2. Fill in the blanks to factor the trinomial 3x² + 13x - 10 by grouping.
3x² + 13x - 10 = 3x² -
=
3x²-x+.
_X+X-10
(3x - 2) +(3x - 2)
+
)(3x - 2)

In 24-hour period there will be 94143178827 virus in system.

A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

Given:

A virus reproduces by tripling every half hour.

In start the virus is 1.

After half an hour, virus= 3

After one hour= 9 virus

After 1 1/2 hour= 27

We get a geometric Sequence

1, 3, 9, 27, 81, ....

Using

[tex]a_n = a_1 (r)^{n-1[/tex]

[tex]a_{24} = 1 ( 3/1)^ {23[/tex]

[tex]a_{24[/tex] = 94143178827

Hence, In 24-hour period there will be 94143178827 virus in system.

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The value of measure m∠ABC will be 24°.

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.

The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.

As per the given m∠ABD is a straight angle.

m∠ABD = 180°

m∠ABC  + m∠CBD = m∠ABD

6x - 60 + 8x + 16 = 180°

14x - 44 = 180

14x = 224

x = 14

Thus, m∠ABC = 6(14) - 60 = 24°

Hence "Measure ∠ABC will equal 24° in value".

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The correct question below,

The measure of angle n is 73°, the measure of angle m is 51° and the line p measures 24 cm.

The midpoint theorem states that the line segment joining the midpoints of any two sides of a triangle is parallel to the third side and equal to half of the length of the third side.

From the given figure, n is the midpoint of one side of the quadrilateral and m is the midpoint of other side of the quadrilateral.

Pair of opposite sides are parallel

Since, m and n are midpoints on two sides of quadrilateral, so the line passes through the midpoints is parallel to other two sides

Then, ∠n =73° and ∠m =51°

p = 1/2 ×48

⇒ p =24 cm

Therefore, the length of line p is 24 cm.

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Answer:

see explanation

Step-by-step explanation:

After solving a system of equations.

the solution is

36 = 32 ← not possible

the fact that we have 36 = 32, an impossible equation, means that the system has no solution.

The triangle pair that is similar from the given pair is "Triangle Pair 2" .

In the question ,

four triangle pairs are given ,

we have to select the triangle pair that is similar ,

In triangle Pair 2 ,

In triangle BAD and triangle BCD ,

angle A = angle C     ....given ,

side BD = side BD   ......because common side

side AD = side BC     ....because opposite side of parallelogram are equal.

So , the triangle BAD is congruent to triangle BCD ,

So , the triangle pair 2 is congruent .

Therefore , the correct option is (b) Triangle Pair 2   .

The given question is incomplete , the complete question is

Similar Triangles Sorting Activity , Which triangle pair shows similar triangles ?

(a) Triangle Pair 1

(b) Triangle Pair 2

(c) Triangle Pair 3

(d) Triangle Pair 4

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Answer: True

Step-by-step explanation:

The slope is the rate of change, to find it, you can get rise/run or use the equation y2 - y1 / x2 - x1

So it is true!

Answer:

2.94

Step-by-step explanation:

I just found 1%

Which is 0.98

then times that by 3 which is 2.94

hope that helps!

the environmental protection agency (epa) rates the mean highway gas mileage of the 2013 ford edge to be 27 miles per gallon. assume the standard deviation is 3 miles per gallon. a rental car company buys 60 of these cars, 0.2979 is the probability that the average mileage of the fleet is less than 26 miles per gallon.

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A probability value between 0 and 1 represents an occurrence.

The four primary categories of probability are axiomatic, classical, empirical, and subjective. Since probability is the same as possibility, you might argue that it is the likelihood that a specific event will occur.

