P, Q, R, S, T and U are different digits.
PQR + STU = 407

the factored form of the equation is 2(13x - 2) = 0, and the solution to the equation is x = 2/13.

Why it is and what is Zero-Product formula?

First, we can simplify the equation by combining like terms:

28x - 4 = 2x - x

Simplifying further:

26x - 4 = 0

Now, we can factor out 2 from the left side of the equation:

2(13x - 2) = 0

Using the zero-product principle, we can set each factor equal to zero:

2 = 0 or 13x - 2 = 0

The first equation is impossible since 2 is not equal to zero. Solving the second equation, we get:

13x - 2 = 0

Adding 2 to both sides:

13x = 2

Dividing both sides by 13:

x = 2/13

Therefore, the factored form of the equation is 2(13x - 2) = 0, and the solution to the equation is x = 2/13.

The zero-product property or formula states that if the product of two factors is zero, then at least one of the factors must be zero. In other words, if a and b are real numbers such that ab = 0, then either a = 0, b = 0, or both a and b are zero. This property is often used to solve polynomial equations by factoring the expression and then setting each factor equal to zero.

To know more about Zero-Product formula visit:

https://brainly.com/question/16199547

#SPJ1

Answer:

Step-by-step explanation:

15426.80

Answer: 15426.82

Step-by-step explanation:

15426.82 is also 15426.82000

Since 2 is the hundredth number (behind the decimal point) and the next number is 0, it will be rounded down.

Therefore 15426.82 to the nearest hundredth is 15426.82

The amount of water that was in the cooler before it started leaking was 6 gallons.

Integration is a mathematical process that involves finding the integral of a function. It is the reverse operation of differentiation, which involves finding the derivative of a function. The integral of a function is a measure of the area under the curve of the function, between two given limits of integration.

The graph shows the rate at which water leaks from the cooler as a function of time, which means that the y-axis represents the rate of leakage in gallons per minute (gal/min), and the x-axis represents the time in minutes.

Since we know that the cooler emptied in 2 minutes, we can integrate the leakage rate over the time interval [0, 2] to find the total amount of water that leaked out:

Total amount of water leaked = ∫[0,2] leakage rate(t) dt

The leakage rate is given by the graph, which consists of a straight line connecting two points: (0,6) and (2,0). We can express this line as a linear equation in slope-intercept form:

leakage rate(t) = mt + b

where m is the slope of the line and b is the y-intercept. To find the slope, we can use the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (0,6) and (x2, y2) = (2,0). Plugging in the values, we get:

m = (0 - 6) / (2 - 0) = -3

So the equation of the line is:

leakage rate(t) = -3t + 6

Now we can integrate this equation over the time interval [0, 2] to get the total amount of water leaked:

Total amount of water leaked = ∫[0,2] (-3t + 6) dt

= [-3t²/2 + 6t] from 0 to 2

= (-3(2)²/2 + 6(2)) - (-3(0)²/2 + 6(0))

= (6 - 0) - (0 - 0)

= 6 gallons

Therefore, the amount of water that was in the cooler before it started leaking was 6 gallons.

To know more about amount visit:

https://brainly.com/question/14806644

#SPJ1

The complete question is :

Answer: y = -2x -3

Step by step explanation

First, we find the gradient of the line 4x + 2y = 10 by making y the subject of the formula.

4x + 2y = 10

2y = 10 - 4x which is the same as 2y = -4x + 10

Divide each term by 2

2y/2 = -4x/2 + 10/2

y = -2x + 5

From the equation, the gradient (coefficient of x) is -2

Since the line is parallel to 4x+2y=10, therefore the gradient of the lines are the same

The equation of the line can be gotten from y - y1 = m(x -x1)

where y1 = 5, x1 = -4 and m = -2

Therefore subtitiuiting into y - y1 = m(x -x1)

y - 5 = -2(x-(-4))

y - 5 = -2(x + 4)

y - 5 = -2x - 8

y = -2x -8 + 5

y = -2x -3

you can see that the gradients are the same (coefficent of x = -2)

The probability that the ball transferred was red, given that a red ball was drawn from urn B, is 21/55, or about 0.382.

