write an inequality that represents the graph

Answer:

y = 5/9

Step-by-step explanation:

   To simplify the expression, isolate y. To isolate y, divide both sides by 2.

 \(\sf 2y =\dfrac{10}{9}\\\\\text{Divide both sides by 2,}\\\\y = \dfrac{10}{9*2}\\\\y=\dfrac{5}{9}\)

Answer:

4) 10

Step-by-step explanation:

The number with x is slope and the other number is y-intercept so it's 10

Answer:

1. 3 times x

2. 3 times 4

                    U get 5x-3x+12

3. 5x-3x

                    u get 2x

4. Final solution: 5x+12

Step-by-step explanation:

Speed is the ratio of distance and time.

It shows how fast an object is moving at a given time.

The rate of change of the distance below the sea level with respect to time is 11 feet per second.

Speed is the ratio of distance and time.

It shows how fast an object is moving at a given time.

We have,

The table has a linear relationship.

We can choose two data from the table.

At time = 15,

Distance below the sea level = 545 feet.

At time = 27,

Distance between the sea level = 677

Now,

The rate of change of the distance below the sea level with respect to time.

Slope:

= (677 - 545) / (27 - 15)

= 132 / 12

= 11 feet per second

Thus,

The rate of change of the distance below the sea level with respect to time is 11 feet per second.

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The rate of change of distance for the submarine is given by 11 feet/sec.

In order to find the slope between two points (x₁, y₁) and (x₂, y₂), take the ratio of the difference of the respective coordinates as (y₂ - y₁)/(x₂ - x₁).

Given that,

The table for distance travelled versus time taken for a submarine.

In order to find the slope, take two values of distance and time from the given table as  380 feet at t = 0 and 545 feet at t = 15.

Now, the slope can be found as,

slope = (545 - 380)/(15 - 0)

         = 165/15

         = 11

Hence, the rate of change of distance below sea level with respect to time is given as 11 feet/sec.

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Answer:

\((1,13)\)

Step-by-step explanation:

\(p=-5t^2+18t\)

\(p=-2t+15\)

\(-5t^2+18t=-2t+15\)

\(-5t^2+20t=15\)

\(-5t^2+20t-15=0\)

\(-5(t^2-4t+3)=0\)

\(t^2-4t+3=0\)

\((t-1)(t-3)=0\)

\(t_1=1\), \(t_2=3\)

Since we want the position to be when the ball FIRST crosses the path of the bird, we will need to choose \(t_1=1\) as our solution.

Therefore, the position would be:

\(p=-2t+15\)

\(p=-2(1)+15\)

\(p=-2+15\)

\(p=13\)

\((1,13)\)

The shape of the sampling distribution is attached below

What is standard deviation?

The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.

The mean of the sampling distribution of the sample means is the mean of the population from which the scores were sampled.

The standard error of the mean is the standard deviation of the sampling distribution of the sample mean.

A Z-score indicates the number of standard deviations an element is deviated from the mean.

Using Central limit theorem,

If (n >30) is sufficiently large then the sampling distribution of sample mean follows a normal distribution with mean µx = µ

and standard error

σx = σ / √n

The formula for mean of the sample mean is,

µx = µ

The formula for standard deviation of the sample mean is,

σx = σ / √n

µ = 10.05

σ = 3

n = 64

∴The  value or mean of the sample mean is,

µx = µ

     = 10.05

The standard deviation of the sample mean is,

σx = σ / √n

    = 3 / √64

    = 0.375

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The correct graph which represents the equation y = 1/2x - 1 is,

⇒ Graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The equation is,

⇒ y = 1/2x - 1

Now, After draw the equation we get;

Graph of a line passing through the points (-2, - 2) and (0, - 1).

Thus, The correct statement is,

⇒ Graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1.

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Answer:

$100,000

Step-by-step explanation:

Let the total income of the store = \(\$x\)

Total spends on salaries = \(\frac{1}{4}\) of total income

Total spends on advertising = \(\frac{1}{6}\) of total income

Also, we are given that:

Total money paid as salaries = $150,000

To find:

Total spends on advertising ?

Solution:

As per question statement, we can write the following equation:

\(\dfrac{1}{4}x =\$150000\\\Rightarrow x =\$150000\times 4\\\Rightarrow x = \$600000\)

Now, as per the given statement, total spends on advertising are:

\(\dfrac{1}{6}x =\dfrac{1}{6}\times 600000 = \bold{\$100,000 }\)

Therefore, the answer is $100,000

, A0=50 and Al=0.Legendre polynomial series expansion for r=2 and l=0,1:u(r=2,θ)=B0/r+B1/r2+A1r. Therefore, B0=0, B1= -15/2, and A1=0.(a)The temperature on the outer surface as u(r=2.0)=D.GP(cos0).SP(θ) is givenas; u(r=2.0)=30cos8Where D is the constant.

From the fact that this has to be equal to 50 cos2 e, the coefficients c can be found by inspection. Therefore, D=15 and GP(cos0)=cos(8).From the expansion of u(r,θ)= ΣΡ(θ)D.GP(cos0), where l is the degree of the Legendre polynomial and m is the order of the Legendre polynomial. Therefore, D=15 and GP(cos0)=cos(8).(b)The temperature on the inner surface as u(r=1.0)= D. d4P(cosa) is given as;u(r=1.4) = 50cos(e)From the fact that u(r=1.8)#150cos, the coefficients d can be found by inspection. Therefore, D= 25/2 and d=3/2.

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Answer:

10,597.50 cubic mm

Step-by-step explanation:

V(cone) = [3.14(h)(r²)] ÷ 3

= 3.14(15)(15²) ÷ 3

= 10,597.5

(a) No, a triangle cannot have two obtuse angles. (b) No, a triangle cannot have two right angles.
(c) If no angle of a triangle measures more than 60°, then the triangle is an acute triangle.


(a) In a triangle, the sum of all three angles must be 180°. Since two obtuse angles would sum to more than 180°, it is not possible for a triangle to have two obtuse angles.
(b) In a triangle, the sum of all three angles must be 180°. Since two right angles would sum to 180°, it is not possible for a triangle to have two right angles.
(c) In an acute triangle, all three angles are less than 90°. If no angle of a triangle measures more than 60°, then all three angles are less than 90°, making it an acute triangle.

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Answer:

The pattern described in the question follows the rule that each consecutive line has a number that is one less than twice the previous line. Starting with 2 as the first line, the pattern can be written as follows:

1st line: 2

2nd line: 2(2) - 1 = 3

3rd line: 2(3) - 1 = 5

4th line: 2(5) - 1 = 9

5th line: 2(9) - 1 = 17

6th line: 2(x) - 1 (unknown)

To find the number of marbles in the 6th line, we can use the rule of the pattern and solve for x:

2(x) - 1 = 2(17) - 1 (substitute 17 for the number in the 5th line)

2x - 1 = 33

2x = 34

x = 17

Therefore, the 6th line of the pattern would have 17 marbles

Step-by-step explanation:

The pattern is described as having a number in each line that is one less than twice the previous line.

Write out the first few lines of the pattern, starting with 2 as the first line:

1st line: 2

2nd line: 2(2) - 1 = 3

3rd line: 2(3) - 1 = 5

4th line: 2(5) - 1 = 9

5th line: 2(9) - 1 = 17

To find the number of marbles in the 6th line, use the pattern rule and substitute the value for the 5th line:

6th line: 2(x) - 1

Substitute 17 for x (the value in the 5th line):

2(x) - 1 = 2(17) - 1

Simplify the right-hand side:

2(x) - 1 = 33

Add 1 to both sides:

2(x) = 34

Divide both sides by 2:

x = 17

Therefore, the 6th line of the pattern would have 17 marbles.

The complete pattern in the given question is: 2, 3, 5, 9, 17, 33.

To solve this problem, we need to apply the given rule to generate the numbers in the sequence and then find the sixth number.

Starting with two, we can apply the rule to generate the next few numbers:

First line: 2

Second line: 2(2) - 1 = 3

Third line: 2(3) - 1 = 5

Fourth line: 2(5) - 1 = 9

Fifth line: 2(9) - 1 = 17

Now we can apply the rule again to find the sixth number:

Sixth line: 2(17) - 1 = 33

Therefore, the sixth line must have 33 marbles.

The pattern starts with two, which is the first line.

The second line follows the given rule: "every consecutive line has a number that is one less than twice the previous line". We can apply this rule to the first line by multiplying it by 2 and subtracting 1: 2(2) - 1 = 3. Therefore, the second line has 3 marbles.

To find the third line, we can apply the same rule to the second line: 2(3) - 1 = 5. Therefore, the third line has 5 marbles.

Similarly, we can find the fourth line by applying the rule to the third line: 2(5) - 1 = 9. Therefore, the fourth line has 9 marbles.

We can find the fifth line by applying the rule to the fourth line: 2(9) - 1 = 17. Therefore, the fifth line has 17 marbles.

Finally, to find the sixth line, we apply the rule again to the fifth line: 2(17) - 1 = 33. Therefore, the sixth line has 33 marbles.

So, the complete pattern is: 2, 3, 5, 9, 17, 33.

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Answer:

Explanation: Realize that 4x2−25 is a difference of squares. Differences of squares, such as a2−b2 , can be factored into (a+b)(a−b) . Since 4x2=(2x)2 and 25=(5)2 , we can say that 4x2−25=(2x+5)(2x−5)

Step-by-step explanation:

Answer:

(2x + 5)(2x - 5)

Step-by-step explanation:

a² - b² = (a + b)(a - b)

4x² = 2²x²= (2x)²

25= 5* 5 = 5²

4x² - 25 = (2x)² -  5²         {a= 2x  ; b = 5}

             = (2x + 5)(2x - 5)

Answer:

y=(slope)*x+(y-intercept)

Step-by-step explanation:

The m is the slope, the b is the y-intercept, & the x and y are just the values.

The slope is equal to rise/run.

The y-intercept is where the line crosses the y axis.

The y axis is vertical and the x axis is horizontal.

Hope this helps! :)

Answer:

P(7,4)= 840

Step-by-step explanation:

The given integral is ∫(0 / x² √(2² + 490)) dx. To solve this integral, we can make a substitution by letting x = 7tan(θ), where θ is between -π/8 and π/8. Then, dx = 2sec²(θ) dθ. The given integral is ∫(0 / x² √(2² + 490)) dx, and after making the substitution x = 7tan(θ), the integral becomes ∫(0 / 98sec³(θ) √(1 + 122.5tan²(θ))) dθ.

Substituting these expressions in the integral, we have ∫(0 / (7tan(θ))² √(2² + 490))(2sec²(θ)) dθ. Simplifying further, we get ∫(0 / 49tan²(θ) √(4 + 490))(2sec²(θ)) dθ. Rearranging the expression under the square root, we have ∫(0 / 49sec²(θ) √(4(1 + 122.5tan²(θ))))(2sec²(θ)) dθ. This can be simplified to ∫(0 / 98sec³(θ) √(1 + 122.5tan²(θ))) dθ.

In summary, the given integral is ∫(0 / x² √(2² + 490)) dx, and after making the substitution x = 7tan(θ), the integral becomes ∫(0 / 98sec³(θ) √(1 + 122.5tan²(θ))) dθ.

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The given integral is ∫(0 / x² √(2² + 490)) dx. To solve this integral, we can make a substitution by letting x = 7tan(θ), where θ is between -π/8 and π/8. Then, dx = 2sec²(θ) dθ. The given integral is ∫(0 / x² √(2² + 490)) dx, and after making the substitution x = 7tan(θ), the integral becomes ∫(0 / 98sec³(θ) √(1 + 122.5tan²(θ))) dθ.

Substituting these expressions in the integral, we have ∫(0 / (7tan(θ))² √(2² + 490))(2sec²(θ)) dθ. Simplifying further, we get ∫(0 / 49tan²(θ) √(4 + 490))(2sec²(θ)) dθ. Rearranging the expression under the square root, we have ∫(0 / 49sec²(θ) √(4(1 + 122.5tan²(θ))))(2sec²(θ)) dθ. This can be simplified to ∫(0 / 98sec³(θ) √(1 + 122.5tan²(θ))) dθ.

In summary, the given integral is ∫(0 / x² √(2² + 490)) dx, and after making the substitution x = 7tan(θ), the integral becomes ∫(0 / 98sec³(θ) √(1 + 122.5tan²(θ))) dθ.

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Correlation coefficient of 0.82 is relatively high and suggests that the relationship between length and chest girth is statistically significant.

a. Based on the correlation coefficient of 0.82, we can infer that there is a strong positive relationship between length and chest girth of female bears. This means that as the length of the bear increases, the chest girth will also increase.

b. The correlation coefficient of 0.82 indicates that there is a strong linear relationship between length and chest girth of female bears. This means that the two variables are closely related and that they tend to move in the same direction. A correlation coefficient of 0.82 is relatively high and suggests that the relationship between length and chest girth is statistically significant.

c. If the measurements were made in centimeters instead of inches, the value of the correlation coefficient would not change. This is because correlation coefficients are not affected by changes in the units of measurement. The correlation coefficient only measures the strength and direction of the relationship between two variables, and this relationship would be the same regardless of whether the measurements were in inches or centimeters.

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a. When the length of the bear (x) is increased, based on the positive correlation coefficient (r = 0.82), we can infer that the chest girth (y) is also expected to increase. In other words, there is a positive relationship between the length and the chest girth of the female bears.

b. The correlation coefficient of 0.82 indicates a strong positive linear relationship between the length and chest girth of the female bears. This means that as the length of the bear increases, there is a strong tendency for the chest girth to also increase. The closer the correlation coefficient is to 1 (in this case, 0.82 is reasonably close to 1), the stronger the linear relationship.

c. If the measurements were made in centimeters instead of inches, the correlation coefficient would not change. The correlation coefficient is a measure of the strength and direction of the linear relationship between two variables and is independent of the unit of measurement. Therefore, the value of the correlation coefficient would still be 0.82, indicating the same strength and direction of the relationship between the length and chest girth, regardless of whether the measurements are in inches or centimeters.

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Answer:

slope = -2

y-intercept = 7

Step-by-step explanation:

Slope formula: y=mx+b

In every equation that follows this formula, m is slope and b is y-intercept.

Answer:

-2 - slope

7 - y-intercept

Step-by-step explanation:

The equation is in slope-intercept form.

y = mx + b

m - slope

b - y -intercept

'-2' is in m's spot. It is the slope.

'7' is in b's spot. It is the y-intercept.

Hope this helps!

The variable and units in this regression is drop in unit and in feet, The unit of the slope is seconds per foot and the slope must be positive.

a) Drop, which indicates the roller coaster's drop height in feet, is the predictor variable in this regression, and its units are feet. The response variable is Duration, which reflects the ride's duration in seconds and is measured in seconds.

The variables are ride duration (in seconds) and drop height (in feet).

b) The slope in this regression is measured in seconds per foot. This indicates that with every unit increase in drop height in feet, the ride time rises or reduces by the slope value, measured in seconds per foot.

unit of slope = unit of y (drop height) / unit of x (ride duration)

Thus,

unit of slope = seconds/foot. (seconds per foot).

c) The slope is most likely negative since a higher drop height often results in a longer ride time, and the Tower of Terror coaster, which has an extremely short duration despite a high drop height, has been excluded from the research.

I think the slope will be positive as the time it would take to traverse a larger distance is a larger time. Thus, the slope must be positive.

Although there is a lot of variation in the association between drop height and ride time among the roller coasters in the sample, the low R-squared value of 29.4% shows that there is a general declining tendency.

