consider the following table. age group frequency 18-29 9831 30-39 7845 40-49 6869 50-59 6323 60-69 5410 70 and over 5279 if you created the probability distribution for these data, what would be the probability of 30-39?

The area of a triangle with base of 4cm and height of 9cm will be 18cm².

The area of a triangle can be found using the following formula:

Area = (base * height) / 2

where base is the length of any one side of the triangle and height is the perpendicular distance from that side to the opposite vertex.

You can use this formula to find the area of a triangle given its base and height or given its three sides using Heron's formula.

The area of a triangle with base of 4cm and height of 9cm will be:

= 1/2 × base × height

= 1/2 × 4 × 9

= 18cm²

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Complete question

Find the area of a triangle with a base of 4cm and height of 9cm.

Th length of the rectangle, in decimal form, would be = 14.05ft

A perimeter of defined as the total area of all the edges that surrounds an object such as a rectangle.

The perimeter of a rectangle = P = 2(length+width)

The perimeter = 27.2ft

The width = 7.9 ft

Therefore the length = ?

That is,

27.2 = 2( L + 7.9)

27.2 = 2L + 55.3

2L = 55.3-27.2

2L = 28.1

L = 28.1/2

L = 14.05ft

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Answer:

0, 1, 2, and 3

Step-by-step explanation:

make a number line -5 to 5, mark the spots -1 and 4. the numbers in between are your answer!

The hourly rate that they are paid is $24 per hour

An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.

Let us assume that all of them are paid the same amount of money per hour.

Let x represent the amount of money each is paid per hour.

Joshua worked five hours, Katleho worked for three hours and Pevashnee worked for four hours if they paid R288. Hence:

5x + 3x + 4x = 288

12x = 288

x = 24

Their hourly rate is $24 per hour

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Answer:

Option B)

Step-by-step explanation:

The inequalities are y ≥ (2/3)x + 1 and y < (-1/4)x + 2 and (−6, −3) satisfied the inequality.

What is inequality?

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

As per the given phrase,

y is greater than or equal to two-thirds times x plus 1 ⇒ y ≥ (2/3)x + 1

y is less than negative one-fourth times x plus 2 ⇒ y < (-1/4)x + 2

Substitute, point (−6, −3)

-3 ≥ (2/3)(-6) + 1

-3 ≥ -3  

Substitute in second inequality,

-3 < (-1/4)(-6) + 2

-3 < 7/2

Hence "The inequalities are y ≥ (2/3)x + 1 and y < (-1/4)x + 2 and (−6, −3) satisfied the inequality".

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The values 8, 15 and 17 is a Pythagorean triple and therefore a right angle triangle.

A Pythagorean triple is a set of three positive integers, a, b, and c, such that a^2 + b^2 = c^2, which represents the sides of a right-angled triangle, where c is the hypotenuse.

In this problem, we can we can check if the values are for a right angle triangle.

Assuming this is a right angle triangle which obeys Pythagoras theorem, the longest side will be the hypothenuse.

c² = a² + b²

17² = 15² + 8²

289 = 225 + 64

289 = 289

From the calculation above, the values of is a Pythagorean triple.

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Answer:

x=2

Step-by-step explanation:

-3x-2(5x-7)=-12

-3x-10x+14=-12

-13x=-26

x=2

Answer:

see below

Step-by-step explanation:

when you divide a fraction, it's better to use multiplication of its reversed fraction = flip the y fraction upside down & multiply the first one

then you'll cancel the y & x and result in

y/x

Possible economic gain is not a disadvantage of buying.

Financial risk refers to the likelihood of losing money on a business or investment decision. Risks associated with finances can result in capital losses for individuals and businesses. There are several financial risks, such as credit, liquidity, and operational risks.

Given here: Disadvantages of buying

The different types of risks are categorized in several different ways. Risks are classified into some categories, including market risk, credit risk, operational risk, strategic risk, liquidity risk, and event risk.

Clearly Financial risk, limited mobility, Higher living costs are all disadvantages of buying but possible economic gains is not a disadvantage.

