Las edades de una madre y su hija se diferencian en 26 años, hace 10 años la madre tenía el triple que su hija. ¿Cuáles son las edades actuales de las dos?

The Cartesian equation in the form x = f(y) for the given parametric equations is \(x = -4(y - 2)^2/25\)

To eliminate the parameter t and express the given parametric equations in Cartesian form, we need to solve one equation for t and substitute it into the other equation.

Given:

\(x(t) = -4t^2\)

y(t) = 2 + 5t

We'll start by solving the second equation for t:

y = 2 + 5t

Subtracting 2 from both sides:

y - 2 = 5t

Dividing both sides by 5:

t = (y - 2)/5

Now, we'll substitute this value of t into the first equation:

\(x = -4t^2\\x = -4((y - 2)/5)^2\)

Simplifying:

\(x = -4(y - 2)^2/25\)

Therefore, the Cartesian equation in the form x = f(y) for the given parametric equations is:

\(x = -4(y - 2)^2/25\)

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Triangle in (22) have value of side z = 4, and angles x = 53°, y = 37°. The triangle in (23) have the value of it sides x = 35, z = 83, and an angle y = 65°. Using trigonometric ratios to the nearest whole numbers.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

(22). by Pythagoras rule;

z = √(5² - 3²) = 4

sin x = 4/5

x = sin⁻¹(4/5) {cross multiplication}

x = 53.1301

y = 180 - (53 + 90) {sum of interior angles of a triangle}

y = 37°

(23). cos 25 = 75/z {adjacent/hypotenuse}

z = 75/cos 25 {cross multiplication}

z = 82.7533

sin 25 = x/82.7533

x = 82.7533 × sin 25 {cross multiplication}

x = 34.9731

y = 180 - (25 + 90)

y = 65°

Therefore, the triangle in (22) have value of side z = 4, and angles x = 53°, y = 37°. The triangle in (23) have the value of it sides x = 35, z = 83, and an angle y = 65°. Using trigonometric ratios to the nearest whole numbers.

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Answer:

? = 9

Step-by-step explanation:

you know 99 + 33 = 132 so you can substitute that: 132 = 11 (? + 3). im going to change ? into x for now: 132 = 11 (x + 3). then distribute the 11 so 132 = 11x + 33. then subtract 33 from both sides (99 = 11x) and divide both side by 11 (x = 9) and you get 9!

hope this helps!

Answer:

6√7=15.874507866387543=√252

Step-by-step explanation:

hope this is helpful

The expression that are equivalent to √252 are \(252^{\frac{1}{2} }\) and 6√7.

Applying the surd rule,

√a = \(a^{\frac{1}{2} }\)

Hence,

\(\sqrt{252}=252^{\frac{1}{2} }\)

using surd rule, we can also decompose √252

Therefore,

√252 = √36 × 7 = 6√7

Hence, the equivalent expression of √252 are as follows:

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In summary d²y/dx² in terms of x and y is given by: d²y/dx² = 3/2 x + 1/4 y

Why is it?

To find d²y/dx², we need to differentiate the given differential equation with respect to x:

dy/dx = x² - 1/2 y

Differentiating both sides with respect to x:

d²y/dx² = d/dx(x² - 1/2 y)

d²y/dx² = d/dx(x²) - d/dx(1/2 y)

d²y/dx² = 2x - 1/2 d/dx(y)

Now, we need to express d/dx(y) in terms of x and y. To do this, we differentiate the original differential equation with respect to x:

dy/dx = x² - 1/2 y

d/dx(dy/dx) = d/dx(x² - 1/2 y)

d²y/dx² = 2x - 1/2 d/dx(y)

d²y/dx² = 2x - 1/2 (d²y/dx²)

Substituting this expression for d²y/dx² back into our previous equation, we get:

d²y/dx² = 2x - 1/2 (2x - 1/2 y)

d²y/dx² = 2x - x/2 + 1/4 y

d²y/dx² = 3/2 x + 1/4 y

Therefore, d²y/dx² in terms of x and y is given by:

d²y/dx² = 3/2 x + 1/4 y

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The magnitude of the child's linear velocity (p) can be calculated using the formula: p = 2πr/T, where r is the radius of the carousel (7.2 m) and T is the period of revolution (9.0 seconds). Substituting the values into the formula, we get:

p = (2π)(7.2 m)/(9.0 s)
p = 5.0265482457 m/s

The direction of the child's linear velocity is tangential to the carousel at the point where the child is sitting. This means that the direction is constantly changing as the carousel completes one revolution.

The net force acting on the child is the centripetal force, which can be calculated using the formula: Fc = mv^2/r, where m is the mass of the child (37 kg), v is the linear velocity (5.0265482457 m/s), and r is the radius of the carousel (7.2 m). Substituting the values into the formula, we get:

Fc = (37 kg)(5.0265482457 m/s)^2/(7.2 m)
Fc = 122.21695682 N

The objects in the surroundings that exert this force are the wooden horse and the carousel itself. The wooden horse exerts an upward normal force on the child, while the carousel exerts a centripetal force on the child, causing the child to move in a circular path.

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Answer:

2 2/3 is your answer

Step-by-step explanation:

You want to flip the fractions and divide

Hello! Your answer is 2 2/3

The minimum number of supports required is 7.

To determine the minimum number of supports required for the twenty-four feet (six 4-ft sections) of track lighting to be installed in a continuous row in a retail store, follow these steps:

1. Determine the total length of the track lighting: 6 sections * 4 feet per section = 24 feet.

2. Consider that a support is needed at the beginning and end of the track.

3. Assess the spacing between supports. For instance, let's assume supports can be placed every 4 feet.

4. Calculate the number of supports in between the ends: (24 feet - 4 feet) / 4 feet = 5 supports.

5. Add the supports at the beginning and end: 5 supports + 2 supports = 7 supports.

The minimum number of supports required is 7.

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The reasoning provided, "If you build it, they will come. You build it. Therefore, they will come," is an example of deductive reasoning.

Deductive reasoning is a logical process that involves drawing specific conclusions based on general principles, premises, or known facts. In this example, the premise is "If you build it, they will come," which establishes a cause-and-effect relationship. The subsequent statement, "You build it," serves as a confirmation of the premise. From these premises, the conclusion is drawn: "Therefore, they will come." The conclusion logically follows from the premises, making it an example of deductive reasoning.

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The phase change line, also known as the phase boundary or phase transition line, is a line on a graph that represents a change in conditions for a substance. This line shows the temperature and pressure conditions at which a substance will change from one phase to another, such as from a solid to a liquid or from a liquid to a gas.

The phase change line is represented on a graph by a diagonal line that separates two regions where the substance is in different phases. This line usually slopes upwards from left to right, indicating that higher temperatures and pressures are needed to change the substance from one phase to another.

The phase change line is an important concept in thermodynamics and is used to understand the behavior of substances under different conditions. For example, the phase change line for water shows that at normal atmospheric pressure, water will freeze at 0°C and boil at 100°C. However, at higher pressures, the freezing and boiling points will change, and water may exist in different phases, such as a supercritical fluid.

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The sum of four times a number ,r, and 16 is equal to 20 less than 10 times the number, r.then the value of r is -9

The sum of

(prepare to add)

four times a number and 10 is equal to

4      *          r           +   10        =

the difference of

(prepare to subtract)

twice the number and 8.

   2r                    -  8

Putting it all together:

4r + 10 = 2r - 8

solving for the value of r we get

r = -9

The sum of four times a number ,r, and 16 is equal to 20 less than 10 times the number, r.then the value of r is -9

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Answer:

Least common denominator = (x - 1)²(x - 2)

Step-by-step explanation:

Least common denominator of two rational expressions = LCM of the denominator of the expressions.

\(\frac{x^3}{x^2-2x+1}\) and \(\frac{-3}{x^{2}-3x+2}\)

Factorize the denominators of these rational expressions,

Since, \(x^{2}-2x+1\) = x² - 2x + 1

                             = (x - 1)²

And x² - 3x + 2 = x² - 2x - x + 2

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

                         = (x - 1)(x - 2)

Now LCM of the denominators = (x - 1)²(x - 2)

Therefore, Least common denominator will be (x - 1)²(x - 2).

Answer:

5 : 7

Step-by-step explanation:

groom's side: 40

bride's side: 56

ratio groom to bride = 40/56 = 20/28 = 10/14 = 5/7

Answer: 5 : 7

Answer:

The measure of arc SQ is 95° ⇒ (1)

Step-by-step explanation:

In the given circle

∵ S lies on the circumference of the circle

∴ ∠QSR is an inscribed angle

∵ ∠QSR is subtended by arc QR

→ By using the 2nd rule above

∴ m arc QR = 2 × m∠QSR

∵ m∠QSR = 95°

∴ m arc QR = 2 × 95

∴ m arc QR = 190°

→ By using the 1st rule above

∵ m of the circle = m arc QR + m arc SQ + m arc SR

∵ m arc SR = 75° and m arc QR = 190°

→ Substitute them in the equation above

∴ 360 = 190 + m arc SQ + 75

→ Add the like term in the right side

∴ 360 = 265 + m arc QS

→ Subtract 265 from both sides

∵ 360 - 265 = 265 - 265 + m arc SQ

∴ 95° = m arc SQ

∴ The measure of arc SQ is 95°

The most accurate statement about the p-value for this test is: 0.05 < p-value < 0.10.

In a hypothesis test, the null hypothesis can be rejected at the .10 level but cannot be rejected at the .05 level. This means that the p-value for the test falls between these two levels.

A p-value is a measure of the strength of evidence against the null hypothesis. It represents the probability of obtaining a test statistic as extreme as, or more extreme than, the observed value, assuming that the null hypothesis is true.

In this case, the fact that the null hypothesis can be rejected at the .10 level means that the p-value is less than .10. However since the null hypothesis cannot be rejected at the .05 level, it implies that the p-value is greater than .05.

This indicates that the evidence against the null hypothesis is not strong enough to reject it at the .05 level, but it is strong enough to reject it at the .10 level. The p-value falls between these two values, providing a range of uncertainty in the results of the hypothesis test.

In summary, the p-value in this scenario is greater than .05 but less than .10, indicating moderate evidence against the null hypothesis.

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In a hypothesis test, the null hypothesis can be rejected at the 0.10 level but cannot be rejected at the 0.05 level. This means that the p-value obtained in the test falls between these two levels.

The p-value is a measure of the strength of evidence against the null hypothesis. It represents the probability of observing the data or more extreme data, assuming that the null hypothesis is true.

When the p-value is less than the chosen significance level (alpha), typically 0.05, it indicates that the data provides strong evidence against the null hypothesis. In this case, we reject the null hypothesis in favor of the alternative hypothesis.

However, if the p-value is greater than the significance level, such as 0.10, it means that the data does not provide enough evidence to reject the null hypothesis. We fail to reject the null hypothesis and do not have sufficient evidence to support the alternative hypothesis.

Therefore, for this given hypothesis test, since the null hypothesis can be rejected at the 0.10 level but not at the 0.05 level, the most accurate statement about the p-value is:

0.05 < p-value < 0.10

This means that the p-value falls between 0.05 and 0.10, indicating moderate evidence against the null hypothesis, but not strong enough to reject it at the 0.05 level.

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The volume of the right triangular prism is 112 cubic centimeters (cm^3).

To find the volume of a right triangular prism, we need to multiply the area of the triangular base by the height of the prism.

In this case, we have:

The base of the triangular prism has a width of 4 cm and a height of 4 cm, so its area is (1/2) x 7 cm x 4 cm = 14 cm^2.

The height of the triangular prism is 8 cm.

Therefore, the volume of the triangular prism is:

Volume = Base area x Height

Volume = 14 cm^2 x 8 cm

Volume = 112 cm^3

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Answer:4

Step-by-step explanation:22-4=18-4=14-4=10-4=6=2

The length of the arc opposite a central angle that measures 46 degrees is 2.72 cm.

What is circle?

The measurement of the circle's boundaries is called as the circumference or perimeter of the circle. whereas the circumference of a circle determines the space it occupies. The circumference of a circle is its length when it is opened up and drawn as a straight line. Units like cm or unit m are typically used to measure it. The circle's radius is considered while calculating the circumference of the circle using the formula. As a result, in order to calculate the circle's perimeter, we must know the radius or diameter value.

in a circle of radius 3.4 cm

central angle that measures 46 degrees

length of arc = (46/360) * 2π*3.4

=2.72cm

Hence the length of the arc opposite a central angle that measures 46 degrees is 2.72 cm

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The number of times in milligram the aluminium is 3030 times the gold present in human body.

What are indices?

Indices are defined as the numeric values that are acts as the power of a number in other words these are the exponents to a particular number.

The gold present in 154 pound man is \(2*10^{-1}mg\) and the aluminium found in that man is \(6*101=606 mg\)

Now the amount of gold in  milli grams that is required to make it equal to the amount of aluminium that is present in the human body is

\(\frac{606}{0.2}=3030.\)

Hence, the number of times in milli grams the amount of aluminium that is present in a 154 pound man is 3030 times the amount of gold present in that body.

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Answer:

Triangle I and II

Step-by-step explanation:

Hope my solution helps you and don't forget to help me with my maths questions....Check my questions..

Answer:

I and II

Step-by-step explanation:

the first one because the one on the far left is just smaller than the one in the middle

Answer:

x =-26

Step-by-step explanation:

-15x = 390

Divide each side by -15

-15x/-15 = 390/-15

x =-26

Answer:

X = -26

Step-by-step explanation:

Divide both sides by -15.

390/-15 = -26

X is equal to -26.

Case-control study

This type of study is referred to as a case-control study. In such studies, people with a particular disease or condition (cases) are compared to people without that disease or condition (controls) to see if the condition is linked to a particular exposure or risk factor.What is a case-control study?A case-control study is a research method in epidemiology, which is the study of illness patterns in populations. This research investigates whether a suspected risk factor is linked to an outcome or disease. This approach involves identifying people who have the disease (cases) and people who do not (controls).The individuals are then assessed to see whether they have been exposed to a particular risk factor or not, and the odds of developing the disease in the exposed group are compared to the odds of developing the disease in the non-exposed group. Therefore, the type of study described above is referred to as a case-control study.

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The measure of DE, given that Triangle ABC is similar to Triangle DEF, is 53. 09 units .

To find the measure of DE, you need to use the corresponding sides of BC and EF to find the scale factor that shows the difference in the sizes of corresponding sides.

The scale factor is:

= 31 / 8

= 3. 875

Now, since the value of the corresponding side of AB is 13.7 units, the measure of DE would be :

= 13. 7 x 3. 875

= 53. 09 units

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The term ‘arterial’ is used to describe roads and streets which connect to the highways. These roads are designed to help people move around easily and quickly. The study of arterial roads is an important area of transportation engineering.

