seven cars need to pass across a bridge that is wide enough to allow four cars. in how many orders seven cars can form groups of four to pass across the bridge?

Answer:

it is b y=7 done okays hope you like it

Answer:
B, y = 7.

Step-by-step explanation:
If 6y = 42, then all we have to do is divide both sides by 6.

Therefore,
y = 42/6
y = 7.

The variable "Points scored in a football game" , is a numerical variable, specifically a discrete variable.

The Discrete Numerical Variables represent counts or whole numbers, such as the number of students in a class or the number of items sold in a store.

The Continuous Numerical Variables represent measurements, such as height, weight, or time, and can take on any value within a range.

In this case, the variable represents the number of points scored in a game, and it can only take on specific integer values (for example, 0, 1, 2, etc.) and cannot take on fractional or decimal values.

The given question is incomplete , the complete question is

State whether the Variable is Categorical or Numerical ?

If the variable is numerical, then specify whether the variable is discrete or continuous.

(a) Points scored in a football game .

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There were 34 mosquitoes on 2 June, the date when the mosquito population is 46000 is 22985 days into June and  the mosquito population on 30 June was 59.

Two or more expressions with an Equal sign is called as Equation.

For 0 ≤ t ≤ 10:

N = 2t + 30 for 0 ≤ t ≤ 10.

The table of values are:

t   0    1    2   3   4   5    

N 30 32 34 36 38 40

The graph will be a line with a positive slope, increasing from N = 30 when t = 0 to N = 50 when t = 10.

The number of mosquitoes on 2 June can be found by using t = 2 in the formula.

N = 2(2) + 30 = 34.

So there were 34 mosquitoes on 2 June.

(ii) To find the date when the mosquito population is 46 000, we can use the formula and solve for t.

N = 2t + 30

46000= 2t + 30

Subtract 30 on both sides

2t =  45970

t=22985

So the date when the mosquito population is 46000 is 22985 days into June.

iii) To find the mosquito population at the end of June, we need to find the population on 10 June and then increase it by 18%.

The population on 10 June can be found by using t = 10 in the formula:

N = 2(10) + 30 = 50

The graph will be a line with a positive slope, increasing from N = 30 when t = 0 to N = 50 when t = 10.

N = 50 (1 + 0.18)

N=59

So the mosquito population on 30 June was 59.

Hence,  there were 34 mosquitoes on 2 June, the date when the mosquito population is 46000 is 22985 days into June and  the mosquito population on 30 June was 59.

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The total interest charger after 20 years for the balloon mortgage would be = $170,500

Simple interest is defined as the extra amount of money that is being paid to an individual following an amount of money that was invested for a stated period of time.

The formula for simple interest= P×T×R/100

The principal amount for the mortgage = 275,000

The time for the mortgage = 20 years

The rate = 3.1%

Therefore interest generated;

= 275,000×3.1×20/100

= 17050000/100

= $170,500

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The measure of the angles numbered 1 and 2 in the figure of the kite are;

m∠1 = 90°

m∠2  = 72°

A kite is a quadrilateral that has consecutive congruent sides and perpendicular diagonals. A kite has a reflection symmetry across one of the diagonals.

The specified quadrilateral in the figure has a reflection symmetry about the horizontal diagonal,  the figure is therefore a kite

The diagonals of a kite are perpendicular, therefore, the measure of the angle ∠1, by the definition of perpendicular lines, is 90°

m∠1 = 90°

The base angles in the 90° clockwise rotated isosceles triangle are the same
The angle on the other side of the horizontal diagonal at the right vertex is also 18°

The measure of the angle ∠2 is therefore;

m∠2 = (180° - 2 × 18°)/2 = 72°

m∠2 = 72°

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The standard deviation of x is 3 cars. So the option A is correct.

Suppose that x is the number of cars per minute that pass through a certain intersection, and that x has the Poisson distribution.

If the mean of x is equal to 9 cars, then we have to determine the standard deviation of x.

An indicator of how much variance from the mean there is is the standard deviation, which can be expressed as spread, dispersion, or spread. A "typical" departure from the mean is represented by the standard deviation. As a result of returning to the data set's original units of measure, it is a well-liked measure of variability.

