A diesel train left Abuja and traveled west.Two hours later a freight train left traveling 15 mph faster in an effort to catch up to it. After six hours the freight train finally caught up. Find the diesel train's average speed. (Need to have chart and explanation)

Answer:

Rs 700

Step-by-step explanation:

If S.P = 595

discount = 15%

Then C.P = 100/100 - 15×595

= Rs 700.

Given statement solution is :- (a) 1 route is possible from A to P.

(b) 1 route is possible from A to P with a stop at C.

(c) 1 route is possible from A to P with stops at both C and S.

To determine the number of possible routes from point A to point P, we can use the concept of combinations and permutations. Assuming each intersection on the map is a distinct point, and the driver can only travel south or east, we can consider this as a grid problem.

(a) Without any additional stops:

In this case, the driver can only travel south or east until they reach point P. Since the driver cannot backtrack, there is only one path to reach point P from A. Therefore, the answer to part (a) is 1.

(b) If you insist on stopping off at the Chipotle at C:

In this case, the driver needs to pass through point C before reaching point P. We can break down the problem into two parts: the number of routes from A to C and the number of routes from C to P.

From A to C:

Since the driver can only travel south or east, there is only one path to reach point C from A.

From C to P:

Similarly, there is only one path to reach point P from C.

Therefore, the answer to part (b) is 1 (from A to C) multiplied by 1 (from C to P), which equals 1.

(c) If you wish to stop off at both the Chipotle at C and the Sonic at S:

In this case, we can again break down the problem into three parts: the number of routes from A to C, the number of routes from C to S, and the number of routes from S to P.

From A to C:

There is one path from A to C.

From C to S:

Since the driver can only travel south or east, there is only one path from C to S.

From S to P:

Similarly, there is only one path from S to P.

Therefore, the answer to part (c) is 1 (from A to C) multiplied by 1 (from C to S) multiplied by 1 (from S to P), which equals 1.

In summary:

(a) 1 route is possible from A to P.

(b) 1 route is possible from A to P with a stop at C.

(c) 1 route is possible from A to P with stops at both C and S.

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To calculate the optimal profit, we need to find the value of D when the total cost is \($30,500\) and then substitute it into the given equation.

To find D, we can rearrange the equation to solve for D: Given:\(p = 180 - 0.2D\) and total cost =\($30,500\) Now, substitute the total cost ($30,500) into the equation to find D:

Since D cannot be negative in this context, it means that the given equation is not applicable for a total cost of \($30,500\). it is not possible to calculate the optimal profit using the given equation and the total cost of \($30,500\).

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Logarithmic function log₍ₓ₊₂₎(4) = 3x can be written in exponential form as  4 = 3x ⁽ˣ⁺²⁾

Which property of log function is used?

The properties of log are nothing but the rules of logarithms and these are derived from the exponent rules.

These properties of logarithms are used to solve the logarithmic equations and to simplify logarithmic expressions.

A log function can be written in exponential form using

logₐ m = x ⇒ m = ax

According to the given question:

The given logarithmic function is

log₍ₓ₊₂₎(4) = 3x

On applying the property we get

4 = 3x ⁽ˣ⁺²⁾

Hence the required exponential form is 4 = 3x ⁽ˣ⁺²⁾

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Answer:

Step-by-step explanation:

\((n-5)^{2} -(n-3)^{2} =n^{2} -10n+25-n^{2} +6n-9=-4n+16=-4(n-4)\\\)

if  you divide it with 4

you'll get -(n-4)=4-n

If teacher is distributing sheets in a class, then the equation which is used to find number of students in class is (d) 2x+8 = 3x - 11​.

A "Linear-Equation" is a mathematical equation that represents a straight line in a coordinate plane. It is of form : y = mx + b

where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept (the point at which the line crosses the y-axis).

Let number of students in class be denotes as "x",

If each student get 2 sheets, then 8 sheets are remaining, it is mathematically represented as : 2x + 8 ,

If each student get 3 sheets each, then there would be 11 sheets less, and this is represented as : 3x - 11,

So, the equation which is used to find number of students in class is 2x+8=3x-11,

Therefore, the correct option is (d).

