#12 please help me gang gang

Answer:

Yes, Chen is correct.

Step-by-step explanation:

Chen has 1/4 chance of getting a 4, whereas Megan has 1/5 chance of getting a 4.

1/4 = 0.25

1/5 = 0.20

Therefore, Chen is correct.

If \($\alpha$\)and \($\beta$\) are the roots of \($3 x^2-5 x+2=0$\), then the value of \($\frac{\alpha}{\beta}+\frac{\beta}{\alpha}$\) is 13/6

\($\alpha, \beta$\) are roots of\($3 x^2-5 x+2=0$\)

\(& \alpha+\beta=-\frac{b}{a}=\frac{5}{3} a=3, b=-5, c=2 \\\)

\(& \alpha \beta=\frac{c}{a}=\frac{2}{3} \\\)

\(& \frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha \beta} \\\)

\(& =\frac{(\alpha+\beta)^2-2 \alpha \beta}{\alpha \beta} \\\)

Simplifying the question

\(& =\frac{\left(\frac{5}{3}\right)^2-2\left(\frac{2}{3}\right)}{\frac{2}{3}} \\\)

\(& =\frac{\frac{25}{9}-\frac{4}{3}}{\frac{2}{3}}=\frac{25-12}{9} \\\)

We get,

\(& =\frac{13}{9} \times \frac{3}{2}=\frac{13}{6}\)

The complete question is,

If \($\alpha$\)and \($\beta$\) are the roots of \($3 x^2-5 x+2=0$\), then find the value of \($\frac{\alpha}{\beta}+\frac{\beta}{\alpha}$\)

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The calculated value of the commission percentage is 4%

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

Hourly rate = $15

Commission = x%

So, the function of the earnings is

f(x) = x% * 1400 + Hourly rate * Number of hours

This gives

When the total earning is 176, we have

x% * 1400 + 15 * 8 = 176

This gives

x% * 1400 + 120 = 176

So, we have

x% * 1400= 56

Divide

x = 4

Hence, the commission percentage is 4%

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We can see here that proving ∠A ≅ ∠E, we have that:

Congruency is a mathematical concept that refers to the property of having the same shape and size. When two objects are congruent, they have exactly the same dimensions and are said to be identical in shape and size. The concept of congruency is used in various areas of mathematics, including geometry, algebra, and trigonometry.

In geometry, congruency is used to compare two figures. For example, two triangles are congruent if they have the same shape and size, which means that their corresponding sides and angles are equal. In algebra, congruency is used to compare two expressions. For example, two algebraic expressions are congruent if they have the same value for all possible values of the variables.

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The proof that shows that ∠A ≅ ∠E is explained below using the ASA congruence theorem and CPCTC.

The ASA congruence theorem states that two triangles can be said to be congruent to each other if they have two pairs of congruent angles and a pair of congruent sides.

Thus, the two-column proof proves that angles A and E are congruent as explained below:

Statement                                             Reason                                      

1. BD ⊥ AB, BD ⊥ DE, BC ≅ DC          1. Given

2. ∠CBA and ∠CDE are right angles 2. Def. of right angles

3. ∠CBA ≅ ∠CDE                                3. All right angles are congruent

4. ∠DCE ≅ ∠BCE                                3. Vertical angles theorem

5. ΔCBA ≅ ΔCDE                                4. ASA congruence theorem

6. ∠A ≅ ∠E                                          5. CPCTC

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7 gallons are needed to cover 1241 square feet.

In this question,

Each gallon of porch and deck paint covers 200 square feet.

To find out how many gallons of paint needs, we have to divide the total area of deck by the amount of deck that one gallon covers.

We use the unitary method to find out how many gallons of paint needs.

Using unitary method,

1241 / 200 = 6.205

However, we cannot buy a fraction of a gallon of paint.

So, the amount of gallons of paint needed is approximately equal to 7 gallons.

Therefore, 7 gallons are needed to cover 1241 square feet.

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Answer:

Yes

Step-by-step explanation:

This is a function because each x value is given one y value. More simply, no x value was repeated.

The value of the test statistic in a reputable poll of 1145 adults is -6.25

The claim made in this context is that fewer than 92% of adults have cell phone.

Given in a reputable poll of 1145 adults, 87% said that they have a cell phone.

To find the value of the test statistic we will use the following formula;

Z = (p - P) / sqrt[P * (1 - P) / n]

Where P  = 0.92 (Given percentage value of the claim), n = 1145, p = 0.87 (Given percentage value of adults having a cell phone).

On substituting the given values we get,

Z = (0.87 - 0.92) / sqrt[0.92 * (1 - 0.92) / 1145]

Z = -0.05 / sqrt[0.92 * 0.08 / 1145]

Z = -0.05 / 0.008

Z = -6.25

The value of the test statistic is -6.25

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Answer:

x = 41°

Step-by-step explanation:

Complementary angles are angles that add up to 90°

y = x + 8

x + y = 90°

Plug in x+8° for y:

-Chetan K

SOLUTION

Consider the drawing below

Using pythagorean theorem, it follows

Hence using trigonometrical ratio it follows:

This is simplified to give:

Also

Finally it follows:

Answer:

119 is the value of x when y = 7

Step-by-step explanation:

Since y varies inversely with x, we can use the following equation to model this:

y = k/x, where

Step 1:  Find k by plugging in values:

Before we can find the value of x when y = k, we'll first need to find k, the constant of proportionality.  We can find k by plugging in 49 for y and 17 for x:

Plugging in the values in the inverse variation equation gives us:

49 = k/17

Solve for k by multiplying both sides by 17:

(49 = k / 17) * 17

833 = k

Thus, the constant of proportionality (k) is 833.

Step 2:  Find x when y = k by plugging in 7 for y and 833 for k in the inverse variation equation:

Plugging in the values in the inverse variation gives us:

7 = 833/x

Multiplying both sides by x gives us:

(7 = 833/x) * x

7x = 833

Dividing both sides by 7 gives us:

(7x = 833) / 7

x = 119

Thus, 119 is the value of x when y = 7.

A

1) In this picture, we can see clearly a triangle with an adjacent leg to an angle of 50º and an opposite leg (that tree).

2) So the trigonometric ratio to be used is the one that relates both legs:

3) Hence, the answer is A

the width of the path is approximately 6.67 meters or 6.7 meters to one decimal place.

Let the width of the uniform path be w meters.

therefore, the width of the pool will be 20 - 2w meters and the length of the pool will be 28 - 2w meters.

The area of the pool will be:

L * W = (20 - 2w) * (28 - 2w) = 560 - 96w + 4w²

The combined area of the pool and the path will be:

L * W = (20 + 2w) * (28 + 2w) = 784 + 96w + 4w²

The difference between the two areas will be:

Combined Area - Pool Area = 784 + 96w + 4w² - (560 - 96w + 4w²) = 224 + 192w = 16(14 + 12w)

We know that the combined area is 1280 square meters.

Therefore:1280 = 16(14 + 12w)80 = 14 + 12w6.67 = w

Thus, the width of the path is approximately 6.67 meters or 6.7 meters to one decimal place.

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Answer:

24 boys & 20 girls

Step-by-step explanation:

Last year:

Number of boys = x

Total number = 45

Number of girls = 45 - x

An increase of 20% is the same as multiplying by 1.2

A decrease of 10% is the same as multiplying by 0.8

This year:

New number of boys: 1.2x

New number of girls: 0.8(45 - x)

New total number = 45 - 1 = 44

1.2x + 0.8(45 - x) = 44

1.2x + 36 - 0.8x = 44

0.4x + 36 = 44

0.4x = 8

x = 20

Last year there were 20 boys and 25 girls.

This year there are 20 * 1.2 = 24 boys

and 44 - 24 = 20 girls

Answer: 24 boys & 20 girls

The mean median mode of the data 9,10,9,9,11,9,10,9,9,10 is

Mean =9.5

Median = 11 or 9

Mode is 9

Given that,

The data is 9,10,9,9,11,9,10,9,9,10

The data's mean, median, and mode must be determined.

We know that,

The arithmetic mean of the provided data is another name for mean. If the data are grouped and sorted in ascending order, the median is the value that falls in the middle of the set of grouped data. The value that dominates the data is known as the mode. The Mean, Median, and Mode formulas are described independently for the group of data in the sections that follow.

The data is 9,10,9,9,11,9,10,9,9,10

Mean = 9+10+9+9+11+9+10+9+9+10/10 =95/10=9.5

Median = 11 or 9

Mode is 9

Therefore, The mean median mode of the data 9,10,9,9,11,9,10,9,9,10 is

Mean =9.5

Median = 11 or 9

Mode is 9

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The value of sin(u+v) given tan u = 15/8 is -9/221

Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the their angles.

A right-angled triangle has 3 sides, hypotenuse, opposite and adjacent. The following should be noted:

Sin = Opposite / Hypothenuse

Tan = Opposite / Adjacent

Cos = Adjacent / Hypothenuse

When tan u = 15/8

Opposite = 15

Adjacent = 8

Hypothenuse will be:

= ✓(15² + 8²)

= ✓(225 + 64)

= ✓289

= 17

Therefore sin u = 15/17

When cos v = -5/13, it should be noted that sin v will be -12/13.

Therefore, sin(u + v) will be:

= 15/17 + (-12/13)

= 15/17 - 12/13

= 195/221 - 204/221

= -9/221

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Answer:i don't know I just need the points

Step-by-step explanation:

Answer:

y = x + 4

Step-by-step explanation:

We want to form an equation to represent the table. I will form an equation in standard y-intercept form. I can either calculate the slope mathematically, or look at the table and see that as x increases by 1, so does the respective value of y.

y = mx + b

m is slope and b is the y-intecept.

\(m = \frac{-2 - (-3)}{2-1} \\m = \frac{-2 + 3}{2 - 1}\\m = \frac{1}{1} \\m = 1\)

So now we have the slope of our equation.

y = x + b

We can find the y-intecept two ways, use the table, or plug in a point from the table in calculate b from our equation. Should we choose to use the table, remember that y-intercept means that at that point x = 0. Following the pattern from the table, we can infer that when x = 0, y = -4. So the y-intercept of the function is -4.

y = x + b

Substitute the point (4, 0) into the equation to calculate b.

0 = 4 + b

b = -4

So our equation of the function is y = x + 4.

You can check this by substituting any point from the table into our equation.

The probability that x is less than 0.5 and y is greater than 0.6 is 0.0087.

The given joint probability density function of x and y is:

f(x,y) = {

x × y^8, 0 <= x <= 1, 0 <= y <= 1,

0, elsewhere

}

To determine the marginal probability density function of x, we integrate the joint probability density function over the y-axis:

f(x) = \(\int [0,1] x\times y^8 dy\)

=\(x \times [y^{9/9}]_{[0,1]}\)

= x/9

Similarly, to determine the marginal probability density function of y, we integrate the joint probability density function over the x-axis:

f(y) = \(\int[0,1] x \times y^8 dx\)

= \(y^8 \times [x^{2/2}] _{[0,1]}\)

= \(y^{8/2}\)

To determine the probability that x is less than 0.5 and y is greater than 0.6, we use the joint probability density function and integrate over the given region:

P(x < 0.5 and y > 0.6) = \(\int[0.6,1] \int[0,0.5] x\times y^8 dx dy\)

= \(\int[0.6,1] y^{8/2} \times [x^{2/2}][0,0.5] dy\)

= \(\int[0.6,1] y^{8/16} dy\)

= \([y^9/144][0.6,1]\)

= 0.0087

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The probability that x is less than 0.5 and y is greater than 0.6 is approximately 0.00011.

To determine the probability that x is less than 0.5 and y is greater than 0.6, we need to integrate the joint probability density function over the specified region.

Given the joint probability density function:

f(x, y) = {

x × y^8, 0 ≤ x ≤ 1, 0 ≤ y ≤ 1,

0, elsewhere

}

To find the probability, we integrate the joint density function over the region:

P(x < 0.5 and y > 0.6) = ∫∫R f(x, y) dxdy

= ∫[0,0.5] ∫[0.6,1] (x × y^8) dy dx

= ∫[0,0.5] [((x × y^9)/9) |_0.6^1] dx

= ∫[0,0.5] (x/9 - (0.6^9 × x)/9) dx

= [(x^2)/18 - (0.6^9 × x^2)/18] |_0^0.5

= [(0.5^2)/18 - (0.6^9 × 0.5^2)/18] - [0 - 0]

= (1/72 - (0.6^9)/18) ≈ 0.00011

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The text describes various techniques for identifying potential sites for plants or facilities. These techniques include the centroid method, factor-rating systems, linear programming, the transportation method of decision analysis, and regression analysis.

