55. TECHNOLOGY
If f is a linear function, f(0.1) = 11.5, and f(0.4) = -5.9, find an equation for the function.

The average rate of change from x=1 to x= 4 is -0.7

We have f(1) to be 3

while we have f(4) as 1

The average rate of change can be solved as

f(4) - (f(1) / 4 - 1

This is solved as

1 - 3 / 4 - 1

= -2 / 3

= -0.7

Hence the average rate of change for the graph that we have above is -0.7

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Answer:

a = 2

Step-by-step explanation:

[tex] \frac{a - ( - 6)}{ - 8 - a} = - \frac{4}{5} [/tex]

[tex] \frac{a + 6}{a + 8} = \frac{4}{5} [/tex]

[tex]4(a + 8) = 5(a + 6)[/tex]

[tex]4a + 32 = 5a + 30[/tex]

[tex]a = 2[/tex]

Step-by-step explanation:

5,000 by dividing 10.000

$5000 of the new deposits is the bank required to keep on hand.

The answer is option A.

Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.

Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.

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The inverse function of f(x) is [tex]f^{-1}(x) = \sqrt[3]{x + 1} - 3[/tex]

The function is given as:

f(x) = (x + 3)^3 - 1

Rewrite as:

y = (x + 3)^3 - 1

Swap x and y

x = (y + 3)^3 - 1

Add 1 to both sides

(y + 3)^3 = x +  1

Take the cube root of both sides

[tex]y + 3 = \sqrt[3]{x + 1}[/tex]

Subtract 3 from both sides

[tex]y = \sqrt[3]{x + 1} - 3[/tex]

Rewrite as:

[tex]f^{-1}(x) = \sqrt[3]{x + 1} - 3[/tex]

Hence, the inverse function of f(x) is [tex]f^{-1}(x) = \sqrt[3]{x + 1} - 3[/tex]

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Answe1/5 of r = 15

Step-by-step explanation:

1/5 r=

Answer:

The answer is D(f-g)

Step-by-step explanation:

Profit minus expenses

Answer:

D

Step-by-step explanation:

The profit can be defined as (cost of production) - (revenue) and since the cost is defined as g(x) = x^2 and the revenue is f(x) = 4x+1. The profit can be defined as [tex](f-g) = (4x+1)-x^2 = -x^2+4x+1[/tex]. After 2 months you can calculate the profit by simply plugging in 2 as x. This gives you the equation: [tex](f-g) = (4(2) + 1) - 2^2 = 9-4 = 5\$[/tex]

If function has points (1/2,0) and (6,0) then [tex]g(x)=2x^{2} -13x+6\\[/tex]

Given x-intercepts at (1/2,0)(6,0) and we have to find the function g(x)

If the x-intercepts lie at (1/2,0)(6,0) then the function has roots of 6 and 1/2. Function is a relationship between variables having value of y for each value of x. Value of x is domain and value of y is known as codomain.

If we insert x=6 or x=1/2 into the equation of g(x) we will obtain 0 as under:

g(6)=0

In order to get 0 the equation will be x-6.

In order to get 0 for root the equation will be x-1/2.

but x-1/2 does not appear in any of these but its multiples can be there :

[tex]2(x-1/2)=2x-1[/tex]

Therefore the function will be as under:

[tex]g(x)=(x-6)(2x-1)[/tex]

[tex]g(x)=2x^{2} -x-12x+6[/tex]

[tex]g(x)=2x^{2} -13x+6[/tex]

Hence the function g(x) is [tex]g(x)=2x^{2} -13x+6[/tex].

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The system of linear inequalities which satisfy the region R in the graph above are:

Mathematically, the general equation of a straight line is given by y = mx + b.

In order to determine the system of linear inequalities that satisfy the region R, we would identify the points through which these straight lines passes through.

For the left line, we have:

y-intercept = 3.

x-intercept = -3/2.

Points (x, y) = (0, 3) and (-3/2, 0).

Thus, the inequality is given by:

(x/-3/2) + y/3 ≤ 1.

-2x + y ≤ 3

y ≤ 2x + 3

For the right line, we have:

y-intercept = 4.

x-intercept = 4.

Points (x, y) = (0, 4) and (4, 0).

Thus, the inequality is given by y ≥ -x + 4

For the lower line, we have:

y-intercept = 0.

x-intercept = 4.

Points (x, y) = (4, 0)

Thus, the inequality is given by y ≤ x + 4

In conclusion, the system of linear inequalities which satisfy the region R in the graph above are:

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Answer:

a. a is bigger than -a

b. a is equal to -a

c. a is less than -a

Step-by-step explanation:

Let's say a = 2

If a > 0, 2 > -2

If a = 0, 0 = -0; -0 and 0 are the same

Let's say a = -1

If a < 0, -1 ? -(-1)

-1 < 1

Answer:

74 yards squared

Step-by-step explanation:

Divide the shape up into 2 3x5 rectangles and one 11x4 rectangle

2(3x5)+11x4=30+44=74

74 yards squared

Answer:

they reached the shore they get 135 miles

The linear model for the data is expressed as: R = 20p - 160.

Using two pairs of values from the table values, say, (32, 480) and (33, 500), find the unit rate (m).

Unit rate (m) = (500 - 480)/(33 - 32) = 20/1

Unit rate (m) = 20.

Substitute (p, R) = (32, 480) and m = 20 into R = mp + b to find b

480 = 20(32) + b

480 = 640 + b

480 - 640 = b

b = -160

To write the linear model, substitute m = 20 and b = -160 into R = mp + b:

R = 20p - 160

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Answer:

2304 cm³

Step-by-step explanation:

To find the volume of a composite figure, it is easiest to break it down into smaller, more recognizable shapes.

here, we can break our shape into two sections: the green section and the blue section

then, we will add the volumes of these shapes together

green section's volume:

note: you could also calculate this as four separate cubes

to find the volume of a rectangle, we need to multiply

length × width × height

here, our length is 12 (6 + 6); our height is 12 (6 + 6); and our width is 6

let's multiply these together: (12)(12)(6) = 864

so, the volume of the green section is 864 cm³

now, let's work with the blue section:

once again, the volume for a rectangle is length × width × height

here, our length is 18, our height is 10, and our width is 8

let's multiply these together: (18)(10)(8) = 1440

so, the volume of the blue section is 1440cm³

now, we can add our sections together:

1440 + 864 = 2304

meaning that the volume of the composite figure is 2304 cm³

hope this helps!! have a lovely day :)

Answer:

we will use democracy so that everyone gets a say in what happens to the colony, second the government will make the decisions and the people will provide options and different ideas, and i believe its the best type because everyone has a say in what happens and the government isn't too powerful and has as much power as the people do.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

[tex] \frac{x}{y} = \frac{10}{5} \\ = \frac{5}{1} [/tex]

1. •°• y is 5 times x

[tex] \frac{x}{y} = \frac{30}{5} \\ = \frac{6}{1} [/tex]

2. •°• y is 6 times x

[tex] \frac{x}{y} = \frac{56}{8} \\ = \frac{7}{1} [/tex]

3. •°• y is 7 times x

[tex] \frac{x}{y} = \frac{88}{11} \\ = \frac{8}{1} [/tex]

4. •°• y is 8 times x

[tex]2 \times \frac{7}{4} [/tex]

•°• y is 2 times x

[tex]5 \times \frac{7}{4} [/tex]

•°• y is 5 times x

[tex]8 \times \frac{7}{4} [/tex]

•°• y is 8 times x

[tex]11 \times \frac{7}{4} [/tex]

•°• y is 11 times x

Answer:

17.6 ft

Step-by-step explanation:

tan 37 = 130/x

x = 130/tan 37 = 130/0.7536 = 172.5 feet

tan 40 = 130/y

y = 130/tan 40 = 130/0.8391 = 154.9

172.5 - 154.9 = 17.6 ft

Answer:

17.6 Ft

Step-by-step explanation:

Geometry B E2020!! :3

Answer: (1, -5)

x = 1

y = -5

*Hope this helps, enjoy the rest of your day! ♥️*

Answer: (1, -5)

Step-by-step explanation:

I got you...

In solving system of equations there are three ways..

lets use addition

First we need to cancel out one of the variables

Lets cancel out the y

In order to do this lets multiply the top equation by -2 to get 2y and 4y to cancel out.

(-2)(-9x+2y) = -19(-2)

18x - 4y = 38

Now our system looks like this:

18x - 4y = 38

5x  + 4y = -15

lets add these together

18x - 4y = 38

5x  + 4y = -15   +

= 23x = 23

x = 1

We know x = 1, so substitude 1 for x in one of the equations

5(1) + 4y = -15

5 + 4y = -15

4y = -20

y = -5

This is the y value

Our final answer is (1, -5)

As an ordered pair

The Expected value of XX is 1.00.

Given that a box contains 8 cameras and that 4 of them are defective and 2 cameras is selected at random with replacement.

The probability distribution of the hypergeometric is as follows:

[tex]P(x,N,n,M)=\frac{\left(\begin{array}{l}M\\ x\end{array}\right)\left(\begin{array}{l}N-M\\ n-x\end{array}\right)}{\left(\begin{array}{l} N\\ n\end{array}\right)}[/tex]

Where x is the success in the sample of n trails, N represents the total population, n represents the random sample from the total population and M represents the success in the population.

The probability distribution for X is obtained as below:

From the given information, let X be a random variable, that denotes the number of defective cameras following hypergeometric distribution.

Here, M = 4, n=2 and N=8

The probability distribution of X is obtained below:

The probability distribution of X is,

[tex]P(X=x)=\frac{\left(\begin{array}{l}5\\ x\end{array}\right)\left(\begin{array}{l}8-5\\ 2-x\end{array}\right)}{\left(\begin{array}{l} 8\\ 2\end{array}\right)}[/tex]

The probability distribution of X when X=0 is

[tex]\begin{aligned}P(X=0)&=\frac{\left(\begin{array}{l}4\\ 0\end{array}\right)\left(\begin{array}{l}8-4\\ 2-0\end{array}\right)}{\left(\begin{array}{l} 8\\ 2\end{array}\right)}\\ &=\frac{\left(\begin{array}{l}4\\ 0\end{array}\right)\left(\begin{array}{l}4\\ 2\end{array}\right)}{\left(\begin{array}{l} 8\\ 2\end{array}\right)}\\ &=\frac{\left[\left(\frac{4!}{(4-0)!0!}\right)\times \left(\frac{4!}{(4-2)!2!}\right)\right]}{\left(\frac{8!}{(8-2)!2!}\right)}\\ &=0.21\end[/tex]

The probability distribution of X when X=1 is

[tex]\begin{aligned}P(X=1)&=\frac{\left(\begin{array}{l}4\\ 1\end{array}\right)\left(\begin{array}{l}8-4\\ 2-1\end{array}\right)}{\left(\begin{array}{l} 8\\ 2\end{array}\right)}\\ &=\frac{\left(\begin{array}{l}4\\ 1\end{array}\right)\left(\begin{array}{l}4\\ 1\end{array}\right)}{\left(\begin{array}{l} 8\\ 2\end{array}\right)}\\ &=\frac{\left[\left(\frac{4!}{(4-1)!1!}\right)\times \left(\frac{4!}{(4-1)!1!}\right)\right]}{\left(\frac{8!}{(8-2)!2!}\right)}\\ &=0.57\end[/tex]

The probability distribution of X when X=2 is

[tex]\begin{aligned}P(X=2)&=\frac{\left(\begin{array}{l}4\\ 2\end{array}\right)\left(\begin{array}{l}8-4\\ 2-2\end{array}\right)}{\left(\begin{array}{l} 8\\ 2\end{array}\right)}\\ &=\frac{\left(\begin{array}{l}4\\ 2\end{array}\right)\left(\begin{array}{l}4\\ 0\end{array}\right)}{\left(\begin{array}{l} 8\\ 2\end{array}\right)}\\ &=\frac{\left[\left(\frac{4!}{(4-2)!2!}\right)\times \left(\frac{4!}{(4-0)!0!}\right)\right]}{\left(\frac{8!}{(8-2)!2!}\right)}\\ &=0.21\end[/tex]

Use E(X)=∑xP(x) to find the expected values of a random variable X.

The expected values of a random variable X is obtained as shown below:

The expected value of X is,

E(X)=∑xP(x-X)

E(X)=[(0×0.21)+(1×0.57)+(2×0.21)]

E(X)=[0+0.57+0.42]

E(X)=0.99≈1

Hence, the binomial probability distribution of XX when X=0 is 0.21, when X=1 is 0.57 and when X=2 is 0.21 and the expected value of XX is 1.00.

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Answer:

D

Step-by-step explanation:

D is correct because the sqrt of 91 is 9.5 and 9<9.5<10 makes absolute sense

C is not correct because the sqrt of 33 is 5.7 and 6<5.7<7 does not make sense

B is not correct because the sqrt of 13 is 3.6 and 4<3.6<5 does not make sense

A is not correct because the sqrt of 65 is 8.06 and 7<8.06<8 does not make sense

Considering the number of legs of each animal, it is found that there are 56 legs on the ground.

Hence the number of legs on the ground is given by:

N = 2 x 4 + 4 x 9 + 1 x 4 + 1 x 2 + 3 x 2 = 56.

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The area of the trapezoid is 87.5 square cm if the parallel side lengths are 10 and 15 cm, the height is 7 cm.

It is defined as the quadrilateral having four sides in which two sides are parallel to each other, it is a 2-dimensional geometry.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have a trapezoid ABCD shown in the picture.

As we know the area of the trapezoid is given by:

= (a+b)h/2

= (10+15)(7/2)

= 87.5 square cm

Thus, the area of the trapezoid is 87.5 square cm if the parallel side lengths are 10 and 15 cm, the height is 7 cm.

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The confidence interval for the true mean coefficient of restitution is (29.9911,30.0089).

Given sample mean coefficient of restitution 0.835,population standard deviation of 0.019 and the confidence level of 0.835.

We have to find the confidence interval for the true mean coefficient of restitution.

We can easily find the confidence interval through the formula of margin of error.

Margin of error is the difference between the calculated values and the real values.

Margin of error=z*σ/[tex]\sqrt{n}[/tex]

where z is the z value of p value,

σ is population mean or sample mean,

n is the sample size.

In our problem the sample size is 30.

z value for the p value of 0.99 is 2.576.

Margin of error=2.576*0.019/[tex]\sqrt{30}[/tex]

=0.048944/5.4772

=0.0089

Upper level=mean +margin of error

=30+0.0089

=30.0089

Lower level=Mean-margin of error

=30-0.0089

=29.9911.

Hence the confidence interval for the true mean coefficient of restitution is (29.9911,30.0089).

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Using translation concepts, the algebraic equation that matches the graph is given by:

y = |x - 1| - 1

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, the function y = |x| is:

Thus the algebraic equation that matches the graph is given by:

y = |x - 1| - 1

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Answer:

84 mm (C)

Step-by-step explanation:

We are given the centimeter/millimeter side of the ruler. It is probably easier to first look at the centimeters since the lines are much bigger. We can see that the line goes from 0cm to around 8.4cm. Now, we can convert centimeters to millimeters because we know that there are 10 millimeters in one centimeter. 8.4cm * 10 gives us 84 millimeters (C)

Answer:

here is what I came up with 26.4

The integer that represents Omar's score is -14.

Integers are whole numbers. It is a number without a fraction or decimal component. Integers can either be positive, negative or zero.

When Omar wins, the points are added and when he losses, the points are subtracted.

0 + 8 - (6 x 4) + 2

0 + 8 - 24 + 2 = -14

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The number of integer values of n for which the value 4000 × (0.4)ⁿ is an integer is; 9

We are given the expression;

4000 × (0.4)ⁿ

This can also be expressed as;

4000 × (²/₅)ⁿ which can further be expressed in exponent form as;

(2⁵ × 5³) × (²/₅)ⁿ = 2⁽⁵ ⁺ ⁿ⁾ × 5⁽³ ⁻ ⁿ⁾

Since this expression is an integer, we need:

1) 5 + n ≥ 0 for which n ≥ -5

2) 3 - n ≥ 0 for which n ≤ 3

Taking the intersection gives;

-5 ≤ n ≤ 3

Thus;

Number of Integer Values = 3 - (-5) + 1 = 9

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1) [tex]\overline{AC}[/tex] and [tex]\overline{BD}[/tex] bisect each other (given)

2) [tex]\overline{AE} \cong \overline{EC}[/tex] (a bisector splits a segment into two congruent parts)

3) [tex]\overline{BE} \cong \overline{ED}[/tex] (a bisector splits a segment into two congruent parts)

4) [tex]\angle BEA \cong \angle CED[/tex] (vertical angles are congruent)

5) [tex]\triangle BEA \cong \triangle DEC[/tex] (SAS)

6) [tex]\angle EBA \cong \angle EDC[/tex] (CPCTC)

7) [tex]\overline{AB} \parallel \overline{CD}[/tex] (converse of alternate interior angles theorem)

8) [tex]\angle DEA \cong \angle BEC[/tex] (vertical angles are congruent)

9) [tex]\triangle AED \cong \triangle BEC[/tex] (SAS)

10) [tex]\angle BCE \cong \angle EAD[/tex] (CPCTC)

11) [tex]\overline{BC} \parallel \overline{AD}[/tex] (converse of alternate interior angles theorem)