Points B, C and D lie on a straight line.
AC is perpendicular to BD.
BC = 4cm and BD = 24 cm.
Triangle ABC has area 36 cm^2
Calculate the size of angle x.

The distance that a function's graph moves above and below its midline is referred to as its amplitude. When graphing a sine function, the amplitude's value corresponds to the sine function's coefficient.

The distance that a function's graph moves above and below its midline is referred to as its amplitude. When graphing a sine function, the amplitude's value corresponds to the sine function's coefficient. The height between the center line and the peak is known as the amplitude (or to the trough). Alternatively, we might multiply the height from highest to lowest places by 2. The Phase Shift is the horizontal displacement of the function from its initial point.

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The average of first 50 numbers is 25.5 because average is computed by adding a set of numbers and then dividing by the total number of those numbers.

The average of a list of data is a mathematical expression for the central value of a set of data. The ratio of all the data points to all the units in the list is how it is mathematically defined. The average of a specific set of numerical data is also referred to as the "mean" in statistics.

The four sorts of average that we recognize are mean, mode, median, and range. Although the others are our most popular "measures of central tendency," range is actually a measure of spread or distribution.

The first 50 natural numbers are 1,2,3,...,50

The sum of first n natural numbers = n(n+1)/2

Sum of first 50 natural numbers is  50(51)/2

=25(51)/2=1275

Hence, average of first 50 natural numbers is  

1275/50

=25.5

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Hence the complete table is ,

=>  laps        Miles

       3             3.75

       7              8.75

       8              10

      13              16.25

What is miles ?

   A mile is a unit of length that is exactly equal to 5280 feet, or 1760 yards, and was standardised as exactly 1609.344 metres by an International agreement in 1959. It is the largest unit commonly used to measure the distance between distant locations.

Here the distance 2 laps = 2.5 miles. Then ,

=> 1 laps = 2.5/2 = 1.25 miles.

Now 3 laps = 3*1.25 = 3.75 miles

Here n laps = 8.75 miles .

=> n* 1.25 = 8.75

=> n = 7 laps .

Now 8 laps = 8*1.25 = 10 miles.

And n laps = 16.25

=> n = 16.25/1.25 = 13 laps. miles

Hence the complete table is ,

=>   laps        Miles

       3             3.75

       7              8.75

       8              10

      13              16.25

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If a decision maker wishes to reduce the margin of error associated with a confidence interval estimate for a population mean, she can increase the sample size.

The margin of error refers to the statistic measurement that expresses the level of random sampling error in the outcomes of a survey. If the margin of error of the result is high, the confidence level would be low that a result reflects the census of the entire population. It indicated the difference between the actual and estimated results in a random survey sample. The margin of error is generally used in non-survey contexts to show observational error in reporting measured quantities. In order to minimize the margin of error associated with a confidence interval estimate for a population mean, the researchers can increase the sample size to capture the actual trend of the population more accurately.

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Nadia made $975 last week and $50, 700 in 2011.

The amount earned last week = Percentage of comission × earnings

The amount earned last week = 13% × 7500

The amount earned last week = 13 × 75

Performing multiplication on Right Hand Side of the equation

The amount earned last week = $975

As per the known fact, 1 year has 52 weeks. So, the commission earned in 2011 = 52 × 975

Performing multiplication on Right Hand Side of the equation

The commission earned in 2011 = $50, 700

Thus, the amount earned last week is $975 and comission earned in 2011 is $50, 700.

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Answer:

$27.00

Step-by-step explanation:

8 : 20 = 10.80 : x

x = 20 * 10.80 / 8

x = 5 * 10.80 / 2

x = 5 * 5.40

x = $27.00

The equation of the line (-4,3) and (2,-4) is y = -7/6x -5/3.

What is equation of line?

The equation of a line is the algebraic representation of a line using cartesian coordinates. The general form of the equation of a straight line is written as y = mx + c. Where m is the gradient of the straight line and c  is the y y-intercept of the straight line.

Given, the points are (-4,3) and (2,-4)

m = -4-3/2+4

m = -7/6

The equation we get

y = -7/6x +b

the point (-4,3), we get

3 = -7/6(-4) +b

3 = 14/3 +b

3-14/3 = b

b = -5/3

Hence, the equation of line is y = -7/6x -5/3.

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97.5% of American women have shoe sized less than 11.19 according to standard deviation of 1.49 .

What is standard deviation?

It is a measure of how spread out numbers are. It is the square root of the Variance, and the Variance is the average of the squared differences from the Mean.

Main Body:

Here, we want to use the empirical rule to find the percentage of women with shoe sizes less than 11.19

The first thing we shall do here is to find the z-score

Mathematically, that will be calculated using the formula;

z = (x-mean)/SD

z = (11.19-8.21)/1.49

z = 2

We can see that the given value is 2 standard deviation away to the right of mean

So, we want to get the percentage that is between the mean and two standard deviations away from it using the empirical rule

So according to the empirical rule

The percentage will be

= 100-2.35-0.15

= 100-2.5 = 97.5%

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The simplified form of the expression ( -4 + 9i )² such that it takes the form a + bi is; -65 - 72i.

