Two trains leave towns 785 miles apart at the same time and travel toward each other. One train travels 21
faster than the other. If they meet in 5 hours,
h
what is the rate of each train?

Answer:

8

Step-by-step explanation:

i think this is right     if not it would be 2

Answer:

d

Step-by-step explanation:

10/100 ×3400×36

\(10 \div 100 \times 3400 \div 36\)

Full question attached

Answer:

Option C: because the percent of children compared differ too much

Explanation:

Sample Proportion of students from Montessori = students that participated from Montessori /total number of students assigned to Montessori

=30/54= 0.56

Sample proportion of students from other schools = students that participated I'm the study /total number of students assigned to other schools

=25/112

=0.22

We observe that there is a large difference(0.56-0.22) between the two sample proportions hence the bias

Answer:

0.89

Step-by-step explanation:

The probability that a randomly selected male's systolic blood pressure will be less than 108 is 0.25.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Here, mean  = 110, standard deviation = 8

P = \(\frac{x_{mean}-x }{SD}\)

P = (110 - 108)/8

P = 2/8 = 0.25

P(Z<0.25) = 0.5 - 0.25 = 0.25

Thus, The probability that a randomly selected male's systolic blood pressure will be less than 108 is 0.25.

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Answer:

f(x) = -2|x| + 1

Step-by-step explanation:

The graph shifts one unit up the y axis since there's a value outside the absolute value which directly adds 1 to it.

Answer:

c

Step-by-step explanation:

By using the facts given, 60.5 cm is 0.605 m or 0.605 meters.

Given: Convert 60.5 cm to meters

And the facts are as follows:

1000 milli-meters (mm) - 1 meter (m)

100 centimeters (cm) - 1 meter (m)

10 decimeters (dm) - 1 meter (m)

1 deka-meter (dam) -10 meters (m)

1 hectometer (hm) - 100 meters (m)

1 kilometer (km) - 1000 meters (m)

What is the length?

Length is the measurement of something from one point to another point.

Length can also be the distance between two points.

The shortest length between two times is known as displacement.

There are different ways to measure the length between two points or objects.

The SI unit of length is metered (m)

Also, kilometers or miles are used to measure large distances.

How to convert from centimeters (cm) to meters (m)?

1 meter or 1 m is equivalent to 100 centimeters or 100 cm. So let us apply the unitary method.

100 cm = 1 m

So 1 cm = 1 / 100 m

Therefore, x cm will be x / 100 m

Let’s solve the problem.

Given 60.5 cm to show in meters

So 100 cm = 1 m

1 cm = 1 / 100 m

60.5 cm = 60.5 / 100 m

60.5 cm = 0.605 m

Hence by using the facts given 60.5 cm is 0.605 m or 0.605 meters.

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Answer:

Option D

S=8/1-.2

Step-by-step explanation:

Edg

The sum of the sequence will be S = 8 / (1 – 0.2). Then the correct option is D.

Let a be the first term and r be the common ratio. Then the sum of the geometric series will be

S = a / (1 – r) if r < 1

S = a / (r – 1) if r > 1

The sum of \(\rm \Sigma_{n = 1}^{\infty} 8(0.2)^{n - 1}\).

Then the first term of the geometric sequence will be 8.

And the common difference between the successive terms will be 0.2.

The common ratio less than one, then the formula for the sum will be given as

S = a / (1 – r) if r < 1

Then the sum of the sequence till infinity will be

S = 8 / (1 – 0.2)

S = 8 / 0.8

S = 10

Thus, the sum of the sequence will be S = 8 / (1 – 0.2).

Then the correct option is D.

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Answer:

Bucket a would be a darker shade because the white makes bucket b lighter.

Answer:

D.strong

Step-by-step explanation:

Answer:

strong

Step-by-step explanation:

definitely not parabolic

pretty positive (not negative)

pretty strong (not weak)

I guess strong

(don't be angry if it is wrong, I'm not a regression and best fit expert)

Answer:

y = -8/3x + 8

Step-by-step explanation:

Step 1:  Identify which values we have and need to find in the slope-intercept form:

The general equation of the slope-intercept form of a line is given by:

y = mx + b, where

Since we're told that the y-intercept is 8, this is our b value in the slope-intercept form.

