The number of games that would make the cost equal in both locations is 5. The total cost is $10.50.
The equation that can be used to determine the total cost of renting shoes at both locations is:
total cost = fixed cost + variable cost
Total cost of renting at Bowler World = $5 + $1.1x
Total cost of renting at Lucky Spares = $3 + $1.50x
Where
x = number of games played
In order to determine the number of games that would make the cost
equal in both locations, the following steps would be taken:
$5 + $1.1x = $3 + $1.50x
Combine similar terms
$5 - $3 = $1.50x - $1.1x
$2 = $0.40x
Divide both sides of the equation by $0.4
x = 2 / 0.4
x = 5 games
Total cost = $5 + $1.1(5) = $5 + $5.5 = $10.50
Learn more about the cost estimation here :
https://brainly.com/question/2611396
#SPJ4
a 400-gal tank initially contains 100 gal of brine containing 50 lb of salt. brine containing 1 lb of salt per gallon enters the tank at the rate of and the well-mixed brine in the tank flows out at the rate of how much salt will the tank contain when it is full of brine?
The tank will contain 350 lb of salt when it is full of brine.
What is rate ?
A rate is the ratio between two related quantities in different units. If the denominator of the ratio is expressed as a single unit of one of these quantities.
The amount of salt in the tank can be calculated using the principle of mass conservation. The rate at which salt is entering the tank is equal to the rate at which it is flowing out, so the total amount of salt in the tank will remain constant.
Let x be the amount of salt in the tank when it is full. Then:
x = 50 + 1 * (400 - 100) = 50 + 300 = 350 lb
So, the tank will contain 350 lb of salt when it is full of brine.
To learn more about rate visit : brainly.com/question/14731228
#SPJ4
The tank will contain 350 lb of salt when it is full of brine.
A rate is the ratio between two related quantities in different units. If the denominator of the ratio is expressed as a single unit of one of these quantities.
The amount of salt in the tank can be calculated using the principle of mass conservation The rate at which salt is entering the tank is equal to the rate at which it is flowing out, so the total amount of salt in the tank will remain constant.
Let x be the amount of salt in the tank when it is full. Then:
x = 50 + 1 * (400 - 100) = 50 + 300 = 350 lb
So, the tank will contain 350 lb of salt when it is full of brine.
To learn more about rate:
brainly.com/question/14731228
#SPJ4
PLEASE HURRY LIMITED TIME, TEST QUESTION!!!
Question- Given the equation x^2+ y^2+ 20x + 12y + 111 = 0, write the standard form equation in the form (x-h)^2 + (y-k)^2 = r^2, and list the center and radius. Show ALL WORK using the equation editor.
*For full credit you must have 3 things: All work with the standard form equation, the center and the radius listed
The standard form of the equation is (x - -10)² + (y - -6)² = 5² with center (-10, -6) and radius 5.
What is the Standard form of a Circle?Standard form of a circle is given by the equation,
(x - h)² + (y - k)² = r²
where, (h, k) is the center of the circle and r is the radius of the circle.
Given equation is,
x² + y² + 20x + 12y + 111 = 0
Rearranging the equation with like terms together,
(x² + 20x) + (y² + 12y) + 111 = 0
(x² + (2 × 10 x)) + (y² + (2 × 6 y)) + 111 = 0
Writing 111 = 100 + 36 - 25, we get,
(x² + (2 × 10 x)) + (y² + (2 × 6 y)) + (100 + 36 - 25) = 0
(x² + (2 × 10 x) + 100) + (y² + (2 × 6 y) + 36) - 25 = 0
We have the algebraic identity, a² + 2ab + b² = (a + b)².
(x² + (2 × 10 x) + 10²) + (y² + (2 × 6 y) + 6²) = 25
(x + 10)² + (y + 6)² = 5²
(x - -10)² + (y - -6)² = 5², which is the standard form.
Center = (-10, -6) and Radius = 5
Hence the the circle with the equation (x - -10)² + (y - -6)² = 5² has center (-10, -6) and radius 5.