It follows from the task content that the simplified form of the expression is to be determined.

Hence, since the given expression is; ( -4 + 9i )², we have;

( -4 + 9i ) ( -4 + 9i )

= 16 -36i - 36i + 81i²

However, recall that the i² = -1 which follows from the fact that i = √-1.

On this note, the expression can be written as;

= 16 - 72i + 81 (-1)

= 16 - 72i - 81

= -65 - 72i.

Hence, the required simplified form of the expression is; -65 - 72i.

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You did not post enough information.

Answer:

See below

Step-by-step explanation:

By "gradient of the given line" the question is asking to find the slope of the line.  If we rearrange each equation inrto slope-intercept format of y = mx + b, we can find the slope easily, since m is the slope (b is the y-intercept).

y = 4x + 3

 The slope is 4.

y= -8x + 6

  The slope is -8

4y = 8x +3

y = 2x + (3/4)   Rearrange to y = mx + b

  The slope is 2

y+x=8

y = -1x + 8       Rearrange

    The slope is -1

y -x = 5

      y = x + 5   Rearrange

      The slope is 1

4y + 5x = 30

       y = -(5/4)x + (30/4)

       The slope is -(5/4)

Answer:

53

Step-by-step explanation:

if x is 13, you would simply do the following:

multiply 5 by 13 which is 65.

then subtract 65 by 12 which is your final answer, 53!

30 is the area of the rectangle changing at the instant when the other side is 12 cm and increasing at 3cm per minute.

Rectangle's area is equal to its length times its width.

Given,

A rectangle has a 10 cm side.

Consequently, 30 is the area of the rectangle that changes at the instant when the other side is 12 cm and growing at a rate of 3 cm per minute.

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Answer: 8%

Step-by-step explanation: Rate = Interest 484 ÷ Principle (550) x Time (11), with this formula the answer is 8%.

True, we can compare a model before using a transformation on x or y to a mode before using a transformation by using the corresponding values of the sum of squares error SSE.

      For example, to compare two models, one of which has a transformation on the outcome of the variable, that is:

First model[tex]y=x+z[/tex]

Second model:[tex]y^{1/k} =x+z[/tex]

The best logical approach might be to look at the comparative performance obviously with predicted transformed values back-transformed and then look at the models sum of squares error of these predictions. It has to be random predictions and comparisons because the error distributions are also transformed.

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The answer of the inequality is [tex]-3 < k < -\frac{1}{3}[/tex]

What does algebraic inequality mean?

An inequality in maths shows the relationship between the two values in an uneven algebraic expression. A sign of inequality can be employed to indicate that one of the two variables is less than, greater than or equal to, less than, or equal to another value.

Given That:
-16<6k+2<0
Now to solve this equation we will subtract 2 from all the side
-16-2<6k<-2
now we will divide by 6 on all the side
-18/6<k<-2/6
[tex]-3 < k < -\frac{1}{3}[/tex]
Hence this the answer to the question

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Answer:

f(5) = 3(5+2) - 8

f(5) = 15+6 -8

f(5) = 21 - 8

f(5) = 13

The measure of angle B is 40 degrees.

In this question, we have been given angle A and angle B are supplementary angles.

m∠A=(4x−16)°

and m∠B=(x+1)°

since angle A and angle B are supplementary angles,

angle A + angle B = 180°

So we get an equation,

(4x − 16)° + (x + 1)° = 180°

5x - 16 + 1 = 180

5x = 180 + 15

5x = 195

x = 39

So, x + 1 = 39 + 1

              = 40°

Therefore, the measure of angle B is 40 degrees.

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The correct compound inequality to the amount of money Wren can spend with a monthly budget for housing between 25% and 35% will be:

224.0< h< 313.60

Given that:

wren own an average weekly net pay $ 896.00

and, Wren can spend with a monthly budget for housing between 25% and 35%.

Now, Spend money for housing by 25% = 25% of $896.00

= 25÷100 × 896

= 0.25 ×896

= $ 224.00

Again, spend money for housing by

35%=  35% of 896                                                            

=35÷100 × 896

= 0.35 × 896

= $ 313.60

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Answer:

72.6%

Step-by-step explanation:

Percentages are simple

(Number given / Total given ) × 100 = ?%

(363 / 550 ) × 100 =

0.726 × 100 = 72.6

This should be our final answer of 72.6%

Hope this helped and have a good day

Using the z table, the probability that a standard normal random variable will be between 0.3 and 3.2 is 0.3814.

In the given question,

We have to find that the probability that a standard normal random variable will be between 0.3 and 3.2 .

We firstly learn about a standard normal random variable which is expressed with a mean and standard deviation.