However, the text does not mention one of these techniques as a way to identify potential sites. The technique that is not mentioned in the text is option D, the transportation method of decision analysis. The transportation method is a mathematical technique used to determine the optimal transportation of goods from one location to another. It involves minimizing transportation costs while meeting supply and demand requirements. While this technique can be useful in logistics and supply chain management, it is not typically used to identify potential sites for plants or facilities.

In summary, the techniques mentioned in the text for identifying potential sites are the centroid method, factor-rating systems, linear programming, and regression analysis. The transportation method of decision analysis is not mentioned in the text as a technique for identifying potential sites.

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Answer: 15.4

Step-by-step explanation:

12(12 + 26) = 15(15 + x)

144 + 312 = 225 + 15x

456 = 225 + 15x

456 - 225 = 15x

231 = 15x

231/15 = x

x = 15.4

Answer: The diameter is 28cm

Step-by-step explanation:

Circumference is \(2\pi r\) where r is the radius or just \(\pi d\) where d is the diameter. For this, we'll use the one with the diameter.

\(87.92=3.14d\\\frac{87.92}{3.14} =\frac{3.14d}{3.14} \\28=d\)

Answer:

x² + 34x + 104 = 0

x² + 34x = -104

x² + 34x + ((1/2)(34))² = -104 + ((1/2)(34))²

x² + 34x + 17² = -104 + 17²

x² + 34x + 289 = 185

(x + 17)² = 185

x + 17 = +√185

x = -17 + √185

The Jacobian matrix for the given transformation is:

Jacobian = | 6v 6u | = | 9 -1 |

The Jacobian of the transformation for the given equations is a 2x2 matrix that represents the partial derivatives of the new variables (x and y) with respect to the original variables (u and v). In this case, the Jacobian matrix will have the following form:

Jacobian = | ∂x/∂u ∂x/∂v |

| ∂y/∂u ∂y/∂v |

To find the Jacobian, we need to calculate the partial derivatives of x and y with respect to u and v, respectively.

In the given transformation, x = 6u v and y = 9u - v. Taking the partial derivatives, we have:

∂x/∂u = 6v (partial derivative of x with respect to u)

∂x/∂v = 6u (partial derivative of x with respect to v)

∂y/∂u = 9 (partial derivative of y with respect to u)

∂y/∂v = -1 (partial derivative of y with respect to v)

Plugging these values into the Jacobian matrix, we obtain:

Jacobian = | 6v 6u | = | 9 -1 |

So, the Jacobian matrix for the given transformation is:

Jacobian = | 6v 6u | = | 9 -1 |

This matrix represents the rate of change of the new variables (x and y) with respect to the original variables (u and v). The elements of the Jacobian matrix can be used to compute various quantities, such as gradients, determinants, and transformations in multivariable calculus and differential geometry.

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The required ratio of the surface area of the given pyramids is (A) 3:2.

A ratio can be used to show a relationship or to compare two numbers of the same type.

To compare things of the same type, ratios are utilized.

We might use a ratio, for example, to compare the proportion of boys to girls in your class.

If b is not equal to 0, an ordered pair of numbers a and b, denoted as a / b, is a ratio.

A proportion is an equation that equalizes two ratios.

For illustration, the ratio may be expressed as follows: 1: 3 in the case of 1 boy and 3 girls (for every one boy there are 3 girls)

So, the given surface area is:

- 21 in

- 14 in

Now, calculate the ratio as:

= 21/14

= 3/2

= 3:2

Therefore, the required ratio of the surface area of the given pyramids is (A) 3:2.

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Answer:

21 Remainder 16

Step-by-step explanation:

I used a calculator bcuz I'm  s t o o p i d :')

Answer:

What is the shape? Btw, heres a tip although I havent seen the actual problem, if you know the area, simply divide the area by the width to get your length!

Step-by-step explanation: