On a map, 2 inches represents 350 miles. If the distance between 2 cities
is 875 miles, how many inches apart are they on the map?

The correct answer is D. Ted had a better year because of a lower z-score.

The following formula can be used to determine Ted and Julie's respective z-scores:

z = (x - )/, where:

x is the individual's ERA, the mean ERA for each group, and the standard deviation of the ERA for each group.

To Ted:

x (Ted's ERA) = 2.78; the mean ERA for males is 4.767; the standard deviation for males is 0.859. Regarding Julie:

The z-scores were calculated as follows: x (Julie's ERA) = 2.84  (mean ERA for females) = 3.866  (standard deviation for females) = 0.937

z (Ted) = (2.78 - 4.767) / 0.859  -2.32 z (Julie) = (2.84 - 3.866) / 0.937  -1.09 Add two decimal places to the z-scores.

Ted's z-score is lower (-2.32) when compared to Julie's (-1.09) when the z-scores are compared.

A person's value (ERA) is further below the mean when compared to their peers if their z-score is lower. As a result, Ted outperformed Julie in comparison to his peers.

The right response is D. Ted had a superior year in view of a lower z-score.

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Answer:

center = origin (0,0)

radius = 3

to graph it, draw a circle that goes through the points (3,0), (0,3), (-3,0), (0,-3)

Step-by-step explanation:

Answer:

13 + \(\sqrt{89}\)

or

22.43398... (depends on how you round it)

Step-by-step explanation:

1. The question stated that the radius of the circle O is 5, so the length of AO and CO is 5.

2. Since line AB and line CB are both tangent to the circle, they have the same length. CB is 8, so AB will also be 8.

--> Both triangle AOB and COB share one side, and the other side (radius) has the same length, so the third side must be the same length

3. Tangent means having a 90-degree angle with the radius. We know that the triangle AOB is a right triangle since the angle OAB is 90 degrees.

We can use the Pythagorean theorem to find side OB. OB^2 = AO^2 + AB^2.

--> OB^2 = 25 + 64

--> OB^2 = 89

--> OB = \(\sqrt{89}\)

Now that we know the lengths of all three sides, we can add them up.

--> 5 + 8 + \(\sqrt{89}\)

--> 13 + \(\sqrt{89}\)

or

--> 22.43398113....

The mass of 1500 liters of gasoline is 1110 grams, and the specific weight is approximately 0.007252 g/cm³.

To calculate the mass of 1500 liters of gasoline, we need to know the density of gasoline. The density of gasoline is typically around 0.74 grams per milliliter. Since there are 1000 milliliters in a liter, we can convert the volume to milliliters by multiplying 1500 liters by 1000, which gives us 1,500,000 milliliters. Then, we can calculate the mass by multiplying the volume in milliliters by the density, which gives us 1,500,000 milliliters * 0.74 grams per milliliter = 1,110,000 grams or 1110 kg.

The weight-specific or specific weight of a substance is the weight per unit volume. It can be calculated by multiplying the density of the substance by the acceleration due to gravity. In the case of gasoline, the specific weight would be approximately 0.74 grams per milliliter * 9.8 m/s² = 0.007252 g/cm³.

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The roots of the auxiliary equation are 0 (repeated root) and -b, where b is a constant.

To find the roots of the auxiliary equation for a homogeneous linear fourth-order differential equation with constant coefficients, we need to substitute the given solution into the differential equation and solve for the roots.

The given solution is:  \(y = 1 - x + 6x^2 + 3e^x.\)

The general form of a fourth-order homogeneous linear differential equation with constant coefficients is:

ay'''' + by''' + cy'' + dy' + ey = 0.

Let's differentiate y with respect to x to find the first and second derivatives:

\(y' = -1 + 12x + 3e^x,\)

\(y'' = 12 + 3e^x,\)

\(y''' = 3e^x,\)

\(y'''' = 3e^x.\)

Now, substitute these derivatives into the differential equation:

\(a(3e^x) + b(3e^x) + c(12 + 3e^x) + d(-1 + 12x + 3e^x) + e(1 - x + 6x^2 + 3e^x) = 0.\)

Simplifying the equation, we get:

\(3ae^x + 3be^x + 12c + 3ce^x - d + 12dx + 3de^x + e - ex + 6ex^2 + 3e^x = 0.\)

Rearranging the terms, we have:

\((6ex^2 + (12d - e)x + (3a + 3b + 12c + 3d + 3e))e^x + (12c - d + e) = 0.\)

For this equation to hold true for all x, the coefficients of each term must be zero. Therefore, we have the following equations:

6e = 0 ---> e = 0,

12d - e = 0 ---> d = 0,

3a + 3b + 12c + 3d + 3e = 0 ---> a + b + 4c = 0,

12c - d + e = 0 ---> c - e = 0.

