A train leaves the station traveling north at 85 km/h. Another train leaves at the same time and travels south at 95 km/h. How long will it take before the trains are 990 km apart

Answer:

b = [tex]\frac{S-2la}{h+l}[/tex]

Step-by-step explanation:

S = bh + lb + 2la ( reversing the equation )

bh + lb + 2la = S ( subtract 2la from both sides )

bh + lb = S - 2la ← factor out b from each term on the left side

b(h + l) = S - 2la ← divide both sides by (h + l)

b = [tex]\frac{S-2la}{h+l}[/tex]

Answer: x < -46/17

Step-by-step explanation:

To solve the inequality:

1/3x - 1/4(x + 2) > 3x - 4/3

First, we simplify the left-hand side by finding a common denominator:

4(1/3x) - 3/4(x + 2) > 3x - 4/3

4/3x - 3/4x - 9/2 > 3x - 4/3

Next, we simplify the equation:

7/12x - 9/2 > 3x - 4/3

To isolate the variable x on one side of the inequality, we will move all the x terms to the left-hand side and all the constants to the right-hand side:

7/12x - 3x > 9/2 - 4/3

-17/12x > 23/6

Finally, we can solve for x by dividing both sides by -17/12, remembering to reverse the inequality because we are dividing by a negative number:

x < (23/6) ÷ (-17/12)

x < -46/17

Therefore, the solution to the inequality is:

x < -46/17

Using trigonometric functions, the value of the side AC = 2.85 units.

The right triangle's angle serves as the domain input value for the six fundamental trigonometric operations, and the output is a range of numbers.

The angle, given in degrees or radians, is the domain of the trigonometric function, sometimes referred to as the "trig function," of  f(x) = sin, and the range is [-1, 1]. The other functions have a similar domain and scope. Trigonometric functions are widely used in algebra, geometry, and calculus.

Now in the given figure,

The angle is a right-angled triangle.

Now as per the trigonometric functions,

Sin 35° = AC/AB

⇒ 0.57 = x/5

⇒ x = 0.57 × 5

= 2.85.

The length of the opposite side AC is 2.85 units.

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Answer:

Step-by-step explanation:

The slope between the points (-3, 0) and (0, -1) is -1/3.

The slope of a line serves as a gauge for its steepness. It may be calculated by dividing the difference in y-coordinate by the difference in x-coordinate between any two points on a line. A line's slope might be zero, positive, negative, or undefinable. A line with a positive slope is moving upward from left to right, a negative slope is moving downward from left to right, and a line with a zero slope is level. The line is vertical if the slope is undefinable.

Let us consider the first two points (-3, 0) and (0, -1).

The slope of the line is given as:

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

Substituting the values we have:

m = (-1 - 0) / (0 - (-3)) = -1/3

Hence, the slope between the points (-3, 0) and (0, -1) is -1/3.

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Answer:

Step-by-step explanation:

We can simplify the expression by factoring out a common factor of 5^1999 from the numerator:

5^2000 + 5^1999

= 5^1999(5 + 1)

= 5^1999(6)

And we can also factor out a common factor of 5^1997 from the denominator:

5^1999 - 5^1997

= 5^1997(5^2 - 1)

= 5^1997(24)

So the entire expression simplifies to:

(5^2000 + 5^1999) / (5^1999 - 5^1997)

= (5^1999 * 6) / (5^1997 * 24)

= (6/24) * 5^2

= 5/2

Therefore, the value of the expression is 5/2.

The weight becomes 1/4 of its original value when the distance is multiplied by 2.

According to the question, "the weight of a body above the surface of the earth is inversely proportional to the square of its distance from the center of the earth." We need to determine the effect on the weight when the distance is multiplied by 2.

Let w be the weight of a body, d be the distance from the center of the earth, and k be the constant of variation. According to the question,

w = k / d²

When the distance is multiplied by 2, the new distance is 2d. Therefore, the new weight is given by:

w' = k / (2d)²

w' = k / 4d²

w' = w / 4

Therefore, the weight becomes 1/4 of its original value when the distance is multiplied by 2.

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The centripetal force is 7384.80 N.

For the centripetal force in N on the end of a 52 m (radius) wind turbine blade that is rotating at 0.3 rev/s and assuming the mass is 2 kg.

Use the following formula:

Centripetal force = (mass x velocity²) / radius

Where; mass = 2 kg

In this case, the radius of the wind turbine blade is 52 m, and it is rotating at 0.3 rev/s, which means that the angular velocity is:

ω = 2π * f = 2π * 0.3 = 1.884 rad/s

where f is the frequency or revolutions per second.

The linear velocity at the end of the blade can be calculated as:

v = r * ω ⇒ 52 * 1.884 ⇒ 98.088 m/s

radius = 52 m

Centripetal force = (2 x 98.088²) / 52

Centripetal force  = 7384.80 N

Therefore, the centripetal force on the end of a 52 m wind turbine blade rotating at 0.3 rev/s with a mass of 2 kg is 7384.80 N.

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To estimate the distance traveled  we need to find the area under the velocity-time graph from 0 to 8 seconds So,The estimate for the distance the car traveled for the first 8 seconds is 4000 meters.

A velocity-time graph is a graphical representation that shows the velocity of an object on the y-axis and time on the x-axis. It is used to depict the change in velocity over time and can provide information about the acceleration or deceleration of an object.

The height of each strip can be estimated by taking the average of the velocities at the beginning and end of the strip.

Using the trapezium rule, the estimated area of each strip is:

Strip 1: 0.5 x (0 + 2) x (0 + (-500)) = -500 m/s

Strip 2: 0.5 x (2 + 4) x (-500 + (-1000)) = -1500 m/s

Strip 3: 0.5 x (4 + 6) x (-1000 + (-500)) = -1500 m/s

Strip 4: 0.5 x (6 + 8) x (-500 + 0) = -500 m/s

The total estimated area is the sum of the areas of the 4 strips:

Total estimated area = -500 + (-1500) + (-1500) + (-500) = -4000 m/s

Since the area represents the distance traveled by the car, we can take the absolute value of the area to get the estimated distance traveled:

Estimated distance traveled is = |-4000| = 4000 meters

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The coordinate of centroid of the triangle is (2, 8/3), the coordinate of the circumcenter is (-7/32, 121/24) and the coordinate of orthocenter is (2, 9/2)

a. To find the centroid of a triangle, we take the average of the x-coordinates and the average of the y-coordinates of the vertices. Therefore, the x-coordinate of the centroid is:

(x₁ + x₂ + x₃) / 3 = (-4 + 2 + 8) / 3 = 2

Similarly, the y-coordinate of the centroid is:

(y₁ + y₂ + y₃) / 3 = (0 + 8 + 0) / 3 = 8/3

So the coordinate of the centroid is (2, 8/3).

b. The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect. To find the circumcenter, we can find the equations of the perpendicular bisectors of any two sides of the triangle and solve for their intersection point.

Let's take the sides formed by vertices (-4, 0) and (2, 8), and vertices (-4, 0) and (8, 0). The midpoint of the first side is ((-4+2)/2, (0+8)/2) = (-1, 4), and the slope of the line passing through the two points is (8-0)/(2-(-4)) = 8/6 = 4/3. Therefore, the equation of the perpendicular bisector passing through (-1, 4) is:

y - 4 = (4/3)(x + 1)

Simplifying this equation, we get:

y = (4/3)x + 13/4

Similarly, the midpoint of the second side is ((-4+8)/2, (0+0)/2) = (2, 0), and the slope of the line passing through the two points is (8-0)/(2-8) = -8/6 = -4/3. Therefore, the equation of the perpendicular bisector passing through (2, 0) is:

y = -(4/3)(x - 2)

To find the intersection point of these two lines, we can set the equations equal to each other and solve for x:

(4/3)x + 13/4 = -(4/3)(x - 2)

x = -7/32

Substituting x = -7/32 into either of the equations, we get:

y = (4/3)(-7/32 + 1) + 4 = 121/24

So the coordinate of the circumcenter is (-7/32, 121/24).

c. The orthocenter of a triangle is the point where the altitudes of the triangle intersect. An altitude of a triangle is a line segment from a vertex of the triangle perpendicular to the opposite side.

Let's take vertex (-4, 0) and find the equation of the line passing through this vertex and perpendicular to the opposite side formed by vertices (2, 8) and (8, 0). The slope of the opposite side is (0-8)/(8-2) = -8/6 = -4/3, so the slope of the line we want is the negative reciprocal of this, which is 3/4. Therefore, the equation of the altitude passing through (-4, 0) is:

y - 0 = (3/4)(x + 4)

Simplifying this equation, we get:

y = (3/4)x + 3

Let's now take vertex (2, 8) and find the equation of the altitude passing through it. The slope of the opposite side formed by vertices (-4, 0) and (8, 0) is (0-0)/(8-(-4)) = 0, which means the altitude passing through (2, 8) is a vertical line passing through (2, 0). Therefore, the equation of this altitude is:

x = 2

Now we need to find the intersection point of these two altitudes. Substituting y = (3/4)x + 3 into the equation x = 2, we get:

y = 9/2

The coordinate of the orthocenter is (2, 9/2)

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In conclusion, we can prove that[tex](A -B) U (A C)[/tex] is a superset of[tex]A - (B nC)[/tex] using both the choose-an-element method and the algebra of sets.

To answer this question, let's first draw two Venn diagrams to represent the sets A, B, and C. In the first Venn diagram, shade the region that represents[tex]A - (B nC)[/tex].

This is the region outside of the intersection of B and C and inside of A. In the second Venn diagram, shade the region that represents [tex](A -B) U (A C).[/tex] This is the union of the region outside of B and the region outside of C, both of which are inside of A. Based on these diagrams, we can make the conjecture that (A -B) U (A C) is a superset of A - (B nC).

To prove this conjecture, we can use the choose-an-element method. Let a be an element of A - (B nC). This means that a is in A, but not in B or C. Since a is in A, it is also in (A -B) U (A C), and therefore (A -B) U (A C) is a superset of A - (B n C).

We can also use the algebra of sets to prove this conjecture.[tex]A - (B n C) = (A -B) U (A -C) since A - (B n C)[/tex]is the union of the regions outside of B and outside of C, both of which are inside of A. This implies that (A -B) U (A C) is a superset of A - (B nC).

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He bought 4.29 Kilos of fruit.

4+0.29=4.29

Luke bought 4.29 kilograms of fruit in all

Step-by-step explanation:

Simple addition will be used to find the total fruit Luke bought.

Given

Amount of apples he bought  = 4 kilograms

Amount of oranges he bought = 0.29 kilograms

so the total fruit will be:

[tex]\text{total fruit}=\text{Apples}+\text{oranges}[/tex]

[tex]=4+0.29[/tex]

[tex]=4.29[/tex]

So,

Luke bought 4.29 kilograms of fruit in all

Keywords: Measurement, addition

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The country won 45 silver medals and 75 bronze medals, for a total of 45 + 75 = 120 non-gold medals.

A medal is a small, flat, and usually round piece of metal that is awarded to individuals or groups as a symbol of recognition or honor for achievement, bravery, or other notable deeds. Medals can be made of various materials, such as gold, silver, bronze, or other alloys, and they often feature intricate designs or engravings that reflect the significance of the award.

According to the circle graph, gold medals make up 20% of the total medals, which means the country won 20% of 150 medals as gold, or 0.2 x 150 = 30 gold medals.

Similarly, silver medals make up 30% of the total medals, which means the country won 30% of 150 medals as silver, or 0.3 x 150 = 45 silver medals.

