The price of an item has been reduced by $3.49. The new sale price is $84.42. What was the original price?
$
X
3

a) 32.4% probability that exactly 3 drivers text while driving if a police officer pulls over five drivers.

b)  2.76% probability the next driver texting while driving that the police officer pulls over is the fifth driver.

It is a branch of mathematics that deals with the occurrence of a random event.

Using Binomial distribution,

[tex]P(x) = C_{n , x} * p^{x}* (1-p)^ {n-x}[/tex]

We have, p= 0.52

A) probability that exactly 3 drivers text while driving if a police officer pulls over five drivers

[tex]P(x) = C_{5 , 3} * (0.52)^{3}* (0.48)^ {2}[/tex]

P(x) = 10* 0.140608* 0.2304

P(x)= 0.3239

32.4% probability that exactly 3 drivers text while driving if a police officer pulls over five drivers.

B) probability the next driver texting while driving that the police officer pulls over is the fifth driver

[tex]P(x) = C_{4 , 0} * (0.52)^{0}* (0.48)^ {4}[/tex]

P(x) = 1 * 1 * 0.053084

P(x) = 0.053084

So, 0.0531*0.52 = 0.0276

Hence, 2.76% probability the next driver texting while driving that the police officer pulls over is the fifth driver.

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The total number of possible fivey sequences are; 6

We are told we are dealing with a fivey sequence which means that all the terms of the sequence must be positive integers and they must add up to 5.

Now, the possible numbers that can be used are;

1, 2 and 3.

If we start with 3, number of possible sequences is; 1

If we start with1, number of possible sequences is; 3 ways

If we start with 2, number of possible sequences is; 2 ways

Thus;

Total number of fivey sequences is 1 + 2 + 3 = 6 possible sequences

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The number of tickets for adults is 210 and the number of tickets for children is 83.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Let x be the number of tickets for adults and y be the number of tickets for children.

From the problem:

x + y = 293

25.50x + 8y = 6019

After solving with the substitution method:

[tex]\rm 25.5\left(293-y\right)+8y=6019[/tex]

y = 83

x = 210

Thus, the number of tickets for adults is 210 and the number of tickets for children is 83.

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Answer:

-3 (v+4) + 6v

-3v - 12 + 6v

arranging like terms

-3v + 6v - 12

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

-3(v+4)+6v, simplify

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

[tex]\multimap\bf{-3(v+4)+6v}=-3v-12+6v[/tex] | combine the like terms

[tex]\multimap\bf{3v-12}[/tex]

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

                [tex]\bf{=3v-12}[/tex]

[tex]\LARGE\boxed{\bf{aesthetic \not1\theta l}}[/tex]

Answer:

our volume is 4500cm³

Step-by-step explanation:

note: the following will be assuming that this fish tank is rectangular, as most fish tanks are

To find the volume of a rectangular structure, we multiply :

length × width × height

here, we know our

length to be 12 cm

width to be 15 cm

and height/depth to be 25 cm

so, we can follow our volume formula (length × width × height) using these values

length × width × height = volume

12 × 15 × 25 = 4500

so, our volume is 4500cm³

(also called 4500cubic centimeters)

(we write volume as cubed--units³)

hope this helps! have a lovely day :)

Answer:

a and c = 115 and b and d = 65

Step-by-step explanation:

Hope this helps :)

The equation of the line through the points is y = 3/5 + 1/5.

First, we find the Slope using the formula: m = y2 - y1/x2 - x1

You may choose any two points but I will use these two for no reason at all.)

Points: (3,2) and (8,5)

m = y2 - y1/x2 - x1

m = 5 - 2/8 - 3

m = 3/5

Now that we have the slope, we can now find the Slope-Intercept Form by using the Slope Form Formula. (need at least one point and slope.)

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

Point: (3,2)

y - y1 = m(x - x1)

y - 2 = 3/5(x - 3)

y - 2 = 3/5x - 9/5

y - 2 = 3/5x - 9/5

y = 3/5x - 9/5 + 10/5 (2 can be is any fraction that consists of the numerator multiplied twice by the denominator, such as 2/1, 4/2, 8/4, etc.)

y = 3/5 + 1/5

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Answer:

4

Step-by-step explanation:

The common difference is found by subtracting the 2nd term from the 1st term. In this example we can say 11 is the 2nd term and 7 is the 1st term. 11 - 7 = 4.