What is probability ?
Probability is a mathematical concept that measures the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 means that the event is impossible, and 1 means that the event is certain to happen.

To calculate probability, we usually take the number of favorable outcomes and divide it by the total number of possible outcomes. For example, if we flip a coin, the probability of getting heads is 1/2 because there is only one favorable outcome (heads) out of two possible outcomes (heads or tails).

According to the question:
Let's use Bayes' theorem to find the probability that the ball transferred was red:

Let R be the event that a red ball is drawn from urn B, and T be the event that the transferred ball was red.

Then we want to find P(T = red | R = red).

By Bayes' theorem, we have:

P(T = red | R = red) = P(R = red | T = red) * P(T = red) / P(R = red)

We can calculate each of these probabilities as follows:

P(R = red | T = red): The probability of drawing a red ball from urn B, given that a red ball was transferred from urn A to urn B, is 1/4, since urn B originally contained 1 red ball out of 7 total balls (3 black, 3 white, and 1 red) and we added one more red ball to it.

P(T = red): The probability that a red ball was transferred from urn A to urn B is 3/10, since urn A originally contained 3 red balls out of 10 total balls and we transferred one ball at random.

P(R = red): The overall probability of drawing a red ball from urn B is:

P(R = red) = P(R = red | T = black) * P(T = black) + P(R = red | T = red) * P(T = red)

where T = black means that a black ball was transferred from urn A to urn B. We can calculate each of these conditional probabilities as follows:

P(R = red | T = black): The probability of drawing a red ball from urn B, given that a black ball was transferred from urn A to urn B, is 1/7, since urn B originally contained 1 red ball out of 7 total balls (3 black, 3 white, and 1 red) and we did not add any more red balls to it.

P(T = black): The probability that a black ball was transferred from urn A to urn B is 4/10, since urn A originally contained 4 black balls out of 10 total balls and we transferred one ball at random.

Therefore, we have:

P(R = red) = 1/7 * 4/10 + 1/4 * 3/10 = 1/35 + 3/40 = 11/140

Putting it all together:

P(T = red | R = red) = (1/4) * (3/10) / (11/140) = 21/55

So the probability that the ball transferred was red, given that a red ball was drawn from urn B, is 21/55, or about 0.382.

To know more about probability visit:
https://brainly.com/question/28146099
#SPJ1

Answer:

-4(x - 5) + 8x = 9x - 3

Simplifying the left side:

-4x + 20 + 8x = 9x - 3

4x + 20 = 9x - 3

Subtracting 4x from both sides:

20 = 5x - 3

Adding 3 to both sides:

23 = 5x

Dividing both sides by 5:

x = 23/5

Therefore, the equation equivalent to the given equation is:

5x - 23 = 0

The list that shows a comparison of the measures of central tendency from the least to the greatest is mean, median and mode. (option D)

The dataset represented with the dot plot is 2, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8,8, 8, 8, ,8, 8, 8, 8, 8, 8

Mean is the average of the dataset.

Mean = sum of numbers / total number in the dataset

[(2 x 1) + (5 x 4) + (6 x 4) + (7 x 6) + (8 x 10)] / 25 = 6.72

Median is the number at the center of the dataset.

The median = 1/2(n + 1)

1/2 x (26) = 13th number = 7

Mode is the number that occurs most frequently. The number that occurs the most in the dataset is 8.

