Express the following argument mathematically and give the rule(s) that could be used to prove or disprove them. a. The children are sick. The doctors are not here. Therefore the doctors are not here and the children are sick. [2 marks]?​

Answer:

soln

6+r =2r+3

6-3=2r-r

3=r

Answer: (x+2)(x-8)

Step-by-step explanation:

x^2-6x-16
x^2-8x+2x-16
x(x-8)+2(x-8)
(x+2)(x-8)

Check the picture below.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{22}\\ a=\stackrel{adjacent}{6}\\ o=\stackrel{opposite}{PQ} \end{cases} \\\\\\ PQ=\sqrt{ 22^2 - 6^2}\implies PQ=\sqrt{ 484 - 36 } \implies PQ=\sqrt{ 448 }\implies PQ\approx 21.17[/tex]

[tex] \angle3 \: and \: \angle4 [/tex] are complementary.

What is Complementary angle?

If sum of two angles is 90° then we can say that those angles are complementary.

For example, if [tex] \angle \: a + \angle \: b = {90}^{o} [/tex] then angle a and angle b are complementary.

Here are some examples of complementary angles:

Here given,

[tex] \angle1 \: and \angle2[/tex] are complimentary.

So,

[tex] \angle1 + \angle2 = {90}^{o} [/tex]

It is clear that [tex] \angle1, \angle2, \angle3, \angle4[/tex] are making a straight angle.

So, we can write,

[tex] \angle1 + \angle2 + \angle3 + \angle4 = {180}^{o} \\ {90}^{o} + \angle3 + \angle4 = {180}^{o} \\ \angle3 + \angle4 = {180}^{o} - {90}^{o} \\ \angle3 + \angle4 = {90}^{o} [/tex]

Here sum of angle 3 and angle 4 is 90°.

According to definition angle 3 and angle 4 are complimentary angles.

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Answer:

38/15

Step-by-step explanation:

4 1/5 - 5/3

4 1/5 = 21/5

21/5 - 5/3 = 63/15 - 25/15 = 38/15

So, the answer is 38/15

The monthly interest yield on Tom's retirement account for a 30-year period would be $637.71.

Assuming that the interest is compounded monthly, the monthly yield on Tom's retirement account with an APR of 4.57% for a 30-year period can be calculated using the formula:

Monthly Yield = (Principal × Monthly Interest Rate) ÷ (1 - (1 + Monthly Interest Rate[tex])^{(-Number of Months)}[/tex]

Here, Principal = $160,000

APR = 4.57%,

Number of Months = 30 years ÷ 12 months/year = 360 months.

First, we need to convert the APR to a monthly interest rate by dividing it by 12:

Monthly Interest Rate = 4.57% × 12

Monthly Interest Rate = 0.3808%

Monthly Yield = (160000 × 0.3808%) ÷ (1 - (1 + 0.3808%[tex])^{-360}[/tex]

Monthly Yield = $637.71

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In the excerpt from "The City Lost in the Snow," the statement that best reflects how the cultural setting influences Sigismondo's attitude is: C.

The scarcity of jobs makes Sigismondo appreciate the temporary employment the snow provides. T

his statement reflects the importance of the cultural setting, as it shows that Sigismondo values the opportunity to work and earn money, even if it's temporary, due to the scarcity of jobs in the city.

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Answer:

yes

Step-by-step explanation:

john has 34 marbles

Answer: X= -4

Step-by-step explanation:

Answer:

338262.124

Step-by-step explanation:

127.6/10 = 12.76 (depending on how many zero is how much you'll move the decimal to the left)

12.76^5 = 338262.124 because it's 12.76x12.76x12.76x12.76x12.76

Answer:

0.7 = 0.70, so 0.17 < 0.70

Answer:

Step-by-step explanation:

Area of rectangle+area of triangle

hope the picture helps

Erin's capital gains are the sum of her long-term capital gains (LTCG) and short-term capital gains (STCG), which is $2,600 + $24,400 = $27,000.

