For this problem, write the numbers in scientific notation. 2,156 A. 21.56 × 102 B. 2.156 × 103 C. 2.156 × 102

Answer:5.3

Step-by-step explanation:

using the Pythagorean theorem 8²-6²=28    √28=5.3

5

Step-by-step explanation:

Pythagoras theorem states that

a²+b²=c²

therefore a²=b²-c²

a²=8²-6²

a=√8²-6²

=√64-36

=√28

=5.3 or approximately 5

Answer:

x=10.5

Step-by-step explanation:

The new function p(x) =  2x³+3x²-23x-12  is the product of expressions x+4, x-3, and 2x+1

A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input

Given: the expressions x+4, x-3, and 2x+1

The product of the expressions  is:

p(x) = (x+4)(x-3)(2x+1)

      = (x²-3x+4x-12)(2x+1)

     =  (x²+x-12)(2x+1)

    = 2x³+2x²-24x+x²+x-12

   =  2x³+3x²-23x-12

Therefore, the new function is p(x) =  2x³+3x²-23x-12.

Since the new function is a polynomial, it demonstrates the Fundamental Theorem of Algebra which states that every polynomial equation of degree n with complex number coefficients has n roots, or solutions, in the complex numbers

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Answer: 0.8

Step-by-step explanation:

Answer:

[tex]-4i\sqrt{3}[/tex]

Step-by-step explanation:

Answer:

[tex] - 4 \sqrt{3i} [/tex]

The price of ticket will be $26 approximately in 2009 using the concept of the linear equation and slope.

Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is fairly simple (x and y). When attempting to solve systems of two linear equations, this form is also very helpful.

Here,

The line has 2 points,

(2001,18) and (2005,22)

m=(22-18)/(2005-2001)

m=1

y-y1=m(x-x1)

y-18=x-2001

x-y=1983

(2009,y) is on that line,

2009-y=1983

y=26

Using the idea of the linear equation and slope, the ticket price in 2009 will be approximately $26.

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Answer:

about 77.2°

Step-by-step explanation:

The figure is omitted--please sketch it.

Make sure your calculator is in degree mode.

[tex] \cos( \alpha ) = \frac{2}{9} [/tex]

[tex] \alpha = {cos}^{ - 1} \frac{2}{9} = 77.2[/tex]

77.2 degrees

Answer:

m+n=x/p

p×(m+n)=(x/p)×p

x=pm+pn

The amount to be paid to the broker is 2167.025. Therefore option b is correct.

Percentage:

A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction. All of something is 100 percent, half of it is fifty percent, and none of something is zero percent. To determine a percentage, you divide the portion of the whole by the whole itself and multiply by 100.

Here we have to find the amount to pay to the broker.

The given values are:

Market rate = 86.681

The commission charges by broker = 2.5%

The broker has to pay = 86.681 × 2.5% × 1000

                                     = 86.681 × 2.5/100 × 1000

                                    = 86681 × 0.025

                                    = 2167.025

Therefore the amount paid to the broker is 2167.025.

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Answer:

B

I got it right

Step-by-step explanation:

The answer is 237.55

Define Percentage

A ratio or figure stated as a fraction of 100 is called a percentage. Although the abbreviations "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.

Given expression is,

125.8% of £188.83

Rewrite it as,

⇒ 125.8 / 100 * 188.83

⇒ 1.258 * 188.83

⇒ 237.54814

⇒ 237.55 (rounded to 2 Decimal places)

Hence, the answer is 237.55

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If increase the amount of the ingredients by 5 and by 20 is 51.75 grams and 207 grams respectively.

Given that, Ingredients: 2 teaspoons Worcestershire sauce

Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.

Converted to Metric measurements : 10.35 g

Increased by 5 = 10.35 × 5

= 51.75 grams

Increased by 20 = 10.35 × 20

= 207 grams

Therefore, if increase the amount of the ingredients by 5 and by 20 is 51.75 grams and 207 grams respectively.

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Answer:

B.

Step-by-step explanation:

The area of one triangle is 28 cm².​

From the question, we have

area = 1/2*base*height

=  1/2*8*7

=28 cm².

