what is 2.35 times 2/3

El certificado de depósito ganó un interés de aproximadamente $1.72. Cabe mencionar que este cálculo se basa en la suposición de que el certificado de depósito no tiene ninguna penalización o retención de impuestos.

Para calcular el interés ganado en el certificado de depósito, necesitamos utilizar la fórmula del interés simple: Interés = (Principal × Tasa de interés × Tiempo).

En este caso, el principal es de $450 y la tasa de interés es del 4.6% anual. Sin embargo, debemos convertir la tasa de interés a una tasa mensual, ya que el certificado de depósito es mensual.

Para convertir la tasa anual a una tasa mensual, dividimos la tasa anual entre 12: 4.6% / 12 = 0.3833% (aproximadamente). Ahora tenemos la tasa mensual: 0.3833%.

El tiempo es de un mes, por lo que sustituimos los valores en la fórmula del interés simple: Interés = ($450 × 0.3833% × 1 mes).

Calculando el interés: Interés = ($450 × 0.003833 × 1) = $1.72 (aproximadamente).

For more such questions on interés

https://brainly.com/question/25720319

#SPJ8

The percentage of students who got a final grade higher than a specific value cannot be determined without knowing the value.

To determine the percentage of students who got a final grade higher than a specific value, we need to know the actual value. Without this information, we cannot calculate the percentage accurately.

For example, if we have the grades of 100 students and we want to know the percentage of students who scored higher than 80, we would need to count the number of students who scored higher than 80 and divide it by 100 (the total number of students) to get the percentage.

Without specifying the specific value or providing the necessary data, it is not possible to calculate the percentage of students who got a final grade higher than a certain value.

Learn more about Percentage

brainly.com/question/32197511

brainly.com/question/28998211

#SPJ11

By following the critical value approach and the p-value approach, we have examined the hypothesis and reached conclusions based on the test statistic and the significance level.

(i) Formulate the hypothesis:

The hypothesis testing can be done by following the given steps:

Step 1: State the hypothesis

Step 2: Set the criteria for the decision

Step 3: Calculate the test statistic and probability of the test statistic

Step 4: Make the decision in light of steps 2 and 3

The null hypothesis H0: μ ≥ 6

The alternative hypothesis H1: μ < 6

Where μ = Population Mean

(ii) State your conclusion using the critical value approach with a distribution graph:

The critical value is determined by:

α/2 = 0.05/2 = 0.025

Degrees of freedom = n - 1 = 12 - 1 = 11

Level of significance = α = 0.05

Critical value = -t0.025, 11 = -2.201

The test statistic, t = (x - μ) / (s / √n)

Where,

x = Sample Mean = 5.69

μ = Population Mean = 6

s = Sample Standard Deviation = 1.58

n = Sample size = 12

t = (5.69 - 6) / (1.58 / √12) = -1.64

The rejection region is (-∞, -2.201)

The test statistic is outside of the rejection region, thus we reject the null hypothesis. Hence, there is sufficient evidence to support the claim that the delivery time is less than 6 minutes.

(iii) State your conclusion using the p-value approach and a distribution graph:

The p-value is given as P(t < -1.64) = 0.0642

The p-value is greater than α, thus we accept the null hypothesis. Therefore, we cannot support the restaurant's claim that the average delivery time of its service is less than 6 minutes.

Learn more about standard deviation

https://brainly.com/question/29115611

#SPJ11

John needs to make a 16 inches cut of the tiles along the median. The correct answer is option C. 16 inches.

When cutting the tile along the median, we need to find the length of the cut that divides the trapezoid into two equal areas.

The median of a trapezoid is the line segment connecting the midpoints of the two non-parallel sides. In this case, the top base of the trapezoid is 13 inches and the bottom base is 19 inches.

To find the length of the cut, we can take the average of the lengths of the top and bottom bases. The average of 13 inches and 19 inches is (13 + 19) / 2 = 32 / 2 = 16 inches.

Therefore, John will need to make a 16-inch cut along the median to cut the tiles in half and create the desired pattern on his floor.

Option C, 16 inches, correctly represents the length of the cut required to cut the tiles along the median.

For more such answers on median

https://brainly.com/question/26177250

#SPJ8

The trigonometric identity sinθtanθ = 2√2/3.

