How do I get full marks on this question?

(i)   a

(ii)  {x | x ∈ R, x ≠ 3, x ≥ 1}

(i) To evaluate f(4), f(5), and f(a + 1), we replace x with 4, 5, and a + 1 in f(x) respectively. We have; f(4) = √ 4 − 1 4 − 3= √ 3 1= √ 3f(5) = √ 5 − 1 5 − 3= √ 4 2= 2f(a + 1) = √ a + 1 − 1 a + 1 − 3= √ a 2= a

(ii) Domain of f:The expression in the denominator cannot be equal to zero, so we must ensure that x − 3 ≠ 0. Therefore, x ≠ 3The expression in the square root must be greater than or equal to zero, so we must ensure that x − 1 ≥ 0. Therefore, x ≥ 1The domain of f is {x | x ∈ R, x ≠ 3, x ≥ 1}.

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An equation for the balance, b, in the student's savings account after n months is b = d - wn.

An equation is a mathematical or algebraic statement showing that two or more mathematical or algebraic expressions are equal or equivalent.

An equation is denoted using the equal symbol (=), which an algebraic expression lacks.

Mathematical expressions combine variables with numbers, constants, or values using mathematical operands.

The amount in the savings account = d

Monthly withdrawals = w

The period of withdrawals = n

Let the balance in the account after n months = b

Therefore, the balance after n months will be represented by the equation, b = d - wn.

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A student has a savings account with d dollars in it. The student plans to withdraw w dollars each month for n months. Enter an equation for the balance, b, in the account after n months.

The baker can decorate 1.4 or 1 1/3 of cupcakes in a minute.Step-by-step explanation: 42 cupcakes in 30 minutes so if you divide 42 cupcakes in 30 groups you get 1 in each group and 12 left so if make 30 in 3 it makes 4 in each group but it is 30 so you make the four in to a 0.4 or 1/3 which is 1.4.You can also multiply if you make 1.4 into 14 x 3 = 42 same as 1.4 x 30 = 42 so the answer is 1.4.

Answer:99

Step-by-step explanation:

Answer: 99

Step-by-step explanation:

135 is 9 times of 15

To get the missing number, multiply 11 by 9,

11 x 9 = 99

Answer:

3.9 miles

Step-by-step explanation:

To find:-

Answer:-

The given situation is represented in the attachment.

We can see that there is a formation of right angled triangle , hence we can use Pythagoras theorem here , according to which,

[tex]\rm\implies a^2+b^2=h^2 \\[/tex]

where h is the longest side (hypotenuse) of the triangle of the triangle . From the attached figure we can see that 8miles is hypotenuse and one of the other side is 7miles .

On substituting the respective values, we have;

[tex]\rm\implies 7^2+b^2=8^2 \\[/tex]

[tex]\rm\implies 49+b^2=64 \\[/tex]

[tex]\rm\implies b^2 = 64-49\\[/tex]

[tex]\rm\implies b =\sqrt{15}\\[/tex]

[tex]\rm\implies \red{b = 3.9 } \\[/tex]

Hence the distance between the swimming pool and the Library is 3.9 miles .

The cοrrect answer is d. 11.5°, This is because the equatiοn 4x = 46 can be rearranged tο x = 46/4 = 11.5.

An equatiοn is a mathematical statement that describes the relatiοnship between twο values using an equal sign. It cοnsists οf twο expressiοns οn either side οf the equal sign, and the expressiοns must be equal in οrder fοr the equatiοn tο be true. Equatiοns are used tο sοlve prοblems and tο understand hοw different variables interact with each οther.

Fοr example, the equatiοn "2 + 2 = 4" is true because twο plus twο dοes in fact equal fοur. Equatiοns can alsο be used tο represent physical phenοmena, such as the equatiοn F = ma, which describes the relatiοnship between fοrce and mass. Equatiοns can be used tο sοlve many prοblems in mathematics, science, engineering, ecοnοmics, and οther fields.

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A line is breaking a segment into two making two angles, one of the angle is 46° which 4 times the other angle x. Solve for x

a. 4°

b. 4. 5°

c. 6°

d. 11. 5°

The final component, either before or after C, is F.

Ingredients A through F must be combined (left goes first, right goes last). Also, we are aware that: Ingredients A and D are introduced in succession; B is added before to A; and F is not added immediately prior to or following C.

Which component should be inserted last?

The aforesaid issue is easily resolved by doing the following:

Ingredient labeling: A, B, C, D, E, and F

It is given,

Ingredient A is added before D in the order of adding ingredients A and D.

To A, B is added first.

F is no longer put immediately before or after C.

The leftover ingredients are C, E, and F.

F cannot come before or after C because of this.

C can therefore come after D.

component following C = E

Ingredient list = F

The complete question is-

The following table shows the order in which certain ingredients, labeled A through F, need to be mixed (left goes first, right goes last). Additionally, we know that: Ingredients A and D are added in consecutive steps; B is added before A; F is not added right before or after C. Which ingredient needs to be added last?

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The birthday supper cost $94.73 and also the tax rate is $72.72 and was paid by Mr. Shoaf's mother.

A flat charge called valuation tax (VAT) is imposed on a purchase. It resembles a sales tax in the some ways, but unlike with a state taxes, the consumer pays the entire amount due to the government at the moment of sale.

Value added tax is levied by the Dutch government on all products and services. VAT is added by businesses to the sales price to determine the final amount that customers pay. Businesses must pay taxes to the Customs and Tax Administration when goods are sold.

Cost of the meal [tex]= 76.55 -[/tex] (5% of 76.55)

Cost of the meal [tex]= 76.55 - 3.83[/tex]

Cost of the meal [tex]= 72.72[/tex]

calculate tip,

Tip = 25% of the cost of the meal

Tip [tex]= 0.25 *72.72[/tex]

Tip [tex]= 18.18[/tex]

calculate the total amount paid

Total amount paid = cost of the meal + sales tax + tip

Total amount paid [tex]= 72.72 + 3.83 + 18.18[/tex]

Total amount paid [tex]= 94.73[/tex]

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Answer:25 percent​ means ​one fourth​. To calculate 25 percent of a number, simply divide it by 4. For example, 25 percent of 12 is 12 divided by 4, or 3

Answer: B and D

Step-by-step explanation:

Answer:

x ≈ 12.33

Step-by-step explanation:

given 2 secants from an external point to the circle, then the product of the measures of one secant's external part and the entire secant is equal to the product of the measures of the other secant's external part and that entire secant, that is

DC × (DC + x) = BC × (BC + AB) , that is

6(6 + x) = 5 × (5 + 17) = 5 × 22 = 110

36 + 6x = 110 ( subtract 36 from both sides )

6x = 74 ( divide both sides by 6 )

x = 12.33 ( to the nearest hundredth )

Answer: A geometric figure which touches only the sides (or interior) of another figure.

Step-by-step explanation:

its inside but does not go past the innner edges

Therefore, the value of sin105° is: = 0.7123

Value is a measure of the worth or importance of something. It is a subjective measure, as it is based on a person's individual beliefs, experiences, and values. Value can be seen in the monetary cost of a product or service, the quality of a product or service, the time spent on a task, or the amount of effort put into creating something. Value can also be intangible, such as the feeling of having achieved a goal or a sense of accomplishment. Value can be used to assess the worth of something, as well as to determine whether something is worth pursuing or investing in.

The value of sin105° can be determined by applying the compound angles formula. The formula states that the sine of an angle is equal to the product of the sine and cosine of the other two angles that make up the original angle.

For the angle 105°, the two other angles are 75° and 30°. Therefore, the sine of 105° can be calculated as follows:

sin105° = sin75° x cos30° + cos75° x sin30°

Using the values of sin75° and cos30° from a trigonometry table, we can calculate the sine of 105° as:

sin105° = 0.9659 x 0.5 + 0.2588 x 0.5

Therefore, the value of sin105° is:

sin105° = 0.7123

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Answer:

The outcomes when rolling a fair six-sided die are: 1, 2, 3, 4, 5, and 6.

a. The probability of getting a 1, 3, or a 6 is 3/6 or 1/2.

b. The probability of getting a number less than 5 is 4/6 or 2/3.

