Question 1 (10 points)

P(X < 4) = 0.8059

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

In this problem we have that:

In which

P(X < 4) = 0.8059

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Answer:

8

Step-by-step explanation:

Answer:

[tex]\dfrac{1}{16}[/tex]

Step-by-step explanation:

Probability Distribution Table for X

Where X is the score on a fair, six-sided dice:

[tex]\begin{array}{|c|c|c|c|c|c|c|}\cline{1-7} x & 1 & 2 & 3 & 4 & 5 & 6\\\cline{1-7} \text{P}(X=x) \phantom{\dfrac11}&\frac{1}{6} & \frac{1}{6} & \frac{1}{6} & \frac{1}{6} & \frac{1}{6} & \frac{1}{6} \\\cline{1-7}\end{array}[/tex]

Probability Distribution Table for Y

Where Y is the score on an unfair, six-sided dice, and the probabilities of rolling numbers 2, 3, 4, 5 and 6 are equal, and the probability of rolling a 1 has a different value:

[tex]\begin{array}{|c|c|c|c|c|c|c|}\cline{1-7} y & 1 & 2 & 3 & 4 & 5 & 6\\\cline{1-7} \text{P}(Y=y) \phantom{\dfrac11}&1-5k&k&k&k&k&k\\\cline{1-7}\end{array}[/tex]

Note:  The probabilities of all the possible values that a discrete random variable can take add up to 1.

The outcomes of rolling one 3 and one 4 are:

Given the probability of rolling one 3 and one 4 is ¹/₂₄:

[tex]\implies \text{P}(X=3)\; \text{and} \; \text{P}(Y=4) \; \text{or} \; \; \text{P}(X=4) \; \; \text{and} \; \; \text{P}(Y=3)=\dfrac{1}{24}[/tex]

[tex]\implies \dfrac{1}{6} \times k +\dfrac{1}{6} \times k=\dfrac{1}{24}[/tex]

[tex]\implies \dfrac{k}{6} + \dfrac{k}{6}=\dfrac{1}{24}[/tex]

[tex]\implies \dfrac{2k}{6}=\dfrac{1}{24}[/tex]

[tex]\implies 24(2k)=6[/tex]

[tex]\implies 48k=6[/tex]

[tex]\implies k=\dfrac{1}{8}[/tex]

Therefore:

[tex]\implies 1-5k=1-\dfrac{5}{8}=\dfrac{3}{8}[/tex]

Hence, the probability distribution table for the unfair 6-sided dice is:

[tex]\begin{array}{|c|c|c|c|c|c|c|}\cline{1-7} y & 1 & 2 & 3 & 4 & 5 & 6\\\cline{1-7} \text{P}(Y=y) \phantom{\dfrac11}&\frac{3}{8} & \frac{1}{8} & \frac{1}{8}& \frac{1}{8} & \frac{1}{8}& \frac{1}{8} \\\cline{1-7}\end{array}[/tex]

There is only one possible outcome of rolling two 1's, so the probability of rolling two 1's is:

[tex]\implies \text{P$(X=1)$ and P$(Y=1)$}=\dfrac{1}{6}\times\dfrac{3}{8}=\dfrac{3}{48}=\dfrac{1}{16}[/tex]

Note:  Please see attachment for the sample-space diagram showing the possible outcomes of rolling two dice. The possible outcomes of rolling one 3 and one 4 are highlighted in yellow. The possible outcome of rolling two 1's is highlighted in blue.

If new mobile device has a value of $256.25 and its value changes by [tex]22\frac{1}{2}[/tex]% each year, then the value of phone after two years is $153.76

The value of new mobile device = $256.25

The percentage of value change =  [tex]22\frac{1}{2}[/tex]%

Convert the mixed fraction to decimal form

[tex]22\frac{1}{2}[/tex]% = 22.5%

After one year mobile value = 256 - (256×22.5/100)

= 256-57.6

= $198.4

After two year the mobile value = 198.4-(198.4×22.5/100)

= 198.4-44.64

= $153.76

Hence, if new mobile device has a value of $256.25 and its value changes by [tex]22\frac{1}{2}[/tex]% each year, then the value of phone after two years is $153.76

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Answer:

3-[tex]\sqrt{3}[/tex] is the exact form

-5 is the common difference of the arithmetic sequence.

