ABCD is a regular tetrahedron. MandN are the mid points of the edges AB and CD. It the length of AB is a, then |MN|^2 = ...?

To make x the subject of the expression, we have; x = 16y^2 - 5.

Subject of formula is a topic in mathematics which involves expressing an alphabet in terms of other alphabets in the given expression. From the given question, to make x the subject implies expressing x in terms of other variables in the given expression.

So that, [tex]\frac{\sqrt{x + 5} }{4}[/tex] = y

square both sides of the expression to have;

(x + 5)/ 16 = y^2x + 5

= 16y^2x = 16y^2 - 5

Therefore to express x as a subject of formula for the given expression, we have;

x = 16y^2 - 5

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The measure of the angle x in the isosceles triangles are;

x = 44°

1) x = 80°

An isosceles triangle is a triangle that has a pair of congruent sides and a pair of congruent angles.

The measure of the specified angle are found as follows;

The isosceles triangle that has 92° as the exterior angle, indicates that we get;

Base angles of the isosceles triangle = (180° - 92°)/2 = 44°

Vertical angles theorem, indicates that the vertical angle and the base angles of the second isosceles triangle are congruent.

Base angles of the second isosceles triangle = 44°

1) The angle adjacent to the angle x is a base angle of the isosceles triangle that has a base angle of 70°

The vertex angle of the isosceles triangle = 180° - 2 × 70° = 40°

The measure of the section of the indicated 90° angle that is a part of the isosceles triangle that has angle x as the vertex angle = 90° - 40° = 50°

The measure of angle x found using the relationship between the angles in an isosceles is; x = 180° - 2 × 50° = 80°

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Categorical data can be either numeric or nonnumeric. Numeric data includes values such as integers, decimals, and percentages. Nonnumeric data includes values such as text, dates, and names.

Categorical data is a type of data that can be either numeric or nonnumeric. Numeric data includes values such as integers, decimals, and percentages, while nonnumeric data includes values such as text, dates, and names. Categorical data is often used to indicate either how much or how many of something there is. For example, a survey might ask respondents to choose between several options, such as “none,” “some,” and “many,” which are all nonnumeric values, but can still provide useful information about how much of something a respondent has. In addition, categorical data can also be numeric, such as when data is collected on the number of hours a respondent works each week. Categorical data is useful for understanding the characteristics of a population in a more qualitative way.

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The smallest possible value is 44%.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. 

Given that,

If only three persons are running for the office and the third-place candidate received 28 votes and the second-place candidate received 98 votes, the winner could have received only 99 votes.

In this case, the total number of votes cast would be 28 + 98 + 99  =  225 votes.

The percentage for the winning candidate would be:  99 / 225  =  44%

Therefore, the smallest possible value of x is 44%.

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Answer:

n = 13

Step-by-step explanation:

n - 26 = - 13 ( isolate n by adding 26 to both sides )

n = - 13 + 26

n = 13

Answer:

70% of the data points

Step-by-step explanation:

To calculate the percentage of data points that fall within one standard deviation of the mean, you can follow these steps:

Calculate the mean of the data set: (55+54+66+38+53+56+57+66+45+65)/10 = 55

Calculate the standard deviation of the data set: √ (((55-55) ²+(54-55) ²+(66-55) ²+(38-55) ²+(53-55) ²+(56-55) ²+(57-55) ²+(66-55) ²+(65-55)²)/9) = 7.8

Determine the range for data points within one standard deviation of the mean: Mean ± 1 * standard deviation = 55 ± 1 * 7.8 = [47.2, 62.8]

Count the number of data points that fall within this range: 55, 54, 53, 56, 57, 45, and 65 fall within this range.

Calculate the percentage of data points that fall within this range: (7/10) * 100 = 70%

Therefore, 70% of the data points in the given data set fall within one standard deviation of the mean.

Using simple mathematical operations, we know that we can have 10 different arrangements to plant 2 apple trees and 5 pear trees in a row.

An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.

The operation's arity is determined by the number of operands.

A rule that specifies the right procedure to follow while evaluating a mathematical equation is known as the order of operations.

Parentheses, Exponents, Multiplication, and Division (from Left to Right),

Addition, and Subtraction are the steps that we can remember in that order using PEMDAS (from left to right).

