How many 2-digit special numbers are there?.

Answer:

y = -3x + 10

Step-by-step explanation:

Here m is the slope and b is the y-intercept.

  m = -3

y = -3x + b

Now (6,-8) is passing through this line. So, substitute the x and y coordinates in the above equation and find the value of 'b'.

      -8 = -3*6 + b

     -8 = -18 + b

-8 +18 = b

   b = 10

Equation of the line:

    y = -3x + 10

Answer:

y=-3x+10

Step-by-step explanation:

slope intercept form is y=mx+b

m is slope

b is y intercept

So we fill in what we know to find b

-8=-3(6)+b

-8=-18+b

+18 +18

10=b

Now we can finish our equation

y=-3x+10

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Shelly needs 168 blocks to cover the area of the square gap

A square is a two-dimensional shape quadrilateral with four sides equal and parallel to each other. The angles in this shape are measured as 90 degrees.

The gap is 36 mm deep and it's length is assumed to be 36 mm too

The area of the gap will be calculated using area of square

Area of square = L²

Area of square = 36²

Area of square = 1296mm²

However, the block has a shape of rectangle and the area of rectangle is given as

Area of Rectangle = L * W

Area of the rectangular blocks = 4 * 2 = 8mm²

The number of blocks required to fill the square gap will be

1296 / 8 = 162 blocks

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Answer:

The radius is 7.

Step-by-step explanation:

To find the radius of this circle, we would have to find the diameter first. This can be found by looking at both the directions of the origin (left and right) and counting how many spots it goes until the circle ends.

On the left, there is 6 spots. On the right, there is 8. So we would add to find the full way around or the diameter (6 + 8) and we get 14.

Now, since radius is halfway around or is half of the diameter, we simply divide 14 by 2 which is 7.

Therefore, the answer is 7.

(1) $132,000 is the net income

(2) $66,000 total income

Selling price per unit:

= Sales ÷ No. of units

= $456,000 ÷ 5,700

= $80

Variable cost per unit:

= variable cost ÷ No. of units

= $102600 ÷ 5,700

= $18

Alternative 1:

Contribution margin = Sales - variable cost

                                 = (5,700 × $80 × 1.1) - (5,700 × $18)

                                 = $440,000 - $210,000

                                 = $230,000

Net income = Contribution margin - Fixed cost

                  =  $230,000 - $98,000

                  = $132,000

Alternative 2:

Contribution margin:

= sales - variable cost

= $456,000 - ($456,000 × 59%)

= $456,000 - $236,000

= $164,000

Net income = Contribution margin - Fixed cost

                  =  $164,000 - $98,000

                  = $66,000

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The correct option are; b. Perpendicular and d. Transversal; are the lines that intersects and are coplaner lines.

Perpendicular lines:

Transversal:

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The trigonometric expression (cos²α - cot²α)/(sin²α - tan²α) = cot⁶α

Trigonometric expressions are equations that contain the trigonometric ratios.

Given the trigonometric expression

(cos²α - cot²α)/(sin²α - tan²α)

To simplify the expression, we proceed thus

(cos²α - cot²α)/(sin²α - tan²α) = (cos²α - 1/tan²α)/(sin²α - tan²α)

= (cos²α - [cos²α/sin²α])/(sin²α - [sin²α/cos²α])

=  (cos²α - [cos²α/sin²α])/(sin²α - [sin²α/cos²α])

Factorizing out cos²α and sin²α, we have

=  (cos²α - [cos²α/sin²α])/(sin²α - [sin²α/cos²α])

=  cos²α(1 - 1/sin²α])/(sin²α(1 - 1/cos²α])

= [cos²α(sin²α - 1)/sin²α]/[sin²α(cos²α - 1)/cos²α]

= cos²α(sin²α - 1)/sin²α × cos²α/[sin²α(cos²α - 1)

= cos²α × -(1 - sin²α)/sin²α × cos²α/[sin²α × -(1 - cos²α)

= cos²α(1 - sin²α)/sin²α × cos²α/[sin²α(1 - cos²α)

= cos²α × cos²α/sin²α × cos²α/[sin²α × sin²α] (since cos²α = 1 - sin²α and sin²α = 1 - cos²α)

= cos²α × cos²α × cos²α/[sin²α × sin²α × sin²α]

= cos⁶α/sin⁶α

= (cosα/sinα)⁶

= cot⁶α

So, (cos²α - cot²α)/(sin²α - tan²α) = cot⁶α

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For n is positive integer and d is a digit such that gives the numerical value and satisfied all given conditions. We get the base value i.e n is 9

and d = 2 . So, required value n+d = 11 .

