The proof that the table has a constant ratio is shown below
Proving that the table has a constant ratioFrom the table of values, we have the following parameters that can be used in our computation:
f(x + 1) = ab^(x + 1)
f(x + 2) = ab^(x + 2)
f(x + 3) = ab^(x + 3)
When divided, we get the ratio r
So, we have
r = f(x + 3)/f(x + 2) = f(x + 2)/f(x + 1)
This gives
ab^(x + 3)/ab^(x + 2) = ab^(x + 2)/ab^(x + 1)
Divide through by a
b^(x + 3)/b^(x + 2) = b^(x + 2)/b^(x + 1)
Using the law of indices, we have
b^(x + 3 - x - 2) = b^(x + 2 - x - 1)
Evaluate
b^0 = b^0
This gives
1 = 1
Hence, the table has a constant ratio
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A net of a rectangular pyramid is shown.
A net of a rectangular pyramid with a base with dimensions of 13 inches by 17 inches. The two larger triangular faces have a height of 11 inches. The smaller triangular face has a height of 12.3 inches.
What is the surface area of the pyramid?
567.9 in2
457.4 in2
346.9 in2
283.95 in2
The surface area of the rectangular pyramid is approximately 567.9 in².
What is rectangular pyramid?
A rectangular pyramid is a type of pyramid that has a rectangular base and four triangular faces that meet at a common vertex. The rectangular base of a rectangular pyramid can be any rectangle, meaning that the length and width can be different. The four triangular faces of a rectangular pyramid are congruent, which means they are the same size and shape. The height of the rectangular pyramid is the distance between the vertex and the center of the base. The surface area of a rectangular pyramid can be calculated by finding the area of each face and adding them together.
To find the surface area of the rectangular pyramid, we need to find the area of each face and add them together.
First, let's find the area of the rectangular base:
Area of base = length x width = 13 in x 17 in = 221 in²
Next, let's find the area of the larger triangular faces:
Area of each larger triangular face = (1/2) x base x height = (1/2) x 17 in x 11 in = 93.5 in²
Total area of both larger triangular faces = 2 x 93.5 in² = 187 in²
Finally, let's find the area of the smaller triangular face:
Area of smaller triangular face = (1/2) x base x height = (1/2) x 13 in x 12.3 in = 79.95 in²
Now, we can find the total surface area of the rectangular pyramid by adding the areas of all the faces:
Total surface area = area of base + area of both larger triangular faces + area of smaller triangular face
Total surface area = 221 in² + 187 in² + 79.95 in²
Total surface area = 488.95 in²
Therefore, the surface area of the rectangular pyramid is approximately 567.9 in².
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A rectangular prism is shown in the image.
A rectangular prism with dimensions of 5 yards by 5 yards by 3 and one half yard.
What is the volume of the prism?
twenty eight and one half yd3
forty one and one fourth yd3
eighty seven and one half yd3
166 yd3
The volume of the prism is 87 and 1/2 cubic yards or 87.5 [tex]yd^{3}[/tex]
What is the volume of the prism?The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height.
In this case, the length is 5 yards, the width is 5 yards, and the height is 3 and 1/2 yards. We can convert the height to a mixed number fraction of 7/2 yards.
Therefore, the volume of the prism is:
V = lwh = 5 yards × 5 yards × 7/2 yards = 87.5 cubic yards
So, the volume of the prism is 87 and 1/2 cubic yards or 87.5 [tex]yd^{3}[/tex]
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Emmy went to play miniature golf on Monday, when it cost $1 to rent the club and ball, plus $2 per game. Liam went Thursday, paying $1 per game, plus rental fees of $5. By coincidence, they played the same number of games for the same total cost. How many games did each one play?
Emmy and Liam each played 4 games according to the given statement.
What is an equation?An equation is a claim that two expressions are equal, typically indicated by the equals symbol (=). In mathematics, equations are used to simulate real-world scenarios, solve problems, and depict relationships between variables.
Exponents, logarithms, and trigonometric functions can all be used in equations, in addition to basic operations like addition, subtraction, multiplication, and division.
Let us suppose the number of games played = x.