Thus Possible economic gain is the odd one out of the options.

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Answer:

47500

Step-by-step explanation:

5 x 19=95

95 x 25=2375

2375 x 4=9500

9500 x 5= 47500

hope this is correct :)

There would be 40,320 different types of burgers.

If each burger must have all of the ingredients listed (cheese, lettuce, tomato, pickles, onions, mayo, catsup, and mustard), and the order of the ingredients is important, then the number of different types of burgers would be 8! (8 factorial), which is the number of permutations of 8 items.

8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40320

So there would be 40,320 different types of burgers that can be made with all of the ingredients and the order of placement is important.

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The description of the translation is given as follows:

To get the function g, shift f up by 4 units and to the left by 2 units.

A translation happens when either a figure or a function are moved horizontally or vertically.

The four translation rules for functions are given as follows:

Hence the changes to the function in this problem are described as follows:

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Height from window = 450ft  the tomato passes your window after 2 seconds and hits the ground 5 seconds after it was thrown. neglect air resistance

Time taken to get from window to ground = 2 secs

V0, initial speed of tomato from drop point = 0 ft/s

Acceleration due to gravity = 32.2 ft/s

When the tomato gets to the observer at the window, its initial speed is no longer 0ft/s but an unknown value, u.

We can apply one of the equations of linear motion to then find this initial velocity at the window using the other parameters given i.e.  

s = ut + [tex]\frac{1}{2}[/tex] [tex]at^{2}[/tex]

= 450ft

t = 2 secs

a = g = 32.2ft/sec

=> 450 = (u*2) + (1/2 * 32.2 * 2^2)

450 = 2u + 64.4

2u = 450 – 64.4

2u = 385.6

=> u = 192.8ft/s

Now that we know this initial velocity, we can use another equation of linear motion to find the height distance between the drop point and the window for the resistance

[tex]v^{2}[/tex] - [tex]u^{2}[/tex] = 2gs

where s = distance between drop point and window

v = 192.8ft/s

u = 0ft/s;

=> [tex]192.8^{2}[/tex] - 0^2 = 2*32.2*s

37171.84 = 64.4s

=> s = 37171.84/64.4

s = 577.20ft

Hence, distance from drop point to the ground, H, will be the addition of s and the height from the window to the ground:

=>H = 577.20 + 450

H = 1027.2ft

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The value of n is 8.

Binomial theorem is the method of expanding an expression consisting of two terms raised to any power.

Using the expansion of Binomial theorem, we can write,

(2 + 3x)ⁿ = ⁿC₀ (2)ⁿ (3x)⁰ + ⁿC₁ (2)ⁿ⁻¹ (3x)¹ + ⁿC₂ (2)ⁿ⁻² (3x)² + ⁿC₃ (2)ⁿ⁻³ (3x)³ + ⁿC₄ (2)ⁿ⁻⁴ (3x)⁴ + .............

Coefficient of x³ is  ⁿC₃ (2)ⁿ⁻³ (3)³ and the coefficient of x⁴ is ⁿC₄ (2)ⁿ⁻⁴ (3)⁴.

Ratio of these coefficients is 8 : 15.

[ⁿC₃ (2)ⁿ⁻³ (3)³] / [ⁿC₄ (2)ⁿ⁻⁴ (3)⁴] = 8 / 15

Simplifying,

(4 × 2) / [(n - 3) 3] = 8/15

8 / 3n - 9 = 8 /15

Equating, we have,

3n - 9 = 15

3n = 24

n = 8

Hence the value of n is 8.

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Answer:

x=16/squared

Step-by-step explanation:

divide each term in 3xsquared = 48 by 3squared and simplify.