The Mean = 9 cars

Standard Deviation = Square Root of Mean

Standard Deviation = √9

Standard Deviation = 3 cars

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The required quarts of frozen yogurt made in 36 hours as per the given information is equal to 720 quarts.

Quarts of frozen yogurt made by factory is equal to 100 quarts

Time required to make 100 quarts of frozen yogurt is equal to 5 hours

Let 'x' quarts of frozen yogurt made in 36 hours

5 hours = 100 quarts of frozen yogurt

⇒ 1hour = ( 100 / 5 ) quarts of frozen yogurt

⇒ 36 hours =  ( 100 / 5 ) × ( 36 ) quarts of frozen yogurt

⇒ 36 hours =  ( 20 ) × ( 36 ) quarts of frozen yogurt

⇒ 36 hours =  ( 720 ) quarts of frozen yogurt

Therefore, the quarts of frozen yogurt made in 36 hours is equal to 720 quarts.

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The conclusion is that there is sufficient evidence at the 0.01 level to support the mayor's claim that under 62% of the residents favor construction of the bridge.

The mayor rejects the null hypothesis at the 0.01 level, which means that the results from the hypothesis test show that the actual proportion of residents who favor construction is less than 62%. The alternative hypothesis would be that the true proportion is less than 62%. After gathering information from 110 voters, the results of the hypothesis test were used to make a decision on whether to reject or fail to reject the null hypothesis. If the hypothesis test showed that the null hypothesis could be rejected at the 0.01 level, it means that there was sufficient evidence to support the mayor's claim that less than 62% of the residents favor the bridge construction. However, it's important to note that hypothesis testing is not a perfect method and other factors such as sample size and sampling method should also be considered when interpreting the results.

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1. Yes 2. no 3. no 4. yes

1. -.5g + 2.5

2. .5g - 2.5

3. -.5g - 2.5

4. -.5g + 2.5

To find the average, one adds up all the scores and then divides by the total number of scores.

Joan had to find the average of the scores of her friends. To find the average, one adds up all the scores and then divides by the total number of scores. In this case, Joan had to find the sum of 10 different scores of her friends and then divide by 10. This will give her the average of the scores of her friends, which is a single value representing the central tendency of the scores. The average is a commonly used statistical measure that provides an overall idea of the data. In this case, the average of the scores of Joan's friends will give her an idea of the overall performance of her friends in the test she is preparing for.

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The given example of a high school student regarding video game playing is quantitative data collection.

Quantitative data can be measured or counted. The high school student in this example is compiling numerical information about how much time each member of their homeroom class spends playing video games.

The student can first add up the total number of hours each person spends playing video games each week in order to determine the average number of hours spent playing video games each week.

The student can then divide the total number of hours spent playing video games by the number of students in their homeroom class to determine the weekly average.

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Answer:

Step-by-step explanation:The given equations are :

y=-x+2  ....(1)

y = -4x +7 ....(2)

From equation (1) and (2)

-x+2 = -4x +7

Taking like terms together

-x+4x=7-2

3x = 5

x = 1.667

Put the value of x in equation (1)

y=-(1.667)+2

y = 0.333

The solution of the equations are (1.667,0.333). The attached figure shows the graph for the equations.

Step-by-step explanation: The given equations are : y=-x+2 ....(1) y - 1

The solution of the given expression (0.4k^3)^3 can be simplified as :0.064K^9.

The concept that will be used is simpilification. To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. Be aware of the workflow. You can't just multiply, add, subtract, and so on in a straight line when simplifying math formulas.

The given expression is (0.4k^3)^3

This can be simplify as :

(0.4)^3 *(k^3)^3

This can be further simplified by finding the cubing the terms involved which can be done as :

0.064K^9

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The normal probability plot can reveal information about the population from which the data were drawn. A straight line pattern indicates normality, whereas deviations from the straight line indicate non-normality.

A normal probability plot is a graphical method for determining whether a set of data values is normally distributed. The plot depicts sample data values on the y-axis and theoretical normal deviate values on the x-axis.

If the plotted points follow a roughly straight line, the population is likely to be normally distributed. If the points plotted deviate significantly from a straight line, the population is not normally distributed.

As a result, the shape of the normal probability plot can provide insight into the normality of the population from which the data were drawn. A straight line pattern indicates that the distribution is normal, whereas deviations from the straight line indicate non-normality.

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The values of the function when x = -2 and when = 4 are,

⇒ g (-2) = 0

⇒ g (4) = - 4

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

We have to given that;

The function is,

⇒ g (x) = 6 ; - 8 ≤ x < - 2

           = 0 ; - 2 ≤ x ≤ 4

           = - 4 ; 4 ≤ x ≤ 10

Now, The value of function are,

At x = - 2;

⇒ g (x) =  6 ; - 8 ≤ x < - 2

           = 0 ; - 2 ≤ x ≤ 4

           = - 4 ; 4 ≤ x ≤ 10

⇒ g (- 2) = 0

At x = 4;

⇒ g (x) =  6 ; - 8 ≤ x < - 2

           = 0 ; - 2 ≤ x < 4

           = - 4 ; 4 ≤ x ≤ 10

⇒ g (4) = - 4

Thus, The values of the function when x = -2 and when = 4 are,

⇒ g (-2) = 0

⇒ g (4) = - 4

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Answer:

you take the perimeter and subtract 2*the length. Then you divide that answer by 2

Step-by-step explanation:

This is because a rectangle is made up of 2 pairs of heights. 2 equal sides represent the height and 2 equal sides represent the width.

When we subtract the lengths of the 2 sides that represent the height we get a number that we then have to divide by 2 to get the width of the triangle.

Hope this helps. It's a little difficult to explain but the answer is correct :)

The sample of 100 students is a simple random sample (SRS) of the population of all students, and it provides evidence about the proportion of students who completed their assigned homework last week.

The sample proportion of students who completed their assigned homework is calculated as the number of students in the sample who completed their homework divided by the total number of students in the sample.

If the sample proportion is less than 60%, then this is evidence that less than 60% of all students completed their assigned homework last week. However, it is important to keep in mind that the sample proportion is just an estimate of the population proportion, and it may not be exactly equal to the population proportion. The sample proportion can vary from sample to sample due to random sampling error.

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By critically observing the triangular prism shown in the image attached above, the base shape of this triangular prism is a:

C) triangle.

A triangular prism can be defined as a geometric shape (figure) with five (5) faces in total. Generally, a triangular prism comprises two (2) triangular bases and three (3) rectangular lateral faces.

Now, By critically observing the triangular prism, we can logically deduce that the base shape of this prism is a triangle.

Hence, A triangular prism has five faces in total.

There are two triangular bases and three rectangular lateral faces. Few examples of triangular prism are - a camping tent, Toblerone chocolate shape. The base of a prism is also a face.

In conclusion, the base shape of this triangular prism is a triangle.

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The direct variation equation in the form x and y is y = 7.25x

As per the given data, the cost of renting a scooter y varies directly with the number of hours the scooter is rented x.

Suppose it costs $21.75 to rent the scooter for 3 hours.

Here we have to determine a direct variation equation in the form of y.

The renting cost (y) is directly proportional to the hours (x).

y ∝ x

y = kx.....(1)

Here k is known for the proportionality constant

From the given information we can find the value of k.

21.75 = k (3)

k = [tex]$\frac{21.75}{3}[/tex]

k = 7.25

Now we have to substitute the value of k in the equation (1)

We get:

y = 7.25x

Therefore a direct variation equation is y = 7.25x.

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The slope of these lines are:

Slope can be calcualted by comparing the change in y-axis with the change in x-axis. Then, let's discuss every lines we have:

1. We take 2 points: (3, 1) and (-2, -1)

m = y₂ - y₁

      x₂ - x₁

m = -1 - 1

      -2 - 3

m = - 2/ -5

m = 2/5

2. We take 2 points: (2, 2) and (-3, -3)

m = y₂ - y₁

      x₂ - x₁

m = -3 - 2

     -3 - 2

m = -5/-5

m = 1

3. We take 2 points: (1, 3) and (-1, -2)

m = y₂ - y₁

      x₂ - x₁

m = -2 - 3

      -1 - 1

m = -5 / -2

m = 5/2

4. We take 2 points:  (1, 0) and (-1, -2)

m = y₂ - y₁

      x₂ - x₁

m = (-2 - 0) / (-1 - 1)

m = -2/-2 = 1

We subtitute one point: (1, 0)

y = mx + c

0 = 1 (1) + c

c = -1 --> y = x - 1

5. We take 2 points:  (3, -1) and (-2, -2)

m = y₂ - y₁

      x₂ - x₁

m = -2 - (-1)

      -2 - 3

m = -1 / -5 = 1/5

We subtitute one point: (3, -1)

y = mx + c

-1 = 1/5 (3) + c

-5/5 = 3/5 + c

c = -8/5 --> y = 1/5 x - 8/5

6. We take 2 points: (2, -1) and (-1, 3)

m = y₂ - y₁

      x₂ - x₁

m = (3 - (-1)) / (-1 - 2)

m = 4/(-3)

m = - 4/3

We subtitute one point: (2, -1)

y = mx + c

-1 = - 4/3 (2) + c

-3/3 = -8/3 + c

c =5/3 --> y = -4/3 x + 5/3

7. m = Δy / Δx

m = 8/24

m = 1/3

8. m = Δy / Δx

m = 100/1000

m = 1/10

9. (1, 3) and (4, 7)

m = y₂ - y₁

      x₂ - x₁

m = (7 - 3) / (4 - 1)

m = 4/3

10. (3, 5) and (2, 6)

m = y₂ - y₁

      x₂ - x₁

m = (6 - 5) / (2 - 3)

m = 1 / (-1) = -1

11. (4, 0) and (5, 5)

m = y₂ - y₁

      x₂ - x₁

m = (5 - 0) / (5 - 4)

m = 5/1 = 5

Please refer to the graphs attached below for the graph number 4, 5, and 6.

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A) (i) (1, 5) is possible solution of equation.

(ii) (-2, 0) is not possible solution of equation.

B)  Solution of graph 1);

⇒ (- 2, - 2)

And, Solution of graph 2);

⇒ (4, 1)

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

A) Substitute the given coordinate in system of equation and check it is solution or not as;

1) System of equation are,

⇒ - 5m + 6n = 25

⇒ - 7m + 8n = 33

Coordinate = (1, 5) = (m, n)

Substitute in equations;

⇒ - 5m + 6n = 25

⇒ - 5 (1) + 6(5) = 25

⇒ - 5 + 30 = 25

⇒ 25 = 25

⇒ - 7m + 8n = 33

⇒ - 7(1) + 8(5) = 33

⇒ - 7 + 40 = 33

⇒ 33 = 33

Thus, (1, 5) is possible solution of equation.

2) System of equation are,

⇒ 8x - 3y = - 16

⇒ - 9x - 2y = 50

Coordinate = (- 2, 0) = (x, y)

Substitute in equations;

⇒ 8x - 3y = - 16

⇒ 8(-2) - 3(0) = - 16

⇒ - 16 = - 16

⇒ - 9x - 2y = 50

⇒ - 9(-2) - 2(0) = 50

⇒ 18 ≠ 50

Thus, (-2, 0) is not possible solution of equation.

B) The solution of graph of lines are intersection point of both lines.

Hence, Solution of graph 1);

⇒ (- 2, - 2)

And, Solution of graph 2);

⇒ (4, 1)

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The type of sample is a Simple Random Sample.

Hence, option (C) is correct choice.

Simple random sampling is a form of probability sampling in which a selection of participants is chosen at random from a population. Each person in the population has an equal probability of getting chosen.

Using basic random sampling allows researchers to generalise about a certain demographic while eliminating bias. Inferences and predictions about the population can be formed using statistical techniques without having to survey or gather data from every individual in that population.

A Simple Random Sample is a sort of random sample in which every member of the population has an equal probability of being chosen. In this situation, every one of the 40 students has an equal chance of being chosen, making this a simple random sample.

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Answer: 90

Step-by-step explanation:

The number that you need to find because it is missing in the equation is 48.

Let's assume the number we're trying to find is "x."

According to the problem, one-third of the number is (1/3)x, and one-fourth of the number is (1/4)x.

We're told that the sum of one-third of the number and one-fourth of the number is 28, so we can write the equation as follows:

(1/3)x + (1/4)x = 28

To solve this equation, we need to find a common denominator. The least common multiple of 3 and 4 is 12, so we can rewrite the equation as:

(4/12)x + (3/12)x = 28

Combining the fractions, we get:

(7/12)x = 28

To isolate x, we multiply both sides of the equation by the reciprocal of (7/12), which is (12/7):

x = 28(12/7)

Simplifying the right side of the equation, we have:

x = 48

Therefore, the number we're looking for is 48.

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Answer: D. 121.5

Step-by-step explanation: Use the formula [tex]\frac{4}{3}[/tex]×[tex]r^{3}[/tex], (where r is the radius, as in this case the diameter is 9 so divide that by 2 and you get the radius) and the "unit" is π. Search math w ay on the internet for any further math questions. :)

The correlation coefficient with the correct association is listed as:

-0.86  = 1

-0.66 = 1

-0.01 = 2

0.52 = 3

0.93 = 1

Correlation is a statistical measure that describes the extent to which two variables are linearly related to each other.

A negative correlation is when two variables move opposite each other i.e. when one variable increases, the other decreases

For  absolute values of the correlation coefficient:

0-0.19 => very weak

0.2-0.39 => weak

0.40-0.59 => moderate

0.6-0.79 => strong

0.8-1 => very strong

Thus, the matching is listed below:

-0.86  = strong

-0.66 = strong

-0.01 = weak

0.52 = moderate

0.93 = strong

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the greatest distance the dog can be from the origin is 15 feet.

A Cartesian plane (named after French mathematician Rene Descartes, who formalized its use in mathematics) is defined by two perpendicular number lines: the x-axis, which is horizontal, and the y-axis, which is vertical. Using these axes, we can describe any point in the plane using an ordered pair of numbers.

Well first we have to find the distance from the origin to the point (4,3). Now to do this we use the distance formula. I didn't want to type this out so i found a picture.

Now the origin point is (0,0) So now we have two points we can plug in to find the difference between them. Now the X1 and X2 as well as y1 and y2 are interchangeable within their brackets.

So D= [tex]\sqrt{(4)^{2} } + (3^{2} )[/tex] Which means D= the square root of 25 which is 5. This means the distance from the origin to (4,3) is 5 feet. Now the dog can go 10 more feet in the opposite direction of the origin so 5 + 10 (pretty easy math) = 15. The dog can be (at its farthest) 15 feet from the origin.

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At present, Tyrone is 48 years old and his daughter is 24 years old.

Let's start by using variables to represent the ages of Tyrone and his daughter.

Let T be Tyrone's current age and D be his daughter's current age.

We know that Tyrone is twice as old as his daughter, so we can write:

T = 2D

We also know that in 6 years, Tyrone's age will be three times what his daughter's age was six years ago. Six years ago, Tyrone's age was T - 6 and his daughter's age was D - 6. So we can write:

T + 6 = 3(D - 6)

Now we have two equations with two variables, so we can solve for T and D.

First, substitute T = 2D from the first equation into the second equation:

2D + 6 = 3(D - 6)

Simplifying this equation, we get:

2D + 6 = 3D - 18

Add 18 to both sides:

2D + 24 = 3D

Subtract 2D from both sides:

24 = D

So Tyrone's daughter is 24 years old now.

We can use the first equation to find Tyrone's age:

T = 2D = 2(24) = 48

Therefore, Tyrone is 48 years old now.

So at present, Tyrone is 48 years old and his daughter is 24 years old.

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Tyrone is twice as old as his daughter. in 6 years Tyrone's age will be three times what his daughters age was six years ago. how old will they be at present?

Check the picture below.

so the triangle with the 35° angle is an isosceles, namely a triangle with twin sides stemming from the center of the circle, well, twin sides make twin angles, and since the center of the circle makes a central angle, well, any arc will get its degrees from that.

Let's call the two-digit number "x" and its two digits "a" and "b".

We know that:

x = 5 * (a + b)

We also know that the reverse of x is 9 times greater than x:

x + 9 * x = 100 * a + 10 * b

Expanding x using the first equation:

10 * x = 5 * (a + b) + 9 * 5 * (a + b) = 100 * a + 10 * b

Combining like terms:

10 * x = 100 * a + 10 * b

Solving for x:

x = 10 * a + b

Since x is a two-digit number, 10 * a + b must be between 10 and 99. The only solution that meets this requirement is a = 5 and b = 6. Therefore, the number is 56.

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