To calculate the Time Mean Speed (TMS), first, the total distance covered by the vehicles needs to be calculated. Here, the distance covered by the vehicles is 2000 ft or 0.38 miles (1 mile = 5280 ft).Next, the total travel time for all vehicles is calculated as follows:40.5 + 44.2 + 41.7 + 47.3 + 46.5 + 41.9 + 43.0 + 47.0 + 42.6 + 43.3 = 437.0 secondsNow, the time mean speed (TMS) can be calculated as follows:TMS = Total Distance / Total Time = 0.38 miles / (437.0 seconds / 3600 seconds) = 24.79 mphThe Space Mean Speed (SMS) can be calculated by dividing the length of the segment by the average travel time of vehicles. Here, the length of the segment is 2000 ft or 0.38 miles (1 mile = 5280 ft).

The average travel time can be calculated as follows: Average Travel Time = (40.5 + 44.2 + 41.7 + 47.3 + 46.5 + 41.9 + 43.0 + 47.0 + 42.6 + 43.3) / 10= 43.7 seconds Now, the Space Mean Speed (SMS) can be calculated as follows: SMS = Segment Length / Average Travel Time= 0.38 miles / (43.7 seconds / 3600 seconds) = 19.54 mp h Therefore, the Time Mean Speed (TMS) and Space Mean Speed (SMS) for these vehicles are 24.79 mph and 19.54 mph respectively.

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P(X ≤ 4) by using the Cumulative Poisson Probabilities table in : P(X ≤ 4) = 0.785.

In this problem, we are given that the number of failures X in a cast-iron pipe of a particular length follows a Poisson distribution with an expected value (mean) of μ = 1.

To find P(X ≤ 4), we need to calculate the cumulative probability up to 4, which includes the probabilities of 0, 1, 2, 3, and 4 failures. We can use the Cumulative Poisson Probabilities table in the Appendix of Tables to find the cumulative probabilities.

From the table, we can look up the values for each number of failures and add them up to find P(X ≤ 4).

The cumulative probabilities for each value of k are:

P(X = 0) = 0.367

P(X = 1) = 0.736

P(X = 2) = 0.919

P(X = 3) = 0.981

P(X = 4) = 0.996

P(X ≤ 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.367 + 0.736 + 0.919 + 0.981 + 0.996 = 0.785

Therefore, P(X ≤ 4) is approximately 0.785 (rounded to three decimal places).

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Complete question

The article "Expectation Analysis of the Probability of Failure for Water Supply Pipes"† proposed using the Poisson distribution to model the number of failures in pipelines of various types. Suppose that for cast-iron pipe of a particular length, the expected number of failures is 1 (very close to one of the cases considered in the article). Then X, the number of failures, has a Poisson distribution with μ = 1. (Round your answers to three decimal places.)

(a) Obtain P(X ≤ 4) by using the Cumulative Poisson Probabilities table in the Appendix of Tables. P(X ≤ 4) =

Answer:

C

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Conservation of number, which is the understanding that the quantity of an object remains the same even if its appearance or arrangement changes.

Four-year-old Dimitri has not acquired the concept of conservation.

Conservation refers to the understanding that certain properties of objects, such as quantity, remain the same even when their appearance changes, as long as nothing is added or removed.

In this case,

Dimitri incorrectly believes that increasing the spacing between nickels in one row results in more nickels, failing to understand that the quantity remains the same.

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Amount of one tin of paint is $14 and the total amount Mr. Chong  have is $172.

Let amount of one tin of paint = x

Let the total amount Mr. Chong  having = y

On buying 18 tins of paint, he will need another $80. This can we mathematically represented as,

18x = y + 80            

On rearranging this equation can be written as,

18x - y = 80                                         equation 1

On buying 10 tins of paint, he will will have $32 left. This can we mathematically represented as,

10x = y - 32

On rearranging this equation can be written as,

-10x + y = 32                                      equation 2

On adding equation 1 and equation 2, we get

18x - y -10x + y = 80 + 32

8x = 112

x = (112/8) = 14

On substituting x = 14 in equation 2 , we get

-140 + y = 32

y = 172

So, amount of one tin of paint is $14 and the total amount Mr. Chong  have is $172.

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