We can use the trigonometric identity [tex]sin^2θ + cos^2θ = 1[/tex] to find sinθ. Since cosθ = 2/3, we can square it and subtract from 1 to find sinθ. Then, we can multiply sinθ by tanθ to get the desired result.

sinθ = √(1 - cos^2θ) = √(1 - (2/3)^2) = √(1 - 4/9) = √(5/9) = √5/3

tanθ = sinθ/cosθ = (√5/3) / (2/3) = √5/2

sinθtanθ = (√5/3) * (√5/2) = 5/3√2 = 2√2/3

b) Simplify sin(180∘ - θ) + cosθ * tan(180∘ + θ).

sin(180∘ - θ) + cosθ * tan(180∘ + θ) = -sinθ + cotθ.

By using the trigonometric identities, we can simplify the expression.

sin(180∘ - θ) = -sinθ (using the identity sin(180∘ - θ) = -sinθ)

tan(180∘ + θ) = cotθ (using the identity tan(180∘ + θ) = cotθ)

Therefore, the simplified expression becomes -sinθ + cosθ * cotθ, which can be further simplified to -sinθ + cotθ.

c) Solve cos^2x - 3sinx + 3 = 0 for 0∘ ≤ x ≤ 360∘.

The equation has no solutions in the given range.

We can rewrite the equation as a quadratic equation in terms of sinx:

cos^2x - 3sinx + 3 = 0

1 - sin^2x - 3sinx + 3 = 0

-sin^2x - 3sinx + 4 = 0

Now, let's substitute sinx with y:

-y^2 - 3y + 4 = 0

Solving this quadratic equation, we find that the solutions for y are y = -1 and y = -4. However, sinx cannot exceed 1 in magnitude. Therefore, there are no solutions for sinx that satisfy the given equation in the range 0∘ ≤ x ≤ 360∘.

Learn more about solving trigonometric equations visit:

https://brainly.com/question/30710281

#SPJ11

(i) The Laplace transform of t² is (2/s³), the Laplace transform of t³ is (6/s⁴), the Laplace transform of cos(7t) is (s/(s²+49)), and the Laplace transform of [tex]e^(^s^t^)[/tex] is (1/(s-[tex]e^(^-^s^t^)[/tex])))). Therefore, the transformed function is (2/s³) + (6/s⁴) * (s/(s²+49)) + (1/(s-[tex]e^(^-^s^t^)[/tex])).

(ii) The Fourier series representation of the function f(t) = sin(t/2) with period 27 is given by f(t) = (4/π) * (sin(t/2) + (1/3)sin(3t/2) + (1/5)sin(5t/2) + ...).

In the first step, we are asked to transform each of the given functions using the Table of the Laplace transform. For function (i), we have to find the Laplace transforms of t² , t³, cos(7t), and  [tex]e^(^s^t^)[/tex]. Using the standard formulas from the Laplace transform table, we can find their respective transforms. The transformed function is the sum of these individual transforms.

For  t² its (2/s³),

For t³ its (6/s⁴),

For cos(7t) its (s/(s²+49)),

For [tex]e^(^s^t^)[/tex] its (1/(s-[tex]e^(^-^s^t^)[/tex])))).

the transformed function is (2/s³) + (6/s⁴) * (s/(s²+49)) + (1/(s-[tex]e^(^-^s^t^)[/tex])).

In the second step, we are asked to find the Fourier series representation of the function f(t) = sin(t/2) with a period of 27. The Fourier series representation of a function involves expressing it as a sum of sine and cosine functions with different frequencies and amplitudes.

For the given function, the Fourier series representation can be obtained by using the formula for a periodic function with a period of 27. The formula allows us to find the coefficients of the sine terms, which are then multiplied by the respective sine functions with different frequencies to obtain the final representation.

The function f(t) = sin(t/2) with a period of 27 can be represented by its Fourier series as f(t) = (4/π) * (sin(t/2) + (1/3)sin(3t/2) + (1/5)sin(5t/2) + ...).

Learn more about Laplace transform

brainly.com/question/30759963

#SPJ11

The values of ai in the given equation are not specified. More information is needed to determine the values of ai.

In the given equation, "d8 day +3 dn³ Find the values of ai," it is not clear what the specific values of ai are. The equation seems to involve derivatives (d) with respect to time (t), and the symbols day and dn represent different orders of differentiation.

However, without further information or context, it is not possible to determine the specific values of ai.

To provide a solution, we would need additional details or equations that define the relationship between the variables and derivatives involved. Without these details, it is not possible to solve the equation or find the values of ai.

Learn more about derivatives

brainly.com/question/25324584

#SPJ11

The work required to pitch a 6.6 oz softball at 90 ft/sec is approximately 37.125 ft-lb.

To find the work required to pitch a softball, we can use the formula:

Work = Force * Distance

In this case, we need to calculate the force and the distance.

Force:

The force required to pitch the softball can be calculated using Newton's second law, which states that force is equal to mass times acceleration:

Force = Mass * Acceleration

The mass of the softball is given as 6.6 oz. We need to convert it to pounds for consistency. Since 1 pound is equal to 16 ounces, the mass of the softball in pounds is:

6.6 oz * (1 lb / 16 oz) = 0.4125 lb (rounded to four decimal places)

Acceleration:

The acceleration is given as 90 ft/sec.

Distance:

The distance is also given as 90 ft.

Now we can calculate the work:

Work = Force * Distance

= (0.4125 lb) * (90 ft)

= 37.125 lb-ft (rounded to three decimal places)

Therefore, the work required to pitch a 6.6 oz softball at 90 ft/sec is approximately 37.125 ft-lb.

Learn more about softbal here:

https://brainly.com/question/15069776

#SPJ11

Substituting a = 2, b = 6, and c = 3 into the expression:

1

2

(

3

)

(

6

+

2

)

2

1

​

(3)(6+2)

Simplifying the expression:

1

2

(

3

)

(

8

)

=

12

2

1

​

(3)(8)=12

Therefore, when a = 2, b = 6, and c = 3, the expression

1

2

�

(

�

+

�

)

2

1

​

c(b+a) evaluates to 12.

To evaluate the expression

1

2

�

(

�

+

�

)

2

1

​

c(b+a) when a = 2, b = 6, and c = 3, we substitute these values into the expression and perform the necessary calculations.

First, we substitute a = 2, b = 6, and c = 3 into the expression:

1

2

(

3

)

(

6

+

2

)

2

1

​

(3)(6+2)

Next, we simplify the expression following the order of operations (PEMDAS/BODMAS):

Within the parentheses, we have 6 + 2, which equals 8. Substituting this result into the expression, we get:

1

2

(

3

)

(

8

)

2

1

​

(3)(8)

Next, we multiply 3 by 8, which equals 24:

1

2

(

24

)

2

1

​

(24)

Finally, we multiply 1/2 by 24, resulting in 12:

12

Therefore, when a = 2, b = 6, and c = 3, the expression

1

2

�

(

�

+

�

)

2

1

​

c(b+a) evaluates to 12.

Learn more about expression here:

brainly.com/question/14083225

#SPJ11

Answer:

30 units

Step-by-step explanation:

(4,5) to (4,-1) = 6

(4,-1) to (-5,-1) = 9

(-5,-1) to (-5,5) = 6

(-5,5) to (4,5) = 9

6+9+6+9=30

you may first send the diagram

The value of x, considering the similar triangles in this problem, is given as follows:

x = 2.652.

El valor de x es el seguinte:

x = 2.652.

Two triangles are defined as similar triangles when they share these two features listed as follows:

The proportional relationship for the side lengths in this triangle is given as follows:

x/3.9 = 3.4/5

Applying cross multiplication, the value of x is obtained as follows:

5x = 3.9 x 3.4

x = 3.9 x 3.4/5

x = 2.652.

More can be learned about similar triangles at brainly.com/question/14285697

#SPJ1

There are 167,960 ways to choose which countries to visit from a total of 20 countries when you can only visit 9 of them.

To calculate the number of ways you can choose which countries to visit from a total of 20 countries when you have time to visit only 9 of them, we can use the concept of combinations.

The number of ways to choose a subset of k elements from a set of n elements is given by the binomial coefficient, also known as "n choose k," denoted as C(n, k). The formula for C(n, k) is:

C(n, k) = n! / (k! * (n - k)!)

In this case, you want to choose 9 countries out of 20, so the number of ways to do this is:

C(20, 9) = 20! / (9! * (20 - 9)!)