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The given question is incomplete, the complete question is

If a teacher were to distribute sheets of paper so that each student got two sheets, there would be 8 sheets remaining. However, if three sheets were given to each student, the teacher would be 11 sheets short. Which equation could be used to find how many students are in the class?

(a) 2(x - 8) = 3(x + 11)

(b) 2(x + 8) = 3(x - 11)

(c) 2x-8 = 3x + 11

(d) 2x+8 = 3x - 11​

The dial for the standard combination lock is fastened to a spindle. The spindle travels through many wheels and a drive cam inside the lock. Every number has one wheel, hence the number of wheels in a wheel pack depends on how many numbers are in the combination.

The lock uses the numbers 0 to 39 and has 64,000 distinct combinations.

How many possible three-number combinations are there?

You have 10 options for the first digit, 9 options for the second digit, and 8 options for the third digit, giving you 10x9x8 = 720 if you want all three possible numbers with no duplication of the digits.

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Answer: I think 43

Step-by-step explanation:

Draw on a graph out the points and then add up the middle of your shape.

Your welcome!

Answer:

The surface area of the square pyramid with dimensions 17 ft x 9 ft x 17 ft is 595 square feet.

Step-by-step explanation:

To calculate the surface area of a square pyramid, we need to add the area of the base to the sum of the areas of the four triangular faces.

For a square pyramid with side length s and slant height l, the surface area can be calculated as follows:

Surface area = s^2 + 2sl

where s is the length of one side of the square base, and l is the slant height of the pyramid, which is the height of each of the four triangular faces.

In your case, the dimensions given are 17 ft for the base and 9 ft for the height, which is also the slant height. Therefore, we can calculate the surface area as:

Surface area = 17^2 + 2(17)(9)

Surface area = 289 + 306

Surface area = 595

The distance from the earth to venus is an illustration of the sine ratio

The distance from the earth to venus at that time is 1.12 au

See attachment for the diagram that illustrates the complete question.

Start by calculating the angle V using the following sine ratio

SE/sin(V) = VS/sin(E)

This gives

1/sin(V) = 0.723/sin(39.4)

Take the inverse of both sides

sin(V)/1 = sin(39.4)/0.723

Evaluate the quotient

sin(V) = 0.8779

Take the arcsin of both sides

V = 61.4

Calculate the measure of angle S

<S + <V + <E = 180

This gives

<S  = - <V - <E + 180

Substitute known values

<S  = -61.4 - 39.4 + 180

<S  = 79.2

The distance (VE) is then calculated using the following sine ratio

VE/sin(S) = VS/sin(E)

This gives

VE/sin(79.2) = 0.723/sin(39.4)

Multiply bot sides by sin(79.2)

VE = sin(79.2) * 0.723/sin(39.4)

Evaluate the product

VE = 1.12

Hence, the distance from the earth to venus at that time is 1.12 au

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Answer:

x = 2

Step-by-step explanation:

AE is equal to the sum of AB and BE because of segment addition postulate, we can substitute to get AE = 11 + x + 1 = x + 12

DE is equal to the sum of DC and CE because of segment addition postulate, we can substitute to get DE = 1 + x + 4 = x + 5

To solve the problem, we can use power of a point, more specifically exterior secants products scenario. In this case, we can get the equation:

AE * BE = DE * CE

Now, we can substitute and solve:

(x + 12)(x + 1) = (x + 5)(x + 4)

x^2 + 13x + 12 = x^2 + 9x + 20

13x + 12 = 9x + 20

4x + 12 = 20

4x = 8

x = 2

first, we find the percentage of the commission earned:

$278,000 ----> 100%

$16,680 ------> x

then solve

therefore the commission is 6%. So,

$324,000 ------> 100%

y -------------------> 6%

answer: $ 19,440

Answer:

Final cost of item = initial price(1 – rate)

Step-by-step explanation:

y(1 – .18) = .82y

Answer:   c. The pattern shows the points are far from the zero line, indicating a good fit for a nonlinear model.

d. The pattern is not random, indicating a good fit for a nonlinear model.