Answer:

Below

Step-by-step explanation:

You want to divide 81 into (2+1 = 3) parts

   81 / 3 = 27   for each part

    2 parts would be  2 * 27 = 54    

          so 2:1    would be   54:27

There are four numbers: 8, 15, 100 and 123.

Number is a mathematical object used to count, measure, and label. It is used in many different contexts, from everyday life to scientific research. Numbers can be represented in various forms, such as symbols, digits, and words. They are used to represent quantities, distances, time, and other concepts. Numbers can also be used to represent relationships, such as equations, which are statements that describe how two or more things are related.

To solve this problem, it is best to line the numbers up on the y axis or x axis. To multiply the numbers, start by multiplying the numbers on the y axis first. So, 8 x 15 = 120. Then, multiply the result by the number on the x axis which is 100. 120 x 100 = 12,000. Finally, multiply 12,000 by the last number on the x axis which is 123. 12,000 x 123 = 1,476,000. Therefore, the answer to the problem is 1,476,000.

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The greatest possible difference between David's result and Armen's result is 5.

Let's first consider the maximum number of odd shirts Armen can count. Since there are only 5 odd numbers between 1 and 9, the maximum number of odd shirts Armen can count is 1+3+5+7+9 = 25.

Now, let's consider the maximum number of even shirts David can count. Since there are only 4 even numbers between 1 and 9, the maximum number of even shirts David can count is 2+4+6+8 = 20.

Therefore, the greatest possible difference between David's result and Armen's result is

= 25 - 20

Subtract the numbers

= 5

The maximum difference occurs when Armen counts all 5 odd shirts and David counts all 4 even shirts.

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Stockton lake lost the least amount of water.

What is Denominator?

In mathematics, the denominator is the bottom number in a fraction that indicates the number of equal parts into which a whole is divided.

To compare the amount of water lost by each lake, we need to express the amounts lost in the same units. One way to do this is to find a common denominator for the fractions and percentages involved.

Lake Jensen lost 5/6 of its water, which can be expressed as a fraction with a common denominator of 300:

5/6 = 250/300

Lake Parlow lost 85% of its water, which can be expressed as a fraction with a denominator of 100:

85% = 85/100 = 255/300

Lake Stockton lost 246/300 of its water, which is already in terms of a common denominator of 300.

Now we can compare the amounts lost directly:

Lake Jensen lost 250/300 of its water

Lake Parlow lost 255/300 of its water

Lake Stockton lost 246/300 of its water

To determine which lake lost the least amount of water, we need to find the smallest fraction among these three.

We can see that Lake Stockton lost the least amount of water, since 246/300 is smaller than both 250/300 and 255/300. Therefore, Lake Stockton lost the least amount of water.

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The two plans will cost the same if Kira drives 90 miles over the weekend.

The two plans cost the same when Kira drives 90 miles, and the cost of each plan is $72.

To find the mileage for which the two plans cost the same and the cost at that mileage, you should set the cost expressions for both plans equal to each other. After that, you will solve for the mileage (x).

The steps to do this are as follows:Let the mileage be x

The cost of plan 1 (C1) is given by:

C1 = 45 + 0.30x

The cost of plan 2 (C2) is given by:

C2 = 0.80 x

To find the mileage at which both plans cost the same, set C1 equal to C2 and solve for x:

45 + 0.30 x = 0.80 x x (0.30 - 0.80) = - 45- 0.50 x = -45 x = -45/-0.50 x = 90

To find the cost when the two plans cost the same,

substitute x = 90 into one of the expressions for cost.

C1 = 45 + 0.30x = 45 + 0.30(90) = 45 + 27 = $72C2 = 0.80x = 0.80(90) = $72

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For the equation [tex]x^8-1=0[/tex], the graph with magnitudes of the roots is plotted on complex plane.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The equation is given as [tex]x^8-1=0[/tex].

We can start by factoring the left-hand side of the equation using the difference of squares formula -

[tex](x^4 - 1)(x^4 + 1) = 0[/tex]

Now we have two factors that can each be set equal to zero and solved separately -

[tex]x^4 - 1 = 0[/tex] or [tex]x^4 + 1 = 0[/tex]

The first equation can be factored as a difference of squares again -

(x² - 1)(x² + 1) = 0

Setting each factor equal to zero gives -

x² - 1 = 0 or x² + 1 = 0

These equations have solutions x = ±1 and x = ±i, respectively.

