If the exponent of the leading term of the numerator is higher than the exponent of the leading term of the denominator, what can we conclude?.

If the cake can be represented as 1 = 10/10, that means we can find out how much cake is left by taking and then subtracting the amount Samuel ate. The expression [1 - 1/10] represents this situation.

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

Cake = 1 or 10/10

Samuel's bite = 1/10

The amount remaining is calculated as

Amount remaining = Cake - Samuel's bite

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

Amount remaining = 1 - 1/10

The above represents the required expression

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Answer:

1/ We use the SSS method to prove that triangle CBD = triangle ABD

2/ We use the AA method to prove that <CBD equal < ABD

Step-by-step explanation:

1/ SSS, or side side side method, is the method we use to see if triangles are the same or not, and we know that the sides of both triangles are equal; this proves that both triangles are equal!

2/ AA, or Angle Angle method, is the method we use to see if the angles of triangles are the same or not, and we know that there are marks at <C and <A, these marks prove that both angles are equal! So, <CBD equal <ABD

Solution is 225/42 or 5.35

According to question

5 6/7 + (-2 1/3) + 1 5/6

As it is a mixed fraction we will first solve it

To solve it denominator will get multiplied with the whole number and the solution will be get added to the numerator and the new numerator will get formed.

∴ 41/7 +(-7/3) + 11/6

⇒246-98+77/42.                              (LCM of 7,3,6 is 42)

⇒225/42

∴5.35

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The common difference in the sequence 7, 12, 17, 22, 27,… is that the difference between two numbers increases by five in the ascending order.

A sequence can be referred to or considered as the set of observations, which usually consists of numbers arranged in such a way that they described a common characteristic between them. A sequence can be exhaustive or inclusive, depending upon the numbers being used in the continuity of the sequence. It can also be said that a sequence is a logical arrangement.

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Complete question

what is the common difference in the sequence 7, 12, 17, 22, 27, ...?

Answer:

Step-by-step explanation:

The greatest common divisor of two integers a and b is a divisor common to both integers that is greater than any other common divisor. The least common multiple of two integers a and b is the smallest positive integer that is a multiple of both a and b.

To find the smallest possible value of a+b, we can start by trying to find the smallest possible values of a and b that satisfy the given conditions.

Since the greatest common divisor of a and b is 5, we know that both a and b must be divisible by 5. We can write a = 5x and b = 5y, where x and y are positive integers.

The least common multiple of a and b is 55, so we know that both a and b must be factors of 55. We can write 55 as the product of its prime factors: 55 = 5 * 11. Since a is divisible by 5, we know that a must be equal to 5 or 25. Similarly, since b is divisible by 5, we know that b must be equal to 5 or 25.

There are four possible pairs of values for a and b: (5,5), (5,25), (25,5), and (25,25). The smallest of these is (5,5), which gives us a+b = 5+5 = 10. Therefore, the smallest possible value of a+b is 10.

Using the arithmetic progression, If a theatre has 30 rows of seats there are 22 seats in the first row,21 in the second row, 51 in the third row, then the total number of people that the theatre hold is 2400

The total number of rows = 51

Number of seats in the first row = 22

Number of seats in the second row = 21

Number of seats in the third row = 51

Common difference= Second term - first term

= 26-22

= 4

The given sequence is in arithmetic progression

Substitute the values in the equation

= 15[44+29×4]

= 15[44+116]

= 15×160

= 2400

Hence, using the arithmetic progression, if a theatre has 51 rows of seats  and there are 22 seats in the first row,21 in the second row, 51 in the third row, then the total number of people that the theatre hold is 2400

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Answer:

62.5% or in decimal form 0.625

Step-by-step explanation:

Add missing statements and reasons.

    Statement                            Reason                              

Answer: 5x + 10y = or > 75

Step-by-step explanation:

make the number of cookies sold  = x, and the number of cupcakes sold = y, since we don't know the number.

each cookie is $5 so it is 5 times x, and each cupcake is $10 so it is 10 times y.

add those together, and the sum must equal 75. If you have already learned this, it would be an equal to or greater than sign. if not then just use an equal sign.

Answer:

false

Step-by-step explanation:

The left side equals 0.01

The right side equals 0.4

The two sides are not equal. This is a false equation.

