What is the value of m in this proportion?1/2/3/5=1/3/m

Therefore, the distance between Car A and Car B when they meet is 150 miles (distance from Fresno to Los Angeles) - 90 miles (distance covered by Car A) = 60 miles. Thus, they meet 60 miles away from Fresno, which is 200 miles away from Fresno along the entire route.

To determine the distance from Fresno where the cars meet, we need to consider the relative speeds and the time it takes for each car to travel. Car A starts in Sacramento and travels at a speed of 30 mph, while Car B starts in Los Angeles and travels at a speed of 75 mph.

Car A starts one hour earlier than Car B, so it has a head start. In that one hour, Car A would have traveled 30 miles (30 mph x 1 hour). The remaining distance between Car A and Fresno would be 400 miles - 30 miles = 370 miles.

Now, we need to calculate the time it takes for Car B to travel from Los Angeles to Fresno, which is 150 miles. Using the formula Time = Distance / Speed, the time taken by Car B would be 150 miles / 75 mph = 2 hours.

Since Car B starts at noon, it will take 2 hours to reach Fresno, which means it will arrive at Fresno at 2pm. At that time, Car A would have been traveling for 3 hours (11am to 2pm). Given that Car A's speed is 30 mph, it would have covered a distance of 30 mph x 3 hours = 90 miles.

Therefore, the distance between Car A and Car B when they meet is 150 miles (distance from Fresno to Los Angeles) - 90 miles (distance covered by Car A) = 60 miles. Thus, they meet 60 miles away from Fresno, which is 200 miles away from Fresno along the entire route.

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There are two possible values for t: one positive and one negative. However, since time cannot be negative, we only consider the positive value: t ≈ 2.02 seconds; So, it will take approximately 2.02 seconds for the stone to hit the water.

To find out how long it will take for the stone to hit the water, we need to determine when h(t) equals 0 (since the water's surface is considered to be at height 0). We can use the given function: h(t) = -4.9t^2 + t + 10.

Set h(t) to 0 and solve for t:

0 = -4.9t^2 + t + 10

Now, we need to solve this quadratic equation for t. We can do this by applying the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / 2a

In our case, a = -4.9, b = 1, and c = 10. Plugging these values into the formula:

t = (-(1) ± √((1)^2 - 4(-4.9)(10))) / 2(-4.9)

t = (-1 ± √(1 + 196)) / -9.8

t = (-1 ± √197) / -9.8

There are two possible values for t: one positive and one negative. However, since time cannot be negative, we only consider the positive value:

t ≈ 2.02 seconds

So, it will take approximately 2.02 seconds for the stone to hit the water.

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The people having to be in a room in order that the probability that at least two of them celebrate their birthday in the same month is at least 1/2 is 5.

X = No of people having same month birth day

We need, P(X 2) ≥ 1/2

= 1-P(X ≤1) ≥ 1/2

1-P(No one having same month birth day) ≥ 1/2

P(No one having same month birth day)≤ 1/2..........................(1)

Now, k = Minimum no of people required to satisfy (1)

P(No one having same month birth day) =

\(\frac{11*10*9......*(12-k+1)}{12*12*12......*12}\)

for k= 4

P(No one having same month birth day) =

\(\frac{11.10.9}{12.12.12} = 0.572 \geq 0.5\)

for k= 5

P(No one having same month birth day) =

\(\frac{11.10.9.8}{12.12.12.12} = 0.38 \leq 0.5\)

Therefore , the people having to be in a room in order that the probability that at least two of them celebrate their birthday in the same month is at least 1/2 is 5.

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Answer:

x= 53 and y= 143

Step-by-step explanation:

x= 90-37

x= 53

y= 53+90

y= 143

Answer:

ty for the fr$e points it's B

Step-by-step explanation:

ywwwww

The solution set is r = (+4, -4) .

Answer:

It is given that in every 1/2 hours  Brandon bikes .

The distance 8 1/2 miles  is in the form of mixed fraction.

Therefore, the distance 8 1/2 miles can be written in the form of decimal as follows:

8 1/2 miles = 8.5 miles

Brandon bike's 8.5 miles  in every 1/2 hours .

We know that 1 hour   is equivalent to 60 minutes .

So,  0.5 hours can be converted into minutes as follows:

1 hour = 60 minutes

1.5 hours= 30 minutes

Therefore, in every 30 minutes Brandon bikes .

So, in next 30 minutes Brandon also bikes 8.5 miles .

In every 1 hour   Brandon travels  = 8.5+8.5 = 17 miles.

In every 1:30  Brandon travels  17 +8.5 =25.5 miles.

Method 2:

Speed of Brandon’s bike can be calculated as ,

speed = distance/time

Here, d  is the distance and t is the time.

Now, substitute d=8.5  and t= 0.5 in the equation (1)

Therefore, the rate of travelling of Brandon’s bike is .

The expression (1.4 × 10¹)(8 × 10⁴) in scientific notation is 1.12 × 10⁵ and for expression (1.1 × 10⁻⁵)(3 × 10²) the  scientific notation is 3.3 × 10⁻³

The given expressions are (1.4 × 10¹)(8 × 10⁴) can be calculated as:

Firstly we will multiply the decimal numbers and whole numbers

1.4 × 8

One point four times eight is equal to eleven point two

= 11.2

Now we multiply the base with ten

10¹ × 10⁴

We know that when the bases are same then the powers will be added in multiplication

= 10⁵

Combining these results, we have 11.2 × 10⁵

Therefore, the result in scientific notation is 1.12 × 10⁵

Similarly, for (1.1 × 10⁻⁵)(3 × 10²)

We will multiply the decimal numbers and whole numbers

1.1 × 3 = 3.3

Now the base with ten will be multiplied

10⁻⁵ × 10²

The bases are same the powers will be added

= 10⁻³

Combining these results, we have 3.3 × 10⁻³

Therefore, the result in scientific notation is 3.3 × 10⁻³

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Answer:

x = 12

Step-by-step explanation:

Let y = (1/2)x

y^2 + 8^2 = 10^2

y^2 + 64 = 100

y^2 = 36

y = 6

x = 2y = 12

Answer: C x = 12

Answer: The given vector can be expressed as a linear combination of u, v, and w as (14, 9, 14) = u - v + 3w.

Question: Express the following as a linear combination of u =(3, 1,6), v = (1.-1.4) and w=(8,3,8). (14, 9, 14) = ____ u- _____ v+ _____

Current Progress: To express the given vector as a linear combination of u, v, and w, we need to find scalars a, b, and c such that (14, 9, 14) = a*u + b*v + c*w.

Step 1: Write the equation in component form:
(14, 9, 14) = (3a + b + 8c, a - b + 3c, 6a + 4b + 8c)

Step 2: Equate the corresponding components and solve for a, b, and c:
3a + b + 8c = 14
a - b + 3c = 9
6a + 4b + 8c = 14

Step 3: Solve the system of equations using any method (substitution, elimination, etc.). One possible solution is a = 1, b = -1, and c = 3.

Step 4: Plug the values of a, b, and c back into the linear combination equation:
(14, 9, 14) = 1*u + (-1)*v + 3*w

Step 5: Simplify the equation:
(14, 9, 14) = u - v + 3w

Answer: The given vector can be expressed as a linear combination of u, v, and w as (14, 9, 14) = u - v + 3w.

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Answer:

alternate exterior

Solution to given logarithmic equations and inequalities are;

x = 1

x = 9

x = 261

x = 10/3

x = 4

3x² - 2x - 1 = 0

x = 1 or x = -1/3

x = 13

x = 0

x = 0 or x = 5

1. 3x = log6 216

Using the definition of logarithm, we have:

\(6^{3x} = 216\)

\(6^{3x} = 6^3\)

3x = 3

x = 1

2. x - 4 = log3 243

Using the definition of logarithm, we have:

\(3^{x - 4} = 243\)

\(3^{x - 4} = 3^5\)

x - 4 = 5

x = 9

3. log4 (4x - 20) = 5

Using the definition of logarithm, we have:

4⁵ = 4x - 20

1024 = 4x - 20

4x = 1044

x = 261

4. log9 (3 - x) = log9(5x – 15)

Using the property of logarithms that states that if log a b = log a c, then b = c, we have:

3 - x = 5x - 15

20 = 6x

x = 10/3

5. log81 (x + 20) = log81 (6x)

Using the property of logarithms that states that if log a b = log a c, then b = c, we have:

x + 20 = 6x

20 = 5x

x = 4

6. log9 (3x²) = log9 (2x + 1)

Using the property of logarithms that states that if log a b = log a c, then b = c, we have:

3x² = 2x + 1

3x² - 2x - 1 = 0

7. Using the quadratic formula, we have:

x = (-(-2) ± √((-2)² - 4(3)(-1))) / (2(3))

x = (2 ± √(16)) / 6

x = (2 ± 4) / 6

x = 1 or x = -1/3

8. log4(x - 1) = log4(12)

Using the property of logarithms that states that if log a b = log a c, then b = c, we have:

x - 1 = 12

x = 13

9. log7(5 - x) = log7 (5)

Using the property of logarithms that states that if log a b = log a c, then b = c, we have:

5 - x = 5

x = 0

10. logx (5x) = 2

Using the definition of logarithm, we have:

x² = 5x

x² - 5x = 0

x(x - 5) = 0

x = 0 or x = 5

Note that x = 0 is not a valid solution, since log 0 is undefined. Therefore, the only solution is x = 5.

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The probability of ending up in the bench seat on the carousel is 2/9.

To calculate the probability, we need to determine the total number of possible arrangements on the carousel.

There are 7 horses and 1 bench seat that can hold 2 people. The person can sit on any of the 8 available spots. Therefore, the total number of possible arrangements is given by 8P2 (permutation of 8 objects taken 2 at a time), which can be calculated as:

8P2 = 8! / (8 - 2)! = 8! / 6! = 8 * 7 = 56

Out of these 56 possible arrangements, only 2 of them have both you and your friend on the bench seat. Therefore, the probability of ending up in the bench seat is 2/56, which simplifies to 1/28 or approximately 0.036.

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Answer:

Step-by-step explanation:

must be r and s

because right at in middle of  the distance between them is 0

Answer:

A.) $10,400

Contribution every payday = $60

Pay periods in a year = 26

Step-by-step explanation:

Assume her salary, that is total cost = y

Percentage deduction 15% of total cost

biweekly paychecks = $60

Therefore, 15% of y = $60

(15/100)y = 60

15y = 6000

y = 400

Total value of contribution:

$400 × number of biweeks in a year

If number of weeks in a year = 52

No of bi-weeks = 52/2 = 26

$400 × 26 = $10400

Answer:

the correct answer is $9,750.00

got it right

Step-by-step explanation:

Answer:

(20,32)

Step-by-step explanation:

20 apples and 32 pears

0.40 x 20= 8

24-8=16

0.50 x 32= 16

16-16=0

Therefore, the probability that the team is comprised of 2 men and 2 women is approximately 0.4545, which is true.

To calculate the probability that the team is comprised of 2 men and 2 women, we need to determine the number of favorable outcomes (teams with 2 men and 2 women) and the total number of possible outcomes (all possible teams).

The number of ways to choose 2 men from 6 men is given by the combination formula: C(6, 2) = 6! / (2! * (6-2)!) = 15.

Similarly, the number of ways to choose 2 women from 6 women is also C(6, 2) = 15.

Therefore, the number of favorable outcomes is the product of the number of ways to choose 2 men and 2 women: 15 * 15 = 225.

Now, let's calculate the total number of possible outcomes. We need to choose 4 members from a total of 12 members, which is given by C(12, 4) = 12! / (4! * (12-4)!) = 495.

The probability that the team is comprised of 2 men and 2 women is the ratio of favorable outcomes to the total number of outcomes: 225/495 = 45/99 ≈ 0.4545 (rounded to four decimal places).

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None of the given options matches this general solution, so the answer is E. None of the options.

To solve the given ordinary differential equation:

y'' + 2y' + 5y = e^t sin(t)

We first find the characteristic equation:

r^2 + 2r + 5 = 0

Using the quadratic formula, we find the roots to be:

r = (-2 ± sqrt(4 - 4(1)(5))) / 2

r = -1 ± 2i

The characteristic equation has complex roots, so the general solution is:

y(t) = e^(-t)(Acos(2t) + Bsin(2t))

Next, we find the particular solution by guessing a solution of the form:

y_p(t) = Ae^t sin(t) + Be^t cos(t)

Taking the first and second derivatives, we get:

y_p'(t) = Ae^t sin(t) + Ae^t cos(t) + Be^t sin(t) - Be^t cos(t)

y_p''(t) = 2Ae^t cos(t) - 2Be^t sin(t)

Substituting these expressions into the original equation and simplifying, we get:

(2A - B) e^t sin(t) + (-2B - A) e^t cos(t) = e^t sin(t)

We need the coefficients of e^t sin(t) and e^t cos(t) to be equal to 1 and 0, respectively, in order to obtain a particular solution. This gives us the system of equations:

2A - B = 1

-2B - A = 0

Solving for A and B, we get:

A = 1/5

B = -2/5

Therefore, the particular solution is:

y_p(t) = (1/5) e^t sin(t) - (2/5) e^t cos(t)

The general solution is then the sum of the homogeneous and particular solutions:

y(t) = e^(-t)(Acos(2t) + Bsin(2t)) + (1/5) e^t sin(t) - (2/5) e^t cos(t)

To solve for the constants A and B using the initial conditions, we can substitute y(0) = 0 and y'(0) = 1 into the general solution and solve the resulting system of equations. However, since the question asks us to avoid solving for the constants, we can simply write the general solution as:

y(t) = e^(-t)(Acos(2t) + Bsin(2t)) + e^t (Csin(t) + Dcos(t))

where A, B, C, and D  are constants that we do not need to solve for.

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Answer:

9 / 40 or 0.225

Step-by-step explanation:

total marbles : 9 + 12 + 13 + 6 = 40 marbles

probability of taking red = total red marbles/ total number of marbles

probability of taking red = 9 / 40

Answer:

no solution

Step-by-step explanation:

|x| = -10

Absolute value means that it is positive or 0

It cannot be negative

There is no solution

Step-by-step explanation:

There is no solution

|A|

can be only 0 or positive number

can't be -

from the rule of Mathematics

Answer:

The answer is obtuse

Step-by-step explanation:

a = 4

b = 28

c = 31

If a² + b² > c²    -  the angle is acute

a² + b² = 4² + 28² = 16 + 784 = 800

c² = 31² = 961

   800 < 900

a² + b² < c²  

Therefore, the angle is obtuse

Answer:

point A: 2

point B: -3

your friend is incorrect

Step-by-step explanation:

Answer:

point A: 2

point B: -3

your friend is incorrect

Step-by-step explanation:

From the graph, the domain of the function will be {x| x = −2,1}. Then the correct option is D.

An asymptote is a line that constantly reaches a given curve but does not touch at an infinite distance.

From the graph, the domain of the function will be

The function is not defined for x = 2 and x = -1.

Then the domain will be

{x| x = −2,1}

Then the correct option is D.

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Answer:

Step-by-step explanation:

y = 3x -6

x = -2, y = -12

x = -1, y = -9

x = 0, y = -6

x = 1, y = -3

x = 2, y = 0

x= 3, y = 3

x    -2       -1        0        1          2         3

y    -12     -9       -6       -3         0         3