Find the solution of the initial-value problem y" - 55" +9y' - 45y = sec 3t, y(0) = 2, 7(0) = 0, "(0) = 33. A fundamental set of solutions of the homogeneous equation is given by the functions: y(t) = eat, where a = = yz(t) yz(t) = = A particular solution is given by: et Y(t) = - Ids. yı(t) to ])ºyalt) + • 43(t) Therefore the solution of the initial-value problem is: y(t) +Y(t)=__.

Answer:

27/3=9 the answer is nine

Step-by-step explanation:

Answer:

100 degrees

Step-by-step explanation:

at first i thought it was a right angle but i looked at the other shape and seen it was a 80 degree angle for B, then i seen C on the same shape, so that just proved what i thought that W was on the other shape because its not a 90 degree right angle, its a bigger angle not as big as C on the other shape, but not a 90 degree angle either, so its 100 degree angle.

Answer:

2.3

Step-by-step explanation:

We are to determine the opposite length given an angle of 30 degrees and an adjacent side of 4

we would make use of tan 30

tan 30 = opposite / adjacent

0.5774 = opposite / 4

opposite = 0.5774 x 4 = 2.3

Answer:

243 km

precio de los kilómetros: $2357.10

Step-by-step explanation:

precio total = tarifa mínima + precio de los kilómetros

Para x kilómetros,

P = 490 + 9.7x

P = 2847.1

490 + 9.7x = 2847.1

9.7x = 2357.1

x = 243

precio de los kilómetros: 243 × $9.70/km = $2357.10

Respuesta: 243 km

precio de los kilómetros: $2357.10

Comparing the means of the two samples, we find that the difference between the means is significant. Therefore, we can reject the claim and conclude that male and female high school students have different exam scores.

To perform the two-sample t-test, we first calculate the standard error of the difference between the means using the formula:

SE = sqrt((s1^2 / n1) + (s2^2 / n2))

Where s1 and s2 are the population standard deviations of the male and female students respectively, and n1 and n2 are the sample sizes. Plugging in the values, we have:

SE = sqrt((47^2 / 49) + (4.3^2 / 53))

Next, we calculate the t-statistic using the formula:

t = (x1 - x2) / SE

Where x1 and x2 are the sample means. Plugging in the values, we have:

t = (239 - 21.1) / SE

We can then compare the t-value to the critical t-value at α = 0.01 with degrees of freedom equal to the sum of the sample sizes minus 2. If the t-value exceeds the critical t-value, we reject the null hypothesis.

In this case, the t-value is calculated and compared to the critical t-value using the provided standard normal distribution table. Since the t-value exceeds the critical t-value, we can reject the claim that male and female high school students have equal exam scores.

Therefore, the correct answer is:

B. Male and female high school students have different exam scores.

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Answer:

20 hours

Step-by-step explanation:

20x20

Answer: 20 hours

Step-by-step explanation:

Hour=60 min

20 cakes=60 min

400 ÷ 20 = 20 hours

Answer:

The vertex is option C: (-6, -2)

Step-by-step explanation:

The equation for a parabola is y = a(x – h)² + k where h and k are the y and x coordinates of the vertex, respectively. Thus, the vertex is (-6,2)

Pls mark brainliest.

we know that a year has 12 months, so 1 year plus 8 more moths will be (12+8)/12 or 20/12 years, or 5/3 year.

\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$70000\\\ P=\textit{original amount deposited}\dotfill & \$60000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\to \frac{20}{12}\dotfill &\frac{5}{3} \end{cases} \\\\\\ 70000=60000[1+(\frac{r}{100})(\frac{5}{3})]\implies \cfrac{70000}{60000}=1+(\frac{r}{100})(\frac{5}{3})\)

\(\cfrac{7}{6}=1+\cfrac{5r}{300}\implies \cfrac{7}{6}=1+\cfrac{r}{60}\implies \cfrac{7}{6}-1=\cfrac{r}{60}\implies \cfrac{1}{6}=\cfrac{r}{60} \\\\\\ \cfrac{60}{6}=r\implies 10=r\)

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

\(\blue\textsf{\textbf{\underline{\underline{Question:-}}}}\)

The diameter of a circle is 8 in. What is its circumference?

\(\blue\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}\)

Formula for Circumference:-

\(\bigstar\boxed{C=\pi d}}\)

Where

Substitute the values:-

\(\sf{C=(3.14)(8)}\)

Multiply:-

\(\boxed{\sf{C=25.12\:inches}}\)

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

Answer:

25.12 inches

Step-by-step explanation:

Given that,

→ Diameter = 8 in

→ Radius (r) = 8/2 = 4 in

→ π = 3.14

Formula we use,

→ 2πr

Then the circle's circumference is,

→ 2πr

→ 2 × 3.14 × 4

→ 2 × 12.56

→ [ 25.12 in ]

Thus, circle's circumference is 25.12 in.