Step 2:  Find m, the slope of the line:

Thus, we can find m, the slope of the line by plugging in (3, 0) for (x, y) and 8 for b:

0 = m(3) + 8

0 = 3m + 8

-8 = 3m

-8/3 = m

Thus, the slope is -8/3.

Therefore, the the equation of the line in slope-intercept form whose x-intercept is 3 and whose y-intercept is 8 is y = -8/3x + 8.

Optional Step 3:  Check the validity of the answer:

Thus, we can check that we've found the correct equation in slope-intercept form by plugging in (3, 0) and (0, 8) for (x, y), -8/3 for m, and 8 for b and seeing if we get the same answer on both sides of the equation when simplifying:

Plugging in (3, 0) for (x, y) along with -8/3 for m and 8 for b:

0 = -8/3(3) + 8

0 = -24/3 + 8

0 = -8 = 8

0 = 0

Plugging in (0, 8) for (x, y) along with -8/3 for m and 8 for b;

8 = -8/3(0) + 8

8 = 0 + 8

8 = 8

Thus, the equation we've found is correct as it contains the points (3, 0) and (0, 8), which are the x and y intercepts.

Answer:

6

Step-by-step explanation:

318 / 53  = 6

the remainder is 0

The definition of terms are given below:

(a) Loan: A loan is an amount of money borrowed from a lender with the agreement that it will be repaid with interest over a specified period.

(b) Hire purchase: Hire purchase is an arrangement whereby the buyer pays for goods in instalments while using them. Ownership of the goods is transferred to the buyer after the final payment is made.

(c) Credit: Credit is an agreement in which a borrower receives something of value, such as money or goods, with the promise to repay the lender at a later time.

(d) Monthly instalment: A monthly instalment is the amount of money that a borrower agrees to pay the lender each month as part of a loan repayment plan.

(e) Interest: Interest is the additional cost of borrowing money from a lender, calculated as a percentage of the loan amount.

Calculations for the loan:

The monthly installments are different because the repayment term and the fees charged for each loan option vary.

As the repayment term increases, the monthly installments decrease, but the total amount repaid increases due to the additional interest charges.

1.3.1

Using the first row of the table (12 monthly instalments), the total amount Mr Naidoo will pay is:

Total amount = Loan amount + Initial fee + (Admin fee x number of instalments) + (Monthly instalment x number of instalments)

Total amount = 25 000 + 1 140 + (57 x 12) + (2 283 x 12)

Total amount = 25 000 + 1 140 + 684 + 27 396

Total amount = 54 220

Therefore, the total amount Mr. Naidoo will pay at the end of the 12 monthly installments is R54 220.

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The horizontal shift is to the right.

The exact period is 8/7.

In a trigonometric function, written of the form

y = A csc (Bx - C)

the parameters are interpreted as follows

A is the amplitude

B is period / 2π

C is the horizontal shift

comparing with the equation y = 2 csc (7π/4x - 21π/2). we have that

horizontal shift = -21π/2 since it is positive it is to the right

The exact period is

Period = 2π / (7π/4)

= 8/7

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Answer:

from my calculation, the answer is B

The midpoint of the segment between the points (15,−9) and (−2,−18) will be (−13/2, −27/2). Then the correct option is C.

Let C be the mid-point of the line segment AB.

A = (x₁, y₁)

B = (x₂, y₂)

C = (x, y)

Then the midpoint will be

x = (x₁ + x₂) / 2

y = (y₁ + y₂) / 2

The midpoint of the segment between the points (15,−9) and (−2,−18) will be

x = (15 – 2) / 2

x = –13 / 2

y = (–9 – 18) / 2

y = –27/2

Then the correct option is C.

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The result of the multiplication of the complex numbers z₁ and z₂ expressed in their polar form is -0.866 + 0.5i.

To multiply complex numbers expressed in polar form, we need to multiply their magnitudes and add their angles.