Learn more about Circle here :
https://brainly.com/question/13658927
#SPJ1
*URGENT*
Solve the triangle: If it is not possible, say so
Answer:
a
Step-by-step explanation:
What is 36.3 Celsius in Fahrenheit?
The conversion from Fahrenheit to Celsius is 36.3 to 97.34.
How To Convert 36.3 C to F?Converting degrees of temperature from Celsius to Fahrenheit
Since boiling (hot) water is 21 degrees Fahrenheit and 0 degrees Celsius, respectively, the formula to convert between the two is
F = C x (9/5) + 32
A simple example can help you to understand the math in this situation. Suppose we need to convert 36.3 Celsius to Fahrenheit!
Entering the data into the converter equation will convert 36.3 degrees Celsius to Fahrenheit.
F = 36.3 x (9/5) +32
F 97.34 degrees
This means that the answer is after using the formula to change 36.3 Celsius to Fahrenheit:
36.3°C = 97.34°F
or
The conversion from Fahrenheit to Celsius is 36.3 to 97.34.
To Learn more About Celsius to Fahrenheit Refer To:
brainly.com/question/894531
#SPJ4
reliability is measured as the amount of time the system is running and functioning properly. this includes the system’s hardware and software. What is the correct question for the statement above?
How frequently and how long is the system in use function
A system's reliability can be used to gauge how well it is operating and performing. It considers both the system's software and hardware components. This includes how long the system can function without experiencing any issues, how frequently it bounces back from a crash or failure, and how rapidly it reacts to information or service demands. The frequency and length of any system outages, as well as how quickly and dependably the system recovers from failure, must all be determined in order to assess a system's reliability. The user experience should also be taken into account because people may assess the reliability of a system based on how fast and effectively it answers to their requests. In order to determine a system's reliability with precision,
Learn more about function here
https://brainly.com/question/29633660
#SPJ4
The complete question is
reliability is measured as the amount of time the system is running and functioning properly. this includes the system’s hardware and software. What is the correct question for the statement above. How frequently and how long is the system in use function ?
Identify which drawing of 1,2,3,4,5,6-hexamethylcyclohexane has all the methyl groups in axial positions, and which has all the methyl groups in equatorial positions
1,2,3,4,5,6-hexamethylcyclohexane is a six-membered ring molecule with six methyl groups attached to it. The arrangement of the methyl groups can be either axial or equatorial.
In an axial arrangement, the methyl groups are positioned along the axis of the ring and point up or down. An equatorial arrangement, on the other hand, has the methyl groups positioned on the equator of the ring, in a more coplanar arrangement. It is easier to distinguish between the two arrangements by visualizing the molecule in a chair conformation. In a chair conformation, the ring is twisted and two of the substituents are in axial positions and two are in equatorial positions. If all of the methyl groups in the molecule are in axial positions, they would point up or down in the chair conformation. If all of the methyl groups are in equatorial positions, they would be coplanar with the ring plane in the chair conformation.
In conclusion, the drawing of 1,2,3,4,5,6-hexamethylcyclohexane with all the methyl groups in axial positions shows the methyl groups pointing up or down in a chair conformation. The drawing with all the methyl groups in equatorial positions shows them to be coplanar with the ring plane in a chair conformation.
Learn more about methyl :
https://brainly.com/question/12484834
#SPJ4
A jogging path runs along the river from point C to point E ,passing through point A. You want to find the distance DE across a river using indirect measurement. Which congruence theorem can be used to show that ABC=ADE
To find the distance DE across a river using indirect measurement, you can use the Angle-Angle (AA) Congruence Theorem.
A jogging path runs along the river from point C to point E ,passing through point A.
To find the distance DE across a river using indirect measurement, you can use the Angle-Angle (AA) Congruence Theorem.
This theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are congruent. In this scenario, you can measure the angles at A in both triangles ABC and ADE, and if they are congruent, you can conclude that the triangles are congruent by AA Congruence Theorem.
