In which of the following cases is the construction of a triangle ABC possible?
(a) AB = 4cm, CA= 3cm, BC=1cm
(b) AB= 8cm, CA= 10cm, BC=8 cm
(c) AB= 7cm, BC= 10cm, CA=8 cm

False. An objective function is necessary for both maximization and minimization problems.

An objective function is an equation that represents the goal of an optimization problem. It is used to evaluate the performance of a certain set of decisions. Regardless of whether the goal is to maximize or minimize an outcome, the objective function is a necessary component of an optimization problem. In a maximization problem, the objective function is used to determine the highest possible output that can be achieved. In a minimization problem, the objective function is used to determine the lowest possible output that can be achieved. Therefore, an objective function is necessary for both maximization and minimization problems.

Learn more about function here

https://brainly.com/question/29633660

#SPJ4

The composite function (f.g)(x) has a value of (d) (f.g)(x) = 3x³ + 12x² - 7x - 28

From the question, we have the following parameters that can be used in our computation:

f(x) = x +4

g(x) = 3x² - 7

The composite function is given as

(f.g)(x)

This is calculated as

(f.g)(x) = f(x) * g(x)

Substitute the known values in the above equation, so, we have the following representation

(f.g)(x) = (x + 4) * (3x² - 7)

So, we have

(f.g)(x) = 3x³ + 12x² - 7x - 28

Hence, the function is (d) (f.g)(x) = 3x³ + 12x² - 7x - 28

Read more about composite function at

https://brainly.com/question/10687170

#SPJ1

There may be differences between correlations based on a subset of all potential scores and correlations based on the entire range. Range restriction is the name given to this idea.

When observed sample data are not available across the complete range of interest, it is said to have a restricted range. The most typical situation is when there is a bivariate correlation between two normally distributed variables, one of which has a smaller range than is typically seen in the population as a whole. If data from the complete possible range were studied, the observed connection would be attenuated (lower) than it is in these situations.

Although the variables themselves are not under the researchers' control, correlations are used by researchers to determine whether a relationship between two or more variables exists. A statistical measure known as correlation expresses how closely two variables are related linearly (meaning they change together at a constant rate). It's a typical strategy for describing simple relationships without making a declaration about cause and effect.

To learn more about correlations visit : brainly.com/question/28175782

#SPJ4

Z-score of Kevin's shoe size compared to the normal population is, 2.5.

How to find comparation of Kevin shoe size to normal population?

Learn more about Z-score calculation here: brainly.com/question/29187588

#SPJ4

Answer:

g = 109 degree

h = 71 degree

m = 71 degree

k = 84 degree

Step-by-step explanation:

g= 109 degrees because it is a vertical angle to the 109-degree angle, that is why it is 109 degree

h= 71 degrees because they are supplementary angles which means they add up to 180 degrees. We see that one is 109 degrees, so the other must be 71 degrees.

k = 84 degrees because it is a vertical angle to the 84-degree angle, which is why it is 84 degrees.

m= 71 degrees because m and g must add up to 180 degrees, and we know that g is 109 degrees, so m is 71 degrees!

Answer:

y = 2x + 6

Step-by-step explanation:

The equation c = 2h + 6 represents the cost of renting tools for a given number of hours. The slope of this line is the rate at which the cost of renting the tools increases as the number of hours increases. Since the cost increases by $2.00 for each hour that the tools are rented, the slope of the line is 2.

A graph of this line would be a straight line with a slope of 2 and a y-intercept of 6. This means that the graph would pass through the point (0, 6), which represents the cost of renting the tools for 0 hours. The correct solution is therefore the graph of the equation y = 2x + 6.

Answer:

the vertex is a maximum at (-4,0)

Step-by-step explanation:

Using the mathematical operations of multiplication, if Elyse owns 2,000 shares of a corporation that pays a quarterly dividend of $0.51 per share, she should expect yearly dividends of $4,080.

Mathematical operations involve the use of operands and mathematical operators to solve mathematical problems.

Mathematical operations follow the PEMDAS rule, which states that Parentheses, Exponents, Multiplication, and Divisions in that order should be solved first before  Additions and Subtractions.

The number of shares owned = 2,000

Quarterly dividend per share = $0.51

Quarters in a year = 4

Yearly dividends = $4,080 (2,000 x $0.51 x 4)

Thus, applying the multiplication operation, the annual dividend Elyse should receive is $4,080.

Learn more about mathematical operations at https://brainly.com/question/20628271

#SPJ1

The amount that would a taxi ride cost for 7 miles is $7.75 and The amount that would a taxi ride cost that is m miles long is $(2.5 + 0.75m).

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign. It shows that the expressions printed on the left and right sides have an equal relationship.

Given:

The taxi charges $2.50 just for the pickup and then an additional $0.75 per mile driven,

Write the equation for the following statement,

y = 2.5 + 0.75x

Here, y is the total amount and x is the number of miles,

Calculate the cost of the ride, put x = 7

y = 2.5 + 0.75 × 7

y = 7.75

Calculate the cost of the ride, put x = m

y = 2.5 + 0.75m

To know more about equation:

https://brainly.com/question/12788590

#SPJ1

No, the statistical notion of an outlier as an infrequently observed value is not meaningful for this data.

Since the points are uniformly distributed on the interval [0,1], they should all be observed with the same frequency. Therefore, there are no outlier values.The statistical notion of an outlier is an infrequently observed value, meaning that it is an observation that is far away from the rest of the data. For a set of points that are uniformly distributed on the interval [0,1], however, all the points should be observed with the same frequency since they are evenly spaced. Therefore, there is no outlier value and the statistical notion of an outlier is not meaningful for this data.

Learn more about statistics here

https://brainly.com/question/29093686

#SPJ4

At [tex]$5 \%$[/tex] level, the data is not strong enough to establish the claim of toothpaste advertisement.

It is recommended to switch to new toothpaste.

(a)

The null and alternative hypotheses are,

[tex]$$\begin{aligned}& H_0: \mu=3 \\& H_1: \mu < 3\end{aligned}$$[/tex]

Here, [tex]$\mu$[/tex] is the hypothesized mean.

Let the sample size be [tex]$n=2500$[/tex].

Let the sample mean be [tex]$\bar{x}=2.95$[/tex].

Let the population standard deviation be [tex]$\sigma=1$[/tex].

Since, the population standard deviation is known, one sample z-test is used to test the claim.

The test statistic is,

[tex]$$\begin{aligned}z & =\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}} \\= & \frac{2.95-3}{\frac{1}{\sqrt{2500}}} \\& =-2.5\end{aligned}$$[/tex]

So, the test statistic is, [tex]$z=-2.5$[/tex].

Let the level of significance be [tex]$\alpha=0.05$[/tex].

Find the critical value.

Using the standard normal distribution area tables, the left tail critical value is,

[tex]$$z_{0.05}=-1.645$$[/tex]

z score table attached at the end of solution.

The test statistic value is falls in the rejection region. Reject the null hypothesis. Therefore, it can be concluded that this does not support the null hypothesis at 5 percent level. So, at [tex]$5 \%$[/tex] level, the data is not strong enough to establish the claim of toothpaste advertisement.

(b)

The value of test statistic is also less than [tex]$-Z_{0.1}=-2.33$[/tex].

So, the claim cannot be established even at 1 percent level. It is recommended to switch to new toothpaste.

For more questions on standard deviation

https://brainly.com/question/29678689

#SPJ4

The angle θ is maximized when c = 2 (halfway between two points).

The maximum angle at which a conveyor may be inclined and still deliver a predetermined quantity of bulk material within a given time. As the maximum angle is approached, the rate of handling of bulk material is usually decreased.

Given that, in the figure, find the value of c in the interval [0, 4] on the x-axis that maximizes angle θ.

Express θ as a function of c, Let α be the angle to the left of θ and let β be the angle to the right, then,

tanα = 2/c

and tanβ = 2/(4-c)

At this point, we suppose that it might be easier to use cotangent in order to keep c inn numerator,

cotα = c/2

cotβ = (4-c)/2

We have, α+β+θ = π, so,

θ = π-α-β

= π-cot⁻¹c/2-cot⁻¹(4-c)/2

Differentiate, set equal to 0 and solve

dθ/dc = 1/1+(c/2)².1/2+1/1+(4-c/2)²(1/2)

Put dθ/dc = 0

1/1+(c/2)².1/2+1/1+(4-c/2)²(1/2) = 0

1/1+(c/2)²-1/1+(4-c/2)² = 0

1/1+(c/2)² = 1/1+(4-c/2)²

(4-c/2)² = (c/2)²

(c/2) = (4-c/2)

4-c = c

2c = 4

c = 2

Hence, The angle θ is maximized when c = 2 (halfway between two points).

