Arthur starts his first workout routine by doing 10 push-ups. Each workout after the first, he plans to do 2 more push-ups than in the previous workout. By his 20th workout, how many total push-ups will Arthur have done?

The length and the width of the rectangle are 61 inches and 19 inches, respectively

The mathematical statement from the question is given as

Length of a rectangle is four more than triple its width.

Mathematically, this can be represented as

Length = 3Width + 4

The perimeter is given as

Perimeter = 160 meters

The perimeter is calculated as

Perimeter = 2 x (Length + Width)

So, we have

2 x (3Width + 4 + Width) = 160

Divide by 2

3Width + 4 + Width = 80

This gives

4Width= 76

Divide by 4

Width = 19

Recall that

Length = 3Width + 4

So, we have

Length =  3 * 19 + 4

Evaluate

Length =  61

Hence, the dimensions are 61 inches by 19 inches

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The half-life of this isotope (in hours) is 13.0

Isotopes are variations of chemical elements that have a varied number of neutrons but the same number of protons and electrons. In other words, isotopes are different forms of the same element that have different amounts of nucleons (the sum of protons and neutrons) because of variations in the total number of neutrons in each of their individual nuclei.

An important application of isotopes is in the determination of the isotopic signature of element samples via isotope analysis. This is generally done via the process of isotope ratio mass spectrometry.

28% decay means, 72% remains.

Now,

\(N=N_{n} (\frac{1}{2})^{t/t_{12} } \\72=100(\frac{1}{2} )^{\frac{6.16 hours}{t_{1/2} } } \\(\frac{72}{100} )=(\frac{1}{2} )^{\frac{6.16 hours}{t_{1/2} } } \\\)

Taking long as both sides & solving we get,

\(t_{\frac{1}{2} } = 13.0 hours\)

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The value of X is 2/3 and -3/2.

According to the statement

we have given equation is 6x^2+5x-6 =0

and we have to find x by the factorization.

Factorization defines the the operation of resolving a quantity into factors.

So, by factorization method the equation is written as

6x^2+5x-6 =0

After forming factors the equation becomes

6x^2+9x-4x-6 =0

3x(2x+3) -2(2x+3) =0

By taking common

(3x-2) (2x+3) = 0

Now equate values equal to 0. and after that the output will get in the form of value of X.

Here the value of x is 2/3 and -3/2

So, the value of X is 2/3 and -3/2.

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(i) The pre-experimental planning is clear research, précised sample size, sampling method, experimental design and protocol. (ii) Two major sources of variation that would be difficult to control are Environmental factors and Variation in the quality.

(i) The pre-experimental planning for this experiment design would include the following steps:

Clearly define the research question and the population of interest.

Determine the sample size required to achieve a desired level of precision and confidence.

Identify the appropriate sampling method to use (e.g., simple random sampling, stratified sampling, cluster sampling).

Determine the appropriate experimental design to use (e.g., randomized controlled trial, quasi-experimental design).

Develop a detailed experimental protocol, including the procedures for collecting and recording data, as well as any necessary ethical considerations.

(ii) Two major sources of variation that would be difficult to control in this experiment are:

Environmental factors, such as temperature, humidity, and atmospheric pressure, which can affect the popping rate of popcorn kernels.

Variation in the quality of the popcorn kernels themselves, such as differences in moisture content, size, and shape, which can affect the popping rate.

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Because we know one point and an axis of symmetry, we know that the point (2, -7) must lie on the graph.

If a function has a line of symmetry at x = x₀, then we know that:

f(x₀ + x) = f(x₀ - x).

So we have symmetry around that line.

Then, if the line of symmetry is at x = 5 and we know that:

f(8) = f(5 + 3) = -7

We also must have:

f(2) = f(5 - 3) = -7

Then the point (2, - 7) must be on the graph.

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Given:

Consider the below figure attached with this question.

∠EFH = (5x + 1)°, ∠HFG = 62°, and ∠EFG = (18x + 11)°

To find:

The measure of ∠EFH.

Solution:

From the figure it is clear that ∠EFG is divide in two parts ∠EFH and ∠HFG. So,

\(\angle EFG=\angle EFH+\angle HFG\)

\(18x+11=(5x+1)+(62)\)

\(18x+11=5x+63\)

Isolate variable terms.

\(18x-5x=63-11\)

\(13x=52\)

Divide both sides by 13.

\(x=\dfrac{52}{13}\)

\(x=4\)

The value of x is 4.

\(\angle EFH=(5x+1)^\circ\)

\(\angle EFH=(5(4)+1)^\circ\)

\(\angle EFH=(20+1)^\circ\)

\(\angle EFH=21^\circ\)

Therefore, the measure of ∠EFH is 21°.

Thus, the possible values for d are 10, 11, and 12. The sum of all possible values of d is 10 + 11 + 12 = 33.

The given integer has 4 digits when written in base 8, meaning its general form can be represented as: N = a * 8^3 + b * 8^2 + c * 8^1 + d * 8^0, where 0 ≤ a, b, c, d ≤ 7.

Since N has 4 digits, a must be nonzero, so 1 ≤ a ≤ 7.

Now, we need to find the number of digits (d) when this integer is written in base 2. To do so, we first express the integer in terms of powers of 2.

N = a * (2^3)^3 + b * (2^3)^2 + c * (2^3)^1 + d * (2^3)^0
N = a * 2^9 + b * 2^6 + c * 2^3 + d

Since 1 ≤ a ≤ 7, the minimum value for a is 1 and the maximum value is 7. Therefore, the smallest possible value for N in base 2 is 1 * 2^9 (which has 10 digits in base 2) and the largest possible value is 7 * 2^9 + 7 * 2^6 + 7 * 2^3 + 7 (which has 12 digits in base 2).

Thus, the possible values for d are 10, 11, and 12. The sum of all possible values of d is 10 + 11 + 12 = 33.

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Linear Pair of Angles: two angles that form a straight line - they are supplementary.A linear pair of angles refers to two adjacent angles that add up to 180 degrees.

It is important to note that the sum of the angles in a linear pair of angles will always equal 180 degrees. A linear pair of angles must be adjacent, meaning that they share a common vertex and a common side but no other interior points.

Linear pairs of angles can be used to solve problems involving complementary, supplementary, and vertical angles. Since they add up to 180 degrees, they are considered to be supplementary angles. This is because supplementary angles are two angles that add up to 180 degrees.

Therefore, a linear pair of angles is also supplementary because it contains two adjacent angles that add up to 180 degrees. In other words, if two angles form a straight line, then they are considered to be supplementary.

The use of linear pairs of angles is prevalent in geometry problems involving parallel lines, triangles, and polygons.

The concept of a linear pair of angles is also important in understanding the different types of angles, including acute, obtuse, and right angles. For instance, an acute angle can form a linear pair with an obtuse angle, while a right angle can only form a linear pair with another right angle.

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The pattern shows multiplication because the earnings are 12 times the number of hours worked in each pair of values.

We are given a graph. The graph shows the number of hours worked versus the earnings in dollars. The values of the x-coordinates are 0, 1, 2, 3, 4, and 5. The corresponding values of the y-coordinates are 0, 12, 24, 36, 48, and 60. We need to find the pattern among these values.

We can see from the data that the values are in a straight line in the graph. The coordinates have the same proportion. The constant of proportionality is calculated below.

k = 12/1 = 12

Hence, the pattern is multiplicative because the earnings are 12 times the number of hours worked for each pair of values.

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a) Probability that the first component drawn is defective P(A) = 3/9 = 1/3 ≈ 0.3333

b)  Probability that the second component drawn is defective, given that the first component drawn is defective. P(B|A) = 2/8 = 1/4 = 0.25

c)  Probability that both the first and second components drawn are defective P(A and B) = P(A) * P(B|A) = (1/3) * (1/4) = 1/12 ≈ 0.0833

d) A and B are not independent events since the probability of their intersection is different from the product of their probabilities.

To solve this problem, we can use the concept of conditional probability and independence.

Given:

Total components (N) = 9

Defective components (D) = 3

(a) P(A) - Probability that the first component drawn is defective.

Since there are 3 defective components out of a total of 9 components, the probability of drawing a defective component as the first component is P(A) = D/N.

P(A) = 3/9 = 1/3 ≈ 0.3333

(b) P(B|A) - Probability that the second component drawn is defective, given that the first component drawn is defective.

After drawing the first defective component, there are 8 components left, out of which 2 are defective. So, the probability of drawing a defective component as the second component, given that the first component was defective, is P(B|A) = (D-1)/(N-1).

P(B|A) = 2/8 = 1/4 = 0.25

(c) P(A and B) - Probability that both the first and second components drawn are defective.

The probability of drawing a defective component as the first component is 1/3 (from part a). After drawing a defective component, there are 8 components left, and the probability of drawing another defective component is 2/8 (from part b).

P(A and B) = P(A) * P(B|A) = (1/3) * (1/4) = 1/12 ≈ 0.0833

(d) To determine whether A and B are independent events, we compare the product of their probabilities (P(A) * P(B)) with the probability of their intersection (P(A and B)).

