The distance between Town P and Town Q is 237.5 Km. At 11.30 a.m a van travels from
Town P to Town Q at an average speed of 35 km/h. At the same time, a car travels from
Town Q to Town P along the same route at an average speed of 60 km/h.
a)At what time will the vehicles meet on the way?

b) How far will each vehicle have travelled when they meet?

The inequality represent the given graph is y≤1.4x+2.5.

From the graph, the line passes through (0, 2.5) and (3.5, 0).

Here, slope (m) = (3.5-0)/(2.5-0)

= 3.5/2.5

= 1.4

Substitute m=1.4 and (x, y)=(0, 2.5) in y=mx+c, we get

2.5=1.4(0)+c

c=2.5

So, the equation of a line is y=1.4x+2.5

So, the inequality is y≤1.4x+2.5

Therefore, the inequality represent the given graph is y≤1.4x+2.5.

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The value of sin(A-B) is 2334/6625

Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation.

Example of trigonometric identity include;

cos 2 θ + sin 2 θ = 1 cos 2 θ + sin 2 θ = 1.

1 + cot 2 θ = csc 2 θ 1 + cot 2 θ = csc 2 θ

1 + tan 2 θ = sec 2 θ 1 + tan 2 θ = sec 2 θ

Sin(A-B) = = sin A cos B- cos Asin B

if tan A = 4/3, then 4 is the opp and 3 is the adj,

hyp² = 4²+3²

= 16+9

hyp² = 25

hyp = √25

= 5

cos A = 3/5 and sinA = 4/5

if sinB = 28/53, then opp is 28 is the opp and 53 is the hyp

adj = √ 53²-28²

adj = √ 2809 - 784

adj = √2025

adj = 45

cos B = 45/58

sin(A-B) = 4/5 × 45/58 - 3/5× 28/53

= 18/29 - 84/265

= (4770-2436)/6625

= 2334/6625

therefore the value of sin(A-B) = 2334/6625

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As A is the only option that is three units distant from (5, 3), the response is: A) (1, 3) (1, 3) .

The placement of a point in a particular space or on a certain graph is represented by coordinates, which are numbers. Coordinates are normally two figures written in parenthesis and separated by a comma in two-dimensional space, where x denotes the point's horizontal position and y denotes its vertical position. Three integers enclosed in parentheses and separated by commas are used to indicate coordinates in three-dimensional space. The three numbers are generally represented as (x, y, z), where x, y, and z stand for the positions all along x-, y-, and z-axes, respectively. The location of objects, points, and other entities in space is described using coordinates frequently in the domains of mathematics, physics, engineering, and many others.

given

Any other vertex must be three units away from the specified vertex because the square has three units on each side.

The distance between the supplied vertex (5, 3) and each of the possible answers can be calculated using the distance formula:

Option A: Distance between (1 and 3) = sqrt((1 - 5)2 + (3 - 3)2) = sqrt(16) = 4 (not three units away)

Option B: Distance between (8 and 6) = sqrt((8 - 5)2 + (6 - 3)2) = sqrt(27) (not three units away)

Option C: (4, 0)

Distance is equal to sqrt((4 - 5)2 + (0 - 3)2 = sqrt(10) (not three units away)

Option D: Distance = sqrt((2 - 5)2 + (1 - 3)2) = sqrt(10) for the pair (2, 1). (not three units away)

As A is the only option that is three units distant from (5, 3), the response is: A) (1, 3) (1, 3) .

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Answer:

Step-by-step explanation:

8,800x0.09=792. The salesperson earns $792 in commission.

Answer:

$792

Step-by-step explanation:

8800×0.09= 792

9÷100=0.09

commission =$792

Answer:

3 yards

Step-by-step explanation:

Answer: To calculate the mean weekly earnings for each occupation in 2010, we need to add up the weekly earnings for each occupation and divide by the number of occupations.

For Forestry, logging and support:

Mean weekly earnings = (971) / (1) = $971

For Manufacturing:

Mean weekly earnings = (977) / (1) = $977

For Transportation and warehousing:

Mean weekly earnings = (900) / (1) = $900

For Construction:

Mean weekly earnings = (1071) / (1) = $1071

For Retail trade:

Mean weekly earnings = (501) / (1) = $501

Therefore, the mean weekly earnings for workers in the listed occupations in 2010 are:

Forestry, logging and support: $971

Manufacturing: $977

Transportation and warehousing: $900

Construction: $1071

Retail trade: $501

Step-by-step explanation:

The subtraction of the two matrix is   [31    6     12    -14     57 ]

                                                                [-19  -27  -18     18     27 ]

                                                                [ 47    14     -1    -40     9 ]

                                                                [10     12    -19    -15   -58]

                                                                [-14   -23    10     4       19]

The subtraction of the two matrix is calculated as follows;

The result to 4 multiplied by D is calculated as;

4[D] = [28   -24    12    -32     -36]

         [8      -36   -24     24      36]

         [32     8      20     -40     -12]

         [40   -12      -16    12     - 28]

         [4      -8       16     -20     -8 ]

The result to 3 multiplied by B is calculated as;

3[B] = [-3    -30  -24   -18     21]

         [27    -9    -6      6       9]

         [-15    -6    21     0      -21]

         [30    -24   3    27      30]

         [18     15     6   -24     -27]

The subtraction of the two matrix is calculated as follows;

4[D] - 3[B] =  [31    6     12    -14     57]

                    [-19  -27  -18     18     27 ]

                    [ 47    14     -1    -40     9 ]

                    [10     12    -19    -15   -58]

                    [-14   -23    10     4      19]

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scientific notation to express the number of bacteria that would be in a sample weighing 19 grams would be 1.634 ×[tex]10^9[/tex].

With scientific notation, one can express extremely big or extremely small values.

When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation. For instance, 650,000,000 can be represented as 6.5 108 in scientific notation.

The given number of bacteria in the dirt sample is 8.6 × [tex]10^7[/tex], and the weight of the sample is 1 gram. To find the number of bacteria in a sample weighing 19 grams, we can use the following proportion:

number of bacteria / weight of sample = constant

We can solve for the constant by using the given information:

8.6 ×[tex]10^7[/tex] / 1 gram = constant

constant = 8.6 × [tex]10^7[/tex]

Now we can use this constant to find the number of bacteria in a 19-gram sample:

number of bacteria / 19 grams = 8.6 × [tex]10^7[/tex]

number of bacteria = 8.6 ×[tex]10^7[/tex] × 19 grams

To express the answer in scientific notation, we can multiply the two numbers and adjust the exponent accordingly:

number of bacteria = 1.634 × [tex]10^9[/tex]

Therefore, the number of bacteria in a sample weighing 19 grams would be 1.634 ×[tex]10^9[/tex]

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Therefore, the probability of spinning a 2 or 3 on the spinner and drawing a blue tile is 1/6.

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible, and 1 indicating that the event is certain to occur. Probability theory is an important branch of mathematics used in many fields, including statistics, economics, engineering, and science, to help make predictions and informed decisions based on data and uncertain events.

Here,

Based on the given tree diagram, the probability of spinning a 2 or 3 on the spinner is 1/2 since there are two possible outcomes (2 or 3) out of four equally likely outcomes (1, 2, 3, or 4).

The probability of drawing a blue tile after spinning a 2 or 3 is 1/3 since there is only one blue tile out of three possible outcomes (blue, green, or red) for each spin result of 2 or 3.

To calculate the probability of both events happening together (spinning a 2 or 3 and drawing a blue tile), we need to multiply the two probabilities:

P(2 or 3 and blue) = P(2 or 3) x P(blue | 2 or 3)

= (1/2) x (1/3)

= 1/6

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Answer:

The answer is -5

Step-by-step explanation:

Each number moves down 5 as it moves to the right 1. Right is positive, and down is negative. -5 divided by 1 is -5.

well, let's find out how much she made on each week

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{8\% of 4700}}{\left( \cfrac{8}{100} \right)4700}\implies 376\qquad \textit{ first week} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{9\% of 5500}}{\left( \cfrac{9}{100} \right)5500}\implies 495\qquad \textit{ second week}\hspace{8em}\underset{ \textit{more on the 2nd week} }{\stackrel{ 495~~ - ~~376 }{\text{\LARGE 119}}}[/tex]

The statistical questions are:

A statistical question is a question that can be answered by collecting and analyzing data. It is a question that expects a variability in the response, meaning different individuals may give different answers. Statistical questions usually ask about a population, a group of individuals or objects that share a common characteristic or feature, and seek to understand a pattern or trend within that population.