Let z₁ = r₁(cosθ₁ + isinθ₁) and z₂ = r₂(cosθ₂ + isinθ₂) be two complex numbers in polar form. Then their product is given by:

z₁*z₂ = r₁r₂(cosθ₁cosθ₂ - sinθ₁sinθ₂ + i(cosθ₁sinθ₂ + sinθ₁cosθ₂))

In this case, we have z₁ = 230° and z₂ = 540°. So, we need to convert these angles to radians and then find the cosine and sine values:

z₁ = 230° = 230/180 * π radians = 1.27 radians

z₂ = 540° = 540/180 * π radians = 3π radians

Now we can substitute these values in the formula above:

z₁z₂ = r₁r₂(cosθ₁cosθ₂ - sinθ₁sinθ₂ + i(cosθ₁sinθ₂ + sinθ₁cosθ₂))

= 1 * 1(cos1.27cos3π - sin1.27sin3π + i(cos1.27sin3π + sin1.27*cos3π))

= -0.866 + 0.5i

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The sum of any matrix with the identity matrix of the same size, with respect to addition, will give the matrix itself. Therefore, the sum of matrix A and B, where B is the identity matrix, will give the matrix A.

9514 1404 393

Answer:

  8%

Step-by-step explanation:

The fraction donated was $632/$7900.

As a percentage, that is ...

  632/7900 × 100% = 0.08 × 100% = 8%

The store donated 8% of sales to charity.

Answer:

Do you have a picture?

Step-by-step explanation:

Answer:

C

Step-by-step explanation

I think im not very sure

Thus, an equation to show the overall price y of renting shoes and bowling x equipment is: y=4x+b.

The task is to create an equation that use the total expense (y) and the total number of bowled games (x). Hence, the way that we will begin is by entering the knowing into the formula of slope intercept form:  y=mx+b.

Thus, we include them in the formula: y=4x+b.

14 = 4(3)+b

Find b

14 = 12+b

14 - 12=b

b = 2

Thus, an equation to show the overall price y of renting shoes and bowling x equipment is: y=4x+b.

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Complete question:

The total cost for bowling includes the fee for shoe rental plus a fee per game. The cost of the game increases the price by $4. After 3 games, the total cost with shoe rental is $14.

a.write an equation to represent the total cost y to rent shoes and bowl x games.

Answer:

1

Step-by-step explanation:

The answer is 1.

Answer: The answer is 1 100%

Step-by-step explanation: i took the test

Answer:

  61.03°

Step-by-step explanation:

You want the angle opposite the side of length 7 in the triangle with other sides of lengths 4 and 8.

The law of cosines relates the angles of a triangle to the side lengths. For triangle ABC with opposite sides a, b, c, the relation is ...

  c² = a² +b² -2ab·cos(C)

Solving for angle C, we have ...

  cos(C) = (a² +b² -c²)/(2ab)

  C = arccos((a² +b² -c²)/(2ab))

In this triangle, that means ...

  C = arccos((4² +8² -7²)/(2·4·8)) = arccos(31/64)

  C ≈ 61.03°

The angle of interest is about 61.03°.

__

Additional comment

We get the same result from a triangle solver. See the second attachment. (The angle we want is angle B in that attachment.)

<95141404393>

Answer:

Your answer is in the attachment!!

The side lengths of the given right triangle are 6m and 8m respectively.

A right triangle is a triangle that has an interior angle of right angle.

Given, the hypotenuse of a right triangle is 10 m.

Let, the shorter leg is x m.

Therefore, the other leg is (x + 2) m.

Now for the given right triangle, \(x^{2} + (x+2)^{2} = 10^{2}\)

⇒ \(x^{2} + x^{2} +4x + 4= 100\)

⇒ \(2x^{2} +4x + 4 - 100 = 0\)

⇒ \(2x^{2} +4x - 96 = 0\)

⇒ \(x^{2} + 2x - 48 = 0\)

⇒ \((x+8)(x-6) = 0\)

⇒ \(x = 6\) (ignoring the negative value)

Therefore, the shorter leg is 6 m.

Now, the other leg is

\((6+2)m\\= 8 m\)

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The value of x in the parallelogram is 112°.

In a parallelogram, adjacent angles are always supplementary. This means that the sum of two adjacent angles in a parallelogram is always 180 degrees.