We can start by setting up an equation to convert 32d base n to base 10. To convert this to base 10, it would be 3n²+2n+d. Because it is equal to 263, we can set this equation to 263. Finally, subtract d from both sides to get

3n²+2n = 263-d.

We can also set up equations to convert 324 base n and 11d1 base 6 to base 10. The equation to covert 324 base n to base 10 is 3n²+2n+4. The equation to convert 11d1base 6 to base 10 is 6³+ 6²+6d+1.

Simplify , 6³+6²+6d+1 so it becomes 6d+253. Setting the above equations equal to each other, we have3n²+2n+4 = 6d+253. Subtracting 4 from both sides gets 3n²+2n = 6d+249.

We can then use equations

3n²+2n = 263-d

3n²+2n = 6d+249 to solve for d.

Set 263-d equal to 6d+249 and solve to find that d=2.

Plug d=2 back into the equation 3n²+2n = 263-d. Subtract 261 from both sides to get your final equation of 3n²+2n-261 = 0.

We solve using the quadratic formula to find that the solutions are 9 and -10. Because the base must be positive, n=9.

Adding 2 to 9 we get, n+ d = 9+2 = 11

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The number of terms and the degree of the polynomial are 3 and 2 respectively.

The terms of the polynomial = The parts of the polynomial

                                                = -8rt ,- s² ,- 3t

The number of terms of the polynomial  = 3    

The degree of the polynomial =  Highest degree of the polynomial

The highest degree of the polynomial = 2

So, the polynomial degree is 2

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The maximize revenue the ticket prices should be $5.5.

Consider a stadium that holds 58, 000 spectators, with ticket prices at $10, with an

Average attendance 5, 000.

Suppose the ticket prices were lowered to $8, then the average attendance rise to 15, 000.

Let R be the revenue, x be the average attendance, p(x) demand

The total revenue function R(x) is,

R (x) = p (x) x

=11 -x/5000*

=11x-x²/5000

Differentiate of R(x) with respect to x.

2x

R'(x) =11 - 2x/5000

=11-x/2500

Set R'(x ) = 0 to solve for x.

X = 27500

Therefore, the average attendance of spectators is 27,500 and, 27,500 fans will buy tickets.

Substitute x = 27,500 in p(x) =11-x/5000

p(x) = 5.5

Therefore, the maximize revenue the ticket prices should be $5.5.

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The positive square root of 5⁴ × 7² using index notation 5²×7

Index notation is a way of writing numbers and letters that have been multiplied by themself multiple times e.g 2×2×2 = 2³

Given: 5(to the power of 4) x 7 (to the power of 2). That is 5⁴ × 7²

In order to find the positive square root of 5⁴ × 7² using index notation, we have to separate the number into two identical parts. Thus:

5⁴×7² = 5²×5²×7×7 = ( 5²×7) × ( 5²×7)

Therefore, the positive square root of 5⁴×7² is 5²×7

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Approximately normal with mean of 140 seconds and standard deviation of 10 seconds.

Given,

In the question:

The times to pop a regular bag of microwave popcorn without burning it are Normally distributed with a mean time of 140 seconds and a standard deviation of 20 seconds. The times to pop a mini bag of microwave popcorn without burning it are Normally distributed with a mean time of 90 seconds and a standard deviation of 15 seconds.

Central Limit Theorem:-

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean  and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 140, standard deviation of 20, sample of 4:

By the Central Limit Theorem, the distribution is approximately normal.

Mean is the same, of 140.

n = 4 , σ = 20, thus:

s = σ / [tex]\sqrt{n}[/tex]  = 20/[tex]\sqrt{4}[/tex] = 10

Thus, the correct answer is:

Approximately normal with mean of 140 seconds and standard deviation of 10 seconds.

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Answer:

50

Step-by-step explanation:

b

To use graphing to solve a set of linear equations.

