Write an equation that can be used to determine the angle measure, in degrees, of angle DBC. Let n represent the measure of angle DBC. Then determine the measure of n

Answer:

n(A U B) = n(A) + n(B) – n(A ∩ B)

putting values we get

50 = 2a + a - 20

solving eqn.

70 = 3a

a = 70 / 3

now n(a) = 2a

= 2 x 70/3

= 140/3

hence, n(a) = 140/3

Note that  the following probability as a simplified fraction and as a decimal is:  0.88617886178 and 109/123

Note that the key phrase here is “given that this person is a man.”

This means that all we are interested in is the row labeled Male.

           Married      Never      Div       Widowed    Total

Male    69                  40       11                   3           123    

We are asked to find the probability that the person was either Married or Never. So the fraction you want is (69 + 40) / 123.

⇒ (69 + 40) / 123.

⇒ 109/123

or 0.886179

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Express the following probability as a simplified fraction and a decimal.

if one person is selected from the population described in the table, find the probability that the person has never been married or is married, given that this person is a man.

  Married  Never Married  Divorced   Widowed   Total

Male    69    40     11     3     123

Female  67    33     20     5     125

Total    136    73     31     8     248

Question 1.Express the probability as a simplified fraction

The correct sequence to model the given scenario is (b) f(n) = 1.12f(n-1)(1- f(n-1/6000)), and we can use this formula to calculate the oxygen released by the tree in each year, option (b) is correct.

The amount of oxygen released by the tree increases at a rate of 12% per year, which is represented by the factor 1.12f(n-1).

However, the tree cannot generate more than 6000 pounds of oxygen per year, which is represented by the limiting factor:

(1- f(n-1/6000)).

To understand this better, let's calculate the oxygen released by the tree in the second year using the formula

f(n) = 1.12f(n-1)(1- f(n-1/6000)).

f(2) = 1.12f(1)(1- f(1)/6000)

= 1.12(250)(1- 250/6000)

= 295.67 pounds of oxygen

Hence, option (b) is correct.

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The correct question is:

Which sequence below would best model the following description? A newly planted tree releases 250 pounds of oxygen over the period of its first year. The amount of oxygen released by the tree grows at a rate of 12% per year, but the tree cannot generate more than 6000 pounds of oxygen per year.

a. f(n) = 1.12f(n-1)(1+ f(n-1/6000)

b. f(n) = 1.12f(n-1)(1- f(n-1/6000)

c. f(n) = 1.12f(n-1) {6000/f(n-1)}

d. f(n) = 1.12f(n-1)(f(n-1) -6000)

Here, We provide a general explanation of how to calculate the mean, mode, median, and range from a set of data.

To find the mean (average) of a set of data, add up all the values in the set and divide by the number of values. For example, if the maximum temperatures of the 30 days are:

25, 28, 29, 27, 26, 30, 31, 32, 29, 27, 26, 24, 23, 25, 28, 30, 32, 33, 34, 31, 29, 28, 27, 26, 25, 24, 23, 21, 20, 22

The sum of the values is:

25 + 28 + 29 + 27 + 26 + 30 + 31 + 32 + 29 + 27 + 26 + 24 + 23 + 25 + 28 + 30 + 32 + 33 + 34 + 31 + 29 + 28 + 27 + 26 + 25 + 24 + 23 + 21 + 20 + 22 = 813

Dividing by the number of values (30), we get:

Mean = 813/30 = 27.1

To find the mode of a set of data, identify the value that occurs most frequently. In this example, there are two values that occur most frequently, 27 and 29, so the data has two modes.

To find the median of a set of data, arrange the values in order from smallest to largest and find the middle value. If there are an even number of values, take the mean of the two middle values. In this example, the values in ascending order are:

20, 21, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 27, 28, 28, 29, 29, 29, 30, 30, 31, 31, 32, 32, 33, 34

There are 30 values, so the median is the 15th value, which is 28.

To find the range of a set of data, subtract the smallest value from the largest value. In this example, the smallest value is 20 and the largest value is 34, so the range is:

Range = 34 - 20 = 14

To create a frequency table for the maximum temperature data, we need to group the data into intervals and count the number of values that fall into each interval. For example, we could use the following intervals:

20-24, 25-29, 30-34

The frequency table would look like this:

Interval | Frequency

20-24 | 4

25-29 | 18

30-34 | 8

To calculate the size of the angles for the pie chart, we need to find the total frequency (30) and divide 360° by the total frequency to get the proportion of each interval in degrees. For example, for the interval 25-29:

Proportion = Frequency/Total frequency = 18/30 = 0.6

Angle = Proportion x 360° = 0.6 x 360° = 216°

We can repeat this calculation for each interval to obtain the angles for the pie chart.

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Answer:

C. Luisa is incorrect, it's not 0. It's only zero when you get "x=0" as an answer but the variable x got canceled here. And as 3=3, it is a true statement so it includes all real numbers. If you had gotten 3=8 for example, it would be a fake statement, so then no solution.

And for the second part,

1. No solution

5x+24=5x+25

24=25

It's false

2. One solution

12p-7=-3p+8

15p=15

P=1

3. One solution.

3x+20=5x

20 = 2x

X = 10

The amount of medication should they receive per dose is,

⇒ 363.6 mg

Given that;

A patient weighs 160 pounds and needs medication with dosage instructions of 15 mg/kg/day.

And, It is to be given in 3 doses each day.

Hence, We get;

1 pounds = 1/2.2 kg

160 pounds = 160 x 1/2.2 kg

                  = 72.72 kg

Since, It is to be given in 3 doses each day.

Hence, The amount of medication should they receive per dose is,

⇒ 72.72 x 15 / 3

⇒ 363.6 mg

Thus, The amount of medication should they receive per dose is,

⇒ 363.6 mg

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If a candle having diameter as 9 cm, height as 12 cm is placed in a cylindrical box, then the height of the cylindrical box will be 13cm.

The "cylindrical-candle" diameter is given as = 9 cm;

The "cylindrical-candle" height is given as = 12 cm;

The candle is placed in a box which has a space of 0.5 cm between the candle and the box for packaging material;

which means that, there will an additional 0.5 cm in the top and bottom of the candle,

So, the height of the "cylindrical-box" is written as : 0.5 + 12 + 0.5;

Therefore, the "cylindrical-box" has a height of 13 cm.

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The correct function that models the balance B of Lily’s account as a function of time in months is option A, which is B(t) = 325(1 − 0.005)ᵗ.

To see why, we can start with the initial balance of $325 and note that each month, the bank charges a monthly fee of 0.5%, which is equivalent to a monthly interest rate of 0.005. This means that after one month, the balance will be reduced by 0.5% or 0.005 times the original balance, giving:

B(1) = 325 - 0.005(325)

Similarly, after two months, the balance will be reduced by another 0.5% of the new balance, giving:

B(2) = (325 - 0.005(325)) - 0.005(325 - 0.005(325))

We can simplify this expression by factoring out the common factor of 325(1 - 0.005) after each term, giving:

B(2) = 325(1 - 0.005)²

Generalizing this pattern, we can see that after t months, the balance will be:

B(t) = 325(1 - 0.005)ᵗ

Therefore, option A is the correct function that models the balance of Lily’s account.

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The synthetic division of the polynomial indicates that other factor of the polynomial is; x² - 3·x + 13

A polynomial consists of terms that have positive integer powers or index of variables joined together by addition and subtraction symbols.

The possible polynomial in the question is; x³ + 5·x² - 11·x + 104

The factor of the polynomial is; (x + 8)

The steps for the synthetic division includes on the left side of the vertical line, placing the opposite sign of the constant term of the factor.

The other steps of synthetic division can then be presented, summarily as follows;

Therefore;

-8 | 1[tex]{}[/tex]   5     -11   104

   |   [tex]{}[/tex]   -8    24  104          

     1   -3    [tex]{}[/tex] 13      0

The factors of the polynomial

The values in the above last row of the long division indicates that the other factor of the polynomial is; x² - 3·x + 13

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In linear equation, 9 is the constant of variation k.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                             Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to be linear equations. axe+b = 0 is a one-variable example in which a and b are real numbers and x is the variable.

given x varies inversely with y then

xy = k ← k is the constant of variation

to find k use the condition x = - 4 when y = - 9, hence

k = -4 × -9 = 36

 x = 36/y

 when x = 4 , then  y = 36/4

                                  x = 9

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The exponential value decay equation is solved and the value of the vehicle after 11 years is A = $ 13,413

Given data ,

Let the initial cost of the vehicle be = $ 29,800

Now , the rate of depreciation be r = 7 %

Let the number of years be n = 11 years

And , the exponential decay is given by the equation ,

x ( t ) = x₀ × ( 1 + r )ⁿ

On simplifying , we get

x ( 11 ) = 29800 ( 1 - 0.07 )¹¹

x ( 11 ) = 29800 ( 0.93 )¹¹

x ( 11 ) = 13,413.085

Hence , the cost of the vehicle after 11 years is A = $ 13,413

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The surface area of the rectangular prism is 24.62 square units

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

2.5 by 2.14 by 1.5

The surface area of the rectangular prism is calculated as

Area = 2 * (Length * Width + Length * Height + Height  * Width )

substitute the known values in the above equation, so, we have the following representation

Area = 2 * (2.5 * 2.14 + 2.5 * 1.5 + 2.14 * 1.5)

Evaluate

Area = 24.62

Hence, the surface area is 24.62 square units

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Answer:

1/4

Step-by-step explanation:

The scaled image is 1/4 of the size of the original, we can see this as one side of the original shape is 4 units, and the scaled side is 1 unit.

The median number of eggs laid in a year is 231 from the given data, option A is correct.

The data table shows the numbers of eggs laid by individual chickens in a year.

Now, We can arrange it into ascending order as;

⇒ 222, 229, 229, 231, 234, 235, 262

Since, There are 7 terms

Hence, Median = (7 + 1)/2

= 4th term

= 231

Hence, the median number of eggs laid in a year is 231, option A is correct.

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Answer:

2600This is a probability conversion problem.

You are on the right track! To find the equation of the parabola given by the equation x^2 + 6x + 8 = 0, you can use the standard form of a quadratic equation, which is:

where (h, k) is the vertex of the parabola and a is a coefficient that determines the shape of the parabola.

To get the equation of your parabola, you first need to complete the square on the x terms of the given equation:

From this equation, you can see that the vertex of the parabola is at (-3, -1) and the value of a is positive. This means that the parabola opens upwards.

To find the value of a, you can compare the equation with the standard form of the quadratic equation:

where h = -3, k = -1, and a is the coefficient you need to find. Substituting these values into the equation gives:

So the equation of the parabola is:

To plot the parabola, you can use the vertex (-3, -1) as a starting point and then use the coefficient a to determine the shape of the parabola. Since a is positive, the parabola opens upwards.

8.69 is the length of the right angle.

Let's call the length you are trying to find x.

Using trigonometry, we know that:

cos(75) = x/9

Solving for x:

x = 9sin(75)

The sine function (sin) is a mathematical function commonly used in trigonometry. It relates the ratio of the length of the side opposite an angle in a right triangle to the length of the hypotenuse.

Using a calculator to find the cosine of 75 degrees:

x ≈ 8.69

Therefore, the length you are trying to find is approximately 8.69.

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The value of side length c is 13.55 units.

The length of side c is calculated by applying sine rule as shown below;

The formula for sine rule is given as;

a/sinC = b/sinA

For the given question, we will have the following equation,

c/sin (34) = 11 / sin (27)

The value of c in the triangle is calculated as follows;

c = (sin 34 / sin 27 ) x 11

c = 13.55 units

Thus, the value of side length c is determined by applying sine rules.

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Therefore , the solution of the given problem of trigonometry comes out to be approximately 21.424 metres long when the sun is 35 degrees above the horizon.

Some people assert that the growth of astrophysics was influenced by the merging of various fields. Many metric problems can be solved or the result of a calculation can be ascertained with the use of exact mathematical techniques. Trigonometry is the study of the six basic geometric calculations from a scientific perspective. They go by many other names and acronyms, including sine, variance, direction, and others. (csc).

Here,

When the sun is at a 35° elevation angle and the structure is 15 metres tall, we want to determine the length of the shadow (on the next side).

Let x represent the desired shadow's length. Next, we have

=> tan 35° = 15/x

When we multiply both sides by x, we obtain:

=> x tan 35° = 15

By dividing both sides by 35° of tan, we obtain:

=> x = 15 / tan 35°

We may calculate the value of the tangent of 35 degrees using a calculator:

=> tan 35° ≈ 0.7002

Next, we have

=> 15x/0.702x=21.424 metres

Consequently, a building 15 metres high will create a shadow that is approximately 21.424 metres long when the sun is 35 degrees above the horizon.

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Answer:

128 servings

Step-by-step explanation:

It takes 1 1/4 cups to make 10 servings

1 1/4 as a mixed fraction = 5/4  

So 5/4 cups makes 10 servings

1 cup makes 10 ÷ 5/4

Use the fraction rule for division
a/b ÷ c/d = a/b x c/d

10 ÷ 5/4 = 10 x 4/5 = 8 servings from 1 cup

1 gallon = 16 cups

At 8 servings per cup, total number of servings for 16 cups
= 8 x 16 = 128 servings ANSWER

The missing step of the congruent triangles is ΔMDA ≅ ΔMBC by ASA theorem

Given data ,

Let the two triangles be represented as ΔMDA and ΔMBC

Now , the measure of side MD ≅ MB ( given )

And , the measure of angle ∠DMA ≅ ∠BMC ( vertical angles theorem )

Now , the measure of ∠MDA ≅ measure of ∠MBC ( alternate interior angles)

Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)

So , ΔMDA ≅ ΔMBC by ASA theorem

Hence , the congruent triangles are solved

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Therefore , the solution of the given problem of fraction comes out to be 3/4 cups of yoghurt to the blender.

Any configuration of identically sized parts can be combined to represent the total. In Standard English, quantity is defined as "a portion" within a specific measurement. 8, 3/4. Wholes also include fractions. These serve as the divisor of the ratio, which in mathematical terms would be a pair of numbers. Here are a few illustrations of how to convert simple halves into whole numbers.

Here,

A visual fraction model can be used to illustrate the various fractions in a cup of yoghurt that you want to add in portions to a blender.

For instance, you may divide the cup into four equal parts and use one of those parts to represent 1/4 cup of yoghurt in the blender.

You can divide the cup into two equal parts and display two of those parts to symbolise the addition of 1/2 cup of yoghurt.

You would have added

=> 1/4 + 1/2 = 3/4 cups of yoghurt to the blender.

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Answer:1020 ft (squared)

Step-by-step explanation:

Base width 1 (28 ft) x Base width 2 (40 ft) x height (6 ft) = 1020 ft (squared)

Answer: 1/2, the same as getting tails 5 times

Step-by-step explanation:

hope this helps

The clear difference between an angle bisector and a segment bisector is that angle bisector passes through the apex of an angle while segment bisector passes through the midpoint of the line segment.

An angle bisector is defined as the line the divides an angle into two equal parts by passing through its apex.

A segment bisector is defined as the line that divides a segment at the midpoint into two parts.

The difference between angel bisector and segment bisector is that angle bisector passes through the apex of an angle while segment bisector passes through the midpoint of the line segment.

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Answer:

The distribution is symmetric

Step-by-step explanation:

Because in both sides it has the same structure, so that means that the value is the same in both sides