Multiplication:

In mathematics, multiplying the numbers is used to find the product of two or more numbers. We carry out one of the basic mathematical operations on a regular basis. The main application that is obvious is using multiplication tables. Mathematicians use the multiplication of two integers to express the repeated addition of one number to another. These numbers can be natural numbers, fractions, integers, whole numbers, etc. M is either added to itself 'n' times or subtracted from itself when m is multiplied by n.

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The number of student like at least one kind of ice cream is given by (d) 275.

Let C be the student who like chocolate ice cream and P be the student who like Pistachio ice cream.

Now given that, n(C) = 145, n(P) = 150

Also given that, 123 students do not like neither chocolate or pistachio ice cream.

So, n(P' and C') = 123

The required number of student like at least one kind of ice cream is given by,

N = 398 - n(P' and C') = 398-123 = 275

Hence the correct option is (d).

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After simplification, the value of y is 7 when x=9.

In the given question, if y varies inversely as x and y=3 when x=21, find y when x=9.

From the given question y varies inversely as x i.e.

y ∝ 1/x

When we remove the inversly sign then their is one variable should be added. Let the variable should be k.

Now the expression is

y = k/x

As we know that y=3 when x=21.

Now putting the value.

3 = k/21

Multiply by 21 on both side, we get

k = 3*21

k = 63

Now the value of k is 63.

Now finding the value of y when x=9

y = 63/9

y = 7

Hence, the value of y is 7 when x=9.

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Answer:

4x + y = 21

Step-by-step explanation:

1. distribute in the parenthesis first, so the right side of the equation is not -4x+24

Right now the total equation looks like y+3 = -4x+24

2. Now we add the 4x to both sides to cancel it out on the left side, so we're left with:

4x+y+3=24

3. After that we can subtract the 3 from both sides to leave us with:

4x+y=21

The triangles are congruent by ASA(angle side angle) theorem

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.

In other words, triangles are congruent when they have exactly the same three sides and exactly the same three angles.

There are different ways to find that out that triangles are congruent.

If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

Therefore, the triangles are congruent by ASA(angle side angle) theorem.

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Answer:

Math: the science and study of quality, structure, space, and change.

a)The probability of exactly 5 accidents will occur is 0.1008.

b) The probability of fewer than 3 accidents will occur is 0.42318.

It is predicated on the likelihood that something will occur. The justification for probability serves as the basic foundation for theoretical probability. For instance, the theoretical chance of receiving a head while tossing a coin is 12. Mathematics' study of random events is known as probability, and there are four primary types of probability: axiomatic, classical, empirical, and subjective. Since probability is the same as possibility, you could say that it is the likelihood that a specific event will occur.

Given,

Mean = 3

a) By using Poission probability formula,

P( X = 5) = e⁺³ (3)⁵/5!

P(X = 5) = 0.1008

The probability of exactly 5 accidents will occur is 0.1008.

b) fewer than 3 accidents will occur:

P( X <3) = e⁻³ (3)⁰ + e⁻³ (3)¹ + e⁻³(3)²

P( X< 3) = 0.4978 + 0.14936 + 0.22404

P( X < 3) = 0.42318

The probability of fewer than 3 accidents will occur is 0.42318.

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A. The expression in the simplest form that represents the amount (in dollars) it costs to adopt x dogs is 195x

B. The coefficient of the expression in part (a) represents D. The the total amount the animal shelter earns when x dogs are adopted

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

In this situation, to adopt a dog from an animal shelter, you must pay $80 for vaccinations, $65 to spay or neuter the dog, and $50 for a wellness exam by a veterinarian.

Therefore, the expression to adopt x dogs will be:

= 80(x) + 65(x) + 50(x)

= 80x + 65x + 50x

= 195x

This is the cost for x dogs.

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The way that one number in the second equation be changed so the system has only one solution is;  to divide each term by 2 to get the coefficient of y as 5.

There are different methods to solve simultaneous equations such as;

We are given the equations as;

3x + 5y = 4

16x + 10y = 4

Now, we want to perform an operation whereby we make the second equation be changed so the system has only one solution. This method is the elimination method.

The elimination method is the process that we use to eliminate one of the variables in the system of linear equations with the aid of the addition or subtraction methods as well as multiplication or division of coefficients of the variables.

Now, since we have 5y in the first equation, the first step to carry out on the second equation is to divide each term by 2 to get the coefficient of y as 5.

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a. The system of inequalities that best represent how much of the agricultural products of soybeans and corn the river barge can carry is

b. option A

c. The river barge can safely ship the agricultural products

information gotten from the question include

Corn weighs about 60 pounds per bushel

soybeans weigh about 90 pounds per bushel

A river barge can safely carry up to 4,500,000 pounds of cargo.

Let x = bushels of corn and y = bushels of soybeans.

a. From the statement, it can be deduced that the equation is

A. 60x + 90y ≤ 4,500,000, x ≥ 0, y ≥ 0

b. some interpretation on inequality

from the interpretation

the correct option is A (graph attached)

c. 60 * 24000 + 90 * 24000

= 3,600,000

The value is ≤ 4,500,000 hence the river barge can carry it

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The number of different sequences of stops that the driver can make is 24.

Permutation is simply used it illustrate the number of ways for a given information. The formula is illustrated as:

n! / (n – r)!

N is the number of things you are choosing from,

r is the number of items.

“!” is a factorial of a number

Since the delivery truck has 4 stops to make in a neighborhood, the sequences of stops will be:

= n! / (n – r)!

= 4!

= 4 × 3 × 2

= 24 stops.

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Answer: it is not 27%

Step-by-step explanation:

The members who have registered for both batting and fielding are 306.

The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other terms, it is a relationship where the worth of the entire is always considered to be 100.

Total members = 850

Number of members registered for batting = 80%

Number of members registered for fielding = 56%

Members who participated in both,

80% of 850 + 56% of 850 - x = 850

680 +476 -x = 850

x = 1156 - 850

x = 306.

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Main Answer:

The constant term of h(x) is 4x^3 - 16x^2 - 75x - 63\

Supportive Question and Answer:

What is an Algebraic Expression?

An expression that includes variables, constants, and algebraic operations is an algebraic expression in mathematics (addition, subtraction, etc.). Terms combine to form expressions.

Solution Explained:
Given,
h(x) = f(x).g(x)

h(x) = (x-7)(2x+3)^2

now, simplify,

(x-7)(2x +3)                                                    Expand the expression
           

(x-7)((2x)^2+2 X 2x X 3+3^2)                        Simplify the expression

(x-7)(2^2 X x^2 +2 X 2x X 3+3^2)                Calculate

(x-7)(4x^2+2 X 2x X 3 + 9)                            Mutiply

(x-7)(4x^2 + 12x + 9)                                       Expand the expression

x X 4x^2 + x X 12x + x X 9 - 7 X 4x^2 - 7 X 12x -7 X 9       Mutiply

4x^3 + 12x^2 + 9x - 28x^2 84x - 7 X 9           Calculate

4x^3 + 12x^2 + 9x - 28x^2 - 84x - 63                    Combine like terms

Hence, the constant term for h(x) is 4x-16x-75x 63.

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Answer:

DEFG = (1/2)a^2

Step-by-step explanation:

tells us ∠FDG = 45° and ∠EGD = 45° and by corresponding angles related to parallel lines ∠FBD = 45°. Then ∠DFB = 90°!

So DFB- (1/2)(DF)(FB)=(1/2)a2

The initial amount of the deposit is $7234.23

Compound interest is calculated on a deposit's or a loan's initial principal as well as the accrued interest from earlier periods. Compound interest's impact is frequency-dependent. The most frequent compounding occurs with continuously compounded rewards. The mathematical maximum that compound interest can achieve is continuous compounding. Since most interest is compounded on a monthly, quarterly, or semiannual basis, this is an extreme example of compounding.

For compound continuous problems, we use the formula [tex]A = Pe^{rt}[/tex]

where A = final amount

P = principal amount invested

e = exponent

r = rate of interest

t = time period in years

[tex]12680 = Pe^{.08(7)} \\12680 = Pe^{0.56}\\ 12680 = P*1.7506\\[/tex]

P = $7243.23

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GIVEN :

TO FIND :

OPTIONS :

(A) 20 ducks, 15 buffalo

(B) 15 ducks, 20 buffalo

CASE (i) - 20 ducks, 15 buffalo

= 20·2 + 15·4

= 40 + 60

= 100

CASE (ii) - 15 ducks, 20 buffalo

= 15·2 + 20·4

= 30 + 80

= 110

FINAL ANSWER :

Therefore, the number of ducks are 15 and 20 buffalo.

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