Answer:

0.36ml

Step-by-step explanation:

Note: micrograms = [tex]10^{-6} g[/tex]

Given the concentration,

[tex]500*10^{-6} g = 1ml\\1*10^{-6}g =\frac{1}{500} ml\\180*10^{-6} g=(\frac{1}{500} *180)ml\\180micrograms = 0.36ml[/tex]

The answer choice which must be true regarding the linear function is; The set must have a constant additive rate of change.

Since a linear function typically takes the slope-intercept form; f(x) = mx +c.

It therefore follows that the equation must have a constant slope m, which is the described additive constant rate of change.

It therefore follows that, the answer choice which is true regarding the linear function is therefore; The set must have a constant additive rate of change.

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If graphed on the same grid, the diagrammatic representation of the parabola gives an upward curve.

The graph of the function is a diagrammatic representation of the slope, x-intercept, and y-intercept of the given function.

From the information given:

y = 2.5x²

Here,

x-intercept = (0,0)

y-intercept = (0,0)

Therefore, if graphed on the same grid, the diagrammatic representation of the parabola gives an upward curve.

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Answer:

4² + b² = 12²

16 + b² = 144

b² = 144 - 16

b² = 128

b = √128

b = 11.3 feet

Step-by-step explanation:

Answer:

330°

Step-by-step explanation:

Multiply by the conversion factor of [tex]\frac{180}{\pi }[/tex]

Answer:

vii. x = 70°           viii. x = 60°

Step-by-step explanation:

vii.

The purple line drawn is parallel to the lines PQ and ST.

∴  ∠ a + 130° = 180°     [alternate angles]

⇒ ∠ a = 50°

x = a + 20°                  [Co-interior angles with angle [tex]x[/tex]]

⇒ x = 50° + 20°

⇒ x = 70°

viii.

The yellow line drawn and the line AB are parallel.

∴ n° + 130° = 180°        [Co-interior angles]

n = 50°

The green line and line DE are parallel.

∴ m° + 110° = 180°        [Co-interior angles]

m = 70°

n + m + x = 180°             [Angles on a straight line]

⇒ 50° + 70° + x = 180°

⇒ x = 60°

Answer:

vii) x = 70° viii) x = 60°

Step-by-step explanation:

Please refer to the attached photos for better understanding (Apologies for the terrible drawing.)

vii) Angle RSV + Angle RST  = 180° (Sum of angles in a straight line)

Angle RSV + 130°  = 180°

Angle RSV = 180° - 130°

                  = 50°

Angle RVS + Angle RSV + Angle SRV = 180° (Sum of angles in a triangle)

Angle RVS + 50°+ 20° = 180°

Angle RVS = 180° - 70° = 110°

Angle RVX + Angle RVS = 180° (Sum of angles in a straight line)

Angle RVX + 110° = 180°

Angle RVX = 180° - 110° = 70°

Angle x = Angle RVX = 70° (Corresponding Angles)

viii) Angle FDG + Angle CDE = 180° (Sum of angles in a straight line)

     Angle FDG + 110° = 180°

     Angle FDG = 180° - 110°

                         = 70°

Angle BGC = Angle FDG = 70° (Corresponding Angles)

Angle CBG + Angle ABC = 180° (Sum of angles in a straight line)

Angle CBG + 130° = 180°

Angle CBG = 180 - 130°

                   = 50°

Angle x + Angle CBG + Angle BGC = 180° (Sum of angles in a triangle)

Angle x + 50° + 70° = 180°

Angle x = 180° - 120° = 60°

Answer:The answer is 27.04

Step-by-step explanation:

The solution is in the attached

Answer:

-76

Step-by-step explanation:

121 - y = 197

-121        -121

-y = 76

*-1   *-1

y = -76

This value is approximate

=======================================================

Work Shown:

[tex]\log_{10}(2) \approx 0.301\\\\\log_{10}(3) \approx 0.477\\\\\log_{10}(6) = \log_{10}(2*3)\\\\\log_{10}(6) = \log_{10}(2)+\log_{10}(3) \ \text{ see note below}\\\\\log_{10}(6) \approx 0.301 + 0.477\\\\\log_{10}(6) \approx 0.778\\\\[/tex]

Note: I used the rule that log(A*B) = log(A)+log(B) which works for any valid log base.

Step-by-step explanation:

Since the question has already been answered, I'd like to add something new, and explain why: [tex]log_b(a*c)=log_ba+log_bc[/tex]

So let's just say that:

[tex]x=log_ba[/tex] and that [tex]y=log_bc[/tex]

This means that: [tex]b^x=a[/tex] and that [tex]b^y=c[/tex].