Knowing that ABC and ADE are congruent, you can use the Side-Side-Side (SSS) Congruence Theorem to find that their corresponding sides are congruent.
In particular, you can conclude that AB = AD, BC = DE, and AC = AE, which means that DE can be found by simply measuring AC and subtracting AB.
Therefore, we can use the Angle-Angle (AA) Congruence Theorem.
For more such questions on Angle-Angle Congruence Theorem.
https://brainly.com/question/3168048
#SPJ4
their respective positionfunctions are given by x1 = sin t and x2 =e-2t-1. For how many values of t do the particles havethe same velocity?
(A) None
(B) One
(C) Two
(D) Three
(E) Four
For only one value of t particles have the same velocity, Option (b) is correct.
What do you mean by velocity?Velocity is a vector quantity in physics that describes the rate of change of an object's position in space. It is defined as the derivative of an object's position with respect to time, and it has both magnitude and direction.
Velocity is measured in units of length per unit time, such as meters per second (m/s). The magnitude of velocity is the speed of an object, which is the rate at which an object is moving, while the direction of velocity is the direction in which an object is moving.
Velocity is a crucial concept in mechanics and is used to describe the motion of objects and to analyze the interactions between objects. For example, the velocity of an object can be used to calculate its acceleration, which is the rate of change of its velocity. The velocity of an object can also be used to calculate its displacement, which is the change in its position over a certain period of time.
The velocity of the first particle is given by x1'(t) = cos(t), and the velocity of the second particle is given by x2'(t) = [tex]-2e^{(-2t-1)}[/tex]. To find when the two velocities are equal, we set x1'(t) = x2'(t) and solve for t:
cos(t) = [tex]-2e^{(-2t-1)}[/tex]
[tex]e^{(2t+1)}[/tex] = -1/2cos(t)
Since cos(t) is positive for 0 <= t <= , we can take the logarithm of both sides to get:
2t + 1 = ln(-1/2cos(t))
We now have an implicit equation that relates t to cos(t). To find how many solutions this equation has, we would need to graph the two functions and find their intersection points, if any.
Therefore, as the question asks for how many values of t the particles have the same velocity, the answer is (B) One.
To know more about equation visit:
brainly.com/question/29174899
#SPJ4
Solve quadratic equation
The solution to the quadratic equation x² + 4x + 4 = 0 is x = -2 and x = -2
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.
The standard form of a quadratic equation is:
y = ax² + bx + c
Where a, b and c are constants
Given the quadratic equation:
x² + 4x + 4 = 0
x² + 2x + 2x + 4 = 0
x(x + 2) + 2(x + 2) = 0
(x + 2)(x + 2) = 0
x + 2 = 0; and x + 2 = 0
x = -2 and x = -2
The solution to the quadratic equation is x = -2 and x = -2
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
how many cups in a liter
The 1 liter of a quantity contains 4.22675 of cups.
What is the relation between a liter and a cup?A cup is a volume unit in the imperial and US customary measurement systems.In cooking, the cup is commonly used to measure liquids and bulk foods, often in the context of serving sizes. Actual drinking cups vary greatly in size and are therefore not a good representation of this unit. Instead, standardized measuring cups are used.Cups and liters both estimate the volume of liquids, so whether you want to know how many cups are in a liter of water, oil, or a bottle of soda, the answer is always 4.22675 cups.We will multiply the number of cups by 0.236588 liters per cup to convert cups to liters.To learn more about liters refer to :
https://brainly.com/question/3950831
#SPJ4
Solve the following linear system by elimination
The solution to the system of equation -3x = 2y - 34 and 3y = 13 + 5x is x = 4 and y = 11
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.
Given the equations:
-3x = 2y - 34
multiply the equation by 3:
-9x = 6y - 102
-9x - 6y = -102 (1)
And:
3y = 13 + 5x
multiply the equation by 2:
6y = 26 + 10x
-10x + 6y = 26 (2)
To solve by elimination method, add equation 2 and 1 to get:
-19x = -76
x = 4
Put x = 4 in the equation:
-3x = 2y - 34
-3(4) = 2y - 34
2y = 22
y = 11
The solution to the equation is x = 4 and y = 11
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
can someone pls answer these 2 stats problems worth 65 points ty!!!
The county health inspector will select a random sample of 4 community swimming pools in the county to investigate the pH levels.
(b) Describe the sampling distribution of the sample mean for samples of size 4 (shape, center, and spread).
(c) Consider the situation in which the health inspector find the sample mean of the 4 pools to be outside the safe pH levels. As a result, the inspector declares that the population mean is not 7. 5. However, if the population mean really is 7. 5, the inspector will have made an error. Such an error is called a Type I error. Find the probability that the inspector will make a Type I error with the sample of 4 pools. Show your work
(b) The sampling distribution of the sample mean is a normal distribution with a center of 7.5 and spread equal to the standard error (SE) of the mean.
The standard error of the mean is calculated using the formula SE = SD/√n, where SD is the standard deviation of the population and n is the sample size. In this case, the sample size is 4, so the standard error of the mean is equal to SE = SD/√4.
(c) The probability of making a Type I error is equal to the probability of observing a sample mean outside the safe pH levels given that the population mean is 7.5. This can be calculated using the formula for a normal distribution:
P(x < x1 or x > x2) = P(x < x1) + P(x > x2)
where x1 and x2 are the lower and upper boundaries of the safe pH levels. To calculate the probability, we need to find the z-scores of x1 and x2 using the formula
z = (x - µ)/SE
where µ is the population means and SE is the standard error of the mean. In this case, µ = 7.5 and SE = SD/√4. We can then use the z-score to calculate the probability of observing a sample mean outside the safe pH levels. The probability of making a Type I error is equal to the sum of these two probabilities.
For more questions like Probability click the link below:
https://brainly.com/question/30034780
#SPJ4
factor each expression
5a -25
On solving the provided question, we can say that the provided expression is = 5a -25 since it is linear expression, so it will have only one factor, a = 5
What is factor ?In mathematics, the integer m serves as the divisor (also known as factor n) of an integer n, which may be multiplied by the integers to get n. We may also state that n in this situation is a multiple of m. A number without a residue that divides another number is said to be a factor. In other words, if you multiply two integers to create a product, the numbers you multiply are factors of the product since the result is divisible by the numbers you multiply. Factors can be found using either division or multiplication.
the provided expression is = 5a -25
since it is linear expression, so it will have only one factor
5a -25
5a = 25
a = 5
To know more about factor visit:
https://brainly.com/question/29128446
#SPJ1
how do I find a probability?
Answer:not sure
Step-by-step explanation:
Answer:
See explanation and examples below.
Step-by-step explanation:
The probability that an event (desired outcome) will occur is the quotient of the number of ways the event can occur (desired outcomes) and the total number of possible outcomes.
For example, consider a die. A die is a 6-faced cube with numbers 1 through 6 on its faces.
The total number of possible outcomes is 6 since it can land with any face with numbers 1 through 6 facing up.
What is the probability if getting a 5?
Here the desired outcome is a 5. There is only one desired outcome since only 1 face has a 5. The total number of possible outcome is 6.
p(5) = 1/6
The probability of getting a 5 is 1/6.
Another example:
A spinner has 4 sections of equal size.
1 section is red.
1 section is blue.
1 section is green.
1 section is yellow.
What is the probability of landing on red?
Desired outcome: landing on red
Number of desired outcomes: 2
Total number of possible outcomes: 4
p(red) = 1/4
Using the same spinner, what is the probability of landing on yellow or green?
Landing on the green section or landing on the yellow section are both desired outcomes, so the number of desired outcomes is 2.
The total number of outcomes is 4.
p(yellow or green) = 2/4 = 1/2
is it possible for one of φ∧(ψ ∨θ) and (φ∧ψ)∨(φ∧θ) to be true and the other false?
By examining the truth table, we can determine the two expressions are equivalent and it is possible for one of them to be true and the other false.
Given two Boolean expressions, it is possible for one of them to be true and the other false if they are not equivalent. For example, consider the two expressions: φ ∧ (ψ ∨ θ) and (φ ∧ ψ) ∨ (φ ∧ θ).
It is possible to construct a truth table for these two expressions, which shows all possible combinations of truth values for φ, ψ, and θ, along with the corresponding truth values for the two expressions.
Boolean logic is a branch of mathematical logic that deals with binary operations (i.e., true or false values) and is often used in computer science. One of the basic operations in Boolean logic is the logical conjunction (denoted by ∧), which represents the and operator. For example, if φ and ψ are two propositions, then φ ∧ ψ is true if and only if both φ and ψ are true.
Here you can learn more about Boolean expressions
https://brainly.com/question/13265286#
#SPJ11
Which interval in the histogram contains the median guinea pig weight?
The histogram in question is a visual representation of the weights of guinea pigs. It indicates that the median weight is located in the interval between 250 and 300.
This is determined by first looking at the shape of the histogram. The histogram is approximately symmetrical, meaning that the median is going to be located in the middle of the data points. When looking at the intervals listed in the histogram, the interval between 250 and 300 is the middle interval, thus indicating that the median weight falls in this range.
In addition, the peak of the histogram is located in this interval, which further confirms that the median weight falls in the interval between 250 and 300. Overall, the interval between 250 and 300 contains the median guinea pig weight.
know more about histogram here
https://brainly.com/question/30354484#
#SPJ11
Given trapezoid WXYZ, what is XY?
The value of XY in the given trapezoid is 30 ft
What is trapezoid?A quadrilateral with at least one pair of parallel sides is called a trapezoid.
Given that, a trapezoid WXYZ we need to find XY,
We need that,
Midsegment of a trapezoid = M = 1/2 (b1 + b2), where b1 and b2 are parallel sides,
Therefore,
35 = (xy + 4xy/3) / 2
70 = 7xy / 3
210 = 7xy
xy = 30
Hence, the value of XY is 30 ft
Learn more about trapezoid, click;
https://brainly.com/question/12623349
#SPJ1
The area of the circular base of a cone is 9π cm², and the slant height of the cone is four times the radius of the cone.
What is the approximate lateral area of the cone?
Use π≈3.14.
Enter your answer rounded to the nearest whole number in the box.
cm²
The lateral area of the cone is 113.1 cm²
How to find the lateral areaLet the radius of the circular base of the cone be r. Then the slant height, L of the cone is 4r.
The formula for the area of a circle is given by the formula
= πr^2.
Since the area of the circular base of the cone is 9π cm², we can write the following equation:
πr^2 = 9π
Dividing both sides by π, we get:
r^2 = 9
Taking the square root of both sides, we get:
r = 3
The lateral area of a cone can be calculated using the formula:
= πrL,
where L is the slant height of the cone.
Lateral area = π * r * L
= π * 3 * 4r
= 3 * 4 * 3 * π
= 36π
So, the approximate lateral area of the cone is 36π cm², which is approximately 113.1 cm².
Learn more about lateral area of cone at:
https://brainly.com/question/27440713
#SPJ1
Look at pic for directions
13) name four angles that are congruent
14) name two angles that are supplementary
15) name a pair of alternate interior angles
13. ∠1, ∠4, ∠5, and ∠8 are congruent
14. ∠1 and ∠3 are supplementary
15. ∠1 and ∠4 are a pair of alternate interior angles
Naming and determining specific anglesFrom the question, we are to name four angles that are congruent.
Congruent angles are the angles that have equal measure.
In the given diagram,
angle 1, angle 4, angle 5, and angle 8 area congruent.
That is,
m ∠1 ≅ m ∠4 ≅ m ∠5 ≅ m ∠8
14. Supplementary angles are angles that sum up to 180°
In the given diagram,
angle 1 and angle 3 are supplementary angles
15. We are to determine a pair of alternate interior angles
In the given diagram,
angle 3 and angle 6 are a pair of alternate interior angles
Hence, ∠1 and ∠4 are a pair of alternate interior angles
Learn more on Naming and determining specific angles here: https://brainly.com/question/13156570
#SPJ1
It takes 6 cubic inches of colored sand to fill a plastic cone. How many cubic inches will it take to fill a plastic cylinder with the same base and height as the cone?.
