Find the surface area of a square pyramid with side length 1 km and slant height 2 km.

The domain of a function can be determined​ by getting the set of input values of the function it can take

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

The definition of a function

As a general rule

The domain of a function is the set of input values of the function

Take for instance, the domain of y = x + 2 is all real number

This is so because it can accept all real numbers as its input

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(i) Probability is a notion in Mathematics which describes the likelihood of an event or a set of events occurring. It is a measure of uncertainty when estimating the outcome of an experiment or an observation.

(ii) The axioms of probability are:

the non-negativity (that the probability of an event is greater than or equal to zero), and

the additivity (that the probability of the union of two or more mutually exclusive events is equal to the sum of their individual probabilities).

(iii) When two fair dice are thrown the probability of getting:

a) The sum of 9 = 1/9

b) Two odd numbers = 1/4

c) two prime numbers = 1/9

d)  two factors of 12 = 1/9

(iv) Statistics is a branch of mathematics that deals with data collection, analysis, interpretation, presentation, etc.

To find probability when two dice are thrown, we have:

(a) The sum of 9:

We will estimate the number of ways to get a sum of 9: (3,6), (4,5), (5,4), and (6,3) = 4 ways

A die has 6 possible outcomes, the total number of possible outcomes is 6x6=36 = 4/36 = 1/9.

(b) Two odd numbers:

We count the number of ways to get two odd numbers: (1,3), (1,5), (1,7), (3,1), (3,5), (3,7), (5,1), (5,3), and (5,7).

possible outcomes = 9,

So, the total possible outcomes = 6x6=36 = 9/36 = 1/4.

(c) Two prime numbers

We estimate the number of ways we can get two prime numbers: (2,3), (3,2), (5,2), and (2,5)

possible outcomes = 4,

So, the total possible outcomes = 6x6 =36 = 4/36, = 1/9.

(d) Two factors of 12:

We count the number of ways and divide by the total possible outcomes.

The factors of 12 are 1, 2, 3, 4, 6, and 12: (2,6), (3,4), and (4,3) = 3 ways

possible outcomes = 6

Therefore, the total number of possible outcomes = 6x6=36 = 3/36, = 1/12

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The ratio of apple oranges and bananas cannot be calculated with the given information

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

Fruits = Orange, Bananas and Apple

Total number of fruits = 48

The available parameters is not enough to determine the ratio

Assuming that we have

Banana = 10

Orange =  20

Apple = 18

Then the ratio would be:

Apple : oranges : bananas = 18 : 20 : 10

Simplify

Apple : oranges : bananas = 9 : 10 : 5

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The quantity of cats that will be in the pet daycare when there are 40 dogs would be = 120 cats.

Ratio can be defined as the comparison of two values that shows the amount of one value that can be found in the other value.

The initial amount of dogs = 20

The initial amount of cats = 60

The final amount of dog = 40

The final amount of cats = ?

That is;

20 dogs = 60 cats

40 dogs = X cats

make X the subject of formula;

X = 40×60/20

= 2400/20

= 120 cats

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The measures of the angles are ∠1 = 35 and ∠2 = 30

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

The figure

Using the sum of opposite internal angles in a triangle, we have

∠1 + 80 = 115

Subtract 80 from both sides

So, we have

∠1 = 35

Using the same theorem of sum of opposite internal angles in a triangle, we have

∠2 + 85 = 115

Subtract 85 from both sides

So, we have

∠2 = 30

Hence, the angles are ∠1 = 35 and ∠2 = 30

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The value of c as per the law of cosines, to the nearest tenth, is 5.1 units.

Given information:

a = 8, b = 9 C = 34°.

To find the value of C:

According to the Law of Cosines, for any triangle ABC:

c² = a² + b² - 2ab cos(C)

Substituting the given values:

c² = 8² + 9² - 2(8)(9) cos(34°)

c² = 64 + 81 - 144 cos(34°)

c² = 145 - 144 cos(34°)

Taking the square root of both sides:

c = √(145 - 144 cos(34°))

Using a calculator:

c ≈ 5.1 units (rounded to the nearest tenth)

Therefore, the value of c is approximately 5.1 units.

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If 75% of Brannan's class attended her twelfth birthday party, we can find the number of students who came to the party by multiplying the total number of students in the class by the percentage that attended.

First, we need to convert 75% to a decimal by dividing by 100:

75% = 75/100 = 0.75

Next, we can multiply the total number of students in the class by the decimal that represents the percentage who attended:

Number of students who came to the party = 0.75 * 24

Number of students who came to the party = 18

Therefore, 18 students came to Brannan's twelfth birthday party.

The value of the expression is 2x³ + 3x² - 27x + 40

It is important we know that algebraic expressions are described as expressions that are composed of factors, constants, variables, coefficients and terms.

