Which of the following equations describes the graph?
Identify a transformation of the function f(x) = x by observing the equation of the function g(x) = x − 90.

The base graph has been shifted down 90 units.

The base graph has been shifted right 90 units.

The base graph has been shifted left 90 units.

The base graph has been shifted up 90 units.

The correct answer for the situation is q(p(4)) = q(1) = 2(1) + 4 = 2 + 4 = 6

Therefore, (q ᵒ p)(4) = 6.

To evaluate the composition of functions p and q at a specific value, we substitute the inner function's result into the outer function.

Given:

p(x) = x - 3

q(x) = 2x + 4

To find (p ᵒ q)(4), we first substitute 4 into the function q(x):

q(4) = 2(4) + 4 = 8 + 4 = 12

Next, we substitute the result of q(4) into the function p(x):

p(q(4)) = p(12) = 12 - 3 = 9

Therefore, (p ᵒ q)(4) = 9.

To find (q ᵒ p)(4), we perform the composition in the reverse order.

First, we substitute 4 into the function p(x):

p(4) = 4 - 3 = 1

Next, we substitute the result of p(4) into the function q(x):

q(p(4)) = q(1) = 2(1) + 4 = 2 + 4 = 6

Therefore, (q ᵒ p)(4) = 6.

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By incorporating conic sections into the design, the robotic prototype can achieve optimal functionality, improved maneuverability, precise data collection, and effective communication.

Purpose: The robotic prototype will be designed to assist in agriculture by automating the process of crop planting and harvesting in large-scale farms.

Incorporating Conic Sections:

1. Circular Base: The robot can have a circular base that allows for efficient movement in any direction. The circular base can provide stability and smooth rotation, enabling the robot to navigate through fields and maneuver around obstacles.

2. Elliptical Arms: The robot can be equipped with elliptical arms that can extend and retract. These arms can be used for tasks such as seed planting or harvesting. The elliptical shape allows for a wide range of motion, reaching different areas within the farm while maintaining precision and efficiency.

3. Parabolic Sensors: To detect and analyze the quality of crops or soil conditions, the robot can be equipped with parabolic sensors. The parabolic shape of the sensors helps focus and collect data accurately, allowing the robot to assess crop health, moisture levels, and nutrient content with greater precision.

4. Hyperbolic Communication System: The robot can utilize a hyperbolic communication system to transmit data and receive instructions from a central control system or farm management software. The hyperbolic shape aids in efficient long-range communication, ensuring reliable connectivity and enabling real-time monitoring and control of the robot's activities.

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Answer:

The circumference is:

\(C=84.8\: cm\)

Step-by-step explanation:

The pizza is a circle, so the circumference equation is given by:

\(C=2\pi R\)

Where:

Therefore, the circumference is:

\(C=2\pi*13.5\)

\(C=84.8\: cm\)

I hope it helps you!

Answer:

it will be -10/-2 which will get you a slope of positive 5 since the negatives cancel out with each other

Step-by-step explanation:

Answer:

Its an up slope function that measures up to 10 apart diagonal. Also, I included a picture.

hope this helps!

A standardized test  is any test that is usually commercially produced and requires a common set of administration and scoring procedures.

A standardized test serves as a test that   requires all test  the participant to answer the same questions.

In this test there  is usually a  selection of questions from common bank of questions there is usually a  “standard” or consistent  way of assessment.

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Answer:

mr martin was a hero in my eyes he saved many lives and was one of the strongest people to ever live (who is mr martin?)

Step-by-step explanation:

Two supplementary angles equal 180 degrees.

Let the first angle = x

The second angle is 30 degrees more so this would be x + 30

Now add the two angles together to equal 180:

X + x+ 30 = 100

Combine like terms:

2x + 30 = 180

Subtract 30 from both sides:

2x = 150

Divide both sides by 2:

X = 75

One angle = x = 75

The other angle is x + 30 = 75 + 30 = 105

The smaller angle is 75 degrees.

Answer:

x = 24.5

Step-by-step explanation:

given a line parallel to a side of a triangle and intersecting the other 2 sides, then it divides those sides proportionally, that is

\(\frac{6}{27-6}\) = \(\frac{7}{x}\)

\(\frac{6}{21}\) = \(\frac{7}{x}\) ( cross- multiply )

6x = 147 ( divide both sides by 6 )

x = 24.5

The value of sin θ, in the third quadrant where cos θ = -(4/5), should be found in this question. The trigonometric ratios of the angle θ, in the third quadrant where cos θ = -(4/5), should be identified and solved in this question. The third quadrant, which is located in the lower-left corner of the coordinate plane, is identified by the location of θ. A line that runs through the origin of the plane and is inclined to the positive x-axis at an angle of θ degrees, is referred to as an angle. On the coordinate plane, angles can be placed in one of four quadrants. In this scenario, the given angle θ is located in the third quadrant. An angle in the third quadrant has a cosine value of negative and a sine value of negative too.Let's use the Pythagorean Theorem, sin²θ + cos²θ = 1. We have,cos θ = -(4/5), hence sin θ = ± √(1 - cos²θ)= ± √[1 - (4/5)²] = ± √(1 - 16/25) = ± √(9/25)= ± (3/5)However, θ is located in the third quadrant, so it has a negative sine. So, sin θ = -3/5. An angle in the third quadrant has a cosine value of negative and a sine value of negative too. Therefore, sin θ = -3/5.

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Answer:

Your answer would be B.

Step-by-step explanation:

Hope this helps!

Using combinations, we know that 4 different types of items will be selected.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.

We can choose the components of combos in any order.

Permutations and combinations can be mixed up.

Combination formula: \(n C r=\frac{n !}{(n-r) ! r !}\)

So, this formula, commonly known as the NCR formula, determines the number of combinations that may be made with r items out of the n available options.

We, therefore, have 4 objects, and a person chooses 3 at random.

\(\begin{aligned}& n C r=(n, r)=(4,3) \\& =\frac{4 !}{3 !(4-3) !} \\& =4 ! / 3 ! \\& =4\end{aligned}\)

Therefore, using combinations, we know that 4 different types of items will be selected.

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Answer: x * 12 + 25 = 75

Step-by-step explanation:

product of a number and twelve — x*12

Twenty five more than the product of a number and twelve — x * 12 + 25

Twenty five more than the product of a number and twelve is seventy five — x * 12 + 25 = 75

Answer:

Problem: 5.24 - 4.93

Step-by-step explanation:

You subtract just like a normal Addition problem however you MUST make sure the decimal point line up,...

\(5.24\\4.93\\\)

1st: subtract the 3 from the 4 [0.01]

2nd: subtract the 9 from the 2 (make the 2 a 12 (by carrying a one from the 5 (which then becomes a 4))) [0.30]

3rd: Finally subtract the 4 from the 4,... 0

Answer = 0.31,...

A more summed up answer: Subtracting (and adding for that matter) decimals happens exactly like normal. However you MUST MAKE SURE that your decimal points are lined up,... if you are subtracting a 0.09 from a 4.5 and the 4.5 doesn't have a hundredths place just remember that you can add a 0 on the end (4.50) without chancing it's value. (and then just subtract like normal)

Answer:

D (42,-56)

Step-by-step explanation:

Scale factor means you multiply, so you multiply (6,-8) by 7.

6 x 7 is 42 and 7 x -8 is -56. So your answer is D (42,-56).  

Answer:

x = 11

Step-by-step explanation:

\(3x - 5 = \frac{12 + 4x}{2} \)

Cross multiply expressions

2(3x - 5) = 12 + 4x multiply inside the parenthesis with 2

6x - 10 = 12 + 4x transfer like terms to the same side of the equation

6x - 4x = 12 + 10 add/subtract

2x = 22 divide both sides by 2

x = 11

Answer:

The area is 4,3 large than the other one

Answer:

7.22

Step-by-step explanation:

base x height / 2

3.8 x 3.8 = 14.44

14.44 / 2

7.22

Answer:

The third answer is correct

Step-by-step explanation:

Given:

A net of a rectangular prism

l (length) = 11,75 cm

w (width) = 5,75 cm

h (height) = 4 cm

Find: A (surface area) - ?

The surface area is equal to the sum of the areas of all the sides

There are:

2 sides with dimensions of 11,75 cm and 4 cm

2 sides with dimensions of 5,75 cm and 11,75 cm

2 sides with dimensions of 4 cm and 5,75 cm

\(a(surface) = 4 \times 11.75 \times 2 + 5.75 \times 11.75 \times 2 + 4 \times 5.75 \times 2 = 275.125 = 275 \frac{1}{8} \: {cm}^{2} \)

option b is the correct answer

Answer:

3rd one

Step-by-step explanation:

The most effective chunking of the digit sequence 14929111776 would depend on the purpose of chunking.