Using the same rectangular coordinate system, graph the second equation.

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(a) P( Type -I error) = P (rejecting [tex]H_0[/tex] |  when  [tex]H_0[/tex] is true )

(b)  P( Type -II error)= P(not rejecting  [tex]H_0[/tex] |  when  [tex]H_0[/tex] is false )

Given,

In the question:

We are interested in testing whether or not a coin is balanced based on the number of heads Y on 36 tosses of the coin.

To find the:

a) the value of α

b) the value of β if p = .7

Now, According to the question:

Hypothesis Testing:

The hypothesis testing evaluates two mutually exclusive statements about the population parameters to determine which statement is correct among them. There are two types of error :

1. Type -I

2. Type -II

The data is given as:

X ~ Bin(36, p)

[tex]H_0:p = 0.5\\\\H_1:p \neq 0.5[/tex]

(a) P( Type -I error) = P (rejecting [tex]H_0[/tex] |  when  [tex]H_0[/tex] is true )

                               = P(|X- 18| [tex]\geq[/tex] 4 ; p = 0.5)

                               = 1 - {P(14 < X < 22)}

                               = 1 - {P(X < 22) - P(X < 14)}

                                = 1 -  {P(X ≤ 21) - P(X ≤ 13)}

                                = 1 - {0.87851 - 0.066249}

                                = 0.18774

(b)  P( Type -II error)= P(not rejecting  [tex]H_0[/tex] |  when  [tex]H_0[/tex] is false )

                                  = P(|X- 18| [tex]>[/tex] 4 ; p = 0.7)

                                  = P(14< X < 22)

                                  =  P(X < 22) - P(X < 14)

                                  =  P(X ≤ 21) - P(X ≤ 13)

                                  = 0.091662 - 0.018322

                                  = 0.07334

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[tex]\huge \boxed{\sf 8+4\sqrt{5} }\\\\\\\displaystyle \sf Four\ lines\ are\ equal \\\\BC+CD+EF+FA = 2 \\\\Pythagorean\ theorem \\\\AB = DE= \sqrt{4^2 + 2^2} = 2\sqrt{5} \\\\ The\ sum\ of\ all\ individual\ segments \\\\ (4)2+(2 )2\sqrt{5}=8+4\sqrt{5}[/tex]

The perimeter of the polygon with the given vertices is 16.94 units.

From the graph:

Polygon ABCDEF with vertices A(0,4),B(2,0),C(2,-2),D(0,-2),E(-2,2) and F(-2,4).

Distance between AB = [tex]\sqrt{(2-0)^2+(0-4)^2}[/tex]

= [tex]\sqrt{2^2+4^2}[/tex]

= [tex]\sqrt{20}[/tex]

we know that opposite sides in polygon are equal.

AB = DE = [tex]\sqrt{20}[/tex]

Distance between BC = [tex]\sqrt{(2-2)^2+(-2-0)^2}[/tex]

= [tex]\sqrt{2^2}[/tex]

= [tex]\sqrt{4}[/tex]

= 2 units.

BC = EF = 2

Distance between CD = [tex]\sqrt{(2-0)^2+(-2+2)^2}[/tex]

= [tex]\sqrt{2^2}[/tex]

= 2

CD = FA = 2

The perimeter of polygon = [tex]\sqrt{20}[/tex] + 2+2+2+2+[tex]\sqrt{20}[/tex]

= 8+2[tex]\sqrt{20}[/tex]

= 8+4[tex]\sqrt{5}[/tex]

= 8+8.94

= 16.94 units

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Answer:

Step-by-step explanation:

answer is -25

Answer:

-25

Step-by-step explanation:

-15/1 / 3/5

(-15/1)(5/3) Do reciprocal on the second fraction  

(-5)(5) = -25 Cancel out common factors then multiply

Answer:

13.  7.5 square units

14.  24.5 square units

Step-by-step explanation:

Given vertices:

As points E and F share the same x-value and points F and G share the same y-value, the polygon is a right triangle with base GF and height FE.

