Solve
(x-6)-(4.5-x)=-1.5

\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

The given triangles are congruent by :

because they have Two Angles and a side between them equal to the corresponding Angles and side of the another triangle.

By definition, direct variation takes the following form:

y=kx

Where k is the proportionality constant.

You can find k given the information in the problem:

7=3k

k=3/7

You can now find y when x=7 as follows:

y=(7*3)

Values can be substituted. Then:

y=(7*7)/3

y=49/3

If y varies directly from x, then the value of y = 49/3 when x = 7.

If y varies directly from x, we can write its relationship in the form of the equation below :

y = m*x

Where m is the slope of the line on the graph.

From the given data:

y=7

x=3,

We can substitute these values in the above equation and find m :

7 = m*3

m = 7/3

So, the equation can also be written as follow:

y = 7/3 x

Finding y when x=7, then substituting the x value in the above equation we get:

y = (7/3)*(7)

y = 49/3

Therefore the value of the y = 49/3.

to learn more about the slope:

https://brainly.com/question/28645794

The side lengths of RS and PR are 12 units

Similar triangles are triangles whose corresponding sides are in proportion to one another.

In most cases, one triangle is dilated to form the other triangle

Dilation involves enlarging or reducing the side length of a shape to create another shape by a constant scale factor, where the scale factor does not equal one.

The corresponding triangles are given as:

PQR and PSQ

This means that

PQ corresponds to PS

PR corresponds to PQ

QR corresponds to QS

Where

PQ = 18

QR = 14

QS = 21

So, we have:

PR : QR = PQ : QS

This gives

PR : 14 = 18 : 21

Express as fraction

PR / 14 = 18 / 21

Multiply through by 14

PR = 14 * 18 / 21

Evaluate

PR = 12

The corresponding triangles are given as:

PQR and PSQ

This means that

PQ corresponds to PS

PR corresponds to PQ

QR corresponds to QS

Where

PQ = 18

QR = 14

QS = 21

So, we have:

RS = PR

This gives

RS = 12

Hence, the side lengths of RS and PR are 12 units

Read more about similar triangles at

https://brainly.com/question/14285697

#SPJ1

Based on the provided information, the Type 1 error is that you conclude the weightlifting bar can withstand weights of greater than 800 pounds when, in fact, the weightlifting bar can withstand weights of less than or equal to 800 pounds. (Option C)

In statistical hypothesis testing, a Type I error refers to the rejection of null hypothesis when it's actually true while a type II error is the failure to reject a null hypothesis that is actually false. Type I error means to conclude that results are statistically significant when, in actuality they are caused purely by chance or because of unrelated factors. The risk of committing this error is the significance level (alpha or α) chosen. As the null hypothesis states that weightlifting bar can withstand weights of 800 pounds or less while alternative hypothesis states that weightlifting bar can withstand weights of over 800 pounds, the type I error would be to conclude that weightlifting bar can withstand weights of greater than 800 pounds when, in fact, it cannot.

Note: The question is incomplete. The complete question probably is: Suppose the null hypothesis, H0, is a weightlifting bar that can withstand weights of 800 pounds and less. The alternative hypothesis, Ha, is a weightlifting bar can withstand weights greater than 800 pounds. What is the Type 1 error in this scenario? Select the correct answer below: A) You cannot conclude the weightlifting bar can withstand weights of greater than 800 pounds when, in fact, the weightlifting bar can withstand weights of greater than 200 pounds B) You cannot conclude the weightlifting bar can withstand weights of greater than 800 pounds when, in fact, the weightlifting bar can withstand weights of less than or equal to 800 pounds. C) You conclude the weightlifting bar can withstand weights of greater than 800 pounds when, in fact, the weightlifting bar can withstand weights of less than or equal to 800 pounds. D) You conclude the weightlifting bar can withstand weights of greater than 100 pounds when, in fact, the weightlifting bar can withstand weights of greater than 800 pounds.

Learn more about Type I error:

https://brainly.com/question/16012410

#SPJ4

Answer:

a soln

x+52=180(co interior angles)

x=180-52

x=128

The acute angle between the lines x - 3y + 6 = 0 and x + 2y - 7 = 0 is approximately 45°, and the obtuse angle is approximately 135°.

To determine the acute and obtuse angles between the lines, we can start by finding the normal vectors of the lines.

For the line x - 3y + 6 = 0, the coefficients of x and y give us the normal vector (1, -3).

For the line x + 2y - 7 = 0, the coefficients of x and y give us the normal vector (1, 2).

The dot product of two vectors is equal to the product of their magnitudes and the cosine of the angle between them:

N1 · N2 = |N1| |N2| cos θ

where N1 and N2 are the normal vectors, and θ is the angle between the lines.

Let's calculate the dot product:

(1, -3) · (1, 2) = (1)(1) + (-3)(2) = 1 - 6 = -5

The magnitudes of the normal vectors are:

|N1| = √(1^2 + (-3)^2) = √(1 + 9) = √10

|N2| = √(1^2 + 2^2) = √(1 + 4) = √5

Now we can find the cosine of the angle between the lines:

cos θ = (N1 · N2) / (|N1| |N2|) = -5 / (√10 √5) = -√2 / 2

To find the acute angle, we can take the inverse cosine of the absolute value of the cosine:

θ_acute = cos^(-1)(|-√2 / 2|) = cos^(-1)(√2 / 2) ≈ 45°

To find the obtuse angle, we subtract the acute angle from 180°:

θ_obtuse = 180° - θ_acute ≈ 180° - 45° = 135°

Therefore, the acute angle between the lines x - 3y + 6 = 0 and x + 2y - 7 = 0 is approximately 45°, and the obtuse angle is approximately 135°.

Learn more about obtuse angles

https://brainly.com/question/29077542

#SPJ11

Answer:

Problem 1: Given initial volume of gas (V1) at 45°C, find the volume of the gas (V2) at 0°C, assuming constant pressure.

Problem 2: Given initial volume of gas (V1) at 27°C and 700 mmHg, find the pressure of the gas (P2) at 45°C and 780 mmHg.

Step-by-step explanation:

Answer:

200 kilometers

Step-by-step explanation:

since the driver goes 50 kilometers at a constant rate for 4 hours, you multiply it by 4, and you get 200.

An easy way to multiply these numbers is to multiply the 4 and 5, which equals 20, then add the extra zero from the 50.

Yes, two samples can have the same range but different means. The range of a dataset is a measure of the spread or dispersion and is determined by the difference between the maximum and minimum values. The mean, on the other hand, represents the average value of the dataset.

To illustrate this concept, let's consider two different samples:

Sample 1: 1, 5, 6, 9, 10

Sample 2: 2, 4, 7, 8, 10

Both samples have a range of 9 (10 - 1).

However, the means of the samples are different. The mean of Sample 1 is

(1 + 5 + 6 + 9 + 10) / 5 = 6.2,

while the mean of Sample 2 is

(2 + 4 + 7 + 8 + 10) / 5 = 6.2.

Despite having the same range, the means differ between the two samples.

The range only considers the extreme values of the dataset, whereas the mean takes into account all values and provides an average measure. It is possible for the individual values within the samples to be distributed differently, resulting in different means, even if the range remains the same.

Therefore, the range and the mean are distinct measures that capture different aspects of the dataset. While it is possible for two samples to have the same range, they can still have different means based on the specific values and their distribution within each sample.

To learn more about range

https://brainly.com/question/16444481

#SPJ11

To estimate the mean EPA combined city and highway mileage, the automaker conducted EPA mileage tests on a random sample of 35 midsize cars. The sample mean is 24, and the population standard deviation is 1.2. The task is to calculate the 70% confidence interval for the population mean.

To calculate the confidence interval, we can use the formula:

Confidence Interval = Sample Mean ± (Critical Value) * (Standard Deviation / √(Sample Size))

First, we need to determine the critical value associated with a 70% confidence level. The critical value can be found using a standard normal distribution or a t-distribution, depending on the sample size and whether the population standard deviation is known.

Since the sample size is relatively large (n = 35), we can use the standard normal distribution. The critical value for a 70% confidence level corresponds to a z-score of ±1.036.

Next, we calculate the margin of error:

Margin of Error = (Critical Value) * (Standard Deviation / √(Sample Size)) = 1.036 * (1.2 / √35) ≈ 0.380

Finally, we can calculate the lower and upper bounds of the confidence interval:

Lower Bound = Sample Mean - Margin of Error = 24 - 0.380 ≈ 23.62

Upper Bound = Sample Mean + Margin of Error = 24 + 0.380 ≈ 24.38

Therefore, the 70% confidence interval for the mean EPA combined city and highway mileage is approximately 23.62 to 24.38.

Learn more about standard deviation here: brainly.com/question/29808998

#SPJ11

Answer: 20

i just got it from the calculator

The sampling technique used in this scenario is simple random sampling.

Simple random sampling involves randomly selecting a subset of elements from a population in such a way that every element has an equal chance of being chosen.

In this case, the gardener randomly chose 2 plants from a total of 20 plants. By randomly selecting the plants, the gardener ensured that each plant had an equal probability of being included in the sample.

Simple random sampling is a common and straightforward technique used to obtain a representative sample from a larger population. It helps minimize bias and allows for generalization of the findings from the sample to the entire population.

By inspecting the randomly selected plants, the gardener can make inferences about the development of the tomato plants as a whole, assuming that the selected plants are representative of the entire population of tomato plants.

Therefore, the gardener utilized a simple random sampling technique by randomly selecting and inspecting two out of twenty tomato plants to assess their development.

To know more about simple random sample, refer here:

https://brainly.com/question/30403914#

#SPJ4

5) Area of sector is,

⇒ Area of sector = 31.4 units²

6) The value of x is, 5.8 units

Now, We can simplify as,

1) Radius of circle = 6

Central angle = 100 degree

We know that,

Area of sector = (θ/360) πr²

Hence, We get;

⇒ Area of sector = (θ/360) πr²

⇒ Area of sector = (100/360) x 3.14 x 6 x 6

⇒ Area of sector = 31.4 units²

2) We have to given that,

Chord = 10

Perpendicular distance from center to chord = 3 units

Hence, By Pythagoras theorem, we can formulate,

⇒ x² = 3² + 5²

⇒ x² = 9 + 25

⇒ x² = 34

⇒ x = √34

⇒ x = 5.8 units

Learn more about the circle visit:

https://brainly.com/question/24810873

#SPJ1

Answer:

95 people ate pizza

Step-by-step explanation:

Add the ones highlighted

Results:

(i)The amount Willow would lose in profit per mug if she uses the printing company = $12.50.

(iii) the total profit she would lose after selling all 65 mugs at $22 per mug = $812.50

To calculate the profit Willow would lose per mug, we use the formula:

Profit (P) lost per mug = Selling price (SP) per mug - Cost Price (CP) per mug:

$22 - $9.50 = $12.50

Thus, Willow will lose $12.50 in profit per mug if she uses the printing company.

To calculate the total profit, she would lose after selling all 65 mugs, we  multiply the profit lost per mug by the number of mugs:

$12.50 x 65 = $812.50

Therefore, Willow would lose $812.50 in profit after selling all 65 mugs at $22 per mug using the printing company instead of her own printing press.

Learn more about profit at brainly.com/question/29785281

#SPJ1

The probability of rolling a 6 with the red die, a 5 with the green die, and a 4 with the blue die at the same time is 1/216, or approximately 0.46%.

Assuming that each die is fair and that the outcome of rolling one die does not affect the outcome of rolling the others, the probability of rolling a 6 with the red die is 1/6, the probability of rolling a 5 with the green die is also 1/6, and the probability of rolling a 4 with the blue die is 1/6.

Since the three events of rolling each die are independent of each other, we can multiply their probabilities to get the probability of all three events happening at the same time, i.e., rolling a 6 with the red die, a 5 with the green die, and a 4 with the blue die:

Probability of rolling 6 with the red die = 1/6

Probability of rolling 5 with the green die = 1/6

Probability of rolling 4 with the blue die = 1/6

Probability of rolling 6 (R), 5 (G), 4 (B) at the same time = Probability of rolling R and G and B together = Probability of R × Probability of G × Probability of B

= 1/6 × 1/6 × 1/6 = 1/216

Therefore, the probability of rolling a 6 with the red die, a 5 with the green die, and a 4 with the blue die at the same time is 1/216, or approximately 0.46%.

To learn more about probability please click on below link.

https://brainly.com/question/30034780

#SPJ4

You have three dice: one red (R), one green (G), and one blue (B). When all three dice are rolled at the same time, calculate the probability of the following outcome: 6 (R), 5 (G), 4 (B)?

To use the critical value table, you must first decide on the level of significance for your hypothesis test. This is usually represented by alpha (α) and is the probability of rejecting the null hypothesis when it is actually true. Common levels of significance include 0.05 and 0.01.

A critical value table is a tool used in hypothesis testing to help determine whether or not to reject the null hypothesis. This table provides the critical values for a given level of significance and sample size for various statistical distributions such as the normal, t, chi-squared, and F distributions.

Once you have determined the level of significance, you can use the critical value table to find the critical value for your chosen distribution.

For example, if you are using a t-distribution with a sample size of 30 and a significance level of 0.05, you would look in the t-distribution section of the critical value table for the row with a sample size of 30 and find the critical value in the column corresponding to a significance level of 0.05.

Here you can learn more about critical value table

https://brainly.com/question/29672811#

#SPJ11

It take 2 minutes to cross this bridge at a constant speed of 20 miles per hour.

The unitary method is a method for figuring out a single unit's value, then multiplying that value by itself to get the required value. An individual or singular unit is referred to as unitary. Because of this, the goal of this method is to determine values in reference to a single unit. The unitary technique can be used, for instance, to determine how many kilometers a car can go on one litre of gas if it can travel 44 km on two litres of gas. A single unit's value is determined using the unitary approach, and the value of the necessary number of units can then be determined using this value.

To know more about unitary method ,visit:

brainly.com/question/28276953

#SPJ4

Answer:

Two methods both tell us the ball is at 20 feet height at 0.783 seconds going up and 1.28 seconds on the way down.

Step-by-step explanation:

The question can be answered by either calculation or by graphing.

Calculation:

Set the equation to h = 20 feet and solve with the quadratic equation.

h= 4 + 33t - 16t^2

4 + 33t - 16t^2 = 20

- 16t^2 + 33t + 4 = 20

- 16t^2 + 33t - 16 = 0

I find solutions of 0.779 and 1.28 seconds.  

Graphing:

See the attached graph.

The graph shows solutions of 0.783 and 1.28 seconds.

Both methods show the ball to be at 20 feet height at 0.783 seconds going up and 1.28 seconds on the way down.

The complete true mathematical statement is 4 4/5 + 3 2/3 < 8 1/2

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

4 4/5 + 3 2/3 ________ 8 1/2

Evaluate the sum of the integer parts of the fractions

So, we have the following representation

7 4/5 + 2/3 ________ 8 1/2

Next, we take the LCM of 5 and 3 and evaluate the sum

This gives

7 (12 + 10)/15  ________ 8 1/2

Evaluate the sum of 12 and 10

So, we have

7 (22)/15  ________ 8 1/2

Simplify

7 + 1 7/15  ________ 8 1/2

Add 7 and 1

8 7/15  ________ 8 1/2

7/15 is less than 1/2

So, we have

8 7/15  < 8 1/2

Hence, the operator that completes the statement is <

Read more about expressions at

https://brainly.com/question/4344214

#SPJ1

Answer:

The answer is -3

Step-by-step explanation:

Slope means the rate of change of a line which is the letter m. Whenever you need to find slope remember this: m= y2-y1 over x2-x1.

(x1,y1)= (-3,7), ( x2, y2) = (0,-2) so the slope is -3.

In order to completely delta hedge 480 shares of ABC company with an option delta of 0.6, you would need 3 call options.

To completely delta hedge your holdings of 480 shares of ABC company, you would need to calculate the number of call options required based on the delta of the option. The delta represents the change in the option price relative to the change in the underlying stock price. In this case, since the delta is given as 0.6, it means that for every $1 increase in the stock price, the option price will increase by $0.6.

To calculate the number of call options needed for delta hedging, you can use the following formula:

Number of call options = (Delta * Number of shares) / 100

Plugging in the given values, we have:

Number of call options = (0.6 * 480) / 100

Number of call options = 2.88

Since you cannot have a fractional number of options, you would need to round up to the nearest whole number. Therefore, you would need 3 call options to hedge your 480 shares of ABC company.

In summary, to completely delta hedge 480 shares of ABC company with an option delta of 0.6, you would need to acquire 3 call options.

To know more about delta hedging, refer here:

https://brainly.com/question/32697213#

#SPJ11

The data includes a concave mirror with a radius of curvature of +31.5 cm and magnification of m = 3.40. The formula for magnification is m = v/u, and the focal length is f = r/2. Substituting the values, we get u = v/m, and using the mirror formula, the distance of the object from the mirror is 10.15 cm.

Given data: Radius of curvature of a concave mirror, r = +31.5 cm Magnification produced by the mirror, m = 3.40

We know that the formula for magnification is given by:

m = v/u where, v = the distance of the image from the mirror u = the distance of the object from the mirror We also know that the formula for the focal length of the mirror is given by :

f = r/2where,f = focal length of the mirror

Using the mirror formula:1/f = 1/v - 1/u

We know that a concave mirror has a positive focal length, so we can replace f with r/2.

We can now simplify the equation to get:1/(r/2) = 1/v - 1/u2/r = 1/v - 1/u

Also, from the given data, we have :m = v/u

Substituting the value of v/u in terms of m, we get: u/v = 1/m

So, u = v/m Substituting the value of u in terms of v/m in the previous equation, we get:2/r = 1/v - m/v Substituting the given values of r and m in the above equation, we get:2/31.5 = 1/v - 3.4/v Solving for v, we get: v = 22.6 cm Now that we know the distance of the image from the mirror, we can use the mirror formula to find the distance of the object from the mirror.1/f = 1/v - 1/u

Substituting the given values of r and v, we get:1/(31.5/2) = 1/22.6 - 1/u Solving for u, we get :u = 10.15 cm

Therefore, the distance of the mirror from the face is 10.15 cm. The units are centimeters (cm).Answer: 10.15 cm.

To know more about concave mirror Visit:

https://brainly.com/question/31379461

#SPJ11

A∗ is an algorithm that uses a heuristic function f(n) in its search for a solution. The heuristic function f(n) estimates the distance from node n to the goal.

The estimation should be consistent, meaning that the heuristic should never overestimate the distance, and should be admissible, meaning that it should not overestimate the minimum cost to the goal.  

The A∗ heuristic function uses two types of estimates: heuristic function h(n) which estimates the cost of reaching the goal from node n, and the actual cost g(n) of reaching node n. The cost of a path is the sum of the costs of the nodes on that path. Therefore, f(n) = g(n) + h(n).

A∗ is more effective than greedy best-first because it uses a heuristic function that is both admissible and consistent. Greedy best-first, on the other hand, uses a heuristic function that is only admissible. This means that it may overestimate the cost to the goal, which can cause the algorithm to overlook better solutions.

A∗, on the other hand, uses a heuristic function that is both admissible and consistent. This means that it will never overestimate the cost to the goal, and will always find the optimal solution if one exists.Admissible and consistent are two properties that a heuristic function must have for A∗ to return the minimum-cost solution. Admissible means that the heuristic function never overestimates the actual cost of reaching the goal.

This means that h(n) must be less than or equal to the actual cost of reaching the goal from node n. Consistent means that the estimated cost of reaching the goal from node n is always less than or equal to the estimated cost of reaching any of its successors plus the cost of the transition.

Mathematically, this means that h(n) ≤ h(n') + c(n,n'), where c(n,n') is the cost of the transition from node n to its successor node n'.

To know more about algorithm visit:

https://brainly.com/question/28724722

#SPJ11

Answer:

13,666.7

Step-by-step explanation:

you have to divide 6 into 55,000 and get 9,166.7, so then you add 4,500 with 9,166.7 to get 13,666.7.

The recurring decimal 1.52 (52 is recurring) can be expressed as an improper fraction of 152/99.

To convert the recurring decimal 1.52 (52 is recurring) into an improper fraction, we can follow a systematic approach. Let's represent the recurring part 52 with the variable 'x'. We can write the original decimal as:

1.52 = 1 + 0.52 = 1 + 0.52/1

To remove the recurring part, we multiply both sides of the equation by a power of 10 that eliminates the decimal places. Since there are two digits in the recurring part, we multiply by 100:

100 * 1.52 = 100 * (1 + 0.52/1)

152 = 100 + 52x

Now, let's subtract the original equation from this new equation:

152 - 1.52 = 100 + 52x - (1 + 0.52/1)

150.48 = 99x

To isolate 'x', we divide both sides by 99:

150.48/99 = x

1.52 (recurring) = x

Now we can express the recurring decimal as an improper fraction. The numerator is obtained by subtracting the non-recurring part (1) from the original number:

Numerator = 1.52 - 1 = 0.52

The denominator is the same as the number of nines in the denominator of the fraction 99:

Denominator = 99

Therefore, the recurring decimal 1.52 (52 is recurring) can be expressed as an improper fraction:

1.52 (recurring) = 0.52/99 = 152/99

Learn more about improper fraction here:

https://brainly.com/question/21449807

#SPJ11

Answer:

8/9

Step-by-step explanation:

This 0.888... as a fraction is 8/9. Any number over 9, the decimal is going to a repeating number.

Answer:

8/9

Step-by-step explanation:

10x = 8.88..

-   x = 0.88

9x = 8

= 8/9