Solve the system of equations below by using SUBSTITUTION and record your sol y = 3x+5 4x + 2y = 30 y

The instantaneous rate of change at x = 2 is equal to the derivative, which is 2.

The derivative of f(x) = 2x - 5 with respect to x can be found by applying the power rule of differentiation, which states that the derivative of x^n is n*x^(n-1).

Taking the derivative of f(x) = 2x - 5:

f'(x) = 2 * (d/dx)(x) - (d/dx)(5)

= 2 * 1 - 0

= 2.

The derivative of f(x) with respect to x is a constant, 2, indicating that the function has a constant slope.

Therefore, the instantaneous rate of change at x = 2 is equal to the derivative, which is 2.

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Answer:

42c² + 11c - 3

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Step 1: Define

(6c - 1)(7c + 3)

Step 2: Expand

Answer:

42c²+11c+2

Step-by-step explanation:

6c(7c+3) -1(7c+3)

42c²+18c-7c+2

42c²+11c+2

i ain't sure if it is

the central angle of the arc is π/3 radians.

What is circumference of a circle?

Circumference or perimeter of a circle refers to the measuring of its limits. Contrarily, a circle's radius influences the amount of space it takes up. If a circle is opened up and represented by a straight line, its circumference is equal to its length. It is usually measured in units like centimetres or metres. While utilising the formula, the radius of the circle is taken into account when calculating the circle's circumference. Therefore, we need to know the radius or diameter value to determine the circle's perimeter.

Central angle (in radians) = arc length / radius

In this case, we are not given the radius of the circle directly, but we know that the circumference of the circle is 6. We can use the formula for circumference to find the radius:

Circumference = 2 * pi * radius

6 = 2 * pi * radius

radius = 3 / pi

Now we can use the formula for the central angle:

Central angle (in radians) = arc length / radius

Central angle = 1 / (3/pi) = pi/3

Therefore, the central angle of the arc is π/3 radians.

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Answer:

6 times or 6.4

The variance of Billy's grades obtained from his test scores is 15.76

The variance is a measure of variability or spread a dataset. The variance can be calculated from the sum of the square of the differences of the data points from the mean divided by the number or count of the data points.

The variance of Billy's test scores can be calculated by finding the mean or the average of the scores, then finding the sum of the squares of the differences of each score from the mean as follows;

The mean score = (89 + 88 + 93 + 90 + 81)/5 = 88.2

The square of the differences of the values from the mean can be calculated as follows;

(89 - 88.2)² = 0.64, (88 - 88.2)² = 0.04, (93 - 88.2)² = 23.04, (90 - 88.2)² = 3.24, and (81 - 88.2)² = 51.84

The sum of the square of the differences is therefore;

0.64 + 0.04 + 23.04 + 3.24 + 51.84 = 78.8

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"97.72% of the female students have scores above," seems to be a misinterpretation as the correct statement is that approximately 99.72% of the female students have scores between the lower and upper limits

To calculate the scores that are three standard deviations above and below the mean, we use the formula:

Lower limit = Mean - (Standard Deviation * 3)

Upper limit = Mean + (Standard Deviation * 3)

Given:

Mean = 269

Standard Deviation = 33

Using the formula, we can calculate the limits:

Lower limit = 269 - (33 * 3) = 269 - 99 = 170

Upper limit = 269 + (33 * 3) = 269 + 99 = 368

Therefore, the lower limit is 170 and the upper limit is 368.

To calculate the probability that a female student will have a score between these limits, we need to find the area under the normal distribution curve between the lower and upper limits. This can be calculated using a standard normal distribution table or calculator.

Since the distribution is assumed to be normal, approximately 99.72% of the scores will fall within three standard deviations from the mean. Therefore, the probability that a female student will have a score between these limits is approximately 99.72%.

For a score of 302, which is above the mean of 269, we can calculate the percentage of female students with scores below 302:

Percentage = (1 - Probability) * 100

= (1 - 0.9972) * 100

= 0.0028 * 100

= 0.28%

Therefore, approximately 0.28% of the female students have scores below 302.

It's important to note that the value mentioned, "97.72% of the female students have scores above," seems to be a misinterpretation as the correct statement is that approximately 99.72% of the female students have scores between the lower and upper limits

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Answer:

50.75

Step-by-step explanation:

We have:

\(E[g(x)] = \int\limits^{\infty}_{-\infty} {g(x)f(x)} \, dx \\\\= \int\limits^{1}_{-\infty} {g(x)(0)} \, dx+\int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx+\int\limits^{\infty}_{6} {g(x)(0)} \, dx\\\\= \int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x+3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x)\frac{2}{x} } \, dx + \int\limits^{6}_{1} {(3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {8} \, dx + \int\limits^{6}_{1} {\frac{6}{x} } \, dx\\\\\)

\(=8\int\limits^{6}_{1} \, dx + 6\int\limits^{6}_{1} {\frac{1}{x} } \, dx\\\\= 8[x]^{^6}_{_1} + 6 [ln(x)]^{^6}_{_1}\\\\= 8[6-1] + 6[ln(6) - ln(1)]\\\\= 8(5) + 6(ln(6))\\\\= 40 + 10.75\\\\= 50.74\)

Answer:

(7, 10)

Step-by-step explanation:

The vector has an x component of 5 and a y component of 7, so we can add each of these components to the coordinates of B to get its image:

B(2,3)

B'(2 + 5, 3 + 7) = B'(7, 10)

The image will be located at (7, 10).

Vectors, in Maths, exist as objects which have both, magnitude and direction. Magnitude determines the size of the vector. It exists described by a line with an arrow, where the length of the line exists the magnitude of the vector and the arrow displays the direction.

The vector has an x component of 5 and a y component of 7, so we can add each of these components to the coordinates of B to get its image:

B(2,3)

B'(2 + 5, 3 + 7) = B'(7, 10)

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Answer:

me too (help)

Step-by-step explanation:

The correct answer is B. The sample represents a proportion of the population.

A point estimate is a single value used to estimate a population's unknown parameter. The sample proportion (denoted by p), in the context of determining the population proportion, is a widely used point estimate. The sample proportion is determined by dividing the sample's success rate by the sample size.

The sample must be representative of the population for it to be a reliable point estimate of the population proportion. To accurately reflect the proportions of various groups or categories present in the population, the sample should be chosen at random.

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Answer:

65.7 mg/l.

Step-by-step explanation:

Answer:

A. 65.7 mg/l.

B. iv. No. The average chlorine compound concentration (mg/l) is too high.

Step-by-step explanation:

Given:

Outflow = 36%

= 36 l in 100 l of wetland

Seepage = 47%

= 47 l in 100 l of wetland

Evaporates = 8%

= 8 l in 100 l of wetland

Water volume = 9%

= 36 l in 100 l of wetland

Outflow = 53.6 mg/l

Seepage = 73.9mg/l

Remaining due to evaporation = 57.0mg/l

Water volume = 74.0 mg/l

Concentration of Chlorine compounds:

Outflow = 36/100 * 53.6

= 19.3 mg/l of outflow chlorine in the wetlands.

Seepage = 47/100 * 73.9

= 34.73 mg/l of seepage chlorine in the wetlands.

Evaporates = 8/100 * 57

= 4.56 mg/l of evaporates chlorine in the wetlands.

Water volume = 9/100 * 74

= 6.66 mg/l of outflow chlorine in the wetlands.

Weighted average concentration of chlorine compounds in 100 l of wetland = total(X*W)/totalW

Where,

Total w = 0.36 + 0.47 + 0.08 + 0.09

= 1

Total X*W = 19.3 + 34.73 + 4.56 + 6.66

= 65.65/1

= 65.7 mg/l.

While an absolute value may be any number, the output from an absolute value expression is always greater than or equal to zero

The absolute value | x | of a real number x is defined as the non-negative value of x without regard to its sign. For example, the absolute value of 3 is 3, and the absolute value of −3 is also 3. The absolute value of a number may be thought of as its distance from zero along real number line.

The absolute value of any number is seen to be always greater than or equal to zero. Both a number and its opposite are the same distance from zero on the number line. Since they have the same distance from zero, they have the same absolute value.

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Answer:

-35/-7=5

Step-by-step explanation:

Diviser par de nombre négatif alors sa devient positif pareil pour la multiplication

The solution to the equation is \(324=4(3)^2^x\)x = 2.

Given exponential equation

\(324=4(3)^2^x\\\)

\(4(3)^2^x=324\)

\(3^2^x=\frac{324}{4}\)

\(3^2^x=81\)

\(3^2^x=3^4\)

When bases are equal, power should be equal.

2x = 4

x = 2

Hence, the solution to the equation is x = 2.

An equation is a mathematical statement that asserts the equality of two expressions, usually separated by an equal sign (=). It typically involves one or more variables, which are unknowns to be determined or solved for. Equations can be algebraic or numerical, and they are often used in mathematics, science, engineering, and many other fields to model real-world situations, make predictions and solve problems. Solving an equation involves finding the values of the variables that satisfy the equation, and this can be done using various techniques such as substitution, elimination, graphing, or numerical methods.

We can simplify the left side of the equation using the exponent rule that states: \((a^n)^m = a^(n*m).\) Therefore, we have:

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The solution to the equation \($\mathrm{324 = 4 ( 3 )^{ 2x}}$\)  is x = 2. Thus, option C is correct.

An equation is a mathematical statement that asserts the equality of two expressions, usually separated by an equal sign (=). It typically involves one or more variables, which are unknowns to be determined or solved for.

Equations can be algebraic or numerical, and they are often used in mathematics, science, engineering, and many other fields to model real-world situations, make predictions and solve problems. Solving an equation involves finding the values of the variables that satisfy the equation, and this can be done using various techniques such as substitution, elimination, graphing, or numerical methods.

Given exponential equation:

\(324 = 4 ( 3 )^{ 2x}\)

\(4 ( 3 )^{ 2x} =324\)

\(( 3 )^{ 2x} = \dfrac{324}{4}\)

\(( 3 )^{ 2x} = 81\)

\(3 ^{ 2x} = 3^4\)

When bases are equal, power should be equal:

2x = 4

x = 2

Hence, the solution to the equation is x = 2.

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Complete question:

Select the correct answer.

What is the solution to this equation?

\(\mathrm{324 = 4 ( 3 )^{ 2x}}\)

A. x = 8

B. x = 1

C. x = 2

D. x = 4

\(\dfrac{7!4!}{5!3!}=6\cdot7\cdot4=168\)

1/1728 is the value of negative integers .

What in math is an integer?

= 12⁻³

= 1/12³

=  1/1728

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Answer:

y=1/2x  or y=.5x

Step-by-step explanation:

The exponential regression equation is y = 172.21(0.99)ˣ and at x = 60 minutes y = 94.22 degree Fahrenheit and at x = 240 minutes y = 15.43 degree Fahrenheit.

It is defined as the relation between two variables which is a quantitative type and gives an idea about the direction of these two variables.

\(\rm r = \dfrac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{{[n\sum x^2- (\sum x)^2]}}\sqrt{[n\sum y^2- (\sum y)^2]}}\)

We have data shown in the table:

We can find the exponential regression equation using the data shown.

\(\rm y = ab^x\)

After calculating from the data:

a = 172.21 and b = 0.99

\(\rm y = 172.21(0.99)^x\)

The correlation coefficient will be:

r = -0.99

The range will be all real numbers.

The domain will be y > 0

As we can see in the graph x ∈R and y>0

After an hour,

Plug x = 60 minutes in the exponential regression equation:

\(\rm y = 172.21(0.99)^{60}\)

y = 94.22 degree Fahrenheit

After 4 hours, plug x = 240

\(\rm y = 172.21(0.99)^{240}\)

y = 15.43 degree Fahrenheit

Similarly, we can find any data from the exponential regression equation.

Thus, the exponential regression equation is y = 172.21(0.99)ˣ and at x = 60 minutes y = 94.22 degree Fahrenheit and at x = 240 minutes y = 15.43 degree Fahrenheit.

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Answer:

1 1/6

Step-by-step explanation:

Edwin used a quantity of 2.833 gallons of paint for the mural which is the difference between the quantity of paint at the beginning and the used for the bedroom.

We have been given that Edwin has 3 1/2 gallons of green paint. He uses 2/3 of the paint to paint his bedroom. He uses the rest of the paint for a mural in his garage.

A fraction is defined as a numerical representation of a part of a whole that represents a rational number.

To determine the quantity of paint Edwin used for the mural.