Since we have to find the probability that a standard normal random variable will be between 0.3 and 3.2 .

So The probability should be

P(0.3<z<3.2)=P(z<3.2)−P(z<0.3)

From the standard value of z

P(0.3<z<3.2)=0.9993−0.6179

Simplifying

P(0.3<z<3.2)=0.3814

Hence, the probability that a standard normal random variable will be between 0.3 and 3.2 is 0.3814.

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When x = -0.5, the value of y is -0.33. When y varies directly with respect to x, the equation y = kx is used. where k is the constant of proportionality

Therefore,

When X equals 3, Y equals 2.

We solve for k by plugging in 3 for x and 2 for y.

y = kx \s 2 = k(3) (3)

Subtract 3 from both sides.

2/3 = k

Now we plug in 2/3 for k

y = 2/3 x

Given x = -0.5  simplifying we get,

y = 2/3 (-0.5)

y = -0.33

Hence, the value of y is -0.33 when x = -0.5

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The amount of pure acid present in 780 milliliters of a 18% solution is 140.4 milliliter .

In the question ,

it is given that

the amount of solution = 780 milliliter

we need to find the amount of pure acid in the solution .

amount of pure acid in the solution can be calculated using the formula ,

amount of pure acid = 18% of 780 milliliter

the term of represents, multiplication ,

So , the amount of pure acid = 18% × 780

= 0.18 × 780

= 140.4 milliliter

Therefore , The amount of pure acid present in 780 milliliters of a 18% solution is 140.4 milliliter .

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Answer:

The equation of the circle is (x-2)^2+(y-1)^2=13

Step-by-step explanation:

The solution to the compound inequality is x > -3. The correct option is the third option x > -3

From the question, we are to solve the given compound inequality

2x - 2 > -8 or -4x ≤ -36

Solving the first inequality

2x - 2 > -8

Add 2 to both sides of the inequality

2x -2 + 2 > -8 + 2

2x > -6

Divide both sides by 2

2x/2 > -6/2

x > -3

Solving the second inequality

-4x ≤ -36

Divide both sides of the inequality

-4x/-4 ≤ -36/-4

x ≥ 9

From the two solutions, we can conclude that x > -3

Hence, the solution is x > -3

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Rearranging [1/3, 0.3, 33%, 8/25, 33.6%] in the ascending order of magnitude, we get, [33.6%, (1/3), 33%, (8/25), 0.3].

As per the question statement, we are provided with a set of values       [1/3, 0.3, 33%, 8/25, 33.6%],

And we are required to rearrange the above mentioned set in the ascending order of magnitude.

To answer this question, we will have to convert all the values into fractions with a common denominator, and then arrange the fractions in an ascending order of magnitude of their numerators to obtain our desired answer, that is,

[(1/3) = 0.33333333...]

[(0.3) = (3/10) = (30/100)],

[(33%) = (33/100) = 0.330],

[(8/25) = (32/100) = 0.320]

And, [33.6% = (33.6/100) = 0.336]

Since (0.336 > 0.333 > 0.330 > 0.320 > 0.300),

Therefore, rearranging [1/3, 0.3, 33%, 8/25, 33.6%] in the ascending order of magnitude, we get, [33.6%, (1/3), 33%, (8/25), 0.3]

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1.2113 ft/s is the speed at which the radius of the sphere is changing when the radius is 6 feet .

Mensuration is a division of mathematics that studies geometric figure calculation and its parameters such as area, length, volume, lateral surface area, surface area, etc. It outlines the principles of calculation and discusses all the essential equations and properties of various geometric shapes and figures.

Mensuration is a subject of geometry. Mensuration deals with the size, region, and density of different forms both 2D and 3D. Now, in the introduction to Mensuration, let’s think about 2D and 3D forms and the distinction between them.

The rate of change of volume will be the product of the rate of change of radius and the area of the sphere. The area of the sphere is ...

 A = 4πr² = 4π(6 ft)² = 144π ft²

Then the relationship above is ...

dV/dt = A·dr/dt

548 ft³/s = (144π ft²)·dr/dt

dr/dt = (548 ft³/s)/(144π ft²) = 137/(36π) ft/s ≈ 1.2113 ft/s

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The amount of money (principal)  that Hsu-Mel would need to invest in an account now with 7.4% APR, compounded daily, in order to reach her goal in 3 years is $7206.24.

Mathematically, compound interest can be calculated by using this formula:

A(t) = P(1 + r/n)^{nt}

Where:

Note: The annual percentage interest (APR) rate would be divided by 365 since it is compounded daily.

Substituting the given parameters into the formula, we have;

9,000 = P(1 + 0.074/265)^{365 × 3}

9,000 = P(1.00023)^{1095}

9,000 = P(1.2489)

Principal, P = 9000/1.2489

Principal, P = $7206.24.

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Answer:

56

Step-by-step explanation: