alis teacher plotted the numbers 1/2 and 2/3 on the number line. She asked ali to find and plot a rational number between these two numbers in a number line, Can you help Ali in plotting a rational number between them on a number line?

Answer:

Mason's has 4 cars more.

no, it is still not the same ratio.

Step-by-step explanation:

each lot has 60 vans.

the ratio of cars/vans at Mason's is 7:5.

this means for every group of 5 vans there are 7 cars.

how many groups of 5 vans are there ? 60/5 = 12

so, for each of the 12 groups of 5 vans there are 7 cars.

=> 12×7=84

another way to get there (and faster) :

you can also say that a ratio is actually a division.

7:5 is 7/5

so, 60 × 7/5 = 12 × 7 = 84

in any case, Mason's has therefore 60 vans and 84 cars.

Hyland also has 60 vans, but a ratio of cars to vans of 4:3.

let's do the fast route :

60 × 4/3 = 20 × 4 = 80

Hyland has therefore 60 vans and 80 cars.

so, Mason's has more cars (4 more than Hyland).

now Hyland adds 2 vans, having then 62 vans and still 80 cars.

so, the ratio cars to vans is now 80:62. or 80/62

=> 80/62 = 40/31 which cannot be further simplified, as 31 is a prime number.

40/31 is not equal to 7/5. so, it is still not the same ratio.

Factor of the expression 18n - 30 using the greatest common factor of the terms is A 6(3n - 5)

Greatest common factor, as the name implies, is greatest among all common factors among the quantities given.

We can factorize the quantities in smallest relative factors possible (one level of factors over which all quantities can form themselves), and collect as many common factors as we could. Those will together compose GCF(Greatest common factor).

We are given that  the expression 18n - 30

WE need to find Factor of the expression 18n - 30 using the greatest common factor of the terms.

then;

18n - 30

18 = 6 x 3

30 = 6 x 5

Factor out the common part;

6(3n - 5)

Therefore, the correct option is A

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The fifth term of the arithmetic sequence is -1190.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. To find the fifth term, we can use the formula for the nth term of an arithmetic sequence:

aₙ = a₁ + (n - 1) * d

where aₙ represents the nth term, a₁ is the first term, n is the position of the term, and d is the common difference.

Given that the 100th term is -1240 and the common difference is -25, we can substitute these values into the formula.

Since the fifth term corresponds to n = 5, we can calculate:

a₅ = -1240 + (5 - 1) * (-25)

= -1240 + 4 * (-25)

= -1240 - 100

= -1340

Therefore, the fifth term of the arithmetic sequence is -1190.

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Answer:

\( - {( {x}^{2} - 6x)}^{ \frac{ - 1}{2} } - ( {x}^{2} - 6x) {}^{ \frac{ - 3}{2} } (x - 3)(5 - x) \\ \\ = {( {x}^{2} - 6x) }^{ \frac{ - 3}{2} } \{ {1 - ( {x}^{2} - 6x)}^{ \frac{1}{3} } (x - 3)(5 - x) \} \\ \\ \)

Answer:

-12?

Step-by-step explanation:

I think it might be that beacause 4 - 8 = -4 so then -4 x 3 = -12??? I am just guessing!!:)

Answer:

B

Step-by-step explanation:

r=√gm/v^2

Answer:

They will end up walk 6 miles

The transformations applied are: reflection about the x-axis, horizontal shift 10 units to the right, and vertical shift 400 units up.

A parabola is a symmetrical, U-shaped curve that can be formed by intersecting a plane with a cone. It is defined by the quadratic equation \(y = ax^2 + bx + c.\)

Solution:

To identify the transformations that have been applied to the graph of \(f(x) = x^2\)to produce the graph of \(g(x) = -5x^2 + 100x - 450\) we can start by looking at the standard form equation for a parabola:

\(y = a(x - h)^2 + k\)

where (h, k) is the vertex of the parabola and "a" determines the shape and direction of the parabola.

For\(f(x) = x^2\), we have a = 1, h = 0, and k = 0, so the vertex is at (0, 0).

For \(g(x) = -5x^2 + 100x - 450\), we can rewrite it as:

\(g(x) = -5(x^2 - 20x + 90)\)

Completing the square inside the parentheses, we get:

\(g(x) = -5(x - 10)^2 + 400\)

So the vertex of the parabola is (10, 400), and the "a" value is -5, which means the parabola is upside-down compared to\(f(x) = x^2.\)

Therefore, the transformations that have been applied to f(x) to obtain g(x) are:

1. The graph is reflected vertically (flipped upside-down) due to the negative "a" value.

2. The graph is shifted 10 units to the right and 400 units up, which corresponds to a horizontal translation of 10 units and a vertical translation of 400 units.

In summary, the transformations applied are: reflection about the x-axis, horizontal shift 10 units to the right, and vertical shift 400 units up.

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In the given diagram, the length of OQ is 11

From the question, we are to determine the length of OQ

From the given information,

OP = 17

QP = 6

In the diagram, we can observe that

OQ + QP = OP

∴ OQ + 6 = 17

Subtract 6 from both sides

OQ + 6 - 6 = 17 - 6

OQ = 11

Hence, the length of OQ is 11

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\(\huge \boxed{\sf 11}\\\\\\\displaystyle \sf OP=OQ+QP\\\\OQ=OP-QP\\\\OQ=17-6\\\\OQ=11\)

The 95% left-sided confidence interval for the true proportion of tall students is approximately 0.825.If 63% is a possible true percentage of tall Science students. Since 63% is outside the interval is NO.

To determine if any conditions are violated and calculate a confidence interval for the true proportion of tall students, the formula for a confidence interval for a proportion:

p ± Z × √((p× q ) / n)

Where:

P is the sample proportion (177/219)

q is the complement of the sample proportion (1 - p)

n is the sample size (219)

Z is the Z-score corresponding to the desired confidence level (95% left-sided corresponds to a Z-score of -1.645)

calculate the confidence interval:

p = 177/219 =0.807

q = 1 - p = 1 - 0.807 =0.193

n = 219

Z = -1.645

Confidence interval formula:

0.807 ± -1.645 ×√((0.807 × 0.193) / 219)

Calculating the confidence interval:

0.807 ± -1.645 × √(0.156051 / 219)

0.807 ± -1.645 × 0.010941

0.807 ± -0.017989

0.789 to 0.825 (rounded to three decimal places)

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Answer:

It's April

Step-by-step explanation:

Answer: B

April

Step-by-step explanation:

Answer:

x=8

Step-by-step explanation:

set up a proportion:

\(\frac{20}{4}=\frac{4x-7}{5}\)

simplify:

\(5 =\frac{4x-7}{5}\)

now solve this equation for x:

\(5 = \frac{4x-7}{5} \\25 = 4x - 7\\32 = 4x\\x = 8\)

The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.

The population proportion who participated in voting is given as 63% of all registered voters.

This means that out of every 100 registered voters, 63 participated in voting.

In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.

Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .

Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.

It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.

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The expressions with the options that will give 4^-12 are

The expression is an exponent of negative integer. The options are simplified further to their simplest forms as shown below

A. 4^-10 * 4^-2

The equation is multiplied to give a result of 4^-12

B. (1/4^-3)^4

= (4^3)^4

= 4^12

C. (4^-16)^4

= 4^(-16+4)

= 4^-12

D. 4^3 / 4^15

= 4^(3 - 15)

= 4^-12

E. (4^-7 * 4^-2) / 4^3

= 4^(-7 + (-2) + 3)

= 4^6

Hence the expression that will result to 4^-12 are A, C, and D

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Shryia was reading at a speed of 524.67 pages per hour, and it took her approximately 917.06 hours to read the entire book.

To find Shryia's reading speed, we can use the formula:

\(reading speed = (total pages - pages left) / time\)

We are given that the book has 481481481 pages, and after reading for 1.5 1.51, point, 5 hours, Shryia had 403403403 pages left to read. So, the total number of pages she read is:

481 - 403 = 787

The time taken to read these pages is:

1.5 hours

So, her reading speed is:

reading speed = 787 / 1.5 = 524.67 pages per hour

To find how long it took her to read the entire book, we can use the formula:

time = total pages / reading speed

So, the time taken to read the entire book is:

time = 481481481 / 524.67 ≈ 917.06 hours

Therefore, Shryia was reading at a speed of 524.67 pages per hour, and it took her approximately 917.06 hours to read the entire book.

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To project the life expectancy of men born in this community in 2020, plug x = 60 (since 2020 is 60 years after 1960) into your linear function E(x). Calculate the value of E(60) to find the projected life expectancy in years

To answer your question about male life expectancy in a certain community, I will break down the solution into three parts as requested:
a. To create a scatter plot, first note down the data points. Let x represent the number of birth years after 1960 and y represent male life expectancy. The six selected years are: 1960, 1967, 1971, 1969, 1971, and 1975. Their respective life expectancies are 66, 67, 69.6, 71.2, 73.9, and 75.4. Plot these points on a rectangular coordinate system.
b. To draw a line through the two points for 1980 and 2000, find the coordinates of these points first. For 1980, x = 20 (since it's 20 years after 1960) and for 2000, x = 40. Use the scatter plot to find the corresponding life expectancies (y values) for these points. Next, choose the correct graph that shows the line passing through these two points.
c. To write a linear function, E(x), that models life expectancy for men born in this community x years after 1960, use the coordinates of the two points for 1980 and 2000. Find the slope, m, by using the formula (y2 - y1) / (x2 - x1) and then find the y-intercept, b, by substituting one of the points' coordinates into the equation y = mx + b. Your function will be in the form E(x) = mx + b.
Finally, to project the life expectancy of men born in this community in 2020, plug x = 60 (since 2020 is 60 years after 1960) into your linear function E(x). Calculate the value of E(60) to find the projected life expectancy in years.

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Step-by-step explanation:

URGENTLY!!

higher mathematics

Solve the system of equations by Cramer's method.

For the correct execution of the task I give 25 points!

Answer:

5/4 cups of flour

Step-by-step explanation:

3/4+1/2 = 1 1/4 or 5/4

Answer:

240

Step-by-step explanation:

If u take 244-4 then u get 240 but it isn't always the case of inverse...

The equation of the parabola is y = 2(x - 1)² + 3

From the question, we have the following parameters that can be used in our computation:

Vertex = (1. 3)

Point = (2, 5)

These parameters can be expressed as

(h, k) = (1, 3)

(x, y) = (2. 5)

A parabola can be represented as

y = a(x - h)² + k

Substitute the known values in the above equation, so, we have the following representation

y = a(x - 1)² + 3

Next, we have

5 = a(2 - 1)² + 3

Evaluate the difference and the exponent

5 = a + 3

So, we have

a = 2

Substitute a = 2 in y = a(x - 1)² + 3

y = 2(x - 1)² + 3

Hence, the equation is y = 2(x - 1)² + 3

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Answer:

The value of x is 30.

We have to find the value of x in the given equation.  

Using distributive property  

We have,

\(1/2(x+6)=18\\a.(b+c)=a.b+a.c\\1/2(x+3)=18\\1/2x=15\\x=3\)

other are also solve by this methode;)

The required solution of the expression \(1/2(x+6) = 18\) is 30.

To solve the equation using the distributive property and properties of equality. One-half (x + 6) = 18 and value of x to be determined.

The equation is the well-organized link of the variables of two expressions that contain equal between them.

distributive properties are used to evaluate the math problem easily by distributing numbers to the numbers present in parenthesis. eg, if we apply the distributive property of multiplication to solve the expression
a( b + c ) = a.b + a.c

\(1/2(x+6) = 18\)
Using distributive property a( b + c ) = a.b + a.c

\(1/2.x+1/2*6 = 18\\1/2x+3=18\\1/2x=18-3\\1/2x=15\\x=2*15\\x=30\\\)

Thus, The required solution of the expression \(1/2(x+6) = 18\) is 30.

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The container that holds the largest amount of soil is Container C. So option b is the correct answer.

To determine which container holds the largest amount of soil, we need to calculate the volume of each container using the formulas for volume.

The formulas for volume are as follows:

Volume of a rectangular prism: V_rectangular_prism = length * width * height

Volume of a cylinder: V_cylinder = π * radius² * height

Let's calculate the volume of each container:

Container A:

Volume of Container A = length * width * height

= 2 ft * 2 ft * 3.5 ft

= 14 ft³

Container B:

Volume of Container B = π * radius² * height

= π * (1.5 ft)² * 2.5 ft

= 11.78 ft^3

Container C:

Volume of Container C = π * radius² * height

= π * (2 ft)² * 1.5 ft

≈ 18.85 ft³

Comparing the volumes of the three containers, we can see that:

Container A has a volume of 14 ft³.

Container B has a volume of approximately 11.78 ft³.

Container C has a volume of approximately 18.85 ft³.

Therefore, the container that holds the largest amount of soil is Container C. Hence, the correct answer is b) Container C.

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Yes, the set of all solutions of a system of m homogeneous equations in n unknowns is a subspace of \($\mathbb{R}^n$.\)

A subspace is a set of vectors that is closed under linear combinations. This means that if two vectors in the set are added together, the result is also in the set. A system of m homogeneous equations in n unknowns can be represented as a system of linear equations. The solution set of the system is the set of all vectors that satisfy the linear equations. Since the solution set is closed under addition, it is a subspace of \($\mathbb{R}^n$\)Furthermore, any linear combination of two solutions of the system is also a solution of the system, which further confirms that the solution set is a subspace of \($\mathbb{R}^n$\)

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If 150 town residents were asked about their age and yogurt , then the probability that a randomly selected customer prefers Swirl if age is at least 25 years old is 0.66 .

let X be = the selected customer that prefers swirled yogurt or is at least 25 years old ;

The sum of all the customers that are "at least 25 years old" = 21 + 30 + 24 = 75 ;

the sum of all the customers that " like Swirl Yogurt" is = 24 + 24 = 48 ;

the total number of residents = 150 students ;

So , the probability is calculated as : ( 75+48 -24)/150 = 0.66 .

Therefore , the required probability is 0.66 .

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The given question is incomplete , the complete question is

The 150 residents of the town of wonderland were asked their age and whether they preferred vanilla, chocolate, or swirled frozen yogurt. the results are displayed next.

     Age                               Chocolate      Vanilla      Swirl

under 25 years old                  22                 29             24

at least 25 years old                21                  30             24

What is the probability a randomly selected customer prefers Swirl Yogurt given he or she is at least 25 years old ?

The valid way to reduce overfitting in CART (Classification and Regression Trees) is option a. Pruning and early stopping. Therefore, the correct answer is option a. Pruning and early stopping.

Pruning is a technique used in CART to reduce overfitting by trimming the branches of the decision tree. It involves removing or collapsing nodes in the tree that do not contribute significantly to the overall accuracy of the model. By pruning the tree, we can prevent it from becoming too complex and overly fitting the training data, which improves its ability to generalize to unseen data.

Early stopping is another technique used to prevent overfitting. It involves stopping the tree-building process before it reaches its maximum depth or complexity. By stopping the growth of the tree early, we can avoid capturing noise or irrelevant patterns in the data, which can lead to overfitting. Option b (reducing the training data) and option c (reducing the number of features) can be valid strategies in some cases, as they can help reduce the complexity of the model and prevent overfitting. However, option a (pruning and early stopping) is specifically associated with CART and is a more direct and common approach to address overfitting in decision trees. Option d (increasing the depth of the tree) is not a valid way to reduce overfitting. Increasing the depth of the tree can lead to more complex and detailed splits, which may exacerbate overfitting by capturing noise or specific patterns in the training data that do not generalize well.

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well, let's take a look at the tickmarks on the triangle, the tickmarks mean that AC = CB, both AC and CB stemming out of vertex C, and both twin sides will make twin angles at the "base" or namely ∡A = ∡B, that means that 34 = x - 5, let's also recall that the sum of all interior angles in a triangle is 180°, so

\(34=x-5\implies \boxed{39=x} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\measuredangle A}{34}~~ + ~~\stackrel{\measuredangle B}{34}~~ + ~~\stackrel{\measuredangle C}{4y}~~ = ~~180\implies 68+4y=180 \\\\\\ 4y=112\implies y=\cfrac{112}{4}\implies \boxed{y=28}\)

Answer:

y = 28

Step-by-step explanation:

The dashes on line segments AC and BC indicate that the line segments are equal in length.

Therefore, as the triangle has two sides of equal length, it is an isosceles triangle.

The base angles of an isosceles triangle are equal, therefore ∠A = ∠B.

Interior angles of a triangle sum to 180°.  

Therefore:

⇒ ∠A + ∠B + ∠C = 180°

⇒ 34° + 34° + 4y° = 180°

⇒ 68° + 4y° = 180°

⇒ 4y° = 112°

⇒ y = 112° ÷ 4°

⇒ y = 28

Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

--------------------------------------------------------

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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The required line representing the equation part of the constraint is go through (0, 4) and (7,0).

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

The line representing the equation 7x1 + 4x2 = 28 is a boundary line that separates the feasible solutions from the infeasible solutions in a linear programming problem.

The line passes through two points, which can be determined by substituting the x1 and x2 values into the equation. By substituting the values (4,0) and (7,0) into the equation, we can see that both points satisfy the constraint.

This means that any point on the line also satisfies the constraint, and any point above or to the right of the line would be infeasible as they would not meet the requirement of the constraint.

Understanding the position and shape of the constraint lines is important in solving linear programming problems and finding the optimal solution.

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Answer:

A

Step-by-step explanation:

They are paid a fix rate for each item produced or action performed