To learn more about mode, please check: https://brainly.com/question/16505756

#SPJ1

Answer:

Difference=£2.4

Step-by-step explanation:

Here in shop A

130 cm=£1.82

1 cm=£1.82/130

1 cm=0.014

Now

400 cm=0.014*400

=£5.6

Again, In shop B

235cm=£1.88

1 cm=£1.88/235

1 cm=£0.008

Now

400cm=0.008*400

=£3.2

Now,

Difference=£5.6-£3.2

=£2.4

Answer:

x= 13 =smaller number

Step-by-step explanation:

let x=smaller number

y=2x-6=larger number

x+y=45

x+2x-6=45 (equation)

3x=39

x=13

Answer:

[tex]x = 13[/tex] ..... smaller number

and

[tex]y = 32[/tex] ....... larger number

Step-by-step explanation:

Greetings!!!

Let the two numbers be X and Y

[tex]x + y = 45........ \:equation \: 1[/tex]

The larger number is y and is 6 less than twice the smaller number. which means:-

[tex](y - 6) = 2x........... \: equation \: 2[/tex]

so, now solve for y. from equation 2

[tex]y - 6 = 2x \\ y = 2x + 6[/tex]

Substitute equation 1 into equation 2

[tex]x + y = 45 \\ x + (2x + 6) = 45 \\ 3x + 6 = 45 \\ 3x = 45 - 6 \\ 3x = 39....divide \: both \: sides \: by \: 3 \\ x = 13[/tex]

To solve for y substitute x into the first equation

[tex](13) = + y = 45 \\ y = 45 - 13 \\ y = 32[/tex]

Finally, to be more sure make a cross check

[tex]y - 6 = 2x \\ 32 - 6 = 2(13) \\ 26 = 26[/tex]

If you have any questions tag it on comments

Hope it helps!!!

Answer:

D

Step-by-step explanation:

Mean- 6.78

Median- 7

Mode- 8

n(A ∩ B ∩ C^c) = 15 there are 15 elements in the intersection of sets A and B but not in set C.

What is a circle?

A circle is a two-dimensional geometric figure that consists of all the points in a plane that are equidistant from a given point called the center. The distance from the center to any point on the circle is called the radius, which is denoted by the letter "r".

To find the cardinality of n(A∩B∩C^c), we need to know the number of elements that are in the intersection of A and B but not in C.

One way to approach this is to use the principle of inclusion and exclusion. This states that:

n(A ∪ B ∪ C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(A ∩ C) - n(B ∩ C) + n(A ∩ B ∩ C)

We can rearrange this formula to solve for n(A ∩ B ∩ C^c):

n(A ∩ B ∩ C^c) = n(A ∩ B) - n(A ∩ B ∩ C) - n(B ∩ C) + n(A ∩ C) + n(B) + n(C) - n(A)

Plugging in the values we have been given, we get:

n(A ∩ B ∩ C^c) = 4 - 3 - 9 + 7 + 11 + 15 - 10

Simplifying this expression, we get:

n(A ∩ B ∩ C^c) = 15

Therefore, there are 15 elements in the intersection of sets A and B but not in set C.

To learn more about Circle from the given link:

https://brainly.com/question/29142813

#SPJ1

Answer: an estimated 15% tip on a dinner bill of $58.12 would be $8.72.

Step-by-step explanation:

First, we can calculate 10% of $58.12 by moving the decimal point one place to the left, which gives us $5.81.

Then, we can calculate half of 10%, which is 5%, by dividing $5.81 by 2, giving us $2.91.

Finally, we add 10% and 5% to get the estimated tip amount:

$5.81 + $2.91 = $8.72

Therefore, an estimated 15% tip on a dinner bill of $58.12 would be $8.72.

The surface area of the triangular pyramid is the sum of the lateral surface area and the base area.

Lateral Surface Area: The lateral surface area of a triangular pyramid is equal to the product of the slant height and the perimeter of the base.

Slant height = √ ( (length of side)2 + (height)2 )

Perimeter of the base = 3 x length of side

Therefore, the lateral surface area = √ ( (length of side)2 + (height)2 ) x 3 x length of side

Base Area: The base area of the triangular pyramid is equal to one-half of the product of the three side lengths.