Calculating the above expression:

C(20, 9) = (20 * 19 * 18 * 17 * 16 * 15 * 14 * 13 * 12) / (9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)

Simplifying the calculation:

C(20, 9) = 167,960

Therefore, there are 167,960 ways to choose which countries to visit from a total of 20 countries when you have time to visit only 9 of them.

To know more about combinations, refer to the link below:

https://brainly.com/question/30648446#

#SPJ11

To join the points (2, 16) and (8, 4), we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.

First, let's calculate the slope (m) using the formula:

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

Substituting the coordinates of the two points:

m = (4 - 16) / (8 - 2)

m = -12 / 6

m = -2

Now that we have the slope, we can choose either of the two points and substitute its coordinates into the slope-intercept form to find the y-intercept (b).

Let's choose the point (2, 16):

16 = -2(2) + b

16 = -4 + b

b = 20

Now we have the slope (m = -2) and the y-intercept (b = 20), we can write the equation of the line:

y = -2x + 20

This equation represents the line passing through the points (2, 16) and (8, 4).

[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

♥️ [tex]\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

The probability that a randomly pulled out sock from a drawer containing four white and six black socks is white is approximately 40%.

To find the probability that a randomly pulled out sock from the drawer is white, we divide the number of white socks by the total number of socks. In this case, there are four white socks and a total of ten socks (four white + six black).

Probability of selecting a white sock = Number of white socks / Total number of socks

= 4 / 10

= 0.4

To express the probability as a percentage, we multiply the result by 100 and round it to the nearest whole number.

Probability of selecting a white sock = 0.4 * 100 ≈ 40%

Therefore, the probability that the randomly pulled out sock is white is approximately 40%. Hence, the correct option is d. 40%.

Learn more about Probability

brainly.com/question/31828911

#SPJ11

The probability that exactly three out of six randomly selected Ugandan adults own a cellular phone is approximately 0.1318, or 13.18%.

Use the binomial probability formula to calculate the probability of exactly three out of six randomly selected Ugandan adults owning a cellular phone:

P(X = k) = [tex](nCk) \times (p^k) \times ((1-p)^{(n-k)})[/tex]

We know that;

Using the formula, we can calculate the probability as follows:

P(X = 3) = [tex](6C3) \times ((24/32)^3) \times ((1 - 24/32)^{(6-3)})[/tex]

P(X = 3) = [tex](6C3) \times (0.75^3) \times (0.25^3)[/tex]

We can use the formula to calculate the combination (6C3):

nCk = n! / (k! * (n-k)!)

(6C3) = 6! / (3! * (6-3)!)

     = (6 × 5 × 4) / (3 × 2 × 1)

     = 20

Now, substituting the values into the probability formula:

P(X = 3) = [tex]20 \times (0.75^3) \times (0.25^3)[/tex]

         = 20 × 0.421875 × 0.015625

         ≈ 0.1318359375

Therefore, the probability is approximately 0.1318, or 13.18%.

Learn more about probability https://brainly.com/question/31828911

#SPJ11

Answer:

218 cm²

Step-by-step explanation:

The lateral surface area (LSA) is the area of the sides excluding the top and botton part

LSA formula: 2h(l+b)

For the larger(green) cuboid, h = 4, l = 10, b =5

For the smaller(pink) cuboid, h = 6, l = 2, b =2

Total area = LSA(green) + top part of green + LSA(pink) + top of pink

LSA of green :

2h(l+b) = 2(4)(10+5)

= 8*15

= 120  -----eq(1)

Top part of green:

The area of green cuboid's top- area of pink cuboid's base

= (10*5) - (2*2)

= 50 - 4

= 46  -----eq(2)

LSA of pink:

2h(l+b) = 2(6)(2+2)

= 12*4

= 48  -----eq(3)

Top part of pink:

2*2 = 4  -----eq(3)

Total area:

eq(1) + eq(2) + eq(3) + eq(4)

= 120 + 45 + 48 + 4

= 218 cm²

a. The determinant of A is nonzero (-2 ≠ 0), the system of equations has a unique solution for all values of k.

b. For values of k less than 3, the system of equations has no solution.

c. There are no values of k for which the system of equations has infinite solutions.

To determine the values of k for which the given system of simultaneous equations has a unique solution, no solution, or infinite solutions, let's consider each case separately:

a. To find the values of k for which the equations have a unique solution, we need to check if the determinant of the coefficient matrix is nonzero. If the determinant is nonzero, it means that the equations can be uniquely solved.

To compute the determinant, we can write the coefficient matrix A as follows:
A = [[2, 4, -2], [2, 5, -(k+2)], [-1, k-5, 1]]

Expanding the determinant of A, we have:
det(A) = 2(5(1)-(k-5)(-2)) - 4(2(1)-(k+2)(-1)) - 2(2(k-5)-(-1)(2))

Simplifying this expression, we get:
det(A) = 10 + 2k - 10 - 4k - 4 + 2k + 4k - 10

Combining like terms, we have:
det(A) = -2

Since the determinant of A is nonzero (-2 ≠ 0), the system of equations has a unique solution for all values of k.

b. To find the values of k for which the equations have no solution, we can check if the determinant of the augmented matrix, [A|B], is nonzero, where B is the column vector on the right-hand side of the equations.

The augmented matrix is:
[A|B] = [[2, 4, -2, 4], [2, 5, -(k+2), 3], [-1, k-5, 1, 1]]

Expanding the determinant of [A|B], we have:
det([A|B]) = (2(5) - 4(2))(1) - (2(1) - (k+2)(-1))(4) + (-1(2) - (k-5)(-2))(3)

Simplifying this expression, we get:
det([A|B]) = 10 - 8 - 4k + 8 - 2k + 4 + 2 + 6k - 6

Combining like terms, we have:
det([A|B]) = -6k + 18

For the system to have no solution, the determinant of [A|B] must be nonzero. Therefore, for no solution, we must have:
-6k + 18 ≠ 0

Simplifying this inequality, we get:
-6k ≠ -18

Dividing both sides by -6 (and flipping the inequality), we have:
k < 3

Thus, for values of k less than 3, the system of equations has no solution.

c. To find the values of k for which the equations have infinite solutions, we can check if the determinant of A is zero and if the determinant of the augmented matrix, [A|B], is also zero.

From part (a), we know that the determinant of A is -2.

Therefore, to have infinite solutions, we must have:
-2 = 0

However, since -2 is not equal to zero, there are no values of k for which the system of equations has infinite solutions.

Learn more about 'solutions':

https://brainly.com/question/17145398

#SPJ11

The values of the coefficients A and B in the equation y = A e^(-Bx) are A ≈ 289.693 and B ≈ 0.271.

To determine the values of the coefficients A and B in the equation y = A * e^(-Bx) using the method of least squares, we need to minimize the sum of the squared residuals between the predicted values and the actual data points.

Let's denote the given data points as (x_i, y_i), where x_i represents the x-coordinate and y_i represents the corresponding y-coordinate.

Given data points:

(77, 2.4)

(100, 3.4)

(185, 7.0)

(239, 11.1)

(285, 19.6)

To apply the least squares method, we need to transform the equation into a linear form. Taking the natural logarithm of both sides gives us:

ln(y) = ln(A) - Bx

Let's denote ln(y) as Y and ln(A) as C, which gives us:

Y = C - Bx

Now, we can rewrite the equation in a linear form as Y = C + (-Bx).

We can apply the least squares method to find the values of B and C that minimize the sum of the squared residuals.

Using the linear equation Y = C - Bx, we can calculate the values of Y for each data point by taking the natural logarithm of the corresponding y-coordinate:

[tex]Y_1[/tex] = ln(2.4)

[tex]Y_2[/tex] = ln(3.4)

[tex]Y_3[/tex] = ln(7.0)

[tex]Y_4[/tex] = ln(11.1)

[tex]Y_5[/tex] = ln(19.6)

We can also calculate the values of -x for each data point:

-[tex]x_1[/tex] = -77

-[tex]x_2[/tex] = -100

-[tex]x_3[/tex] = -185

-[tex]x_4[/tex] = -239

-[tex]x_5[/tex] = -285

Now, we have a set of linear equations in the form Y = C + (-Bx) that we can solve using the least squares method.

The least squares equations can be written as follows:

ΣY = nC + BΣx

Σ(xY) = CΣx + BΣ(x²)

where Σ represents the sum over all data points and n is the total number of data points.