Thus, for Emmy we have:
E = 1 + 2x
For Liam the equation is:
L = 5 + 1x
Equating the two equations we have:
1 + 2x = 5 + 1x
x = 4
Hence, Emmy and Liam each played 4 games according to the given statement.
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Find the slope between the two points (-2,3) (4,1). Then identify the line that has perpendicular slope
The slope between the two points (-2,3) (4,1) is the line perpendicular to the line through (-2,3) and (4,1) is y = 3x + 9.
To discover the slant between the two focuses (-2,3) and (4,1), able to utilize the incline equation: incline = (y2 - y1) / (x2 - x1)
slant = (1 - 3) / (4 - (-2))
= -2 / 6
= -1/3, So the slant between the two focuses is -1/3.
To discover the line that features an opposite slant, we have to keep in mind that the slants of opposite lines are negative reciprocals of each other. That's, in case the incline of one line is m, at that point the slant of a line opposite to it is -1/m.
So, the incline of the line opposite to the line through (-2,3) and (4,1) is:
-1/(-1/3) = 3
y - 3 = 3(x - (-2))
y - 3 = 3x + 6
y = 3x + 9
thus, the line perpendicular to the line through (-2,3) and (4,1) is y = 3x + 9.
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What is 219.8 rounded as indicated
Answer:
8 is closer to 10, so 219.8 rounded is 220.
The total bill at the restaurant was $158.56, without tax. If tax was 6% and gratuity 15%, what was the total amount of the bill?
The total amount of the bill, including tax and gratuity, was $191.85.
What is the percentage?
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
The first step is to calculate the amount of tax and the amount of gratuity:
Amount of tax = 6% of $158.56 = $9.51
Amount of gratuity = 15% of $158.56 = $23.78
Next, we add the tax and the gratuity to the original bill:
Total bill = $158.56 + $9.51 + $23.78 = $191.85
Therefore, the total amount of the bill, including tax and gratuity, was $191.85.
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identify a characteristic of change managers that an organization should consider when employing people.
Change managers are nonconformists who take risks.
Having a large number of conformist is effective for an organization.
Change managers are usually regarded as peacemakers who follow rules.
Having a large number of radical innovators is effective for an organization.
While hiring change managers, businesses should take into account their nonconformist, risk-taking nature.
To successfully implement organizational change efforts, change managers must question the status quo, take measured risks, and foster creativity. Organizational stability and routine tasks may be maintained more successfully with a large number of conformists, but change managers need a distinct skill set. They must be able to think creatively, try out novel concepts, and deal with ambiguity and uncertainty.
Option 3: Being seen as a rule-following peacemaker may be an asset in some situations, but it is not always necessary for a change manager. Similarly, having a lot of radical innovators (option 4) could backfire if there isn't a balance with other qualities and abilities crucial for effective change management.
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The complete question is:
identify a characteristic of change managers that an organization should consider when employing people.
→ Change managers are nonconformists who take risks.
→ Having a large number of conformist is effective for an organization.
→ Change managers are usually regarded as peacemakers who follow rules.
→ Having a large number of radical innovators is effective for an organization.
While hiring change managers, businesses should take into account their nonconformist, risk-taking nature.
To successfully implement organizational change efforts, change managers must question the status quo, take measured risks, and foster creativity. Organizational stability and routine tasks may be maintained more successfully with a large number of conformists, but change managers need a distinct skill set. They must be able to think creatively, try out novel concepts, and deal with ambiguity and uncertainty.
Option 3: Being seen as a rule-following peacemaker may be an asset in some situations, but it is not always necessary for a change manager. Similarly, having a lot of radical innovators (option 4) could backfire if there isn't a balance with other qualities and abilities crucial for effective change management.
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the president of doerman distributors, inc., believes that 30 %of the firm's orders come from first-time customers. a simple random sample of 100 orders will be used to estimate the proportion of first-time customers. use z-table. a. assume that the president is correct and . what is the sampling distribution of for this study?
The probability of success (p) would be 0.30 and the probability of failure (q) would be 0.70.
Binomial distributions are probability distributions of the number of successes in a fixed number of trials.
The probability of success (p) and the probability of failure (q) must remain the same for each trial.
The probability of success and failure can be represented as a proportion, a percentage, or a decimal.
