Select the correct answer. Which inequality can this number line represent? A. 7 − x ≥ 1 or 4x + 9 < 13 B. 3x + 2 < 5 or 2x − 1 ≥ 11 C. 7 − x ≥ 1 and 4x + 9 < 13 D. 3x + 2 < 5 and 2x − 1 ≥ 11

Each of the equations should be matched with the value of x that makes them true as follows:

x = 2; x + 2x + 3 = 9, 5(x + 3) = 25, and 4x − (2x + 1) = 3.

x = 3; 2(2x − 3) = 6, 5x - 2x - 4 = 5, and 5x − (3x − 1) = 7.

In order to determine which x-values are true solutions based on the given equations, we would have to test each of the values of x by substituting them into the equations as follows;

When x = 2, we have:

2(2x − 3) = 6

4x − 6 = 6

4(2) - 6 = 6

8 - 6 = 6

2 = 6 (False).

When x = 3, we have:

2(2x − 3) = 6

4x − 6 = 6

4(3) - 6 = 6

12 - 6 = 6

6 = 6 (True).

When x = 2, we have:

5x - 2x - 4 = 5

3x - 4 = 5

3(2) - 4 = 5

6 - 4 = 5

1 = 5 (False).

When x = 3, we have:

5x - 2x - 4 = 5

3x - 4 = 5

3(3) - 4 = 5

9 - 4 = 5

5 = 5 (True).

When x = 2, we have:

x + 2x + 3 = 9

3x + 3 = 9

3(2) + 3 = 12

9 = 12 (False).

When x = 3, we have:

x + 2x + 3 = 9

3x + 3 = 9

3(3) + 3 = 12

12 = 12 (True).

5(x + 3) = 25

5x + 15 = 25

5x = 25 - 15

5x = 10

x = 2 (True).

4x − (2x + 1) = 3

4x - 2x - 1 = 3

2x = 3 + 1

2x = 4

x = 2 (True).

5x − (3x − 1) = 7

5x - 3x + 1 = 7

2x = 7 - 1

2x = 6

x = 3 (True).

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The probability of exactly six will fail = 0.0808

What is Probability?

Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability. It is crucial to grasp this branch's most fundamental concepts in order to fully comprehend it, including the formula for computing probabilities in equiprobable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc.

In the given question, we have:

We know that Probability in binomial distribution with total components ' n ', probability of success ' p ', and the number "of successes " = [tex]{ }^n c_k p^k(1-p)^{n-k}[/tex]

we know that:

[tex]{ }^n c_k=\frac{n !}{(n-k) ! k !}[/tex]

[tex]\begin{aligned}P(\text { success }) &=P(\text { a part fails })=0.35 \text {. So, } \\P(x=5) &={ }^8 C_5 \times(0.35)^5(0.65)^3 \\&=56 \times(0.005252) \times(0.274625) \\&=0.0808 \\& \text { (Round to } 4 \text {-decimals) }\end{aligned}[/tex]

Hence,

The probability of exactly six will fail = 0.0808

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The value of one-sixth times quantity x plus 24 end quantity equals negative 6 is -180.

The expression simply refers to the mathematical statements which have at least two terms that are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

In this case, the expression given will be illustrated as:

1/6x + 24 = -6

Collect like terms

x / 6 = -6 - 24

x/6 = -30

Cross multiply

x = -30 × 6

x = -180

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According to the concept of complex numbers, the solution function is (5 - 6i) (2 + 4i) = (34 + 8i)

Complex numbers:

Complex numbers means a combination of a real number and an imaginary number.

The standard form of complex number is,

a + ib

Where a complex number, where a,b are real numbers and i = √-1.

Given,

Here we have the following complex number expression

(_ + _i) (_ + _i) = 34 + 8i

Here we need find the value of the dashes and the number must lies between -9 to +9.

Let us consider a, b, c and d as the number presented in the dashes then it can be written as,

=> (a + bi) (c + di)

Now, we have to expand this expression then we get,

=> ac + adi + bci + bdi²

Combine the like terms,

=> (ac − bd) + (ad + bc)i

Now, we have to match the coefficients as,

30 < ac − bd < 80

We also know that,

=> ad + bc = 0

Now, we need to pick four integers between -9 and 9 such that these two equations are satisfied.  

We also know that

=> ac − bd = 34

=> ad + bc = 8

Therefore, it makes sense to assume b is negative.  

After some trial and error, one possible answer is a = 5, b = -6, c = 2, d = 4

Therefore, the expression is written as,

=> (5 - 6i) (2 + 4i) = (34 + 8i)

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Proved that Triangle ABD ≅ Triangle CBD

Consider the triangle ABD and the triangle CBD

The length of the side AB = The length of the side BC

The length of the side AD = The length of the side cd

The third side is common

According to the SSS rule congruent . If the three side of the triangle is equal to the three sides of the another triangle then the both triangles are congruent

Then three sides of the triangle ABD is equal to the three sides of the triangle CBD, Therefore the triangle ABD and triangle CBD are congruent

Hence, proved that Triangle ABD ≅ Triangle CBD

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Answer:

Step-by-step explanation:

should be both line GJ and JK as well as line HK and JK

The three consecutive odd intergers are 3,5 and 7

What do you mean by algebraic expression ?

An algebraic expression is the idea of ​​using letters or alphabets to represent numbers without specifying the actual values. Algebra Basics taught us how to use letters like x, y, and z to represent unknown values. These characters are called variables here.

An algebraic expression can be a combination of variables and constants. Any multiplied value that is prefixed to a variable is a factor.

Let the three consecutive odd integers are x, x+2 and x+ 4

Here x is the smallest odd integer and x+4 is the largest odd integer

According to the question:

3(x +4) = 7x

3x + 12 = 7x

7x - 3x = 12

4x = 12

x = 12/4

x = 3  

Three consecutive odd integers become:

x = 3

x + 2 = 3 +2 = 5

x + 4 = 3 + 4 = 7

Hence, the three consecutive odd intergers are 3,5 and 7

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Tyrannosaurus rex weighs about 0.14 times the weight of Patagotitan mayorum

In solving the proportion of the weights we use multiplication of fractions

Multiplication is a mathematical operator to handle such operation

A Tyrannosaurus rex weighed about 1.4 tons more than one tenth the weight of a Patagotitan mayorum

This is is written mathematically as

Tyrannosaurus rex weight, x = 1.4 * 1/10 * Patagotitan mayorum weight, y

x = 1.4 * 1/10 * y

x = 0.14 *y

x = 0.14y

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Answer:

2/sqrt6 = sqrt6/3

3/sqrt54 = sqrt6/6

2/sqrt6 + 3/sqrt54

= sqrt6/2

Step-by-step explanation:

Simplifying when there are radicals involved usually means "rationalizing".

Rationalizing means getting rid of the square root on the bottom of a fraction.

See image.

The account balance after20 ​years will be $6900 and the simple interest for 20 years is $1900

The Principal amount = $5,000

Rate of Interest (r) = 1.9 %

Time Period (t) = 20 years

The Simple Interest is given by

[tex]S.I. = \frac{P*r*t}{100}[/tex]

Now, putting the values on the formula, we get:

[tex]S.I. = \frac{5000*1.9*20}{100} = 1900[/tex]

Hence, the interest will be $1900

Now, The Account Balance after 20 years = $ (1900 + 5000) = $6900

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The equation representing the fact that the product of two consecutive odd Integers is 143 is x(x+2) = 143 where x represents the smaller number and the value of x is 11 or -13.

According to the question,

We have the following information:

The product of two consecutive odd Integers is 143.

Now, let's take the smaller integer to be x.

Now, next consecutive odd integer:

(x+2)

So, we have the following expression:

x(x+2) = 143

[tex]x^{2} +2x = 143\\[/tex]

[tex]x^{2} +2x -143 = 0[/tex]

[tex]x^{2}[/tex]+13x-11x-143 = 0

Taking x as the common factor from first two terms and -11 from the last two terms:

x(x+13)-11(x+13) = 0

(x-11)(x+13) = 0

x-11 = 0 and x+13 = 0

x = 11 or x = -13

Next odd integer = 13 or -11

Hence, the equation representing the fact that the product of two consecutive odd Integers is 143 is x(x+2) = 143 where x represents the smaller number and the value of x is 11 or -13.

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The true statement about the function is that (b) the y-intercept of the function is 3

The mathematical statement of the representation of the function is given as

The function f(x) is the absolute value of 3 more than the value of x.

Mathematically, this can be represented as

f(x) = |x + 3|

To determine the y-intercept, we set the x value of the function to 0

This means that we calculate f(x) when x = 0

i.e. f(0)

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

f(0) = |0 + 3|

Evaluate the sum

This gives

f(0) = |3|

Remove the absolute bracket

f(0) = 3

Hence, the y-intercept is 3

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Possible question

If the function f(x) is the absolute value of 3 more than the value of x. Select all the true statements.

A. The x-intercept of the function is 3.

B. The y-intercept of the function is 3.

Answer:

-1

Step-by-step explanation:

you would do -11 + (-5) which will be -16. Then do -16 - (-15) which will get you -1.

Answer:

x=1.25 y=1.75

Step-by-step explanation:

8/10=5/5+x

50=8(5+x)

50=40+8x

50-40=8x

10=8x

x=10/8

x=1.25

while Y=8/10=7/7+y

70=8(7+y)

70=56+8y

70-56=8y

14=8y

y=14/8

y=1.75

If the expanded volume of a cylinder is 45 in³ , then the compressed volume is 6 in³ .

In the question ,

it is given that ,

the compression ratio in a certain engine is 7.5 : 1 .

the expanded volume of a cylinder is = 45 in³ .

we have to find the compressed volume of the cylinder ,

let the compressed volume of the cylinder be = v .

the above situation can be represented as

7.5 : 1 = expanded volume : compressed volume

7.5/1 = 45/v

7.5 = 45/v

v = 45/7.5

v = 6 cubic inches .

Therefore , If the expanded volume of a cylinder is 45 in³ , then the compressed volume is 6 in³ .

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The answer will be 3 years.

1st 30 pupils at average age of 15.3 yrs. give total age of 15.3 x 30 = 459yrs

2nd group of 30 pupils at average age of 15.2 yrs

give total age of 15.2 x 30 = 456yrs

Difference in age = 459 - 456

= 3 years.

The amount that should be deposited in the account to earn a balance of $5, 000 after 19 years and 6 months is $2, 099.43

First, find the periodic rate:

= 4.5% / 2 semi annual periods per year

= 2.25%

Find the number of periods:

= 19 years and 6 months = 19.5 years

= 19.5 years x 2 semi annual periods per year

= 39 periods

The amount to deposit in the account can be found by the future value formula:

Future value = Deposit x ( 1 + rate) ^ number of periods

5, 000 = Deposit x ( 1 + 2.25%)³⁹

Deposit = 5,000 / ( 1 + 2.25%)³⁹

= $2, 099.43

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Answer:

x = -3

Step-by-step explanation:

Slope = Rise/Run

Slope = Difference in y/Difference in x

Slope = -7/0

Slope = undefined (can not divide by 0)

This means that this is a vertical line

The sentence which supports the idea that people can use the skills they used at their old jobs to make money independently is "If an installer has a place to work, that person can install stereos without a store."

The correct answer option is option C

The essay is about American employees where people who actually needs a job gets a job. Although, this is not always the case especially when the economy slows down.

This slow down in the economy causes businesses to make less profit, thereby, making most people to lose their jobs. The purchasing power of the unemployed (people who lost their job) will reduce causing a decrease in the amount of money made by businesses. This is like a vicious cycle.

However, people who are skilled can still earn a living by doing other available jobs or those who are creative can create new jobs for themselves. For instance, an accountant can become a sales person in a supermarket if he or she lost their job.

In conclusion, a person who lost their job must be determined, hopeful and hard-working and must never give up, most importantly, they should never be idle because an idle mind is the devil's workshop.

Complete question:

Which sentence supports the idea that people can use the skills they used at their old jobs to make money independently?

Answer choices

A"So, car stereo stores have to layoff some of their stereo installers."

B"Often, this person will charge less than the store where he or she used to work."

C. "If an installer has a place to work, that person can install stereos without a store."

D. "At the store where the installer used to work, the store would have made most of the money."

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Answer:

When a die is rolled, here it's Total possible outcome is= 6

and sample space is = 2 ( i.e. 1 & 2)

So. Probability of getting less than 3 =  26

=13

That's it.

Step-by-step explanation:

1. The bank discount on the note of $6,000, which will mature in 160 days at 3.5%, is $93.33.

2. The noteholder will receive total proceeds of $5,906.67 after the 3.5% discount.

Bank discount is the difference between the discounted and face (par) values.

For example, if the bank discounts a note, the holder receives a smaller amount than the face value they would have received had they held the note till its maturity.

The bank discount represents the finance charge for cashing the note earlier than its due date.

Amount due at maturity = $6,000

Discount rate = 3.5%

Time (period) = 160 days

Days in the year for ordinary interest = 360 days

Bank discount = $93.33 ($6,000 x 3.5% x 160/360)

The proceeds = $5,906.67 ($6,000 - $93.33)

Thus, the bank discount refers to the difference between the face value and the discounted value resulting from receiving cash from a note before maturity.

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The Total Distance is 51 yards.

Coordinates are a pair of integers (Cartesian coordinates), or sporadically a letter and a number, that identify a certain place on a grid, also referred to as a coordinate plane. The x axis (horizontal) and y axis are the two axes that make up a coordinate plane (vertical).

Given:

As, A and B have same x- coordinate

AB = | (y- coordinate of A) - (y- coordinate of B)|

     = |5 - (-2)|

     = 7

and, B and C have same y- coordinate

AB = | (x- coordinate of B) - (x- coordinate of A)|

     = |3 - (-7)|

     = 10

Then, Total distance= 7+ 10= 17

and, Total distance in yards = 17 x 3= 51 yards

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The speed of the raft was 2.86 km/hr.

Speed is defined as the rate of change of position of an object in any direction.

Given that, a patrol boat with speed of 12 km/hr caught a raft after travelling for 20 km and patrol boat left the dock after 5 hours and 20 minutes the raft left,

The time taken by the patrol boat to catch the raft is;

t = 20/15 = 5/3 hours

5/3 hours = 1 hour 40 minutes

Thus, it took 1 hour 40 minutes for the patrol boat to catch the raft

Thus, the raft was travelling for 5 hours 20 minutes plus 1 hour 40 minutes which 7 hours,

The speed of raft = 20/7 = 2.86 km/hr

Hence, The speed of the raft was 2.86 km/hr.

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Adam earned $100.12 more interest than the Sophie

Consider Sophie

The principal amount = $3330

The interest rate = 7.4%

The time period = 5 years

Simple interest = PRT

Where P is the principal amount

R is the interest rate

T is the time period

Substitute the values in the equation

Simple interest = 3330× (7.4/100) × 5

= $1232.1

Consider Adam

The principal amount = $2795

The interest rate = 8.1%

The time period = 5 years

Simple interest = 2795 × (8.1/100) × 5

= $1131.98

The difference = 1232.1 - 1131.98

= $100.12

Hence, the Adam earned $100.12 more interest than the Sophie

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The trigonometric measures in the context of this problem are given as follows:

We are given the measure of the sine for the angle and we need to find the three measures, sine, cosine and tangent for half the angle.

To find the measure for half the angle, the cosine is needed to apply the identities, and the cosine is calculated by the following identity:

sin²(x) + cos²(x) = 1

[tex]\left(\frac{2}{3}\right)^2 + \cos^2{x} = 1[/tex]

[tex]\cos^2{x} = 1 - \frac{4}{9}[/tex]

[tex]\cos{x} = \pm \sqrt{\frac{5}{9}}[/tex]

The angle is in the first quadrant, in which the cosine is positive, hence:

[tex]\cos{x} = \sqrt{\frac{5}{9}}[/tex]

[tex]\cos{x} = \frac{\sqrt{3}}{3}[/tex]

Then, applying an identity, the sine for half the angle is given as follows:

[tex]\sin{\left(\frac{x}{2}\right)} = \sqrt{\frac{1 - \cos{x}}{2}}[/tex]

Considering the calculated value for the cosine:

[tex]\sin{\left(\frac{x}{2}\right)} = \sqrt{\frac{1 - \frac{\sqrt{3}}{3}}{2}}[/tex]

[tex]\sin{\left(\frac{x}{2}\right)} = \sqrt{\frac{3-\sqrt{3}}{6}}[/tex]

The identity for the cosine is:

[tex]\cos{\left(\frac{x}{2}\right)} = \sqrt{\frac{1 + \cos{x}}{2}}[/tex]

Hence:

[tex]\cos{\left(\frac{x}{2}\right)} = \sqrt{\frac{3+\sqrt{3}}{6}}[/tex]

The tangent is obtained by the division of the sine and the cosine. The entire division can be placed into a single square root, and the common denominators of six are simplified, hence:

[tex]\tan{\left(\frac{x}{2}\right)} = \sqrt{\frac{3 - \sqrt{3}}{3 + \sqrt{3}}}[/tex]

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The length and width of the rectangular plot that will maximize the area are 50 feet and 25 feet respectively.

The vertex (maximum) of this equation is equal to 1,250 square feet.

Mathematically, the area of a rectangle can be calculated by using this formula:

A = lw

Where:

Since one side of this rectangular plot along the river does not require fencing, the perimeter equation is given by:

P = 2(l + w)

100 = 2w + l      

Making length the subject of formula, we have:

l = 100 - 2w

Therefore, the area of this rectangular plot would now be:

A = (100 - 2w)w

A = 100w - 2w²

Next, we would take the first derivative and equate to zero in order to obtain the maximum area:

dA/dw = 100 - 4w

0 = 100 - 4w

4w = 100

Width, w = 25 feet.

For the length of this rectangular plot, we have:

Length, l = 100 - 2w

Length, l = 100 - 2(50)

Length, l = 50 feet.

Now, we can find the vertex (maximum) of this equation is given by:

Maximum area = 50 × 25

Maximum area = 1,250 square feet.

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There are 2520 possible ways to arrange the programs

From the question, we have

Total number of jockey records, n = 7

Total number of disc jockey records to select, r = 5

To determine the ways the program can be arranged, we make use of permutation

The number of ways of selection could be drawn is calculated using the following permutation formula

Total = ⁿPᵣ

Where

n = 7 and r = 5

Substitute the known values in the above equation

So, we have the following representation

Total = ⁷P₅

Apply the permutation formula

ⁿPᵣ = n!/(n - r)!

So, we have

Total = 7!/2!

Evaluate

Total = 2520

Hence, the number of ways is 2520

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