Keisha's teacher gives her the following information:
• m, n, p, and q are all integers and p = 0 and q +0
• A= and B=;
What conclusion can Keisha make?

The electric field is given by the gradient of the potential function, V, which is:∇V=⟨∂V/∂x,∂V/∂y,∂V/∂z⟩=⟨2x+y^2,2xy,2yz⟩Hence,

the electric field in this region at the coordinate \((-7,3,7) is:∇V(−7,3,7)=⟨2(−7)+3^2,2(−7)(3),2(3)(7)⟩=⟨−8,−42,42⟩\)Therefore, the components of the field vector are -8, -42, and 42.

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Given:

A storeowner made a list of number of greeting cards sold last month.

The store sold 167 thank-you cards, 285 birthday cards and 56 blank cards.

Required:

What is the probability that the next customer will buy a blank card expressed as a percent?

Explanation:

We will find total number of cards sold as:

167 + 285 + 56 = 508

Now we will find percentage of each type of card sold as:

Percentage of blank cards sold

Answer:

Hence, in percent probability of sold blank card is 11%.

rd

a. The values of Q1 = 355, Q2 = 510, Q3 = 910, range = 980 and IQR = 555.

b. The lower bound is not applicable and the upper bound is 1195. There are no outliers.

c.  The value at the 70th percentile is approximately 725.6 calories.

a. For the calories of each burger, we will find the Q1, Q2, and Q3, range, and IQR as follows -

Arranging the calorie values in order from smallest to largest we get,

250, 300, 410, 430, 445, 460, 510, 540, 670, 710, 840, 980, 1230.

The median of the lower half (from 250 to 540) is the average of the two middle values: (300 + 410) / 2 = 355.

Therefore, Q1 = 355.

Arranging the calorie values in order from smallest to largest we get,

250, 300, 410, 430, 445, 460, 510, 540, 670, 710, 840, 980, 1230.

The middle value is the median: Q2 = 510.

Arranging the calorie values in order from smallest to largest we get,

250, 300, 410, 430, 445, 460, 510, 540, 670, 710, 840, 980, 1230.

The median of the upper half (from 670 to 1230) is the average of the two middle values: (840 + 980) / 2 = 910.

Therefore, Q3 = 910.

Range = 1230 - 250 = 980.

IQR = Q3 - Q1 = 910 - 355 = 555.

b. To calculate the outlier boundaries, we need to first calculate the lower and upper limits as follows -

Lower bound: Q1 - 1.5 x IQR

Upper bound: Q3 + 1.5 x IQR

Lower bound: 430 - 1.5 x 310 = -25

Upper bound: 740 + 1.5 x 310 = 1195

Since there are no negative values for the calories of the burgers, the lower bound is not applicable. The upper bound is 1195, which is higher than the highest value in the dataset (1090). Therefore, there are no outliers.

c. To determine the value at the 70th percentile, we need to first order the calorie values from lowest to highest as follows -

250, 300, 410, 430, 445, 460, 510, 540, 670, 710, 740, 840, 980, 1090, 1230

Next, we will calculate the percentile rank of the 70th percentile -

Percentile rank = (70/100) x (n + 1) = 10.6

Since the percentile rank is not a whole number, we need to interpolate between the 10th and 11th values in the ordered list:

10th value: 710

11th value: 740

Using linear interpolation, we get:

Value at the 70th percentile = 710 + 0.6 x (740 - 710) = 725.6

Therefore, the value at the 70th percentile is approximately 725.6 calories.

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The complete question is -

For the calories of each burger:

a. find q1, q2, q3, the range, and the IQR.

b. calculate the outlier boundaries for the data set. are there any outliers? c. determine the value at the 70th percentile.

Using continuous compounding and compound interest, it is found that it takes 5.04 years longer for Ella's money to double than for Penelope's money to double.

The amount of money, after t years, using continuous compounding, is given by:

\(A(t) = A(0)e^{rt}\)

In which:

In this problem, Penelope's interest rate, as a percentage, is:

\(1\frac{3}{8}\% = 1 + \frac{3}{8} = 1.375\%\)

Hence \(r = 0.01375\)

The time to double is t for which A(t) = 2A(0), then:

\(A(t) = A(0)e^{rt}\)

\(2A(0) = A(0)e^{0.01375t}\)

\(e^{0.01375t} = 2\)

\(\ln{e^{0.01375t}} = \ln{2}\)

\(0.01375t = \ln{2}\)

\(t = \frac{\ln{2}}{0.01375}\)

\(t = 50.41\)

It takes 50.41 years for Penelope's amount to double.

Compound interest:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

For Ella's, we have that:

The time to double is t for which A(t) = 2P, hence:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

\(2P = P\left(1 + \frac{0.0125}{365}\right)^{365t}\)

\((1.00003424658)^{365t} = 2\)

\(\log{(1.00003424658)^{365t}} = \log{2}\)

\(365t\log{1.00003424658} = \log{2}\)

\(t = \frac{\log{2}}{365\log{1.00003424658}}\)

\(t = 55.45\)

It takes 55.45 years for Ella's amount to double.

55.45 - 50.41 = 5.04

It takes 5.04 years longer for Ella's money to double than for Penelope's money to double.

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Answer:

a = 12

b = 2

c = 11

Step-by-step explanation:

\( \frac{( {x}^{5}y {z}^{4} )^{3} }{ {x}^{3} yz} = {x}^{a} {y}^{b} {z}^{c} \\ \\ \frac{ {x}^{5 \times 3}y^{3} {z}^{4 \times 3} }{ {x}^{3} yz} = {x}^{a} {y}^{b} {z}^{c} \\ \\ \frac{ {x}^{15}y^{3} {z}^{12} }{ {x}^{3} yz} = {x}^{a} {y}^{b} {z}^{c} \\ \\ {x}^{15 - 3} {y}^{3 - 1} {z}^{12 - 1} = {x}^{a} {y}^{b} {z}^{c} \\ \\ {x}^{12} {y}^{2} {z}^{11} = {x}^{a} {y}^{b} {z}^{c} \\ \\ equating \: like \: terms \: from \: both \: sides \\ \\ {x}^{12} = {x}^{a} \: \implies \: a = \boxed{ 12}\\ \\ {y}^{2} = {y}^{b} \: \implies \: b = \boxed{ 2} \\ \\ {z}^{11} = {z}^{c} \: \implies \: c = \boxed{ 11}\)

Answer:

31 and 37

Step-by-step explanation:

Those are the only two numbers

Answer:

The two numbers between 30 and 40 which have only 2 factors are -

31 and 37

Hope it helps you.

Answer:

\(({3 \times 2})^{2} \)

\( = (6)^{2} \)

\( = 36\)

When a cone with a volume of 5000 m³ is dilated by a scale factor of 15, the volume of the resulting cone is 3375000 m³.

The volume of a cone is given by the formula V = (1/3)πr²h, where r is the radius of the base and h is the height. Since the scale factor of 15 applies to all dimensions of the cone, the new radius and height will be 15 times the original values. Let's assume the original cone has radius r and height h.

After dilation, the new cone will have a radius of 15r and a height of 15h. Plugging these values into the volume formula, we get

V' = (1/3)π(15r)²(15h) = (1/3)π(15²)(r²)(h) = 3375V.

Given that the original cone has a volume of 5000 m³, we can calculate the volume of the resulting cone by multiplying 5000 by 3375:

V' = 5000× 3375 = 3375000 m³.

Therefore, the volume of the resulting cone, after being dilated by a scale factor of 15, is 3375000 m³.

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- For values of 'a' that satisfy (a+5)(a²-10)² - (a+5) ≠ 0, the system of equations has no solutions.

- For values of 'a' that satisfy (a+5)(a²-10)² - (a+5) = 0, the system has infinitely many solutions.

- For all other values of 'a', the system has exactly one solution.

To determine the values of 'a' for which the system of equations has no solutions, exactly one solution, or infinitely many solutions, we can analyze the augmented matrix of the system using row operations.