So, we know that:

Golden delicious apple trees: 2

Bartlett pear tree: 5

Different arrangements that can be made are as follows:
2 * 5

10

Therefore, using simple mathematical operations, we know that we can have 10 different arrangements to plant 2 apple trees and 5 pear trees in a row.

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The zeros of the polynomial y = 3p³ - 8p² + 4p are calculated to be 0, 2/3, and 2.

The zeros of a function, sometimes referred to as the roots or solutions, are the values of the independent variable (x) for which the function equals zero. In other words, these are the x-coordinates of the points where the graph of the function crosses the x-axis. You can get the zeros of a function by setting its value to zero and then figuring out what value(s) of x the equation needs.

For example, if the function is f(x), you would set f(x) to 0 and then find x:

For example, if the function is f(x), you would set f(x) to 0 and then find x:

f(x) = x² + 2x - 3 = 0

This equation can be written as (x-3)(x+1) = 0.

Inferring from the x-values that x - 3 = 3 or x + 1 = -1, x² + 2x - 3 = -1, 3

As a result, the zeros of the function f(x) = x² + 2x - 3 are -1 and 3.

In the issue at hand, y = 3p³ - 8p² + 4p

y = p(3p - 2)(p - 2) (p - 2)

Taking the zeros,

0 = p(3p - 2)(p - 2)

p = 0,

3p - 2 = 0,

p = 2 / 3,

p - 2 = 0, p = 2

The zeros of the polynomial or roots are (0, 2/3, and 2).

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Angle m∠3 is 79degree

What is linear pair?

Linear pair of angles are produced when two lines intersect each other at a point. The sum of angles of the linear pair is always 180 degrees.

Given;

m∠1= (x+70)

m∠2= (5x+54)

Here, m1=m2

substituting the values of m1 and m2

x+70=5x+54

70+54=5x-x

124=4x

x=31 substituting in m2

m2=101

Now, m2+m3=180 (linear pair of angles)

101+m3=180

m3=79degree

So, the measure of angle m3 will be 79degree.

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Answer:

price is now $24.64

and it was $3.36 off

Step-by-step explanation:

Answer:

Hi Hannah!

there's a little tiny mistake in your question

what's the probability of getting what heart spade etc

you didn't specify it

sorry for bothering but this is my favorite questions

Answer:

29$

Step-by-step explanation:

1.60+0.75+0.89=3.24 - dollars per one kid
3.24 * 9 = 29.16 - dollars total
round 29.16 to the nearest dollar - 29$

The amount it would cost to paint the outside of the box is £208

From the question, we are to determine calculate how much it would cost to paint the outside of the box

To do this, we will calculate the surface area of the box

The surface area of a box is given by

S.A = 2(lw + lh + wh)

Where S.A is the surface area

l is the length

w is the width

and h is the height  

From the given information,

l = 10 cm

w = 80 cm

h = 20 cm

Thus,

S.A = 2(10×80 + 10×20 + 80×20)

S.A = 2(800 + 200 + 1600)

S.A = 2(2600)

S.A = 5200 cm²

Also, from the given information

The paint costs £0.04 per cm2

Thus,

The cost is £0.04 × 5200

= £208

Hence, the cost is £208

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234 is the sum of the rotcaf of all the even numbers between 1 and 25.To solve this question use the concept of series.

A rotcaf is the sum of the largest factors of the number that is smaller than the number and the number that is obtained by adding two numbers, the rotcaf of 9, for instance, is 9, 3, or 12.

Here given that,

even numbers between 1 and 25 which is: 2,4,6,8,10,12,14,16,18,20,22,24

for finding rotcaf:

(2 + 1) , (4 + 2), (6 + 3), (8 + 4),.....(24 + 12)

Here two series are present:

(1, 3, 5, 7,......23) and (2,4,6,8,......24)

Now, sum of the series is:

= [12 /2 {2+24}] + [12/2 {1 + 12}

= 156 + 78

= 234

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Answer:

The scatter plot provided shows a relationship between the independent variable (x) and the dependent variable (y) that appears to be non-linear. The data points seem to be scattered around the graph. The best fit line would be a polynomial equation, the degree of the equation depends on the shape of the data points. It is not possible to give an exact equation of the line of best fit without knowing the data points.

(a) It is not possible to give an approximate equation of the line of best fit without knowing the data points or a more detailed information of the graph.

(b) Without a clear equation to predict values, it is not possible to predict the value of y for x = 10.

Answer: Assuming the conditions for inference are met, we can use the difference in proportions of red beads in the two samples to estimate the difference in proportions of red beads in the population. The 95% confidence interval for the difference in proportions of red beads in the two containers is calculated as follows:

Difference in sample proportions = p1 - p2 = (13/50) - (16/50) = -0.03

Standard error of the difference in sample proportions = sqrt{(p1*(1-p1)/n1) + (p2*(1-p2)/n2)} = sqrt{(13/50)(37/50)/50 + (16/50)(34/50)/50} = 0.079

Margin of error = z* * standard error of the difference in sample proportions = 1.96 * 0.079 = 0.155

95% Confidence interval for the difference in proportions of red beads in the two containers = (difference in sample proportions - margin of error, difference in sample proportions + margin of error) = (-0.03 - 0.155, -0.03 + 0.155) = (-0.185, 0.125)

So, we can be 95% confident that the difference in the proportion of red beads in the two containers is between -0.185 and 0.125.

Step-by-step explanation:

The probability of four Kings and four Queens being all next to each other in a well shuffled deck of 52 cards is approximately 0.00000000024 or 0.000000002%.

The probability of four Kings being all next to each other in a well shuffled deck of 52 cards is:

(1/51) * (1/50) * (1/49) * (1/48)

= 0.000000000077 or 0.00000077%

The probability of four Queens being all next to each other in a well shuffled deck of 52 cards is:

(1/51) * (1/50) * (1/49) * (1/48)

= 0.000000000077 or 0.00000077%

The probability of four Kings and four Queens being all next to each other in a well shuffled deck of 52 cards is:

0.000000000077 * 0.000000000077

= 0.00000000024 or 0.000000002%

The probability of four Kings and four Queens being all next to each other in a well shuffled deck of 52 cards is very small, approximately 0.00000000024 or 0.000000002%. This is because there are many other combinations of cards that can occur in a shuffled deck.

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[tex]\tan 40^{\circ} \cot 50^{\circ}-\sec 40^{\circ} \csc 50^{\circ}\\\\=\tan 40^{\circ} \tan 40^{\circ}-\sec 40^{\circ} \sec 40^{\circ}\\\\=\tan^2 40^{\circ}-\sec^2 40^{\circ}\\\\=-1[/tex]

The exact value of a number is often what is meant when the word absolute is used in mathematics.

The absolute value of a number is often what is meant when the word absolute is used in mathematics. For mathematicians, knowing the absolute value is essential. To display a number's absolute value, vertical bars are placed on either side of the number. The absolute value on a number line denotes separation from zero.

The absolute value of a negative number is a positive number. The absolute value of one positive number is equal to that of another positive number. No matter what its sign, a number's absolute value is always its non-negative value. For instance, 5 is also the absolute value of 5, as is the absolute value of -5.

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Answer: labour day

Step-by-step explanation:

The probability of a senior student taking statistics or calculus is 0.82. This is calculated by adding the probability of a senior student taking statistics (0.15) and a senior student taking calculus (0.35).

p(a or b) = p(a) + p(b) - p(a and b)

p(a) = 15/100 = 0.15

p(b) = 35/100 = 0.35

p(a and b) = 15/100 = 0.15

p(a or b) = 0.15 + 0.35 - 0.15 = 0.82

The probability of a senior student taking either statistics or calculus is 0.82. This is calculated by adding the probability of a senior student taking statistics (0.15) and a senior student taking calculus (0.35) and subtracting the probability of a senior student taking both statistics and calculus (0.15). The probability of a senior student taking statistics is calculated by dividing the number of seniors taking statistics by the total number of students surveyed (15/100 = 0.15). The probability of a senior student taking calculus is calculated by dividing the number of seniors taking calculus by the total number of students surveyed (35/100 = 0.35). The probability of a senior student taking both statistics and calculus is calculated by dividing the number of seniors taking both statistics and calculus by the total number of students surveyed (15/100 = 0.15). Therefore, the probability of a senior student taking either statistics or calculus is 0.82.

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Answer:

Commission Pay =  $2,288
Gross Pay = 4,878

Step-by-step explanation:

Amount of Commission: To calculate the amount of commission earned, multiply the sales by the commission rate. In this case, $57,200 x 4% = $2,288.

Gross Pay: To calculate the gross pay, add the salary to the commission earned. In this case, $2,590 + $2,288 = $4,878.