Answer:0.01=0.0001

Step-by-step explanation:

a steep line line has  a  bigger absolute greater slope than a flat line

Answer: the answer should be C :)

Step-by-step explanation:

the slope (x) is -3/4 and the y-intercept is -2

The sum of squares of two sides of a triangle is equal to another side of a triangle is called the Pythagorean theorem.

It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

c^2=a^2+b^2--------(1)

Where a,b, and c are sides of a triangle.

To measure the length of the missing side in a right triangle using the Pythagorean theorem:

c^2=a^2+b^2

By using this formula we can find the length of a missing side.

To understand more we have to solve an example:

let A, B, and C are points of a triangle AB, BC, and CA are the sides of the triangle.

Consider BC=3cm CA=4cm AB=?

Use equation(1) to find the length of AB

AB^2=BC^2+CA^2

AB^2=3^2+4^2

AB^2=9+16=25

AB=5cm

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The value of x for the expression 5log(3x) = 15 is 6.7.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is 5log(3x) = 15. The value of x for the expression will be calculated as,

5log(3x) = 15

log(3x) = 15 / 5

log(3x) = 3

3x = e³

x = 20 / 3

x = 6.7

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Answer:

  111 girls

Step-by-step explanation:

You have 924 people classified as 383 men, 356 women, and the remainder children. 2/5 of the children are boys, and you want to know the number of girls.

The number of children is ...

  924 -383 -356 = 185

The 3/5 of children that are not boys are girls, so ...

  girls = 3/5(185) = 111

There are 111 girls in the theater.

Answer:

39 children, 201 adults

Step-by-step explanation:

Let c = number of children

a = number of adults

c + a = 240

1.50c + 2.25a = 510.75

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

1.50c + 1.50a = 360

1.50c + 2.25a = 510.75

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

.75a = 150.75

a = 201, c = 39

Reflection is a type of rigid transformation in which an object is flipped about a reference point or line to produce the required image. The three statements that apply are:Vertex B is the midpoint of AA'The length of CD is equal to the length of C'D'Vertex C and vertex C are located at the same point

Rigid transformation is a process in which the size, orientation or position of a given object can be changed by applying some principles. Types of rigid transformation are: reflection, translation, dilation, and rotation.

In the given question, the required statements that apply are:

Vertex B is the midpoint of AA'The length of CD is equal to the length of C'D'Vertex C and vertex C are located at the same point

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Answer:

B

Step-by-step explanation:

Answer: The answer is B

Step-by-step explanation:

if you divide 7 by 12 you will get a decimal and a non terminating 3

× is 7

(7×+5) is 54

(5×+19) is 59

Answer:

b) (0.10p + 0.35f) + 0.0875 (0.10p+0.35P)

first is Jamir total cost + the sales tax of 0.0875 of the total cost

a. this is wrong because both is the sales tax only, theres no total cost include

c. wrong because its just also sales tax only

d. wrong because the total cost must only multiplied by the sales tax

PART B

12(0.10) + 8(0.35)

= 1.2 + 2.8

= $4   as the total cost

4(1.035)

= $4.14 as after tax bill

Answer:

89

Step-by-step explanation:

[tex] {3}^{4} + \frac{18}{3} + 2 \\ = 82[/tex]

o Answer:

It's 89 and I didnt mean to reaspond to this question so report it

a. The number of choices possible for each digit of the code is of: 10.

b. The total number of 4-digit passwords that Jess can create is of: 10,000.

c. The number of different ways to create even passwords is of: 5,000.

The Fundamental Counting Theorem states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes is calculated by the multiplication of the number of outcomes for each trial, according to the rule presented as follows:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

Each digit can be between 0 and 9 inclusive, hence the number of outcomes possible for each digit of the password is given as follows:

10.

The password is composed of four digits, hence the total number of passwords possible is of:

N = 10 x 10 x 10 x 10 = 10,000.

Considering that Jess would like an even number, there are only five outcomes possible for the last digit (0, 2, 4, 6 or 8), hence the number of outcomes is of:

N = 10 x 10 x 10 x 5 = 5,000.