Answer:

If squaring a number means multiplying it by itself, according to this rule, you multiply 3 by "x" and then multiply "x" by itself to get 48. In this scenario, you divide 3 by blank squared to get blank. In this case, you set up this problem with division, so we are dividing 3 times blank squared by 3. Whatever the blank value is, we know this equation equals 48, so you must create a mirrored equation of 48 divided by 3. Now that you've divided 48 by 3, that is 16, right? So 16 will be the equivalent of blank squared, or "x" squared. For blank squared, since we are dealing with algebra, the next step is to use square roots using what we know. We know that 16 is composed of 4 squared, right? So turn 4 squared into a radical of √4². This radical is equal to 4, because "radical" = "number" as long as that number is more than or equal to 0. So, in conclusion, x is 4.

Hope this helps!

Lainey cannot descend for more than 3 minutes.

Using the terms greater than, larger than or equal to, less than, or less than or equal to as a declaration of the order connection between two integers or algebraic expressions is known as inequality. Economic inequality comes in many forms, most notably wealth inequality measured by the distribution of wealth and income inequality measured by the distribution of income (the amount of money people are paid) (the amount of wealth people own). There are significant forms of economic inequality amongst various groups of people in addition to economic disparity between nations or states.

Given:

We know that she first descends 22 feet, and then she descends at a rate of 22 feet per minute. Basically, we have 22 feet which have to me summed with 22x, which expresses the ratio per minute, where x is minutes, and these terms cannot be more than 93 feet, so there are equal or less than 93 feet.

The expression would be

22 + 22x ≤ 93

If we solve this, we have,

22 + 22x ≤ 93

22x ≤ 93 - 22

22x ≤ 71

x ≤ [tex]\frac{71}{22}[/tex]

Therefore, She cannot descent for more than 3 minutes.

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The drawings that best describe the way the stars appear to move in the Southern Hemisphere on the horizon is:

When in the Southern Hemisphere, the drawings would appear to move upwards when moving North. The stars would also appear to move down when moving to the South as shown in A.

The East would show drawings moving towards the right as shown in E and the West would show stars appearing to move to the left which is shown with Drawing F.

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To construct frequency and relative frequency distributions, count number of students for each major and divide by total number of students (30) to find the relative frequency.

Use the frequency and relative frequency data to create a bar chart and a pie chart to visualize the data. To construct a frequency distribution and bar chart for the thirty students in the School of Business, we need to count the number of occurrences of each major and create a table. For example, if 9 students chose Management as their major, 9 would be the frequency for Management. We can then plot the frequencies on a bar chart, with each major on the x-axis and its frequency on the y-axis. The bar chart visually represents the distribution of the data.

A relative frequency distribution is a frequency distribution expressed as a proportion or percentage of the total number of observations. To create a relative frequency distribution, we divide each frequency by the total number of students (30 in this case) and multiply by 100%. The relative frequencies can then be used to construct a pie chart, where each major is represented as a wedge or slice of the pie, proportional to its relative frequency. The pie chart visually represents the distribution of the data as a whole.

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The sampling distribution  of the sample proportion is approximately normal when the sample size (n) is large and the population proportion (p) is close to 0.5.

This can be mathematically expressed as follows:

[tex]n*p > 10 and n*(1-p) > 10[/tex]

To illustrate, let's say we are sampling from a population with a proportion of 0.3. For the sampling distribution to be approximately normal, the sample size (n) must be larger than 33.3 (n > 33.3). This is because [tex]33.3*0.3 = 10 and 33.3*0.7 = 23.3[/tex].

In other words, the sample size (n) must be large enough so that the product of the sample size (n) and the population proportion (p) is greater than 10 and the product of the sample size (n) and the population proportion (1-p) is also greater than 10. This ensures that the sampling distribution of the sample proportion is approximately normal.

To sum up, the sampling distribution of the sample proportion is approximately normal when the sample size (n) is large and the population proportion (p) is close to 0.5.

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a) The error first appears between Steps 2 and 4.

b) The value of the expression is given by: 5^(-4) = 1/625.

The power of a power rule is used when a single base is elevated to multiple exponents.

Then the simplified expression is obtained keeping the base, while the exponents are multiplied.

The numerator is simplified as follows:

25^(-4) = 5²^(-4) = 5^(2 x -4) = 5^(-8).

The denominator is given as follows:

5²^(-2) = 5^(-4).