Finally, bronze medals make up 50% of the total medals, which means the country won 50% of 150 medals as bronze, or 0.5 x 150 = 75 bronze medals.

Therefore, the country won 45 silver medals and 75 bronze medals, for a total of 45 + 75 = 120 non-gold medals.

So the answer is 120.

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Question 7. C (rectangular pyramid)

Question 8. 17 cm

Answer:

Question 7:C rectangular pyramid

Question 8: C 120 in

A=2(wl+hl+hw)=2·(10·2+5·2+5·10)=160

Step-by-step explanation:

Answer:

Stacy rented a truck for one day there was a base fee of $16.95 and there was an additional charge of 93 cents for each model driven. stacy had to pay $143.43 when he returned the truck. for how many miles did she drive the truck​

Step-by-step explanation:

Let's start by subtracting the base fee from the total cost:

$143.43 - $16.95 = $126.48

Now, we can divide the remaining cost by the cost per mile:

$126.48 ÷ $0.93/mile ≈ 136 miles

Therefore, Stacy drove the truck for approximately 136 miles.

Answer: 1500000

Step-by-step explanation:

use a calculator

Answer:

1,500,000

Step-by-step explanation:

Breaking it up into an easier problem:

20x50 = 1,000

30x50=1,500

1,000 x 1,500, aka "adding three zeros" to the end of 1,500, as 1,000 is simply 1 x 10 x 10 x 10, and each 10 has one 0 to it.

Thus, the answer is 1,500,000

The probability that more heads are tossed using coin A than coin B is 5/16.

The given data is: Coin A is tossed three times and coin B is tossed two times. We have to find the probability that more heads are tossed using coin A than coin B.

P(E) = Number of favorable outcomes/ Total number of possible outcomes

Coin toss:

There are two possible outcomes in a coin toss, Head or Tail. The probability of getting a head in a coin toss is

1/2 = 0.5.

Therefore, the probability of getting a tail in a coin toss is also 1/2 = 0.5.

Let's calculate the possible outcomes when coin A is tossed three times.

There are 2 possible outcomes when one coin is tossed.

Number of possible outcomes when three coins are tossed = 2 * 2 * 2 = 8

Likewise, the possible outcomes when coin B is tossed two times are:

The number of possible outcomes = 2 * 2 = 4

Therefore, the total number of possible outcomes = 8 * 4 = 32

Now, we will find out the cases where the number of heads is more when coin A is tossed three times.

HHH HHT HTH HTT THH THT TTH TTT HHT HTT THT TTT TTH TTT HTT TTT THT TTT TTT TTT

Therefore, the number of times when more heads are obtained when coin A is tossed three times is 10. (We have to exclude the case when there is an equal number of heads.)

Therefore, the required probability is: P = Number of favorable outcomes/ Total number of possible outcomes

P = 10/32P = 5/16

Therefore, the probability that more heads are tossed using coin A than coin B is 5/16.

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Answer:

Step-by-step explanation:

xs nxqxm,nswjnej,cebxhjme2ckjwadbcweckslnvc

First, we need to find the value of g(pi/2):

g(pi/2) = cos(pi/2) = 0

Now we can substitute this value into f(x):

f(g(pi/2)) = f(0) = sin(0) = 0

Therefore, f(g(pi/2)) = 0.

The equation of the circle is [tex]x^2 + y^2 + 6x - 18y + 65 = 0[/tex].

