Find the area of each triangle. Round to the nearest tenth.

Answer:

122 people

Step-by-step explanation:

Let's call the number of people in a vehicle "x".

From the information given, we can set up two equations to represent the relationship between the number of people and the entrance fee:

2 people: 14 = fee

x people: fee = 14x/2

4 people: 20 = fee

x people: fee = 20x/4

8 people: 32 = fee

x people: fee = 32x/8

Using the information for the bus, we can set up another equation:

x people: fee = 122

Solving for x in each equation and equating the results, we can find the number of people in the bus:

x = 14x/2

x = 20x/4

x = 32x/8

x = 122

Cross multiplying and simplifying, we find:

x = 122

Therefore, the bus contains 122 people.

The vector shown in figure is, (- 2, 1 , - 4)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The graph of the vectors is shown below.

Now, By definition of vectors the sign of coordinates are, ( - , + , - )

Thus, By options the coordinate of vectors are,

⇒ (- 2, 1 , - 4)

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Therefore , the solution of the given problem of graph comes out to be x value is  √2.

Scholars use graphs to visually represent or chart facts or values in a logical way. Usually, a graph point will show the relationship of two or more objects. A graph is a non-linear storage structure made up of nodes, also known as vertices, and edges. The nodes, sometimes referred to as vertices, should be joined with glue. Vertices in this graph are 1, 2, 3, and 5, whereas edges are 1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Graphical depictions of exponential development in statistical charts.

Here,

Given :

=> y =x² -2

To find the value of x :

at y = 0

So,

=> 0 = x² -2

=>x² =2

=>x = √2

Thus, x value is  √2.

Therefore , the solution of the given problem of graph comes out to be x value is  √2.

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The time that it will take until Noah and Andre meet is; 2.5 hours

Let t represent the time it would take for Noah and Andre to meet.

Formula to find distance is;

Distance = speed × time

Noah rides at a constant speed of 4 miles per hour. This tells us that the distance that Noah would cover in t hours is expressed as 4t.

Andre rides at a constant speed of 2 miles per hour. This tells us that the distance that Andre would cover in t hours is 2t

Since the total distance is 15 miles, then we can form the equation as;

4t + 2t = 15

6t = 15

t = 15/6

t = 2.5 hours

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Inequality shown is -3 ≤ x < 2.

Inequality refers to a relationship that makes a non-equal comparison between two numbers or other mathematical expressions.

Given,

Graph of inequality

Line drawn on the number line between circle on -3 and circle on 2.

Here, -3 < 2

If x is the variable, it is between -3 and 2

then, -3 < x < 2

The circle on -3 is filled which means value of x can be equal to -3

then inequality becomes,

-3 ≤ x < 2

Hence, -3 ≤ x < 2 is the inequality shown on the number line.

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By solving a system of equations we will see that:

x = 39

y = 123

First, we know that the sum of the 3 angles on the bottom part should be equal to 180°, then we can write:

(x - 10) + y + (x - 11) = 180

And the angle on the top is a vertical angle to the one that measures y degrees, then:

3x + 6 = y

So we have a little system of equations:

(x - 10) + y + (x - 11) = 180

3x + 6 = y

Replacing the second equation into the first one, we get:

(x - 10) + (3x + 6) + (x - 11) = 180

5x - 15 = 180

5x = 180 + 15

x = 195/5

x = 39

And the value of y is:

3*39 + 6 = y

123 = y

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The required set of numbers includes is given as {-3, -2, 2, 3}. Option B is correct.

Sets are an orderly collection of items in mathematics that can be expressed in set-builder or roster form.

Here,
Integers are whole numbers, both positive and negative, including zero. For example -4, -3, -2, -1, 0, 1, 2, 3, 4, etc. They are used to represent whole quantities and are a basic type of number in mathematics.

Thus, from the options set of numbers includes is given as {-3, -2, 2, 3}. Option B is correct.

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The x‐intercept is x = −5, and the graph approaches a vertical asymptote at x = −6. Then the correct option is A.

The collection includes all locations on the surface of the shape (x, f(x)) that make up a function of f's graph. We may alternatively say that the graph of f is the curve of y = f. (x). As a result, the diagram of an equation is a particular instance of the graphs of functions.

The x-intercept is at (-5, 0). Then the value of the abscissa is given as,

x = -5

The graph begins in the third quadrant near the line x = - 6. Then the equation x = - 6 represents the asymptote.

The x‐intercept is x = −5, and the graph approaches a vertical asymptote at x = −6. Then the correct option is A.

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Answer:

Step-by-step explanation:

11/3- 6/7 = (77-18)/21

= 59/21

The value of distance cover is, 1/4 miles.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

Driving speed = (s - 4) / (s²-9s+20)

And, Time = (s - 5) / 4

Now, We know that;

⇒ Speed = Distance / Time

⇒ Distance = Speed × Time

Substitute the given values, we get;

⇒ Distance = (s - 4) / (s² - 9s + 20) × (s - 5) / 4

⇒ Distance = (s - 4) / (s² - 5s - 4s + 20) × (s - 5) / 4

⇒ Distance = (s - 4) / (s (s - 5) - 4 (s - 5)) × (s - 5) / 4

⇒ Distance = (s - 4) / (s - 4) (s - 5) × (s - 5) / 4

⇒ Distance = 1/4 miles

Thus, The value of distance cover is, 1/4 miles.

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The time it will take Juan and Laura to meet each other is 25.88seconds

Velocity is the rate of change of velocity with time. It is a vector quantity and it is measured in meter per second. It can also be measured in Mikes per hour and so on.

Velocity = displacement /time

displacement = velocity × time

The total distance traveled = 220feet

220 = v1t + v2t

220 = (v1+v2) t

220 = ( 3.5 + 5) t

220 = 8.5 t

divide both sides by 8.5

220/8.5 = t

t = 25.88 seconds

therefore it will take Juan and Laura 25.88 seconds to meet each other

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Make that the target variable is in the numerator, not the denominator, of the rearrangement.

Variable

A variable is a placeholder sign for a varying quantity or other mathematical entity.

Move all other variables to the other side of the equation by applying the opposite function to them, keeping in mind to carry out that operation on both sides of the equation, in order to isolate a single variable when rearranging equations. Make that the target variable is in the numerator, not the denominator, of the rearrangement.

Move all other variables to the other side of the equation by applying the opposite function to them, keeping in mind to carry out that operation on both sides of the equation, in order to isolate a single variable when rearranging equations. Make that the target variable is in the numerator, not the denominator, of the rearrangement.

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A an acute triangle

because all angles are less than 90

Answer: Acute Triangle

Step-by-step explanation:

Using the greatest common factor (GCF), to simplify the expression we have: 5(-4a + 2b - 3)

A common factor is either a number or term that is a common denominator to two or more given expressions. Thus can be used to simplify a given expression by factorization.

To factor the simplified expression, we have:

10a + 5b + 3 - 25a + 2b - 18 + 3b - 5a

collect like terms

10a - 25a - 5a + 2b  + 5b + 3b + 3  - 18 = -20a + 10b - 15

So that the positive greatest common factor (GCF) of the simplified expression is 5.

-20a + 10b - 15 = 5(-4a + 2b - 3)

The required answer is 5(-4a + 2b - 3).

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The correct answer is option C. The system has a nontrivial solution.

One way to determine if a system has a nontrivial solution is to use Gaussian elimination to reduce the augmented matrix to row echelon form. If the row echelon form has a row of zeros except for the last entry in the augmented part, then the system has only a trivial solution.

If there is a row of zeros in the row echelon form that corresponds to a free variable, then the system has a nontrivial solution. In this case, it is possible to use Gaussian elimination to see that the row echelon form of the augmented matrix has a row of zeros except for the last entry in the augmented part, which is not zero, indicating that the system has a nontrivial solution.

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Answer:25.5

Step-by-step explanation:

64.5+90=154

180-154=25.5

The subtraction of fraction numbers 4(2/3) and 3(2/5)  is, 19/15

In mathematics, subtraction is an operation which means taking away a few portions of the group or few things from a whole part.

For example, if we take 4 pencils out of 10 then remaining pencils are 6

so this process is called subtraction.

Given that,

Two fraction numbers,

4(2/3)

And 3(2/5)

Subtraction of both the terms = ?