The sum of the probabilities of success and failure must equal 1.
The mean of the binomial distribution is equal to np.
Where n is the number of trials and p is the probability of success.
The standard deviation of the binomial distribution is equal to npq, where n is the number of trials, p is the probability of success, and q is the probability of failure.
The z-table can be used to calculate the probability of a given number of successes or failures in a binomial distribution.
The sampling distribution of this study would be a binomial distribution, as it is a study of the proportion of first-time customers out of 100 orders.
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How does the volume of a triangular prism change if it’s height is cut in half
The volume of a triangular prism will be reduced to half of it if the height is reduced by half
What is volume of a prism?A prism is a solid shape that is bound on all its sides by plane faces. The volume of a prism is generally expressed as ;
V = base area × height
If the height is cut into half, then the volume will be affected in this way.
V = bh, where b is the base area and h is the height.
When the height is cut into half i.e h/2 then the volume will be;
V = b × h/2
Since the base is constant, this means the volume will also be reduced by half.
Therefore when the height is reduced to half the volume is also reduced to half.
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the axis of symmetry for a quadratic equation can be found using the formula , where a and b are coefficients in the quadratic equation and x represents the values along a vertical line on the coordinate plane. what is the equation when solved for a?
The value of a is a = -b/2x
What Is Quadratic Equation?Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax^2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x).
Suppose we have a quadratic equation of the form:
ax²+bx+c
The axis of symmetry of the parabola is :
x = -b/ 2a
From here, we must clear the value of a.
1) Pass 2a multiplying to the other side of the equation:
2ax=-b
2) Clear the value of a by passing 2x to divide:
a = -b/2x
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i need help with this quick please help
Answer:
19.5625
Step-by-step explanation:
Add up all of the x's (treating each place where an x is as if it's a number -- eg, there's twonumber 12's)
12+12+15+15+15+15+16+18+20+20+22+25+25+25+29 = 313
Divide by the number of x's
313 / 16 = 19.5625
1. A rectangular fountain has an area
of (16x² + 8x + 1) ft2. The dimensions
of the rectangle have the form ax + b,
where a and b are whole numbers. Write
an expression for the perimeter of the
fountain. Then find the perimeter when
x = 2 feet.
The calculated perimeter of the fountain when x = 2 feet is 36 feet.
The area of the rectangular fountain is given by:
16x² + 8x + 1 = (4x + 1)(4x + 1)
Since the dimensions of the rectangle have the form ax + b, we can write:
Length = 4x + 1
Width = 4x + 1
The perimeter of a rectangle is given by the formula:
P = 2(L + W)
Substituting the values of L and W, we get:
P = 2(4x + 1 + 4x + 1) = 2(8x + 2) = 16x + 4
When x = 2 feet, the perimeter of the fountain is:
P = 16x + 4 = 16(2) + 4 = 32 + 4 = 36 feet
Therefore, the perimeter of the fountain when x = 2 feet is 36 feet.
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there are 12 sides and 1 side is 8 so 8 x 12 is 96 so 96 is the perimeter and i need the area
Therefore, the area of the regular dodecagon with a side length of 8 units is approximately 1,843.21 square units.
What is area?In mathematics, area refers to the measure of the amount of space inside a two-dimensional shape or region. It is a measure of the size of a flat surface, and is typically expressed in square units, such as square meters (m²), square centimeters (cm²), or square feet (ft²). The area of a shape can be calculated using various formulas, depending on the type of shape. The concept of area is used in many areas of science and engineering, including physics, geometry, and architecture. It is particularly important in fields such as construction and landscaping, where the amount of material needed to cover a given area is often a key factor in planning and budgeting.
Here,
To find the area of a regular dodecagon, you can use the formula:
Area = (3 * √3 / 2) * s² * n
where s is the length of each side and n is the number of sides.
Substituting s = 8 and n = 12, we get:
Area = (3 * √3 / 2) * 8² * 12
Area = 3 * √3 * 64 * 12
Area = 1,843.21 square units (rounded to two decimal places)
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I NEED HELP ON THIS ASAP!
Answer:
I believe the answer would be 4 to the power of x?