Given:

Equation of the circle is [tex](x+3)^2+(y-9)^2=5^2[/tex]

Expand the equation

[tex](x+3)^2 = (x+3)(x+3) = x^2 + 3x + 3x + 9 = x^2 + 6x + 9[/tex]

[tex](y-9)^2 = (y-9)(y-9) = y^2 - 9y - 9y + 81 = y^2 - 18y + 81[/tex]

[tex]5^2 = 25[/tex]

Then, substitute the expanded expressions into the equation

[tex](x+3)^2+(y-9)^2=5^2\\(x^2 + 6x + 9) + (y^2 - 18y + 81) = 25\\[/tex]

Simplify and combine like terms

[tex](x^2 + 6x + 9) + (y^2 - 18y + 81) = 25\\x^2 + y^2 + 6x - 18y + 90 = 25[/tex]

Rearrange the equation so that one side is 0

[tex]x^2 + y^2 + 6x - 18y + 90 = 25\\x^2 + y^2 + 6x - 18y + 90 - 25 = 0\\x^2 + y^2 + 6x - 18y + 65 = 0[/tex]
Thus, the equation of a circle [tex](x+3)^2+(y-9)^2=5^2[/tex] can be rearranged using the distributive property to form [tex]x^2 + y^2 + 6x - 18y + 65 = 0[/tex], with one side equaling 0.

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Answer:

Cost price (CP) = Rs20

% Profit = 10%

Selling price (SP) = y

By formula:

% Profit = (Profit/CP) x 100%

But Profit= SP - CP

Therefore;

% Profit = [(SP-CP)/C.P)] x 100%

Substituting, we have:

10% = [(y-20)/20] x 100%

10/100 = (y-20)/20

1/10 = (y-20)/20

1 = (y-20)/2

Cross multiply

y - 20 = 2

y = 2 + 20

y = 22

Therefore, the Sale price is Rs 22

The value of x that makes the average between 3.15 and x equal to 40 is 76.85.

In this problem, we are given two numbers, 3.15 and x, and told that the average between them is 40. We can set up an equation to solve for x as follows:

(3.15 + x) / 2 = 40

To find the average between 3.15 and x, we add the two numbers together and divide by 2, which gives us the equation above.

To solve for x, we can start by multiplying both sides of the equation by 2:

3.15 + x = 80

Next, we can subtract 3.15 from both sides of the equation:

x = 76.85

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Answer:

the test does not provide convincing evidence that the proportion is greater than 90%

The simplified expression using De Morgan's law are  a)x'y'z'u  b)x'y'u c): x'y'u and d)x'y'z'+xy'z'+xyz.

The main idea is to simplify each Boolean expression by repeatedly applying De Morgan's law until each complement operation operates on a single variable.

Then, apply the double complement law to simplify the expression further. In the end, the simplified expression should contain only AND and OR operations without any complement operators acting on multiple variables.

a. 1/ x + yz + u can be simplified using De Morgan's law to: (x'y'z')u'. Then, applying the double complement law, we get the simplified expression as: x'y'z'u.

b. 1/x(y + 2)u can be simplified using De Morgan's law to: x'(y'+2')u'. Then, applying the double complement law, we get the simplified expression as: x'y'u.

c. 1/(x + y)(uv + xy) can be simplified using De Morgan's law to: (x'y')(u' + x'y'). Then, applying the double complement law, we get the simplified expression as: x'y'u.

d. 1/xy + yz + xz can be simplified using De Morgan's law to: (x'+y')(y'+z')(x'+z'). Then, applying the double complement law, we get the simplified expression as: x'y'z'+xy'z'+xyz.

In summary, to simplify Boolean expressions, we can apply De Morgan's law repeatedly and then use the double complement law to remove complement operators acting on a single variable twice.

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Answer:

0% (0/40)

Step-by-step explanation:

I feel like this is a trick question. since chicken is not indicated on the graph, I believe chicken is nobodies favorite food

The zeroes of the function are -12 and 5.

Zeros of a function are the values of the input variables that make the output of the function equal to zero. The zeros are the solutions of equation f(x) = 0.

According to the question:

To find the zeros of the function

f(x) = x² + 7x - 60, we must set f(x) equal to zero and solve for x.

So we start with the equation:

x² + 7x - 60 = 0

Next, we need to factor the left side of the equation. We are looking for two numbers that multiply to -60 and add to 7. After some trial and error, we find that the numbers are 12 and -5:

x² + 7x - 60 = (x + 12)(x - 5) = 0

Now we can apply the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero and solve for x:

x + 12 = 0 or x - 5 = 0

Solving for x, we get:

x = -12 or x = 5

The zeros of the function f(x) = x² + 7x - 60 are therefore x = -12 and x = 5.