For more references on maximum angle, click;

https://brainly.com/question/17222426

#SPJ1

When rotated through 180° anticlockwise or clockwise about the origin, the new position of the above points is.

Rotate shape A [tex]$180^{\circ}$[/tex] about point (1,0) is (-1,0)

How do you rotate a shape about a certain point?

Move each point on a shape the specified number of degrees in a circle centered on the point of rotation to rotate it. Make sure that every new point is located the same amount of time away from the point of rotation as its corresponding original point.

There are 360 degrees in a circle's complete revolution. We discovered that a rotation of 270 degrees is virtually a full circle. We learned that a whole rotation of a circle is divided in half by 180 degrees. 90 degrees, or half of 180, are simple to identify as angles.

To learn more about complete revolution visit:https://brainly.com/question/17773408

#SPJ1

The table shows that the cost of going to the movies with a group of people is equal to twice the number of people in the group. For example, if the number of people in the group is 2, the cost is 2 * 2 = $16. Similarly, if the number of people in the group is 4, the cost is 2 * 4 = $32, and if the number of people in the group is 8, the cost is 2 * 8 = $64. Therefore, if Tom wants to go to the movies with a group of n people, the cost will be 2 * n dollars.

one of two or more numbers that multiply together to form a specific product; a number that divides into another number with no remainder is a factor.

A component is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, therefore the numbers we are adding are factors of a product because the product is divisible by them.

Which of these four main types of factoring are they? The Grouping technique, the Differences in Two Squares, the Total or Difference in Cubes, as well as the Greatest Common Factors (GCF) are the four primary methods of factoring.

A factor is a value that completely divides another number. Consequently, the values we are multiplication are factors if multiplying two whole numbers results in a product.

To learn more about factor visit:

https://brainly.com/question/9231261

#SPJ4

The curvature of r(t) = 3t, t2, t3 at the point (3, 1, 1) is 0.178

In this question we need to find the curvature of r(t) = <3t, t^2, t^3> at the point (3, 1, 1).

The derivative of r(t) with respect to t is:

r'(t) = <3, 2t, 3t^2>

The point (3, 1, 1) corresponds to t = 1,

and r′(1) = <3, 2(1), 3(1)^2>

r'(1) = <3, 2, 3>

|r'(1)| = √(3^2 + 2^2 + 3^2)

|r'(1)| = √(9 + 4 + 9)

|r'(1)| = √(22)

|r'(1)| = 4.69

Now, r''(t) = <0, 2, 6t>

and r′'(1) = <0, 2, 6(1)>

r''(1) = <0, 2, 6>

r′(1) × r′′(1) = <0, 4, 18>

|r′(1) × r′′(1) |

= √(0^2 + 4^2 + 18^2)

= √(16 + 324)

= √340

= 18.44

So, the curvature of r(t) would be,

κ(1) = |r′(1) × r′′(1)| ÷ |r′(1)|^3

k(1) = 18.44 / 4.69³

k(1) = 0.178

Learn more about the curvature here:

https://brainly.com/question/30114042

#SPJ4

The rate of gas usage, in miles per gallon, is 35.4 miles/gallon.

A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.

Given that, A table below shows that the number of miles driven by Hakeem is directly proportional to the number of gallons he used.

According to the table,

There are 36, 41, 45 gallons of gas are used for 1274.4 mile, 1451.4 and 1593 miles respectively,

So, for finding unit rates, we will divide the total mile to total gallons used, in one journey,

unit rate = 1593/45 = 1274.4/36 = 1451.4/41 = 35.4

Hence, The rate of gas usage, in miles per gallon, is 35.4 miles/gallon.

For more references on unit rate, click;

https://brainly.com/question/29781084

#SPJ1

An equation of the line that passes through the point (-3, -7) and is parallel to the line 2x-3y=24 can be found by taking the slope of the line 2x-3y=24 and using it to write the equation of the line in point-slope form. The slope of the line 2x-3y=24 is 3/2, so an equation of the line that passes through (-3, -7) and is parallel to the line 2x-3y=24 can be written in the form y-y₁ = m(x-x₁), where m is the slope of the line, which is 3/2 in this case. Plugging in the coordinates of the point (-3, -7) and the slope 3/2, we get the equation y-(-7) = (3/2)(x-(-3)), which simplifies to y+7 = 3/2(x+3). Multiplying both sides of the equation by 2/3 to get rid of the fraction on the right-hand side, we get the final equation: 2/3y + 14/3 = x + 3. This is the equation of the line that passes through the point (-3, -7) and is parallel to the line 2x-3y=24.

It will be parallel to the JK line segment.

What are Parallel Sides ?

If two sides of a geometric shape are not touching or crossing each other and their separation is constant, they are said to be parallel. A shape's parallel sides are opposed, or across from one another, and if they were stretched infinitely beyond the boundaries of the shape, they would not intersect.

According to the given information

Now if a line segment [tex]$3 K$[/tex] is dilated by factor [tex]$0.5$[/tex] about [tex]$p$.[/tex]

The image 3'G' will be of half length as JK and every point on JK at P will be of at half distance.

Therefore,

It will be parallel to the JK line segment.

To know more about Parallel Sides

https://brainly.com/question/22074448

#SPJ1

Answer:

the 4th answer option : shift left by 7 and up by 1

Step-by-step explanation:

the "+1" at the end is simply adding 1 to every y (function result) of f(x). so, that moves everything up by 1.

the "+7" in the function argument is a little bit more complex : it means that the function value of x is the function value that would have been originally created for x+7. so, it happens 7 units "earlier". therefore, this means a shift to the left.

Answer:

x = 13/5 or 2.6

Step-by-step explanation:

First, multiply both sides of the equation by 3.

This leaves us with 5x + 2 = 15.

Next, subtract 2 from both sides to get 5x = 13.

Finally, divide 13 by 5 to get x = 13/5. This cannot be simplified.

Answer:

  3.85 minutes

Step-by-step explanation:

You want to know the time it takes for taxis traveling 33 mph and 45 mph toward each other to meet if they start 5 miles apart.

The speed at which the taxis approach each other is (33 mph +45 mph) = 78 mph. The time it takes to close the 5-mile gap is ...

  time = distance/speed

  time = (5 mi)/(78 mi/h) = 5/78 h ≈ 0.0641 h

In minutes, the time is ...

  (5/78 h)(60 min/h) = 300/78 min ≈ 3.85 minutes

__

Additional comment

That's about 3 minutes 50.8 seconds.

The sheets of metal on the roof must be parallel to each other in order to be perpendicular to the top line of the roof. This means that the sheets of metal are parallel to each other and that their relationship is one of parallelism. This parallelism is necessary so that the roof can maintain its structure and be waterproof.

The relationship between sheets of metal on a roof is one of parallelism. This is because each sheet must be perpendicular to the top line of the roof in order to maintain the structure and be waterproof. In order for the roof to remain secure and waterproof, the sheets must be parallel to each other. This parallelism is necessary in order for the roof to form one complete structure and for the sheets to remain secure. Without the parallelism of the sheets, the roof would be unable to maintain its structure and could easily be damaged by wind and rain. This is why the relationship between the sheets of metal on a roof is one of parallelism.

Learn more about parallel here

https://brainly.com/question/16701300

#SPJ4

Answer: (a) Obtain a point estimate for the population proportion of adults in the country who believe that televisions are a luxury they could do without.

The point estimate for the population proportion is 514 / 1012 = 0.507.

(b) Verify that the requirements for constructing a confidence interval about p are satisfied.

The sample is stated to be a simple random sample.

The value of n * p = 1012 * 0.507 = 514.7796 is greater than or equal to 10.

The value of n * (1 - p) = 1012 * (1 - 0.507) = 497.2204 is greater than or equal to 10.

The population proportion is less than or equal to 5% of the population size.

Therefore, the requirements for constructing a confidence interval are satisfied.