Step-by-step explanation:

A residual plot is a graph that represents

Two main kids of plot are there.

First plot gives a random pattern, indicates a good fit for a linear model.

Other plots are non- random, indicates a good fit for a non- linear model.

Two points are correct for any residual plots :

c. The pattern shows the points are far from the zero line( basically u-shaped), indicating a good fit for a nonlinear model.

d. The pattern is not random, indicating a good fit for a nonlinear model.

To arrive at this answer, you need to multiply the number of drink options (2) by the number of main dish options (4) by the number of dessert options (3).

2 x 4 x 3 = 24

So the food truck is offering a total of 24 different lunch combo meal options.


There are 2 drink options, 4 main dish options, and 3 dessert options. To find the total number of possible combos, we will multiply the number of options in each category:

Total combos = (Drink options) x (Main dish options) x (Dessert options)

Total combos = 2 x 4 x 3

Total combos = 24

So the food truck can serve 24 different lunch combo meals. Your answer is D. 24.

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9514 1404 393

Answer:

  EAGI

Step-by-step explanation:

Your choices are correct except for "B". Graph 3 has a dashed line, so the inequality symbol is <, not ≤.

Answer:

My friend's mower will take approximately 0.75 h to mow the lawn alone.

Step-by-step explanation:

To solve this problem we can use the idea of average speed and apply to this problem, using the appropriate formula shown below:

\(speed = \frac{distance}{time}\)

Where each lawn mower has a speed at which they can mown, the distance is the lawn they're mowing and the time is how long they will take to do it. In the case where my equipment is working alone, its speed "x" can be modeled as below:

\(x = \frac{lawn}{1.5}\)

When my friend's mower does the job, its speed "y" can be seen as:

\(y = \frac{lawn}{time}\)

When both work together the speed can be seen as:

\(x + y = \frac{lawn}{0.5}\)

Applying the first two equations on the second, gives us:

\(\frac{lawn}{1.5} + \frac{lawn}{time} = \frac{lawn}{0.5}\\\frac{1}{time} = \frac{1}{0.5} - \frac{1}{1.5}\\\frac{1}{time} = 2 - 0.667\\\frac{1}{time} = 1.333\\1.333*time = 1\\time = \frac{1}{1.333} = 0.75\)

My friend's mower will take approximately 0.75 h to mow the lawn alone.

Step-by-step explanation:

The volume of a rectangular box is given by the formula:

Volume = length x breadth x height

In this case, the length is a, the breadth is 2b, and the height is 3c. So, the volume can be calculated as:

Volume = a x 2b x 3c

= 6abc

Therefore, the volume of the rectangular box with a, 2b and 3c as length, breadth and height respectively is 6abc.

I'm almost 100% sure its F:(x - 16)(x - 4)

Answer:

15 cookies, 10 brownies.

Step-by-step explanation:

I'm assuming that she is selling the same amount of cookies and brownies per hour. If that is the case...

Multiply it by 5. If 3 cookies were sold in one hour, and there's 5 hours, just multiply 3 by 5. Total number is 15 cookies.

Same goes for brownies. Multiple 2 brownies by 5. That makes 10 brownies.

Given the following equations C = 100 + 0.6YDI = 200G = 150T = 0.1YM = 100 + 0.2YX = 200V- = V - TWe can obtain the equilibrium GDP value by using the formula Y = C + I + G + X - M

We are given that T = 0.1Y and V- = V - T

Therefore, V - 0.1Y = 0.8YD0.9Y = V

We can substitute the value of T and V in the consumption function,

C = 100 + 0.6YD and get

C = 100 + 0.6(0.8Y)C = 100 + 0.48YC + I + G + X - M

= Y

Substituting the given values, we get

100 + 0.48Y + 200 + 150 + 200 - (100 + 0.2Y) = YY

= 900/1.06

≈849.05

Therefore, equilibrium GDP is approximately 849.05.