For the second equation, we can use the fact that i^2 = -1 to rewrite it as -

[tex]x^4 + 1 = (x^2)^2 + 1 = (x^2 + i)(x^2 - i) = 0[/tex]

Setting each factor equal to zero gives -

x² + i = 0 or x² - i = 0

These equations have solutions [tex]x = \pm i\sqrt{2}[/tex] and [tex]x = \pm i\sqrt{-2} = \pm i\sqrt{2i} = \pm \sqrt{2}i[/tex], respectively.

Therefore, the complete set of solutions to the original equation is -

x = ±1, ±i, ±i√(2), ±√2 i

To find the magnitudes of these roots, we can use the formula -

|a + bi| = √(a² + b²)

For example, the magnitude of the root x = i is -

|i| = |0 + 1i| = √(0² + 1²) = 1

Similarly, we can find the magnitudes of the other roots -

|x| = 1 for x = ±1, ±i

|x| = √2 for x = ±i√(2)

|x| = √2 for x = ±√2 i

To draw these roots on the complex plane, we can plot them according to their real and imaginary parts.

The roots ±1 and ±i lie on the unit circle centered at the origin, while the roots ±i√(2) and ±√2 i lie on circles centered at the origin with radii equal to √2.

Therefore, the roots are plotted in complex plane.

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simple interest would produce ₹ 9000 as interest in 2 years? Rate = 12% p.a. Principal = ? Hence, the required principal amount = ₹ 37500

Answer:

SI=P*R*T/100

SI=9000*12*2/100

SI=2160

TOTAL AMOUNT=2160+9000=11160

The sine of the angle passing through point E on the circle is given as follows:

sin(x) = 24/25.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

The equation of the circle is of x² + y² = 625, meaning that the radius, representing the hypotenuse, is of 25 units.

The center of the circle is of (0,0), hence the opposite side to the angle has length of 24 - 0 = 24 units, hence the sine of the angle is given as follows:

sin(x) = 24/25.

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Well, I do agree that if k is a real number, then the compound inequality xk's solution set contains only real numbers.

A sentence with two inequality statements connected by the words "or" or "and" is referred to as a compound inequality. The word "and" indicates that both claims in the compound sentence are true at the same time. It occurs when the multiple statement's solution sets overlap or intersect. Compound inequalities are those that have the conjunctions "and" or "or" between them. It should be understood that plimb[/[/ofs (Ors Or/ Orss ultras "is larger than -2 and less than or equal to 5" should be translated as 2 x 5. x is greater than or equal to 3 or equal to -4, or "x 3." You'll observe that each of these differences has two inequality signals. Inequality that is compounded by two or more factors.

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a) 6272640 cubic inches of water fell on the lot

b) 3630 cubic feet of water fell on the lot

c) the weight of the water that fell on the lot = 112.53 tons

d) gallons of water fell on the lot = 27,115.7 gallons

460 acre=1 [tex]mi^{2}[/tex]

1 acre=1/460 [tex]mi^{2}[/tex]

1 mi=5280 ft

1 mi2=5280×5280[tex]ft^{2}[/tex]

1 acre=(5280×5280)/460

1 acre= 43560 sq ft

As one inch is equal to one-twelfth of a foot, one acre of water that is 1 inch deep takes up 3630 cubic feet (43560×(1/12)).

One cubic foot is equal to 12 inches by 12 inches by 12 inches,

or 12×12×12=1728 cubic inches.

6272640 cubic inches are contained in 3630 cubic feet, or 3630 × 728.

Hence, 6272640 cubic inches of water fell on the lot.

If 1 inch of rain fell over your one acre lot, 3630 cubic feet of water fell on the lot.

3630 times 62 is 225,060 pounds, the weight in pounds.

We are aware that a tons weighs 2000 lb.

225060/2000 = 112.53 tons

Hence, the weight of the water that fell on the lot=112.53 tons.

If there are around 8.3 pounds in 1 gallon of water,

Number of gallons of water fell on the lot

=225060/8.3

=27,115.7 gallons

Hence, gallons of water fell on the lot=27,115.7 gallons.