When two terms have the same base and different exponents and are divided, we keep the base and subtract the exponents, hence:

5^(-8)/[5^(-4)] = 5^(-8 - (-4)) = 5^(-4) = 1/(5^4) = 1/625.

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The inverse matrix is (b) [tex]\left[\begin{array}{ccc}-19&9&-7\\15&-7&6\\-2&1&-1\end{array}\right][/tex]

From the question, we have the following parameters that can be used in our computation:

x + 2y + 5z = 14

3x + 5y + 9z = -1

x + y - 2z = 6

When represented as a matrix, we have

[tex]\left[\begin{array}{ccc}1&2&5\\3&5&9\\1&1&-2\end{array}\right][/tex]

The determinant is calculated as

D = 1 * (5 * -2 - 9 * 1) - 2 * (3 * -2 - 9 * 1) + 5 * (3 * 1 - 5 * 1)

Evaluate

D = 1

This means that the matrix is invertible

Next, we calculate the cofactor elements

5 * -2 - 9 * 1 = -19

3 * -2 - 9 * 1 = -15

3 * 1 - 5 * 1 = -2

2 * -2 - 5 * 1 = -9

1 * -2 - 5 * 1 = -7

1 * 1 - 2 * 1 = -1

2 * 9 - 5 * 5 = -7

1 * 9 - 5 * 3 = -6

1 * 5 - 2 * 3 = -1

So, we have

   [tex]\left[\begin{array}{ccc}-19&-15&-2\\-9&-7&-1\\-7&-6&-1\end{array}\right][/tex]

Next, create the adjoint or the adjugated matrix

[tex]A = \left[\begin{array}{ccc}-19&15&-2\\9&-7&1\\-7&6&-1\end{array}\right][/tex]

Transpose the adjoint

[tex]A^T = \left[\begin{array}{ccc}-19&9&-7\\15&-7&6\\-2&1&-1\end{array}\right][/tex]

Divide by the determinant

[tex]A^T = \left[\begin{array}{ccc}-19&9&-7\\15&-7&6\\-2&1&-1\end{array}\right][/tex]

Hence, the inverse is (b) [tex]\left[\begin{array}{ccc}-19&9&-7\\15&-7&6\\-2&1&-1\end{array}\right][/tex]

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Answer:

x ≥ 1

Step-by-step explanation:

The filled in circle means the inequality includes 1

Hope this helped!

The answer is [tex]L = 624 cm^2; S = 944 cm^2[/tex]  where L is the lateral area and S is the surface area of a right rectangular prism.

The lateral area of a right rectangular prism is given by the formula:

[tex]L = 2(lw + bh)[/tex]

where l and b are the length and width of the base, and h is the height of the prism.

The surface area is given by the formula:

[tex]S = 2(lb + bh + lh)[/tex]

For the given prism with a base of 12 cm by 10 cm and a height of 16 cm, the lateral area is:

[tex]L = 2((12 cm)(10 cm) + (12 cm)(16 cm)) \\= 2(120 cm^2 + 192 cm^2)\\= 2(312 cm^2)\\= 624 cm^2.[/tex]

The surface area is:

[tex]S = 2((12 cm)(10 cm) + (10 cm)(16 cm) + (12 cm)(16 cm))\\ = 2(120 cm^2 + 160 cm^2 + 192 cm^2) \\ = 2(472 cm^2) \\ = 944 cm^2.[/tex]

So the answer is [tex]L = 624 cm^2[/tex] ; [tex]S = 944 cm^2[/tex] .

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Answer:

The correct answer is L=704 cm^2 ; S-944 cm^2

Step-by-step explanation:

p=2l+2w

P=2(12)+2(10)=24+20=44cm

L=(44)(16)=704 cm^2

So the lateral area is 704 cm^2

B=(12)(10)=120cm^2

S=704+2(120)=704+240=944cm^2

So the surface area is 944 cm^2

If x must be a number. The same outcome is obtained by increasing x by 20% as well as by decreasing that product of four with x by 5. x has the value of 25/14.

Let's look up an expression for raising x by 20%. This might be shown as x + 20%. x = x + 0.2x = 1.2x = 6x/5.

The two expressions must now be set to be equal to each other.

6x/5 = 4x - 5

Add 6x/5 to both sides and subtract. To make 4x and 6x/5 have a similar denominator, we can rephrase 4x as 20x/5.

0 = 20x/5 - 6x/5 - 5 = 14x/5 - 5

0 = 14x/5 - 5

We can now increase both sides by five.

5 = 14x/5

Now that we have the reciprocal of 14/5, 5/14, we may multiply either sides by this number.

5(5/14) = (14x/5)(5/14) = x

25/14 = x

Thus, the solution is 25/14.

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Answer: $480

Step-by-step explanation:

Calculators=$80 per 12 calculators

Calculators=$25 for 3 Calculators

80 x 6= 480

Solve linear system: dx/dt = -2x, dy/dt = -2y. Analyze stability using phase portrait & direction field, identify type of critical point.

The given linear system is:

dx/dt = -2x

dy/dt = -2y

To find the stability or instability of the critical point (0, 0), we need to analyze the behavior of the solutions near that point. To do so, we can linearize the system around (0,0), which means we approximate the system with its tangent line at (0,0). The linearized system is given by:

dx/dt = -2x

dy/dt = -2y

The eigen values of the linearized system are -2 and -2. Since both eigenvalues are negative, the critical point (0,0) is a stable node, which means that any solution that starts close to (0,0) will converge to (0,0) as t approaches infinity. The phase portrait of the system is a set of arrows pointing towards the origin, indicating that all solutions converge to (0,0) as time goes on.

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A Type I error that could result from the test is "The test provides convincing evidence that the mean is less than 12 ounces, but the actual mean is at least 12 ounces."

A Type I error occurs when the null hypothesis is rejected when it is actually true. In this case, the null hypothesis is that the mean is at least 12 ounces, and the alternative hypothesis is that the mean is less than 12 ounces. If the test provides convincing evidence that the mean is less than 12 ounces when the actual mean is at least 12 ounces, this is a Type I error. The answer is: The test provides convincing evidence that the mean is less than 12 ounces, but the actual mean is at least 12 ounces. If the test provides convincing evidence that the mean is less than 12 ounces when the actual mean is at least 12 ounces, this is a Type I error.

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it is true in practice, we frequently use a continuous distribution to approximate a discrete one when the number of values the variable can assume is countable but large.

The continuous category of random variables refers to those whose spaces are unions of intervals or intervals rather than a countable number of points. When the sample size is too big to treat each individual event discretely or when a variable does not occur in discrete intervals, continuous distributions are employed as probability models (please see Discrete Distributions for more details on discrete distributions). The main distinction between continuous and discrete distributions is that, while discrete distributions deal with smaller sample populations and cannot be treated as if their random variable values are on a continuum (from negative infinity to positive infinity), continuous distributions deal with a sample size so large that its random variable values are treated on a continuum (from negative infinity to positive infinity).

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The formula for V0 from the expression given will be V0 = V1 - at

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc. In this case, the formula for V0 will be found thus:

a = V1 - V0 / t

Cross Multiply

at = V1 - V0

Subtract V1 from both sides

-V0 = at - V1

V0 = V1 - at

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The area of the enclosed region in the diagram is 20 square units.

The area of the enclosed region in the diagram can be calculated using the formula A = lw, where A is the area, l is the length, and w is the width. The length is 5 units and the width is 4 units, so A = lw = 5 X 4 = 20 square units.

To calculate the area, we first need to find the length and width of the enclosed region. The length can be found by measuring the longest side, which is the bottom side. This side has a length of 5 units. The width can be found by measuring the shorter side, which is the left side. This side has a width of 4 units.

Once we have the length and width, we can use the formula A = lw to calculate the area. In this case, A = 5 X 4 = 20 square units. Therefore, the area of the enclosed region in the diagram is 20 square units.

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