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Complete question;

A dataset on 91 roller coasters lists the Duration of the ride in seconds in addition to the Drop height in feet for some of the coasters. One coaster, the "Tower of Terror," is unusual for having a large drop but a short ride. After setting it aside, a regression to predict Duration from Drop for the remaining 90 coasters has R2 =29.4%

a) What are the variable and units in this regression?

b)  What units does the slope have?

c) Do you think the slope is positive or negative? Explain.

Answer:

Our calculator limits your interest deduction to the interest payment that would be paid on a $1,000,000 mortgage. Interest rate: Annual interest rate for this

Step-by-step explanation:

confidence interval for the mean battery life in the new model is [7.9489, 8.3045].

What is confidence interval ?

A confidence interval, in statistics, refers to the chance that a population parameter can fall between a collection of values for an exact proportion of times.

Main body:

Formula for confidence interval is =

CI = x- bar ± z*s/√n            where,

CI = confidence interval

x- bar = sample mean

z = confidence level value

{s} = sample standard deviation

{n} = sample size  

given ;

n = 6

mean = (8.23+7.89+8.14+8.25+8.30+ 7.95)/6

         =  8.127

value of z for 95% C.I. = 1.96

C.I. = 8.127 ± 1.96 * 0.22/√6

C.I. = 8.127 ± 0.1781

C.I. =[7.9490, 8.3044]

Hence correct option is A.

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The researcher is assessing item equivalence, If a study is in parallel forms of the measurement instrument to the same person. The correct option is C).

When a study introduces parallel forms, the researcher is assessing item equivalence. Item equivalence refers to the extent to which the different forms of the measurement instrument produce similar results for the same individual.

This assessment is crucial in research because it allows researchers to evaluate the consistency and reliability of the measurement instrument across different versions. By administering parallel forms to the same person, any differences in responses can be attributed to individual factors rather than variations in the instrument.

This helps ensure that the instrument is measuring the intended construct consistently and accurately. The correct option is C).

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Answer:

7

hope it helps..........

Given that, when six is subtracted from five times a number, the result is 9. The number is 3.

Given that, when six is subtracted from five times a number, the result is 9.

Let the number be y, such that;

(5 × y) - 6 = 9

Next, we solve for y

(5 × y) - 6 = 9

5y - 6 = 9

5y = 6 + 9

5y = 15

y = 15 / 5

y = 3

Given that, when six is subtracted from five times a number, the result is 9. The number is 3.

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Answer:

It will take Jamie 3 hours to complete it

Step-by-step explanation:

3/4 * 4/1 = 12/4 = 3 hours

Answer:

3 hours

Step-by-step explanation:

3/4x4/1=12/4

12/4=3

discrete, you cannot have 1.5 televisions

generally the number of X is a discrete variable.

continous = can contain decimal value  (float values)

discrete = no decimal  (integers)

Answer: See below

Step-by-step explanation:

640km/16gal

Divide both sides by 16

= 40/1

The unit rate is 40km/1gal

Answer:

11x+2

Step-by-step explanation:

subtract 7 from 9 to equal 2.

Answer:

-0.18181818

Step-by-step explanation:

9+(-7)=2 so

11x +2=???

11x= -2

x= -0.18181818

The volume of the pyramid is approximately 5.9 cm³.

To find the volume of a pyramid with a square base, you can use the formula:

Volume = (1/3) * base area * height

First, let's find the area of the square base. The perimeter of the base is given as 5.7 cm, which means each side of the square has a length of 5.7 cm / 4 = 1.425 cm.

The area of a square is given by the formula:

Area = side length * side length

Substituting the side length, we have:

Area = 1.425 cm * 1.425 cm = 2.030625 cm²

Now, we can calculate the volume of the pyramid:

Volume = (1/3) * base area * height

= (1/3) * 2.030625 cm² * 8.6 cm

= 5.91834375 cm³

Rounding to the nearest tenth of a cubic centimeter, the volume of the pyramid is approximately 5.9 cm³.

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