To understand this concept, let's consider a parallelogram ABCD. The opposite sides of a parallelogram are parallel and equal in length, and the opposite angles are congruent. Adjacent angles are those that share a side. Let's say angle A and angle B are adjacent angles in the parallelogram.

Since opposite angles of a parallelogram are congruent, we have angle A is congruent to angle C, and angle B is congruent to angle D.

Now, let's consider angle A and angle B. The sum of angle A and angle B is equal to the sum of angle C and angle D because opposite angles are congruent.

Therefore, we can conclude that angle A + angle B = angle C + angle D = 180 degrees.

This property holds true for all parallelograms. So, in any parallelogram, the adjacent angles are always supplementary, meaning their sum is 180 degrees.

For the given question, we know x° + 68° = 180°.

Then x° = 180° - 68°

x° = 112°

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The value of expression (s - f) (- 7) would be,

⇒ (s - f) (- 7)  = 119

We have to given that,

Functions are defined as,

⇒ s (x) = 2x²

⇒ f (x) = 3x

Now, We can find the value of (s - f) (- 7) is,

⇒ (s - f) (- 7)

⇒ s (- 7) - f (- 7)

⇒ 2 (- 7)² - (3 × - 7)

⇒ 2×49 + 21

⇒ 98 + 21

⇒ 119

Therefore, The value of expression (s - f) (- 7) would be,

⇒ (s - f) (- 7)  = 119

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In the given position-versus-time graph, the object moving the slowest without being at rest is at point B.

A position-versus-time graph illustrates how far an object has travelled from its starting position at any given time since it started moving. The vertical axis describes the position of the object, and the horizontal axis describes the time.

The slope of the graph indicates the speed of the moving object. Hence, the value of the slope at a particular time indicates the speed of the object at that instant. Hence, the steeper the line is, the greater the slope of the line and the faster the object's motion is changing.

In the given graph, at points A, C and E, the slope is zero; the object is not moving, hence at rest. At the point, D slope is steeper as compared to the slope at point B. Hence, the object is moving slower at point B as compared to point D.

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--The given question is incomplete; the complete question is

"The figure shows the position-versus-time graph for a moving object. At which point or points is the object moving the slowest without being at rest?"--

Answer:

The fox can run faster by a factor of 7 miles per hour

Step-by-step explanation:

If the fox runs 21 miles in half of an hour, that means that by multiplying the fraction 21miles/0.5hours by 2/2 you can find that the fox runs 42 miles per hour, 7 miles per hour faster than the rabbit.

Answer:

The Fox, by 7 Miles per hour

Step-by-step explanation:

The rabbit runs 35 Miles per hour

The Fox runs 21 in half an hour

1 hour - 30 minutes = 30 minutes meaning we have to double the foxes miles

21 x 2 = 42

42>32

To find out by how much do 42-32 and we get 7 Miles per hour.

The weighted average cost of capital for Philips Equipment is 8.09%

The face value of bond is $1,000

Price of bond = 0.965 * 1000 = 965

Market value of bond = 6,500 * 965 = 6,272,500

Market value of preferred stock = 48,000 * 64 = 3,072,000

Market value of common stock = 75,000 * 41 = 3,075,000

Total market value = 6,272,500 + 3,072,000 + 3,075,000 = 12,419,500

Annual preferred dividend = 0.055 * 100 = 5.5

Cost of preferred stock = (Annual dividend / price) * 100

Cost of preferred stock = (5.5 / 64) * 100

Cost of preferred stock = 8.5938%

Cost of equity = Risk free rate + beta (market return - risk free rate)

Cost of equity = 0.022 + 1.32 (0.106 - 0.022)

Cost of equity = 0.13288 or 13.288%

The weighted average cost of capital = Weight of debtafter tax cost of debt + weight of preferred stockcost of preferred stock + weight of equity*cost of equity

Weighted average cost of capital = (6,272,500 / 12,419,500)0.067(1 - 0.21) + (3,072,000 / 12,419,500)0.085938 + (3,075,000 / 12,419,500)0.13288

Weighted average cost of capital = 0.02673 + 0.02126 + 0.0329

The weighted average cost of capital = 0.0809 or 8.09%

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