A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15. The nth term of an arithmetic progression is determined using the arithmetic sequence formula. The series where the common difference between any two next words stays constant is known as an arithmetic sequence.

Given Data

Arithmetic sequence

-19, -14, -9

Common difference = a₂ - a₁

Common difference = -14 - (-19)

Common difference = -14 + 19

Common difference = -5

-5 is the common difference of the arithmetic sequence.

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Using the arithmetic operations, the total change in her monthly electric bill over 5 months is +$10.58

For the past 5 months,

The change in her July electric bill = +$18.02

The change in her August electric bill =  +$1.03

The change in her September electric bill = -$0.44

The change in her October electric bill = -$6.84

The change in her November electric bill = -$1.19

The total change in her monthly electric bill over 5 months = Sum of all changes in her electric bill over 5 months

= +18.02+1.03-0.44-6.84-1.19

= +$10.58

Hence, the total change in her monthly electric bill over 5 months is +$10.58

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Answer:

B 2x² - x - 2

Step-by-step explanation:

When x²+x-3  is subtracted from 3x² - 5

We get (3x² - 5) - (x² + x - 3)

==> step 1 remove parenthesis and change signs

3x² - 5 - x² - x + 3

==> step 2 combine like terms

2x² - x - 2

Remember like terms are terms with the same variable and degree.

For example 3a² and 5a² would be like terms because both terms have a variable of "a" and a degree of 2

The coordinates of point A is (1.7,3.8)

A coordinate plane is a surface with two dimensions made up of two number lines. It is created when the origin, the point at which the X-axis and Y-axis cross, is reached. To locate points, one uses the numbers on a coordinate grid. A coordinate plane is useful for graphing points, lines, and many other things. It serves as a map and provides clear instructions for getting from one place to another.

Start at the point, then move up or down a vertical line until you reach the x-axis. Your x-coordinate is shown there which is 1.7. To get the y-coordinate, repeat the previous step while adhering to a horizontal line you will get y coordinate as 3.8

The coordinates of point A is (1.7,3.8)

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[tex]3(2y+1)[/tex] I believe is the solution you seek.

You factor 3 out of 6y + 3, leaving you with the solution.

Hope this helps!

Answer:

Nickels are equal to 5 cent and pennies are equal to 1 so:

5 times 100 = 500

1 times 60 = 60

500 + 60 = 560

560 converted to dollars would be $5.60!

Step-by-step explanation:

Hope it helps! =D

Andy hired the carpet cleaner for 9 days, bringing the total cost to £82.20.

An equation is an expression that shows the relationship between two or more numbers and variables. Dependent variables depend on other variable while an independent variable .

Let y represent the amount of money paid to the carpet cleaner for working x days. Multiply the number of days by 7.8 and then add 12, Hence:

y = 7.8x + 12

For a total cost of 82.20

82.2 = 7.8x + 12x  = 9.

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Answer:

2/15 mile per minute

Step-by-step explanation:

8 miles in 60 minutes is equivalent to 8/60 miles per minute

= 2/15 mile per minute

Answer:

Step-by-step explanation:

60/8=7.5

The proportional relationships that model each relation are given as follows:

A proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality represented by k, according to the equation below:

y = kx.

Both items in this problem are represented by direct proportional relationships, we just have to identify the constants then graph the relations.

The graph of a proportional relationship is linear with slope given by the constant and intercept at 0, hence the graphs for each item are given at the end of the answer.

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The inequality that is represented by the graph is; y ≤ 1.5x - 3

Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region.

Inequalities that use ≤ or ≥ symbols are plotted with a solid line to show that the line is included in the region.

Now, the given line is a dashed line and shaded below the line and as such we will use the inequality symbol ≤ .

The equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

From the graph, we have that;

c = -3

m = 1.5

Thus, we have the inequality as y ≤ 1.5x - 3

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Answer: 1/24

Step-by-step explanation:

1/2 * 1/12 = 1/24

The inverse of the conditional statement is : if two lines do not intersect, then the lines are not coplanar.