Substituting the calculated values, we have:

ΣY = ln(2.4) + ln(3.4) + ln(7.0) + ln(11.1) + ln(19.6)

Σ(xY) = (-77)(ln(2.4)) + (-100)(ln(3.4)) + (-185)(ln(7.0)) + (-239)(ln(11.1)) + (-285)(ln(19.6))

Σx = -77 - 100 - 185 - 239 - 285

Σ(x^2) = 77² + 100² + 185² + 239² + 285²

Solving these equations will give us the values of C and B. Once we have C, we can determine A by exponentiating C (A = [tex]e^C[/tex]).

After obtaining the values of A and B, round them to 3 decimal places as specified.

By applying the method of Least Squares to the given data points, the calculated values are A ≈ 289.693 and B ≈ 0.271, rounded to 3 decimal places.

Learn more about Least Squares

brainly.com/question/30176124

#SPJ11

y1 = x * sin(4ln(x))

The second solution y2(x) of the given differential equation, we can use the reduction of order method. Let's denote y2(x) as the second solution.

The reduction of order technique states that if we have one solution y1(x) of a linear homogeneous second-order differential equation, then we can find the second solution y2(x) by the following formula:

y2(x) = y1(x) * ∫[e^(-∫P(x)dx) / y1(x)^2] dx

Where P(x) is the coefficient of the first derivative term.

In the given differential equation:

x^2y'' - xy^4 + 17y = 0

We have y1(x) = x * sin(4ln(x)), so we need to find y2(x) using the formula mentioned above.

First, we need to find P(x):

P(x) = -1/x

Next, we substitute y1(x) and P(x) into the formula to find y2(x):

y2(x) = x * sin(4ln(x)) * ∫[e^(-∫(-1/x)dx) / (x * sin(4ln(x)))^2] dx

y2(x) = x * sin(4ln(x)) * ∫[e^(ln(x)) / (x * sin(4ln(x)))^2] dx

y2(x) = x * sin(4ln(x)) * ∫[x / (x^2 * sin^2(4ln(x)))] dx

To simplify this integral, we can cancel out one factor of x from the numerator and denominator:

y2(x) = sin(4ln(x)) * ∫[1 / (x * sin^2(4ln(x)))] dx

This integral is not straightforward to solve, so the resulting expression for y2(x) will be complicated.

Therefore, the second solution y2(x) using the reduction of order method is given by y2(x) = sin(4ln(x)) * ∫[1 / (x * sin^2(4ln(x)))] dx.

To know more about equation, refer here:

https://brainly.com/question/29657983

#SPJ11

The surface integral of the function g(x, y, z) over the surface S is evaluated.

To evaluate the surface integral, we consider the rectangular prism formed by the coordinate planes and the planes x = 2, y = 2, z = 3. This prism encloses a six-sided surface S. The surface integral of a function over a surface measures the flux or flow of the function across the surface.

In this case, we are integrating the function g(x, y, z) over the surface S. The specific form of the function g(x, y, z) is not provided in the given question. To evaluate the surface integral, we need to know the expression of g(x, y, z).

Once we have the expression for g(x, y, z), we can set up the integral by parameterizing the surface S and calculating the dot product of the function g(x, y, z) and the surface normal vector. The integral will involve integrating over the appropriate range of the parameters that define the surface.

Without the specific expression for g(x, y, z) or further details, it is not possible to provide the exact numerical evaluation of the surface integral. However, the general procedure for evaluating a surface integral involves parameterizing the surface, setting up the integral, and then performing the necessary calculations.

Learn more about Surface

brainly.com/question/32235761

brainly.com/question/1569007

#SPJ11

If a car is traveling at a constant rate of 50 miles per hour, we can determine how far it will travel in 12 minutes. We know that 1 hour is equivalent to 60 minutes. Therefore, 50 miles per hour is the same as 50/60 miles per minute, or 5/6 miles per minute.

To find the distance traveled in 12 minutes, we can multiply the speed by the time:distance = speed × time

= (5/6) miles/minute × 12 minutes

= 10 milesSo, a car traveling at a constant rate of 50 miles per hour will travel a distance of 10 miles in 12 minutes.

To know more about constant visit:
https://brainly.com/question/31730278

#SPJ11

The equation of the line passing through the point (5,-3) and perpendicular to the line passing through the points (-1,1) and (-2,2) is y = x - 8.

To find the equation of the line passing through the point (5,-3) and perpendicular to the line passing through the points (-1,1) and (-2,2), we follow these steps:

Step 1: Find the slope of the line passing through (-1,1) and (-2,2).

Using the slope formula, we have:

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

where (x1, y1) = (-1, 1) and (x2, y2) = (-2, 2).

Plugging in the values, we get:

m = (2 - 1) / (-2 - (-1)) = -1.

Step 2: Find the slope of the line perpendicular to the line passing through (-1,1) and (-2,2).

Perpendicular lines have negative reciprocal slopes. Therefore, the slope of the line perpendicular to the line passing through (-1,1) and (-2,2) is the negative reciprocal of -1.

i.e. m' = -1/m' = -1/-1 = 1.

Step 3: Find the equation of the line passing through (5,-3) with slope 1.

We have the slope (m') of the line passing through (5,-3), and we also have a point (5,-3) on the line. We can use the point-slope form of the equation of a line to find the equation of the line passing through (5,-3) and perpendicular to the line passing through (-1,1) and (-2,2).

Point-slope form: y - y1 = m'(x - x1),

where (x1, y1) = (5,-3) and m' = 1.

Plugging in the values, we get:

y - (-3) = 1(x - 5),

y + 3 = x - 5,

y = x - 5 - 3,

y = x - 8.

Thus,y = x - 8 is the equation of the line travelling through the point (5,-3) and perpendicular to the line going through the points (-1,1) and (-2,2).

Learn more about equation

https://brainly.com/question/29865910

#SPJ11

The solution to the equation x² + 3x = -25 by completing the square is:

x = -3/2 ± √(-91)/2, where √(-91) represents the square root of -91.

To solve the equation x² + 3x = -25 by completing the square, we follow these steps:

Step 1: Move the constant term to the other side of the equation:

x² + 3x + 25 = 0

Step 2: Take half of the coefficient of x, square it, and add it to both sides of the equation:

x² + 3x + (3/2)² = -25 + (3/2)²

x² + 3x + 9/4 = -25 + 9/4

Step 3: Simplify the equation:

x² + 3x + 9/4 = -100/4 + 9/4

x² + 3x + 9/4 = -91/4

Step 4: Rewrite the left side of the equation as a perfect square:

(x + 3/2)² = -91/4

Step 5: Take the square root of both sides of the equation:

x + 3/2 = ±√(-91)/2

Step 6: Solve for x:

x = -3/2 ± √(-91)/2

The solution to the equation x² + 3x = -25 by completing the square is:

x = -3/2 ± √(-91)/2, where √(-91) represents the square root of -91.

Learn more about square root from the given link!

https://brainly.com/question/428672

#SPJ11

Answer:

Her total score is 65.

Step-by-step explanation:

Out of 20 questions, Rita get 15 correct answer.

Riya get = 20-15=5 wrong answers.

according to the question,

5 marks awarded for each correct answer and 2 marks deducted for each wrong answer.

so, her total score = (15 * 5 = 75) - (5 * 2 =10)

= 75 - 10 =65

: therefore, her total score is 65.

Answer:

Riya's total score is 65/100

Step-by-step explanation:

You can calculate the total score for a class test by using the following formula:

(Let t = total score)

In our case, if Riya got 15 correct answers out of 20 questions, then she got 5 wrong answers (20 - 15 = 5).

If each question is worth 5 marks for a correct answer and 2 marks for a wrong answer, we can plug in the numbers into the formula:

Solving what is inside of the parenthesis gives us:

Therefore, Riya’s total score is 65 out of a possible 100.

The inverse of the given matrix is: A^-1 = [ 3/2 -7/4][ 1/2 -3/4][ -1 1][1/2]

Given matrix is: A = [-6 0 7 1][ -12 -6 17 9]

To find inverse matrix, we use Gauss-Jordan elimination method as follows:We append an identity matrix of same order to matrix A, perform row operations until the left side of matrix reduces to an identity matrix, then the right side will be our inverse matrix.So, [A | I] = [-6 0 7 1 | 1 0 0 0][ -12 -6 17 9 | 0 1 0 0]

Performing the following row operations, we get,

[A | I] = [1 0 0 0 | 3/2 -7/4][0 1 0 0 | 1/2 -3/4][0 0 1 0 |-1 1][0 0 0 1 |1/2]

So, the inverse of the given matrix is: A^-1 = [ 3/2 -7/4][ 1/2 -3/4][ -1 1][1/2]

Multiplying A^-1 with A, we should get an identity matrix, i.e.,A * A^-1 = [ 1 0][ 0 1]

Therefore, the solution of the system of equations is obtained by multiplying the inverse matrix by the matrix containing the constants of the system.

