Match the key features of functions terms to their corresponding definitions.

The car speed measurements that represent the same level of accuracy compared to the speed limit sign is 64mph (option D).

Accuracy is the exact conformity to truth or the degree of conformity of a measure to a true or standard value.

Accuracy is different from precision as precision deals with the closeness of an observed value with a true value.

According to this question, a highway sign shows a speed limit of 65 miles per hour. This suggests that a car speed measurement that will represent the same level of accuracy compared to the speed limit sign is 64mph.

64mph is the closest speed measurement to 65mph that does not exceed this speed limit. However, 66 mph is also close but exceeds the true value for the speed limit.

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Answer:

[tex]f(g(x))[/tex]  = [tex]\sqrt{8x - 4}[/tex]

Step-by-step explanation:

• [tex]f(x) = \sqrt{x + 8}[/tex]

• [tex]g(x) = 8x - 12[/tex]

[tex]f(g(x))[/tex] is the combination of the functions [tex]f(x)[/tex] and [tex]g(x)[/tex] such that [tex]g(x)[/tex] is the input to the function [tex]f(x)[/tex] .

This means, we have to replace the original input of  [tex]f(x)[/tex], which is [tex]x[/tex], with the function  [tex]g(x)[/tex].

∴  [tex]f(g(x))[/tex] = [tex]f(8x - 12)[/tex]

               ⇒ [tex]\sqrt{8x - 12 + 8}[/tex]

               ⇒ [tex]\sqrt{8x - 4}[/tex]

The complete proof from the figure is:

The given parameter is:

AC ≅ DF; AB ≅ DE; ∠1 ≅ ∠6

Angles 1 and 2, & Angles 5 and 6 are vertical angles

So, we have: ∠1 ≅ ∠2; ∠5 ≅ ∠6 by the definition of vertical angles.

From the figure, triangles ABC and DEF are congruent by the SAS postulate.

So, we have: ΔABC ≅ ΔDEF by the definition of SAS postulate

Angles 3 and 4 are corresponding angles

So, we have: ∠1 ≅ ∠2; ∠5 ≅ ∠6 by the definition of corresponding angles.

Hence, the lines BC and EF are parallel lines

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The coefficient of determination, r, is the amount of variation in the observed values of the response variable that is explained by the regression line.

About Coefficient of Determination:

When forecasting the result of an event, the coefficient of determination is a statistical measurement that looks at how variations in one variable may be explained by differences in a second variable.

In other words, the coefficient of determination, r, which is more frequently used to refer to the strength of a linear relationship between two variables, is a crucial tool for researchers when undertaking trend analysis.

For illustration, this coefficient of determination might be used to consider the possibility that a woman would give birth to her child on a specific date in the future if she became pregnant on a specific day. This metric's objective in this situation is to determine the relationship between the connected occurrences of conception and birth.

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The value of the function (h-g)(2.1) is -3.51

The equations of the functions are given as:

Let g(x)= 2x^2+3x-9 and h(x)=x^2+2x-6

To calculate or find (h-g)(2.1), we start by calculating h(2.1) and g(2.1)

This is calculated as follows:

g(2.1)= 2(2.1)^2+3(2.1)-9

Evaluate

g(2.1)= 6.12

h(2.1)=(2.1)^2+2(2.1)-6

Evaluate

h(2.1)=2.61

The function is then calculated as:

(h-g)(2.1) = h(2.1) - g(2.1)

This gives

(h-g)(2.1) = 2.61 - 6.12

Evaluate the difference

(h-g)(2.1) = -3.51

Hence, the value of the function (h-g)(2.1) is -3.51

As a breakdown

g(x)= 2x^2+3x-9

h(x)=x^2+2x-6

g(2.1)= 2(2.1)^2+3(2.1)-9

g(2.1)= 6.12

h(2.1)=(2.1)^2+2(2.1)-6

h(2.1)=2.61

(h-g)(2.1) = h(2.1) - g(2.1)

(h-g)(2.1) = 2.61 - 6.12

(h-g)(2.1) = -3.51

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Answer is below attached

Step by step. We know y = -3x -5

The first point on the graph is -5 on the y axis. It is your y intercept.

The second point is your slope, which is the number next to the x, stated as y/x, -3/1.

You will graph this from the y-intercept as shown in red.

Then you can connect the points, shown with the blue line.

Correct option is  B)

Cross-multiplication is helpful in Solving proportions.

Solving proportions is simply a matter of stating the ratios as fractions, setting the two fractions equal to each other, cross-multiplying and solving the resulting equation.

Method I: Draw a double-sided number line, label the parts, set up a proportion and solve.

Method II: Using any method, calculate unit rate and then calculate how many pounds you can get for $30. Method III: Graph a point to represent the original ratio.

The product of the means is equal to the product of the extremes.

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I understand the the question you are looking for is :

Cross-multiplication is helpful in:

a. quadratic equations

b. solving proportions

c. linear equations

d. word problems

please select the best answer from the choices provided a b c d

The numbers which is greater than 70 but less than 100, not divisible by 10, not divisible by 4, not an odd number are 74, 78, 82, 86, 94, 98

A number greater than 70 but less than 100

71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 98

Not odd number

72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98

Not divisible by 10

72, 74, 76, 78, 82, 84, 86, 88, 92, 94, 96, 98

Not divisible by 4

74, 78, 82, 86, 94, 98

Therefore, the numbers which is greater than 70 but less than 100, not divisible by 10, not divisible by 4, not an odd number are 74, 78, 82, 86, 94, 98.

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By using the digits 0 to 9, the boxes are filled with their respective numerical values to make the chart accurate as shown in the image attached below.

A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables.

In Mathematics, there are different types of functions and these include the following;

A logarithm function can be defined as a type of function that represents the inverse of an exponential function. Mathematically, a logarithm function is written as follows:

y = logₐₓ

y = log₁₀10

y = log₁₀10 = 1.  

Therefore, if log₁₀x < 1, then, x < 10.  Also, if log₁₀x > 1, then, x > 10.

For this exercise, you should take note of this deductive points:

In conclusion, by using the digits 0 to 9, the boxes are filled with their respective numerical values to make the chart accurate as shown in the image attached below.

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In order to find how many times they will blink at the same time we need to find the common multiple of 4 and 6 between 1 and 60.

The first bulb blinks after every 4 seconds, means it blinks in multiple of 4.

The multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60.

The second bulb blinks after every 6 seconds, means it blinks in multiple of 6.

The multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60.

The common multiple of 4 and 6 = 12, 24, 36, 48, 60.

∴

in sixty seconds they will blink 5 times at the same time.

Answer:

(8,14)

Step-by-step explanation:

3x+2y=52

3x+1y=38 Subtract these equations using elimination method to get y=14

Then substitute y=14 to either equation

the bottom one is easier so

3x+1(14)=38 distribute 1 to 14 and any number times one is 1

3x+14=38 Subtract 14 from both sides

3x=24 Divide by 3

x=8 so check now

3(8)+1(14)=38

24+14=38?

38=38? yes

Answer:

see explanation

Step-by-step explanation:

3- digit numbers starting with 5 are

528 and 582

3- digit numbers starting with 2 are

258 and 285

3- digit numbers starting with 8 are

825 and 852

there are 6 possible 3- digit numbers

258 , 285 , 528 , 582 , 825 , 852

ADG is an equilateral triangle, then, line AD is equivalent to line AG.

From the information given, we have to prove that;

AD=AG

It is important to note that the triangle ADG is an equilateral triangle.

The properties of an equilateral triangle are;

Since ADG is an equilateral triangle, then, line AD is equivalent to line AG

Thus, since ADG is an equilateral triangle, then, line AD is equivalent to line AG.

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Answer:

Son: 26 yrs. Dad: 58 yrs.

Step-by-step explanation:

Let s equal to the present age of the son and let d equal to the present age of the dad. We can make two equations based on the information given to us. The first is about the fact that the dad is 32 yrs. older than the son:

d = s+32

the second is about the fact that 10 yrs. ago, he was triple his son's age.

d-10 = 3(s-10)

We can use the distributive property and we have:

d-10 = 3s-30

Then, let's add 10 to each side:

d = 3s-20

We can substitute the first equation into the second, resulting in:

s+32 = 3s-20

Adding 20 to both sides:

s+52 = 3s

2s = 52

s = 26

Now that we have the son's age, the dad's age is 26+32 = 58.

Son's age: 26

Dad's age: 58

The exponential model that best represents the data is f(x) = 2(3)x

Exponential equations are inverse of logarithmic equation. Exponential equations are written in the form y = ab^x

where

a is the base

x is the exponent

Using the coordinate points (0, 2) and (1, 6)

Substitute

2 = ab^0
6 = ab

Take the ratio
6/2 = ab/a
3 = b

Determine the value of 'a"

Recall that

6 = ab

6 = 3a

Divide both sides by 3

3a/3 = 6/3

a = 2

Hence the exponential model that best represents the data is f(x) = 2(3)x

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Answer: 6,760,000

Step-by-Step Explanation:

Substitute [tex]y=\sin^{-1}\left(\frac x4\right)[/tex], so that

[tex]dy = \dfrac{dx}{4\sqrt{1-\left(\frac x4\right)^2}} = \dfrac{dx}{\sqrt{16 - x^2}}[/tex]

Then the integral is

[tex]\displaystyle \int \frac{\left(\sin^{-1}\left(\frac x4\right)\right)^2}{\sqrt{16-x^2}} \,dx = \int y^2 \, dy[/tex]

and by the power rule,

[tex]\displaystyle \int y^2 \, dy = \frac13 y^3 + C[/tex]

so that the original integral is

[tex]\displaystyle \int \frac{\left(\sin^{-1}\left(\frac x4\right)\right)^2}{\sqrt{16-x^2}} \,dx = \boxed{\frac13 \left(\sin^{-1}\left(\frac x4\right)\right)^3 + C}[/tex]

Answer: is 48 eggs .

Step-by-step explanation:

3 hens gives 3 eggs in 3 days

Therefore , 1 gives 1 egg in 3 days

So

3days = 1egg

After that 12 days\/3 times = 4 eggs (in 12 times )

So 1 hen offers 4 eggs in 12 days after that

12 hens x 4 eggs = 48 eggs (in 12 days by 12 hens)

There are 7 ones on the left and only 2 on the right. The two sides need to be even, or balanced.

7 = 2 + r

r = 5

Hope this helps!

Answer:

Step-by-step explanation:

[tex]\dfrac{ 1 }{ 2 } \times 12\times 15\times \sin ( 110 )[/tex]

==> 84.57

The extra amount that Mauro has to pay in federal taxes because he won the lottery would grossly amount to $336100.50. Option B

The term tax refers to money that the citizens of a country are mandatorily required to pay to the government from their income. This money is used for the provision of basic amenities for the people of the country.

We are able to understand from all the information provided in the question that that the extra amount that Mauro has to pay in federal taxes because he won the lottery would grossly amount to $336100.50.

Tax paid before lottery is;:

= $4386.25 + [($34500 - $31850) × 0.25]

= $4386.25 + ($2650 × 0.25)

= $4386.25 + $662.50

= $5048.75

Tax paid after lottery is:

= [($1000000 + $34500 - $349700) × 0.35)] + $101469.25

= $239680 + $101469.25

= $341149.25

Tax difference is:

= $341149.25 - $5048.75

= $336100.50

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Missing parts;

Mauro just won $1,000,000 from the lottery! despite his excitement in winning a tremendous amount of money, his brother (who is an accountant) warns him not to spend it all at once and hands him this tax rate schedule for single taxpayers. taxable income federal tax $0-$7,825 10% of amount $7825.01-$31,850 $725.50 plus 15% of amount over 7,825 $31,850.01-$77,100 $4,386.25 plus 25% of amount over 31,850 $77,100.01-$160,850 $15,698.75 plus 28% of amount over 77,100 $160,850.01-$349,700 $39,148.75 plus 33% of the amount over 160,850 $349,700.01 and up $101,469.25 plus 35% of amount over 349,700 using this chart, a taxpayer who makes $58,000 annually (line 3) will have to pay $4,386.25 plus 25% of the differene of 58,000 and 31,850 or 4,386.25 + (0.25)(58,000-31,850) = $10,923.75. before winning the lottery, mauro's annual income was $34,500. use the chart to determine mauro's federal tax before winning the lottery and after winning the lottery. how much extra does he have to pay in federal taxes because he won the lottery?

a. $5,048.75

b. $336,100.50

c. $341,149.25

d. $676,260.76

Answer:

16b > 94

Step-by-step explanation:

16b > 94

b > 5.875

Crystal needs 6 boxes to fit all 94 discs.

Considering their graphs, the interval in which both functions are positive is:

(0, 2)

A function is positive when it's graph is positioned above the x-axis.

Looking at the graph, the functions are positive for x between 0 and 2, hence the interval in which both functions are positive is stated as follows:

(0, 2)

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Answer:

○ [tex]3x + 4y = 7[/tex]

Step-by-step explanation:

The general form of the equation of a straight line is as follows:

[tex]\boxed{y = mx + c}[/tex],

where:

m = slope

c = y-intercept.

This means that m, which is the coefficient of [tex]x[/tex], needs to be [tex]-\frac{3}{4}[/tex].

Therefore we have to rearrange each equation given to make y the subject, and then check if the coefficient of [tex]x[/tex] becomes [tex]-\frac{3}{4}[/tex].

• First option:

[tex]4x - 3y = 7[/tex]

⇒ [tex]-3y = -4x + 7[/tex]

⇒ [tex]y = \frac{4}{3}x -{ \frac{7}{3}[/tex]

∴ 'm' is [tex]\bf \frac{4}{3}[/tex], not  [tex]-\frac{3}{4}[/tex], therefore this option is incorrect.

• Second option:

[tex]4x + 3y = 7[/tex]

⇒ [tex]3y = -4x + 7[/tex]

⇒ [tex]y = -\frac{4}{3}x + \frac{7}{3}[/tex]

∴ 'm' is [tex]\bf -\frac{4}{3}[/tex], not  [tex]-\frac{3}{4}[/tex], therefore this option is incorrect.

• Third option:

[tex]3x + 4y = 7[/tex]

⇒ [tex]4y = -3x + 7[/tex]

⇒ [tex]y = -\frac{3}{4}x + \frac{7}{3}[/tex]

'm' is [tex]\bf -\frac{3}{4}[/tex], therefore this option is correct.

Note:

You can rearrange the equation given in the last option, and see that 'm' comes out to be [tex]\frac{3}{4}[/tex], thereby making it incorrect.

[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]

[tex]\sf{- \dfrac{3}{4}}[/tex]

First, we take all the given options to their slope-intercept form:

[tex]\longrightarrow \sf{y=m x+b}[/tex]

Taking to each equation to its slope-intercept form, you get:

[tex]\small\longrightarrow \sf{-3y = 7 - 4x}[/tex]

[tex]\small\longrightarrow \sf{- \dfrac{4}{ - 3} x + \dfrac{7}{3} }[/tex]

[tex]\small\longrightarrow \sf{y = \dfrac{4}{ 3} x - \dfrac{7}{3} }[/tex]

[tex]\small\longrightarrow \sf{3y = 7 - 4x}[/tex]

[tex]\small\longrightarrow \sf{y = \dfrac{7}{3} - \dfrac{4}{3} x}[/tex]

[tex]\small\longrightarrow \sf{4y y = = 7- 3x}[/tex]

[tex]\small\longrightarrow \sf{y = \dfrac{7}{4} - \dfrac{3}{4} x}[/tex]

[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]

◉ [tex] \bm{3x+4y=7}[/tex]

Answer:

C

Step-by-step explanation:

4 is a perfect square.  2 x 2.  You can pull the 2 out and everything else would be left under the square root symbol.