However, a possible effective chunking could be 14-92-91-11-77-6, which groups the digits into pairs or triplets based on their similarity or pattern. Another possible chunking could be 1492-911-1776, which separates the digits based on significant historical events. Ultimately, the effectiveness of chunking would depend on the context and intended use of the sequence. The most effective chunking of the digit sequence 14929111776 would be to group the numbers into smaller, manageable chunks. One possible way to chunk the sequence is: 149-29-11-17-76. This breaks the sequence into five groups, making it easier to remember and process.

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Given the following function:

Where x is the time in years, models a declining lemming population.

We will find the number of lemmings after 5 years

So, we will substitute x = 5

Rounding to the nearest whole number

so, the number of lemmings after 5 years = 5840

Answer:

the specific answer is 5,840

Sine function relates side lengths of a right triangle to an acute angle.

In a right triangle, the side lengths are related to the acute angles through the trigonometric functions. The side opposite the acute angle is related to the angle through the sine function, the side adjacent to the acute angle is related to the angle through the cosine function, and the hypotenuse is related to the angle through the tangent function.

More specifically, if θ is an acute angle in a right triangle and a and b are the lengths of the side opposite and adjacent to the angle respectively, and c is the length of the hypotenuse, we have:

sin(θ) = a/c

cos(θ) = b/c

tan(θ) = a/b

Thus, we can use these functions to find the length of any side of the right triangle if we know the measure of one of the acute angles and the length of one of the other sides.

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Answer:

About 1,749,638,696 miles.

Step-by-step explanation:

It might be incorrect so don't fully trust me.

The resulting box plot for the given data would show a box ranging from 5.2 to 5.7, with the median at 5.4.

A box plot, also known as a box-and-whisker plot, is a graphical representation of numerical data that displays the distribution of a dataset. It provides a visual summary of the minimum, first quartile, median, third quartile, and maximum values, as well as any outliers that may be present.

To construct a box plot from the given data (diameters of cans in an assembly line: 5.7, 5.6, 5.1, 5.4, 5.2, 5.6, 5.7, 5.3, 5.8, 5.2), follow these steps:

1. Sort the data in ascending order: 5.1, 5.2, 5.2, 5.3, 5.4, 5.6, 5.6, 5.7, 5.7, 5.8.

2. Find the median (middle value) of the dataset, which is 5.4.

3. Determine the first quartile (Q1), which is the median of the lower half of the data. In this case, it is the median of the numbers below 5.4: 5.2.

4. Find the third quartile (Q3), which is the median of the upper half of the data. In this case, it is the median of the numbers above 5.4: 5.7.

5. Calculate the interquartile range (IQR) by subtracting Q1 from Q3: 5.7 - 5.2 = 0.5.

6. Identify any outliers in the dataset. Outliers are values that fall below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR. In this case, there are no outliers.

7. Construct the box plot using a number line. Draw a box from Q1 to Q3, with a line inside representing the median. Add whiskers (lines) extending from the box to the minimum value (5.1) and the maximum value (5.8).

The resulting box plot for the given data would show a box ranging from 5.2 to 5.7, with the median at 5.4. The whiskers would extend from 5.1 to 5.8. This visual representation provides an overview of the distribution and key statistical measures of the diameters of cans in the assembly line.

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The mean absolute deviation for the data-set is given as follows:

2.86.

The mean of the data-set is given as follows:

(10 + 11 + 13 + 18 + 17 + 14 + 8)/7 = 13.

The deviations of the data-set are given as follows:

3, 2, 0, 5, 4, 1, 5.

Hence the MAD is given as follows:

(3 + 2 + 0 + 5 + 4 + 1 + 5)/7 = 2.86.

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Answer:

1,4,9,16,25,40,49. I am not sure, but if somebody else solves it and it matches with mine, then you will know that its correct.

Answer:

5.44 yards

Step-by-step explanation:

a) the unsigned decimal value of the binary number 10110110 is 182.

the signed decimal value of the binary number 10110110 is -74.

b) the unsigned decimal value of the hexadecimal number C1B3 is 49687.

the signed decimal value of the hexadecimal number C1B3 is -16049.

a) Binary number: 10110110

Unsigned decimal value:

To convert the binary number to its unsigned decimal value, we can use the positional value of each bit in the binary number.