Given that,

μ =  27

σ =  3

n =  60

As we know,

= p ( 26  <  x(avg.)  < 26.8 )

= p (26  - 27 / 0.3873 ) < ( x(avg.)  - μ(avg.)x /σx(avg.) )  <  (26.8- 27/0.3873)

= p ( -1/ 0.3873  <  z < -0.2 / 0.3873 )

= p ( -2.5820 <  z  <  -0.5164 )

= p ( z  < -0.5164) - p ( z < -2.5820 )        

Using z table, we get -

= 0.3028- 0.0049

= 0.2979

Thus, probability = 0.2979

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Answer: √-18 = 3√2 i

Because i is √-1 so think like √18 x √-1 which means √18 i so answer is 3√2 i

Answer:208

Step-by-step explanation:

204+206+208.

Step-by-step explanation:

let the even numbers be :

x+(2+x)+(4+x)

so 3x+6=618

3x=618-6

3x/3=612/3

x=204

The answer is 54√2.

What is simplest radical form?

The radical form is fairly simple. It refers to the form of numbers or algebraic expressions below radicals. However, this can be improved by manipulating numbers or algebraic expressions in their radical form into what is called the simplest radical form. There are no longer any square, cube, fourth, or other roots to be found when a radical is simplified into its simplest possible form. It also entails eliminating any radicals from the fraction's denominator.

SSolving the equations,

=6√3 × 3√6

=( 6 × 3 )√( 6 × 3 )

=18√18

= 18√(2×9)

=18 ( √2 × √9 )

=(18 × 3)√2

= 54√2

Therefore, The answer is 54√2.

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Answer: sqrt 10

Step-by-step explanation:

3.16227...

Answer:

-6

Step-by-step explanation:

-6

Subtraction property will satisfy given inequality option D.

Let's understand what is the Subtraction property

By balancing an equation with the same mathematical operation on both sides, the term "subtraction property of equality" is used.

Given inequality m< A + M <B = M<C. if we subtract both side equal value then we will get M<A = M<C - M<B. then we will get this result

or we can do cross-verify all other option

Transitive-According to the transitive property, "all the quantities are equal to each other if two quantities are equal to the third quantity."

Symmetric-Actually quite straightforward, equality has the symmetric property. According to this property, if a = b, then b must also be a. In other words, even if two equations' sides are switched, the.

Reflexive - It is said that a number is always equal to itself because of the reflexive property of equality. The equality's reflexive quality. If a is a number, then. a = a. a=a.

So here we can see option D is most probable solution for given inequality.

Given Question is incomplete complete Question here

Name the Property of Equality that justifies the statement:

If m< A + M <B = M<C.

Then, M<A = M<C - M<B

Transitive Property

Symmetric Property

Reflexive Property

Subtraction Property

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Solution for the equation x² + 81 = 0 is x =  ± 9i.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

The given equation is,

x² + 81 = 0

To find the solution of the given equation,

Simplify the equation,

x² = -81

x = √-81

x = ±9√-1

Since, i = √-1

x = ± 9i

The solution for the given equation is x =  ± 9i.

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Answer:

8

Step-by-step explanation:

The first step would be to determine if both the numerator and the denominator have a highest common factor. If they do, then the number can be simplified into a smaller fraction. Here, the denominator can be fully divided out by 64 to make the whole number 8

The range of horn lengths for the middle 95% of Texas Longhorn cattle is (51 inches, 69 inches)

What is a normal distribution?

A continuous probability distribution for a real-valued random variable is called a normal distribution or a Gaussian distribution.

Here, we have

Given:

Horn lengths of texas longhorn cattle are normally distributed

The mean horn spread:  μ = 60 inches

With a standard deviation:  σ = 4.5 inches

According to the normal distribution, the range for the middle 95% of the values is: (μ  - 2σ,  μ + 2σ)

Replacing the given values:

(60 inches  - 2(4.5 inches), 60 inches + 2(4.5 inches))

(60 inches  - 9 inches, 60 inches + 9 inches)

(51 inches, 69 inches)

Hence, the range of horn lengths for the middle 95% of Texas Longhorn cattle is (51 inches, 69 inches)

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A total of $316.67 has to be saved per month for the vacation at Disney.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis of the given problem.