If A and B are independent events, then P(A and B) = P(A) * P(B).

However, in this case, P(A) * P(B) = (1/3) * (1/4) = 1/12 ≠ 1/12 ≈ 0.0833 (from part c).

Therefore, A and B are not independent events since the probability of their intersection is different from the product of their probabilities.

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Answer:

x = -3

y = 4

Step-by-step explanation:

the volume of the region contained in the cylinder x² + y² = 9, bounded above by the plane z = x and below by the xy-plane is 0.

Given: The cylinder is x² + y² = 9, bounded above by the plane z = x and below by the xy-planeWe know that, the cylinder is x² + y² = 9Which is (x/a)² + (y/b)² = 1Where a = 3 and b = 3The plane is z = xThe region is bounded below by the xy-plane Thus, the volume of the region can be found by integrating z = x with limits of x² + y² ≤ 9.So, V = ∭ dx dy dz where the limits are given by the cylinder and the plane.V = ∫∫∫ (x) dV ... (1)Now, converting the integral into cylindrical coordinates we have,∫∫∫ (x) dV = ∫θ = 0 to 2π ∫r = 0 to 3 ∫z = 0 to r cos θ (r cos θ) rdzdrdθ ... (2)x = r cos θ, y = r sin θ, and z = z.We know that the limits of x² + y² ≤ 9 in cylindrical coordinates are 0 ≤ θ ≤ 2π, 0 ≤ r ≤ 3, 0 ≤ z ≤ r cos θ.Using (2) in (1), we haveV = ∫θ = 0 to 2π ∫r = 0 to 3 ∫z = 0 to r cos θ (r cos θ) rdzdrdθ= ∫θ = 0 to 2π ∫r = 0 to 3 [r² cos θ / 2] dr dθ= ∫θ = 0 to 2π [ 9 cos θ / 2 ] dθ= 9 [ sin θ ]θ = 0 to 2π= 0Thus, the volume of the region contained in the cylinder x² + y² = 9, bounded above by the plane z = x and below by the xy-plane is 0.

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Answer:

total=16pens and 10 red pens so ratio=10:16 fraction =5/8

Step-by-step explanation:

Answer:

11/4m

hope it's helpful ❤❤❤❤❤❤

THANK YOU.

#

Answer:

True.

Step-by-step explanation:

True.

Let's say A = 5, and B = 10.

We need to swap the contents of A and B, so A will end up with 10 and B will end up with 5.

A = 5

B = 10

Introduce variable C.

C = A (now C contains 5)

A = B (now A contains 10)

B = C (now B contains 5)

In the last two steps above, you see that the values of A and B were swapped.

Answer:

123

Step-by-step explanation:

82/2=41

41x3=123

The radius of the pool with height as 0.5 cm and volume as 12,000 cm³ is 87.39 cm.

We have that:

Radius of the water pipe = 0.74 cm

r = 0.74 cm

It fills a 12 L bucket in 4 minutes

1 L = 1000 cm³

12 L = 12,000 cm³

Volume of water put in the pool = 12,000 cm³

Height of the pool that rise = 5 mm = 0.5 cm.

H = 0.5 cm

Let the radius of the pool be R.

Volume = π r² h

Substituting the values, we get that:

12,000 = ( 22 / 7 ) R² ( 0.5 )

R² = 7636.36

R = 87.39 cm

Therefore, we get that, the radius of the pool with height as 0.5 cm and volume as 12,000 cm³ is 87.39 cm.

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First, we need to subtract the last payment from the last month's balance.

Then, apply the interest:

Answer:

Step-by-step explanation:

Plot 213, −56, and −312 on the number line.

The total area filled by a flat (2-D) surface or an object's form is referred to as the area and the required area of the metal frame is 93.76x² unit square.

The area is the total area occupied by a flat (2-D) surface or the form of an object.

Create a square on paper by using a pencil.

Two dimensions make it up.

A form's area on paper is the space it takes up.

So, given, a square metal frame encircles a circular mirror.

The mirror has a 4x radius.

The metal frame's side length is 12x.

According to the basic formula for the area of a circle and a square:

area of a circle = pi * radius * radius

Square Area = Side * Side

In the given situation:

Mirror's Area = pi * 4x * 4x = pi * 16x² = 50.24x

Squared mirror's Area = 12x * 12x = 144x²

The area of the metal frame is the sum of the areas of the squared and round mirrors.

Metal frame area =   144x² -  50.24x²

Metal frame size = 93.76x²

Therefore, the total area filled by a flat (2-D) surface or an object's form is referred to as the area and the required area of the metal frame is 93.76x² unit square.