Therefore, the base area = 1/2 x (length of side) x (length of side) x (length of side)

Surface Area: The total surface area of the triangular pyramid = lateral surface area + base area

Therefore, the surface area = √ ( (length of side)2 + (height)2 ) x 3 x length of side + 1/2 x (length of side) x (length of side) x (length of side)

The conditional relative frequency that a student rides the bus, given that the student is in middle school is 0.16 / 0.96 ≈ 0.17.

Conditional relative frequency is a statistical measure that describes the proportion or percentage of a specific group or category within a subset of data. It is calculated by dividing the frequency of the specific category in the subset by the frequency of the total subset.

To find the conditional relative frequency that a student rides the bus, given that the student is in middle school, we need to divide the frequency of middle school students who ride the bus by the total number of middle school students.

From the table, we see that the frequency of middle school students who ride the bus is 0.16. The total number of middle school students is the sum of the frequencies in the first row, which is 0.20 + 0.16 + 0.12 + 0.48 = 0.96.

So, the conditional relative frequency that a student rides the bus, given that the student is in middle school is:

0.16 / 0.96 ≈ 0.17

Rounded to the nearest hundredth, the answer is 0.17. Therefore, about 17% of middle school students ride the bus.

To know more about frequency visit:

https://brainly.com/question/29269840

#SPJ1

Answer:

  (x -14)² +(y -7)² = 1²

Step-by-step explanation:

You want the equation of the circle that represents the border of a logo centered 14 m right and 7 m up from the lower left corner of a soccer field. The logo is 2 m in diameter.

The equation of a circle with center (h, k) and radius r is ...

  (x -h)² +(y -k)² = r²

Since the origin of the coordinate system is the lower left corner of the field, the center is located at (h, k) = (14, 7). The diameter of 2 m means the radius is 1 m. Using these values in the equation, it becomes ...

  (x -14)² +(y -7)² = 1²

The value of the height of the trapezium is 10.3 cm.

The area of a trapezium is given by the formula:

Area = (1/2) x (sum of parallel sides) x (distance between the parallel sides)

The parallel sides of the trapezium are given as 18 cm and 13 cm

The area of the trapezium is given as 160 cm²

The height of the trapezium = h

The value of the height of the trapezium is calculated as follows;

160 = ¹/₂ (18 + 13) h

2 x 160 = (31)h

320 = 31h

h = 320 / 31

h = 10.3 cm

Learn more about height of trapezium here: https://brainly.com/question/30948495

#SPJ1

Uri paid a total of $85.47 for the landscaping service including tax and tip.

Taxes are compulsory payments made by a government organisation, whether local, regional, or federal, to people or businesses. Tax revenues are used to fund a variety of government initiatives, such as Social Security and Medicare as well as public infrastructure and services like roads and schools. Taxes are borne by whoever bears the cost of the tax in economics, whether this is the entity being taxed, such as a business, or the final users of the items produced by the firm. Taxes should be taken into consideration from an accounting standpoint, including payroll taxes, federal and state income taxes, and sales taxes.

Given that company charged $74 for the service plus 5% tax.

The tax is 5%, that is:

Tax = 5% of $74 = 0.05 x $74 = $3.70

Cost after tax = $74 + $3.70 = $77.70

Now, tip is 10%:

Tip = 10% of $77.70 = 0.10 x $77.70 = $7.77

Total cost = $77.70 + $7.77 = $85.47

Hence, Uri paid a total of $85.47 for the landscaping service including tax and tip.

Learn more about tax here:

https://brainly.com/question/16423331

#SPJ1

The expense incurred by a cοmpany tο prοduce the gοοds οr services sοld within a specific time periοd is knοwn as the cοst οf sales.

It cοmprises all cοsts that are directly related tο the prοductiοn prοcess, such as thοse fοr labοr, utilities, raw materials, and manufacturing equipment depreciatiοn.