10110110 = (1 * 2⁷) + (0 * 2⁶) + (1 * 2⁵) + (1 * 2⁴) + (0 * 2³) + (1 * 2²) + (1 * 2¹) + (0 * 2⁰)

        = 128 + 0 + 32 + 16 + 0 + 4 + 2 + 0

        = 182

Therefore, the unsigned decimal value of the binary number 10110110 is 182.

Signed decimal value:

To determine the signed decimal value of a binary number, we need to determine its sign bit (most significant bit). If the sign bit is 1, the number is negative; if it is 0, the number is positive.

In the given binary number 10110110, the sign bit is 1, indicating a negative number. To find the signed decimal value, we can perform two's complement on the remaining bits (excluding the sign bit) and then apply the negative sign.

To find the two's complement of the remaining bits, we invert all the bits and add 1.

Inverting the bits: 01001001

Adding 1: 01001010

Therefore, the two's complement of the binary number 10110110 is 01001010.

Converting the two's complement to decimal:

01001010 = (0 * 2⁷) + (1 * 2⁶) + (0 * 2⁵) + (0 * 2⁴) + (1 * 2³) + (0 * 2²) + (1 * 2¹) + (0 * 2⁰)

        = 64 + 0 + 0 + 0 + 8 + 0 + 2 + 0

        = 74

Applying the negative sign, the signed decimal value is -74.

Therefore, the signed decimal value of the binary number 10110110 is -74.

b) Hexadecimal number: C1B3

Unsigned decimal value:

To convert the hexadecimal number to its unsigned decimal value, we can use the positional value of each digit in the hexadecimal number.

C1B3 = (12 * 16^3) + (1 * 16^2) + (11 * 16^1) + (3 * 16^0)

    = (12 * 4096) + (1 * 256) + (11 * 16) + (3 * 1)

    = 49152 + 256 + 176 + 3

    = 49687

Therefore, the unsigned decimal value of the hexadecimal number C1B3 is 49687.

Signed decimal value:

In the case of a hexadecimal number, there is no explicit sign bit like in binary numbers. Instead, we interpret the most significant bit of the first hexadecimal digit as the sign bit.

In the given hexadecimal number C1B3, the most significant bit of the first digit (C) is 1, indicating a negative number.

To find the signed decimal value, we can perform two's complement on the remaining bits (excluding the sign bit) and then apply the negative sign.

Inverting the bits: 3E4C

Adding 1: 3E4D

Converting the two's complement to decimal:

3E4D = (3 * 16³) + (14 * 16²) + (4 * 16¹) + (13 * 16⁰)

    = (3 * 4096) + (14 * 256) + (4 * 16) + (13 * 1)

    = 12288 + 3584 + 64 + 13

    = 16049

Applying the negative sign, the signed decimal value is -16049.

Therefore, the signed decimal value of the hexadecimal number C1B3 is -16049.

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James will fully clear the loan after approximately 12 years when the remaining balance reaches zero.

To determine the number of years it will take for James to fully clear the loan, we need to calculate the remaining balance after each payment and divide the initial loan amount by the annual payment until the remaining balance reaches zero.

The loan amount is 9000 euros, and James pays off 770 euros each year. Since the interest is charged at a rate of 3% of the original amount per annum, the interest for each year will be \(0.03 \times 9000 = 270\) euros.

In the first year, James pays off 770 euros, and the interest on the remaining balance of 9000 - 770 = 8230 euros is \(8230 \times 0.03 = 246.9\)euros. Therefore, the remaining balance after the first year is 8230 + 246.9 = 8476.9 euros.

In the second year, James again pays off 770 euros, and the interest on the remaining balance of 8476.9 - 770 = 7706.9 euros is \(7706.9 \times 0.03 = 231.21\) euros. The remaining balance after the second year is 7706.9 + 231.21 = 7938.11 euros.

This process continues until the remaining balance reaches zero. We can set up the equation \((9000 - x) + 0.03 \times (9000 - x) = x\), where x represents the remaining balance.

Simplifying the equation, we get 9000 - x + 270 - 0.03x = x.

Combining like terms, we have 9000 + 270 = 1.04x.

Solving for x, we find x = 9270 / 1.04 = 8913.46 euros.

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