The plastic cylinder will take 18 cubic inches of sand to fill it.
Ratio of volume of a cylinder to the volume of a cone:Let 'r' and 'h' be the radius and height of the both cylinder and cone, then the ratio of the volume of the cylinder to the volume cone can be calculated as given below
=> Volume of cylinder: Volume of cone
=> πr²h : 1/3 πr²h
=> 1: 1/3
=> 3: 1
Ratio of volume of a cylinder to the volume of a cone = 3: 1
which means the volume of the cone is one-third of the volume of the cylinder
Given that
It takes 6 cubic inches of colored sand to fill a plastic cone.
The volume of the cone = 6 cubic inches
It is also given that cylinder has the same base and height as the cone
As we know the volume of the cone is one-third of the volume of the cylinder
Volume of cone = (1/3) × Volume of cylinder
=> Volume of cylinder = 3 × Volume of cone
Volume of the given cylinder = 3 × 6 cubic inches
= 18 cubic inches
Therefore,
The plastic cylinder will take 18 cubic inches of sand to fill it.
Learn more about Volume of a cylinder
https://brainly.com/question/11974575
#SPJ1
resolve the force along u and v axes and determine the magnitudes of the components;
After resolving the force along u and v axes and determine the magnitudes of the components approx F(v) = 293N and F(u) = 566N.
The diagram of the question is given below:
It is necessary to resolve the stated force along the u and v axes. This actually suggests that the 800N force will finally be produced by the sum of the component forces along u and v.
Redraw the diagram in accordance with the force triangle.
According to the diagram:
θ = 180 - 30 - 15
θ = 135
The magnitude of the components will be created when the force along the u and v axes has been resolved.
Using the Sine Rule
F(v)/sin 15 = 800/sin 135 = F(u)/sin 30
Now solving the ratio by taking two ratio
F(v)/sin 15 = 800/sin 135
Multiply by sin 15 on both side, we get
F(v) = 800/sin 135 × sin 15
Using the calculator the value of sin 15 = 0.259 and sin 135 = 0.707
Now putting the value
F(v) = 800/0.707 × 0.259
F(v) = 207.2/0.707
F(v) = 293.1
F(v) = 293N(approx)
Now taking
F(u)/sin 30 = 800/sin 135
Multiply by sin 30 on both side, we get
F(u) = 800/sin 135 × sin 30
Using the calculator the value of sin 30 = 0.5 and sin 135 = 0.707
F(u) = 800/0.707 × 0.5
F(u) = 400/0.707
F(u) = 565.77
F(u) = 566N(approx)
To learn more about magnitude of component link is here
brainly.com/question/29609876
#SPJ4
Which angle must be congruent to /BAC ?
Answer: CDB
Step-by-step explanation: Congruent angles are angles that are identical to each other. For a more in-depth explanation, Congruent angles are basically when two angles "have the same shape and size, or if one has the same shape and size as the mirror image of the other". Out of the choices given, CDB is the most identical to BAC. If you rotate CDB with your mind, you'll notice that you get BAC.
if you have flipped t tails, you need to flip t 1 consecutive heads to win the game. what is the probability to win the game?
The probability of flipping 1 head in a fair coin flip is 0.5. The probability of flipping t heads in a row is [tex]0.5^{t}[/tex]. To win the game, you need to flip t heads after flipping t tails, so the probability of winning the game is ([tex]0.5^{t}[/tex])².
The probability of flipping heads in a fair coin flip is 0.5, meaning that the chance of getting heads on any given flip is 50%. If you have flipped t tails and now need to flip t heads in a row to win the game, then the probability of flipping t heads in a row is [tex]0.5^{t}[/tex].