Grοss prοfit, which is the amοunt οf mοney a firm makes frοm its cοre οperatiοns befοre deducting extra cοsts like marketing, administrative, and financing charges, is calculated by subtracting the cοst οf sales frοm revenue. Tο apprοpriately price their prοducts and assess the prοfitability οf their οperatiοns, firms must have a thοrοugh understanding οf their cοst οf sales.

Learn more about Grοss prοfit, here:

https://brainly.com/question/16999019

#SPJ1

Complete question:

What is the definition of cοst οf sales?

Answer:

going from left to right:

AA

BD

CB

DC

Considering the following equation x³ + 4x² + 4x + 16 = 0 we have the value of x as [-4, -2*I, 2*] in sympy expressions.

Symbolic math is supported by the Python library SymPy (http://www.sympy.org). In symbolic mathematics, mathematical expressions are represented by symbols. This is an illustration of a symbolic arithmetic expression: x2+y2=z. The three variables x, y, and z are present in the formula above.

Considering the following equation x³ + 4x² + 4x + 16 = 0.

CODE:

import sympy #importing SymPy

x = sympy.Symbol('x') #declaring the variable 'x' as the only variable for the expression

result = sympy.solve(x**3 + 4*x**2 + 4*x + 16,x) #using the function solve() to solve the expression.

print(result) #displaying the list 'result'

OUTPUT:

[-4, -2*I, 2*]

Learn more about Sympy Equations:

https://brainly.com/question/15242740

#SPJ4

Indeed, the intermediate value theorem demonstrates that the equation   [tex]x + sin(x) = -1[/tex] must have at least one solution on the interval [-/2, /4]. Thus option B is correct.

The intermediate value theorem states that if a continuous function exhibits values with opposite signs at two places, there must be at least one location in the interval where it equals zero (or crosses the x-axis).

Note that x + sin(x) is a continuous function to see why. When x + sin(x) is evaluated at the interval's left endpoint, x = -/2, the result is  [tex]-/2 + sin(-/2) = -/2 - 1[/tex] , which is less than -1.

The intermediate value theorem states that because x + sin(x) is continuous and can have values both less than and greater than -1 at either end of the range, it must also have a value of -1 somewhere in between.

Therefore, When x + sin(x) is evaluated at the interval's right endpoint, x = /4, the result is  [tex]x + sin(x) = x + 2/2,[/tex]  Which is greater than -1.

Learn more about theorem here:

https://brainly.com/question/30066983

#SPJ1

Answer: D. Square

Step-by-step explanation:

The shape created by the cross section of the cut through a square pyramid is a square.

To see why, imagine the pyramid sitting on a table with its square base flat against the surface. The cut goes through the vertex, which is the point at the top of the pyramid. Since the cut is perpendicular to the base, it divides the pyramid into two smaller pyramids with congruent, but not identical, bases. Each of these smaller pyramids has a triangular base that is an isosceles right triangle. The two triangles share a common hypotenuse, which is the line of the cut.

The cross section of the cut is the shape formed where the two triangles meet along the hypotenuse. Since both triangles are congruent and the hypotenuse is the same for both, the cross section is a square. The sides of the square are equal to the base of the original pyramid, which is one of the legs of the isosceles right triangles formed by the cut. Therefore, the answer is D, a square.

Answer: 3/5

Step-by-step explanation:

Chau had 4/5 of a spool of yarn, and he used 3/5 of it for a project.

The fraction of the spool used for the project is:

3/5

So, 3/5 of the spool was used for the project.

The curvature of the cell surface that has a shape of circle y at the red point x=0.25 is 1.75.

Diameter is a line segment that passes through the center of a circle or sphere and has its endpoints on the circumference of the circle or sphere. The diameter of a circle is twice the length of its radius, so if the radius is given, the diameter can be calculated by multiplying the radius by two.

The equation is given as y = (2 - x)2, where x is the distance from the centre of the circle and y is the curvature of the circle at that distance. To calculate the curvature of the cell surface at any given point, the distance from the centre needs to be known. In this example, the distance from the centre is 0.25, and the curvature of the cell surface at this point is 1.75.