The equilibrium GDP value for the given equations is approximately 849.05.

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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

The correct option is (d) interval/ratio, nominal with 2 or more levels.

In ANOVA (Analysis of Variance), the independent variable is interval/ratio with 2 or more levels, and the dependent variable is nominal with 2 or more levels. Here, ANOVA is a statistical tool that is used to analyze the significant differences between two or more group means.

ANOVA is a statistical test that helps to compare the means of three or more samples by analyzing the variance among them. It is used when there are more than two groups to compare. It is an extension of the t-test, which is used for comparing the means of two groups.

The ANOVA test has three types:One-way ANOVA: Compares the means of one independent variable with a single factor.Two-way ANOVA: Compares the means of two independent variables with more than one factor.Multi-way ANOVA: Compares the means of three or more independent variables with more than one factor.

The ANOVA test is based on the F-test, which measures the ratio of the variation between the group means to the variation within the groups. If the calculated F-value is larger than the critical F-value, then the null hypothesis is rejected, which implies that there are significant differences between the group means.

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The system of equations [x - 3y = -1 and -6x + 19y = 6] can be solved, resulting in x = -1 and y = 0.

To solve the system of equations [x - 3y = -1 and -6x + 19y = 6], we can use the method of substitution or elimination.

Let's solve it using the method of elimination.

First, we can multiply the first equation by 6 and the second equation by -1 to eliminate the x terms.

This gives us [6x - 18y = -6 and 6x - 19y = -6].

Now, subtracting the first equation from the second eliminates the x terms, leaving us with -y = 0. Solving for y, we find y = 0.

Substituting this value back into the first equation, we get x - 3(0) = -1, which simplifies to x = -1.

Therefore, the solution to the system of equations is x = -1 and y = 0.

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Answer:

Step-by-step explanation:

\(14.702 = (1*10) + 4*(1) +(7*\frac{1}{10}) + (2*\frac{1}{1000})\)

Answer:

Step-by-step explanation:

y+18<8y+46 or y+80<67

y+18<8y+46 | -8y

-7y + 18 < 46 | - 18

-7y < 28

y > -4

y + 80 < 67

y < 13

Answer:

Eric drove 28 7/11 miles with 1 gallon of gas.

Step-by-step explanation:

You just use long division and do 315 divided by 11, and you should get 28R7 so you just turn that R7 into 7/11.

Have a nice rest of your day :)

A. The statement "the value of x is 4.8 times as large as the value of y" is true.

B. Let's analyze each statement to determine its validity:

1. "The value of y is 4.8 times as large as the value of a." The given information states the constant rate of change of y with respect to r is 4.8.

This statement does not provide any direct information about the relationship between y and a, so we cannot determine if it is true or false based on the given information.

2. "z = 4.8y." This statement suggests that z is equal to 4.8 times y. However, the value of z is not mentioned in the given information, so we cannot determine the truth of this statement.

3. "The value of x is 4.8 times as large as the value of y." The constant rate of change of y with respect to r being 4.8 implies that for every unit increase in r, y increases by 4.8 units.

Therefore, the statement is true, as it indicates a proportional relationship between x and y.

4. "The change in the value of y is 4.8 times as large as the change in the value of r."

This statement reflects the constant rate of change given, where for each unit increase in r, y increases by 4.8 units.

Hence, this statement is true.

In summary, based on the given constant rate of change, the statements that are true are: "The value of x is 4.8 times as large as the value of y" and "The change in the value of y is 4.8 times as large as the change in the value of r."

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Suppose that the constant rate of change of y with respect to r is 4.8. Which of the following statements are true? (Select all that apply.) the value of y is 4.8 times as large as the value of a z = 4.8y the value of x is 4.8 times as large as the value of y the change in the value of y is 4.8 times as large as the change in the value of the change in the value of r is 4.8 times as large as the change in the value of y