The box-and-whisker plot below represents some data set. What is the range of the data?

According to the order of operations, brackets are solved first which contains the division operation. Hence, 12 is divided by -6 first.  

Order of Operations

Given expression is,

(12 ÷ (-6))(3) + (-2)

According to the BODMAS rule of operations, the precedence order of operations is as follows,

Brackets > Of > Division > Multiplication > Addition > Subtraction

Hence, we will start by solving the brackets first, then solve the division and then the addition.

Evaluation

Solving the given expression as per the order of operations,

Brackets are solved first, then division followed by multiplication and then addition. Division is always of the highest precedence among all operations after brackets and of.

12 ÷ (-6)(3) + (-2)

= 12 ÷ (-6)(3) - 2   [∵ +(-n) = -n]

= (-2)(3) -2

= -6 - 2

= -8

Thus, solving the +(-2) and then division of 12 by (-6) are the first operations to be performed in order to evaluate the given expression.

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The commutative property of multiplication addition is illustrated below.

The commutative property implies that the changing of orders of the numbers doesn't have a effect on the value.

In this case, 5 × 4 = 20. Also, changing them to 4 × 5 is still 20.

Likewise 2 + 5 as 5 + 2 gives 7.

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C) graph of a quadratic function with a minimum at 2.5, negative 2.25 and x intercepts at 1 and 4

Standard Form of a Quadratic Function: ax² + bx + c = 0, where a ≠ 0

Given function: x² - 5x + 4

⇒ a = 1, b = -5, c = 4

The minimum of a function is the lowest point of its parabola. We can use the following formula to find the vertex or the minimum of the function: [tex]x=\dfrac{-b}{2a}[/tex] . This will give us the x-value of the vertex, and we will need to solve for the y-value.

The vertex or minimum.

Step 1: Find the x-value of the vertex.

[tex]\\\implies x=\dfrac{-(-5)}{2(1)}\\\\\implies x=\dfrac{5}{2}=2.5[/tex]

Step 2: Find the y-value of the vertex by substituting 2.5 as the value of x in the given function.

[tex]\\\implies x^2 - 5x + 4\\\\\implies 2.5^2-5(2.5)+4\\\\\implies 6.25-12.5+4\\\\\implies -2.25[/tex]

Vertex: (2.5, -2.25)

The x-intercepts (roots).

We can use the Quadratic Formula to find the roots of this function.

Quadratic Formula: [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex] when [tex]ax^2+bx+c=0[/tex]

Equation: x² - 5x + 4 = 0

⇒ a = 1, b = -5, c = 4

Step 1: Substitute the values of a, b, and c into the formula. 

[tex]\\\implies x=\dfrac{\bold{-(-5)}\pm\sqrt{\bold{(-5)^2}\bold{-4(1)(4)}}}{\bold{2(1)}}\\\\\implies x=\dfrac{5\pm\sqrt{\bold{25-16}}}{2}\\\\\implies x=\dfrac{5\pm\sqrt{\bold{9}}}{2}\\\\\implies x=\dfrac{5\pm3}{2}[/tex]

Step 2: Separate into two possible cases.

[tex]x_1=\dfrac{5-3}{2}\implies \dfrac{2}{2}\implies \boxed{1}\\\\x_2=\dfrac{5+3}{2}\implies \dfrac{8}{2}\implies \boxed{4}[/tex]

The x-intercepts of the given function are 1 and 4.

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Answer: D

Step-by-step explanation:

If the original price was p, a price reduction would be p- the amount. Per the given answers, $275 is used for the reduction amount.

Using the z-distribution, the confidence interval is given by: (11.95, 12.65).

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.

The other parameters are given as follows:

[tex]\overline{x} = 12.3, \sigma = 1.5, n = 50[/tex]

Hence the bounds of the interval are:

[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 12.3 - 1.645\frac{1.5}{\sqrt{50}} = 11.95[/tex]

[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 12.3 + 1.645\frac{1.5}{\sqrt{50}} = 12.65[/tex]

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Answer:

I don't think the answer is in the options.

Answer:

B

Step-by-step explanation:

Let t and d be their ages now.

2 years ago, their ages were t - 2 and d  2.

Now, Tyler is 3 years older than David: t = d + 3

2 years ago, Tyler was 4 times as old as David: t - 2 = 4(d - 2)

The system of equations is:

t = d + 3

t - 2 = 4(d - 2)

Answer: B

Answer:

D

Step-by-step explanation:

Answer:

[tex]\frac{23}{90}[/tex]

Step-by-step explanation:

we require 2 equations with the recurring digit placed after the decimal point.

let x = 0.2555.. ( multiply both sides by 10 and 100 )

10x = 2.555... (1)

100x = 25.555.... (2)

subtract (1) from (2) thus eliminating the recurring digits

90x = 23 ( divide both sides by 90 )

x = [tex]\frac{23}{90}[/tex]

Answer:

[tex]\sf \dfrac{23}{90}[/tex]

Step-by-step explanation:

  x = 0.25555.....  --------------(I)

Number of non-recurring digits is 1. So, multiply equation (I) by 10.

10x = 2.5555.... --------------(II)

Number of recurring digits is 1. So, multiply equation (II) by 10.

 100x = 25.5555...... (III)

Subtract equation (II) from (III)

     100x = 25.5555........

       10x =    2.5555.......

    -             -                      

         90x = 23

             x = 23/90

Based on Cody Ray's credit card details and the unpaid-balance method, Cody Ray's unpaid balance is $144.44 and his previous balance is $144.44. His new balance is $147.04

His unpaid balance is:

= Purchases + Finance charge - (Payments + Credit)

= 376.90 + 17.54 - 250

= $144.44

Previous balance is the $17.54 finance charges.

New balance:

= Unpaid balance + Finance charge + New Purchases

= 144.44 + (144.44 x 1.8%)

= $147.04

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Answer:

14.5 hours to the nearest tenth.

Step-by-step explanation:

4.9% = 0.049.

If the original number is 50 it will double to 100 so

100 = 50(1.049)^t

1.049^t = 2

t * log 1.049 = log 2

t = log 2 / log 1.049

 = 14.49 hours,

Answer: [tex]42x^3 y^2[/tex]

Step-by-step explanation:

[tex]A=(3xy)(14x^2 y)=42x^3 y^2[/tex]

Answer:

Angle CAB and angle CBA are congruent.

Step-by-step explanation:

Isosceles triangles have two sides of equal length as well as two congruent base angles.

Answer:

b

Step-by-step explanation:

Answer:

<1 =73

Step-by-step explanation:

The sum of the angles of a triangle add to 180 degrees

72+ 35 + <1 = 180

Add like terms

107 + <1 = 180

Subtract 107 from each side

<1 = 180-107

<1 =73

The computation of the equation shows.that x is -4 and y is 0.6.

4x + 5y = -1

-5x - 8y = 10

The value of x and y will be calculated thus:

-5 × (4x + 5y = -1)

4 × -(5x - 8y = 10)

-20x - 25y = 5

-20x -32y = 40

Add the equation

57y = 45

y = 45/75 = 0.6

Since 4x + 5y = -1

4x + 5(0.6) = -1

4x + 3 = -1

x = -1 - 3

x = -4

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Answer:

can you give the question?

Step-by-step explanation:

didnt ask a question

Answer:

B.) as x --> -∞, f(x) --> ∞ and x --> ∞, f(x) --> ∞

Step-by-step explanation:

F(x) is another way of representing "y". That being said, the question is asking you the behavior of the graph in terms of the y-axis. On both sides of the function, there is an arrow pointing upwards, towards infinite, positive y-values. Therefore, as "x" approaches -∞ and ∞, f(x) is approaching ∞ (positive infinity).

a. The equation we get is 10(1.5 + x) = 80, where x is the number of hours Sheila can afford to hire the babysitter.

b. Sheila can afford the babysitter for 6 hours and 30 minutes.

c. The equation we get is 15(1 + x) = 80, where x is the number of hours Sheila can afford to hire the new babysitter.

d. Sheila can afford to hire the new babysitter for 4 hours and 20 minutes, while the first babysitter was hired for 6 hours and 30 minutes.

Thus, Sheila can't afford the same amount of babysitting from the second sitter as she could from the first sitter.

a. We assume the hours affordable to Sheila be x hours.

Per hour charge of the babysitter = $10.

Time taken by the babysitter traveling = 1.5 hours.

Therefore, total chargeable time = 1.5 + x.

Therefore, the total charge by the babysitter = $10(1.5 + x).

This needs to be equal to the amount Sheila is willing to spend, that is, $80.

Thus, the equation we get is: 10(1.5 + x) = 80.

b. We are asked to determine the hours Sheila can afford to hire the babysitter.

We have got the equation 10(1.5 + x) = 80, where x is the hours Sheila can afford to hire the babysitter.

Thus, by solving this equation, we can determine the hours Sheila can afford to hire the babysitter.

10(1.5 + x) = 80,

or, 1.5 + x = 8,

or, x = 8 - 1.5 = 6.5 = 6 hours and 30 minutes.

Thus, Sheila can afford the babysitter for 6 hours and 30 minutes.

c. Per hour charge of the new babysitter = $15.

Time taken by the new babysitter traveling = 1 hour.

Therefore, total chargeable time = 1 + x.

Therefore, the total charge by the new babysitter = $15(1 + x).

This needs to be equal to the amount Sheila is willing to spend, that is, $80.

Thus, the equation we get is: 15(1 + x) = 80.

d. We are asked whether Sheila affords the same amount of babysitting from the second sitter as she could from the first sitter.

To determine this, we need to find the hours she affords from the second babysitter, for which, we solve the equation 15(1 + x) = 80 as  follows:

15(1 + x) = 80,

or, 1 + x = 80/15,

or, x = 80/15 - 1 = 65/15 = 13/3 = 4 hours and 20 minutes.

Sheila can afford to hire the new babysitter for 4 hours and 20 minutes, while the first babysitter was hired for 6 hours and 30 minutes.

Thus, Sheila can't afford the same amount of babysitting from the second sitter as she could from the first sitter.

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Answer:

6) Selling price =  ₹ 1608

   Labelled price =  ₹ 2010

7) Profit percentage = 10.5%

Step-by-step explanation:

Finding the selling price:

6) Cost Price =  ₹ 1200

          [tex]\sf Profit = 33\dfrac{1}{3} \% * Cost\ price\\\\[/tex]

                    [tex]\sf = \dfrac{102}{300}*1200\\\\ = 102 * 4\\\\[/tex]

                    =  ₹ 408

Selling price = Cost price + Profit

                     = 1200 + 408

                     =  ₹ 1608

      Let the labelled price = x

             Discount % = 20%

     (100-20)% of x  = 1200 + 408

            80%  of  x  = 1608

                           [tex]\sf x = 1608*\dfrac{100}{80}\\\\[/tex]

                           x = ₹ 2010

Answer: Selling price =  ₹ 1608

             Labelled price =  ₹ 2010

7) Let the Cost price =  ₹ X

Marked price = (100 + 30)% of  Cost price

                       [tex]\sf = \dfrac{130}{100}X\\\\ = 1.3 X[/tex]

Discount% = 15%

Selling price = (100 - 15)% of 1.3X

                     = 85% * 1.3X

                     = 0.85 * 1.3X

                     = 1.105X

[tex]\sf \boxed{\bf Profit \% =\dfrac{Selling \ price - Cost \ Price}{Cost \ price }*100}[/tex]

             [tex]\sf = \dfrac{1.105X - X}{X}*100\\\\ = \dfrac{0.105X}{X}*100\\\\ = 0.105*100\\\\ = 10.5 \%[/tex]

If the sample of bacteria is growing at an hourly rate of 15% continuously and the  bacteria began with 11 bacteria then there will be 244.178 samples bacteria after 21 hours.

Given growth of bacteria 15% ,bacteria at beginning 11.

We have to find the number of sample of bacteria after 21 hours.

We have to first form exponential function which shows the growth of bacteria in variable t.

Exponential function which shows the sum is y=P[tex]e^{rt}[/tex]

where P is initial amount ,

r is rate and

y is the sum

So in our problem P=11 and r=0.15

y=11*[tex]e^{0.15t}[/tex]

To find the  samples after 21 hours we have to put t=21.

y=11[tex]e^{0.15*21}[/tex]

y=11*[tex]e^{3.1}[/tex]

y=11*22.198  ([tex]e^{3.1}[/tex]=22.198 from e table)

y=244.178

Hence the samples after 21 hours will be 244 approximately.

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Answer:

2/3x

Step-by-step explanation

Answer:

(x³-3x²-3x-1) / (27x³)

Step-by-step explanation:

((x-1) / (3x))³

= (x-1)³ / /3x)³

(x-1)³ = (x-1)(x-1)(x-1) = x³ - 3x² - 3x - 1

then:

(x-1)³ / (3x³) = (x³-3x²-3x-1) / (27x³)

Since the geometric series has 6 terms, increases by a factor of 4, and has a sum of 1365, the value of the first term is 1.

