Complete the equation so that it has no solution.
9(x – 4) – 5x =__x-30

It's because this requires two different processes or pieces, the absolute value function is an example of a piecewise function. A piecewise function is a function in which more than one formula is used to define the output over different pieces of the domain.

The hotel can acquire 5 of these sets in 119/792 different ways and still expect to receive 2 of the defective sets.

As per the stated question.

You can select five television from a possible twelve in the sample space.

To acquire at least 2 faulty, therefore:

¹²C₅ = 12!/(7!)(5!) =12*11*10*9*8/(5*4*3*2*1)

¹²C₅ = 11*9*8

Obtaining two or three defective items. (At least 2).

2 defective items are-

(³C₂)(⁹C₄) = 3*9*8*7*6/(4!)

(³C₂)(⁹C₄) =9*7 =63

Three defective items equal -

(³C₃)(⁸C₂) = 1*8*7/2!

(³C₃)(⁸C₂) = 56

Total defective items is 63+56= 119 ways.

Probability = 119/(11*9*8)

Probability = 119/792

Thus, a hotel can acquire 5 of these sets in 119/792 different ways and still expect to receive 2 of the flawed sets.

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Answer:

-7

Step-by-step explanation:

The probability of getting a number greater than 4 when the dice is rolled 20 times is 7.

The number on dice greater than 4 is 2 (that is 5 and 6 on dice) thus the probability of getting a number greater than 4 is

P = 2/6

P = 1/3

This is the probability if the dice were rolled once but if the dice were rolled 20 times thus the probability, in this case, needs to be multiplied by 20  

P = 1/3*20

P = 6.66

equivalents to 7

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The measure of < BAP in the figure of the circle is 30 degrees

< ACB covers same angle as < APB

therefore

< ACB = < BAP = 120

complete the line PB to form another radius. since radius of a circle are equal, an isosceles triangle is created

Isosceles triangle has a unique  property of 2 equal equal sides and equal base angles. one of the angles of the isosceles triangle is < BAP

solving with the new triangle APB

< BAP = < PBA (base angles of isosceles triangle)

< BAP + < PBA + 120 = 180

2 < BAP = 180 - 120

2 < BAP = 60

< BAP = 30 degrees

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The net yardage the team had after those 4 plays is -32.

From the information, the football team averaged a loss of 8 yards in each of 4 plays.

In a situation where they did not gain any yards, the net yardage the team had after those 4 plays will be:

= Yards loss × Number of matches

= -8 × 4

= -32

This illustrates the concept of multiplication that was used to calculate the net yardage.

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The equations that are quadratic in form include:

A. x⁴ – 6x²– 27 = 0

D. 6x⁴ = -x² + 5

E. 8x⁴ + 2x² – 4x = 0

A quadratic equation simply refers to the equation which is in an algebraic equation that is of the second degree.

It should be noted that a quadratic equation is in the form of ax² + bx + c = 0.

In this situation, a and b are the coefficients while c is the constant in the equation.

Therefore, based in the information given, the correct options are A, D, abd E.

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Answer:

The equations that are quadratic in form include:

A. x⁴ – 6x²– 27 = 0

D. 6x⁴ = -x² + 5

E. 8x⁴ + 2x² – 4x = 0

Step-by-step explanation:

The factor of the expression 32z - 48 will be 16 and (2z - 3). And the greatest common factor is 16.

Simply said, it is the biggest common element. The highest consistent element in the above example is 15, making 15 the greatest common factor amongst 15, 30, and 105. The biggest chunk of the common factors is called the "Greatest Common Factor" (of two or more numbers).

The expression is given below.

⇒ 32z - 48

The expression can be rewritten as,

⇒ 32z - 48

⇒ 16 · 2z - 16 · 3

⇒ 16 (2z - 3)

The factor of the expression 32z - 48 will be 16 and (2z - 3). And the greatest common factor is 16.

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Answer:11

Step-by-step explanation: 44 divided into 4 is 11.

Answer:

The answer would be 11

Step-by-step explanation:

Because, 44 divided by 4 = 11

The number of terms in the expression 5x - 2 is 2

The number of terms in an expression or equation refers to the values separated by a mathematical operator. A mathematical operator could be

The terms can be like terms or unlike terms

The two terms given is separated by the subtraction operator and are both unlike terms

The first term 5x consist of

The second term is just a constant which is 2

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The frequency of data value 1 that is 10 will be 6 as "Dividing each frequency by the total number of data values gives the relative frequency. So multiplying the relative frequency by the total number of data values gives the frequency."

The proportion of outcomes where a specific event occurs to all trials, not in a hypothetical sample space but in a real experiment, is known as the empirical probability, relative frequency, or experimental probability of an event. The relative frequency is calculated by dividing each frequency by the total number of data values. Therefore, the frequency is calculated by multiplying the relative frequency by the total number of data values.

Here,

Value                                           Relative frequency

10                                                  0.15

20                                                 0.30      

30                                                 0.45

40                                                 0.10

data 1 value=10

Dividing each frequency by the total number of data values gives the relative frequency.

So, multiplying the relative frequency by the total number of data values gives the frequency.

40*0.15=6

Since "multiplying the relative frequency by the total number of data values gives the frequency," the frequency of the data value 1 that is 10 will be 6.

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Principal for 6000 frs for 3 years at 4% p.a. and 2000 frs for 2 years 3 months at 3% is 461.5 and 148.1.

Amount A = P(1+rt)

6000 = p(1+4*3)

6000 = p13

p = 6000/13

p = 461.5

Amount A = P(1+9/2*3)

2000 = P*27/2

P = 2000*2/27

P = 148.1

Therefore Principal for 6000 frs for 3 years at 4% p.a. and 2000 frs for 2 years 3 months at 3% is 461.5 and 148.1.

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The sum of the numerator and denominator of the decimal is found as 111.

As for the given question;

The decimal number is given as;

0.12 bar

Decimal to fraction conversion

100(0.12 bar) = 12(0.12 bar)

99.(0.12bar) = 100(0.12bar) - (0.12 bar)

99.(0.12bar) = 12 × 0.12bar - 0.12bar

99.(0.12bar) = 12

0.12 bar = 12/99 (lowest fraction)

Thus, in the result the numerator is found as 12 and the denominator is found as 99.

Add = 12 + 99

Add = 111

Thus, the sum of the numerator and denominator of the decimal is found as 111.

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The ratio of frames to honey is the same as in a smaller beehive. 200 pounds of honey can be found in Bert's new beehive.

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 data:

Number of frame beehives = 6

Pound of honey = 40

Current Frame beehive = 30

The first step is to formulate an equation and then use the formulated equation to find  the number of honey

E = 40 × 30 ÷ 6

E = 40 × 5

E = 200 honey

Therefore the number of honey is 200.

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The total number of medals won by Canada is 3 and Greece's 6,

Here we have to find the number of medals won by Canada and Greece.

The ratio of medals won by Canada and Greece is 1: 2.

The total number of medals won = is 9

The common number is x.

Medal won by Canada = x

Medal won by Greece = 2x

So we get the equation:

x + 2x = 9

3x = 9

x = 3

So the total medal won by Canada = 3

The total medal won by Greece = 2 × 3= 6

Therefore the number of medals won by Canada and Greece is 3 and 6 respectively.

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The value of ∠M is, 30

acc to our question-

Hence,The value of ∠M is, 30

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Answer:

x=21, m<s=95

Step-by-step explanation:

85+5x-10=180

75+5x=180

5x=105

x=21

m<S= 5(21)-10

m<S= 105-10

m<s=95

The converse of the statement that says that If an item is not worth five dimes, then it is not worth two quarters is:  If an item is worth five dimes it is worth two quarters.

By swapping the hypothesis and the conclusion, a statement can be made to mean the opposite. "If two lines don't intersect, then they are parallel" is the inverse of "If two lines overlap, then they are parallel." If q, then p is the opposite of "if p, then q."

The converse of a statement may not always have the same truth value as the original. For instance, "All mammals are tigers" is the polar opposite of "All tigers are mammals." This is undoubtedly untrue.

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The statement that is true on the bowling alley charges and the additional cost for renting bowling shoes is The description shows a linear relationship, but not a proportional relationship.

In a linear relationship, the values of the two variables can be drawn on a graph such that they form a line. There would often be a y-intercept and then a slope or a constant rate of change. In this case the constant rate of change is the $15 per game and the additional cost to rent bowling shoes is the y-intercept. This is therefore a linear relationship.

A proportional relationship would have a constant rate of change but there would be no y - intercept. As there is a y - intercept in this scenario, this is not proportional.

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Answer: A: The description shows a linear relationship, but not a proportional relationship.

Answer:

[tex]\sf s =\dfrac{-q}{pr}[/tex]

Step-by-step explanation:

               q = -spr

            -spr = q

     Isolate 's' by dividing both sides by (-pr).

           [tex]\sf \dfrac{-spr}{-pr}=\dfrac{q}{-pr}\\\\\\ s = \dfrac{-q}{pr}[/tex]

The identification process of direct proportion, inverse proportion and partitive proportion is show below.

Proportion is comparison of things or magnitudes in terms of size, amount.

In direct proportion, when one quantity increase or decreases, the another quantity will also increase or decrease in the same ratio.

In inverse proportion, When one quantity increases, the another quantity decreases and vise versa.

Partitive proportion is when the division of a quantity into two or more equal or unequal parts.

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The percentile rank / score in the setting of statistics denotes the percentage of the population that falls below it when the data is organized in ascending order.

For the given question.

The difference in the percentiles and raw scores is-

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Answer:

800

Step-by-step explanation:

we gotta go with the highest value to round since it’s only one sig fig

In order to round to 1 significance the remaining digit will marks as zero thus 837 to 1 significant figure will be 800.

To round up or down tens place then we need to look at the unit place if it is less than 5 then we need to keep it as it and if it is greater than 5 then we need to round up the tens digit.

In order to round to a hundred, we need to look at the tens digit if it is less than 5 then we keep as it is and if it is 5 or greater than 5 then we will round up.

In order to round to 1 significance the remaining digit will mark as zero

As per the given,

837 Here, 1 significant figure is 8.

The ramainging digit = 3 and 7

Put 0 instant of 3 and 7

837 → 800

Hence "In order to round to 1 significance the remaining digit will marks as zero thus 837 to 1 significant figure will be 800".

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The different-sized groups are three groups of each size (35), five groups of each size (21), and seven groups of each size (15).

Given that;

A landscaper must plant 105 little bushes on a park's grounds. He intends to divide the bushes into equal groups.

We are asked to find what different-sized groups could a landscaper can make.

Here, we use Prime factorization;

Let,

∴ 105 = 3 * 5 * 7

From the above factors, we can find different groups as;

3 groups of each sized 35.

5 groups of each sized 21.

7 groups of each sized 15.

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As there are three players, the game will be played in cycles of 3 rounds. After each cycle is completed, the round after will be the round where every single player has 1 token less than they did at the beginning of the previous cycle.

After the first round of the game, player one will have 12 tokens, player two will have 15 and player three will have 14 left. Looking at this sequence, it is evident that player one will finish first.

Go a few rounds to establish the pattern:

Beginning chips: A B C

15 14 13

1st round:

12 15 14

2nd round: 13 12 15

3rd round: 14 13 12

So after 3 rounds and successive 3 rounds each player has one less than he started with at the beginning of the 3 round series.

So after 36 rounds each will be down 12 from the beginning:

                                            A B C

                                             3 2 1

On the 37 round A will give up his 3 to end at 0

37

For more clear understanding:

As player has one token less at the beginning of a new cycle than he/she had at the beginning of the previous cycle we go (12∗3)+1=37(12∗3)+1=37 to see how many turns it will take them to reach zero.

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Answer:

120,000

Step-by-step explanation:

To estimate the product of 283 × 416, first round each number so that each number contains only 1 non zero digit.

In this case, we will round 283 to the nearest hundred and we will also round 416 to the nearest hundred. To round 283 to the nearest hundred, the number next to two is higher than 5 so we round up. 283 rounds to 300.

416 rounded to the nearest hundred is 400 because the digit to the right of 4 is less than 5 which means we round down. 416 rounds down to 400.

Now we have 300 × 400 which equals 120,000

This means that 283 x 416 is approximately 120,000.

Answer:16 minutes

Step-by-step explanation:

64 errors / 8 errors = 8

8 x 2 minutes = 16 minutes

The equation of the straight lines are:

For m = 6 and (x1, y1) = (2, 8)  => y = 6x - 4

For m = 7 and (x1, y1) = (2, 10) => y = 7x - 4

We know that the equation of a line with gradient m and y-intercept is:

y = mx + c.

We need to find the equation of each of the straight lines, given its gradient and the coordinates of a point on the line.

We know the point-slope form of equation of line,

(y - y1) = m(x - x1)

For m = 6 and (x1, y1) = (2, 8)

(y - 8) = 6(x - 2)

y - 8 = 6x - 12

y = 6x - 4

For m = 7 and (x1, y1) = (2, 10)

(y - 10) = 7(x - 2)

y - 10 = 7x - 14

y = 7x - 4

Therefore,  the equation of the straight lines are:

For m = 6 and (x1, y1) = (2, 8)  => y = 6x - 4

For m = 7 and (x1, y1) = (2, 10) => y = 7x - 4

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Answer:

-30

Step-by-step explanation:

Distribute

5 x -4= -20 2 x -2= -4

-20+(-6)+(-4)

Add together

-20 + -6= -26

-26 + (-4)

Add again

-26 + -4= -30

-30

In the given figure, w= 27

Verification:

Solution

From SAS

XY=QP and YZ=QR

therefore ∠Y = ∠Q

since the interior angles of the triangle are supplementary

∠Y + ∠X +∠Z = 180

∠Y + 22 + 36 = 180

∠Y = 180 - 58 = 122

therefore, ∠Q is also equal to 122

and (4w+ 14) =122

122 - 14 = 4w

108 = 4w

w = 108/4 = 27

Hence, from the SAS criterion

w is equal to 27

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