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 The 32 ways to get a five-card combination containing two jacks and three aces.

(a) A full house consists of three of one kind and two of another kind. Therefore, there are 13 different choices for the rank of the triplet and 4 cards of the same rank. Once the triplet has been chosen, there are 12 choices for the rank of the pair and 4 cards of the same rank. Therefore, the number of ways to get a full house is as follows:$${13}{\times}{4}{\times}{12}{\times}{4}={7488}$$Therefore, there are 7488 ways to get a full house.(b) In this case, the two jacks and three aces must be chosen out of the 4 jacks and 4 aces in the deck. Therefore, the number of ways to get a five-card combination with two jacks and three aces is as follows:$$\frac{{4\choose2}{4\choose3}{44\choose0}}{5!}={32}$$Therefore, there are 32 ways to get a five-card combination containing two jacks and three aces.

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Answer:

Choice 2
∠1 and ∠7, ∠2 and ∠8

Step-by-step explanation:

This is a good example of a problem that can be solved by POE(process of elimination)

First choice: ∠2 and ∠3 are on the same straight line so they cannot be congruent. They are supplementary in that they add up to 180°

The same applies for ∠3 and ∠4 (third choice)

The same applies for ∠1 and ∠4 (fourth choice)

That leaves choice 2

We can prove ∠1 ≅ ∠7 as follows:

∠1 ≅ ∠3 since they are vertically opposite angles

∠3 ≅ ∠7 since they are exterior angles

So ∠1 ≅ ∠7

By similar reasoning,
∠2 ≅ ∠8

So correct choice is Choice 2

Answer:153

Step-by-step explanation:

The Variance Inflation Factor (VIF) measures the degree of correlation or the collinearity of the explanatory variables.

VIF quantifies how much each explanatory variable is correlated with a linear combination of the other variables in a multiple regression model. This can help identify variables that are redundant, irrelevant, or harmful to the model's accuracy. The VIF is calculated for each explanatory variable by dividing the variance of the regression coefficient estimates by the variance of the regression coefficient estimates when that variable is excluded from the model.

If the VIF is greater than 1, it indicates that the variance of the regression coefficient estimate for that variable is inflated by the presence of the other variables, which reduces the model's accuracy. Therefore, a VIF greater than 1 is considered to be an indication of collinearity or multicollinearity in the explanatory variables. The VIF measures the degree of correlation or the collinearity of the explanatory variables, and it can identify variables that are redundant, irrelevant, or harmful to the model's accuracy.

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Tο shift the graph tο the right, we can simply add a pοsitive cοnstant tο the x values οf each pοint befοre plοtting them. Fοr example, if we want tο shift the graph tο the right by 2 units.

The intersectiοn οf twο number lines creates a twο-dimensiοnal plane knοwn as a cοοrdinate plane. The x-axis, a hοrizοntal number line, and the y-axis, a vertical number line, are twο examples οf these number lines.

Tο graph the equatiοn 5x - 3y = 18 οn a cοοrdinate plane, we can fοllοw these steps:

1. Sοlve fοr y in terms οf x:

5x - 3y = 18

-3y = -5x + 18

y = (5/3)x - 6

2. Chοοse sοme values fοr x and use the equatiοn tο find the cοrrespοnding y values. Fοr example, we can chοοse x = 0, 3, and 6:

When x = 0: y = (5/3)(0) - 6 = -6

When x = 3: y = (5/3)(3) - 6 = -3

When x = 6: y = (5/3)(6) - 6 = 2

3. Plοt the pοints (0, -6), (3, -3), and (6, 2) οn the cοοrdinate plane.

4. Draw a straight line passing thrοugh these three pοints. This line represents the graph οf the equatiοn 5x - 3y = 18.

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