The average rate of change over the interval is 2/9

The interval is given as:

-4 ≤ x ≤ 5

From the table, we have:

f(5) = 4

f(-4) = 2

The average rate of change is then calculated as:

[tex]m = \frac{f(5) - f(-4)}{5 --4}[/tex]

This gives

[tex]m = \frac{4 - 2}{5 +4}[/tex]

Evaluate

[tex]m = \frac{2}{9}[/tex]

Hence, the average rate of change over the interval is 2/9

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The greatest common factor for the following sets of numbers are as follows,

24, 34, 567 : 1

23, 36, 52, 11 : 1

37, 53, 72, 11², 13 : 1

1, 2, 3, 4, 6, 8, 12, and 24 make up the number 24.

1, 2, 17, and 34 make to the number 34.

1, 3, 7, 9, 21, 27, 63, 81, 189, and 567 make up the number 567.

Because of this, the case's greatest common factor is 1.

The elements of 11 are: 1, 11

The 23 factors are: 1, 23,

1, 2, 3, 4, 6, 9, 12, 18, and 36 make up the number 36.

The sum of 52's factors is: 1, 2, 4, 13, 26, and 52.

Therefore, 1 is the number that these numbers have the most in common, and thus, 1 is the greatest common factor here.

The elements of 13 are: 1, 13, and

These are the 37 factors: 1, 37

These are the components of 53: 1, 53

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72 make up the number 72.

1, 11, and 121 make up the number 121.

Thus, the greatest common factor for 37, 53, 72, 121, 13 is again 1.

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The Laplace of the given equation is [tex]y=-\frac{15e^2}{8}e^{2t}+\left(-3e^2+\frac{15e^2}{4}\right)e^{2t}t+\frac{e^2t^4}{4}+e^2t^3+\frac{9e^2t^2}{4}+3e^2t+\frac{15e^2}{8}[/tex].

According to the statement

we have given that the equation and we have to solve this problem with the help of the Laplace transform.

So, According to the statement

the given equation is

y'' − 4y' + 4y = t^3e^2t, y(0) = 0, y'(0) = 0

And the Laplace transform is an integral transform method which is particularly useful in solving linear ordinary differential equations.

Firstly fill the value of the Laplace of the second order derivative and put x = 0 in the equation

And same it with the first order of the derivative.

And then the Laplace of the equation become

[tex]y=-\frac{15e^2}{8}e^{2t}+\left(-3e^2+\frac{15e^2}{4}\right)e^{2t}t+\frac{e^2t^4}{4}+e^2t^3+\frac{9e^2t^2}{4}+3e^2t+\frac{15e^2}{8}[/tex]

So, The Laplace of the given equation is [tex]y=-\frac{15e^2}{8}e^{2t}+\left(-3e^2+\frac{15e^2}{4}\right)e^{2t}t+\frac{e^2t^4}{4}+e^2t^3+\frac{9e^2t^2}{4}+3e^2t+\frac{15e^2}{8}[/tex]

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Answer:

  1/2

Step-by-step explanation:

The "Pythagorean relation" between trig functions can be used to find the sine.

The relation between sine and cosine is the identity ...

  sin(x)² +cos(x)² = 1

This can be solved for sin(x) in terms of cos(x):

  sin(x) = √(1 -cos(x)²)

For the present case, using the given cosine value, we find ...

  sin(x) = √(1 -(√3/2)²) = √(1 -3/4) = √(1/4)

  sin(x) = 1/2

__

Additional comment

The sine and cosine of an angle are the y and x coordinates (respectively) of the corresponding point on the unit circle. The right triangle with these legs will satisfy the Pythagorean theorem with ...

  sin(x)² + cos(x)² = 1 . . . . . . where 1 is the hypotenuse (radius of unit circle)

A calculator can always be used to verify the result.