Given is that your parents are saving up for a fun vacation at Disney. They have figured out it will cost them a total of $3,400. They have already saved $1,500 and plan on saving for the next 6 months,

Assume that they will have to save $x every month. So we can write the inequality as -

6x ≥ (3400 - 1500)

6x ≥ 1900

x ≥ (1900/6)

x ≥ 316.67

Therefore, your parents will have to save a total of $316.67 per month for the vacation.

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Answer:

90-15=75

75/90= 5/6

ans: 5/6

1/6

We can combine the two numbers together to get the fraction we are looking for:

15/90

By simplifying, we get:

1/6

We get this answer by dividing the highest possible number by both fractions. In this case, the number would be 15:

15 ÷ 15 = 1

90 ÷ 15 = 6

1/6

1/6

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

The probability that X is greater than 53

What is probability ?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

Formula for calculating the standard score or z score:

z = x-μ/σ, where:

z is the standard score

x is the raw score

μ is the population mean

σ is the population standard deviation

In this question: μ = 61 and σ = 8

The score is greater than 53

Let’s calculate the z score, for x = 53 and then find the probability for x greater than 53

z = (53 - 61)/8

  = -8 / 8

  = -1

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The value will be $371.39.

Compound interest is the interest you earn on interest. This can be illustrated by using basic math: if you have $100 and it earns 5% interest each year, you'll have $105 at the end of the first year. At the end of the second year, you'll have $110.25.

The formula to calculate the compound amount after t years is given by :-

A =P [tex](1 + R)^{T}[/tex]

where the interest rate is r and P represents the principal amount.

Given: $150 is the principal sum.

Interest is charged at a rate of 12%/0.12

A = 150 will be the amount compounded after 8 years.

A = 150 [tex]( 1 + 12 )^{8}[/tex]

A =371.3944

A = $371.39

Hence, the value of $150 after eight years if you earn 12 percent interest per year would be $371.39.

option a. is right

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Simplest Radical Form of the given question is [tex]216\sqrt{10}[/tex].

An phrase that has a root, typically a square or cube root, is referred to as a radical.

The radical consists of three separate parts:

Radicand :This is the one whose root you are discovering.

A radical equation is one that contains the square root, or at least one other variable expression, inside a radical.

Degree: It expresses the degree of radicand multiplication. If a number appears on the root symbol but is absent, it is taken to be 2. (square root).

Symbol: Usually √

Given

[tex]9,8\sqrt{90}\\ 9*8\sqrt{90}=9*8\sqrt{9*10}=9*8*3\sqrt{10} \\=216\sqrt{10}[/tex]

Simplest Radical Form of the given question is [tex]216\sqrt{10}[/tex].

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Answer: use a graf

Step-by-step explanation:

find the negative numbers and positive number

The slope of the line that passes through the given points (-5, 6) and (-2, 4) as required in the task content is; -2 / 3.

It follows from the task content that the slope of the line that passes through the given points; (-5,6) and (-2,4) be determined as required.

On this note, since the slope, otherwise termed the average rate of change is given by the formula;

Slope, m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Therefore, given the points; (-5, 6) and (-2, 4), the required slope of the line is;

m = ( 4 - 6 ) / ( -2 - (-5) )

m = -2 / (-2 + 5)

m = -2 / 3

Therefore, the required slope of the line which passes through the given points is; -2 / 3.

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Answer:

321.2 * 10^6

Step-by-step explanation:

First at all:

4.4 x  10^6 = 4.400.000

Then 73 * (4,4 x 10^6) = 73* 4.400.000

(73)*(4.400.000) = 321.200.000

In scientific notation:

321.2 * 10^6

The study of probability is a field of mathematics that focuses on determining the possibility that an event will occur.

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The coefficient in the expression is 25.

Given is the following expression -

f(p, q) = 25pq

The coefficient in the expression is 25.

Therefore, the coefficient in the expression is 25.

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Answer:

25

Step-by-step explanation: