A fuel company supplies fuel in two different-sized tankers. The first tanker can supply x cubic feet of fuel in one trip and the second tanker can
cubic feet of fuel in one trip. The first tanker makes M trips daily and the second taker makes n trips daily. What does
Mx +Ny represent in expression
Mx +NY,
M+N
total fuel, in cubic feet, supplied by the two tankers in one trip
total fuel, in cubic feet, supplied by the two tankers in one day
o
total fuel, in cubic feet, supplied by the two tankers in one week
total fuel, in cubic feet, supplied by the two tankers in one month

The equation of the line that is parallel and perpendicular to y = -8x + 6 and passes through the point (7, 5) are y = -8x + 61 and  \(y = \frac{1}{8}x + \frac{33}{8}\) respectively.

The slope-intercept form is expressed as;

y = mx + b

Where m is slope and b is the y-intercept.

Given the equation of the original line:

y = -8x + 6

Using the slope intercept:

Slope m = -8

Since the desired line is parallel, it will have the same slope.

Therefore, the slope of the parallel line is also -8.

Plug in the slope m = -8 and the poin (7,5) into the point-slope form:

( y - y₁ ) = m( x - x₁ )

( y - 5) = -8( x - 7 )

Simplify

y - 5 = -8x + 56

y = -8x + 56 + 5

y = -8x + 61

The equation of the parallel line is y = -8x + 61.

For the perpendicular line:

The slope of the perpendicular line will be the negative reciprocal of -8, which is 1/8.

Hence, plug slope m = 1/8 and point (7,5) into the point-slope form:

( y - y₁ ) = m( x - x₁ )

\(y - 5 = \frac{1}{8} ( x + 7 )\\\\y - 5 = \frac{1}{8}x + \frac{7}{8} \\\\y = \frac{1}{8}x + \frac{7}{8} + 5\\\\y = \frac{1}{8}x + \frac{33}{8}\)

Therefore, the perpendicular line is \(y = \frac{1}{8}x + \frac{33}{8}\).

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Answer: The Answer is B the second one.

Step-by-step explanation:

Answer:

it's C

Explanation:

Answer:

  x = 48.40'

  y = 33.01'

Step-by-step explanation:

These are all segments of a right triangle, so the Pythagorean theorem applies.

  x^2 = 46.07^2 +14.82^2 = 2342.0773

  x = √2342.0773 ≈ 48.40

__

  x^2 = 35.39^2 +y^2

  y^2 = 2342.0773 -35.39^2 = 1089.6252

  y = √1089.6252 ≈ 33.01

Units are feet for both numbers:

  x = 48.40'

  y = 33.01'

_____

You always start any question by reading the whole question, identifying the (relevant) given information, and understanding what the question is asking for. You then make an assessment of what you know about the relationships between the given information and what is asked. Finally, you develop a strategy for getting from what you know to what you need to know.

Here, you're given segment lengths of right triangles, and you're asked for other segment lengths. This is not a trig problem--no angles are involved. It is a straight Pythagorean theorem problem. To make use of that theorem, or any formula, you need to have only one unknown. So, you can't start by solving the bottom triangle; you have to start with the upper one where there is only the unknown side x.

After you find x, then you have two known sides in the bottom triangle, so you can find y.

Here, x is an intermediate value in the computation of y. You do NOT use the rounded answer to the question when you're computing y. Rather, you use the full calculator precision for x, so that y can have best accuracy. Only at the end do you round to hundredths.

For 7.45 - 3.029 the reason why they rewrite 7.45 as 7.450 is so as to have both values in three decimal place so the calculation can be easier.

It should be noted that the first digit after the decimal represents the tenths place then the next digit after the decimal  could be reffered to as  hundredths place however the remaining digits continue to fill in the place values until there are no digits left.

It should be noted that Decimal place value  can be described as the place values of all the digits in a given decimal number.

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Answer:

The integers are ..., -4, -3, -2, -1, 0, 1, 2, 3, 4, ... -- all the whole numbers and their opposites (the positive whole numbers, the negative whole numbers, and zero). ... For example, -5 is an integer but not a whole number or a natural number.

Step-by-step explanation:

An order-preserving function is one where x < y implies f(x) < f(y). An isomorphism is a one-to-one order-preserving function between two partially ordered sets, while an automorphism is an isomorphism of a set to itself.

In the given excerpt, it explains the concepts of order-preserving functions, isomorphisms, and automorphisms in the context of partially ordered sets.

Order-Preserving Function:

A function f: P -> Q, where P and Q are partially ordered sets, is said to be order-preserving if for any elements x and y in P, if x < y, then f(x) < f(y). In other words, the function preserves the order relation between elements in P when mapped to elements in Q.

Increasing Function:

If P and Q are linearly ordered sets, then an order-preserving function is also referred to as an increasing function. It means that for any elements x and y in P, if x < y, then f(x) < f(y).

Isomorphism:

A one-to-one function f: P -> Q is called an isomorphism of P and Q if it satisfies two conditions:

a. f is order-preserving: For any elements x and y in P, if x < y, then f(x) < f(y).

b. f is onto (surjective): Every element in Q has a pre-image in P.

When an isomorphism exists between (P, <) and (Q, <), it means that the two partially ordered sets have a structure that is preserved under the isomorphism. In other words, they have the same ordering relationships.

Automorphism:

An automorphism of a partially ordered set (P, <) is an isomorphism from P to itself. It means that the function f: P -> P is both order-preserving and bijective (one-to-one and onto). Essentially, an automorphism preserves the structure and order relationships within the same partially ordered set.

These concepts are fundamental in understanding the relationships and mappings between partially ordered sets, particularly in terms of preserving order, finding correspondences, and exploring the symmetry within a set.

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The table that represents a linear equation is the first one, and the line can be:

y = -4x - 1

A general linear function can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Now, notice that if we evaluate the line in x + 1, we will get:

y = a*(x + 1) + b

y = a*x + a + b

So, for an increase of one unit on the variable x, we have a constant increase in the y value.

Now, if you look at the first table, you can see that for each increase of 1 unit on the value of x, the value of y decreases by 4.

So that is the table that can represent a linear function.

And the line is:

y = -4x - 1

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The area not covered by the white board is 192 cm².We can find by using area of rectangular formula.

A rectangle is a quadrilateral that has its parallel sides equal to each other and all the four vertices are equal to 90 degrees. Hence it is also called quadrilateral. Since the opposite sides are equal and parallel in rectangle.

The area is measurement of the surface of a shape. To find the area of a rectangle or a square you need to multiply the length and the width of a rectangle.The formula for the Area of a Rectangle is A = l × b. The area of any rectangle is calculated once its length and width are known.

Now we find

A white rectangular board 28 cm long and 16 cm wide.

Substitute the respective values

Area of White Board = 28 *16

The area of white board is 448 cm²

Wooden board creates a border of 2 cm around it.

Wooden Board dimension = (28 + 2 + 2) cm long and (16 + 2 + 2) cm wide

Wooden Board dimension = 32 cm long and 20 cm wide.

The area of Wooden board = 32*20=640

The area not covered by the white board is

640 cm² - 448 cm² = 192 cm²

The area not covered by the white board is 192 cm².

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Answer:

The mean of the population with 99% confidence is between 43.1 and 46.1

Step-by-step explanation:

The mean of the population with 99% confidence and The standard deviation of the sample was 2.3, which is between 43.07 to 46.13.

Mean is a measurement of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value."

Given:

A random sample of 15 registered nurses in a large hospital showed that they worked on average 44.6 hours per week, X = 44.6

The standard deviation of the sample was, n = 2.3,

The confidence = 99%,

1 - α = 99%

α = 1 - 0.99

α = 0.01

Calculate the margin of the error as shown below,

\(E = Z_{\alpha /2} \ Mean / standard\ deviation\)

E = 2.576 × 2.3 / √15

E = 1.5298

Calculate the mean as shown below,

X - E < Mean < X + E

44.6 - 1.5298 < Mean < 44.6 + 1.5298

43.07 < Mean < 46.13

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The value of the test statistic is approximately -1.063

We have,

To find the value of the test statistic, we need to calculate the z-score using the given information.

The formula for calculating the z-score is:

z = (x - μ) / (σ / √n)

Where:

x is the sample mean (68.1 bpm)

μ is the population mean (69 bpm)

σ is the standard deviation (11.2 bpm)

n is the sample size (175)

Plugging in the values into the formula, we have:

z = (68.1 - 69) / (11.2 / √175)

Calculating the numerator:

68.1 - 69 = -0.9

Calculating the denominator:

11.2 / √175 ≈ 0.846 (rounded to three decimal places)

Now, we can calculate the value of the test statistic:

z = -0.9 / 0.846 ≈ -1.063 (rounded to three decimal places)

Therefore,

The value of the test statistic is approximately -1.063

(rounded to two decimal places).

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Answer:

11

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

Answer:

it wants me to type more its 24 i searched it up

Answer

The answer is 17.

Explanation

The absolute value of any number is taking the positive part of any number. For example, the absolute value of -2 = | -2 | = 2, the absolute value of -99 = | -99 | = 99.

So, the absolute value of -17 = | -17 | = 17.

Hope this Helps!!!

Answer:

C. Q′ (−3, −4)  

D. Q′ (−4, −3)

Step-by-step explanation:

From looking at the graph it looks like the answer would be

Q= (3, -4) if the X-axis goes first

Q= (-4, 3) if the Y-axis goes first

Answer:

the answer is 2

Step-by-step explanation:

Answer:

Step-by-step explanation:

It is 2, because it is the only factor that can go with both of the numbers.

Answer: The total volume of milk would be \(\dfrac{1}{2}\ gallon\)

Step-by-step explanation:

Since we have given that

Volume = \(\dfrac{1}{4}\ gallon\)

Number of weeks = 2

So, Total volume of milk that Gino's family drank would be

\(\dfrac{1}{4}\times 2=\dfrac{1}{2}\ gallon\)

Hence, the total volume of milk would be \(\dfrac{1}{2}\ gallon\)

Answer:

6 gallons

Step-by-step explanation:

The total cupcakes the bakery sell that day is 80

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

Number of sales = 76

Proportion = 95%

This implies that

Number of sales = Proportion * Total number of cupcakes

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

76 = 95% * Total number of cupcakes

Divide both sides by 95%

Total number of cupcakes = 80

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The statement that is true about histograms graphs is: "Data is organized in equal intervals."

Academics are using graphs to logically chart or graphically depict events or quantities. A graph point is a common way to depict how different things interact. The non-linear storage structure known as a graph is made up of nodes, also referred to as vertices, and lines. Glue ought to be used to connect the edges, also known as nodes , respectively.  (4.5).

Here,

The statement "Data appears as bars that are all about the same height" is false.

A histogram is a graph that represents the distribution of numerical data by organizing it into "bins" or "intervals" and displaying the count or frequency of data points that fall within each interval. The height of each bar represents the frequency or count of data points in that interval. The bars may or may not touch depending on the data and the chosen intervals.

The statement that is true about histograms is: "Data is organized in equal intervals."

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Answer:

y = x + 1

Step-by-step explanation:

Parallel lines have same slope.

y = x - 1

Compare with the equation of line in slope y-intercept form: y = mx +b

Here, m is the slope and b is the y-intercept.

m =1

Now, the equation is,

         y = x + b

The required line passes through (-3 ,-2). Substitute in the above equation and find y-intercept,

        -2 = -3 + b

  -2 + 3 = b

         \(\boxed{b= 1}\)

    Equation of line in slope-intercept form:

                  \(\boxed{\bf y = x + 1}\)      

The equation is :

Solution:

If two lines are parallel to each other, then their slopes are equal. The slope of y = x - 1 is 1. Hence, the slope of the line that is parallel to that line is 1.

We shouldn't forget about a point on the line : (-3, -2).

I plug that into a point-slope which is :

\(\sf{y-y_1=m(x-x_1)}\)

Slope is 1 so

\(\sf{y-y_1=1(x-x_1)}\)

Simplify

\(\sf{y-y_1=x-x_1}\)

Now I plug in the other numbers.

-3 and -2 are x and y, respectively.

\(\sf{y-(-2)=x-(-3)}\)

Simplify

\(\sf{y+2=x+3}\)

We're almost there, the objective is to have an equation in y = mx + b form.