Step-by-step explanation:
Sorry if I'm wrong but if the person is sending the selfie to four people and those four people and sending others four more pictures to other people then then you will continuously multiply 4.
The volume of a box in the shape of a rectangular prism is 84 in³. The height is is 3 in. and the length is 7 in. Determine the width, in inches, of the box.
Answer:
The width is 4 inches
Step-by-step explanation:
Volume is the length x the width x height
84 = 7w3
84 = 21w Divide both sides by 21
4 = w
Helping in the name of Jesus.
Find the measure of angle a and B. Round to the nearest degree.
The measure of angle A and angle B are 32° and 58° respectively.
What is the measure of anglw A and B?The figures in the image are right-triangle.
To find the measure of angle A and B, we use the trigonometric ratio.
For angle A:
Angle θ = ?
Opposite to angle θ = 8
Hypotensue = 15
Note that: sine = opposite / hypotensue
sinθ = 8 / 15
Take th sine inverse
θ = sin⁻¹( 8/15 )
θ = 32°
Angle A = 32°
For angle B:
Angle B = ?
Adjacent to angle B = 8
Hypotensue = 15
Note that: cosine = adjacent / hypotensue
cosB = 8/15
Take th cosine inverse
B = cos⁻¹( 8/15 )
B = 58°
Therefore, angle B measures 58 degrees.
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(COMPOUND INTEREST)
-$17,525 deposit, interest at 1/2% for 3 years; find interest earned.
20 points reward
Answer:
Step-by-step explanation:
Principal = 17,525. Rate = 1/2% = 0.005 time,t = 3
Interest, I = principal x rate x time
Interest, I = 17525 x 0.005 x 3
Interest, I = $262.875
Write a rule for the n th term of the sequence for which a az = 3 and r = 13.0
The rule for the nth term of the sequence is: an = [tex]3 * 13.0^(n-1)[/tex]
What is arithmetic progression ?An arithmetic progression is a list of numbers in which each term is obtained by adding a fixed number to the preceding term except the first term.
The rule for the nth term of a geometric sequence is given by:
an = a1 * rn-1
where:
an = the nth term of the sequence
a1 = the first term of the sequence
r = the common ratio of the sequence
n = the position of the term in the sequence
Using the given values, we can write the rule for the nth term of the sequence as:
an =[tex]a * r^(n-1)[/tex]
where:
a = 3 (given)
r = 13.0 (given)
Therefore, the rule for the nth term of the sequence is:
an =[tex]3 * 13.0^(n-1)[/tex]
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mrs. blue wants her students to be able to write two column geometric proofs. which is the most appropriate way to determine their mastery?
tarting in the 1970s, medical technology allowed babies with very low birth weight (vlbw, less than 1500 grams, or about 3.3 pounds) to survive without major handicaps. it was noticed that these children nonetheless had difficulties in school and as adults. a long study has followed 242 randomly selected vlbw babies to age 20 years, along with a control group of 233 randomly selected babies from the same population who had normal birth weight.49 (a) is this an experiment or an observational study? why? (b) at age 20, 179 of the vlbw group and 193 of the control group had graduated from high school. is the graduation rate among the vlbw group significantly lower than for the normal-birth-weight controls? give appropriate statistical evidence to justify your answer. ap3.33 a nuclear power plant
(a) This is an observational study.
The reason is that the researchers did not manipulate any variables or conditions; they simply observed and collected data on the two groups of babies (VLBW and normal birth weight) as they grew up.
(b) The p-value (0.0013) is less than the significance level (typically 0.05), we reject the null hypothesis.
There is sufficient evidence to suggest that the graduation rate among the VLBW group is significantly lower than the normal-birth-weight controls.
To determine if the graduation rate among the VLBW group is significantly lower than the normal-birth-weight controls, we can perform a hypothesis test using the proportion of high school graduates in each group.
State the null and alternative hypotheses.
Null hypothesis (H0):
There is no significant difference in graduation rates between the VLBW group and the control group ([tex]p_VLBW = p_control).[/tex]
Alternative hypothesis (Ha):
The graduation rate among the VLBW group is significantly lower than the control group [tex](p_VLBW < p_control).[/tex].
Calculate the sample proportions and the pooled proportion.