Know more about matrix  here,

https://brainly.com/question/28180105

#SPJ11

The given vector as a linear combination are

To express the vector (17, 9, 17) as a linear combination of u, v, and w, we need to find the coefficients (i, j, k) such that:

(i)u + (j)v + (k)w = (17, 9, 17)

Substituting the given values for u, v, and w:

(i)(4, 1, 6) + (j)(1, -1, 5) + (k)(4, 2, 8) = (17, 9, 17)

Expanding the equation component-wise:

(4i + j + 4k, i - j + 2k, 6i + 5j + 8k) = (17, 9, 17)

By equating the corresponding components, we can solve for i, j, and k:

4i + j + 4k = 17 (Equation 1)

i - j + 2k = 9 (Equation 2)

6i + 5j + 8k = 17 (Equation 3)

Know more about linear combination here:

brainly.com/question/30341410

#SPJ11

Answer:

26ocm

Step-by-step explanation:

you do 2 plus 4 plus 5.

The function that models the inverse variation between variables a and b is given by b = k/a, where k is the constant of variation.

In inverse variation, two variables are inversely proportional to each other. This can be represented by the equation b = k/a, where b and a are the variables and k is the constant of variation.

To Find the specific function that models the inverse variation between a and b, we can use the given information. When a = 9, b = 5/3.

Plugging these values into the inverse variation equation, we have:

5/3 = k/9

To solve for k, we can cross-multiply:

5 * 9 = 3 * k

45 = 3k

Dividing both sides by 3:

k = 45/3

Simplifying:

k = 15

Therefore, the function that models the inverse variation between a and b is:

b = 15/a

This equation demonstrates that as the value of a increases, the value of b decreases, and vice versa. The constant of variation, k, determines the specific relationship between the two variables.

For more such questions on inverse variation, click on:

https://brainly.com/question/13998680

#SPJ8

Answer:

To determine the time it takes for the coffee to cool to 60°C, we can use Newton's Law of Cooling, which states that the rate of change of temperature of an object is proportional to the difference between its current temperature and the surrounding temperature.

Let's denote:

- T(t) as the temperature of the coffee at time t

- T_r as the room temperature (21°C)

- k as the cooling constant

According to Newton's Law of Cooling, we can write the differential equation:

dT/dt = -k(T - T_r)

To solve this differential equation, we need an initial condition. In this case, we know that at t = 0 (when the coffee is poured into the mug), the temperature of the coffee is T(0) = 90°C.

Now we can solve the differential equation to find the time when the coffee temperature reaches 60°C.

Separating variables and integrating, we get:

∫(1 / (T - T_r)) dT = -∫k dt

ln|T - T_r| = -kt + C

Taking the exponential of both sides:

T - T_r = Ce^(-kt)

Applying the initial condition T(0) = 90°C, we have:

90 - 21 = Ce^(0) => C = 69

Therefore, the equation becomes:

T - 21 = 69e^(-kt)

To find the value of k, we can use the information given that after 1 minute, the coffee temperature is 85°C:

85 - 21 = 69e^(-k * 1)

64 = 69e^(-k)

Dividing both sides by 69:

e^(-k) = 64/69

Taking the natural logarithm of both sides:

-k = ln(64/69)

Solving for k:

k ≈ -0.065

Now we can plug in the values into the equation T - 21 = 69e^(-kt) and solve for the time t when the temperature T equals 60°C:

60 - 21 = 69e^(-0.065t)

39 = 69e^(-0.065t)

Dividing both sides by 69:

e^(-0.065t) = 39/69

Taking the natural logarithm of both sides:

-0.065t = ln(39/69)

Solving for t:

t ≈ -ln(39/69) / 0.065

Using a calculator, we find that t ≈ 4.44 minutes.

Therefore, it will take approximately 4.44 minutes before the coffee temperature reaches 60°C and becomes safe to drink.