As points F and G share the same y-value, the length of line segment GF is the difference between the x-values:

[tex]\begin{aligned} \implies \overline{GF}&=x_F-x_G\\&=3-(-2)\\&=3+2\\&=5\end{aligned}[/tex]

As points E and F share the same x-value, the length of line segment FE is the difference between the y-values:

[tex]\begin{aligned} \implies \overline{FE}&=y_E-x_F\\&=1-(-2)\\&=1+2\\&=3\end{aligned}[/tex]

Therefore, the area of polygon EFG is:

[tex]\begin{aligned}\textsf{Area of a triangle}&=\dfrac{1}{2} \times \sf base \times height\\\\\implies \textsf{Area of polygon $EFG$}&=\dfrac{1}{2} \times \overline{GF} \times \overline{FE}\\\\&=\dfrac{1}{2} \times 5 \times 3\\\\&=\dfrac{15}{2}\\\\&=7.5\;\; \sf units^2\end{aligned}[/tex]

Given vertices:

As points J and K share the same y-value the polygon is a triangle with base JK and height of the difference in y-values of points K and L.

As points J and K share the same y-value, the length of line segment JK is the difference between the x-values:

[tex]\begin{aligned} \implies \overline{JK}&=x_K-x_J\\&=4-(-3)\\&=4+3\\&=7\end{aligned}[/tex]

The height of the triangle is the difference between the y-values of points K and L:

[tex]\begin{aligned} \implies\sf Height&=y_K-y_L\\&=4-(-3)\\&=4+3\\&=7\end{aligned}[/tex]

Therefore, the area of polygon JKL is:

[tex]\begin{aligned}\textsf{Area of a triangle}&=\dfrac{1}{2} \times \sf base \times height\\\\\implies \textsf{Area of polygon $JKL$}&=\dfrac{1}{2} \times \overline{JK} \times \sf height \\\\&=\dfrac{1}{2} \times 7 \times7\\\\&=\dfrac{49}{2}\\\\&=24.5\;\; \sf units^2\end{aligned}[/tex]

It says how many standard deviations the sample mean is away from the population mean.

A population is a collection of associated things or events that are important to a certain subject or experiment. A statistical population can be a group of actual objects or a fictitious, potentially infinite group of things developed from experience. The sample mean is the average value throughout the entire sample. The average value across the entire population is known as the population mean. If the sample was large and random, the sample mean would be a close approximation of the population mean. The standard deviation of a population is determined by taking the square root of the variance of the data set. When making judgments, it is used to compute a confidence interval.

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Using the triangle inequality theorem, the possible values for x is: x < 11.

The triangle inequality theorem states that two sides of a triangle, when added together must be greater than the length of the third side of the triangle.

Applying the triangle inequality theorem, we have the following inequality statement:

15 + 3 > 2x - 4

18 > 2x - 4

Add both sides by 4

18 + 4 > 2x - 4 + 4

22 > 2x

Divide both sides by 2

22/2 > 2x/2

11 > x

or  x < 11.

The possible values for x is x < 11.

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This can be done using statistical tests such as the t-test or ANOVA, which can determine if there is a statistically significant difference between men and women.

Analysis of variance, or ANOVA, is the term. A statistical test is used to assess if the means of two or more groups differ significantly from one another. It is a method used to compare the means of several groups to see if they are comparable or whether there is a notable different purchase between them. ANOVA is frequently used to compare the means of several data sets, such as the means of various test scores or the means of various populations. The ANOVA test is a potent instrument that enables researchers to establish whether there is a significant difference between the means of various groups and to pinpoint which groups differ from one another.

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For the given average principal $28650 of per student loan at the rate of interest increases from 5.05% to 6.8% , the amount of interest increases for the period of 10 years is equal to $8424 (nearest dollars).

As given in the question,

Principal amount owed by student for student loan 'P' = $28,650

Rate of interest increases from 5.05% to 6.8%

Time period of repayment of student loan 'T' = 10-years

Interest for the first rate of interest 'R' = 5.05%

Interest = P ×( 1+ R/100)^T

             = 28,650 × ( 1 + 5.05/100 ) ^10

             = 28,650 × ( 1 + 0.0505 )^10

             = 28,650 × 1.63667

             = $46,890.6

Interest for the second rate of interest 'R' = 6.8%

Interest = P ×( 1+ R/100)^T

             = 28,650 × ( 1 + 6.8/100 ) ^10

             = 28,650 × ( 1 + 0.068 )^10

             = 28,650 × 1.930689

             = $55,314.2

Increase in interest amount for increase in rate of interest from 5.05% to 6.8%

=  $( 55,314.2 - 46,890.6 )

= $8423.6

=$8424 ( nearest dollar)

Therefore,  for the given average principal $28650 of per student loan at the rate of interest increases from 5.05% to 6.8% , the amount of interest increases for the period of 10 years is equal to $8424 (nearest dollars).

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The equation 2y  = 10x - 16 in standard form is  10x - 2y = 16 where A = 10, B = - 2 and C = 16

Linear equation can be represented in various form such as general form, standard form, slope intercept form and point slope form.

Therefore, linear equation in standard form can be represented as follows:

Ax + By = C

where

Therefore, let's write 2y  = 10x - 16 in standard  form.

2y  = 10x - 16

Hence,

10x - 2y = 16

Therefore,

A = 10

B = - 2

C = 16

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"Reflection and dilation" are the series of transformations that would produce a square that was comparable to the original square but not congruent.

Reflection:

Reflection is a method of transformation which it flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance as from mirror line as its mirrored point.

Dilation:

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The relevant parameter of interest for this numerical variable would be the average filling weight of all cereal packages.

What is the standard deviation in statistics?

The standard deviation in statistics is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values are close to the set's mean, whereas a high standard deviation indicates that the values are spread out over a larger range.

If a machine that is programmed to package 1.20 pounds of cereal is being tested for its accuracy. in a sample of 36 cereal boxes, the sample mean filling weight is calculated as 1.22 pounds. the population standard deviation is known to be 0.06 pounds.

The parameter of interest is the average filling weight of all cereal packages.

Hence, the relevant parameter of interest for this numerical variable would be the average filling weight of all cereal packages.

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Answer:

c = 5m + 10

Step-by-step explanation:

Each moth 5 dollars is charge and a one time fee of 10

184.04 ft high the tower with a lean of 6 degrees, the degree measure of this lean is 3.6 degrees and most likely because either the 13ft lean has not been measured to the top edge of the tower or the side of the tower isn't straight.

In the given question, the tower was 184.5 feet tall.

(a) If the article states that when work began the tower Leaned 6° or 13 feet, off the perpendicular then we have to draw a sketch and label the two measurements.

According to given statement the sketch is given below:

(b) We have to find how much high is the tower with a lean of 6 degrees.

From the graph using the Pythagorean Theorem:

H^2 = 184.5^2- 13^2

H^2 =34040.25-169

H^2 = 33871.25

Taking square root on both side

H=184.04 ft

(c) The article goes on to say that the tower now leans 16 inches less we have to draw a new sketch that shows this measurement.

The graph is given below:

(d) Now we have to find the degree measure of this lean.

We know that the tower leans 16 in less.

So 16in= 1 1/3ft = 4/3 ft = 1.33 ft

Consequently the lean after the work is: 13ft - 1.33= 11.67 ft

Then we can find the "lean" after the work as:

sin ("lean") =11.67/184.5

sin ("lean")= 0.0633

Angel of ("lean") after work = 3.6degrees.

(e) Now we have to find the height of the tower with this lean.

Height with reduced lean is found by using Pythagorean Theorem again:

H^2 = (184.5)^2 - (11.67)^2

H^2 = 34040.25 - 136.19

H^2 = 33904.06

Taking square root on both side, we get

H = 184.13

(f) Now comment on the fact that sin 4° =13/184.5 = 0.07046 while sin 6° = 0.10453. We have to check can we reconcile this seeming discrepancy.

Most likely because either the 13ft lean has not been measured to the top edge of the tower or the side of the tower isn't straight.

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The model suggests the equation 3x-4 = 6-2x and the solution is x = 2.

What is equation?

In arithmetic, associate equation could be a formula that expresses the equality of 2 expressions, by connecting them with the sign =

Main body:

According to question,

there are 3 bars for x and 2 bars for -x  so it shows

The equation becomes :

3x - 4 = 6-2x

5x = 10

x =2

Hence the solution to this equation is 2.

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The order of H can be |H| = 84, or |H| = 210 or |H| = 420.