In general, a statistical question is open-ended, does not have a single correct answer, and requires data analysis to arrive at a reasonable conclusion.

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The values of the composite functions are (g o f)(x) = [tex]\frac{9x^2-18x+4}{4}-5[/tex], (j o g)(x) = 3x² - 15x + 1, (g o h)(x) = [tex]\frac{\left(2x-1\right)^2}{1089}-\frac{5\left(2x-1\right)}{33}[/tex] and (g o g)(-2) = 126

Given that we have the function definitions

The composite functions are calculated below

(g o f)(x) = g(f(x))

(g o f)(x) = (f(x))² - 5f(x)

So, we have

(g o f)(x) = (3/2x + 1)² - 5(3/2x + 1)

Evaluate

(g o f)(x) = [tex]\frac{9x^2-18x+4}{4}-5[/tex]

Next, we have

(j o g)(x) = j(g(x))

(j o g)(x) = 3g(x) + 1

So, we have

(j o g)(x) = 3(x² - 5x) + 1

(j o g)(x) = 3x² - 15x + 1

Next, we have

(g o h)(x) = g(h(x))

(g o h)(x) = (h(x))² - 5h(x)

So, we have

(g o h)(x) = ((2x - 1)/33)² - 5((2x - 1)/33)

Evaluate

(g o h)(x) = [tex]\frac{\left(2x-1\right)^2}{1089}-\frac{5\left(2x-1\right)}{33}[/tex]

Lastly, we have

(g o g)(-2) = g(g(-2))

(g o g)(-2) = (g(-2))² - 5g(-2)

So, we have

(g o g)(-2) = ((-2)² - 5(-2))² - 5((-2)² - 5(-2))

(g o g)(-2) = 126

Hence, the values are (g o f)(x) = [tex]\frac{9x^2-18x+4}{4}-5[/tex], (j o g)(x) = 3x² - 15x + 1, (g o h)(x) = [tex]\frac{\left(2x-1\right)^2}{1089}-\frac{5\left(2x-1\right)}{33}[/tex] and (g o g)(-2) = 126

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An equation of the linear function represented by the graph in slope-intercept form is y = 3x + 60.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (75 - 60)/(5 - 0)

Slope (m) = 15/5

Slope (m) = 3

At data point (0, 60) and a slope of 3, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 60 = 3(x - 0)  

y = 3x + 60

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The correct options are rectangular prism, square pyramid.

When a shape has a rectangular cross-section, it means that if the shape is cut perpendicular to its base, the resulting cut will be a rectangle. So, the only shapes that will have a rectangular cross section are those whose base is a rectangle or a shape that can be inscribed within a rectangle.

The shapes that have rectangular cross sections when they are cut perpendicular to the base are:

Rectangular prism

Square pyramid

Therefore, the correct options are rectangular prism, square pyramid.

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Complete question:

The type of distribution pictured in this histogram is skewed.

A skewed distribution is a statistical distribution that is not symmetrical around its mean or median.

In a skewed distribution, the tail of the distribution is pulled in one direction or the other, resulting in a longer tail on one side than the other.

There are two types of skewed distributions: positively skewed and negatively skewed.

The distribution in the image is positively skewed as its is pulled towards the left.

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Answer:

Option C

Step-by-step explanation:

To solve this system of equations, we can use the method of elimination. Adding the two equations together eliminates the y variable, and we get:

2x = 6

Simplifying, we get:

x = 3

Substituting x = 3 into either of the original equations, we get:

3 + y = -4

Solving for y, we get:

y = -7

Therefore, the solution to the system of equations is (3, -7), which is option C.

The image coordinates of NMO after the translation is option d: N′(−5, −6), M′(−2, −5), and O′(−3, −7).