The quantity of paint Edwin used for the mural is the difference between the quantity of paint at the beginning and the used for the bedroom.

The quantity of paint used for the mural = 3 1/2 gallons - 2/3 gallons

The quantity of paint used for the mural = 3.5 - 0.66

The quantity of paint used for the mural = 2.833

Thus, Edwin used a quantity of 2.833 gallons of paint for the mural.

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The required value of trigonometric ratios is,

sin 45° = 1/\(\sqrt{2}\)

cos 30 = \(\sqrt{3}\)/2

tan 60 = 1/  √3

We know that,

Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.

Therefore,

sin 45° = 1/\(\sqrt{2}\)

cos 30 = \(\sqrt{3}\)/2

tan 60 = 1/  √3

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Answer: A. SQRT2 (SQRT3 -1) / 4

explanation:

Just took the quiz on A P E X.

The value of given function \(sin(\frac{5\pi}{12} )\) is approx. 0.97

Option C is correct.

The given trigonometric function is,

                              \(sin(\frac{5\pi}{12} )\)

first we have to convert given angle into degree.

                      \(\frac{5\pi}{12}=\frac{5}{12}*180=75\)

So that,

        \(sin(\frac{5\pi}{12} )=sin(75)=0.9659\)

Hence, the value of given function \(sin(\frac{5\pi}{12} )\) is approx. 0.97

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Step-by-step explanation:

7

√

15

32

=

0.85

Explanation:

sin 2t = 2sin t.cos t

Knowing

cos

t

=

−

7

8

, find sin t.

Trig identity:

sin

2

a

=

1

−

cos

2

a

-->

sin

2

t

=

1

−

cos

2

t

=

1

−

49

64

=

15

64

sin t = +- sqrt15/8.

Arc t is in Quadrant III, then, sin t is negative.

sin

2

t

=

2

(

−

7

8

)

(

−

√

15

8

)

=

7

√

15

32

=

0.85

hope this helps :)

Answer:

x + 2

Step-by-step explanation:

The quotient for the given dividend and divisor is x+2. Therefore, option A is the correct answer.

A quotient is a quantity produced by the division of two numbers. The quotient has widespread use throughout mathematics, and is commonly referred to as the integer part of a division, or as a fraction or a ratio.

Given that, dividend = x²+3x+2 and divisor = x+1

The factorization of x²+3x+2 is

x²+2x+1x+2

= x(x+2)+1(x+2)

= (x+2)(x+1)

Now, x²+3x+2/(x+1)

= (x+2)(x+1)/(x+1)

= (x+2)

So, the quotient is x+2

Therefore, option A is the correct answer.

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The width of the image which was photocopied by Jackie and has an initial length of 6 inches and width of 4 inches is 6 inches.

An area is a unit of measurement used to describe the size of a region on a planar or curved surface. While a plane region or area refers to the area of a shape or planar lamina, a surface region or plane area refers to the area of an open surface or the boundary of a three-dimensional object.

Given:

The initial length of the image, l = 6 inches,

The initial width of the image, w = 4 inches,

The reduced length of the image, L = 4 inches,

The area of the initial image = The area of the reduced image,

l × w = L × W

Here W is the reduced width.

Substitute the values,

6 × 4 = 4 × W

W = 6 inches,

Therefore, the width of the image which was photocopied by Jackie and has an initial length of 6 inches and width of 4 inches is 6 inches.

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Step 1: To construct

The box plot for the given data.

Step 2 : Explanation

Box plots are a graphical tool used in statistics to show the concentration of data. They also demonstrate how far the extreme numbers differ from the majority of the data. The smallest value, the first quartile, the median, the third quartile, and the maximum value are used to create a box plot.

Use a horizontal or vertical number line and a rectangular box to make a box plot. The axis's ends are labelled by the smallest and largest data values. One end of the box is marked by the first quartile, while the other end is marked by the third quartile. Approximately half of the data is included within the box. From the box's ends to the smallest and greatest data values, the "whiskers" extend. The median or second quartile can be in the middle of the first and third quartiles, or it can be either one or the other.

The box plot's five numerical summaries are as follows:

# of movies Frequency Cumulative frequency

0 5 5

1 9 14

2 6 20

3 4 24

4 1 25

N=25

Answer:

0.0015

Step-by-step explanation:

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