The augmented matrix for the system is:

[ 1   2   -3  |  5 ]

[ 3   -1  2   |  3 ]

[ 4   1   (a²-10)²  |  a+5 ]

Performing row operations to bring the matrix to row-echelon form, we have:

[ 1   2   -3  |  5 ]

[ 0   -7  11  |  -12 ]

[ 0   0   (a²-10)² + (5-a)  |  (a+5)(a²-10)² - (a+5) ]

From the row-echelon form, we can determine the cases:

Case 1: No solutions

If the last row of the row-echelon form has a non-zero entry in the augmented column (rightmost column), then the system has no solutions. In this case, we need the expression in the last row's augmented column to be non-zero. Therefore, we require:

(a+5)(a²-10)² - (a+5) ≠ 0

Case 2: Infinitely many solutions

If the last row of the row-echelon form consists of all zeros (except the augmented column), then the system has infinitely many solutions. In this case, we need the expression in the last row's augmented column to be zero. Therefore, we require:

(a+5)(a²-10)² - (a+5) = 0

Case 3: Exactly one solution

For any other value of 'a', the system will have exactly one solution.

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Answer:

3

Step-by-step explanation:

cross multiply it by 2 and 3 respectively

Answer:

WRS and VRT are vertical angles

Step-by-step explanation:

Vertical angles are formed by the same lines and share a vertex

WRS and VRT are vertical angles

All of those values are reflections of well know values of those functions. We are familiar with the sine, cosine and tangent of 30º, 45º, 60º and 90º.

With this previous knowledge(you might look for a table with those values) we can answer those questions.

The first one is direct

-300º is the same as 60º, since a full circle is 360º and with the minus sign it means it was rotating in the other direction, then

Converting from radians

Then

And 450º, is a full circle with an addition of 90º. After a full circle the trigonometric functions repeat their value. Then

Again, we have a similar situation. -45º and 315º are the same angle, just rotations in different directions. The tangent of -45º is just the negative of the tangent of 45º. then

6. x=1 , y=2

7. x=-4 , y=5

8. Infinitely Many Solutions

An argument in which the reasons support the conclusion so that the conclusion follows from the reasons offered is called a valid argument.

In logic and critical thinking, an argument consists of two main components, premises and a conclusion.

The premises are statements or reasons put forth as evidence or support for the conclusion.

The conclusion is the statement that is being asserted or inferred based on the premises.

A valid argument is one in which the logical relationship between the premises and the conclusion is such that if the premises are true.

Then the conclusion must also be true.

In other words, the conclusion logically follows from the premises.

When an argument is valid, it means that the truth or validity of the premises guarantees the truth or validity of the conclusion.

It does not necessarily mean that the premises are true in reality, but rather that if they were true, the conclusion would be true as well.

Here is an example to illustrate a valid argument,

Premise 1

All mammals are warm-blooded animals.

Premise 2

Dogs are mammals.

Conclusion,

Therefore, dogs are warm-blooded animals.

In this example, if we assume that the premises are true, the conclusion logically follows.

The truth of Premise 1 establishes that all mammals are warm-blooded, and Premise 2 identifies dogs as mammals.

This implies, the conclusion that dogs are warm-blooded animals logically follows from the given premises.

A valid argument can still have false premises or a false conclusion.

The validity of an argument simply relates to the logical relationship between the premises and the conclusion.

Rather than the truth or accuracy of the statements themselves.

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The best instrument to determine the predictive validity of a metric scale would be a correlation-coefficient.

This measure assesses the strength of the relationship between two variables, in this case, the metric scale scores and the predicted outcome. A high correlation would indicate that the metric scale is a good predictor of the outcome, whereas a low correlation would indicate that the metric scale is not a reliable predictor.

Cronbach's alpha is a measure of internal consistency and would not be appropriate for determining predictive validity. Fisher's r-to-z test is used to compare the strength of two correlations and is not necessary in this scenario. Therefore, the answer is B, a correlation-coefficient.

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0.0405 is the number that contain the digit 2 once, the digit 3 twice, the digit 4 thrice, and more 5s than threes, leading 0s are allowed.

According to collect from the data

Let us assume that the data as followed by

How many eight digit numbers contain the digit 2 exactly once, the digit 3 exactly twice, the digit 4 exactly thrice and more 5s than threes.

Let many eight digit numbers contain the digit 2 once, the digit 3 twice the digit 4 thrice and more 5s than threes.