To get the image coordinates of the preimage translated -2 units to the left, we simply subtract -2  from the y-coordinates of each vertex:

N' = (Nx - (-2), Ny) = (−5 , 2- (-2)) = (−5, 4)

M' = (Mx - (-2), My) = (−2 , 1 - (-2)) = (−2, 3)

O' = (Ox - (-2), Oy) = (−3 , 3- (-2)) = (−3, 5)

Therefore, based on the above, the image coordinates of NMO after the translation are N′(−5, 4), M′(-2,3 ), O′(−3, 5)

So the reflected vertices are:

The distance from N to the line y = -2 is 4, and -6 - (-2) = -4, so one need to move down 4 units to have  a y-coordinate of -6.

The distance from M to the line y = -2 is 3, and -5 - (-2) = -3, so  one need to move down 3 units to have a y-coordinate of -5.

The distance from O to the line y = -2 is 5, and -7 - (-2) = -5, so  one need to move down 5 units to have  a y-coordinate of -7.

So it will be: N′ (−5, −6), M′(−2, −5), O′(−3, −7)

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Answer:

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

Given triangle MNO with vertices:

It is reflected in line y = - 2.

This reflection doesn't affect the x-coordinates of the vertices and the y-coordinates change.

Since y = - 2 is the line of symmetry,  it also represents midpoints of the segments formed by corresponding endpoints of image and preimage.

Using midpoint equation, find the y-coordinates.

So the coordinates of the image are:

This is matching the option D.

See attached for visual representation of the problem.

(11) The value of expression 3/y + 2y/4 when y = 4 is [tex]2\frac{3}{4}[/tex].

Hence the correct option is (b).

(12) The value of expression 12/y + 3y/4 when y = 8 is [tex]7\frac{1}{2}[/tex].

Hence the correct option is (c).

(13) 2x/3 + 4 = 10 equation does x = 9.

Hence the correct option is (b).

(11) The given expression is,

3/y + 2y/4 = 3/y + y/2

Substituting the value of y = 4 we get,

3/4 + 4/2 = 3/4 + 2 = [tex]2\frac{3}{4}[/tex].

Hence the correct option is (b).

(12) The given expression is,

12/y + 3y/4

Substituting y = 8 in the given equation we get,

12/8 + (3*8)/4 = 3/2 + 6 = 1 + 1/2 + 6 = [tex]7\frac{1}{2}[/tex].

Hence the correct option is (c).

(13) Given the solution is x =9.

For first option: (2/3)*9 - 6 = 6 - 6 = 0

2x/3 - 6 = 12 does not satisfied by x = 9.

For second option: (2/3)*9 + 4 = 6 + 4 = 10

So, x = 9 satisfies 2x/3 + 4 = 10.

For third option: 3*9 - 12 = 27 - 12 = 15

So x = 9 does not satisfy 3x - 12 = 21.

For fourth option: 3*9 + 12 = 27 + 12 = 39

So x = 9 does not satisfy 3x + 12 = 19.

Hence the correct option is (b).

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Answer:

Step-by-step explanation:

it think it 23 becasue u add

1 divide it by 2

Answer:

Simple interest= PRT/100

parameters

price =300

Rate=6%

Time=4years

300*6*4/100

7200/100

=72

Answer:

[tex] {m}^{2} + 7m - 30 = [/tex]

[tex](m - 3)(m + 10)[/tex]

The scale of Sarah's zoomed-in map is 1cm = 1000 cm or 1cm = 10 m. So the answer is (B) 1cm = 10 m.

To find the scale of Sarah's zoomed-in map, we can use the ratio of the width of the park on the map to its actual width.

Let's first convert the width of the park from meters to centimeters, since the width of the park on the map is given in centimeters.

15 m = 1500 cm

Next, we can set up a proportion:

0.5 cm / x = 1500 cm / (3x)

where x is the scale of the zoomed-in map.

Simplifying the proportion, we get:

0.5(3x) = 1500

1.5x = 1500

x = 1000

Therefore, the answer is (B) 1cm = 10 m.