⇒   4(2/3)  - 3(2/5)

Both the numbers can be written in the simplified form as,

⇒   (12 + 2)/3  = 14/3

⇒   (15 + 2)/5  = 17/5

Now, subtracting both the terms,

⇒  14/3 -  17/5

Taking LCM of  3 & 5

LCM(3,5)   = 15

⇒ Now, for making denominator same we multiply and divide each term 14/3 & 17/5 by 5 and  3 respectively,

⇒  (14/3)x(5/5) -  (17/5)x(3/3)

⇒  (14x5)/(3x5)  -  (17x3)/(5x3)

⇒   70/15 - 51/15

Now, denominators are same,

So, it can be written as,

⇒  (70 - 51)/15

⇒   19/15

Hence, the result is 19/15

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Nikhil has been with the company for 24 years, while Mae has been there for 4 years.

Option C is the correct answer.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 2 = 8 is an equation.

We have,

Number of years Nikhil worked =  x

Number of years Mae worked =  y

x = 6y ______(1)

x = 8 + 4y ______(2)

Substituting (1) in (2)

6y = 8 + 4y

Subtract 4y on both sides.

6y - 4y = 8

2y = 8

Divide 2 into both sides.

y = 4

Now,

x = 6y

x = 6 x 4

x = 24

Thus,

The number of years Nikhil worked is 24 years.

The number of years Mae worked 4 years.

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Let $abcd$ and $bedf$ be two $2 \times 3$ rectangles that overlap, the area of the overlap is 6 square unit.

The quantity of space occupied by a flat surface with a specific form is referred to as the area. It is calculated as a "number of" square units.

Given that we have to assume to rectangles

ABCD and BEDF

both have dimensions 2×3.

So the area of rectangles-

A=2(3)=6 square unit

Also given that both the rectangles overlap each other.

Since both the rectangle are of the same dimension so the overlapping area will be equal to their original area.

So the area of overlap- A=6 square unit.

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Answer: 92.0

Step-by-step explanation:

Calculating the perimeter of the rectangle. Perimeter of this rectangle = 2 * (length + width ) = 2 * (30.0 + 16.0) = 92.0 units

Answer: 92

Step-by-step explanation: To find the perimeter you add all four sides of the rectangle your equation should look like 30+30+16+16. Add 30+30 which is 60. Then 16+16 which is 32. Then add 60 plus 32 which equals 92.

The probability that the next customer will pay with a debit card or a credit card is 98% to the nearest whole number.

The probability of the next customer paying with a debit card or a credit card can be calculated by adding the number of customers that paid with a debit card (30) and the number of customers that paid with a credit card (96) together to get a total of 126. The probability of the next customer paying with a debit card or a credit card is then expressed as a percent by dividing the number of customers that paid with a debit card and a credit card (126) by the total number of customers (131) and then multiplying the answer by 100. This calculation can be expressed as the following formula:

P(debit card or credit card) = (30 + 96) / 131 * 100 = 98%

Therefore, the probability that the next customer will pay with a debit card or a credit card is 98% to the nearest whole number.

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Answer: 96%

Step-by-step explanation:

    To answer this question, we will find the probability that the next customer will pay with a debit card or credit card.

    To do this, we will divide the total number of people who paid with a debit or credit card by the total number of customers.

         [tex]\displaystyle \frac{\text{debit and credit cards}}{{\text{total customers}}} =\frac{30+96}{5+30+96} =\frac{126}{131} =0.961832[/tex]

    Next, we will multiply by 100 to transform the decimal into a percent, then we will round to the nearest whole number.

         0.961832 * 100 = 96.1832% ≈ 96%

The range, given the stem and leaf plot above, can be found to be 33

The range of a data set refers to the difference that is seen between the highest number in that data set and the lowest number in that same set.

The highest number as given in the stem and leaf plot above is 50 and the lowest number is 17.

This means that the range is:

= 50 - 17

= 33

We can therefore conclude that the range for the data set is 33.

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The standard deviation of the given variable is 0.95.