2,3,3,4,4,4

now then:

= 8!/2!3!3!4!4!4!

= 8.7.6.5.4!/2×6×6×24×24×4!

= 35/864

Now 0.405 then the eight digit number contains the digit 2 once the digit 3 .

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Answer:

I believe its D

Step-by-step explanation:

because the Xs do not repeat but on the other answer choices , they do .

Hope I could help -

Sleepy~

A parametric description of the solution set of a linear system is the same as solving the system is the false statement.

If a linear system has at least one solution, only then can the solution set be stated using a parametric description. The set of ordered pairs that make up the solution to an equation with two variables is referred to as the solution set. You'll discover what a solution set is in this tutorial and witness an example. By combining two equations with two variables into one equation with one variable, we can solve a system of equations. Since there are two variables in each equation in the system, replacing a variable with an expression can help minimize the number of variables in an equation.

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According to recent data, women make up 34% and 26% of workers in science and technology (STEM) fields in Canada and the United States, respectively. The correct option is A. 34% and 26%.

According to recent data, women make up 34% and 26% of workers in science and technology (STEM) fields in Canada and the United States, respectively. This indicates that women are still underrepresented in STEM fields, despite the fact that there has been an effort to attract more women to STEM fields.

In both Canada and the United States, women have made significant progress in breaking down gender barriers in STEM fields. However, there is still work to be done to close the gender gap and increase representation of women in STEM fields.

Women's representation in STEM fields has increased in both Canada and the United States in recent years, but the percentage of women in STEM fields is still significantly lower than the percentage of men. More efforts are needed to close the gender gap in STEM fields and encourage more women to pursue STEM careers.

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Answer:

560/9 cubes

Step-by-step explanation:

How many 1/3 inch cubes does it take to fill a box

the dimension of the box is

width 2 2/3 inches,

length 3 1/3 inches, and

height 2 1/3 inches

The volume of the box is

volume= L*W*H

volume= 3 1/3 * 2 2/3* 2 1/3

converting to proper fraction

volume= 10/3*8/3*7/3

volume= 10*8*7/3*3*3

volume=560/27 in^3

the volume of the cube is 1/3

so the number of cubes will be

=560/27/1/3

=560/27*3

=560/9

The probability that when a theft occurs, at least one of the 5 systems will detect it is approximately 0.9997.

How likely something is to occur is known as its probability. We can discuss the probabilities of different outcomes, or how likely they are, whenever we are unsure of how an event will turn out.

We can solve this problem using the complement rule. The probability that none of the 5 systems detect the theft is given by:

(1 - 0.82)^5 = 0.00033124

So the probability that at least one system detects the theft is:

1 - 0.00033124 = 0.99966876

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Given:

Each time Sally waters her tomato plants she uses 5 liters of water.

Sally waters her tomato plants 3 times a week.

To find:

How much water, in liters, does Sally use in a week?

Solution:

We have,

Water used in each time = 5 liters

Number of times Sally waters her tomato plants = 3 times

Now,

Water used in 1 time = 5 liters

Water used in 3 time = 3×5 liters

                                   = 15 liters

Therefore, the Sally use 15 liters of water in a week.

Therefore , a)different orders can the spider put on its socks and shoes is  \(\frac{16!}{(2!)^{8} }\)  and b)the total no of ways for people to discharge from lift is 14112 ways.

Selections are another name for combinations. Combinations represent the choosing of items from a predetermined group of items. We're not trying to arrange anything here. We're going to pick them. We write n C r to represent the number of distinct r-selections or combinations among a set of n objects. Compared to arrangements or permutations, combinations are different.

Here,

Each dressing sequence may be uniquely characterized by a series of two 1s, two 2s,..., and two 8s; the spider is said to put the sock on leg x in the first instance, and the shoe on leg x in the second instance.

The solution would be 16! if each number were unique.

However, because 8 words appear twice, the solution is

=>  \(\frac{16!}{(2!)^{8} }\)

Thus different orders can the spider put on its socks and shoes is  \(\frac{16!}{(2!)^{8} }\)

Thus,

Part A: When the elevator operator can't tell who is who.