The sum of a geometric series is given by

Sₙ = a(rⁿ - 1)/(r - 1) with r > 1 where

Now, since our Geometric Series has 6 terms, n = 6. Also, it increases by a factor of 4, so, r = 4 and has a sum of 1365, so Sₙ = 1356. So,we have that

Since we require the first term, a , making a subject of the formula, we have

a = Sₙ(r - 1)/(rⁿ - 1)

Substituting the values of the variables into the equation, we have

a = Sₙ(r - 1)/(rⁿ - 1)

a = S₆(r - 1)/(r⁶ - 1)

a = 1365(4 - 1)/(4⁶ - 1)

a = 1365(3)/(4096 - 1)

a = 4095/4095

a = 1

So, the value of the first term is 1.

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Using the mean concept, the ratio of the number of female attendants to the number of male attendants was of 3.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

In this problem:

Hence:

[tex]\frac{1200f + 800m}{f + m} = 900[/tex]

1200f + 800m = 900f + 900m

100m = 300f

[tex]\frac{f}{m} = 3[/tex]

Hence the ratio was of 3.

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Answer: B

Step-by-step explanation:

There is a hole at x=2, so the numerator and denominator should both have a factor of x-2.

This eliminates everything except for B.

Answer:

95

Step-by-step explanation:

We know the measure of angle 4 is 85, therefore the measure of angle 2 is also 85.

Measure 2 is equal to measure 6, therefore measure 6 also equals 85, measure 8 equals measure 6 giving it the measure of 85.

Now the sum of angles 5 and 7 must equal 190, given we have two 85 degree angles, and the other two are equal, they must sum to 190, since they are equal we will divide 190 into 2, making angles 5 and 7 have a measure of 95.

Answer: 95°

Step-by-step explanation: With 2 parallel lines cut by a transversal, the following conditions are true.

Alternate interior angles are congruent. <4 and <6 are alternate interior angles, and so are <3 and <5.

Corresponding angles are congruent. Corresponding angles are angles that are in the same position in one line as the other. <1 and <5 are corresponding angles, and <4 and <6 are congruent. <2 and <6 are congruent, and <3 and <7 are congruent.

Vertical angles are congruent. Angles that are directly diagonal on the same line are congruent. <5 and <7, and <6 and <8 are examples of this.

Supplementary angles are, well, supplementary. By definition, two angles that are supplementary add up to 180°. Supplementary angles are angles that are on the same line and transversal, but not vertical angles. Rather, the angles are right next to teach other.

Alternate exterior angles are congruent. Alternate exterior angles are angles that are like alternate interior angles, but both share a position on the outside (and are diagonal.) The alternate exterior angles are <2 and <8, and <1 and <7.

Now that we have all definitions and conditions at hand, this will be easy.

If m<4 is 85°, and we want m<5, then we can see that <4 and <3 are supplementary angles. So by definition, <4 + <3 = 180°. We can substitute in <4 since we know it. We get 85° + <3 = 180°. Subtracting 85° from both sides, we get <3 = 95°.

Now we see <3 and <5 are alternate interior angles. By definition they are congruent. Thus, m<5 is 95° too.

Hope this helped!

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I give u the answers of first and second one.

thank you

brainlist please

Answer:

First answer is 9 or 1 . Second answer is 7 or -7.

Step-by-step explanation:

[tex](x-5)^{2} =16[/tex]

[tex]x-5 = 4[/tex]  or [tex]x - 5 =-4[/tex]

so [tex]x = 9[/tex] or [tex]x = 1[/tex]

[tex]2x^{2} = 98[/tex]

[tex]x^{2} =49[/tex]

[tex]x=7[/tex] or [tex]x = -7[/tex]

Answer:

? = 4

Step-by-step explanation:

4/5 = 4/1 x 1/5

4/5 = 4/5

Answer:

64

Step-by-step explanation:

if there 2 to begin with and the bacteria dobles every hour and there were 6 hours it would be 2⁶ and when you time 2 to the power of 6 you get 64

[tex]y = \frac{1}{mx} [/tex]

[tex]11 = \frac{1}{8m} [/tex]

[tex]m = \frac{1}{88} [/tex]

[tex]y = \frac{1}{ \frac{1}{88}x } = \frac{88}{x} [/tex]

[tex]when \: x = 2 \\ y = \frac{88}{2} = 44[/tex]

The value of x from the given expression is 23

Given the following equation

√3x+12 = 9

Square both sides

√3x+12)² = 9²

3x + 12. = 81

Subtract 12 from both sides

3x + 12 - 12 = 81- 12

3x = 69

x = 23

Hence the value of x from the given expression is 23

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