Answer:

208 mm

Step-by-step explanation:

A = Area. P = Perimeter. B = base.

Let's say H = Height

P = 2B + 2H

Now we already know the perimeter is 68 mm, so P = 68:

68 = 2B + 2H

In addition, we know that the base is 26 mm, so B = 26:

68 = 2(26) + 2H

68 = 52 + 2H

16 = 2H ==> subtract 52 on both sides

H = 8  ==> the height of the rectangle is 8 mm

A = B * H  

A = 26 * 8  ==> plugin B=26 and H=8 into the Area formula

A = 208  ==> simplified

Hence, the area is 208 mm.

The four solutions in math include algebraic solutions, geometric solutions, numerical solutions, and analytical solutions.

1. Algebraic solutions involve solving equations with variables and operations such as addition, subtraction, multiplication, and division.

2. Geometric solutions involve visualizing shapes and solving problems related to angles, lines, and shapes.

3. Numerical solutions involve using numbers and operations such as addition, subtraction, multiplication, and division to solve problems.

4. Analytical solutions involve using logic and reasoning to solve problems. This may involve using diagrams, graphs, and other visual tools to help solve a problem.

The four solutions in math include algebraic solutions, geometric solutions, numerical solutions, and analytical solutions. Algebraic solutions involve solving equations with variables and operations, geometric solutions involve visualizing shapes and solving problems related to angles, lines, and shapes, numerical solutions involve using numbers and operations to solve problems, and analytical solutions involve using logic and reasoning to solve problems with the help of diagrams, graphs, and other visual tools.

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It is impossible to say if the rate of change of the volume changes from positive to negative at a specific time.

It is not possible to determine if there is a time t, for 5 < t < 10, at which the rate of change of the volume of water in the tub changes from positive to negative without any more information. The rate of change of the volume of water in the tub is the derivative of the function representing the volume of water in the tub with respect to time. The information provided does not specify the function or the rate of change of the volume of water in the tub so it is impossible to say if the rate of change of the volume changes from positive to negative at a specific time.

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Answer:

[tex]m = \frac{y2 - y1}{x2 - x1} where \: m \: is \: slope[/tex]

(8,3)=(x1,y1)

(10,3)=(x2, y2)

Now,

[tex]m = \frac{3 - 3}{10 - 8} \\ = 0[/tex]

The spread of the sampling distribution is equal to the standard deviation divided by the square root of the sample size.

What is sample size?

The sample size is defined as the number of observations used to estimate a given population. The population was used to determine the size of the sample. The process of selecting a subset of individuals from a population to estimate the characteristics of the entire population is known as sampling. For analysis, the number of entities in a subset of a population is chosen.

The spread of the sampling distribution is proportional to the spread of the sample and its size. We calculate the spread of the sampling distribution as the population standard deviation divided by the square root of the sample size.

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Answer:

3600 square units

Step-by-step explanation:

From inspection of the given diagram, the area of the rectangle is:

[tex]\implies \sf Area=9 \cdot 4 = 36\; units \; squared[/tex]

Given matrix:

[tex]\left[\begin{array}{rr}5&10\\-8&4\end{array}\right][/tex]

To find the area scale factor, find the absolute value of the matrix determinant:

[tex]\implies \left| \:5 \cdot 4 - 10 \cdot (-8) \right|=\left|20+80\right|=100[/tex]

Therefore, the area of the image of the rectangle under the given matrix transformation is:

[tex]\implies \sf Area=36 \cdot 100=3600\;square\;units[/tex]

The equation of the line that passes through (3, 19) and (9, 25) will be y = x + 16.

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).

Then the equation of the line is given as,

[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]

The points are given below.

(3, 19) and (9, 25)

The equation of the line that passes through (3, 19) and (9, 25) will be given as,

(y - 25) = [(25 - 19) / (9 - 3)](x - 9)

y - 25 = (6/6)(x - 9)

y - 25 = x - 9

y = x - 9 + 25

y = x + 16

The equation of the line that passes through (3, 19) and (9, 25) will be y = x + 16.

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Answer:

Step-by-step explanation:

y = x/(2+x²)

2y + yx² = x

yx² - x + 2y = 0

(1±√(1-8y²))/2y

Now, 1 - 8y² ≥ 0

8y²≤1

y² ≤ 1/8

y ∈ (-1/2√2, 1/2√2)
Thanks