No, the two vector-valued functions found in parts a and c should not parameterize the same tangent line. The vector-valued function found in part a is a linear function, while the vector-valued function found in part c is a quadratic function. Therefore, the two functions will not parameterize the same tangent line.
3. Soshi's rhombus has a base of 12 in. and a
height of 10 in. Jack's rhombus has base and
height measures that are double those of Soshis
rhombus. Compare the area of Jack's rhombus to
the area of Soshi's rhombus.
Answer:
The area of Jack's rhombus is four times the area of Soshi's rhombus.
Step-by-step explanation:
First, calculate the area of Soshi's rhombus. Use the formula for the area of a rhombus:
[tex]A = bh=\\A=(12)(10)=\\A=120[/tex]
Now, we have the Soshi's rhombus is 120 [tex]in^2[/tex].
Jack's rhombus' base and height are double those of Soshi's; multiply each value by two.
[tex]12*2=24\\\\10*2=20[/tex]
Now, substitute the values in the formula for the area of a rhombus:
[tex]A = bh=\\A=(24)(20)=\\A=480[/tex]
Notice that 480 is 4 times 120.
This is because area is a two-dimensional measure (measured in units squared, like [tex]in^2[/tex]) while length is a one-dimensional measure (measured in regular units, like cm and in), The one-dimensional measures of Jack's rhombus are double those of Soshi's, and to translate this to the two-dimensional measure of area, square 2 (2 squared is 2 times 2).
2 squared is 4, so:
the area of Jack's rhombus is four times that of Soshi's.
Mrs. Hallmark wants to sell a box of two varieties of
birthday cards for $5. 80. The number of 30¢ cards is six
more than one half the number of 35¢ cards. The number
of 35¢ cards is:
According to unitary method, there are 10 30¢ cards and 8 35¢ cards in the box, which adds up to a total of $5.80.
Let's start by defining our units. In this case, our units are the number of 30¢ cards and the number of 35¢ cards. We know that the box of cards is being sold for $5.80, which means the total value of all the cards in the box is $5.80. We can use this information to set up an equation:
0.30x + 0.35y = 5.80
where x is the number of 30¢ cards and y is the number of 35¢ cards.
Next, we are given the information that the number of 30¢ cards is six more than one half the number of 35¢ cards. Using the unitary method, we can set up an equation that relates the number of 30¢ cards to the number of 35¢ cards:
x = 0.5y + 6
Now we can use this equation to eliminate x from our first equation:
0.30(0.5y + 6) + 0.35y = 5.80
Simplifying this equation gives:
0.15y + 1.80 + 0.35y = 5.80
0.50y = 4.00
y = 8
So there are 8 35¢ cards in the box. We can use the unitary method again to find the number of 30¢ cards:
x = 0.5y + 6
x = 0.5(8) + 6
x = 10
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I need help with this ASAP please
Answer:
y- coordinate = 4
Step-by-step explanation:
consider a right triangle formed by the x- axis, the radius (hypotenuse) of 5 and a vertical line drawn to the x- axis from the point ( 3, - )
using Pythagoras' identity in the right triangle
3² + y² = 5²
9 + y² = 25 ( subtract 9 from both sides )
y² = 16 ( take square root of both sides )
y = [tex]\sqrt{16}[/tex] = 4
the y- coordinate of the point is 4 , that is (3, 4 )
Answer:
y= coordinate 4
right triangle formed by the x- axis, the radius (hypotenuse) of 5 and a vertical line drawn to the x- axis from the point ( 3, - )
using Pythagoras' identity in the right triangle
3² + y² = 5²
9 + y² = 25 ( subtract 9 from both sides )
y² = 16 ( take square root of both sides )
y =
16
16
= 4
the y- coordinate of the point is 4 , that is (3, 4 )
In triangle LMN, angle N = 90 degrees. LM = 10, MN = 6, & LN = 8
What is tan of angle M?.
In a right triangle, tangent of one of non-right angles is equal to ratio of the length of opposite side to the length of adjacent side. The tangent of angle M is 5/3.
In this case, we want to find tangent of angle M.
Let's label the sides of triangle opposite, adjacent, and hypotenuse, as follows:
Opposite: side LM, which is opposite to angle M.
Adjacent: side MN, which is adjacent to angle M.
Hypotenuse: side LN, which is the longest side and opposite to the right angle N.
Using the Pythagorean theorem, we can find the length of the hypotenuse LN:
[tex]LN^2 = LM^2 + MN^2 \\LN^2 = 10^2 + 6^2\\LN^2 = 100 + 36\\LN^2 = 136LN = sqrt(136) = 2*sqrt(34)[/tex]
Now, we can use the tangent formula:
tan(M) = opposite/adjacent = LM/MN
tan(M) = 10/6 = 5/3
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the auto parts department of an automotive dealership sends out a mean of 6.9 special orders daily. what is the probability that, for any day, the number of special orders sent out will be exactly 5 ? round your answer to four decimal places.
The answer to this question is 0.1754
have a new hobby - a saltwater fish tank that will contain mostly live corals (called a reef tank). i am currently in the planning stage and am gathering knowledge to give me the best chance of success with my tank. as part of the planning stage, i reached out to 700 experienced central florida reefers (people who currently have a reef tank) and asked them to provide the following information: size of the tank (in gallons), type of lighting used (florescent, led, hybrid, or other), and how long (in years) they have been in the hobby. part of the analysis involves trying to estimate the proportion of all central florida reefers who use led lighting. a 95% confidence interval was constructed to be: (.755, .816). the sample proportion reported was .7855. was the sample size considered large in the construction of this confidence interval? group of answer choices no, since n is less than 30. yes, since n is at least 30. yes, since np and nq are both at least 15. no, since np and nq are not both at least 15.
This indicates that the sample size was large enough to construct a reasonably precise confidence interval.
Since n is at least 30" or "yes, since np and nq are both at least 15."
The sample size, we cannot definitively choose between these two options.
Information provided; the sample size is not explicitly stated.
Determine whether the sample size is considered large enough for the construction of a confidence interval based on the conditions for using a normal approximation to the binomial distribution.
One condition is that np and nq are both at least 15, where n is the sample size, p is the proportion of interest (in this case, the proportion of central Florida reefers who use LED lighting), and q is the complement of p (i.e., 1-p). This condition ensures that the distribution of the sample proportion is approximately normal.
Another condition is that the sample size is large enough that the standard error of the sample proportion (sqrt[pq/n]) is small enough to use a normal approximation.
This condition is not explicitly stated, but it is typically considered to be met when n is at least 30.
Since we do not know the sample size, we cannot directly determine whether the conditions are met.
That a 95% confidence interval was constructed with an interval estimate of (.755, .816) and a sample proportion of .7855.
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you want to rent an unfurnished one-bedroom apartment for next semester. the mean monthy rent for a random sample of 45 apartments advertised in the local newspaper is $775. assume the standard deviation is $110. find a formula used to generate the 98% confidence interval for the mean monthly rent for unfurnished one-bedroom apartments available for rent in this community.
Formula:
98% Confidence Interval = (Mean - (2*Standard Deviation/√n), Mean + (2*Standard Deviation/√n))
98% Confidence Interval = ($775 - (2*$110/√45), $775 + (2*$110/√45))
98% Confidence Interval = ($735.56, $814.44)
how many atheletes in total were acccused of using performance-enhancing drugs? of these, how many were using and how many were not? what percentage of those accused of using were falsely accused?
There have been numerous cases of athletes being accused of using performance-enhancing drugs, and the numbers may vary depending on the sport, country, and time period in question.
Additionally, determining how many athletes were using or not using performance-enhancing drugs would require specific information on individual cases.
Regarding the percentage of athletes falsely accused of using performance-enhancing drugs, it is difficult to determine an accurate figure without examining each case in detail. False accusations may occur due to various reasons, such as flawed testing procedures or contaminated supplements, and the percentage of false accusations may vary depending on the situation.
If you have a specific case or sport in mind, I can try to provide you with more information on that topic.
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Verify Associative property: 2/3 + (3/4 + 1/5) = (2/3 + 3/4) + 1/5..
Please help tomorrow is my final exam
We verified that the associative property of addition holds for the given expression below
Verifying the Associative propertyLet's verify the associative property of addition for the given expression:
2/3 + (3/4 + 1/5) = (2/3 + 3/4) + 1/5
We can simplify both sides of the equation by finding a common denominator for the fractions:
2/3 + (3/4 + 1/5) = (2/3 + 3/4) + 1/5
Multiplying 2/3 by 20/20, we get:
40/60 + (3/4 + 1/5) = (2/3 + 3/4) + 1/5
Multiplying 3/4 by 15/15, we get:
40/60 + 45/60 + 1/5 = (2/3 + 3/4) + 1/5
Combining the first two terms on the left-hand side, we get:
85/60 + 1/5 = (2/3 + 3/4) + 1/5
Simplifying the fraction 85/60, we get:
17/12 + 1/5 = (2/3 + 3/4) + 1/5
Multiplying 2/3 by 4/4, we get:
17/12 + 1/5 = (8/12 + 9/12) + 1/5
Combining the fractions in the parentheses, we get:
17/12 + 1/5 = 17/12 + 1/5
Since both sides of the equation are equal, we have verified that the associative property of addition holds for the given expression:
2/3 + (3/4 + 1/5) = (2/3 + 3/4) + 1/5.
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a marketing organization claims that less than 15% of its employees are paid minimum wage. if a hypothesis test is performed that fails to reject the null hypothesis, how would this decision be interpreted? g
If a hypothesis test is performed and fails to reject the null hypothesis, it would mean that there is not enough evidence to support the claim that less than 15% of the marketing organization's employees are paid minimum wage.
Therefore, it would not be concluded that the claim is true. The null hypothesis assumes that the claim is false or that the percentage of employees paid minimum wage is not significantly different from 15%.
The failure to reject the null hypothesis means that the evidence does not contradict the null hypothesis, but it does not necessarily prove it to be true.
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Find the area of the trapezoid. 1. 6 m
4 m
12 m
2. 10 in. 15 in. 6 in
3. 2 yd
8 yd
6 yd
4. H = 10 cm, b,
= 3 cm, by = 5 cm
The area of the trapezoid is 72 square meters.
In order to find the area of a trapezoid, we need to use the formula:
Area = (b1 + b2) x h / 2
where b1 and b2 are the lengths of the parallel sides, and h is the height of the trapezoid.
In this case, we are given the lengths of the parallel sides as 6m and 12m respectively, and the height of the trapezoid is 4m.
So, we can plug these values into the formula to get:
Area = (6m + 12m) x 4m / 2
Area = 18m x 4m Area = 72m²
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Complete Question:
Find the area of the trapezoid.
Base 1 = 6 m
Height = 4 m
Base 2 = 12 m
Find the three trigonometric ratios. If needed, reduce fractions.
[tex]\sin(X )=\cfrac{\stackrel{opposite}{36}}{\underset{hypotenuse}{45}}\implies \sin(X )=\cfrac{4}{5} \\\\\\ \cos(X )=\cfrac{\stackrel{adjacent}{27}}{\underset{hypotenuse}{45}}\implies \cos(X)=\cfrac{3}{5} \\\\\\ \tan(X )=\cfrac{\stackrel{opposite}{36}}{\underset{adjacent}{27}}\implies \tan(X)=\cfrac{4}{3}[/tex]
find the surface area of a cylinder with a radius of 2 feet and height of 8 feet
A random number generator assigned each pepper to one of two groups. The weights of the peppers in each group, given three randomizations, appear in the tables.
First Randomization
Group A Group B
13.6 9.2
12.1 8.2
15.9 11.5
11.2 13.8
9.7 14.6
Second Randomization
Group A Group B
8.2 12.1
13.8 14.6
15.9 13.6
9.2 11.2
9.7 11.5
Third Randomization
Group A Group B
8.2 12.1
9.7 13.8
11.5 13.6
14.6 11.2
15.9 9.2
For each table, calculate the mean weight for each group,
x
A
¯
and
x
B
¯
, and find the difference of the mean of group A and the mean of group B (
x
A
¯
−
x
B
¯
).
After the first randomization,
x
A
¯
is ,
x
B
¯
is , and (
x
A
¯
−
x
B
¯
) is .
After the second randomization,
x
A
¯
is ,
x
B
¯
is , and (
x
A
¯
−
x
B
¯
) is .
After the third randomization,
x
A
¯
is ,
x
B
¯
is , and (
x
A
¯
−
x
B
¯
) is .
Therefore, the mean weight for each group in the three randomizations are:
First Randomization:
Group A: 12.5
Group B: 11.46
Second Randomization:
Group A: 11.56
Group B: 12.4
Third Randomization:
Group A: 12.18
Group B: 12.18
What is mean?The mean, also known as the average, is a measure of central tendency in statistics. It is found by adding up all the values in a data set and dividing by the number of values in the set. The mean is sensitive to extreme values, or outliers, in the data set, and can be influenced by them. It is one of the most commonly used measures of central tendency, along with the median and mode.
Here,
First Randomization:
Group A: (13.6 + 12.1 + 15.9 + 11.2 + 9.7) / 5 = 12.5
Group B: (9.2 + 8.2 + 11.5 + 13.8 + 14.6) / 5 = 11.46
Second Randomization:
Group A: (8.2 + 13.8 + 15.9 + 9.2 + 9.7) / 5 = 11.56
Group B: (12.1 + 14.6 + 13.6 + 11.2 + 11.5) / 5 = 12.4
Third Randomization:
Group A: (8.2 + 9.7 + 11.5 + 14.6 + 15.9) / 5 = 12.18
Group B: (12.1 + 13.8 + 13.6 + 11.2 + 9.2) / 5 = 12.18
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Answer:
LOOK BELOW FOR ANSWER !!
Step-by-step explanation:
After the first randomization,
A is 12.5
B is 11.46
and A-B is 1.04
After the second randomization,
A is 11.36
B is 12.6
A and B is -1.24
After the third randomization,
A is 11.98
B is 11.98
A and B is 1
.
assuming we are testing a hypothesis using the one-way anova test with more than 2 independent normally distributed populations, how can the f-statistic be calculated?
One measure we use to determine the F-statistics is the ratio of the variability within and across groups when we are doing the one way-ANOVA test.
We are interested in discovering whether there are significant differences between the means of the populations when doing a one-way ANOVA test on more than two independent normally distributed populations. A test statistic used to reach this conclusion is the F-statistic.
The ratio of the variability of the between group and within group is the a tool that we use to find the F-statistics.
F is equal to (SSB/k-1) / (SSW/N-k)
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Which simulation is a representation of independent events?
The independent events are the ones in the third option, spinning the spiner twice.
Which simulation represents independent events?Two events are called independent if the outcome of the first event does not affect the outcome of the second event.
From the given options, the only two that are independent are spining the spinner two times.
For example in the case of the candy, when you pull one candy and eat it, you can't pull it again, so the outcomes for the second event are modified.
In the case of the spinner that does not happen, that is why the events are independent.
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3. What is the surface area of this composite solid? Show your work.
The surface area of the composite solid is 162 unit²
What is surface area?The area occupied by a three-dimensional object by its outer surface is called the surface area.
The composite solid has 6 faces . The area of each face is calculated as follows;
Face 1
area = 5×7 = 35 units²
face 2
area = 1/2bh + l×b
= 1/2 ×3×4 + 3×4
= 6+12 = 18units²
face 3 = face 2
area = 18units²
face 4
area = 3× 7 = 21units²
face 5
area = 4×7
= 28units²
face 6
area = 3×7 + 3×7
= 21+21 = 42units²
Therefore total surface area = 42+28+21+18+18+35
= 162 units²
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A can contains
15/16 pounds of vegetables. One serving of these vegetables weights
pound.
What is the total number of servings of vegetables in the can?
As portion of the vegetables weights 1/4 pound and totals **15/16 pounds , the can has **3 and 3/4 servings** of veggies.
What does pound and weight mean?A pound is a unit of weight or mass measurement. The Latin word "libra," which means "weight" or "balance," denotes a measurement system employed in ancient Rome and which is equivalent to around 12 ounces.
Mass is the quantity of matter in a thing, whereas weight is the force of gravity acting on the object
Each portion of the vegetables weights 1/4 pound and totals **15/16 pounds** in the can. We must divide the can's overall weight by the weight of one serving to determine how many servings of veggies are included therein.
We thus have:
'''The can weighs 15/16 pounds in total.
Weight of one serving is one-fourth of a pound.
We divide the entire weight of the can by the weight of one serving to get how many servings are in it:
``` (15/16) ÷ (1/4) = (15/16) × (4/1)
= 60/16 = 3 3/4 ```
As a result, the can has **3 and 3/4 servings** of veggies.
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Determine if I triangle can be constructed with the following sides. Explain
2/3 , 4/5 , 1/2
what value of x would allow a triangle to be constructed with the following measures?
a. 21,8,x
b. 13,7,x
With the image Find x
Yes, a triangle can be constructed with sides of 2/3, 4/5, and 1/2. the value of x is 17.
Since a triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.
To determine if a triangle can be constructed, we need to check if the sum of the two smaller sides is greater than the largest side.
In this case, we can see that
2/3 + 1/2 > 4/5,
2/3 + 4/5 > 1/2,
1/2 + 4/5 > 2/3,
Therefore, a triangle can be formed.
The value of x can be calculated as;
45 + 68 + 3x + 16 = 180
3x = 51
x = 17
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A gray whale swims 161 kilometers in 24 hours. The equation below can be used to find the rate (r), in kilometers per hour (kph), at which the gray whale swims. Rounded to the nearest tenth, what is the rate at which the gray whale swims?
The rate at which the gray whale swims is 6.7 kilometers per hour.
What is the equation that relates the distance, rate, and time?
The equation that relates the distance, rate, and time is distance = rate × time
This equation can be used to calculate any one of the three variables if the other two are known.
For example, if you know the rate at which an object is moving and the time it has been moving, you can use this equation to find the distance it has traveled. Or, if you know the distance traveled and the time it took to travel that distance, you can use this equation to find the average rate of travel.
We are given that the distance traveled by the gray whale is 161 kilometers in 24 hours. Therefore, we can use the equation to find the rate at which the gray whale swims,
rate = distance / time = 161 km / 24 h ≈ 6.7 kph
Rounding to the nearest tenth, the rate at which the gray whale swims is approximately 6.7 kilometers per hour.
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in the chi square test of hypothesis, the null hypothesis states that the variables are select one: a. dependent b. independent c. causally related d. non-random
Option b is correct.
The null hypothesis in the chi-square test of hypothesis states that the two categorical variables under consideration are independent of each other, meaning that there is no relationship or association between them.
What is chi-square test of hypothesis? Explain more indetail?In the chi-square test of hypothesis, the null hypothesis states that the variables under consideration are independent. That is, there is no relationship between the two variables being studied.
The chi-square test is a statistical method used to determine if two categorical variables are associated or independent. Categorical variables are those that take on values that are categories or labels.
For example, gender (male or female) or educational level (high school, college, graduate school) are categorical variables.
The chi-square test determines the expected frequency of each category based on the null hypothesis, which assumes independence between the two variables.
The observed frequency is then compared to the expected frequency, and if the difference is significant enough, it suggests that the null hypothesis should be rejected, and the two variables are considered to be associated or dependent.
Therefore, in summary, the null hypothesis in the chi-square test of hypothesis states that the two categorical variables under consideration are independent of each other, meaning that there is no relationship or association between them.
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suppose a scientist designs an experiment to test a hypothesis. which of the following is true? 1 point if the experimenter does the test correctly, the hypothesis will be proven correct. a good experiment is one that produces the most data. an experiment should always be done in a professional science lab, using lab equipment. the results of the experiment might support the hypothesis, or might not.
The results of the experiment might support the hypothesis, or might not.
The correct statement is that the results of the experiment might support the hypothesis, or might not. It is important to design a well-controlled experiment that tests the hypothesis in a rigorous and systematic way. The goal is not to prove the hypothesis correct, but rather to gather evidence that either supports or contradicts the hypothesis. It is also important to conduct the experiment in a suitable environment with appropriate equipment and procedures to ensure accurate and reliable results.
Your question focuses on understanding the relationship between a hypothesis, an experiment, and the possible outcomes.
An experiment is designed to test a hypothesis, which is an educated guess or prediction about a phenomenon. When conducting an experiment, the results might either support the hypothesis or contradict it, leading to further investigation and refinement of the hypothesis. A well-designed experiment should be able to provide valuable data and insights, regardless of the outcome.
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The statement that is true is:
"The results of the experiment might support the hypothesis or might not."
A scientist designs an experiment to test a hypothesis.
In such a scenario, it is important to note that the outcome of the experiment cannot be predicted with certainty.
The scientific method involves formulating a hypothesis, designing an experiment to test the hypothesis,
collecting and analyzing data and drawing conclusions.
The hypothesis is an educated guess that can be tested through experimentation.
It is important to remember that a hypothesis can never be proven to be 100% correct, only supported or refuted by the evidence obtained through experimentation.
It is not accurate to say that if the experimenter does the test correctly, the hypothesis will be proven correct.
This is because there are many variables that can affect the outcome of the experiment, and it is impossible to control all of them.
Additionally, a good experiment is not necessarily one that produces the most data.
A good experiment is one that is well-designed, carefully controlled, and yields reliable results.
The use of lab equipment is also not a requirement for conducting experiments.
While it is often necessary for certain types of experiments, many experiments can be conducted with simple materials and equipment.
Ultimately, the results of the experiment might support the hypothesis, or might not. If the results support the hypothesis, it can be considered a step towards validating the hypothesis.
The results do not support the hypothesis, it does not necessarily mean that the hypothesis is incorrect.
It could mean that the experiment was flawed, or that the hypothesis needs to be revised based on the new information obtained from the experiment.
Designing and conducting experiments is an important part of the scientific method.
Guarantee that an experiment will yield the desired results, a well-designed and carefully controlled experiment can provide valuable information that can help scientists understand the natural world.
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Find the differential of the function. Z = e−4x cos(4πt)
The differential of the function Z is -4e⁻⁴ˣcos(4πt) - 4πsin(4πt)e⁻⁴ˣ
To find the differential function of Z = e⁻⁴ˣ cos(4πt), we will use the product rule of differentiation. The product rule states that the derivative of the product of two functions is equal to the first function multiplied by the derivative of the second function plus the second function multiplied by the derivative of the first function.
Let's apply the product rule to our function Z:
First, we differentiate the first function e⁻⁴ˣ with respect to x. The derivative of e⁻⁴ˣ is -4e⁻⁴ˣ.
Next, we differentiate the second function cos(4πt) with respect to t. The derivative of cos(4πt) is -4πsin(4πt).
Therefore, the differential function of Z is:
dZ/dt = -4e⁻⁴ˣcos(4πt) - 4πsin(4πt)e⁻⁴ˣ
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Claire works at the Sweet Shop, where candy is bagged and sold by its weight. Claire's last 4 sales of gourmet gummy worms are shown in the table.
The cost of the gummy worms is proportional to the amount, in pounds, of gummy worms purchased.
This situation can be represented by an equation in the form y = kx, where k is the constant of proportionality.
Gourmet
Gummy Worms,
x (pounds)
Cost,
y
0.75 $6.30
2.5 $21.00
4 $33.60
7 $58.80
What is the constant of proportionality?
The constant of proportionality is $8.40
What is constant of proportionality?The constant of proportionality is a value that relates two quantities that are proportional to each other. It is represented by the letter k and is found by dividing the dependent variable by the independent variable. In this case, the constant of proportionality is $8.40 for the given data set.
According to the given information:
To find the constant of proportionality, we can use any two data points from the table and plug them into the equation y = kx.
Let's use the first and second data points: (0.75, $6.30) and (2.5, $21.00).
We can set up the equation as:
$6.30 = k(0.75)
Solving for k, we get:
k = $6.30/0.75 = $8.40
Now, we can check our work by using another data point. Let's use the third data point: (4, $33.60).
Plugging in the values, we get:
$33.60 = k(4)
k = $33.60/4 = $8.40
Since we get the same value for k, we can be confident that our answer is correct.
Therefore, the constant of proportionality is $8.40.
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Does anyone know what 3D model this is?-
The given 3D model is a trapezoidal pyramid.
What is pyramid?A pyramid is a 3D polyhedron having three or more triangle-shaped faces that meet above the base and a polygonal base. The point above the base is referred to as the apex, while the three sides are referred to as faces. The base and apex are joined to form a pyramid. To distinguish them from the base, the triangular sides are also also referred to as lateral faces. In a pyramid, the apex, which creates the triangle face, is connected to each base edge.
Hence, the given 3D model is a trapezoidal pyramid.
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If each book is 5$ and I have 133$ then how many books can I buy?
Answer:
26
Step-by-step explanation:
You just divide 133 and 5 and you get 26.6
Answer:
26
Step-by-step explanation:
[tex]\frac{133}{5}[/tex] = 26.6
You cannot buy part of a book, so you can buy 26 books
26 x 5 = 130. You will have $3.00 left over.
Helping in the name of Jesus.
Taylor is proving the Pythagorean theorem.
(photo attached)
How could Taylor use the diagram to prove the Pythagorean theorem?
A. Taylor could set the area of a square with side length a + b equal to the sum of the areas of the 4 triangles and the square with side length c.
B. Taylor could set the area of the square with side length c equal to the sum of the areas of the 4 congruent triangles.
C. Taylor could find the ratio of the area of the square with side length a + b to the area of one of the congruent triangles.
D. Taylor could find the ratio of the area of the square with side length a + b to the area of the square with side length c.
If Taylor is proving the Pythagorean theorem. Taylor can use the diagram to prove the Pythagorean theorem by: A. Taylor could set the area of a square with side length a + b equal to the sum of the areas of the 4 triangles and the square with side length c.
How could Taylor use the diagram to prove the Pythagorean theorem?To prove the Pythagorean theorem, we want to show that in a right triangle with legs a and b and hypotenuse c, the square of the hypotenuse c^2 is equal to the sum of the squares of the legs a^2 + b^2.
From the given diagram, we can see that we have a square with side length a+b, which is divided into 4 congruent right triangles and a smaller square with side length c. Each of the 4 triangles has legs a and b, which are also the legs of the right triangle we want to prove the theorem for. The smaller square with side length c has an area equal to c^2, which is the square of the hypotenuse of the right triangle.
The area of the square with side length a+b is (a+b)^2 = a^2 + 2ab + b^2. The area of one of the congruent right triangles is (1/2)ab, so the sum of the areas of the 4 triangles is 2ab. Therefore, the sum of the areas of the 4 triangles and the smaller square is:
a^2 + 2ab + b^2 + c^2
But this is also equal to the area of the larger square with side length a+b, which is (a+b)^2. So we have:
a^2 + 2ab + b^2 + c^2 = (a+b)^2
Expanding the right-hand side gives:
a^2 + 2ab + b^2 + c^2 = a^2 + 2ab + b^2
Canceling the common terms on both sides gives:
c^2 = a^2 + b^2
This is the Pythagorean theorem, which we have proved using the given diagram.
Therefore, option A is the correct answer.
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4 √(20) + 6 √(45) - √(80)
Answer:
22√5
Step-by-step explanation:
√20=√4x5 = √4 x √5 = 2√5
√45 = √9 x 5 = √9 x √5 = 3√5
√80 = √16 x 5 = √16 x √5 = 4√5
4√20 = 6 √45 - √80 = 4(2√5) + 6(3√5)- 4√5
8√5 + 18√5 - 4√5 = 22√5
So its 22√5
Answer:
[tex]22 \sqrt{5} [/tex]
Step-by-step explanation:
the explaination is avaliable in the picture i sent you
and please give me branliest
the equations y = a and x = a are perpendicular true or false
Answer: True
Step-by-step explanation:
trust
Answer:
I believe they are true
Step-by-step explanation:
PLEASE HELP AND EXPLAIN AND SHOW WORK ON HOW YOU GOT THE ANSWER I WILL MARK YOU BRAINLIEST