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Answer:

The IQR (interquartile range) of 13 is the most accurate measure of variability to use in this case, since the data is skewed and contains some outliers.

The IQR is a measure of variability that is less sensitive to extreme values than the range, and is calculated as the difference between the upper and lower quartiles (the 75th and 25th percentiles). It provides a measure of the spread of the middle 50% of the data, which is useful for understanding the typical range of donations received.

In this case, the IQR is calculated as follows:

- The median of the data is 51 (the value in the middle).

- The lower quartile (Q1) is the median of the lower half of the data, which is 42.

- The upper quartile (Q3) is the median of the upper half of the data, which is 54.

- The IQR is the difference between Q3 and Q1: IQR = Q3 - Q1 = 54 - 42 = 12.

So the IQR of 13 is a useful measure of variability to use for this data set, since it captures the spread of the middle 50% of the data while being less sensitive to the outliers at the higher end of the distribution.

Answer:

Larger number: 36

Smaller number: 13

If the side AB=12 and side A'B'=9, then the scale factor of the dilation is 3/4.

The "Scale-Factor" of a dilation is the ratio of the corresponding side lengths of the two similar figures.

In this case, we can find the scale factor by dividing the length of side A'B' by the length of the corresponding side AB:

So, scale factor = A'B'/AB,

Substituting the values,

We get,

Scale factor = 9/12,

Scale Factor = 3/4,

Therefore, the scale factor of the dilation is 3/4. This means that all corresponding side lengths of the dilated triangle A'B'C' are 3/4 of the length of the corresponding side lengths of the original triangle ABC.

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Tthe reserve rate was approximately 0.9434, or 94.34%.

This is a geometric series with first term 3000r and common ratio (1-r), so we can use the formula for the sum of a geometric series:

sum = a(1 - r^n) / (1 - r)

where a = 3000r is the first term.

As the cycle continues indefinitely, the amount loaned out eventually becomes the final amount of $50,000. Therefore:

3000r/(1-r) = 50,000

Solving for r, we get:

r = (50,000)/(3000 + 50,000) = 0.9434

Therefore, the reserve rate was approximately 0.9434, or 94.34%.

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By using the corresponding angles, vertically opposite angles, alternate interior angles, and linear pair theorems, the measure of the angles are:

m ∠1 = 39°

m ∠2 = 141°

m ∠3 = 141°

m ∠4 = 39°

m ∠5 = 39°

m ∠6 = 141°

m ∠7 = 39°

From the question, we are to calculate the measure of the unknown angles in the given diagram

By the Linear pair theorem,

We can write that

m ∠5 + 141° = 180°

Thus,

m ∠5 = 180° - 141°

m ∠5 = 39°

Likewise

m ∠7 + 141° = 180°

m ∠7 = 180° - 141°

m ∠7 = 39°

By the vertical angles theorem,

We can write that

m ∠6 = 141° (Vertically opposite angles)

By the corresponding angles theorem,

We can write that

m ∠2 = 141° (Corresponding angles)

m ∠2 = m ∠3 (Vertically opposite angles)

Therefore,

m ∠3 = 141°

m ∠4 = m ∠5 (Alternate interior angles)

m ∠4 = 39°

m ∠1 = m ∠4 (Vertically opposite angles)

Therefore,

m ∠1 = 39°

Hence,

The measure of angle 1 is 39°

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An equation that models the position of the object at time t is:

s(t) = -2cos(2πt/5).

The general form for the equation that will model a wave is:

±a (sin/cos) (2π(x - p)/T)

where:

a is the amplitude

p is the phase shift

T is the period.

The ± will become +ve provided that the graph starts in the positive direction, and the will become -ve provided it starts in the negative direction.

The (sin/cos) will become sine provided the graph starts at 0 before it is being shifted. Then, it becomes cosine provided that the graph starts at the amplitude.

In this case, our graph begins at negative, and the at the amplitude that has no phase shift, the ±ve will become -ve, (sin/cos) will now become cos, and p will become zero. Plugging in the values that were given in the problem, we see that a = 2 and T = 5.

Thus, this equation is: s(t) = -2cos(2πt/5).

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