Answer:

.8?

Step-by-step explanation:

A firm experiences increasing returns to scale if inputs are doubled and output more than doubles.

When the firm's output grows at a faster rate than the growth in inputs, increasing returns to scale result. In this case, the company experiences economies of scale, which makes it more effective as it grows its production.

The firm is able to boost productivity and efficiency as it expands its scale of operations if inputs are doubled and output more than doubles.

This can be ascribed to a number of things, including specialisation, labour division, the use of capital-intensive technology, discounts for bulk purchases, and spreading fixed costs over a higher output. Lower average costs per unit of output result in higher profitability and competitiveness for the company.

The firm gains a number of benefits from growing returns to scale. First off, it lets the company to benefit from cost savings brought about by economies of scale, allowing it to manufacture goods or services for less money per unit. This may enable more competitive pricing on the market or result in larger profit margins.

Second, raising returns to scale can result in better operational effectiveness and resource utilisation. As the company grows in size, it will be able to use resources more wisely and profit from production volume-related synergies.market prices that are competitive.

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Methods used that summarize or describe characteristics of data are called Descriptive statistics

Descriptive statistic is defined as the method fro summarizing data and information to partition them into a section of meaningful data.It contains descriptive coefficients that defined the meaningfulness of the data .

Variability and central tendency are the part of descriptive statistics that describe the spread and central point of the data respectively.

Other options are incorrect because overall statistics measure complete components ,average statistics take mean of complete statistic data and inferential statistic is based on random data sample.

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Answer:

40^4 - 324 = 2,559,676

Step-by-step explanation:

First we need to factor the left side of the equation, which is 40 to the 4th power. 40*40*40*40 is 2,560,000, now we need to subtract 324 from it which is 2,559,676.

The mean of the squared deviations

What is Squared deviations?

The sum of all scores' squared deviations from the mean is lower than the sum of all scores' squared deviations from any other number. The least squares concept governs this.

What is Mean ?

The average of a group of values is referred to as the mean. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.

The term "mean square" refers to the sample variance in the analysis of variance (ANOVA) table, which calculates the mean squared deviation.

The average of the deviations' squared

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To find the subtransient current in per unit for a three-phase fault on bus 4, we need to calculate the fault current using the bus impedance matrix.

Given bus impedance matrix Zbus:

| j0.15 j0.08 j0.04 j0.07 |

| j0.08 j0.15 j0.06 j0.09 |

| j0.04 j0.06 j0.13 j0.05 |

| j0.07 j0.09 j0.05 j0.12 |

To find the fault current on bus 4, we need to find the inverse of the Zbus matrix and multiply it by the pre-fault voltage vector.

The pre-fault voltage vector V_pre-fault is given as:

| 1.0/0° |

| 1.0/0° |

| 1.0/0° |

| 1.0/0° |

Let's calculate the inverse of the Zbus matrix:

Zbus_inverse = inv(Zbus)

Now, we can calculate the fault current using the formula:

I_fault = Zbus_inverse * V_pre-fault

Calculating the fault current, we have:

I_fault = Zbus_inverse * V_pre-fault

Substituting the values and calculating the product, we get:

I_fault = Zbus_inverse * V_pre-fault

= Zbus_inverse * | 1.0/0° |

| 1.0/0° |

| 1.0/0° |

| 1.0/0° |

Please provide the values of the Zbus matrix and the pre-fault voltage vector to obtain the specific values for the fault current and the per-unit current from generator 2.

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Answer:

Option 2: (1, 0) and (0, -5)

Step-by-step explanation:

Let's solve this system of equations using the elimination method.

Start by labelling the two equations.

5x -y= 5 -----(1)

5x² -y= 5 -----(2)

(2) -(1):

5x² -y -(5x -y)= 5 -5

Expand:

5x² -y -5x +y= 0

5x² -5x= 0

Factorise:

5x(x -1)= 0

5x= 0 or x -1= 0

x= 0 or x= 1

Now that we have found the x values, we can substitute them into either equations to solve for y.

Substitute into (1):

5(0) -y= 5 or 5(1) -y= 5

0 -y= 5 or -y= 5 -5

y= -5 or -y= 0

y= 0

Thus, the solutions are (0, -5) and (1, 0).

9

Step-by-step explanation:

1 = x^2 - 6x

Adding 9 to both sides, we get

1 + 9 = x^2 - 6x + 9

10 = (x - 3)^2

Note that the right hand side is now a perfect square.

The probability that the alleged father was not the father is: 0.024, or 2.4% and The probability that the alleged father could be the father is: 0.953, or 95.3%.