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I think the answer be 12 and -18 D

In order to solve a quadratic equation with one unknown, we need to factor it. If at first glance we can't find easy roots, we do a discrimination.

If this value is less than zero, Δ[tex]< 0,[/tex] we determine that it has no solution belonging to the set of real numbers. We will find a conjugate and two complex roots. ([tex]a+bi[/tex])

Let's use the following formulas to find the roots.

Complex Solutions:

To find the amount of extra money Robert will have after two years if he compounds continuously instead of collecting simple interest monthly, we need to calculate the compound interest on the investment.

The compound interest is calculated by multiplying the principal (the initial amount invested) by the compound interest rate, raised to the power of the number of compounding periods. In this case, the compound interest rate is 1.9%/12 = 0.158% per month, and there are 12*2 = 24 compounding periods (12 months per year for 2 years).

The compound interest is therefore calculated as follows:

Compound interest = $20,000 * e^(0.158%*24) - $20,000

= $20,000 * e^0.3832 - $20,000

= $20,000 * 1.454 - $20,000

= $4,080 - $20,000

= -$15,920

So the amount of extra money Robert will have after two years if he compounds continuously instead of collecting simple interest monthly is -$15,920. Therefore, the correct answer is [A] $800.

Amount of each monthly statement is 1400.

According to question ,

Cash price of refrigerator =34500

Deposit money=6500

Outstanding money=28000

Rate of interest=10%

Time period=24 months or 2 years

∴Simple interest =(principal ×rate of interest×time)÷100

⇒(28000×10×2)÷100

⇒5600

∴The total amount to be paid in 2 years is 28000+5600 =33600

∴Amount to be paid in one month =33600÷24=1400

∴Amount of each monthly statement is 1400.

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The formula for calculating the change in consumption is MPC x Change in Disposable Income.Thus, Tamba's change in consumption = 0.75 x $860 = $645

The marginal propensity to consume (MPC) is a measure of the proportion of an increase in disposable income that is spent on consumption. In Tamba's case, his MPC is 0.75, which means that for every $1 increase in his disposable income, he will spend 75 cents on consumption. The formula for calculating the change in consumption is MPC x Change in Disposable Income. Therefore, when Tamba's disposable income increased by $860, his consumption increased by 0.75 x $860 = $645.

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By applying the algebra concept, we can conclude that the movie that Mario and his friend watched starting at 7 PM

The use of algebra in everyday life.

Algebra is a branch of mathematics that uses numbers, symbols, or letters to solve math problems. In everyday life, algebra is often used for financial planning, traveling time calculation, and so on.

In the above problem, we can take some notes as follows:

Departure time (x) = 5:15 PM

Travel time (t) = 1 hour 20 minutes

Arrival time (y) = 25 minutes

If z is the playing time of the movie, then z can be expressed mathematically in the following way:

z = x + t + y

= 5:15 + 1 hour 20 minutes + 25 minutes

= 6:60 PM or generally written 7:00 PM

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The remainder of the polynomial using the remainder theorem and factor theorem is 6.

Apply the remainder theorem,

When we divide a polynomial

f(x) by (x − c)

f(x) = (x − c)q(x) + r

f(c) = 0 + r

Here,

f(x)=(x−c)q(x)+rf(c)=0+r

and (x−c) is (x−(−2))

Therefore,

f(−2) = [tex](-2)^{4} - (-2)^3 - 3(-2)^2 + 4(-2) + 2[/tex]

= 16 + 8 − 12 − 8 + 2

= 6

Hence, the remainder of the polynomial using the remainder theorem is 6.

Whereas using the factor theorem and doing synthetic division, we get,  

x = -2 is a zero of f(x), and x+2 is a factor of f(x). To factor f(x), we divide

the coefficients of the polynomial as follows -

         -2   |   1  -1    -3     4      2

                      -2   6    -6      4

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

                    1   -3   3    -2     6

Hence, we get that 6 is the remainder when ([tex]x^4-x^3-3x^2+4x+2[/tex]) ÷ (x+2), using the factor theorem.

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The complete question is -

Find the remainder using the Remainder Theorem and Factor Theorem using the synthetic division of the given polynomial, [tex]x^4-x^3-3x^2+4x+2[/tex] ÷ (x+2)