A low curvature, such as 1.75, will allow for more vesicles to form on the surface of the cell. A low curvature will allow for more vesicles to form, and a high curvature will prevent the formation of vesicles.

The equation for a circle with a diameter of 2μm is given as y = (2 - x)2. Substituting x = 0.25 into the equation yields y = (2 - 0.25)2 = 1.75.

For more questions related to circumference

https://brainly.com/question/20489969

#SPJ1

The circle-shaped cell surface's (or circumference's) curvature at the red spot x=0.25 is 0.66.

A circle or sphere's diameter is defined as a line segment with its endpoints on the circumference and that travels through the middle of the object. If the radius is known, the diameter can be determined by multiplying the radius by two since the diameter of a circle is twice the length of its radius.

It is possible to compute the cell surface's curvature at x = 0.25 as follows:

Let's look at the circle's calculation.

y = √(2 - x)x

Now, when x = 0.25,

y = √(2 - 0.25)×0.25

y = √1.75×0.25

y = 0.66

As a result, the cell surface's slope at x = 0.25 is 0.66.

For more questions related to circumference

https://brainly.com/question/20489969

#SPJ1

5 years longer then Bill, 2x5=10.

10+2=12.

12-5=7

Hoang has be there for 12 years. Bill has for 7 years.

The number of hours it will take the same dog to run 26 1/10 miles is 7.2 hours

7 1/4 miles in 2 hours

26 1/10 miles in x hours

Equate miles ratio hours

7 ¼ miles : 2 hours = 26 ⅒ miles : x hours

7.25 / 2 = 26.10 / x

cross product

7.25 × x = 26.10 × 2

7.25x = 52.20

divide both sides by 7.25

x = 52.20 / 7.25

x = 7.2 hours

Ultimately, it will take 7.2 hours for the dog to run 26⅒ miles.

Read more on ratio:

https://brainly.com/question/2328454

#SPJ1

Answer:

t=7.7 s

Step-by-step explanation:

h=ut+1/2gt²

-76=113t+1/2(-32)t²

-76=113t-16t²

16t²-113t-76=0

[tex]t=\frac{113\pm\sqrt{(-113)^2-4 \times 16 \times(-76)} }{2 \times 16} \\t=\frac{113 \pm\sqrt{12769+4864} }{32} \\t=\frac{113 \pm\sqrt{17633} }{32} \\t=\frac{113+\sqrt{17633} }{32} \approx 7.68~s \approx7.7 s\\or\\t=\frac{113-\sqrt{17633} }{32} \approx~-0.62 ~s \approx-0.6~s[/tex]

negative~sign~rejected.

The standard normal area is the region under the standard normal distribution curve, which has a mean of 0 and a standard deviation of 1. One is equal to the entire area under the normal distribution curve.

To determine the probability for the above intervals using a typical normal distribution table or a calculator with a normal distribution function:

[tex]P(1.22 < Z < 2.15) = 0.1143[/tex]

[tex]P(2.00 < Z < 3.00) = 0.0228[/tex]

[tex]P(-2.00 < Z < 2.00) = P(Z < 2.00) - P(Z < -2.00) = 0.9772 - 0.0228 = 0.9544[/tex]

The number of standard deviations the variable is from the mean is shown by the ensuing Z-score. The chance of detecting a certain value of the variable in a given interval can then be determined using the standard normal area.

Therefore, The symmetry of the normal distribution allows us to use the third interval's coverage of 4 standard deviations to simplify the calculation, as illustrated above.

Learn more about standard here:

https://brainly.com/question/12972781

#SPJ1

Answer:

30623 yards

Step-by-step explanation:

Answer:

In the NFL, the perimeter of a football field, excluding the end zones, is 30623 yards. The field is how many feet wide... A football field in the United States is 120 yards long (including the end zones).

Step-by-step explanation:

Brainliest pls