Algebraic expressions are also made up of arithmetic operations, such as;

From the information given, we have;

1. (x + 5)(2x² -7x + 8)

expand the bracket

2x³ - 7x² + 8x + 10x² -35x + 40

collect like terms

2x³ - 7x² + 10x² + 8x - 35x + 40

Add the like terms

2x³ + 3x² - 27x + 40

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Answer:

x+y-7=0

Step-by-step explanation:

y=-(x-3)+4

y=-x+3+4

y=-x+7

x+y-7=0

The volume of the pyramid is  9333 cubic centimetres

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

Base dimensions = 40 cm by 20 cm

Height = 35 cm

The volume of the pyramid is calculated as

Volume = Product of Base dimensions and Height/3

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

Volume = 40 * 20 * 35/3

Evaluate

Volume = 9333

Hence, the volume is 9333

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The proof for  AB ≅ CD is:

Step                 Statement                                Reason

 1              ∠B ≅ ∠D, BC || AD                          Given

 2               ∠BCA ≅ ∠CAD                Alternate Interior angles

 3                      AC ≅ AC                             common side

 4                 ΔABC ≅ ΔADC         Angle-Angle-Side rule of congruency

 5                   AB ≅ CD            Corresponding sides of congruent triangle

Consider triangle ABC and triangle ADC.

Here, side BC is parallel to side AD.

From the attached figure we can observe that AC is a transversal.

so, ∠BCA and ∠CAD would be alternate angles formed by two parallel lines and transversal.

By property of  Alternate Interior angles,

∠BCA ≅ ∠CAD

Also, we can observe that side AC is common side to ΔABC and ΔADC.

We rewrite this proof as,

Step                 Statement                                Reason

 1              ∠B ≅ ∠D, BC || AD                          Given

 2               ∠BCA ≅ ∠CAD                Alternate Interior angles

 3                      AC ≅ AC                             common side

 4                 ΔABC ≅ ΔADC         Angle-Angle-Side rule of congruency

 5                   AB ≅ CD            Corresponding sides of congruent triangle

This is the required proof.

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The amounts needed to make 6 servings are given as follows:

Sauce: 12 servings.

Oregano: 3/4 teaspoons.

Here, we have,

The needed amounts to make 6 servings of the recipe are obtained applying the proportions in the context of the problem.

From the first line of the table, we get the amounts of sauce and oregano per serving are follows:

Sauce: 8/4 = 2 cups.

Oregano: 0.5/4 = 1/8 teaspoons per serving.

Hence the amounts for six servings are given as follows:

Sauce: 6 x 2 = 12 servings.

Oregano: 6 x 1/8 = 6/8 = 3/4 teaspoons.

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Answer:

90 children's tickets and 200 adult tickets were sold.

Step-by-step explanation:

Let's use the variables c and a to represent the number of children's and adult tickets sold, respectively.

From the problem, we know that:

The total number of tickets sold is 290: c + a = 290

The total revenue from ticket sales is $2250: 5c + 9a = 2250

We now have two equations with two unknowns. We can use substitution or elimination to solve for c and a. Here's one way to use elimination:

Multiply the first equation by 5 to get 5c + 5a = 1450

Subtract the above equation from the second equation to eliminate c: 5c + 9a - (5c + 5a) = 2250 - 1450

Simplify: 4a = 800

Solve for a: a = 200

Substitute a = 200 into the first equation to solve for c: c + 200 = 290

Simplify: c = 90

Therefore, 90 children's tickets and 200 adult tickets were sold.

The calculated surface area of the triangular prism is 976 square meters

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

The dimensions of the triangular prism

The surface area of the triangular prism is the sum of the individual shapes

So, we have the following formula

Surface area = Area of rectangle + Area of the 2 triangles + Area of the 2 rectangles

Using the dimensions, we have

Surface area = 10 * 14 + 2 * 1/2 * 24 * 14 + 2 * 25 * 10

Evaluate

Surface area = 976

Hence, the surface area is 976

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From the data given, we can see that as you move upward in the atmosphere from sea level, the temperature generally decreases such as from 28 degree to negative degree.

This is because earth atmosphere is heated from bottom-up by the Earth's surface, so, the nearest air to the ground is warmer than the air at higher altitudes. When we climb higher, the air pressure decreases and this causes the air to expand and cool.

This decrease in temperature with increasing altitude is known as the adiabatic lapse rate, but this is known to vary depending on factors such as humidity and atmospheric conditions.

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The amount for one dose of IV vancomycin for this child is 350 mg.

The recommended dosage of IV vancomycin is 40 mg/kg/day divided q6h.

The child weighs 35 kg.

To calculate the amount for one dose, we need to first calculate the total daily dose and then divide it by the number of doses per day.

Total daily dose = 40 mg/kg/day x 35 kg = 1400 mg/day

Since the medication is divided q6h (every 6 hours), there are 4 doses per day.

Amount for one dose = Total daily dose / Number of doses per day

= 1400 mg/day / 4 doses per day

= 350 mg/dose

Therefore, the amount for one dose of IV vancomycin for this child is 350 mg.