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Correct question:

A circular mirror is surrounded by a square metal frame. The radius of the mirror is 4x. The side length of the metal frame is 12x. What is the area of the metal​ frame?

A qualitative research paradigm is a research approach that focuses on understanding and interpreting subjective experiences, meanings, and social phenomena.

It involves collecting and analyzing non-numerical data to gain insights into individuals' perspectives and the social context in which they exist. Focus group techniques are one of the methods used within the qualitative research paradigm to gather data through group discussions.

The qualitative research paradigm aims to explore and understand the complexity and nuances of human experiences, behaviors, and social phenomena. It recognizes the importance of context and seeks to generate rich and in-depth understandings rather than generalizable conclusions. Qualitative research methods involve collecting data through methods such as interviews, observations, and document analysis. The data collected is typically in the form of words, images, or other non-numerical formats. Researchers then analyze the data using various techniques, such as thematic analysis or grounded theory, to identify patterns, themes, and meanings.

Focus group techniques are one of the commonly used methods within the qualitative research paradigm. Focus groups involve bringing together a small group of participants who share common characteristics or experiences to engage in a facilitated discussion on a specific topic of interest. The group interaction allows participants to share their perspectives, experiences, and opinions while also influencing and being influenced by others in the group. This method provides rich qualitative data and allows researchers to explore group dynamics, collective meanings, and shared understandings.

Overall, the qualitative research paradigm and focus group techniques emphasize the importance of understanding subjective experiences, social interactions, and contextual factors to gain insights into human phenomena.

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Answer:

x=17 i think

Step-by-step explanation:

Answer:

x = 17

Step-by-step explanation:

18 = x + 1

18 - 1 = x

17 = x

Statistical Process Control (SPC) is a methodology used in quality management to monitor and control processes. It involves the application of statistical techniques to measure.

Statistical Process Control (SPC) is a powerful tool used to monitor and control processes in various industries. It utilizes statistical techniques to analyze process data, identify trends, and make informed decisions to improve process performance.

The primary objective of SPC is to ensure that a process operates within its specified limits and meets the desired quality standards. SPC involves the collection.

Analysis of data over time to understand process behavior and make necessary adjustments to maintain control. By monitoring and controlling the process variation, SPC helps to reduce defects and improve overall quality.

The key components of SPC include:

1. Control Charts: Control charts are graphical tools used to plot process data over time. They provide a visual representation of process variation and help identify when a process is in or out of control.

Control charts have upper and lower control limits that define the acceptable range of variation. Any data points outside these limits indicate special causes of variation that require investigation and action.

2. Data Collection and Analysis: SPC requires the collection of accurate and representative data. Data is collected at regular intervals and analyzed using statistical techniques such as mean, range, standard deviation, and process capability analysis.

These analyses help understand process performance, identify trends, and evaluate the capability of the process to meet customer requirements.

3. Process Monitoring and Improvement: SPC enables real-time process monitoring and provides timely feedback on process performance. It helps identify and address issues before they lead to defects or non-conformances.

By detecting trends or shifts in process performance, SPC allows for proactive intervention to maintain control and prevent quality problems.

4. Continuous Improvement: SPC is a fundamental aspect of a continuous improvement culture. By regularly monitoring process data, analyzing performance, and making data-driven decisions, organizations can identify areas for improvement and implement targeted changes to enhance process efficiency and quality.

Statistical Process Control (SPC) is a systematic approach to monitor and control processes using statistical techniques. It helps organizations maintain control, reduce defects, and improve overall quality by analyzing process data, identifying sources of variation, and making data-driven decisions.

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Answer:

it will be 100

Step-by-step explanation:

Answer:

Slope is -2

Step-by-step explanation:

rise/run

Hoep this helsp. Pls give brainliest.

Answer:I think it's -23.72

Step-by-step explanation:Step 1: Reduce the fraction

Step 2: Multiply

Step 3: Calculate

step 4: solution

Klyancey, this is the solution:

Let's recall the formula for calculatin the Present Value:

PV = A * (1/1 + r*t)

Replacing by the values we know:

PV = 16,000 * (1/1 + 0.03 * 4)

PV = 16,000/1.012

PV = $ 14, 285.71 (Rounding to the nearest cent)

Answer:

1/2

Step-by-step explanation:

to solve this equation you must find the greatest common factor or gcf to make the denominators the same

that happens to be 6

so

-4 5/6 + 5 2/6

then you add

you can break them up at add them like this

(-4 + 5) + (-5/6 + 2/6)

1 + -3/6

-3/6 is also -1/2

1 + -1/2

1/2

that is your answer