To win the game, you need to flip t heads after t tails, so the overall probability of winning the game is ([tex]0.5^{t}[/tex])², which is the probability of flipping t heads multiplied by the probability of flipping t tails. In other words, the chance of winning the game is the product of the individual probabilities of each coin flip outcome. The probability of winning the game decreases as the number of heads you need to flip in a row increases.
To simplify the answer, let's assume that you need to flip t=3 heads in a row to win the game after flipping t=3 tails
The probability of flipping one head is 0.5, so the probability of flipping 3 heads in a row is (0.5)³ = 0.125.
The probability of flipping one tail is also 0.5, so the probability of flipping 3 tails in a row is (0.5)³ = 0.125.
The probability of winning the game, which is flipping 3 heads after flipping 3 tails, is (0.125)² = 0.015625.
So, the probability of winning the game is approximately 0.016, or 1.56%.
To learn more about probability visit: https://brainly.com/question/13604758
#SPJ4
What is the slope of the line?
Answer:
m = 5/4
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick 2 points (0, -3) (4, 2)
We see the y increase by 5 and the x increase by 4, so the slope is
m = 5/4
A number conit of two digit whoe um i 9. If 9 i added to the number it digit are inter changed. Find the number
The number is: 9.
The number we are trying to find consists of two digits, with the units digit being 9.
So, let's call the number x. The number would be 10x + 9.
Next, we add 9 to the number, and the digits are interchanged. This means the number becomes 10 + x.
Now, we have two equations:
The original number is 10x + 9The number after adding 9 is 10 + xBy comparing the two equations, we can deduce that x = 10 + x - 9.
Solving for x, we get x = 9.So, the original number was 9, and after adding 9, it became 10 + 9 = 19, which has its digits interchanged.
Complete Question:
"A number consists of two digits, with the units digit being 9. If 9 is added to the number, its digits are interchanged. Find the number."
To know more about Find the number, click on the link below:
brainly.com/question/28279284
#SPJ4
A rectangle is to be inscribed in a semicircle of radius r cm. If the height of the rectangle is h, write an expression in terms of r and h for the Area and Perimeter of the rectangle. What dimensions of the rectangle yield the maximum Area?
The required expression are A = l * h = 2 * h * [tex]\sqrt(r^2 - h^2)[/tex] , 2 * (2 * [tex]\sqrt(r^2 - h^2)[/tex] + h).
How to go through this problem of rectangle?A rectangle inscribed in a semicircle of radius r cm will have its sides parallel to the diameter of the semicircle, with one side coinciding with the diameter and the other side forming a chord of the circle.
Let the length of the rectangle be l cm. Then, the height of the rectangle h and the radius of the semicircle r form a right triangle with hypotenuse r and legs h and l/2. By the Pythagorean theorem, we have:
According to question:r^2 = h^2 + (l/2)^2
Expanding and solving for l, we have:
l = 2 √(r^2 - h^2)
The area A of the rectangle can be found by multiplying the length and height:
A = l * h = 2 * h * [tex]\sqrt(r^2 - h^2)[/tex]
The perimeter P of the rectangle can be found by adding up the lengths of the four sides:
P = 2l + 2h = 2 * (2 * [tex]\sqrt(r^2 - h^2)[/tex] + h)
To find the dimensions that yield the maximum area, we can differentiate the expression for A with respect to h and set the derivative equal to zero:
dA/dh = 2 * [tex]\sqrt(r^2 - h^2)[/tex] - 2 * h^2 / [tex]\sqrt(r^2 - h^2)[/tex]= 0
Solving for h, we have:
h = r / [tex]\sqrt(2)[/tex]
Substituting this value of h back into the expression for l, we have:
l = 2 * [tex]\sqrt(r^2 - (r / \sqrt(2))^2) = 2 * r / \sqrt(2)[/tex]
So the dimensions that yield the maximum area are a length of 2r/sqrt(2) cm and a height of r/sqrt(2) cm. The maximum area is given by:
A = 2 * (r / [tex]\sqrt(2)) * r / \sqrt(2)[/tex] =r²/√2.