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The volume of the rectangular inflatable swimming pool is approximately 29.4 cubic yards.

The volume of an object is the amount of space it occupies in three dimensions, typically measured in cubic units. In this case, we're trying to find the volume of a rectangular pool that is 3 yards long, 14/5 yards wide, and 7/2 yards tall.

To find the volume of a rectangular object, we use the formula:

Volume = length x width x height

In this case, we can plug in the values we have:

Volume = 3 yards x 14/5 yards x 7/2 yards

To simplify the calculation, we can convert the fractions to decimals:

Volume = 3 yards x 2.8 yards x 3.5 yards

Volume = 29.4 cubic yards

In this case, the second decimal place is a 4, so we leave the digit in the first decimal place (9) as-is.

Therefore, we round our answer to 29.4 cubic yards to the nearest tenth.

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The probability that at least 29% of the sample are from poverty-level households is 0.17% and we do not have enough evidence to reject the null hypothesis that the population proportion is equal to 22%.

According to government data, 22% of American children under the age of 6 live in households with incomes less than the official poverty level. A study of learning in early childhood chooses an SRS of 300 children from one state and finds that at least 29% of the sample are from poverty-level households.

To answer part (a) of the question, we can use the normal approximation to the binomial distribution. The mean of the distribution is np = 300 * 0.22 = 66 and the standard deviation is sqrt(np(1-p)) = sqrt(66 * 0.78) = 7.09. We can use the normalcdf function to find the probability that at least 29% of the sample are from poverty-level households:

normalcdf(87.5, 300, 66, 7.09) = 0.0017

So the probability is 0.17%.

For part (b) of the question, we need to determine if there is convincing evidence that the percentage of children under the age of 6 living in households with incomes less than the official poverty level in this state is greater than the national value of 22%.

Since the probability that at least 29% of the sample are from poverty-level households is 0.17%, which is very small, we can conclude that there is not convincing evidence that the percentage of children under the age of 6 living in households with incomes less than the official poverty level in this state is greater than the national value of 22%.

The small probability suggests that the observed sample result is unlikely to occur by chance if the true population proportion is 22%, so we do not have enough evidence to reject the null hypothesis that the population proportion is equal to 22%.

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Answer:

(3, 8)

Step-by-step explanation:

Coordinate (-3, -8)

Reflect across the y-axis. The x will change to the opposite, and the y will remain the same. So, the coordinate is (3, -8)

Then reflect the result across the x-axis. The y will change to the opposite, and the x will remain the same. So, the coordinate is (3, 8)

So, the coordinate of the final point is (3, 8)

Hence, in response to the provided question, we can say that As a result,  function the discus takes approximately 0.03125 seconds to strike the ground.

Mathematicians research numbers and their variants, equation and related structures, objects and their locations, and prospective locations for these things. The term "module" is used to describe the connection that exists in between set of inputs, each of which has a corresponding output. A function is an input-output connection in which each inputs results in something like a single, distinct return. A domain, codomain, or scope is assigned to each function. Functions are usually denoted by the letter f. (x). An x is used for entry. On capabilities, one-to-one capabilities, multiple prowess, in capabilities, and on capabilities are the four major types of accessible functions.

The supplied function for discus height is as follows:

[tex]h(t) = -16t^2 + 38t + 5\\h(0) = -16(0)^2 + 38(0) + 5 = 5[/tex]

As a result, the discus's starting height is 5 feet.

[tex]-16t^2 + 38t + 5 = 0\\[/tex]

To find t, we can apply the quadratic formula:

t = (-b \sqrt(b2 - 4ac)) (2a)

where a=-16, b=38, and c=5.

[tex]t = (-38 + \sqrt(38^2 - 4(-16)(5))) / (2(-16))\\t = (-38 + \sqrt(1524)) / (-32) (-32)\\t = (-38 + 39) / (-32) (-32)\\[/tex]

As a result, [tex]t = (-38 + 39) / (32) or t = (-38 - 39) / (32) (-32)[/tex]

t = 1/32 or t = 77/32

As the negative value doesn't make sense in this situation, we chose the positive value:

t = 1/32

As a result, the discus takes approximately 0.03125 seconds to strike the ground.

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