Erin's capital losses are the sum of her long-term capital losses (LTCL) and short-term capital losses (STCL), which is ($9,600) + ($15,600) = ($25,200).

Since Erin's capital gains exceed her capital losses, she has a net capital gain of $27,000 - $25,200 = $1,800.

The nature of Erin's capital gains and losses are as follows:

Step-by-step explanation:

In order to find the f(x) or y value, you have to replace x with the given one in the table:

x = -1,

[tex]y = \sqrt[3]{ - 1 - 7} = \sqrt[3]{ - 8} = - 2[/tex]

.

x = 6,

[tex]y = \sqrt[3]{ 6 - 7} = \sqrt[3]{ - 1} = - 1[/tex]

.

x = 7,

[tex]y = \sqrt[3]{7 - 7} = \sqrt[3]{0} = 0 [/tex]

.

x = 8,

[tex]y = \sqrt[3]{8 - 7} = \sqrt[3]{1} = 1 [/tex]

.

x = 15,

[tex]y = \sqrt[3]{15 - 7} = \sqrt[3]{8} = 2[/tex]

Also, the correct graph is in the 2nd photo, where the root is (7; 0)

Answer:

it should be B but I could be wrong

Step-by-step explanation:

B

Answer: 98 cm²

Step-by-step explanation:

When a cartographer enlarges a map with a scale factor, both the length and the width are multiplied by the scale factor. In this case, the scale factor is 3.5.

Original dimensions of Colorado on the map:

Length: 4 cm

Width: 2 cm

Enlarged dimensions using the scale factor of 3.5:

Length: 4 cm × 3.5 = 14 cm

Width: 2 cm × 3.5 = 7 cm

To find the area of the enlarged map, multiply the enlarged length and width:

Area = Length × Width

Area = 14 cm × 7 cm

Area = 98 cm²

The area of the enlarged map is 98 cm².

Answer: a = -2

Step-by-step explanation:

8a = -12 + 2a

8a - 2a = -12
6a = -12
a = -12/6

a = -2

Answer:

[tex](3x, 3y)[/tex]

Step-by-step explanation:

The scale factor is 3 so you multiply 3 by the (x,y) to get (3x,3y) as the scale factor

Answer:

34

Step-by-step explanation:

5+5+2=12

12+6+3=21

21+8+5=34

Answer:45

Step-by-step explanation:

5+5(8)=45

The graph of [tex]g(x)[/tex] is the result of taking the graph of [tex]f(x)\\[/tex], shifting it right three units and down two units.

The only equivalent expression is option (a) [tex]7^x[/tex].

What is expression ?

An expression in mathematics is a group of symbols that represent a statistical correlation or quantity, such as integers, variables, and operators. It may contain exponents, logarithms, and trigonometric functions in addition to mathematical operations like addition, multiplication, multiplication, and division. It may also contain constants, variables, and functions. Expressions can be used in a variety of subjects, including mathematics, calculus, geometry, and statistics, to represent mathematical models, resolve equations, and carry out calculations.

To find equivalent expressions for[tex]21^x/3^x[/tex], we can try to simplify the expression using exponent rules.

21 can be factored as 7*3, so we can write:

[tex]21^x/3^x = (7 × 3)^x/3^x = 7^x × 3^x/3^x = 7^x[/tex]

Therefore, we can see that option (a) 7^x is equivalent to the given expression.

To check the other options:

b) [tex](7/3)^x[/tex] = [tex](7^x)/(3^x)[/tex] which is not equivalent to the given expression.

c) [tex]3^(2x+1)[/tex] can be written as [tex]3^(2x)[/tex] × [tex]3^1[/tex] = [tex](3^2)^x[/tex] × 3 = [tex]9^x[/tex] × 3 which is not equivalent to the given expression.

d) [tex]7^(x-1)[/tex] can be written as [tex]7^x/7[/tex] which is not equivalent to the given expression.

e) [tex](3/7)^x[/tex] is not equivalent to the given expression.

Therefore, the only equivalent expression is option (a) [tex]7^x[/tex].

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The complete question is:

Which expressions are equivalent to [tex]21^x/3^x[/tex]? Check all that apply.

a) [tex]7^x[/tex]

b) [tex](7/3)^x[/tex]

c) [tex]3^(2x+1)[/tex]

d) [tex]7^(x-1)[/tex]

e) [tex](3/7)^x[/tex]

Answer:

2x^2+8x-4

Step-by-step explanation:

The BMI​ of a person whose weight is 176 lb and whose height is 77 inches is 21.

First, let's use the given information to find the constant of proportionality in the BMI formula:

BMI = k × (weight in pounds) / (height in inches)²

When the 6-foot-tall person weighing 177 lb has a BMI of 24, we can plug in the values and solve for k:

24 = k ₓ 177 / (72²)

k = 24 ₓ (72²) / 177

k ≈ 9.94

Now we can use this value of k to find the BMI of the person whose weight is 176 lb and whose height is 77 in:

BMI ≈ 21

BMI = 9.94 ₓ 176 / (77²)

Therefore, the BMI (to the nearest whole number) of the person is 21, which falls within the healthy weight range of 19 to 25.

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The description of the incident is shown below

One incident that shows how selection works in the process of perception is when you are at a party and you hear your name being mentioned in a conversation across the room. In this situation, your attention is immediately drawn to the conversation, and you focus on it while filtering out other sounds and distractions around you.

This is an example of selective attention, where you choose to focus on a particular stimulus and ignore others.

As for an example of a stereotype that I have, it is that all people who live in a certain region or country behave in a particular way.

For instance, I may have the stereotype that people from a particular country are loud and aggressive.

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The tax rate of a house valued at $115,000 with a property tax of $1265 is 110%. or $110 per $1,000 of property value.

The property tax is the levy imposed on the assessed value of the property of an individual or corporation.

Property tax is usually levied as a percentage of the assessed value.

Property tax = $1265

House value - $115,000

Tax rate = 110% [tex](\$1265\div\$115000 \times 100)[/tex]

Thus, the tax rate of a house valued at $115,000 with a property tax of $115,000 is 110%. or $110 per $1,000 of property value.

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Answer:

55% of the whole wall is covered in paint of any color.

Step-by-step explanation:

To determine what percentage of the wall is covered in paint, we need to add the fractions of the wall covered by each color of paint and then convert the result into a percentage.

Red paint: 1/5

Blue paint: 1/10

Green paint: 1/4

First, we need to find a common denominator, which is the least common multiple (LCM) of the denominators 5, 10, and 4. The LCM of 5, 10, and 4 is 20. Now, we can convert the fractions to equivalent fractions with a denominator of 20:

Red paint: (1/5) * (4/4) = 4/20

Blue paint: (1/10) * (2/2) = 2/20

Green paint: (1/4) * (5/5) = 5/20

Now, add the fractions:

Total paint coverage = 4/20 + 2/20 + 5/20 = (4 + 2 + 5)/20 = 11/20

To convert this fraction to a percentage, we can divide 11 by 20 and multiply the result by 100:

(11/20) * 100 = 0.55 * 100 = 55%

Thus, 55% of the whole wall is covered in paint of any color.

Answer:

Step-by-step explanation:

it’s equals 0 I think

Using factors, we can conclude that the new product will be 48 time more than the old product.

In mathematics, the factor of a number is a divisor of the inputted integer that entirely divides it, leaving no residue. We can use a variety of techniques, including the division method and the multiplication method, to identify a number's components.

Let the product be P.

Let the numbers be a and b.

Now,

P = a × b

According to the question.

Let a is increased by a factor of 12 and b by 4:

P = 12a × 4b

P = 48 × a × b

Hence, we can conclude that the product will increase by a factor of 48.

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