A = r²/√2
To know more about Pythagorean theorem visit:
brainly.com/question/14930619
#SPJ4
HURRY FAST!!!!
what is the 10th term of the geometric sequence -9, 27, -81...
The 10th term of the geometric sequence would be 3 × (-3)¹⁰.
What is a geometric sequence?A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio.Given is the geometric sequence -
- 9, 27, - 81 ...
We can write the common ratio as -
r = 27/-9 = -3
{r} = - 3 ... Eq { 1 }
a{10} = (-9)(-3)⁹
a{10} = 3(-3)¹⁰
Therefore, the 10th term of the geometric sequence would be 3 × (-3)¹⁰.
To solve more questions on sequences, visit the link below-
brainly.com/question/1041084
#SPJ1
match the direction fields labeled a through d with the differential equation below. 1. y′=y 2x 2. y′=y−2x 3. y′=1−xy 4. y′=xy y
The solutions that match the given differential equation are a)y=0 and b)y=2x.
The differential equation is a homogeneous linear differential equation with constant coefficients, which can be written in the form of y" + p(x)y' + q(x)y = 0. The general solution to this type of equation is y = c1e^(rx) + c2e^(rx) where r is the root of the characteristic equation r^2 + p(x)r + q(x) = 0.
In this case, the equation is of the form xy'' - y' = 0. By dividing both sides by x, we get y'' - (1/x)y' = 0, which is a homogeneous linear differential equation with constant coefficients. The characteristic equation is r^2 - (1/x)r = 0. The roots of this equation are r1 = 0 and r2 = 1/x.
Therefore, the general solution to this differential equation is y = c1 + c2x.
y=0 is a solution of the differential equation since it satisfies the equation when plugged in.
y=2x is also a solution of the differential equation since it also satisfies the equation when plugged in.
y=2x^2 and y=2 are not solutions of the differential equation because when plugged into the equation they don't satisfy it.
For more questions equations click the link below:
brainly.com/question/14620493
#SPJ4
Here is part of the menu price list at a takeaway. Chips Peas Rice Pickled onion Fish 45p Sausage 90p Bread roll 25p Samosa £1.20 b) Taha buys one fish, a portion of peas and a pickled onion. lowan buys a portion of rice, a sausage and a bread roll. How much more (in £) does Taha pay than lowan? Optional working Answer: £ £2.70 £1.60 30p 75p
The required money that Taha paid more than lowan is £0.6, as per the given condition.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
Taha buys one fish, a portion of peas, and pickled onion.
taha paid = 2.70 + 0.45 + 0.25
= £3.40
Lowan buys a portion of rice, a sausage, and a bread roll.
Total money lowan to pay
= 0.90 + 1.60 + 0.30
= £2.80
Money Taha pays more than lowan = 3.40 - 2.80
= £0.6
Thus, the required, money that Taha paid more than lowan is £0.6, as per the given condition.
Learn more about arithmetic here:
https://brainly.com/question/11424589
#SPJ1
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.y = ex, y = 0, x = −2, x = 2;about the x-axisV =Sketch the region.
The required volume of the solid which was obtained by rotating the region bounded by the curve about a line is equal to ( π/2 ) ( e⁻⁴ + e⁴).
Graph is attached.
Volume of the solid rotating the region bounded by the curves about a line with y = eˣ with x = −2, x = 2 about x-axis.
=π [tex]\int_{-2}^{2}[/tex] [( eˣ - 0)² ] dx
= π [tex]\int_{-2}^{2}[/tex] e⁽²ˣ⁾ dx
= π (e²ˣ) / ( 2 [tex]|_{-2}^{2}[/tex]
= ( π/2 )[ e⁻⁴ - e⁴ ]
= ( π/2 ) ( e⁻⁴ + e⁴ )
Graph is attached.
Therefore, the volume of the solid of the rotating region bounded by curves about line is equal to ( π/2 ) ( e⁻⁴ + e⁴ ).
Graph is attached.
Learn more about volume here
brainly.com/question/13338592
#SPJ4