Work out the area of a rectangle with base,
b
= 14mm and height,
h
= 10mm.

Answer: 30 2 point and 8 5 point

Step-by-step explanation: 30 times 2 = 60 8 times 5 = 40 60+40 = 100

The coordinates of each vertex after the translation and reflection can be written as an ordered pair. The coordinates for W' are (6, 0), for X' are (0, 3), for Y' are (6, 6), and for Z' are (0, 9).

This means that point W' has been moved 6 units to the left, X' has been moved 6 units to the left and 3 units down, Y' has been moved 6 units to the left and 6 units down, and Z' has been moved 6 units to the left and 9 units down, and then all the points have been reflected across the x-axis. This transformation results in a figure that is the same size and shape as the original figure, but shifted and reflected across the x-axis.

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The solution is (-5,0), the interval in which the function is increasing.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

In case when you tracking the finger across the line, at which there is an increase or decrease in y axis so this is we called intervals. Moreover, the interval notation is also necessary as it depicts the beginning and ending points. In this, the first number denotes the minimum number while the second number denotes the maximum number

For Decreasing:

(-8,-5)

(4,8)

For Increasing:

(-5,0)

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The denominator of the formula for the variance of a sample is given as follows:

N - 1.

A fraction is a numerical representation of the division of the two terms x and y that composed the fraction, as follows:

Fraction = x/y.

The terms are named as follows:

The formula for the variance of a sample is given as follows:

[tex]s^2 = \frac{sum (X - \overbar{X})^2}{N - 1}[/tex]

Hence the denominator is the bottom term, which is of N - 1.

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The horizontal asymptote is y = X, and the vertical asymptotes are x = 2 and x = 1.

A curve is a continuous, smooth, and often repeating shape in the plane or in space. It is a geometric object that can be described mathematically by an equation or a set of points.

In mathematics, curves are used to model real-world phenomena and to study geometric and mathematical properties. For example, curves can be used to describe the shape of objects, the path of moving objects, or the graph of a mathematical function.

There are many types of curves, including lines, circles, ellipses, parabolas, hyperbolas, and spirals, among others. Each type of curve has unique properties and characteristics, and they are studied and used in different ways in different fields of mathematics and science.

The horizontal asymptotes are found by examining the degree of the numerator and denominator when x approaches infinity or negative infinity.

Since the numerator is of degree 3 and the denominator is of degree 2, the horizontal asymptote is y = X3 - x / x² – 3x + 2 = X.

For the vertical asymptotes, we look for the values of x that make the denominator equal to zero and the numerator either equal to zero or undefined.

The denominator x² – 3x + 2 = 0 has roots at x = 1 and x = 2.

At x = 1, the numerator x³ - x = 0, so the function has a hole at x = 1 and y = 0.

At x = 2, the function is undefined, so x = 2 is a vertical asymptote.

Thus, the horizontal asymptote is y = X, and the vertical asymptotes are x = 2 and x = 1.

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The value of x is 6 using logarithmic properties.

The power to which a number must be increased in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents). For instance, the logarithm of 100 in base ten is 2, since ten multiplied by two equals 100: log 100 = 2, since 102 = 100.

The Scottish mathematician John Napier reported his findings on logarithms in 1614. He was there to aid with the multiplication of quantities known as sines at the time.

Given,

Log2+ log3= logx

To find= We need to find the value of x

The value of log2=  0.301

The value of log 3= 0.477

Now, putting the value in the given expression, we get:

0.301+ 0.477= logx

logx= 0.778

Now, taking the antilog os=f x:

x= antilog(0.778)

x= 5.99=6

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First, we need to set up the bounds for the integral. The lower and upper limits of the integral are x = 1 and y = x2, respectively. The integral ∫x1 [cos(x2)dx] is equal to -2/3.

Next, we can substitute the upper limit of the integral into the integrand to get:

∫x1 [cos(x2)dx]

Then, we can use integration by parts to solve the integral. We let u = cos(x2) and dv = dx. This gives us:

du = -2x sin(x2) dx

and

v = x

This gives us:

∫x1 [cos(x2)dx] = x cos(x2) - ∫x1 [-2x sin(x2)dx]

Now, we can solve the second integral. We let u = x2 and dv = -2 sin(x2)dx. This gives us:

du = 2x dx

and

v = -cos(x2)

This gives us:

∫x1 [-2x sin(x2)dx] = -x2 cos(x2) - ∫x1 [2x dx]

Finally, we can solve the last integral. We let u = x and dv = 2 dx. This gives us:

du = dx

and

v = x2

This gives us:

∫x1 [2x dx] = x3 + c

where c is the constant of integration.

Putting it all together, we get that

∫x1 [cos(x2)dx] = x cos(x2) - x2 cos(x2) - x3 - c

Substituting in the limits of the integral, we get that

∫x1 [cos(x2)dx] = 1 - x2 - x3 - c

Since the lower limit of the integral is x = 1, we have that

∫x1 [cos(x2)dx] = -x2 - x3 - c

Substituting in the upper limit of the integral, we get that

∫x1 [cos(x2)dx] = -1 - x2 - x

The integral ∫x1 [cos(x2)dx] is equal to -2/3.

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Using relations in a right- triangle, the equation can be used to break for the measure of angle ABC is  tan x = 2.4/10

The relations in a right triangle are given as follows

The sine of an angle is given by the length of the contrary side to the angle divided by the length of the hypotenuse.

The cosine of an angle is given by the length of the conterminous side to the angle divided by the length of the hypotenuse.

The digression of an angle is given by the length of the contrary side to the angle divided by the length of the conterminous side to the angle.

For angle Alphabet = x, we've that

The length of the contrary side is of2.4 cm.

The length of the conterminous side is of 10 cm.

Hence, the equation is tan x = 2.4/10.

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The expression is obtained on subtracting 4x + 6 from 7 + 2x is -2x + 1

Given the two expressions in the question;

( 4x + 6 ) and ( 7 + 2x )

To subtract  4x + 6 from 7 + 2x simply means ( 7 + 2x ) - ( 4x + 6 ).

Now, simplify

( 7 + 2x ) - ( 4x + 6 )

Distribute the negative sign to all the terms in the second expression.

( 7 + 2x ) -4x - 6

Now collect and add like terms

2x - 4x - 6 + 7

Add 2x and -4x

-2x - 6 + 7

Add -6 and 7

-2x + 1

Therefore, the resulting expression is -2x + 1.

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The required systolic pressure will be lower when the patient takes the blood pressure medication at 7 a.m. between the interval of 7 a.m. to 9 a.m.

A piecewise function is one that is constructed from pieces of different functions at different intervals.

Here,
A graph of the piecewise function is shown, from the graph it's clear that systolic pressure is low for the interval 5 < x < 9, such that the patient takes the medication at 7 A. M. So, corresponding to that required systolic pressure will be lower between 7 a.m. to 9 a.m.

Thus, the required systolic pressure will be lower when the patient takes the blood pressure medication at 7 a.m. is 7 a.m. to 9 a.m.

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John scored 110 points in total.

A equation is used to equate two expressions. For example -

4x + 4 = 7

Given is that John, scores 35 more than triple the amount of points than Amy. Amy scores 25 points.

The total points scored by john would be -

{p} = 3{a} + 35                                                        .... Eq { 1 }

{p} = 3 x 25 + 35

{p} = 110 points

Therefore, John scored 110 points in total.

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You have to put the value of the variables in the given column. Then press the button to calculate to find the regression line.

What is the regression line?

The linear equation that best fits the points is linear regression.

There are various methods for selecting the best-fitting line, with ordinary least squares being the most popular (OLS). The dependent variable (Y) and the independent variables are related according to linear regression (X).

Based on the independent variables, the linear regression model calculates the dependent variable (DV) (IV, predictors).

Select the type of regression line

Step 1: First make the column

Step 2: Then input the value of the variables.

Step 3: Press shift + 0 to get the menu option.

Step 4: from the menu select regression line number.

Step 5: Get the equation of the regression line.

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The regression line can be calculated by finding the slope and intercept. The equation of the regression line is y = slope * x + intercept.

To calculate the regression line, we need to find the slope and intercept of the line. Let's denote the independent variable as x and the dependent variable as y. The given data can be represented as a set of (x, y) pairs:

(x1, y1), (x2, y2), ..., (xn, yn)

To calculate the slope, we need to calculate the following sums:

Using these sums, the slope can be calculated as:

slope = (nΣxy - ΣxΣy) / (nΣx^2 - (Σx)^2)

Next, we can calculate the intercept using the following formula:

intercept = (Σy - slopeΣx) / n

Once we have the slope and intercept, we can write the equation of the regression line as:

y = slope * x + intercept

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The perimeter of the rectangle ABCD is 22 cm.

What is the perimeter of a rectangle?

In order to find the perimeter or distance around the rectangle, we need to add up all four side lengths. This can be done efficiently by simply adding the length and the width, and then multiplying this sum by two since there are two of each side length.

Perimeter = (length+width)×2 is the formula for the perimeter.

The perimeter of a rectangle is the sum of the lengths of all four sides.

If the sides of a rectangle have lengths of 6 cm and 5 cm, then the perimeter can be calculated as follows:

6 cm + 6 cm + 5 cm + 5 cm = 22 cm

The perimeter of a rectangle with sides 6 cm and 5 cm is 22 cm (2 * 6 cm + 2 * 5 cm = 22 cm).

Hence, the perimeter of the rectangle ABCD is 22 cm.

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Picture - 1 from left representation shows what balloon Z resembles after each change occurs when the pressure is halved and the Kelvin temperature is halved.

we have relation ,

PV= nRT ,  from ideal gas law

V = nRT /P

when P is halved P becomes P/2 and when T is halved it becomes T/2

V= nR ( T/2) / ( P/2)

     = nRT

Thus volume is unchanged   hence correct representation is  same size balloon  i.e middle

2)  The pressure is 2.5 atm  surrounding balloon. This makes balloon contract  since pressure outside balloon is higher than pressure inside balloon.

Thus correct representation of change is smaller balloon i.e picture 1 from left

(The pictures are attached below )

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The addition property and division properties are used to solve the expression.

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 expression is,

⇒ 3x - 4 = 1

Now, We can solve as;

⇒ 3x - 4 = 1

Add 4 both side,

⇒ 3x - 4 + 4 = 1 + 4

⇒ 3x = 5

Divide by 3;

⇒ x = 5/3

Thus, The addition property and division properties are used to solve the expression.

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The surface area of a cone is 103.6 in².

Option B is the correct answer.

It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.

We have,

Cone:

Diamter = 6 in

Radius = 3 in

Slant height.

s = 8 in

Now,

The surface area of a cone.

= πrs + πr²

= πr (s + r)

= 3.14 x 3 (8 + 3)

= 3.14 x 3 x 11

= 103.62 in²

Thus,

103.62 in² is the surface area of a cone.

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The area of the cone that was painted black is given by 47.66 ft²

For a right circular cone of radius 'r', height 'h', and slant height 'l', we have; Curved surface area of the right circular cone = π r l. The total surface area of a right circular cone = π(r + l) r. The volume of a right circular cone = 1/3π r2 h.

Given here: The height of the cone is 12 feet and circumference of the base of the cone is 8π

We know the base of the cross section is always a circle.

Thus  we have

2πr=8π

2r=8

r=4

Now slant height of the cone is given using the pythagoraes theorem as follows

l=[tex]\sqrt{4^2+12^2}[/tex]

=12.65 feet

Thus lateral surface area of the cone is L= πrl

                                                                   =3.14×4×12.65

                                                                   =158.884 ft²

Now we can infer from the question that 30% of the lateral surface area is painted black thus

Area painted black is = 30%×158.884

                                    =0.3×158.884

                                    =47.66 ft²

Hence, The area of the cone that was painted black is given by 47.66 ft²

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Answer: 47.7

Step-by-step explanation:i took the quiz the guy on top is wrong

The equation  models the problem is 54

The given parameters that will help us to determine the number are

During the first weekend of December, 43 pine trees were sold. The farm sold 97 trees in all that weekend.

There are two kinds of trees

Tir and Pine.  On the farm and in the weekend as 97 trees were sold with 43 pine tress.

Let f represent fir trees

This implies that f+43 = 97

⇒f= 97-43

f=54 tress

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Answer: 1. No, because figure 1 is 5 squares and figure 2 is 6 squares

Step-by-step explanation:

Word form One hundred three and five hundred three thouandth

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The car traveled 80.02  kilometer per hour on the average

It is a physical quantity that indicates the displacement of a mobile per unit of time, it is expressed in units of distance per time, for example (miles/h, km/h).

The formula and procedure we will use to solve this problem is:

v= x/t

Where:

Information about the problem:

Applying the velocity formula we have:

v = x/t

v = 600.15 km / 7.5 h

v = 80.02 km/h

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You need 500 factors to rank up and come to be Virtuoso in Brainly app.

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For the above system of equations 2x+4y+3z=11, 2y+5z=-9, x=11+6z,The value of y=-8, z=7/5, x=97/5.

An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the connection between two expressions on opposite sides of the sign. It generally consists of one variable and one equal to symbol.

Here,

x-6z=11

2x+4y+3z=11

2y+5z=-9

x=11+6z

substitute and calculate,

y=-8

z=7/5

x=97/5

The value of y=-8, z=7/5, x=97/5 for the given system of equation: 2x+4y+3z=11, 2y+5z=-9, x=11+6z.

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The rate of change for a health club is, 24.

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)

We have to given that;

A health club charges a $20 one-time sign-up fee and a monthly membership fee of $54 per month.

Hence, The equation to represents that the health club charges,

⇒ y = 24x + 54

Since, The general form of the slope - intercept equation is :

⇒ y = mx + c

Where, m = slope = rate of change in y per change in x

Therefore, By comparing the expressions, the slope of the cost function given is 24.

Hence, The rate of change = 24

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A frequency table is a simple tabular representation of the number of times a particular value or range of values appears in a data set.

It lists the values in one column and the corresponding frequencies in another column. For example, if we have data on the heights of a group of people, a frequency table could list the heights (in cm) in one column and the number of people with that height in the other column.

A frequency distribution is a graphical representation of the same information as a frequency table. It shows the number of occurrences of values in a data set by grouping the values into classes or intervals, and then plotting the frequency of each class or interval. For example, a histogram is a type of frequency distribution where the data is divided into equal-width intervals and the height of each bar represents the frequency of the data that falls within that interval.

A frequency table can be used for both qualitative and quantitative data, whereas a frequency distribution can only be used for quantitative data. This is because the classes or intervals used in a frequency distribution require a numerical representation of the data, which is not possible for qualitative data.

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So the probability that at least 3 customers out of the first 6 will buy bread is 0.7929 or about 79.29%.

To determine the appropriate probability, we may utilise the binomial distribution's cumulative distribution function (CDF). The likelihood that the number of successful occurrences in a specified number of independent trials is less than or equal to a specific value is given by the binomial distribution's CDF.

Let X represent the proportion of the first 6 clients who purchase bread. Then, X has a binomial distribution with n = 6 and p = 0.65 as its parameters. One less than the likelihood that fewer than three consumers will purchase bread results in the chance that at least three will:

P(X >= 3) = 1 - P(X < 3)

Using a cumulative distribution function of the binomial distribution, we can calculate P(X < 3) as:

P(X < 3) = CDF(2, n=6, p=0.65)

Using a binomial calculator or a programming library that implements the CDF of the binomial distribution, we find that P(X < 3) = 0.2071. Therefore, the desired probability is:

P(X >= 3) = 1 - P(X < 3) = 1 - 0.2071 = 0.7929

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