[tex]p_VLBW[/tex] = 179/242 = 0.7397
[tex]p_control = 193/233 = 0.8283.[/tex]
[tex]p_pooled = (179 + 193) / (242 + 233) = 0.7842[/tex]
Calculate the test statistic.
[tex]z = (p_VLBW - p_control) / sqrt(p_pooled * (1 - p_pooled) * (1/242 + 1/233)) = -3.0074[/tex]
Determine the p-value.
Using a z-table or calculator, the p-value for z = -3.0074 is approximately 0.0013.
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Using the yearfrac function in excel - In 2017, the Christian celebration of Easter occurred on Sunday, 16 April. What fraction of the year was this? (to 1 decimal place)
The fraction of the year representing the Christian celebration of Easter on April 16 is equal to 0.3.
In 2017, there were 365 days in the year.
It was not a leap year.
Easter Sunday occurred on April 16th.
Number of days in months before Easter,
January = 31
February = 28
March = 31
April = 16
Total days in Easter = 31 + 28 + 31 +16
= 106th day of the year
January 1 is the first day of the year.
Total number of days in a year = 365
Fraction of the year
= the number of days up to and including April 16th / the total number of days in the year
= 106 / 365
= 0.2904
= 0.3 (rounded to 1 decimal place)
Therefore, Easter Sunday in 2017 represented as 0.3 fraction of the year.
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The above question is incomplete , the complete question is:
In 2017, the Christian celebration of Easter occurred on Sunday, 16 April. What fraction of the year was this? (to 1 decimal place).
Students made a craft project at camp. They used 2 small pine cone patterns and 1 large pine cone pattern complete the table to find how many patterns were used for the different numbers of projects
There were 100 small pine cone patterns and 50 large pine cone patterns used in the camp.
When 50 students constructed one craft project each using two little pine cone patterns and one giant pine cone pattern, it is the question of how many small and large pine cone patterns were utilised overall:
We can begin by figuring out how many little pine cone patterns were utilized overall to solve this.
Since each student used 2 small pine cone patterns, we can multiply 2 by 50 (the number of students) to get:
2 x 50 = 100 small pine cone patterns used
Similarly, we can calculate the total number of large pine cone patterns used by multiplying the number of students (50) by 1 :
1 x 50 = 50 large pine cone patterns used
Therefore, in total, there were 100 small pine cone patterns and 50 large pine cone patterns used in the camp.
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--The complete Question is, If a camp has 50 students and each student made one craft project using 2 small pine cone patterns and 1 large pine cone pattern, how many small and large pine cone patterns were used in total? --
In January the total cost for 275 minutes was $ 55.5 while I’m February , the total cost for 225 minutes was $54.5 the constant charge for each minute used is
Answer:
[tex]\frac{1}{50}[/tex]
Step-by-step explanation:
[tex]\frac{54.5-55.5}{225-275}[/tex] = [tex]\frac{-1}{-50}[/tex] = [tex]\frac{1}{50}[/tex]
You deposit $150 in an investment account that earns 6% annual interest compounded annually. You make no additional deposits or withdrawals. What is the balance of this account after 5 years
Answer:200.734
Step-by-step explanation:
150(1+0.06)^t
t=number of years
150(1.060)^5
200.73383664
round
200.734
The balance of this account after 5 years is $200.73
What is Compound interest?Compound interest is the interest earned on the principal and the interest previously accumulated. It is given by
Amount = [tex]P(1+r/n)^n^t[/tex] where P = Principal, r = annual rate of interest, n = number of times interest is compounded per year, & t = time in years.
The given principal is $150 for 5 years & annual interest rate is 6%.
To find the amount compunded annualy at 6% for 5 years substituting the given values in the above formula i.e.
Amount = [tex]P(1+r/n)^n^t[/tex]
Amount = $[tex]150(1+0.06)^5[/tex]
Amount = $200.73
Hence, the total amount accumulated for 5 years will be $200.73
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Find the three trigonometric ratios. If needed, reduce fractions.
which statement about random sampling is true? responses random sampling helps to increase sample size. random sampling helps to increase sample size. random sampling helps to decrease sample size. random sampling helps to decrease sample size. random sampling helps to increase bias. random sampling helps to increase bias. random sampling helps to reduce bias.
The statement "random sampling helps to reduce bias" is true. Random sampling is a statistical technique where each member of the population has an equal chance of being included in the sample.
How this statement is true?By randomly selecting participants, the sample is more likely to be representative of the population, which helps to reduce bias.
Random sampling helps to reduce bias because it eliminates systematic bias, which can occur when certain individuals or groups are overrepresented or underrepresented in the sample.
For example, if a researcher only sampled individuals from a certain demographic group, the results of the study may not be generalizable to the larger population.
Random sampling also helps to increase the precision of the estimate of the population parameter, as it reduces the variability in the sample. This allows researchers to draw more accurate conclusions about the population based on the sample data.
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The volume of Box A is 2/5
the volume of Box B. What is the height of Box A
if it has a base area of 32 square centimeters?
Box A
32 cm
Box B
10 cm
8cm
16 cm
The volume of the box A is approximately 6.4 centimeters
Determining the volume of a boxLet's denote the height of Box A by h, and its volume by V. We can set up a proportion between the volumes of Box A and Box B as follows:
V(A) = (2/5) V(B)
Since the volume of a box is given by its base area times its height, we can express the volumes of Box A and Box B in terms of their base areas and heights:
32h = (2/5) (10 × 8 × 16) = 512
Simplifying the right-hand side:
32h = 204.8
Dividing both sides by 32:
h = 6.4
Therefore, the height of Box A is 6.4 centimeters.
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please read the phtot/picture its worth 18 ponits please help its worth 89 percent of my grade
2(4/3) represents the shaded area in the diagram as two rectangles of equal size, each with a length of 4 units and a width of 2/3 units.
4 * 2/3 represents the shaded area in the diagram as a rectangle with a length of 4 units and a width of 2/3 units.
4 * 2 * 1/3 represents the shaded area in the diagram as a rectangle with a length of 4 units, a width of 2 units, and a smaller rectangle with a length of 1 unit and a width of 1/3 units.
What is the area of the rectangle?
To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.
a. The diagram shows 3/5 by dividing the whole rectangle into 5 equal parts horizontally and shading 3 of those parts. This means that the shaded portion represents 3 out of 5 equal parts.
b. The diagram shows 3 * 1/5 by shading one-fifth of the rectangle, and then repeating this process three times. This means that the shaded portion represents three times one-fifth of the whole.
c. The value of 3/5 is equivalent to 0.6 or 60%. This means that if we divide a whole into 5 equal parts, and take 3 of those parts, we have 60% of the whole.
a. The expression 2(4/3) represents the shaded parts of the diagram by first finding the area of one shaded rectangle, which is 4/3. Then, we multiply this area by 2 because there are two shaded rectangles in the diagram. Therefore, 2(4/3) gives us the total shaded area.
b. The expression 4 * 2/3 represents the shaded parts of the diagram by multiplying the width of the shaded rectangle (2 units) by its height (2/3 units), and then multiplying that by the number of shaded rectangles (4). Therefore, 4 * 2/3 gives us the total shaded area.
c. The expression 4 * 2 * 1/3 represents the shaded parts of the diagram by multiplying the length of the shaded rectangle (4 units) by its width (2 units) by its height (1/3 units), and then multiplying that by the number of shaded rectangles (4). Therefore, 4 * 2 * 1/3 gives us the total shaded area.
Hence, 2(4/3) represents the shaded area in the diagram as two rectangles of equal size, each with a length of 4 units and a width of 2/3 units.
4 * 2/3 represents the shaded area in the diagram as a rectangle with a length of 4 units and a width of 2/3 units.
4 * 2 * 1/3 represents the shaded area in the diagram as a rectangle with a length of 4 units, a width of 2 units, and a smaller rectangle with a length of 1 unit and a width of 1/3 units.
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5.
Records of randomly selected births were obtained and
categorized according to the day of the week that they occurred.
A reasonable claim is that births occur on the different days with
equal frequency. Use a 0.01 significance level to test that claim.
Find the test statistic and critical value for the goodness-of-fit
needed to test the claim.
Day
Number
of Births
Sun
77
Mon
110
Tues Wed
124
122
test statistic x² = 21.005, critical value x² = 12.592
test statistic x² = 21.005, critical value x² = 16.812
Thurs
120
Fri
123
Sat
97
The critical value from the chi-square distribution table is 15.51 for 11 degrees of freedom and a 0.01 significance level. Since the chi-square statistic (23.9) is greater than the critical value (15.51), we can reject the null hypothesis
What is chi-square goodness-of-fit test?Chi-square goodness-of-fit test is used to compare observed data with theoretical data, in order to determine how closely the two sets of results match. It is used to assess whether a sample data fits a given distribution.
To test the claim that the rate of violent crime is the same for each month, we can use a chi-square goodness-of-fit test.
The null hypothesis is that the rate of violent crime is the same for each month, while the alternative hypothesis is that the rate of violent crime is not the same for each month.
The chi-square statistic is calculated as follows:
X₂ = Σ(Oi - Ei)2 / Ei
where Oi is the observed number of crimes for each month and Ei is the expected number of crimes for each month.
The expected number of crimes for each month can be calculated by dividing the total number of crimes (8,814) by 12, which gives us an expected value of 734.5.
Using these values, we can calculate the chi-square statistic:
X₂ = (786 - 734.5)2 / 734.5 + (704 - 734.5)2 / 734.5 + (835 - 734.5)2 / 734.5 + (826 - 734.5)2 / 734.5 + (900 - 734.5)2 / 734.5 + (868 - 734.5)2 / 734.5 + (920 - 734.5)2 / 734.5 + (901 - 734.5)2 / 734.5 + (856 - 734.5)2 / 734.5 + (862 - 734.5)2 / 734.5 + (783 - 734.5)2 / 734.5 + (797 - 734.5)2 / 734.5
X₂ = 23.9
We can compare this value to the critical value from the chi-square distribution table, which is 15.51 for 11 degrees of freedom and a 0.01 significance level.
Since the chi-square statistic (23.9) is greater than the critical value (15.51), we can reject the null hypothesis and conclude that the rate of violent crime is not the same for each month.
This indicates that there is a statistically significant difference in the rate of violent crime for each month.
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Question 8(Multiple Choice Worth 2 points)
(Creating Graphical Representations MC)
The number of milligrams of Vitamin C from 100 different gummy vitamins sold in the world was collected.
Which graphical representation would be most appropriate for the data, and why?
Box plot, because the median can easily be determined from the large set of data
Stem-and-leaf plot, because you can see the shape of the data
Histogram, because it shows each individual data point
Bar chart, because the data is categorical
Histogram would be the most appropriate graphical representation for the collected data, because it shows each individual data point.
How to plot a histogram?A histogram is a graphical representation of a distribution of continuous data that is used to visualize the underlying frequency distribution of a set of data. Here are the general steps to plot a histogram:
1. Choose the appropriate number of bins: The first step in creating a histogram is to choose the number of bins or intervals that the data will be divided into. This decision is based on the number of data points and the range of the data.
2. Determine the range of the data: Determine the range of the data, which is the difference between the largest and smallest values in the data set.
3. Calculate the width of each bin: Divide the range of the data by the number of bins to determine the width of each bin.
4. Plot the horizontal axis: The horizontal axis of the histogram represents the range of the data and is divided into the chosen number of bins.
5. Plot the vertical axis: The vertical axis of the histogram represents the frequency or density of the data.
6. Count the number of observations: Count the number of observations that fall into each bin.
7. Plot the bars: Plot the bars of the histogram such that the height of each bar corresponds to the number of observations in each bin.
8. Label the axes and title: Finally, label the horizontal and vertical axes appropriately and give the histogram an appropriate title.
Histogram would be the most appropriate graphical representation for the collected data of milligrams of Vitamin C from 100 different gummy vitamins sold in the world.
A histogram is a graph that displays the distribution of a continuous data set using bars. It is useful for showing the frequency distribution of a large data set and helps to identify patterns or outliers in the data.
In this case, the milligrams of Vitamin C is a continuous variable, and the histogram would display the frequency of different milligram ranges. It would show the concentration range of the vitamin C in the gummy vitamins sold worldwide and provide an overall picture of the distribution of the data.
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