. your history teacher is giving a 10-question quiz friday. you estimate your probability of getting any particular question right is 95%. you need to answer at least 9 questions correctly to get an a on the quiz. find the probability that you get an a.

a. Scatter plot: we can use the Years as the x-axis and Damage as the y-axis.

b. Regression line equation: y = -2.2909 + 1.3636x.

c. Scatter plot with regression line: [Insert scatter plot with regression line here].

d. Correlation coefficient: r ≈ 0.949.

e. Sum of squared deviations (SSD): SSD ≈ 170.94.

Prediction for a person who has smoked for 30 years: Predicted percentage of lung damage ≈ 38.963%.

a. To create a scatter plot, we can use the Years as the x-axis and Damage as the y-axis. Below is the resulting scatter plot.

b. To determine the equation of the best-fit regression line, we can use the formula y = a + bx, where a is the y-intercept and b is the slope. The values of a and b can be calculated using the following formulas:

b = (n∑xy - ∑x∑y) / (n∑x^2 - (∑x)^2)

a = (∑y - b∑x) / n

Here, n represents the sample size, ∑x, and ∑y are the sums of the x and y values, and ∑xy and ∑x^2 are the sums of the products and squares of the x and y values, respectively.

After performing the necessary calculations, we find:

b = (7(1924) - (173)(262)) / (7(642) - (173)^2) ≈ 1.3636

a = (176/7) - (1.3636/7)(118) ≈ -2.2909

Therefore, the equation of the regression line is y = -2.2909 + 1.3636x.

c. We can plot the regression line on the scatter plot. Here is the updated scatter plot with the regression line:

d. The correlation coefficient measures the strength and direction of the linear relationship between two variables. It ranges from -1 to +1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and +1 indicates a perfect positive correlation.

The formula for the correlation coefficient is:

r = (n∑xy - ∑x∑y) / √[(n∑x^2 - (∑x)^2)(n∑y^2 - (∑y)^2)]

After performing the calculations, we find:

r = (7(1924) - (173)(262)) / √[(7(642) - (173)^2)(7(2878) - (176)^2)] ≈ 0.949

Therefore, the correlation coefficient is r ≈ 0.949.

e. The sum of squared deviations (SSD) is a measure of the variation around the regression line. The formula for SSD is:

SSD = Σ(yi - yi)^2

where yi is the observed value and yi is the predicted value.

After substituting the values, we find:

SSD = (20 - 15.3)^2 + (14 - 9.1)^2 + (54 - 39.8)^2 + (63 - 59.6)^2 + (17 - 11.8)^2 + (71 - 67.1)^2 + (23 - 18.4)^2 ≈ 170.94

Therefore, the SSD is approximately 170.94.

To predict the percentage of lung damage for a person who has smoked for 30 years, we can substitute x = 30 into the regression equation:

y = -2.2909 + 1.3636(30) ≈ 38.963

Therefore, the predicted percentage of lung damage for a person who has smoked for 30 years is approximately 38.963%.

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a) The probability of randomly selecting a ball bearing with a diameter which exceeds 5.03mm is 4.78%.

b) The percentage of ball bearings will be discarded is 0.26%

c) We would expect to find approximately 78 faulty ball bearings in a batch of 30,000.

d)  We need to produce 30,008 ball bearings to fulfill the order for exactly 30,000 ball bearings.

e) If a small batch of 100 ball bearings are randomly and independently selected for quality control, then the probability that only 5 out of 100 ball bearings will be faulty is approximately 0.2195 or 21.95%.

a) To calculate the probability of randomly selecting a ball bearing with a diameter exceeding 5.03mm, we can use the normal distribution function with a mean of 5mm and a standard deviation of 0.02mm. The formula for the normal distribution function is:

f(x) = (1/σ√(2π)) * \(e^{-(x-\mu)^2\)/(2σ²))

Where μ is the mean, σ is the standard deviation, x is the value we want to find the probability for, e is the mathematical constant approximately equal to 2.71828, and π is the mathematical constant approximately equal to 3.14159.

We want to find the probability that x is greater than 5.03, so we need to find the area under the normal distribution curve to the right of 5.03. We can use a standard normal distribution table or calculator to find that the probability is approximately 0.0478 or 4.78%.

b) To determine the percentage of ball bearings that will be discarded due to their diameter being outside the range of 4.95mm to 5.05mm, we need to find the area under the normal distribution curve that falls outside of this range.

P(x < 4.95 or x > 5.05) = P(x < 4.95) + P(x > 5.05)

= (1/0.02√(2π)) * \(e^{(-((4.95-5)^2)}\)/(20.02²)) + (1/0.02√(2π)) * \(e^{(-((4.95-5)^2)}\)/(20.02²))

= 0.0013 + 0.0013

= 0.0026

Percentage of ball bearings that will be discarded = 0.0026 * 100%

= 0.26%

c) To find the expected number of faulty ball bearings in a batch of 30,000, we can use the mean and standard deviation of the normal distribution to calculate the expected value of the number of ball bearings that fall outside of the range of 4.95mm to 5.05mm.

We can calculate the expected value of the number of faulty ball bearings as follows:

E(X) = μ * n

= (P(x < 4.95 or x > 5.05)) * n

= 0.0026 * 30,000

= 78

d) To fulfill an order for exactly 30,000 ball bearings, we need to produce more than 30,000 ball bearings to account for the percentage of ball bearings that will be discarded. We can use the percentage of ball bearings that will be discarded (0.26%) from part (b) to calculate the total number of ball bearings that need to be produced. The formula is:

Total number of ball bearings needed = 30,000 / (1 - percentage of ball bearings that will be discarded)

= 30,000 / (1 - 0.0026)

= 30,007.8 (rounded up to the nearest whole number)

e) To find the probability that only 5 out of 100 ball bearings will be faulty, we can use the binomial distribution function.

In this case, n = 100, x = 5, and p is the probability that a ball bearing is faulty, which we can calculate using the probability from part (b) (0.0026).

f(5) = (¹⁰⁰C₅) * 0.0026⁵ * (1-0.0026)¹⁰⁰⁻⁵

= (100! / (5! * 95!)) * 0.0026^5 * 0.9974^95

= 0.2195 or 21.95%.

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Answer:

15.21 yd

Step-by-step explanation:

The maximum height is the value of the y- coordinate of the vertex.

Given a parabola in standard form y = ax² + bx + c ( a ≠ 0 ), then

the x- coordinate of the vertex is

\(x_{vertex}\) = - \(\frac{b}{2a}\)

y = - 0.04x² + 1.56x ← is in standard form

with a = - 0.04 and b = 1.56 , thus

\(x_{vertex}\) = - \(\frac{1.56}{-0.08}\) = 19.5

Substitute x = 19.5 into the equation for corresponding value of y

y = -0.04(19.5)² + 1.56(19.5) = - 15.21 + 30.42 = 15.21 yd

Maximum height is 15.21 yd

The approximate maximum height of the football is 15.21 yd.

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given that, the path of a football kicked by a field goal kicker can be modeled by the equation y = -0.04x² + 1.56x, where x is the horizontal distance in yards and y is the corresponding height in yards,

We need to find the maximum height of the football,

So, the function is :-

y = f(x) = -0.04x² + 1.56x

Since, we need to find maximum height and y represents that height we need to find extremes of the function.

Finding first derivative of function :-

y' = -0.08x + 1.56

Make it equal to 0 and solve for x :-

-0.08x + 1.56 = 0

x = 19.5

Put the value of x in the original function,

y = -0.04(19.5)² + 1.56 × 19.5 = 15.21

Hence, the approximate maximum height of the football is 15.21 yd.

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Answer:

C. 2/3

Step-by-step explanation:

To find the slope of a line from two points, use this formula.

\(m=\frac{y^2-y^1}{x^2-x^1}\)

The variable 'm' means slope in algebra.

y² means the second y-coordinate and y^1 means the first y-coordinate.

Based on the previous definition, it should be easy to figure out what x² and x^1 mean.

\((2,4),(5,6)\)

\(m=\frac{6-4}{5-2} =\frac{2}{3}\)

Therefore, the slope of the line passing through the points (2,4) and (5,6) is 2/3.

Let me know if you have any questions.

Using the Central Limit Theorem, it is found that the mean of the sampling distribution of the sample proportion of the responses is of 0.78.

In this problem, an article written for a magazine claims that 78% of the magazines subscribers report eating healthily the previous day, hence \(p = 0.78\).

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Answer:

c

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Hey there! I'm happy to help!

For the x value of the midpoint, you add the x values and divide by 2. For the y value of the midpoint, you add the y values and divide by 2.

First we add the x values.

-4+10=6

And divide by 2.

6/2=3

Then we add the y values.

3+7=10

And divide by 2.

10/2=5

Therefore, our midpoint is (3,5).

Have a wonderful day! :D

Answer:

(3,5)

Step-by-step explanation:

Midpoint= (x1 +x2)/2 , (y1 + y2)/2

x1= -4 , x2= 10 , y1= 3 , y2= 7

M= (-4+10)/2 , (3+7)/2

M= (3, 5)

Answer:

Train B

Step-by-step explanation:

Answer:

83 percent

Step-by-step explanation:

10/12= 0.83

move up the decimal point and your answer is 83%

hope that helps :)

Answer:

side a = Smallest = 9 inches

side b = 18 inches

side c = 17 inches

Step-by-step explanation:

The formula for the perimeter of a triangle = side a + side b + side c

side a = Smallest

The perimeter of a triangle is 44 inches.

The length of one side is twice the length of the shortest side

Hence:

b = 2a

The length of the other side is eight inches longer than the length of the shortest side.

Hence,

c = 8 + a

Hence, we substitute into the Intial formula

a + 2a + 8 + a = 44 inches

4a + 8 = 44

4a = 44 - 8

4a = 36

a = 36/4

a = 9 inches

Solving for b

b = 2a

b = 2 × 9 inches = 18 inches

Solving for c

c = a + 8

c = 9 inches + 8 = 17 inches

Answer:

Step-by-step explanation:

sum of ratio=3+7=10

total=120 ml

first part=3/10×120=36 ml

second part=7/10×120=84 ml

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

Explanation:

For the x value x = 3, the observed y value is y = 6 which is from the point (3,6).

The predicted y value is found by plugging x = 3 into the line of best fit equation

y = 5x-2.5

y = 5(3)-2.5

y = 12.5

The residual is the difference between the two y values

e = residual

e = (observed y value) - (predicted y value)

e = 6 - 12.5

e = -6.5

The negative residual tells us the observed y value is smaller than the predicted y value for this given x value.

Answer:

3 to 4

Step-by-step explanation:

12÷4=3

16÷4=4

so that makes it 3 to 4

Answer:

I do not understand the question?

Step-by-step explanation:

Answer:

Step-by-step explanation:

take a right triangle ABC...

right angled at B...

let AB be the height of the water tank...=52feet

AC hypotanuse...

BC is the length of the shadow..=78feet

tan thete=Opp/adj=AB/BC=52/78------eq1

tan theta in both cases remain the same,

hence,

take a right triangle PQR...

right angled at Q...

let PQ be the height of the water tank...

PR hypotanuse...

QR is the length of the shadow...=6feet

tan theta=52/78 (from 1)

tan thete=Opp/adj=PQ/QR = PQ/6-----eq2

hence, from 1, 2

52/78=PQ/6....

52x 6/78=PQ

52/13=PQ

Hence,4m=PQ=height of the boy...

Thank you, Hope this helps you dear friend,,,,

Answer:

The volume of a cylinder is calculated by multiplying the area of the base by the height. The area of the base of a cylinder is πr², where r is the radius of the cylinder. In this case, the radius is 8 centimeters, so the area of the base is 201.06 cm². The height of the cylinder is 17 centimeters, so the volume of the cylinder is 3417.02 cm³.

The volume of a rectangular prism is calculated by multiplying the length, width, and height. In this case, the length is 15 centimeters, the width is 12 centimeters, and the height is 9 centimeters. The volume of the rectangular prism is 1620 cm³.

Since the volume of the cylinder is less than the volume of the rectangular prism, the water will not overflow.

Here is an argument that can be used to defend this solution:

The volume of the cylinder is calculated by multiplying the area of the base by the height.

The area of the base of a cylinder is πr², where r is the radius of the cylinder.

In this case, the radius is 8 centimeters, so the area of the base is 201.06 cm².

The height of the cylinder is 17 centimeters, so the volume of the cylinder is 3417.02 cm³.

The volume of a rectangular prism is calculated by multiplying the length, width, and height.

In this case, the length is 15 centimeters, the width is 12 centimeters, and the height is 9 centimeters.

The volume of the rectangular prism is 1620 cm³.

Since the volume of the cylinder is less than the volume of the rectangular prism, the water will not overflow.

Step-by-step explanation:

Answer:

A1 = 18

A(n) = A (n-1) -2

Step-by-step explanation:

N represents the number in a sequence and the difference in the sequence is -2 since each time the number is listed in the sequence it is divide by 2.

Answer:

The distance would be 6.7 or 3✓5

Step-by-step explanation:

Im sure there's a faster way to find this, but I'm in 8th grade sooo yeah.

First things first we can use the equation

d=✓(X2-X1)*2+(Y2-Y1)*2

X2= 8

X1= 5

Y2= 13

Y1= 7

From here, you plug in the values and do as followed. You subtract the values to get the answer. For example 8-5 would get us (3)*2.

From here you square the 3 to get 9. You also do the same to the right side of the equation.

Now you have d=✓(3)*2 + (6)*2

From here you square it and you get d=✓9+36

Now we have: d✓45

Now we square the 45 to get 6.7082..., but we round the answer to get 6.7!

Hope this helps! If you have any questions please feel free to ask, as I understand the struggle of math! :)

Answer:

the distance would be 6.7

Step-by-step explanation:

Answer: Question 1: A. 48 would the answer

Answer: Question 2: C. 48 would be the answer

Hope this help...

Have a great day.

Answer:

C ) 48

Step-by-step explanation:

To begin, you have to figure out which angles correspond on the two triangles.

So here are the angles that correspond:

U = N

T = M

S = L

So, ST would be similar to LM so 32 and 8 will be similar.

And UT will be similar to NM so the missing length and 12 are similar.

To begin, find out the scale factor by dividing 32 by 8 to get 4.

Then, multiply 12 by 4 to get 48 for the missing length.

Answer:

about 45%

Step-by-step explanation:

it should be right

Complete question :

A company has two manufacturing plants with daily production levels of 5x + 11 items and 2x - 3 items, respectively, where x represents a minimum quantity. The first plant produces how many more items daily than the second plant?

Answer:

3x + 14

Step-by-step explanation:

Given that:

Production level of plant 1 = 5x + 11

Production level of plant 2 = 2x - 3

The first plant produces how many more items daily than the second plant :

Plant 1 production - plant 2 production

(5x + 11) - (2x - 3)

Open the bracket :

5x + 11 - 2x + 3

5x - 2x + 11 + 3

3x + 14

Daily production of plant 1 exceeds that of plant 2 by 3x + 14

A.p:40 his friends alex

Answer:

the answer is p<40

Step-by-step explanation:

(: ur welcome

The function f(x) = x^4 - 12x^3 + 48x^2 - 64x has no horizontal asymptotes, a y-intercept at (0, 0), and its maximum value is located at the critical points (3, 27) and (-3, 27).

To sketch the curve of the function f(x)=x4−12x3+48x2−64xf(x)=x4−12x3+48x2−64x, let's analyze its various properties.

Domain:

The function f(x)f(x) is a polynomial, and polynomials are defined for all real numbers. Therefore, the domain of f(x)f(x) is (−∞,∞)(−∞,∞).

X-Intercepts:

To find the x-intercepts, we set f(x)f(x) equal to zero and solve for x:

x4−12x3+48x2−64x=0x4−12x3+48x2−64x=0

Factoring out an x, we get:

x(x3−12x2+48x−64)=0x(x3−12x2+48x−64)=0

By inspection, we can see that x=0x=0 is one of the x-intercepts. To find the remaining x-intercepts, we need to solve the equation x3−12x2+48x−64=0x3−12x2+48x−64=0. Unfortunately, this equation does not have easily factorizable solutions, so we will need to use numerical methods or a graphing calculator to find the remaining x-intercepts. Let's assume that there are additional x-intercepts at x=ax=a and x=bx=b.

Y-Intercept:

To find the y-intercept, we set x=0x=0 in the equation of f(x)f(x):

f(0)=04−12(0)3+48(0)2−64(0)=0f(0)=04−12(0)3+48(0)2−64(0)=0

Therefore, the y-intercept is at the point (0, 0).

Asymptotes:

Since f(x)f(x) is a polynomial function, it does not have vertical asymptotes. However, it may have horizontal asymptotes. To check for horizontal asymptotes, we examine the end behavior of the function as xx approaches positive or negative infinity.

As xx approaches positive infinity:

f(x)=x4−12x3+48x2−64xf(x)=x4−12x3+48x2−64x

As xx becomes very large, the highest-degree term dominates the equation. The term x4x4 grows much faster than the other terms, so the function will increase without bound. Therefore, there is no horizontal asymptote as xx approaches positive infinity.

As xx approaches negative infinity:

f(x)=x4−12x3+48x2−64xf(x)=x4−12x3+48x2−64x

As xx becomes very large in the negative direction, the highest-degree term x4x4 dominates the equation. However, since the exponent of x4x4 is even, the function will mirror the behavior of x4x4 as it approaches negative infinity. Since x4x4 is always positive, the function will also be positive. Therefore, there is no horizontal asymptote as xx approaches negative infinity.

In summary, f(x)f(x) does not have any horizontal asymptotes.

Intervals of Increase/Decrease:

To find the intervals of increase and decrease, we examine the sign of the derivative of f(x)f(x). Let's find the derivative of f(x)f(x):

f′(x)=4x3−36x2+96x−64f′(x)=4x3−36x2+96x−64

To determine the sign of f′(x)f′(x), we need to solve the inequality f′(x)>0f′(x)>0. Unfortunately, the solutions to this inequality are not easily obtained, so we will use a graphing calculator or numerical methods to find the intervals of increase and decrease.

Local Extreme Values:

To find the local extreme values, we need to identify the critical points of the function. The critical points occur where f′(x)=0f′(x)=0 or where the derivative is undefined. Let's set f′(x)=0f′(x)=0 and solve for xx:

4x3−36x2+96x−64=04x3−36x2+96x−64=0

Similar to finding the x-intercepts, this equation does not have easily factorizable solutions, so we need to use numerical methods or a graphing calculator to find the critical points. Let's assume that the critical points are at x=cx=c and x=dx=d.

Intervals of Concavity:

To find the intervals of concavity, we need to examine the sign of the second derivative of f(x)f(x). Let's find the second derivative:

f′′(x)=12x2−72x+96f′′(x)=12x2−72x+96

To determine the sign of f′′(x)f′′(x), we need to solve the inequality f′′(x)>0f′′(x)>0. Similar to previous cases, we will need to use numerical methods or a graphing calculator to find the intervals of concavity.

Inflection Points:

The inflection points occur where the concavity of the curve changes. These points correspond to the solutions of f′′(x)=0f′′(x)=0 or where the second derivative is undefined. Let's set f′′(x)=0f′′(x)=0 and solve for xx:

12x2−72x+96=012x2−72x+96=0

Again, we need to use numerical methods or a graphing calculator to find the inflection points. Let's assume the inflection points are at x=ex=e and x=fx=f.

After obtaining all this information, we can sketch the curve of the function f(x)f(x) using the x-intercepts, y-intercept, asymptotes, intervals of increase/decrease, local extreme values, intervals of concavity, and inflection points. However, since we don't have the specific values of the x-intercepts, critical points, and inflection points, it's not possible to provide an accurate sketch without additional information or numerical calculations.

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The NPV is positive, it is worth taking the Investment.

Net Present Value (NPV) is an assessment method that determines the attractiveness of an investment. It is a technique that determines whether an investment has a positive or negative present value.

This method involves determining the future cash inflows and outflows and adjusting them to their present value. This helps determine the profitability of the investment, taking into account the time value of money and inflation.The formula for calculating NPV is:

NPV = Σ [CFt / (1 + r)t] – CIWhere CFt = the expected cash flow in period t, r = the discount rate, and CI = the initial investment.

The given problem can be solved by using the following steps:

Calculate the present value (PV) of the expected cash inflows:

Year 1: $28,000 / (1 + 0.08)¹ = $25,925.93Year 2: $28,000 / (1 + 0.08)² = $24,009.11Year 3: $28,000 / (1 + 0.08)³ = $22,173.78Total PV = $72,108.82

Calculate the PV of the initial investment: CI = $7,000 / (1 + 0.08)¹ + $35,000 / (1 + 0.08)²CI = $37,287.43Calculate the NPV by subtracting the initial investment from the total PV: NPV = $72,108.82 – $37,287.43 = $34,821.39

Since the NPV is positive, it is worth taking the investment.

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The eye color of respondents in a survey is qualitative data at the nominal level of measurement.

The eye color of respondents in a survey can be categorized as qualitative data because it represents a characteristic or attribute rather than a numerical quantity. Qualitative data is descriptive and categorical.

In terms of the level of measurement, the eye color variable can be classified as nominal level data. Nominal data is the lowest level of measurement and simply categorizes observations into different groups without any inherent order or magnitude. In this case, eye colors such as blue, brown, green, hazel, etc. are non-numeric categories without any implied ranking or quantitative relationship.

Nominal data is characterized by the fact that you cannot perform mathematical operations on the categories, and there is no meaningful measure of central tendency or dispersion. Eye color falls into this category since you cannot meaningfully calculate averages or quantify differences between eye colors using mathematical operations.

To summarize, the eye color of respondents in a survey is qualitative data at the nominal level of measurement.

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A discrete probability distribution is a statistical distribution that relates to a set of outcomes that can take on a countable number of values, whereas a continuous probability distribution is one that can take on any value within a given range.Therefore, the main difference between the two types of distributions is the type of outcomes that they apply to.

An example of a discrete probability distribution is the probability of getting a particular number when a dice is rolled. The possible outcomes are only the numbers one through six, and each outcome has an equal probability of 1/6. Another example is the probability of getting a certain number of heads when a coin is flipped several times.

On the other hand, an example of a continuous probability distribution is the distribution of heights of students in a school. Here, the range of heights is continuous, and it can take on any value within a given range.

The expected value of a probability distribution measures the central tendency or average of the distribution. In other words, it is the long-term average of the outcome that would be observed if the experiment was repeated many times.

For a discrete probability distribution, the expected value is computed by multiplying each outcome by its probability and then adding the results. In mathematical terms, this can be written as E(x) = Σ(xP(x)), where E(x) is the expected value, x is the possible outcome, and P(x) is the probability of that outcome.

For example, consider the probability distribution of the number of heads when a coin is flipped three times. The possible outcomes are 0, 1, 2, and 3 heads, with probabilities of 1/8, 3/8, 3/8, and 1/8, respectively. The expected value can be computed as E(x) = (0*1/8) + (1*3/8) + (2*3/8) + (3*1/8) = 1.5.

Therefore, the expected value of the distribution is 1.5, which means that if the experiment of flipping a coin three times is repeated many times, the long-term average number of heads observed will be 1.5.

The transformation of the coordinate (-8, -3)  R 270° and T-2,-1 is (-5, -9)

Transformation is the change of the coordinates of a shape either by rotation, reflection or translation.

Analysis:

When coordinates (x, y) rotate 270° the resulting coordinates become (-y, x)

so coordinates (-8, -3) after 270° rotation becomes ( 3, -8)

When it is translated 2 units to the left and 1 unit down, that is -3 + -2 = -5 and -8 + -1 = -9

Therefore the transformed coordinate becomes (-5, -9)

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Answer:

\(x\ge \:-\frac{15}{2}\)

The graph of the inequality is attached below.

Step-by-step explanation:

Given the inequality

\(-2x-4\le 11\)

\(\mathrm{Add\:}4\mathrm{\:to\:both\:sides}\)

\(-2x-4+4\le \:11+4\)

\(-2x\le \:15\)

\(\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}\)

\(\left(-2x\right)\left(-1\right)\ge \:15\left(-1\right)\)

\(2x\ge \:-15\)

\(\mathrm{Divide\:both\:sides\:by\:}2\)

\(\frac{2x}{2}\ge \frac{-15}{2}\)

\(x\ge \:-\frac{15}{2}\)

The graph of the inequality is attached below.