So now I subtract 2 from each side

\(\sf{y=x+1}\)

The missing values in the ratios are 2/3 and 16/3 in the set of 1, _ , _.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given are two sets of ratios 2, _, _ and 3, 1, 8.

If we observe the first value of the first and second ratio we see that

The second set of ratios is (3/2) or 1.5 times larger than the first set of ratios.

So the second and the third value of the first set of ratios are (1/3/2) = 2/3 and 8/(3/2) = 16/3.

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Answer:

66.99 cm³

Step-by-step explanation:

the volume = ⅓× 3.14 × 4²× 4 = 3.14 × 64/ 3

= 66.99 cm³

10) So here, in the first figure –

We are given a Rectangle and we know formula for perimeter of a rectangle's given

In case of 2nd figure a tiangle's given whose formula of Perimeter will be

According to the question :-

↠Perimeter of rectangle = Perimeter of triangle

↠ x+3 +x+5+x+4 = 2 (x+4+x-2)

↠ 3x + 12 = 2(2x+2)

↠ 2(2x+2) = 3x + 12

↠ 4x +4 = 3x+12

↠ 4x-3x +4-12 = 0

↠ x -8 =0

↠ x = 8

Answer:

In Figure 1 :

We know that, It is a rectangle and the formula for finding the perimeter of a rectangle is :

In Figure 2 :

We know that, it is a triangle and the formula for finding the perimeter of a triangle is :

\( \\ \: \: { \underline{ \underline{ \textbf{\textsf{{ According to the Question \::}{}}}}}}\)

\( \\ \sf \implies \: 2(x - 2 + x+4) = (x + 3) + (x + 4) + (x + 5)\: \: \: \: \: \: \: \\ \\ \sf \implies \: 2(2x +2) = x + 3 + x + 4 + x + 5\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf \implies \: 4x + 4 = 3x + 12 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf \implies \: 4x - 3x = 12 - 4 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf \implies \: x = 8 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\\)

See attachment for the graph of  4 > |x + 1| + 2

The absolute value inequality is given as:

4 > |x + 1| + 2

Subtract 2 from both sides of the absolute value inequality.

So, we have

2 > |x + 1|

Rewrite as

|x + 1| < 2

So, we plot the graph of  |x + 1| < 2 to represent 4 > |x + 1| + 2

See attachment for the graph

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The equation of the line in the slope-intercept form is: y = -2.00 x + 10.

The slope and provided point are both in the equation for the straight line.

The generic point (x, y) must satisfy the equation if we have a non-vertical land in a that passes through any point(x1, y1) has gradient m.

y-y₁ = m(x-x₁)

It is the necessary equation for a line in the form of a point-slope.

That gift card to the Coffee Café has been provided. = $10

Medium coffee = $2.00

customers

The quantity of coffees a consumer can purchase can be represented using a linear equation.

Slope formula

m = (8 - 10)/(1 - 0)

m = -2

Now consider the line's point-slope shape.

y-y₁ = m(x-x₁)

( y - 10) = -2.00 ( x - 0)

y = -2.00 x + 10

The slope: m = - 2.00

The equation of the line: y = -2.00 x + 10

The y-intercept is 10

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Answer:

\(y=\frac{3}{10}\)

Step-by-step explanation:

\(\frac{0.2}{2} :\frac{y}{3}\)

2 × y = 0.2 × 3

2y = 0.6

2y ÷ 2 = 0.6 ÷ 2

y = 0.3

The expression is simplified to a²

Index forms are simply defined as models of writing numbers that are too large or small in a more convenient way.

Other names for index forms are;

Some rules of indices are;

We then have;

a(7)/a(5)

subtract the exponents

a²

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Answer:

3 feet

Step-by-step explanation:

36/12=3

Lizzy's recipe is not a proportional relationship with the brownie recipe because of the difference in ratio.

Brownie recipe:

Ratio of cocoa powder to flour = 3 : 2

Lizzy recipe:

Ratio of cocoa powder to flour = 1 : 1

Therefore, Lizzy's recipe is not a proportional relationship with the brownie recipe because of the difference in ratio

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