Since these values are not equal, Lin and Noah would obtain different volume measurements when using their small cubes to find the volume of the 1 1/2 inch cube.
No, Lin and Noah would not get the same value for the volume of the 1 1/2 inch cube using their small cubes.
The volume of a cube is determined by multiplying the length of its edges three times. Lin's cube has an edge length of 1/2 inch, and Noah's cube has an edge length of 1/4 inch.
For Lin's cube, the volume would be (1/2) * (1/2) * (1/2) = 1/8 cubic inches.
For Noah's cube, the volume would be (1/4) * (1/4) * (1/4) = 1/64 cubic inches.
Lin's cube would yield a volume of 1/8 cubic inches, while Noah's cube would result in a volume of 1/64 cubic inches.
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17. Nikki rides her scooter a distance of
64.75 feet in 7 seconds. Assume the
relationship between distance and
time is proportional.
Part A
Write an equation to represent the
distance traveled, y, after x seconds.
Express your answer in the form
y = kx.
An equation to represent the distance traveled, y, after x seconds is y = 9.25x.
What is a proportional relationship?In Mathematics, a proportional relationship produces equivalent ratios and it can be modeled or represented by the following mathematical equation:
y = kx
Where:
k is the constant of proportionality.y represent the distance.x represent the time.Next, we would determine the constant of proportionality (k) based on the data points provided as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 64.75/7
Constant of proportionality, k = 9.25.
Therefore, the required equation is given by;
y = kx
y = 9.25x
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someone help
me please and asap
Answer:
continuous is the answer cause the number of kittens in a pet store can't stay the same amount.
a bag contains 5 red marbles, 6 blue marbles, 10 white marbles and 9 yellow marbles. you are asked to draw 5 marbles from the bag without replacement. what is the probability of drawing 3 or more white marbles?
the probability of drawing 3 or more white marbles when 5 marbles are drawn from the bag without replacement.
To calculate this probability, we can use the formula for the hypergeometric distribution, which is:
P(X ≥ 3) = [C(10,3) * C(10,2)] / C(30,5) + [C(10,4) * C(10,1)] / C(30,5) + [C(10,5)] / C(30,5)
Where C(n,r) is the number of ways to choose r items from a set of n items.
formula is that we need to consider three different cases: drawing exactly 3 white marbles, drawing exactly 4 white marbles, and drawing all 5 white marbles. For each case, we calculate the probability of drawing the required number of white marbles and the probability of drawing the remaining marbles (non-white marbles), and then multiply them together. Finally, we add up the probabilities for all three cases to get the total probability of drawing 3 or more white marbles.
Using the formula, we get:
P(X ≥ 3) = [(C(10,3) * C(20,2)) + (C(10,4) * C(20,1)) + C(10,5)] / C(30,5)
= [(120 * 190) + (210 * 20) + 252] / 142506
= 0.209
Therefore, the probability of drawing 3 or more white marbles when 5 marbles are drawn from the bag without replacement is 0.209.
using the hypergeometric distribution formula, we can calculate the probability of drawing 3 or more white marbles from a bag containing 5 red marbles, 6 blue marbles, 10 white marbles, and 9 yellow marbles when 5 marbles are drawn without replacement. The probability is 0.209.
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a teacher of saba school wants to estimate the distance students travel to school. the sample mean and population standard deviation are found to be 8 km and 2.25 km, respectively. how large a sample should be selected to be 99% confident that the sample mean differs from the population mean by /- 0.5 km (e) only?
The sample size should be selected as 100 in order to be 99% confident that the sample mean differs from the population mean by ±0.5 km (or within a range of 0.5 km).
To determine the sample size needed to estimate the distance students travel to school with a 99% confidence level and a margin of error of ±0.5 km, we can use the formula for sample size calculation:
n = (Z * σ / E)^2
where:
n = required sample size
Z = Z-score corresponding to the desired confidence level (in this case, 99% confidence level, which corresponds to Z = 2.576)
σ = population standard deviation
E = margin of error
Plugging in the given values:
n = (2.576 * 2.25 / 0.5)^2
Calculating this equation gives us the required sample size:
n ≈ 99.98
Since we cannot have a fractional sample size, we round up to the nearest whole number.
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in 2010, by 40 years of age, _____ percent of individuals had ever been married.
According to the U.S. Census Bureau, in 2010, by the age of 40, approximately 85% of individuals had ever been married.
This statistic is based on data from the American Community Survey, which is conducted by the U.S. Census Bureau. The survey includes questions about marital status and provides information on the percentage of individuals who have ever been married by various ages. The statistic that 85% of individuals had ever been married by the age of 40 suggests that marriage is still a common life experience in the United States. However, it's important to note that this statistic may be influenced by a variety of factors, including changes in societal attitudes towards marriage, cultural and religious practices, and economic factors. Additionally, it's important to consider that this statistic may not be representative of all populations or demographic groups, as marriage rates can vary significantly based on factors such as race, ethnicity, and income.
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A direct variation includes the points (-20,-40) and (7,n) find n
A direct variation includes the points (-20,-40) and (7,n) ,The value of n is 14..
in a direct variation, two variables are related in a way that can be expressed as y = kx, where k is a constant of proportionality. in this case, we are given two points that are related by a direct variation:
(-20,-40) and (7,n)
to find the value of n, we need to first determine the value of k. we can do this by using the formula for a direct variation:
y = kx
using the first point (-20,-40), we can substitute x = -20 and y = -40 to get:
-40 = k(-20)
solving for k, we get:
k = -40/-20 = 2
now that we know k, we can use it to find n using the second point (7,n):
n = kx
n = 2(7)
n = 14
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A shade of paint, Orange Mango, can be made by mixing red paint and
yellow paint in the ratio 2: 5. Teddy has 20 litres of red paint and
40 litres of yellow paint.
Work out the maximum volume of Orange Mango paint that Teddy can
make.
Give your answer in litres.
A shade of paint, Orange Mango, can be made by mixing red paint and yellow paint in a ratio of 2:5. Teddy has 20 litres of red paint and 40 litres of yellow paint.The maximum volume of Orange Mango paint that Teddy can make is 24 litres.
The most quantity of Orange Mango paint that Teddy can make, we need to discover the proscribing thing that stops him from the usage of all of his red and yellow paint. In this method, we need to evaluate the ratio of pink-yellow paint that he has with the ratio of crimson-to-yellow paint that he desires. Here is how we try this:
The ratio of crimson to yellow paint that he has is 20:40, which may be simplified with the aid of dividing each side by means of 20 to get 1:2.
The ratio of crimson to yellow paint that he needs is 2:5, which can be simplified by dividing each aspect by using the finest commonplace element of 2 and 5, that's 1, to get 2:5.
To compare those ratios, we are able to pass-multiply them and notice which aspect is greater. In this approach, we multiply the numerator of one ratio via the denominator of the opposite ratio and compare the effects. Here is how we try this:
1/2 compared to 2/5
(1×5) compared to (2×2)
5 in comparison to 4
We can see that five is larger than 4, this means that the ratio of pink to yellow paint that he has is greater than the ratio of purple to yellow paint that he desires. This means that he has extra crimson paint than he desires, and consequently, purple paint is the restricting component.
To find out how much pink paint he can use, we need to discover how an awful lot yellow paint he wishes for every litre of purple paint. We can do that by way of dividing the numerator and denominator of the ratio of pink to yellow paint that he needs with the aid of the numerator of that ratio. Here is how we do this:
2/5 ÷ 2/1 = 2/5 × 1/2 = 1/5
This manner that for every litre of purple paint, he needs 0.2 litres of yellow paint. Since he has 20 litres of pink paint, he can use it all and multiply it with the aid of 0.2 to discover how much yellow paint he wishes. Here is how we do that:
20 × 0.2 = 4
This means that he needs 4 litres of yellow paint. Since he has 40 litres of yellow paint, he has more than enough and may use the handiest 4 litres.
To discover the most volume of Orange Mango paint that Teddy could make, we need to add up the volumes of purple and yellow paint that he makes use of. Here is how we do this:
20 + 4 = 24
With this approach, he could make 24 litres of Orange Mango paint.
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The maximum volume of Orange Mango paint that Teddy can make is 56 liters.
We have,
The ratio of red paint to yellow paint required to make Orange Mango paint is 2:5.
This means for every 2 liters of red paint, 5 liters of yellow paint are needed.
Teddy has 20 liters of red paint and 40 liters of yellow paint.
To determine the maximum volume of Orange Mango paint Teddy can make, we need to find which paint he has in excess and how much of the other paint he needs to use to create the mixture.
Teddy has 20 liters of red paint, which is equivalent to 20/2.5 = 8 units of the mixture (since 2+5=7 units are needed to make the mixture).
Teddy has 40 liters of yellow paint, which is equivalent to 40/2.5 = 16 units of the mixture.
Since Teddy has more yellow paint, the amount of Orange Mango paint he can make is limited by the amount of red paint he has.
Thus,
Teddy can make a maximum of 8 units of Orange Mango paint, which is equivalent to 8 x 7 = 56 liters of the mixture.
Therefore,
The maximum volume of Orange Mango paint that Teddy can make is 56 liters.
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find the equation in standard form of the line passing through the points (2 -3) and (4 2)
Answer:
5x - 2y = 16
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, - 3 ) and (x₂, y₂ ) = (4, 2 )
m = [tex]\frac{2-(-3)}{4-2}[/tex] = [tex]\frac{2+3}{2}[/tex] = [tex]\frac{5}{2}[/tex] , then
y = [tex]\frac{5}{2}[/tex] x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (4, 2 )
2 = [tex]\frac{5}{2}[/tex] (4) + c = 10 + c ( subtract 10 from both sides )
- 8 = c
y = [tex]\frac{5}{2}[/tex] x - 8 ← equation in slope- intercept form
multiply through by 2 to clear the fraction
2y = 5x - 16 ( subtract 5x from both sides )
- 5x + 2y = - 16 ( multiply through by - 1 )
5x - 2y = 16 ← equation in standard form
let r be the shaded region in the first quadrant enclosed by the graphs of y=e^-x^2
how do you find the area of the region R?
To find the area of the shaded region R enclosed by the graphs of y = e^(-x^2) in the first quadrant, you can use integration.
The integral represents the area under a curve between two x-values. In this case, we want the area in the first quadrant, so we need to integrate the function from x = 0 to some positive x-value.
The integral to find the area of R is given by:
A = ∫[0 to a] e^(-x^2) dx
Unfortunately, there is no elementary function to find the antiderivative of e^(-x^2) in terms of elementary functions. Therefore, the integral cannot be evaluated using simple algebraic methods.
However, the integral can be approximated using numerical methods or specialized techniques such as Gaussian quadrature or Monte Carlo methods. These methods can provide an approximation of the area of the shaded region R.
Alternatively, you can use software or graphing calculators that have built-in functions to find definite integrals to numerically approximate the area under the curve.
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What is the area of the polygon given below?
19
12
2
2
3
Answer: 271 square units
Charlie's teacher claims that he does not study and just guesses on exams. on an exam with 201 true-false questions, Charlie answered 53.7% of the questions correctly. Calculations using these results show that if he were really just guessing, there would be roughly one chance and seven that he would do this well. Is there a statistically significant evidence against the teachers claim that Charlie is just guessing? Why or why not?
Answer:
Step-by-step explanation:
True-False questions consists of 2 possible answer, which are 50% each, so basically is Charlie was just guessing 201 questions, which means his possibility of getting everything correct is [tex]\frac{1}{2^2^0^1}[/tex], which is really small, his chance of getting 53,7% correct is [tex]\frac{1}{2^2^0^1 * 0.537}[/tex] which is roughly arround [tex]\frac{1}{2^2^0^0}[/tex]
Will mark brainliest and give points
A small sample shows that on average 29% of kids in a class spend 4 hours or more
on thier cell phone with a margin of error of +/- 2.5%. The school has 3650 students
in total.
What is the minimum amount of students that spend more than 4 hours on their
phone . What is the maximum amount of students that spend more than 4
hours on thier phone
ROUND TO AND APPROPRIATE POSITION
PLEASE HELP!! DUE TOMORROW!!What is the measure of the unknown angle? (1 point)
straight angle divided into a one hundred four degree angle and an unknown angle
a
72°
b
74°
c
76°
d
79°
Answer:
(c) n = 76
Step-by-step explanation:
a straight line is 180
the angle given is 104
180 - 104 = 76!!
your answer would be c!!
At a car rental office, 63% of the customers are men, and 37% are women. What is the probability that the customer will be a man who requests either a compact car or a luxury car?
The solution is: 3.7%, is the probability that the next customer will be a woman who requests a convertible.
Here, we have,
given that,
At a car rental office, 63% of the customers are men and 37% are women.
If 25% of people request a compact car, 37% request a full-sized, 10% request a convertible,16% request an SUV, and 12% request a luxury car
As per given
P(woman)= 37%
P(convertible) = 10%
So combined probability is:
P = 37%*10%
= 37%*0.1
= 3.7%
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complete question:
At a car rental office, 63% of the customers are men and 37% are women. If 25% of people request a compact car, 37% request a full-sized, 10% request a convertible,16% request an SUV, and 12% request a luxury car, what is the probability that the next customer will be a woman who requests a convertible?
A map of an amusement park is shown on the coordinate plane with the approximate location of several rides.
coordinate plane with points at negative 14 comma 1 labeled Woozy Wheel, negative 6 comma 2 labeled Bumper Boats, negative 2 comma negative 4 labeled Roller Rail, negative 2 comma negative 6 labeled Trolley Train, 2 comma negative 3 labeled Silly Slide, and 6 comma 11 labeled Parachute Plunge
Determine the distance between the Woozy Wheel and the Roller Rail.
119 units
11 units
169 units
13 units
The distance between the Woozy Wheel and the Roller Rail is 13 units.
To determine the distance between the Woozy Wheel and the Roller Rail, we can use the distance formula in the coordinate plane.
The coordinates of the Woozy Wheel are (-14, 1), and the coordinates of the Roller Rail are (-2, -4).
Using the distance formula, the distance (d) between two points (x₁, y₁) and (x₂, y₂) is given by:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
Substituting the coordinates of the Woozy Wheel and the Roller Rail into the formula:
d = √((-2 - (-14))² + (-4 - 1)²)
= √(12² + (-5)²)
= √(144 + 25)
= √169
= 13
Therefore, the distance between the Woozy Wheel and the Roller Rail is 13 units.
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Which of the following is an accurate definition for the power of a statistical test ?
A the probability of supporting true null hypothesis
B the probability of supporting a false null hypothesis
C the probability of rejecting a false null hypothesis
D the probability of rejecting a true null hypothesis
Which of the following is an accurate definition for the power of a statistical test is C. The power of a statistical test refers to the probability of rejecting a false null hypothesis. This means that the test is able to correctly identify when there is a significant difference between two groups or conditions.
statistical tests are used to determine whether the results of an experiment are likely due to chance or whether there is a real effect. The null hypothesis states that there is no significant difference, while the alternative hypothesis states that there is. The power of a statistical test refers to the ability of the test to correctly reject the null hypothesis when it is false, and thus support the alternative hypothesis.
, the power of a statistical test is the probability of correctly rejecting a false null hypothesis, which indicates that there is a significant difference between two groups or conditions.
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Which form of payment can Courtney lose and NOT get back?
Answer: The form of payment that Courtney can lose and not get back would be cash.
Step-by-step explanation:
The reason why cash couldn't be returned back because it doesn't have a piece of U.S money wouldn't have a specific certified owner that they can be returned to.
Other forms of payment like credit cards, debit cards, and checks have specific bank information with the card holder's name on it so if Courtney actually lost one of those, she would be most likely to receive it back without any complicated verification process.
Therefore, Courtney would not be able to receive her cash back if she accidentally loses it. Hope this helps you with your Imagine Math homework or assignment!
-From Certified 5th Grade Honors Student
HELP ME ASAP Solve the application problem.
A student's tuition was $1500. If a scholarship paid for 4/5
of the tuition, how much was the scholarship?
If student's tuition was $1500, if a scholarship paid for 4/5
of the tuition then $1200 is the scholarship
Given that a student's tuition was $1500
If a scholarship paid for 4/5 of the tuition
We need to find the how much was the scholarship
To find this we have to multiply 4/5 with $1500
4/5×1500
$1200
Hence, if student's tuition was $1500, if a scholarship paid for 4/5
of the tuition then $1200 is the scholarship
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4. Two numbers are shown on the number line?
A. ㅠ
9/3
Which value is NOT located between these two
numbers on the number line?
B. 9
2π
C. 픔
D.
이름 이
쯩
ㅠ is not located between these two numbers on the number line.
The values 3 and √9/3 are located at 3 and √3 on the number line, respectively.
The value π is not located between these two numbers on the number line.
π is approximately 3.14, which is between 3 and 4 on the number line, but it is not between 3 and√3.
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Hi can someone who is great at math please help me with this math question. I’m really struggling with it. Find the area of the middle square. And show the steps
The area of the middle square should be = 36.
How to calculate the area of the middle square?To calculate the area of the middle square, the formula for the area of a square should be used an sit is given below:
Area of a square = a²
where;
a = Length of sides
But,the length of sides of a square are equal therefore;
Area of square = 6×6 = 36
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suppose that diameters of a new species of apple have a bell-shaped distribution with a mean of 7.2cm and a standard deviation of 0.38cm . using the empirical rule, what percentage of the apples have diameters that are no more than 6.44cm ? please do not round your answer.
Using the empirical rule, we know that approximately 95% of the data falls within two standard deviations of the mean.
We can use the empirical rule, also known as the 68-95-99.7 rule. According to this rule, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
In this case, we want to know what percentage of apples have diameters that are no more than 6.44cm. To find out, we need to determine how many standard deviations this value is from the mean.
First, we calculate the z-score (number of standard deviations from the mean) using the formula z = (x - μ) / σ, where x is the diameter we're interested in, μ is the mean, and σ is the standard deviation.
z = (6.44 - 7.2) / 0.38 = -2
This means that 6.44cm is 2 standard deviations below the mean.
Using the empirical rule, we know that approximately 95% of the data falls within two standard deviations of the mean. Therefore, we can conclude that approximately 95% of the apples have diameters that are greater than 6.44cm, and the remaining 5% have diameters that are no more than 6.44cm.
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a magazine editor uses a data informed approach to determine which freelance writers should be offered a more permanent position. they take a pool of recommended freelance writers and determine that at least 80% of their work has been accepted for publication over a 2 year period. the editor considers 50 candidates for hire. of the 50 candidates, 20 of them have not been accepted for publication at an acceptable rate. with this data we test the following hypotheses at a 5% significance level: h0: the proportion of accepted publications of writers being recommended for hire is equal to .8 ha: the proportion of accepted publications of writers being recommended for hire is less than .8 the p-value is .01. what should the editor conclude?
The test is conducted at a 5% significance level, and the p-value is 0.01. Since the p-value (0.01) is less than the significance level (0.05), the editor should reject the null hypothesis (H0) and conclude that the proportion of accepted publications of writers being recommended for hire is less than 0.8.
Based on the data and the hypothesis testing, the magazine editor should conclude that the proportion of accepted publications of writers being recommended for hire is less than 0.8. This is because the p-value is 0.01, which is less than the significance level of 0.05. This means that there is strong evidence to reject the null hypothesis (h0) and accept the alternative hypothesis (ha). Therefore, the editor should not offer a more permanent position to the 20 candidates who have not been accepted for publication at an acceptable rate. Instead, they should focus on the remaining 30 candidates who have a higher proportion of accepted publications and are more likely to meet the standards of the magazine. By using a data-informed approach, the editor can make more objective and effective hiring decisions and ensure that the quality of the magazine remains high.
The magazine editor is using a data-informed approach to evaluate freelance writers for a more permanent position. They consider 50 candidates, and out of those, 20 have not been accepted for publication at an acceptable rate (80% acceptance over 2 years). The hypotheses being tested are:
H0: The proportion of accepted publications of writers being recommended for hire is equal to 0.8.
Ha: The proportion of accepted publications of writers being recommended for hire is less than 0.8.
This suggests that the editor may need to refine their selection process to improve the quality of the freelance candidates they consider for permanent positions.
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100 points and mark brainly please hurrryy
Ans: 52 cm²
Ok done. Thank to me >:333
prove that any graph of minimum degree at least three contains a cycle of even length.
Answer:
a cycle is a sequence of non-repeated vertices and the degree of a graph is the number of neighbors the vertex has.
1.1 1.2 1.3 1.4 1.5 1.6 prudence wants to paint the front of the house. She has two identical windows as well as a circular vent near the roof. Gable 1,2 m 0.6 m 1,8 m 0.5m 500 cm Vent Window 2,6 m Use Formulae, to answer the questions that follow. Area = L x B Area = 2 x r²(π = 3,142) Area = ²× b × h Convert 500 cm to m Calculate the area of one window. Calculate the area of the vent. Calculate the area of the rectangular part of the wall. Calculate the area of the gable. Prudence states that the area of the Wall that must pe painted is 14,42 m². Is this statement valid? Set your work out clearly. (PLEASE NOTE THAT THE VENT AND THE WINDOWS WILL NOT BE PAINTED)
The Area of the gable is 0.9 m²
Prudence's statement is not valid.
1. Convert 500 cm to meters:
Since 1 meter is equal to 100 centimeters,
So, 500 cm ÷ 100 = 5 meters
2. The formula for the area of a rectangle is Area = Length x Width.
Given the dimensions:
Length = 1.2 m
Width = 1.4 m
Area of one window = 1.2 m x 1.4 m = 1.68 m²
3. Calculate the area of the vent:
The formula for the area of a circle is Area = π x r².
Radius = (2.6 m) / 2 = 1.3 m
Area of the vent = 3.142 x (1.3 m)² ≈ 5.309 m²
4. Length = 1.1 m
Width = 1.6 m
Area of the rectangular part of the wall = 1.1 m x 1.6 m
= 1.76 m²
5. Calculate the area of the gable:
Given the dimensions:
Base = 0.6 m
Height = 1.8 m
Area of the gable = 0.5 m x 1.8 m = 0.9 m²
Prudence states that the area of the wall that must be painted is 14.42 m².
So, Area of the rectangular part of the wall + Area of the gable
= 1.76 m² + 0.9 m² = 2.66 m²
Therefore, Prudence's statement is not valid.
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A fish is hovering at –320 feet in relation to sea level. Then it descends 2 feet per second for 8 seconds. Brenda says that the new position of the fish in relation to sea level is represented by the equation below.
2 times 8 + (negative 320) = 336
Which explains whether Brenda is correct?
Brenda is correct because her answer represents 336 feet below sea level.
Brenda is correct because Negative 16 + (negative 320) = 336.
Brenda is not correct because the new position is 2 times 8 + (negative 320) = Negative 304.
Brenda is not correct because the equation should be Negative 2 times 8 + (negative 320) = negative 336.
The question presents a scenario where a fish is hovering at a certain depth below sea level, and then descends at a certain rate for a certain duration. So, Brenda is correct because her answer represents the new position of the fish in relation to sea level after the descent.
Brenda has provided an equation that represents the new position of the fish in relation to sea level after the descent. The equation is 2 times 8 + (negative 320) = 336. To determine if Brenda is correct, we need to understand the meaning of each term in the equation. The first term, 2 times 8, represents the distance the fish has descended, which is 16 feet (2 feet per second for 8 seconds).
The second term, negative 320, represents the initial depth of the fish below sea level. When we add these two terms together, we get the new depth of the fish below sea level, which is 336 feet.
Therefore, Brenda is correct because her answer represents the new position of the fish in relation to sea level after the descent. It is important to understand the meaning of each term in an equation to correctly interpret its result.
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The figure shows quadrilateral PQRS. What additional information do you need in order to conclude that △SPR≅△QRP by the ASA Triangle Congruence Theorem? Explain.
The additional information for the figure is
angle SRP ≅ angle QPRHow to find the additional informationFirst lets look at ASA congruence theorem
The ASA Triangle Congruence Theorem also known as the Angle-Side-Angle Congruence Theorem states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
In the figure the included side is PR and one to the angle required that is given is angle SPR ≅ angle PRQ
The additional information will be angle SRP ≅ angle QPR
hence we have that
Angle = angle SPR ≅ angle PRQ
Side = PR ≅ RP
Angle = angle SRP ≅ angle QPR
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Un cubo tiene un área total de 25312
pulgadas cuadradas. ¿Cuál es el área de una cara del cubo en pulgadas cuadradas?
The area of the face of the cube given is 4225 in².
Given that a cube has a total surface area of 25312 in², we need to find the area of one face of the cube,
So,
TSA of a cube = 6 × side²
So,
6 × side² = 25312
side² = 4225
side ≈ 65
Hence the cube has a side length of 65 inches,
Now we know that the face of a cube is in shape of square so the area of the face = side²
= 4225 in²
Hence the area of the face of the cube given is 4225 in².
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The translated question is
A cube has a total area of 25312
square inches. What is the area of a cube face in square inches?
the researchers noticed that the total number of registered users appears to be increasing at about a constant rate. if this pattern continues, which of the following best approximates the total number of registered users, in millions, in year 12 (two years after the last entry in the table) ? responses 30.6 30.6 31.2 31.2 31.8 31.8 32.4
The best approximate for the total number of registered users in year 12 would be B. 31. 2 million.
How to find the approximate ?First, we can find the differences over the years in the total number of registered users.
Year 4 = 26. 9 - 26. 5 = 0. 4
Year 6 = 28.0 - 27. 4 = 0. 6
Year 8 = 29. 1 - 28. 6 = 0. 5
Year 10 = 30. 2 - 29. 6 = 0. 6
This shows that the largest increase has been by 0. 6 in a year. Assuming that there are 0. 6 increases over two years till Year 12, the total number becomes :
= 30. 2 + 0. 6 + 0. 6
= 31. 4
The closest option that is lower is 31. 2 million users so this is the best approximate.
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A curve is described by the parametric equations x = t^2 + 2t and y = t^3 + t^2. An equation of the line tangent to the curve at the point determined by t = 1 is...?
To find the equation of the tangent line, we need to find the derivative of both x and y with respect to t and evaluate them at t = 1 to get the slope of the tangent line. The equation of the line tangent to the curve at the point determined by t = 1 is y = (5/4)(x - 3) + 2.
dx/dt = 2t + 2
dy/dt = 3t^2 + 2t
At t = 1, dx/dt = 4 and dy/dt = 5
So the slope of the tangent line is m = dy/dx = (dy/dt)/(dx/dt) = 5/4
Now we need to find the point on the curve where t = 1.
x = t^2 + 2t = 1^2 + 2(1) = 3
y = t^3 + t^2 = 1^3 + 1^2 = 2
Therefore, the point on the curve where t = 1 is (3, 2)
Using the point-slope form of a line, we can write the equation of the tangent line as:
y - 2 = (5/4)(x - 3)
Simplifying:
y = (5/4)x - (7/2)
So the equation of the line tangent to the curve at the point determined by t = 1 is y = (5/4)x - (7/2).
A curve is described by the parametric equations x = t^2 + 2t and y = t^3 + t^2. An equation of the line tangent to the curve at the point determined by t = 1 is given by the formula y = m(x - x1) + y1, where m is the slope, and (x1, y1) is the point of tangency.
First, find the point of tangency (x1, y1) by plugging t = 1 into the parametric equations:
x1 = (1)^2 + 2(1) = 3
y1 = (1)^3 + (1)^2 = 2
Next, find the derivatives of x and y with respect to t:
dx/dt = 2t + 2
dy/dt = 3t^2 + 2t
Now, find the slope m by dividing dy/dt by dx/dt at t = 1:
m = (dy/dt) / (dx/dt) = (3(1)^2 + 2(1)) / (2(1) + 2) = (5/4)
Finally, plug the slope m and point (x1, y1) into the equation of the tangent line:
y = (5/4)(x - 3) + 2
So, the equation of the line tangent to the curve at the point determined by t = 1 is y = (5/4)(x - 3) + 2.
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