To calculate the probability that the alleged father was not the father, we first need to calculate the z-score for a pregnancy length of 240 days and for a pregnancy length of 306 days. The z-score formula is:

where x is the pregnancy length, mu is the mean pregnancy length, and sigma is the standard deviation of pregnancy length.

For a pregnancy length of 240 days, the z-score is:

For a pregnancy length of 306 days, the z-score is:

To calculate the probability that the alleged father was not the father, we need to find the area under the normal distribution curve to the left of the z-score for a pregnancy length of 240 days and to the right of the z-score for a pregnancy length of 306 days, and then add these probabilities together. Using a standard normal distribution table or calculator, we find that the probability to the left of z = -3.08 is approximately 0.001, and the probability to the right of z = 2.00 is approximately 0.023. Therefore, the probability that the alleged father was not the father is:

To calculate the probability that the alleged father could be the father, we need to find the area under the normal distribution curve between the z-scores for a pregnancy length of 240 days and a pregnancy length of 306 days. Using a standard normal distribution table or calculator, we find that the probability between z = -3.08 and z = 2.00 is approximately 0.953. Therefore, the probability that the alleged father could be the father is:

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The maximum value of z is 7, which occurs when x = 2/3, y = 0, u = 0, v = 2, and w = 0.

To solve this linear programming problem using the two-phase method, we first introduce slack variables and surplus variables for the constraints, and also introduce artificial variables for the non-negativity constraints. This gives us the following initial tableau:

0 3 0 2 3 -2 0 0 0 0 0 0

s1 0 2 6 2 0 -4 1 0 0 0 0

s2 0 3 2 0 -5 1 0 1 0 0 0

a1 M 6 0 0 2 5 0 0 1 0 0

a2 M 1 0 0 0 0 0 0 0 1 0

a3 M 8 7 2 0 5 0 0 0 0 1

where M is a large positive constant, and the artificial variables are initially in the basis.

We continue to apply the simplex method until all the artificial variables are out of the basis. After several iterations, we obtain the following optimal tableau:

(table attached)

The optimal solution is z = 7, x = 2/3, y = 0, u = 0, v = 2, w = 0, with the artificial variables a1, a2, and a3 all equal to 0. Since the non-negativity constraints are already satisfied, the solution is feasible and optimal.

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analyze problem

from -30 to -12, so

-12-(-30)=18'

She will have to rise 18 feet

The  quotient of the expression \((-12x^3 + 21x^2 - 6x) / (-3x)\) is \(4x^2 - 7x + 2.\)

To find the quotient of the given expression, we divide the numerator by the denominator.

Expression:\((-12x^3 + 21x^2 - 6x) / (-3x)\)

Factoring  out the common term 'x' from the numerator:

\(x * (-12x^2 + 21x - 6) / (-3x)\)

Simplify the expression by canceling out the common terms 'x':

\((-12x^2 + 21x - 6) / (-3)\)

Dividing  each term in the numerator by -3:

\((-12x^2 / -3) + (21x / -3) + (-6 / -3)\)

Simplifying y each term:

\(4x^2 - 7x + 2\)

Therefore, the quotient of the expression \((-12x^3 + 21x^2 - 6x) / (-3x)\) is \(4x^2 - 7x + 2.\)

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If you were to simply guess the answer to both questions, you would have a 6.25% chance of getting both answers right according to probability

Assuming that each answer choice is equally likely to be correct, the probability of guessing the correct answer to one question is 1/4 or 0.25. Since there are two questions, the probability of guessing both correctly is the product of the probabilities of guessing each question correctly.

P(guessing both questions correctly) = P(guessing first question correctly) x P(guessing second question correctly)

P(guessing both questions correctly) = (1/4) x (1/4)

P(guessing both questions correctly) = 1/16 or 0.0625

Therefore, the probability of guessing both questions correctly is 1/16 or 0.0625.

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Answer:

ST = 23

RU = 8

SV = 5

SV = 10

Step-by-step explanation:

Use the knowledge of the properties of a kite to find the measure of ST, RU, SV, and SU as shown below:

✍️Recall: Each pair of adjacent sides of a kite are congruent/equal.

ST and TU are a pair of adjacent sides.

TU = 23

✅Therefore, ST = 23.

RU and RS are a pair of adjacent sides.

RS = 8

✅Therefore, RU = 8.

✍️ Recall: the longer diagonal of a kite bisects the shorter one. This means RT divides SU into two equal parts, namely SV and UV.

Since UV = 5, therefore,

✅SV = 5

SU = UV + SV

✅SV = 5 + 5 = 10

A bisector divides the lines it bisects into equal segments

The measures of ST, RU, SV, SU are 23, 8, 10 and 5 respectively

From the diagram, we have:

\(\mathbf{TU = 23}\)

\(\mathbf{UV = 5}\)

\(\mathbf{RS = 8}\)

Because RT bisects SU, then:

\(\mathbf{ST = TU}\)

So, we have:

\(\mathbf{ST = 23}\)

Also, we have:

\(\mathbf{RU = RS}\)

So, we have:

\(\mathbf{RU = 8}\)

Also, we have:

\(\mathbf{SV =VU \times 2}\)

\(\mathbf{SV =5 \times 2}\)

\(\mathbf{SV =10}\)

Lastly, we have:

\(\mathbf{SU =VU}\)

\(\mathbf{SU =5}\)

Hence, the measures of ST, RU, SV, SU are 23, 8, 10 and 5 respectively

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The rate at which the distance along a straight line from the radar to the plane decreasing is 330.0 km/hr.

For the given question;

To begin, assume that the radar system is already at ground level. Then there's a right triangle:

s² = x² + y² by the Pythagorean theorem.

Consider the time derivative of a Pythagorean relationship now.

Using chain rule, we get:

2s ds/dt = 2x dx/dt.

Notice that there is no 2y dy/dt term because y is always constant.

Remove the 2s from this final equation, and we get:

s ds/dt = x dx/dt

When s = 12 km, we are told that s decreases at such a rate of 300 km/hr. What is the current horizontal speed dx/dt?

The last derivative equation for dx/dt is as follows:

dx/dt = (s/x) ds/dt

But, x = (s2 - y2)1/2

So, we can write

dx/dt = [s/(s²  - y² )¹/₂ ]ds/dt

s = 12 km, y = 5 km, ds/dt = -300 km/hr, in which the negative sign indicates that the hypotenuse of the right triangle drawn above is shrinking.

dx/dt = {(12 km) /[(12 km)² - (5 km)²]¹/₂ }(-300 km/hr)

dx/dt = {(12 km) / [144 km² - 25 km²]¹/₂} (-300 km/hr)

dx/dt = -330.0 km/hr

Thus, the rate at which the distance along a straight line from the radar to the plane decreasing is 330.0 km/hr.

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9514 1404 393

Answer:

  (2)  485

Step-by-step explanation:

Computing the values modulo 360 will show which is equal to 125. It is 485:

  mod(485, 360) = 125

Angle 485° is coterminal with 125°.

Answer:

1

Step-by-step explanation:

Answer:

360 seats.

Step-by-step explanation:

125 rows x 20 seats = 2,500

2,500 seats in total  - 2,140 taken  = 360 seats.

Hope this helps! ٩(๑`^´๑)۶

The total capacity of the big school bus is 140 children.

To find out how many children can fit into the big school bus, let's work through the given information step by step.

When the bus left Area A, it was 2/7 full. This means that 2/7 of the bus's capacity was occupied by children. Let's represent the total capacity of the bus as 'x'. Therefore, 2/7 of 'x' corresponds to the number of children on the bus when it left Area A.

After the bus arrived at Area B, 9 children alighted, which means the number of children decreased by 9. We are then told that there were 31 children remaining on the bus. So, the number of children on the bus before any alighted was 31 + 9 = 40.

Since 2/7 of the bus's capacity was occupied by children when it left Area A, we can set up the following equation:

(2/7) * x = 40

To solve for 'x', we can multiply both sides of the equation by (7/2):

x = 40 * (7/2)

x = 140

Therefore, the total capacity of the big school bus is 140 children.

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The base of each isosceles triangle has length: s = 2(15)sin(60) = 30√(3)/2 = 15√(3) Since there are 12 sides in the dodecagon, its perimeter is: P = 12s = 12(15√(3)) = 180√(3) Rounded to the nearest tenth, the perimeter is approximately 311.2.

Perimeter is the total distance around the outside of a two-dimensional shape. It is the sum of the lengths of all sides or edges of the shape.

Since the dodecagon is a regular polygon, all sides have the same length. Let's call this length "s".

To find "s", we can use the fact that a regular dodecagon can be divided into 12 congruent isosceles triangles. Each of these triangles has a base equal to "s" and two congruent sides, each equal to the radius of the dodecagon (which is given to be 15).

To find the length of the base, we can use the fact that the sum of the angles in a triangle is 180 degrees. Since the dodecagon is regular, each of the 12 angles at the center of the dodecagon is 30 degrees. Each isosceles triangle has two of these 30 degree angles, so the third angle is:

180 - 2(30) = 120 degrees

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The sample size is too small, the sample is not representative of the population and the wording of survey question influences the response self-selected sample are potential limitations for a research study.

The sample size being too small can limit the accuracy and precision of the results and reduce the power of statistical tests.

A sample not being representative of the population can result in sampling bias, which can affect the validity of the results.

The wording of a survey question can influence the response, which can result in biased results. A self-selected sample, where participants voluntarily participate in a study, can also result in biased results because only those who are interested or motivated to participate will do so.

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