prime to determine the HCF and LCM of 84 and462
​

The range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

To measure the amount of money college students spend on rent per month, the most appropriate measure of spread would be the range. The range is the simplest measure of spread and is calculated by subtracting the lowest value from the highest value in a data set. In this case, the range would be $1,300 - $300 = $1,000.

The median would not be the best choice in this scenario because it only represents the middle value in a data set. It does not take into account extreme values like the $1,300 rent expense.

Standard deviation would not be the most appropriate measure of spread in this case because it calculates the average deviation of each data point from the mean. However, it may not accurately represent the spread when extreme values like the $1,300 rent expense are present.

The interquartile range (IQR) would not be the best choice either because it measures the spread of the middle 50% of the data set. It does not consider extreme values and would not accurately represent the range of rent expenses in this scenario.

In summary, the range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

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Answer:

18

Explanation:

Vectors u and z are defined below:

The dot product of u and z is evaluated below:

The dot product is 18.

you should invest approximately $500,000 today at 9% simple interest to reach your retirement goal of $1,175,000 in 15 years.

To determine how much you should invest today at 9% simple interest to reach your retirement goal of $1,175,000 in 15 years, we can use the formula for simple interest:

A = P(1 + rt)

Where A is the future value, P is the principal (the amount you should invest today), r is the interest rate, and t is the time in years.

We can rearrange the formula to solve for P:

P = A / (1 + rt)

Plugging in the values, we have:

P = 1,175,000 / (1 + 0.09 * 15)

P = 1,175,000 / (1 + 1.35)

P = 1,175,000 / 2.35

P ≈ $500,000

Therefore, you should invest approximately $500,000 today at 9% simple interest to reach your retirement goal of $1,175,000 in 15 years.

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The requirement that we are strictly failing when using the critical z value is the knowledge of the population standard deviation.

The problem with calculating the confidence interval using the critical z value is that it assumes the population standard deviation is known.

This assumption is often not realistic because in most cases, the population standard deviation is unknown and needs to be estimated from the sample data.

When the population standard deviation is unknown, it is more appropriate to use the t-distribution instead of the standard normal distribution (z-distribution) to calculate the confidence interval.

The t-distribution takes into account the uncertainty introduced by estimating the population standard deviation from the sample.

Therefore, the requirement that we are strictly failing when using the critical z value is the knowledge of the population standard deviation.

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Answer:

3/16

Step-by-step explanation:

Answer:

Es el Pentágono creo amigo nose si sera

Answer:

9+0.6+0.08

Step-by-step explanation:

The given decimal number in expanded form is 9+0.6+0.08.

The given decimal number is 9.68.

Unlike whole numbers, decimal numbers can also be written in the expanded form. For writing the decimals in expanded form, we multiply each of the decimal digits with increasing exponent values of (1/10).

Now, the expanded form of 9.68 is

9×1 + 6×1/10 + 8×1/100

= 9+0.6+0.08

= 9.68

Therefore, the given decimal number in expanded form is 9+0.6+0.08.

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The correct option is (d) interval/ratio, nominal with 2 or more levels.

In ANOVA (Analysis of Variance), the independent variable is interval/ratio with 2 or more levels, and the dependent variable is nominal with 2 or more levels. Here, ANOVA is a statistical tool that is used to analyze the significant differences between two or more group means.

ANOVA is a statistical test that helps to compare the means of three or more samples by analyzing the variance among them. It is used when there are more than two groups to compare. It is an extension of the t-test, which is used for comparing the means of two groups.

The ANOVA test has three types:One-way ANOVA: Compares the means of one independent variable with a single factor.Two-way ANOVA: Compares the means of two independent variables with more than one factor.Multi-way ANOVA: Compares the means of three or more independent variables with more than one factor.

The ANOVA test is based on the F-test, which measures the ratio of the variation between the group means to the variation within the groups. If the calculated F-value is larger than the critical F-value, then the null hypothesis is rejected, which implies that there are significant differences between the group means.

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Answer:

3/1

Step-by-step explanation:

12 blankets / 4 month = 3 blankets / 1 month

To show that w is in the subspace of R4 spanned by V1, V2, and V3, we need to find constants c1, c2, and c3 such that:

w = c1V1 + c2V2 + c3V3

We can write this as a matrix equation:

| 1 -4 -9 -4 | | c1 | | -2 |

| 6 3 5 1 | x | c2 | = | -1 |

| 2 4 11 -8 | | c3 | | -1 |

| -15 7 22 -14 | | -2 |

We can solve this system of equations using row reduction:

| 1 -4 -9 -4 | | c1 | | -2 |

| 6 3 5 1 | x | c2 | = | -1 |

| 2 4 11 -8 | | c3 | | -1 |

| -15 7 22 -14 | | -2 |

R2 = R2 - 6R1

R3 = R3 - 2R1

R4 = R4 + 15R1

| 1 -4 -9 -4 | | c1 | | -2 |

| 0 27 59 25 | x | c2 | = | 11 |

| 0 12 29 -16 | | c3 | | 3 |

| 0 -23 67 -59 | | -32 |

R4 = R4 + 23R2

| 1 -4 -9 -4 | | c1 | | -2 |

| 0 27 59 25 | x | c2 | = | 11 |

| 0 12 29 -16 | | c3 | | 3 |

| 0 0 174 -294 | | 225 |

R3 = R3 - (12/27)R2

R4 = (1/174)R4

| 1 -4 -9 -4 | | c1 | | -2 |

| 0 27 59 25 | x | c2 | = | 11 |

| 0 0 -1 22/3 | | c3 | | -13/3 |

| 0 0 1 -98/87 | | 25/58 |

R1 = R1 + 4R3

R2 = R2 - 59R3

R4 = R4 + (98/87)R3

| 1 0 -13 -10/3 | | c1 | | 21/29 |

| 0 27 0 -2119/87 | x | c2 | = | 2238/87 |

| 0 0 1 -98/87 | | c3 | | 25/58 |

| 0 0 0 1390/2391 | | 1009/2391 |

R1 = R1 + (13/1390)R4

R2 = (1/27)R2

R3 = R3 + (98/1390)R4

| 1

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The correct answers are that Earth’s North Pole is close to the magnetic south pole, magnets allowed to move freely align themselves to point north, and the north pole on a compass is attracted to Earth’s south pole. I really hope this helps you!!

The area of a shape is the amount of space on it:

The shaded area is 314 square centimeters

Start by calculating the area of sectors OFG and OAD using:

\(A = \frac{\theta}{360} * \pi r^2\)

So, we have:

\(OFG = \frac{40}{360} * \pi * 18^2\)

\(OFG = 36\pi\)

Also, we have:

\(OAD = \frac{40}{360} * \pi * 18^2\)

\(OAD = 36\pi\)

Next, calculate the area of the sectors BOE and COH

Note that the radius of these sectors is 6 cm.

So, we have:

\(COH =BOE = \frac{140}{360} * \pi * 6^2\)

\(COH = BOE = 14\pi\)

The shaded area is then calculated as:

\(Shaded = OFG + OAD + COH + BOE\)

This gives

\(Shaded =36\pi + 36\pi + 14\pi + 14\pi\)

\(Shaded =100\pi\)

The equation becomes

\(Shaded =100 * 3.14\)

\(Shaded = 314\)

Hence, the shaded area is 314 square centimeters

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Answer:

GCF of 50 and 100 is...

50

Answer:

13

Step-by-step explanation:

180-96=84

(4x-10)+(4x-10)= 84

X=13

Answer:

The difference is -2x10 is basically-2 times x times 10.

Step-by-step explanation:

Cuz i said so

The x values that makes the given inequality true are -10, -9, -8, -7 and -6.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequality is -2x>10.

Divide -2 on both the sides of an inequality, we get

x<-5

So, the solution is {.......-10, -9, -8, -7, -6}

Hence, the x values that makes the given inequality true are -10, -9, -8, -7 and -6.

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Answer:

A) 2a + 4c = 38.00

B) 3a + 3c = 40.50

We multiply A) by -1.5

A) -3a -6c = -57 then we add B)

B) 3a + 3c = 40.50

-3c = -16.50

c = 5.50

a = 8.00

Step-by-step explanation:

Answer:

  1/5

Step-by-step explanation:

  1/3 of 3/5 is 1/5

The amount of flour you need is 1/5 cup.

Answer:

y8x122

Step-by-step explanation:

Simplify this expression.

The value of x is 2.045 by simple algebra.

Use the time formula, t = d/s, which states that time is equal to distance divided by speed, to solve for time. Time is a function of both speed and distance.

Until it reaches its destination 200 miles distant, a car is driving on a little highway at either 55 or 35 miles per hour, depending on the posted speed restrictions.

x is the duration, in hours, that the vehicle is travelling at 55 mph.

Y is the duration, in hours, that the vehicle is travelling at 35 mph.

55x + 35y = 200 is the equation defining the relationship.

We must locate:

If the trip takes the car 2.5 hours at 35 miles per hour, how long does it take to travel at 55 miles per hour?

∵ 55x + 35y = 200

The drive takes the car 2.5 hours at a speed of 35 mph.

Y shows the duration of time for an automobile travelling at 35 mph.

∴ y = 2.5

- To obtain the value of x, substitute the value of y into the equation.

∴ 55x + 35(2.5) = 200

∴ 55x + 87.5 = 200

- Take 87.5 off of both sides.

∴ 55x = 112.5

- Subtract 55 from both sides.

x equals 2.045 hours.

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Answer:

20m

Step-by-step explanation:

Given that there are m markers in Gino's art box, there are 5m crayons because there are 5 times as many crayons as there are markers. There are 4 times as many colored pencils as there are crayons so 4 x 5m= 20m crayons.

The answer is 20m

Answer:

Step-by-step explanation:

??

Answer:

Step-by-step explanation:

The answer is 20% to 50%

Answer: -2 2/3 or -8/3

Answer:

The right answer is C.