Conditionals are commands used in programming languages to handle decisions.

The contrapositive statement is :  If two lines are not coplanar, then the lines do not intersect.

The converse statement is :  If two lines are coplanar, then the lines intersect.

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Answer:

The first number is 10

The middle number is 11

The last number is 12

Answer:

Дсдслсьмтстстсьсьалалла =4

Answer: 2

Step-by-step explanation:

1. Simplify the expression

[tex]sqrt(12)/sqrt(3)\\3.464/sqrt(3)\\3.464/1.732[/tex]

2. Perform any multiplication or division, from left to right:

[tex]3.464/1.732[/tex]

[tex]2[/tex]

The correct option is A: None; the mode stayed the same.

Mode of a data set is the value that occur most frequently in a data set.

There may be no mode, one mode or more than one mode for a data depending on the number of times values are repeating.

Given that before Samuel taking a test,

Mean = 84.6

Median = 82

Mode = 88

After Samuel took the test,

Mean = 84

Also given that, his score was different from every other students’ score.

This means that from the data of scores, Samuel's score is not repeating.

Mode is the most repeating element.

So Samuel's score does not effect the mode and thus stayed the same.

Hence the mode stayed the same.

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Aaron Rodgers salary is 2.19×[tex]10^1^1[/tex] greater than his backups.

To find how many times a quantity x is greater than y we do subtraction. That is we do [tex]x-y[/tex].

So, here Aaron's salary is given to be $ 2.2× [tex]10^1^0[/tex]

And his quarterback's salary is $ 6.3×[tex]10^5[/tex].

Thus the difference between salaries= 2.2×[tex]10^1^0[/tex] - 6.3 × [tex]10^5[/tex]

                                                            = 2.19×[tex]10^1^1[/tex]

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Examining the given function it could be found that

This makes the third option a more correct option

The term vertex is used most times when the graph discussed is a curve, I t represents the peak of the graph. It may be the lowest or highest value depending on where the graph opens

This graph opens up and the vertex is the least value in the y axis which is 0, that is (2, 0)

The range is in the y axis. It is all the values in the y direction, that is from least to the maximum values. making the value: {y | 0 ≤ y < ∞} correct

This tow values are seen in the third option

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Answer:

-1(x - 5)x

Step-by-step explanation:

7x2 - 5x + 10x -8x2

7x2 + 5x -8x2

7x2 + 5x - 8x2

-1x2 + 5x

-1x2 + 5x

-x2 + 5x

7x2 - 5x + 10x - 8x2

-1 (x2 - 5x)

-1 (x2 - 5x)

-1(x - 5)x

-1(x - 5)x

Answer:

Since r and s are parallel lines, angle 1 = angle 2 (corresponding angles)

75 - 2x = 91 - 3x

x = 16

Angle 1 = 75 - 2(16) = 43°

Angle 2 = Angle 1 = 43°

Solving for the probability using the z-table, the proportion of iPhone owners who use their iPhone between 4 and 7 hours in a day is 0.787.

For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

First, solve for the z-score using the formula below.

z-score = (x – μ) / σ

where x = individual data value (4 and 7)

μ = mean = 5.4

σ = standard deviation = 1.2

z-score = (4 - 5.4) / 1.2     where x = 4

z-score = -1.4 / 1.2

z-score = -7/6 or -1.1667

z-score = (7 - 5.4) / 1.2     where x = 7

z-score = 1.6 / 1.2

z-score = 4/3 or 1.3333

Find the probability that corresponds to the z-score in the z-table. (see attached images)

z-score = -7/6 or -1.1667     probability = 0.12197

z-score = 4/3 or 1.3333     probability = 0.90853

To determine the proportion of iPhone owners who use their iPhone between 4 and 7 hours in a day is the difference between the probabilities of the two values.

proportion = 0.90853 - 0.12197

proportion = 0.787

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Answer:

the answer is 60

Step-by-step explanation:

the answer would be C ( i am not 100% sure though) c= -36x-9

d);

12(3x) = 36x

-12(-3/4) = 9