From the equations e = 0 and d = 0, we can deduce that the differential equation has a repeated root of 0.

Substituting e = 0 into the equation c - e = 0, we get c = 0.

Finally, substituting d = 0 and c = 0 into the equation a + b + 4c = 0, we have a + b = 0, which implies a = -b.

Therefore, the roots of the auxiliary equation are 0 (repeated root) and -b, where b is a constant.

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to convert 25min into hours we divide 25 by 60 so the answer would be 0.416 hours

the formula to find the distance is we multiply speed and time so

distance=4km/p X 0.416 hours =1.664

so now we have the first answer

now we do the same thing for the other part of the question

distance= timeXspeed

distance=0.416X3=1.248

then we add to find total distance

1.248+1.644=2.912

2.912 is the total distance

Answer:

120 feet

Step-by-step explanation:

You would find the perimeter of the fence, which is 40(2) + 20(2)

Answer:

3.75 hours

Step-by-step explanation:

The receptionist takes n hours to do 1 day's worth of work.

The assistant takes 4n hours to the 1 day's worth of work.

In 1 hour, the receptionist does 1/n amount of work.

In 1 hour, the assistant does 1/(4n) amount of work.

Working together, in 1 hour, they do this amount of work:

1/n + 1/(4n)

Working together, the 2 workers do the job in 3 hours.

Working together, in 1 hour, they do this amount of work:

1/3

1/n + 1/(4n) = 1/3

Multiply both sides of the equation by the LCD, 12n.

12 + 3 = 4n

4n = 15

n = 15/4

n = 3.75

Answer: 3.75 hours

At x = 8, the cubic function has a value of 120.

Given that the cubic function has zeros at 2, 3, and -5, then its factors must be (x - 2), (x - 3), and (x + 5).

Therefore, the cubic function can be expressed in the factored form as:

=> f(x) = k(x - 2)(x - 3)(x + 5) ; where k is a constant.

Since f(x) passes through the point (4, 36), we can substitute x = 4 and f(x) = 36 in the above equation to get:

=> 36 = k(4 - 2)(4 - 3)(4 + 5)

=> 36 = k(2)(1)(9)

=> 36 = 18k

=> k = 2

So, the cubic function can be expressed as:

=> f(x) = 2(x - 2)(x - 3)(x + 5)

Now we can find where f(x) has a value of 120 by solving for x:

=> 120 = 2(x - 2)(x - 3)(x + 5)

=> 60 = (x - 2)(x - 3)(x + 5)

Since 2 is a factor of the left-hand side, then we know that one of the factors on the right-hand side must be 2. Therefore, we can write:

=> 60 = 2(x - 2)(x - 3)(x + 5)

=> 30 = (x - 2)(x - 3)(x + 5)

Now we can use trial and error method to find the other two factors that multiply to 30. We can start with (x - 2) = 1, (x - 3) = 5, and (x + 5) = 6. This gives us: x = 3, 8, -11

However, only x = 8 satisfies the condition that f(x) = 120, so the cubic function has a value of 120 at x = 8.

Thus, at x = 8, the cubic function has a value of 120.

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Answer:

7.11

Step-by-step explanation:

You will add all of those numbers and divide them by the amount of numbers you added. And I rounded the answer to 2 decimal places, seeing that it is a recurring decimal.

Answer:

36

Step-by-step explanation:

Given the scale factor k, then

the area factor is k²

Here the scale factor = 6 thus

area factor = 6² = 36

Answer:

50 miles

Step-by-step explanation:

Answer:

the value of x is 9

Step-by-step explanation:

the sum of all angles of a triangle is 180

one side is 90 so,

90+7x+3x = 180

10x = 180-90

10x = 90

x=9

Answer:

2061.9\(mm^{3}\)

Step-by-step explanation:

We can see the original shape of the gold block is a cuboid.

Volume of Cuboid = Length x Width x Height

Volume of Original Gold Block = 27mm x 8mm x 12mm = \(2592mm^{3}\)

Next, we can see the shape of the cut-out hole is a cylinder.

Volume of Cylinder = \(\pi r^{2} h\)

We know that r = 0.5 x diameter = 0.5 x 5 = 2.5mm

Volume of cut-out hole = \(\pi (2.5)^{2} (27)\\\) = \(168.75\pi mm^{3}\)

Volume of Remaining Gold Block = Volume of Original Gold block - Volume of cut-out hole

= \(2592mm^{3} -168.75\pi mm^{3}\)

= 2061.9\(mm^{3}\)

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

Have a Nice Day

Answer:

Step-by-step explanation:

Answer:d. a horizontal stretch to produce a period of 3pi/2 and a horizontal translation of pi/4 units to the right

Step-by-step explanation:

:)

Answer:

A horizontal stretch to produce a period of 3pi/2 and a horizontal translation of pi/4 units to the right

Step-by-step explanation:

While there's not graph provided, I've taken the test a little while ago and it seem to be right.

Answer:

\(\huge\boxed{\sf 3317.5\ cm\²}\)

Step-by-step explanation:

Since the diameter is 12 cm, the radius will be:

r = d/2 = 12/2 = 6 cm

Now,

Surface Area of cylinder:

\(= 2\pi rh+2\pi r^2\\\\Where \ r = 6 \ cm, \ h = 80 \ cm\\\\= 2(3.14)(6)(80)+2(3.14)(6)^2\\\\= 3015.9+2(3.14)(36)\\\\= 3242.12 \ cm^2\)

Surface Area of Cone:

\(= \pi r^2+\pi rl\\\\Where \ r = 6 \ cm, \ l = 10 \ cm\\\\= (3.14)(6)^2+(3.14)(6)(10)\\\\= (3.14)(36)+188.5\\\\= 113.1+188.5\\\\= 301.6 \ cm^2\)

Surface area of the object:

= SA of cone + SA of cylinder - 2πr² (Since the base area isn't included)

= 301.6 + 3242.1 - 2(3.14)(6)²

= 3543.7 - 2(3.14)(36)

= 3543.7 - 226.2

= 3317.5 cm²

\(\rule[225]{225}{2}\)

Hope this helped!

the total surface area of the solid object is \(\bold{\green{1056\pi\: Or\:3317.52\:cm^2}}\)

Answer:

Solution given:

diameter [d]=12 cm

radius [r]=\(\frac{12}{2}=6\) cm

height of cylinder[H]=80cm

slant height [L]=10cm

Now,

Surface Area of cylinder=\(2\pi rH\)

=\(2\pi *6*80=960\pi cm^2\)

Surface Area of Cone:\(\pi rL\)

=\(\pi *6*10=60\pi cm^2\)

Surface area Base of solid=\(\pi r^2=\pi *6^2=36\pi cm^2\)

The total surface area of the object:

=Surface Area of cylinder + Surface Area of Cone+ Surface area Base of solid

=\(960\pi +60\pi +36\pi\)

=\(1056\pi\: Or\:3317.52\:cm^2\)

Step-by-step explanation:

Answer:

DE = 19.5

Step-by-step explanation:

the diagonals of a rectangle are congruent and bisect each other, then

EC = AE , that is

7x - 5 = 3x + 9 ( subtract 3x from both sides )

4x - 5 = 9 ( add 5 to both sides )

4x = 14 ( divide both sides by 4 )

x = 3.5

Then

AE = 3x + 9 = 3(3.5) + 9 = 10.5 + 9 = 19.5

Thus

DE = AE = 19.5

Answer:

1130 grams

Step-by-step explanation:

1.6kg to grams is 160 0grams so 1600 - 470 = 1130 so she has 1130 grams left.

Answer:

Lena has 1130 grams left.

1.6 kg = 1600 grams

Amount of sugar she used = 470 grams

Amount of sugar she has left = 1600 - 470

= 1130 grams

So, Lena has 1130 grams of sugar left.

:)

Increasing the sample size from 1,000 to 2,800 will improve the accuracy and precision of the poll's estimate, providing a more reliable measurement of the proportion of voters who favor the new law banning cell phone use in Internet coffee shops.

We have,

Increasing the size of the random sample from about 1,000 people to about 2,800 people will have a positive effect on the accuracy and precision of the poll's estimate.

When conducting a poll, the sample size is an important factor in determining the reliability of the results.

A larger sample size generally leads to more accurate estimates and reduced sampling error.

By increasing the sample size from 1,000 to 2,800, the polling company is effectively collecting data from a larger and more diverse group of voters.

This larger sample size allows for a better representation of the population, reducing the potential for bias and increasing the reliability of the estimate.

With a larger sample size, the margin of error of the poll is likely to decrease.

The margin of error represents the range within which the true population proportion is likely to fall.

Increasing the sample size reduces the variability of the estimates and narrows the range of the margin of error.

Thus,

Increasing the sample size from 1,000 to 2,800 will improve the accuracy and precision of the poll's estimate.

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The surface area of the bacterium is approximately 2.64 × 10⁻⁷ mm².  The volume of the bacterium is approximately 1.43 × 10⁻³³ cm³ .

To find the volume of a spherical bacterium, we can use the formula for the volume of a sphere: V = (4/3)πr³, where r is the radius of the bacterium. Given that the diameter of the bacterium is 2.9 μm, we can calculate the radius by dividing the diameter by 2: r = 2.9 μm / 2 = 1.45 μm.

Converting the radius to centimeters, we divide by 10,000 (since 1 cm = 10,000 μm): r = 1.45 μm / 10,000 = 0.000145 cm.

Now we can substitute the radius into the volume formula: V = (4/3)π(0.000145 cm)³.

Evaluating the expression, the volume of the bacterium is approximately 1.43 × 10⁻³³ cm³ .

To find the surface area of the bacterium, we use the formula for the surface area of a sphere: A = 4πr².

Substituting the radius into the formula, we get: A = 4π(0.000145 cm)².

Evaluating the expression, the surface area of the bacterium is approximately 2.64 × 10⁻⁷ mm².

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Answer:

please I can see the questions well

Step-by-step explanation:

please I want to help you but

the picture is not clear enough

The probability that a kicker from group i will make a field goal is 1/(i + 1), where i represents the group number.

In the given scenario, the field goal kickers are divided into two groups: group 1 and group 2. Each group has 3i kickers, where i represents the group number.

The probability that a kicker from group i will make a field goal is given by 1/(i + 1). This means that the probability of a successful field goal attempt for a kicker in group 1 is 1/2, and for a kicker in group 2 is 1/3.

The probability of making a field goal is independent of the outcome of any other kicks, meaning that the success or failure of one kicker's attempt does not affect the probability of success for another kicker.

In the collection of field goal kickers divided into groups 1 and 2, the probability of a kicker from group i successfully making a field goal is 1/(i + 1), where i represents the group number. The success or failure of one kicker's attempt does not impact the probability of success for another kicker.

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Answer:

the middle one goes to the top, top one goes to the middle and bottom stays there

Step-by-step explanation:

Answer:

D: {x∈R | -2 ≤ x ≤ 2 }

R: {y∈R | 0 ≤ y ≤ 4 }

Step-by-step explanation:

The domain ranges between -2 and 2

The range ranges between 0 and 4

Using the empirical rule, we can estimate that approximately 97.5% of the students have GPAs that are greater than 1.66 at this university.

The empirical rule, also known as the 68-95-99.7 rule, states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

To apply this rule to the given scenario, we first need to calculate how many standard deviations away from the mean a GPA of 1.66 is.

Z = (X - μ) / σ

Where X is the GPA in question, μ is the mean (2.56), and σ is the standard deviation (0.45).

Z = (1.66 - 2.56) / 0.45 = -2

This tells us that a GPA of 1.66 is 2 standard deviations below the mean.

Now, using the empirical rule, we know that approximately 95% of the data falls within two standard deviations of the mean. Since a GPA of 1.66 is 2 standard deviations below the mean, we can conclude that only about 2.5% (half of the remaining 5%) of the students have a GPA lower than 1.66.

Therefore, the percentage of students who have GPAs that are greater than 1.66 would be approximately 97.5%.

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The true statement is the range of Mrs Plum's class is 14 greater than the range of Mr Scarlet's class.

A box plot is a graph that is used to describe a dataset. A box plot is made up of two lines and a box. The two lines are known as whiskers.

The end of the first whisker represents the minimum number and the end of the second whisker represents the maximum number. The difference between the whiskers is the range.

Range is used to measure the variation of a dataset. It is the difference between the maximum number and the minimum number.

Range = maximum number - minimum number

Range of Miss Scarlet's class = 98 - 65 = 33

Range of Miss Plum's class = 98 - 51 = 47

Difference in range = 47 - 33 = 14

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The exponential function is y = 1200(1.04)^t and the investment amount after 16 years is $2247.58.

What is exponential function?

The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

Jayden invests $1,200 in a savings account. Each year, the value increases by 4%.

Let t = time in years

Let y = amount of money invested in savings account

Start with $1200 and each year add 4% interest to the amount in the bank.

1st year: Interest = 1200 × (0.04) = $48

This is added to the previous amount -

= $1200 + $1200 × (0.04)

= $1200 (1+0.04)

= $1200 (1.04)

= $1248

2nd year: Previous amount + interest on the previous amount

= $1248 (1+0.06)

= $1248 (1.06)

= $1297.92

So, the exponential formula becomes -

y = 1200(1.04)^t

Now, to find the value of investment after 16 years, substitute t = 16.

y = 1200(1.04)^t

y = 1200(1.04)^16

y = 1200(1.87298125)

y =$2247.58

Therefore, the value of investment after 16 years is $2247.58.

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