Step-by-step explanation:

The parent function is:

\(f(x)=x^3\)

If something is subtracted from variable \(x\) it means the graph shifted toward right and something is added to \(y\) value then the graph is shifted up.

\(f(x)=(x-8)^3\)

graph shifted toward right by \(8\) units right

\(f(x)=(x-8)^3+3\)

graph shifted toward right by \(3\) units up

Thus the new function is:

\(g(x)=(x-8)^3+3\)

We need to find the inverse of the function gof (x). First we need to find the composite function gof (x) which is given by:

\(g(f(x)) = g(3x - 6)\)

= \((1/3)(3x - 6) + 1\)

= x - 1 + 1

= x

Thus,

gof (x) = x.

Now we need to find the inverse of the function gof (x) to obtain

\((gof)^-1 (x).\)

We have gof (x) = x

which implies\((gof)^-1 (x)\)

= gof (x)^-1

= x^-1

= 1/x,

x ≠ 0

Therefore,

\((gof)^-1 (x) = 1/x\)

which is option (3) (x+1) since 1/x can be written as 1/(x+1-1), where (x+1-1) is the denominator of 1/x.

Hence, the correct option is (3).

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To find (g(f))^-1 (x), substitute the expression for f(x) into g(x) and simplify. The composition of g(f) is x and its inverse is also x. Therefore, (g(f))^-1 (x) equals x.

To find (g(f))^-1 (x), we need to first find the composition of g(f) and then find its inverse. Start by substituting the expression for f(x) into g(x): g(f(x)) = g(3x-6) = \frac{1}{3}(3x-6) + 1 = x - 1 + 1 = x. So, g(f(x)) = x. Now, to find the inverse of g(f), we switch the x and y variables and solve for y: y = x. Therefore, (g(f))^-1 (x) = x.

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As a result, 210 gallons of oil are thought to have been present in the lake at time 12 (t=12).

A polynomial is a mathematical equation that only uses addition, subtraction, multiplication, and non-negative integer exponents and is made up of variables and coefficients. To put it another way, a polynomial is an algebraic expression made up of terms that are sums, products, and/or products of variables and coefficients. The leading coefficient is the coefficient of the term with the highest degree, while the degree of a polynomial is the maximum power of the variable in the expression.

given

(a) We need to determine Q(10), Q'(10), and Q" in order to determine the second degree Taylor polynomial for Q(t) with a center at t=10 (10).

As we are aware, Q(10) = 200. (given in the problem statement).

We must take the derivative of Q(t) with respect to t in order to determine Q'(10):

Q'(t) = -5t + 250

Q'(10) = -5(10) + 250 = 200

We must take the derivative of Q'(t) with respect to t in order to determine Q"(10):

Q''(t) = -5

Q''(10) = -5

The second degree Taylor polynomial can now be calculated using the following formula: P2(t) = Q(10) + Q'(10)(t-10) + (1/2)Q"(10)(t-10)2.

With the numbers we discovered, we can calculate P2(t) as 200 + 200(t-10) + (1/2)(-5)(t-10)2.

\(P2(t) = 200 + 200(t-10) - (5/2)(t-10)^2\)

(b) We must assess the second degree Taylor polynomial at t=12 in order to determine how much oil is in the lake at that time.

P2(12) = 210 gallons because P2(12) = 200 + 200(12-10) - (5/2)(12-10)2. (rounded to the nearest gallon)

As a result, 210 gallons of oil are thought to have been present in the lake at time 12 (t=12).

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The calculation is performed in three stages, and the result represents the volume of the object in cubic units.

The expression ∭ e ⎛ ⎝y ln x z ⎞ ⎠dv represents a triple integral, which is a type of mathematical operation that calculates the volume of a 3-dimensional object bounded by certain conditions.

In this particular case, the volume is defined by the limits of integration (1 ≤ x ≤ e, 0 ≤ y ≤ ln x, 0 ≤ z ≤ 1), meaning that it considers only the points in the space that satisfy these conditions.

To understand the triple integral, it is important to understand the concept of single and double integrals.

The calculation of a triple integral is performed in three stages.

First, the integral with respect to x is calculated, then the integral with respect to y, and finally the integral with respect to z.

The expression e ⎛ ⎝y ln x z ⎞ ⎠ represents the integrand, or the function that we are integrating. In this case, it is a product of three functions of x, y, and z.

The ∭ symbol represents the triple integral and the dv represents the differential of the volume, which is used to calculate the volume in small increments.

In conclusion, the triple integral

=> ∭ e ⎛ ⎝y ln x z ⎞ ⎠dv

calculates the volume of a 3-dimensional object defined by the limits of integration.

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The experimental probability of spinning a green will be 0.10 or 10%.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

Philip spun a spinner with six sections 125 times and the results are shown in the table.

Color               Frequency

Blue                       25

Green                     15

Purple                    23

Yellow                    22

Red                         21

Pink                         19

The experimental probability of spinning a green will be given as,

P = 15 / 150

P = 0.10 or 10%

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