Currently, there are 6 floors and 10 persons, and each floor loses one.

so 8+6-1=13

applying combination

=>\(C^{13} _{5}\) =  1287 ways.

Part 2: When the elevator attendant separates males from ladies.

There are 3 females and 5 males.

The formula for choosing five men is (5 + 6)-1= (10).

Applying combination  

=> .\(C^{10} _{5}\)= 252 ways

techniques to choose ladies = 3+6-1=8

Applying combination  

=> \(C^{8} _{5}\) = 56 ways

Total no. of ways

=>  252*56 = 14112 ways.

Therefore , the total no of ways for people to discharge from lift is 14112 ways.

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Answer:

x = 1/25

y = 32/25

Step-by-step explanation:

Answer:

yes it does and it need to be a y

Answer:

3:25 pm

Step-by-step explanation:

The distance between New Orleans and Houston is : 353 miles

Departure time of the bus : 12:20 pm

Speed of the bus: 60 mph

After 45 minutes, the bus will be at a distance of : 45/60 * 60 = 45 miles

Distance remaining to cover = 353-45 = 308 miles

Speed of the motorcycle = 72 mph

Relative speed = 60 + 72 = 132 mph

Time the two will meet = 308 / 132 =  7/3 hrs

7/3 hrs = 2 hrs  20 minutes

Time the two will meet is ;

12:20 pm + 45 minutes + 2 hrs 20 minutes

= 3:25 pm

Both the bus and the motorcycle are driving opposite to each other.

From the given data, the time at which both the bus and the motorcycle will pass each other is 3:25 PM

The time at which both the motorcycle and the  bus will pass each other.

Let after t hour from the time when motorcycle starts, they both meet.

Then we have:

353 miles = 45 minute traveled by bus + distance traveled by bus in t hour + distance traveled by motorcycle in t time.

Since 45 minutes is three fourth of an hour, thus:

Distance traveled by bus in 45 minutes is calculated as:

\(D_{Bus}(45 \:\rm min) = 60 \times \dfrac{3}{4} \: \rm miles = 45 \: \rm miles\)

Distance traveled by bus in t hours is:

\(D_{Bus}(t \: \rm hours) = 60 \times t \: \rm miles = 60t \: \rm miles\)

Distance traveled by motorcycle in t hour is:

\(D_{motorcycle}(t \: \rm hours) = 72 \times t \: \rm miles = 72t \: \rm miles.\)

Thus, we have:

\(353 = 60t + 72t + 45\\\\308= 132t\\\\t = \dfrac{308}{132}\\\\t= \dfrac{7}{3}\: \rm hours\\\\t=2 \: \rm hours + 20 \: \rm minutes\)

Thus, time at which they meet was 12:20 PM + 45 minutes + 2 hours + 20 minutes = 3:25 PM

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The velocity of a particle = i + 2t j

The acceleration of a particle = 2 j

The speed of a particle = \(\sqrt{1 + 4t^{2} }\)

Here,

The position function is, \(r (t ) = ti + t^{2} j +2k\)

We have to find, the velocity, acceleration, and speed of a particle with the given position function.

What is Velocity of a particle with the given position function?

The instantaneous velocity v(t) of a particle is the derivative of the position with respect to time. That is, v(t)=dx/dt.

Now,

The position function is, \(r (t ) = ti + t^{2} j +2k\)

The velocity of a particle = \(\frac{d r(t)}{dt}\)

\(r (t ) = ti + t^{2} j +2k\)

\(\frac{d r(t)}{dt} = i + 2t j\)

The acceleration of a particle = \(\frac{d^{2} r(t)}{dt^{2} }\)

\(r (t ) = ti + t^{2} j +2k\)

\(\frac{d r(t)}{dt} = i + 2t j\)

\(\frac{d^{2} r(t)}{dt^{2} }= 2j\)

The speed of a particle = \(| \frac{d r(t)}{dt}| = |v(t)|\)

\(\frac{d r(t)}{dt} = i + 2t j\)

\(|v(t)|=\sqrt{1 + 4t^{2} }\)

Hence, The velocity of a particle = \(i + 2t j\)

The acceleration of a particle = \(2 j\)

The speed of a particle = \(\sqrt{1 + 4t^{2} }\)

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