The standard deviation is a measure of the amount of variation or dispersion of a set of values. It is calculated as the square root of the variance. The variance is calculated by subtracting the mean from each data point and squaring the result. The variance is then divided by the number of data points. The standard deviation for the given table can be calculated as follows:

Mean = [tex](0 * 0.21) + (1 * 0.28) + (2 * 0.3) + (3 * 0.09) + (4 * 0.08) + (5 * 0.04) = 1.92[/tex]

Variance = [tex](0 - 1.92)2 * 0.21 + (1 - 1.92)2 * 0.28 + (2 - 1.92)2 * 0.3 + (3 - 1.92)2 * 0.09 + (4 - 1.92)2 * 0.08 + (5 - 1.92)2 * 0.04 = 0.907[/tex]

Standard Deviation = √0.907 = 0.95

Therefore, the standard deviation of the given variable is 0.95.

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An equation that relates x and y is  y = kx.

A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.

Given:

A proportional relationship between x and y.

That means,

x ∝ y.

y = kx, where k is constant.

y/x = k

When y = 72, x = 3.

That means., k = 24.

The equation is y = kx.

Therefore, the equation is y = kx.

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The solution is,  J. The mean and the median both decreased.

The mean can be calculated only for numeric variables, no matter if they are discrete or continuous. It's obtained by simply dividing the sum of all values in a data set by the number of values. The calculation can be done from raw data or for data aggregated in a frequency table.

here, we have,

The amount of money Cole earned for each of six weeks is shown.

$45, $85, $43, $45, $37, $70

i.e. mean = 54.16

now,

Cole then earned $30 for working a seventh week.

so, now, mean = 50.71

i.e. The mean decreased.

Hence, The solution is,  J. The mean and the median both decreased.

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The Correct answers are:

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

We have to find 70% of 42.

So, first Determine 1% of 42, and multiply the result by 70.

= 42 x 0.01 x 70

= 29.4

second, Determine 10% of 42, and multiply the result by 7.

= 42 x 0.1 x 7

= 29.4

Third, Determine 1% of 42, and multiply the result by 7.

= 42 x 0.01 x 7

= 2.94

Fourth, Determine 10% of 42, and multiply the result by 70.

= 42 x 0.10 x 70

= 294

and, the 70% of 42 = 0.7 x 42 = 29.4

Thus, the correct statement are:

Determine 1% of 42, and multiply the result by 70.

Determine 10% of 42, and multiply the result by 7.

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To determine the magnitude and direction of the resultant force applied at b, we can use vector addition of the tensions in cables AB and BC. Let's assume that the positive x-direction is to the right, and the positive y-direction is upwards.

We can represent the tension in cable AB as a vector T1 = 4500 lb in the direction of AB, and the tension in cable BC as a vector T2 = 2000 lb in the direction of BC.

The magnitude of the resultant force applied at b is given by:

R = √(T1^2 + T2^2) = √(4500^2 + 2000^2) = 5000 lb

The direction of the resultant force can be found using the arctangent function:

θ = tan^-1 (T2/T1) = tan^-1 (2000/4500) = approximately 39.2 degrees

Therefore, the magnitude and direction of the resultant force applied at b are 5000 lb and 39.2 degrees, respectively.

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The group with the greatest percent of students is expected to be the one with grades between 70 and 80 (inclusive), since this is close to the mean of 75 and encompasses approximately 68% of the data in a normal distribution (according to the empirical rule).

The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations.

So, in this case, grades between 70 and 80 (75 - 5 and 75 + 5) would contain approximately 68% of the students in the course.

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The volume is found using cylindrical shells and rotating the region bounded by xy = 3, x = 0, y = 3, and y = 5 about the x-axis.

To find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis, we will use the method of cylindrical shells. First, we need to draw the graphs of the functions given. The graph of xy = 3 is a parabola, x = 0 is a vertical line, y = 3 is a horizontal line, and y = 5 is also a horizontal line. The region bounded by these curves is the area between x = 0, y = 3, and y = 5 and xy = 3. Next, we need to find the area of the cylindrical shell. The area of the shell is given by 2πrh, where r is the radius of the circle and h is the height of the shell. The radius of the circle is the distance from the x-axis to the curve, which in this case is x. The height of the shell is the difference between the upper and lower limits of the integral, which in this case is y2 - y1. We can then integrate the area of the shell over the range of x and y values to get the volume. The integral is ∫[0, 3]∫[3, 5]2π(x)(y2 - y1)dxdy. Finally, we can evaluate the integral to get the volume of the solid.

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