a man is five times as old as his son. if the the sum of their ages is 72, find the difference between their ages *​

Using the SSA method, the maximum number of triangles that can be generate is 1.

In the given question,

In SSA case for an obtuse angle, we have to find the maximum number of triangles that can be generate with the given information.

As we know that,

There cannot be a second obtuse angle if the specified first angle is already obtuse since the triangle's angle total would be greater than 180°. As a result, there is only one way to construct the triangle, making SSA a valid congruence theorem when the supplied angle is acute.

So the maximum number of triangles that can be generate is 1.

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Answer:

Step-by-step explanation:

translate

Answer:

$462.50

Step-by-step explanation:

:))

Answer:

14.2cm

Step-by-step explanation:

Complete question:

In circle O, the length of radius OL is 6 cm and the length of arc LM is 6.3 cm. The measure of angle MON is 75°.  

Rounded to the nearest tenth of a centimeter, what is the length of arc LMN?  

Find the diagram attached

arc LN= arc  LM + arc MN

First we need to get the arc MN

length of an arc = theta/360 * 2πr

length of arc MN = 75/360 * 2(3.14)(6)

length of arc MN = 0.20833*37.68

length of arc MN = 7.85

Hence;

arc LN = 6.3 + 7.85

arc LN = 14.15cm

Hence the length of arc LN is 14.2cm

Answer:

156

Step-by-step explanation:

s8 = n/2 [2t + (n-1)(d)]

= 8/2 [2(2) + (8-1)(5)]

= 4 [4 + (7)(5)]

= 4 (4 + 35)

= 4 (39)

= 156

The choice which is closest to the y intercept of the function is Choice 1); 10

According to the question;

The y-intercept is the value of y when x = 0.

In essence;

.y = 10e⁰ + 1

therefore, the value which is closest to the y-intercept is 10.

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The additional information that would have to be true for the parallelogram to also be a rhombus is D. Opposite angles congruent

All rhombuses are parallelograms, but not all parallelograms are rhombuses. In a rhombus, all four sides are equal and the diagonals intersect at 90 degrees. In a parallelogram, the opposite sides are equal and the diagonals bisect each other.

Because its sides are parallel to one another, a rhombus can also be referred to as a particular kind of parallelogram. 360° is the total number of angles in a rhombus. Angles on either side of one another are equal, and adjacent angles are supplementary angles.

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Barbara draws a parallelogram. Jason thought it might be a rhombus. What additional information would have to be true for the parallelogram to also be a rhombus?a. Opposite sides congruent.b. Diagonals are perpendicular.c. Consecutive angles supplementary.d. Opposite angles congruent.

Answer:

Given that angle APB = 100°

Angle CPB = 180°- 100°. (Angle APB and CPB form a linear pair)

We know all triangles formed here are isosceles

Therefore,

We can take angle PBC= angle PCB = x

Now,

Angle CPB+ x + x = 180°. ( Triangle sum property)

100° + 2x = 180°

2x = 180°- 100°

2x= 80°

x= 80°/2

x= 40°

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According to the equation, the weight of box in ounces is 64.

Firstly let us represent the weight of box with w. Now, the formula to be used for calculation of the weight of box is -

The weight of box in ounces = weight of box in pounds × number of ounces in one pound/one

Keeping the values in formula to find the value of weight of box in ounces.

The weight of box in ounces = 4 × 16/1

Performing multiplication and division on Right Hand Side of the equation to find the weight of box in ounces

The weight of box in ounces = 64 ounces

Thus, the weight of box in ounces is 64.

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For the function F(x, y) = x³ + y³ - 3x² - 6y² - 9x ,  the local maximum value is 5 and the local minimum value is -3. The graph is discontinuous, so we cannot locate the saddle points.

In mathematics, a saddle point or minimax point is a point on the surface of the graph of a function where the slopes (derivatives) in orthogonal directions are all zero (a critical point), but which is not a local extremum of the function.

We have the following function -

F(x, y) = x³ + y³ - 3x² - 6y² - 9x

We will plot the 3 dimensional graph of this function. From the model it can be seen that, the local maximum value is 5 and the local minimum value is -3. Since the graph is discontinuous, we cannot locate the saddle points.

Therefore, for the function F(x, y) = x³ + y³ - 3x² - 6y² - 9x ,  the local maximum value is 5 and the local minimum value is -3. The graph is discontinuous, so we cannot locate the saddle points.

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The relationship between the median and the mean scores is the mean is greater than the median. (option c).

Mathematically speaking, the relationship between the median and the mean can vary depending on the distribution of the data. In a symmetrical distribution, where the data is evenly distributed around the center point, the mean and median will be equal.

Conversely, if the data is skewed to the left, meaning there are a few low values that pull the average down, the mean will be less than the median.

In summary, the relationship between the median and the mean depends on the distribution of the data. If the data is symmetrical, the median and mean will be equal. If the data is skewed, the mean will be pulled towards the direction of the skewness, while the median represents the midpoint of the data regardless of the skewness.

Hence the option (c) is correct.

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Answer:

the answer is 4.344

Step-by-step explanation:

hope this helps :)

Answer:

4

Step-by-step explanation:

4 x .25 = 1

Answer:

its 4

Step-by-step explanation:

1÷4×100

=25%

(1×100)÷25

=4

Answer: Zak - Resp after 24 months = $4,344.00

              Zak - Technology Fund after 24 months = $1,102.98

              Zak's Technology Fund has enough money to buy a laptop.

              Zak's Savings (Resp) will last less than 6 months

Step-by-step explanation for Zak:

January - June 2019

$15/hr x 20 hr x 4 wks x 6 months = $7200 Gross Income

Taxable Income is $7200 - $1080 = $6120    (Annual Income $12,240)

→ $7,200 - ($1080 + $360 + $144 + $0 + $129.60) = $5,486.40 Net Income

Tech Fund (5%): $5486.40(0.05) = $274.32

Food Expense (30%): $5486.40(0.3) = $1,645.92

Clothing Expense (30%): $5486.40(0.3) = $1,645.92

Entertainment Expense (25%): $5486.40(0.25) = $1,371.60

Miscellaneous Expense (10%): $5486.40(0.1) = $548.64      

                                               Other Expenses: $5,212.08

July - December 2019 (excluding August)

$16/hr x 20 hr x 4 wks x 5 months = $6400 Gross Income

Taxable Income is $6400 - $960 = $5440    (Annual Income $11,560)

→ $6,400 - ($960 + $320 + $128 + $0 + $75.20) = $4,916.80 Net Income

Tech Fund (5%): $4916.80(0.05) = $245.84

Food Expense (30%): $4916.80(0.3) = $1,475.04

Clothing Expense (30%): $4916.80(0.3) = $1,475.04

Entertainment Expense (25%): $4916.80(0.25) = $1,229.20

Miscellaneous Expense (10%): $4916.80(0.1) = $491.68      

                                              Other Expenses: $4,670.96

January - June 2020

$17/hr x 20 hr x 4 wks x 6 months = $8160 Gross Income

Taxable Income is $8160 - $1224 = $6936    (Annual Income $13,872)

→ $8,160 - ($1224 + $408 + $163.20 + $0 + $194.88) = $6,169.92 Net Income

Tech Fund (5%): $6169.92(0.05) = $308.50

Food Expense (30%): $6169.92(0.3) = $1,850.98

Clothing Expense (30%): $6169.92(0.3) = $1,850.98

Entertainment Expense (25%): $6169.92(0.25) = $1,542.48

Miscellaneous Expense (10%): $6169.92(0.1) = $616.98      

                                               Other Expenses: $5,861.42

July - December 2020 (excluding August)

$18/hr x 20 hr x 4 wks x 5 months = $7200 Gross Income

Taxable Income is $7200 - $1080 = $6120    (Annual Income $13,056)

→ $7,200 - ($1080 + $360 + $144 + $0 + $129.60) = $5,486.40 Net Income

Tech Fund (5%): $4916.80(0.05) = $274.32

Food Expense (30%): $5486.40(0.3) = $1,645.92

Clothing Expense (30%): $5486.40(0.3) = $1,645.92

Entertainment Expense (25%): $5486.40(0.25) = $1,371.60

Miscellaneous Expense (10%): $5486.40(0.1) = $548.64      

                                              Other Expenses: $5,212.08

\(\boxed{\begin{array}{l|r|r|r|r||r}\underline{ZAK}&\underline{Jan-Jun'19}&\underline{Jul-Dec'19}&\underline{Jan-Jun'20}&\underline{Jul-Dec'20}&\underline{Totals\quad }\\Gross&\$7200.00&\$6400.00&\$8160.00&\$7200.00&\$28960.00\\Resp&\$1080.00&\$960.00&\$1224.00&\$1080.00&\$4344.00\\Net&\$5486.40&\$4916.80&\$6169.92&\$5486.40&\$22059.52\\Other&\$5212.08&\$4670.96&\$5861.42&\$5212.08&\$20956.54\\Tech&\$274.32&\$245.84&\$308.50&\$274.32&\$1102.98\end{array}}\)

To determine an orthonormal basis for the subspace of p2 spanned by the polynomials f(x), g(x), and h(x), we can use the Gram-Schmidt process. This process allows us to transform a set of linearly independent vectors into an orthonormal set.

Let's go through the steps of the Gram-Schmidt process for this specific problem Start with the first polynomial, f(x), as our first vector. Normalize f(x) by dividing it by its magnitude (or norm). This will give us our first orthonormal vector, let's call it u1. Next, we move on to g(x), the second polynomial. Subtract the projection of g(x) onto u1 from g(x) itself. The projection of g(x) onto u1 is found by taking the dot product of g(x) and u1, and then multiplying u1 by this dot product. Subtracting this projection from g(x) gives us a new vector, which we'll call v2.

Normalize v2 by dividing it by its magnitude. This will give us our second orthonormal vector, u2. Finally, we move on to h(x), the third polynomial. Again, we subtract the projections of h(x) onto u1 and u2 from h(x) itself. The projection of h(x) onto u1 and u2 is found by taking the dot product of h(x) and each u vector, and then multiplying the respective u vector by these dot products. Subtracting these projections from h(x) gives us a new vector, which we'll call v3. It's important to note that the Gram-Schmidt process can be applied to any set of linearly independent vectors to obtain an orthonormal basis. The resulting orthonormal basis is useful in various areas of mathematics, such as solving systems of linear equations and diagonalizing matrices.

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Answer:

0.4 batches

Step-by-step explanation:

6 / 13 = 0.4

Either a is a singular matrix (det(a) = 0) or det(a) = 1.

To prove that either a is singular or det(a) = 1, given a² = a, we can proceed as follows:

First, let's assume that a is not a singular matrix. This means that a has an inverse, denoted as a⁻¹.

Now, multiply both sides of the equation a² = a by a⁻¹:

a⁻¹(a²) = a⁻¹(a)

Using the associative property of matrix multiplication, we can simplify this to:

(a⁻¹a)² = a⁻¹a

Since matrix multiplication is associative, we have:

I² = a⁻¹a

The product of a matrix and its inverse is equal to the identity matrix, so we have:

I = a⁻¹a

Taking the determinant of both sides, we get:

det(I) = det(a⁻¹a)

The determinant of the identity matrix is 1, so we have:

1 = det(a⁻¹a)

Using the property of determinants, we can rewrite this as:

det(a⁻¹) * det(a) = 1

Since det(a⁻¹) is the inverse of det(a), we have:

1/det(a) * det(a) = 1

Simplifying, we find:

1 = 1

Therefore, if a is not a singular matrix, we have shown that det(a) = 1.

On the other hand, if a is a singular matrix, it does not have an inverse. In this case, det(a) = 0.

Thus, we have proved that either a is singular (det(a) = 0) or det(a) = 1.

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Step-by-step explanation:

slope, m = (y1-y2) / (x1-x2) =   (8-6) / (  4-8) = 2/(-4) = - 1/2  slope

Answer:

-1/2

Step-by-step explanation:

Slope formula: \(\frac{y^2-y^1}{x^2-x^1}\)

We have to find the slope for the points (4, 8) and (8, 6).

(x1, y1) - coordinates of the first point (4, 8).

(x2, y2) - coordinates of the second point (8, 6).

Now that we know what the variables stand for, we plug the numbers into the formula.

\(\frac{y^2-y^1}{x^2-x^1} =\frac{6-8}{8-4} \\\\= \frac{-2}{4} =\frac{-1}{2}\)NOTE: -1/2 is -2/4 in the simplest form.

So, the slope of this equation is -1/2.

Answer:

32, 43

Step-by-step explanation:

Your welcome! :)

Answer:

The answer is 45,60.

Step-by-step explanation:

We can use a square chart to answer this question.

I will zoom in to the particular ones we need.

\( {6}^{2} = 36\)

\({7}^{2} = 49\)

\( {8}^{2} = 64\)

7 is the square root of 49.

45 lies in between 36 and 49 so its square root is more than 6 but less than 7. It is around 6.708 to the nearest thousandth.

Meanwhile, 60 lies in between 49 and 64 so its square root is more than 7 but less than 8. It is around 7.746 to the nearest thousandth.

Hence, we can say that 7 lies in between the square root of 45 and the square root of 60.

When graphing an exponential function, a T-chart is commonly used to determine the values. The correct answer is option A.

The T-chart employs positive real numbers since this is the most typical form of exponential function.

Exponential functions are utilized to represent processes that increase or decrease exponentially, as well as to model phenomena in many different disciplines, including science, economics, and engineering.

The exponential function can be represented by the following equation:

\(y=a^x\), where a is the base, x is the exponent, and y is the outcome.

When a is a positive number greater than one, the function is called exponential growth, while when a is a fraction between 0 and 1, the function is called exponential decay.

The T-chart is used to determine the values to use in the graph and connect the dots as required. Positive real numbers are used as the values in the T-chart in order to effectively graph the exponential function.

Therefore, the correct answer is option A.

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Options b, d, and e are the true statements about the substitution method.

b. It is useful to solve the integral ∫2x sin x^2 dx.

d. It utilizes the formula ∫ f(u(x))u'(x) dx = ∫ f(u) du.

e. It is based on the chain rule for derivatives.

The true statements about the substitution method are:

b. It is useful to solve the integral ∫2x sin x^2 dx.

The substitution method is commonly used to simplify integrals and make them easier to evaluate. It can be applied to various types of integrals, including the given example.

d. It utilizes the formula ∫ f(u(x))u'(x) dx = ∫ f(u) du.

The substitution method involves making a substitution in the integral by introducing a new variable. This formula represents the fundamental principle of substitution, where the derivative of the substituted function appears in the integral.

e. It is based on the chain rule for derivatives.

The substitution method is based on the chain rule of derivatives. By making an appropriate substitution, the integral can be transformed into a new form that corresponds to a derivative of a simpler function.

Therefore, options b, d, and e are the true statements about the substitution method.

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Step-by-step explanation:

g(x)  is just f(x) shifted UP three units ...so

  g(x) = f(x) +3

Answer:

15

Step-by-step explanation:

Because 15 -3 will give you 12

Answer:

the y intercept is -4 or (0,4)

Step-by-step explanation:

To find the y intercept you have to make x zero, and vice versa. So:

0-3y = 12

-3y = 12

y = 12/-3

y = -4

the y intercept is -4 or (0,4)

Answer:

not equivalent to meteorologists ratio

Step-by-step explanation:

meteorologists ratio is

rainy days : sunny days = 2 : 5

last months weather is

rainy days : sunny days

= 10 : 20 ( divide both parts by LCM of 10 )

= 1 : 2 ← not equivalent to 2 : 5

Answer:

A rational number is any number that can be written as a fraction, where both the numerator (the top number) and the denominator (the bottom number) are integers, and the denominator is not equal to zero.

Step-by-step explanation:

In other words, a rational number can be expressed as p/q, where p and q are both integers and q ≠ 0.

An integer is a number that is not a fraction. So basically, a whole number.

Hope this helped!

Any integer that can be expressed in the form p/q, with q≠0, is referred to as a rational number in mathematics.

What are integers?

The Latin word "Integer," which means entire or intact, is where the word "integer" initially appeared. Zero, positive numbers, and negative numbers make up the specific class of numbers known as integers.

Any number that can be expressed as a fraction and has an integer denominator that is not zero and both the numerator and the numerator are integers is considered to be rational.

To put it another way, a rational number can be written as p/q, where p and q are both integers and q≠0.

Hence, rational number is any integer that can be expressed in the form p/q, with q≠0.

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Answer:

x = 3 oz of seeds

y = 7 oz of seeds

Step-by-step explanation:

1. x + y = 10 oz (total amount of snack mix in ounces; oz)

2. $1.50x + $2.50y = $22 (how much the seeds and dried fruit costs)

3. Solve the system of equations using algebra.

$1.50 x + $1.50y = $15

$1.50 x + $2.50y = $22

There are $1.50x's in both of the equations, so cancel them out.

Subtract $2.50y by $1.50y and $22 by $15. y = 7

4. Plug in the y value in one of the equations.

x + 7 = 10; x = 3

The most appropriate statement is that C. The shaded area represent both 2/3 and 6/9 of the whole shape.

Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.

Given a square.

This square is divided in to 9 equal sized squares, with 3 rows and 3 columns.

Out of the 9 equal sized squares, 6 squares are shaded.

We can write the fraction of shaded squares to total number of squares as 6/9.

In the same way, we have in the question that, 6 squares which are shaded is the squares in the first two columns, where each column has three squares.

So we can say that, out of 3 equal sized columns, two columns are shaded.

Fraction of shaded columns to total columns is 2/3.

So 2/3 = 6/9.

Hence shaded area represent both 2/3 and 6/9 of the whole shape.

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Of these three examples, height and weight are more likely to be normally distributed.

What is continuous variable ?

A continuous variable is a type of quantitative variable that can take on any value within a certain range. Continuous variables can be measured to any degree of precision, meaning they can be broken down into smaller and smaller increments.

Three real-life examples of a continuous variable are:

Height: Height is a continuous variable that can take any value within a certain range. It can be measured to any degree of precision, making it a continuous variable.

Time: Time is another continuous variable that can be measured to any degree of precision, from milliseconds to years.

Weight: Weight is also a continuous variable that can take any value within a certain range. It can be measured to any degree of precision, making it a continuous variable.

This is because these variables tend to follow a bell-shaped curve when plotted, with most values clustering around the mean and fewer values appearing further away from the mean. Time, on the other hand, may not be normally distributed because it can have different distributions depending on the situation, such as a bimodal distribution for the time of day people go to sleep or wake up. However, it's important to note that the normal distribution is just one of many possible distributions for continuous variables and may not always be the most appropriate or accurate for real-life situations.

Therefore, Of these three examples, height and weight are more likely to be normally distributed.

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