of the moving sidewalk be v.

When the moving sidewalk is working, the person's speed is v + w, where w is the walking speed.

And, the time taken to travel the distance L is 65s.

So, using the average speed formula, we have:

(v + w) = L/65

And, when the moving sidewalk is not working, the person's speed is w.

And, the time taken to travel the distance L is 50s.

So, using the average speed formula, we have:

w = L/50

Now, we can equate the above two equations to find the walking speed w.

v + w = L/65

w = L/50

Subtracting the second equation from the first equation, we get:

v = (L/65) - (L/50)

Since, L is common in both the numerators, we can simplify the above expression as:

v = (3/65 - 2/50) L

Thus, the speed of the moving sidewalk is (3/65 - 2/50) L.

Let's assume the walking speed be x.

So, the average speed of the person is (v + x) = (3/65 - 2/50) L + x.

And, the time taken to travel the distance L is t.

Using the average speed formula, we have:

(v + x) = L/t

Substituting the value of v, we get:

((3/65 - 2/50) L + x) = L/t

Simplifying the above equation, we get:

x = (L/t) - (3/65 - 2/50) L

Now, substituting the values of L/50 and L/65, we get:

x = (L/t) - (3/65 - 2/50) L

x = (L/t) - (3/65) L + (2/50) L

So, the walking speed x = (L/t) - (3/65) L + (2/50) L.

Therefore, the walking speed can be calculated using the above expression.

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The complete question is :

When the moving sidewalk at the airport is broken, as it often seems to be, it takes you 50 s to walk from your gate to baggage claim. When it is working and you stand on the moving sidewalk the entire way, without walking, it takes 65 s to travel the same distance.

How long will it take you to travel from the gate to baggage claim if you walk while riding on the moving sidewalk?

Express your answer using two significant figures.

1720 gallons of rainwater are needed to fill the container to the top.

What does have capacity mean?

The ability to use and comprehend data to make decisions and convey those decisions is referred to as capacity.

If the container is 30% filled with rainwater, then it is 70% empty. Let's first calculate the capacity of the container when it is 100% full:

Capacity of container = (100 / 30) * 1290 = 4300 gallons

So, the container has a capacity of 4300 gallons when it is 100% full.

Since the container already has 30% of its capacity filled with rainwater, we need to add enough rainwater to fill the remaining 70% of the capacity. The amount of rainwater needed to fill the container to the top is:

Amount of rainwater needed = 70% of 4300 - 30% of 4300

= 0.7 * 4300 - 0.3 * 4300

= 3010 - 1290

= 1720 gallons

Therefore, 1720 gallons of rainwater are needed to fill the container to the top.

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