So if we were to multiply the two, a and c. You get

[tex]a*c=b^{x+y}[/tex]

This is due to the exponent identity that: [tex]b^a*b^c=b^{a+c}[/tex]

So if you rewrite this in logarithmic form you get:

[tex]log_b{ac}=x+y[/tex]

and remember what x and y are equal to? that's right, it's the logarithms

so now you substitute the logarithms back in and get

[tex]log_b{ac} = log_ba+log_bc[/tex]

Answer:

sii esa misma vaina. loa a pero aya dur 7 dar s servicio rus ser rh r rhr ser ru r de dhd HD. dhs g PG15 BIT

 Answer:

 6x + 47

Step-by-step explanation:

Given following:

While solving these function sums, start from the right then head left.

⇒ f[g(x)]

⇒ f[x + 6]

⇒ 6(x + 6) + 11

⇒ 6x + 36 + 11

⇒ 6x + 47

Step-by-step explanation:

•a reflection and a dilation

Answer: -4

Step-by-step explanation:

[tex]\frac{1}{4}x-\frac{1}{8}=\frac{7}{8}+\frac{1}{2}x[/tex]

Multiplying both sides of the equation by 8,

[tex]2x-1=7+4x\\\\-1=7+2x\\\\-8=2x\\\\x=\boxed{-4}[/tex]

Based on the conditional statement given, the truth value can be found to be T T → T.

The truth value can be found by using the Boolean Table which is shown as:

p        q        p → q

T         T        T

T         F        F

F         T        T

F         F        T

From the table, we can then see that if both p and q are true, then p → q is true as well.

We will then have a truth value of T T → T.

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The mean of the data about students size of Mr. Sirac classes is 24.

Given students size of each of Mr. Sirac'sclasses 21,20,22,23,24,25,26,28,27 and we have to find the mean of the data.

We know that mean is the basically sum of numbers divided by the number. It is also known as average.

Mean =∑X/n where n is number of values and ∑X is sum of all the values.

∑X=21+20+22+23+24+25+26+28+27

=216

n=9

Mean is calculated by dividing sum by n.

Mean =216/9

=24

Hence the mean of the data about students size of each of Mr. Sirac classes is 24.

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1) Between the years 2003 and 2009, 768 students joined the school.

2) It took 6 years for the population to grow from 1219 students to 1987 students.

3) The average population growth per year is 128 students per year.

P = 128 students per year

4) The population of students in the year 2000 was a total of 835 students.

5) 1219 + (p3) = 1987

6) 1987 + (p3) = 2371

P3 = 384

Answer:

35

Step-by-step explanation:

28 Orange Marbles divided by 4 Orange Marbles =

7

5 Blue Marbles for every 7 Orange Marbles =

35

Answer:

C

Step-by-step explanation:

it just is

The graph which has the same end behaviour as the function given; f(x) = (10x³+x² +3)/(2x²+1) is; a linear graph whose slope is 5.

The function given can further be simplified by means of polynomial division in which case;

although not a perfect division; the quotient of the division is; (5x-0.5) and evidently, the function which would have the same end behaviour as the given function is a linear function whose slope is 5.

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Answer:

  (b)  (-3, 2, -5)

Step-by-step explanation:

The solution to the system of equations will satisfy every equation. If it fails to satisfy any equation, it is not a solution.

The system of equations does not seem to lend itself to simple solution by substitution or elimination. Hence, a reasonable strategy for finding the answer is to try the offered choices. Of course, a calculator can be used to find the answer almost as quickly.

Using the third equation, we can check the answer choices fairly easily. That equation involves the least number of arithmetic operations. Substituting for (x, y, z), we have ...

  a) 3(1) -(11) -(5) = -13 ≠ -6

  b) 3(-3) -(2) -(-5) = -6 . . . . . . a potential solution

  c) 3(1) -(8) -(0) = -5 ≠ -6

  d) 3(-1) -(3) -(4) = -10 ≠ -6

The only viable choice is (-3, 2, -5).

Check

In the other two equations, we have for this solution, ...

  2(-3) -2(2) +(-5) = -15 . . . . works in the first equation

  6(-3) -3(2) -(-5) = -18 . . . . works in the second equation

Answer:

32 seats per row

Step-by-step explanation:

Total number of seats in auditorium = 288

Number of rows in which seats evenly distributed = 9

Number of seats per row = 288/9= 32