In the mathematical field of group theory, Lagrange's theorem is a theorem that states that for any finite group G, the order (number of elements) of every subgroup of G divides the order of G.

By Lagrange's Theorem, we know |K| divides |H|, so |H| = 42k for some k (bigger than 1 since K is a proper subgroup of H).

Likewise, 42k divides 840, so k divides 840/42 = 20.

Since H is a proper subgroup of G, we know k < 20,

so either k = 2 , k = 5 or k = 10, and

Hence either |H| = 2(42) = 84, or |H| = 5(42) = 210 or |H| = 10(42) = 420.

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For

Example 1: Pair of lines are parallel.

Example 2: Pair of lines are perpendicular.

Example 3: Pair of lines are not parallel nor perpendicular.

Example 4: Pair of lines are perpendicular.

Example 5: Pair of lines are parallel.

Example 6: Pair of lines are parallel.

Example 7: Pair of lines are perpendicular.

Example 8:  Pair of lines are not parallel nor perpendicular.

What is the slope of the line in the slope-intercept form of the line?

If y = mx + c line is given then 'm' represents the slope of the line. If any pair of lines are given and if they have the same value of the slopes then we can say that the given pair of lines will be parallel in nature and if the slope of the one line is the negative inverse of the other line then we can say that the pair of lines are perpendicular to each other.

For example 1:

      y = 3x + 4 and y = 3x +7

     The slopes of both lines are equal hence, these pair of lines are parallel.

For example 2:

     y = -4x + 1 and 4y = x + 3

    Here, the slope of one line is the negative inverse of the other line hence this pair of lines are perpendicular to each other.

For example 3:

     y = 2x - 5 and y = 5x -5

   In this, the slopes are not equal so we can say that the graph of this pair of equations is not parallel nor perpendicular.

For example 4:

     y = -1/3x + 2 and y = 3x - 5

     Here, the slope of one line is the negative inverse of the other line hence this pair of lines are perpendicular to each other.

For example 5:

     y = 3/5x - 3 and 5y = 3x - 10

    The slopes of both lines are equal hence, these pair of lines are parallel.

For example 6:

     y = 4 and 4y = 6

     The slopes of both lines are equal hence, these pair of lines are parallel.

For example 7:

     y = 7x + 2 and x + 7y = 8

     Here, the slope of one line is the negative inverse of the other line hence this pair of lines are perpendicular to each other.

For example 8:

     y = 5/6x - 6 and x + 5y = 4

    In this, the slopes are not equal so we can say that the graph of this pair of equations is not parallel nor perpendicular.

Hence,

Example 1: Pair of lines are parallel.

Example 2: Pair of lines are perpendicular.

Example 3: Pair of lines are not parallel nor perpendicular.

Example 4: Pair of lines are perpendicular.

Example 5: Pair of lines are parallel.

Example 6: Pair of lines are parallel.

Example 7: Pair of lines are perpendicular.

Example 8:  Pair of lines are not parallel nor perpendicular.

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Using Equivalent equation, equation in option (b) i.e 2x+3 = 4 is equivalent to equation, 6x + 9 = 12. So, The Correct option is Option (b) .

Equivalent equation (Algebra) :

Combine any like terms on each side of the equation: x-terms with x-terms and constants with constants. Arrange the terms in the same order, usually x-term before constants. Then equivalent equation are algebaric expression which having same roots or solution .

We have given an expression as

6x + 9 = 12 --(1)

we have to find out an equation out of given options which is equivalent to equation(1) .

firstly , we evaluate the given expresion and find out solution i.e x .

6x + 9 = 12

Substracts 9 from both sides

=> 6x = 12 -9 = 3

both sides dividing by 6

=> x = 3/6 = 1/2

so, 1/2 is solution

Now, we check the options one by one

a) x + 9 = 6

solving it we get, x = 6- 9 = -3

=> not equivalent

b) 2x + 3 = 4

=> 2x = 4 - 3 = 1

=> x = 1/2

same solution as solution of given expresion

c) 3x+9 = 6

=> 3x = 6-9 = -3

=> x =-1

i.e not equivalent

d) 6x + 12 = 9

=> 6x = 9-12 = -3

=> x = -3/6 = -1/2

=> not equivalent

Hence, the required expression is 2x + 3 = 4

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