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The measure of angles ∠1, ∠3, and ∠4 will be 131°, 131°, and 49°, respectively.

Given that:

∠2 = 49°

The measure of angle ∠1 is calculated as,

∠1 + ∠2 = 180°

∠1 + 49° = 180°

∠1 = 131°

The measure of the angles ∠3 and ∠4 is calculated as,

∠3 = ∠1

∠3 = 131°

∠4 = ∠2

∠4 = 49°

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The solution is,  $ 12833 .59 will he have in the account after 5 years.

Compound interest is a type of interest that is calculated not only on the principal amount of a loan or investment, but also on any interest that has previously accrued. In other words, it is interest that is earned on both the initial principal and any interest that has been added to it over time.

by the question.

We can use the formula for compound interest to solve the problem:

A = P

where:

A = final amount (x in this case)

P = principal or initial amount ($10,000.00)

r = annual interest rate (5% in this case)

n = number of times the interest is compounded per year (12, since it's compounded monthly)

t = time in years (5, since Tyrone opened the account 5 years ago)

Substituting the values given, we get:

A = $ 12833 .59

The solution is,  $ 12833 .59 will he have in the account after 5 years.

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Answer:

Step-by-step explanation:

The population density of the neighborhood is 12000 people per square mile.

Total number of people = 1250

Number of city blocks = 30

Length of the block, l = 1/16 mile

Width of the city block, w = 1/18 mile

Area of one block, A = l x w

A = (1/16) x (1/18)

A = 1/288 square mile

Total area of all the 30 blocks, A' = 30 x A

A' = 30/288 square mile

So, the population density,

D = Total no.of people/A'

D = 1250/(30/288)

D = 1250 x 288/30

D = 12000 people per square mile.

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Answer: c

Step-by-step explanation: I’m smart

Answer:

The answer would be 3.5 in decimal form.

Answer:

The answer is 55/12

Step-by-step explanation:

8-41/12

(8×12+1×(-41))/12

(96-41)/12

55/12

Answer: (f+g)(x) = x² + 3x - 10

Step-by-step explanation:

Answer:

Think about the PEMDAS rules for order of operations.

Multiplication comes before addition or subtraction, so first we have "the product of a number and 5" - that's 5x. Then "six more" than that would be 5x + 6. "Equals" means the "=" sign, so the final answer is 5x + 6 = 8.

The requried measure of the side QT in triangle SQT is 59 units.

A figure is shown with two triangles, SQT and SQR.

Since in the question we are given to RS = ST 81, QR = v + 33, and QT = 3v 19,

As RS = St and SQ is a common side both the triangle are congruent, QT = QR

v + 33 = 3v - 19
52 = 2v
v = 26

Now,
QT = 3(26) - 19
QT = 59

Thus, the requried measure of the side QT in triangle SQT is 59 units.

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The polynomial long division of (5x^4 − 2x^3 − 7x^2 − 39) ÷ (x^2 + 2x − 4) gives a quotient of 5x^2 - 12x + 37

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

(5x^4 − 2x^3 − 7x^2 − 39) ÷ (x^2 + 2x − 4)

Using the polynomial long division setup, we have

x^2 + 2x − 4   |  5x^4 − 2x^3 − 7x^2 − 39

Evaluating the division, we have

                         5x^2 - 12x + 37

x^2 + 2x − 4   |  5x^4 − 2x^3 − 7x^2 − 39

                         5x^4  + 10x^3 - 20x^2

                         ---------------------------------------

                                      -12x^3 + 13x^2 - 39

                                      -12x^3 - 24x^2 - 48

                         ---------------------------------------

                                                    37x^2 + 9

                                                    37x^2 + 74x - 148

                         ---------------------------------------

                                                    -74x + 157

Hence, the quotient is 5x^2 - 12x + 37

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Answer:

The correct answer is C

Step-by-step explanation:

The statements can be arranged correctly as follows:

1. Word Form shows a number written in words.

2. Standard form shows a number written using digits.

3.  Digit is one of the numerals from 0 to 9

4. Place value the position of a digit in a number, which determines its value.

5.  Period each three-digit part of a whole number, separated by commas

6. Expanded form shows a number written as an addition statement

We can determine the terms by first understanding the mathematical meanings. Word form is a term used in math to denote expressions written in word B.

Also, the standard form is a way of shortening large numerical values using digits. Digits are single numbers that run between 0 to 9 and they make up the higher values of numbers.

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Answer:

Step-by-step explanation:

True

187, 500 ml are needed to prepare 750 mg from 1:250.

We have to find amount in ml to prepare 750 mg from 1:250.

let the amount needed in ml be x.

Using proportion

1/750 = 250 / x

x= 750 . 250

x= 187, 500 ml

Thus, to prepare 750 mg 187,500 ml is needed.

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