(c) Construct and interpret a 95% confidence interval for the population proportion of adults in the country who believe that televisions are a luxury they could do without.

The 95% confidence interval for the population proportion is 0.507 +/- 1.96 * sqrt((0.507 * (1 - 0.507)) / 1012) = 0.507 +/- 0.0245 = (0.4825, 0.5315).

We are 95% confident that the proportion of adults in the country who believe that televisions are a luxury they could do without is between 0.4825 and 0.5315.

(d) Is it possible that a supermajority (more than 60%) of adults in the country believe that television is a luxury they could do without? Is it likely?

It is possible that a supermajority of adults in the country believe that television is a luxury they could do without because the 95% confidence interval contains 60%. However, it is not likely because the confidence interval is relatively narrow and the point estimate is far from 60%.

(e) Use the results of part (c) to construct a 95% confidence interval for the population proportion of adults in the country who believe that televisions are a necessity.

The 95% confidence interval for the population proportion of adults who believe that televisions are a necessity is 1 - 0.5315 = 0.4685 to 1 - 0.4825 = 0.5175. Therefore, the 95% confidence interval for the population proportion of adults who believe that televisions are a necessity is (0.4685, 0.5175).

Step-by-step explanation:

Answer:

387

Step-by-step explanation:

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

Answer:

----------------------------------------------------

Simplify the expression:

Answer:

[tex]-11-6\sqrt{2}\:i[/tex]

Step-by-step explanation:

Given expression:

[tex]\left(-9-\sqrt{-32}\right)-\left(2+\sqrt{-8}\right)[/tex]

Remove the parentheses:

[tex]\implies -9-\sqrt{-32}-2-\sqrt{-8}[/tex]

Rewrite -32 as 16 · 2 · -1  and rewrite -8 as 4 · 2 · -1 :

[tex]\implies -9-\sqrt{16 \cdot 2\cdot -1}-2-\sqrt{4 \cdot 2\cdot -1}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]

[tex]\implies -9-\sqrt{16} \sqrt{2} \sqrt{-1}-2-\sqrt{4}\sqrt{2}\sqrt{-1}[/tex]

Simplify and apply the imaginary number rule √(-1) = i

[tex]\implies -9-4\sqrt{2}\:i -2-2\sqrt{2}\:i[/tex]

Group like terms:

[tex]\implies -9-2-4\sqrt{2}\:i -2\sqrt{2}\:i[/tex]

Combine like terms:

[tex]\implies -11-6\sqrt{2}\:i[/tex]

The weight of the piknits can be used to predict the number of goggles as there is a Linear equation in variables that may be defined as a linear courting among x and y, that is, variables.

In this case,  let x is the impartial variable, and y relies upon it, so y is called as the established variable.

linear courting (or linear association) is a statistical period used to explain a straight-line courting among variables. Linear relationships may be expressed both in a graphical layout or as a mathematical equation of the shape y = MX + b.

"There is no linear relationship between the weight and the number of glasses"

"There is a linear relationship.

A. Yes, because the scatterplot shows a linear pattern.

C. Yes, because a random sample was taken from Piknits for the scatterplots of the 4th and 5th residuals.

Read more about numbers;

brainly.com/question/251701

#SPJ4

Answer: Multiple choice

Step-by-step explanation: A contingency table would be used to summarize data such as Multiple Choice company employees by gender and organizational title company employees by gender and age company employees by compensation and age company employees by compensation and years with the company.

Answer:

m∠D = 49°
m∠E = 41°
m∠F = 90°

Step-by-step explanation:

        We know a triangle's angles add up to 180, so we can create an equation and solve for x. We also know the little box represents 90 degrees.

Given:

        90° + 5x° + 14° + 3x° + 20° = 180°

Combine like terms:

        8x° + 124° = 180°

Subtract 124 from both sides of the equation:

        8x° = 56°

Divide both sides of the equation by 8:

        x = 7

        Now, we will plug this value of x back into the angles to solve. Again, the little box represents that Angle F is equal to 90 degrees.

m∠D = 5x° + 14° = 5(7)° + 14° = 49°
m∠E = 3x° + 20° = 3(7)° + 20° = 41°
m∠F = 90°