For the function f(x, y) = 1 - xy + y²= -y = -1, fy(-2,1) = 2y - x = 3.
When y is stationary, the rate of change of f with respect to x is determined by the partial derivative fx. Meanwhile, fy measures the rate of change of f in relation to y while holding x constant.
At the point (-2,1), the fx partial derivative symbolizes the incline of the level curve tangent line that follows the x-direction in relation to f. Its counterpart fy denotes the incline of the level curve tangent line that follows the y-direction regarding f at (-2,1).
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Complete answer - Let f(x, y) = 1 - xy + y² Compute fx(-2, 1) and fy(-2,1), and interpret these partial derivatives geometrically."
How did new leaders gain power in both Germany and Japan after World War I?John threw the Javelin 106 feet in his last track meet. The average throw was 130 ft. The standard deviation was 8 feet. How many standard deviations below the mean did John throw?
John threw the javelin 3 standard deviations below the mean
What is an equation?An equation is an expression that shows how numbers and variables using mathematical operators.
The z score shows by how many standard deviations the raw score is above or below the mean. It is given by:
z = (raw score - mean) / standard deviation
Given that John threw 106 feet. The average throw was 130 ft. The standard deviation was 8 feet. Hence:
z = (106 - 130) / 8
z = -3
John threw 3 standard deviations below the mean
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find the volume and the total surface area
The volume of a trapezoidal prism is 2362.5.
The total surface area is 852.
We have,
The volume of a trapezoidal prism.
V = ((a + b) / 2) × h × l
where:
a and b are the lengths of the two parallel sides (the bases) of the trapezoid
h is the height of the trapezoid (the perpendicular distance between the two bases)
l is the length of the prism (the distance between the two trapezoidal faces)
Now,
a = 9
b = 12
l = 15
Height h can be calculated using the Pythagorean theorem.
15² = (12 - 9)² + h²
h² = 225 + 9
h² = 234
h = √234
h = 15
Now,
The volume of a trapezoidal prism.
V = ((a + b) / 2) × h × l
V = ((9 + 12) / 2) x 15 x 15
V = 2362.5
And,
The surface area (A) of a trapezoidal prism can be calculated using the formula:
A = ph + 2B
where p is the perimeter of the trapezoidal base, h is the height of the prism, and B is the area of one of the bases.
So,
p = 12 + 8 + 12 + 8 = 44
h = 15
B = 12 x 8 = 96
Now,
Total surface area.
= 44 x 15 + 2 x 96
= 660 + 192
= 852
Thus,
The volume of a trapezoidal prism is 2362.5.
The total surface area is 852.
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Put the numbers in order from least to greatest.
4.27, 2.704, 4.2, 2.74, 4.72
Answer: In order least to greatest, our answer would be-
2.704 , 2.74 , 4.2 , 4.27 , 4.72
.70 is less than .74. In the second set of numbers .2 is less than .27, while they are all less than .72, which gives us the number arrangement above.
I hope this helped & Good Luck!!!
Answer: The answer is 2.704, 2.74, 4.2, 4.27, 4.72
Step-by-step explanation:
Beckett asked his classmates, "How many days do you floss your teeth
typical week?" The table shows Beckett's data.
Days of Flossing per Week
7
7
7
4
3
1
0
6
6
7
2.
6
5
3
N
4
How many observations did he record?
A. 20
B. 12
O c. 4
O D. 16
Answer: B
Step-by-step explanation: I did the quiz :p
Hope this helps
The correct answer is B. 12. There are 12 numbers in the table, which represents the number of observations Beckett recorded.
The table shows the number of days each of Beckett's classmates floss their teeth in a typical week. The number of observations recorded is simply the number of classmates, or the number of entries in the table. In this case, there are 12 entries, so the answer is 12.
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12. [0/1 Points] DETAILS PREVIOUS ANSWERS LARCALC9 11.7. Convert the point from rectangular coordinates to spherical coordinates. (7,7, 2/7) (0, 0, 4) = ( 3V 14, 7,61.87 ). x Submit Answer
The spherical coordinates for the given rectangular coordinates (7, 7, 2/7) are (ρ, θ, φ) = (10, 45°, 88.57°) or (10, π/4, 1.545) in radians.
We'll need to find ρ (rho), θ (theta), and φ (phi) using the given rectangular coordinates (x, y, z). Here's the step-by-step process:
1. Calculate ρ (rho): ρ is the distance from the origin to the point in 3D space. You can find it using the formula: ρ = √(x² + y² + z²)
In this case, x = 7, y = 7, and z = 2/7.
Plugging these values into the formula: ρ = √(7² + 7² + (2/7)²) ρ = √(49 + 49 + 4/49) ρ = √(98 + 4/49) ρ = √(4900/49) ρ = 10
2. Calculate θ (theta): θ is the angle in the xy-plane, measured from the positive x-axis. You can find it using the formula: θ = arctan(y/x)
In this case, x = 7 and y = 7.
Plugging these values into the formula: θ = arctan(7/7) θ = arctan(1) θ = 45° (in degrees) or π/4 (in radians)
3. Calculate φ (phi): φ is the angle between the positive z-axis and the line connecting the origin to the point. You can find it using the formula: φ = arccos(z/ρ)
In this case, z = 2/7 and ρ = 10.
Plugging these values into the formula: φ = arccos((2/7)/10) φ = arccos(1/35) φ ≈ 88.57° (in degrees) or ≈ 1.545 (in radians)
So, the spherical coordinates for the given rectangular coordinates (7, 7, 2/7) are (ρ, θ, φ) = (10, 45°, 88.57°) or (10, π/4, 1.545) in radians.
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A boat is heading towards a lighthouse, whose beacon-light is 119 feet above the water. From point A, the boat’s crew measures the angle of elevation to the beacon, 5 , before they draw closer. They measure the angle of elevation a second time from point
B at some later time to be 18∘ Find the distance from point A to point B. Round your answer to the nearest foot if necessary.
If boat is heading towards a lighthouse, whose beacon-light is 119 feet above the water, the distance from point A to point B is approximately 973 feet.
To find the distance from point A to point B, we can use trigonometry and the fact that the angles of elevation from both points are known.
Let x be the distance from point A to the lighthouse, and y be the distance from point B to the lighthouse. We can set up two equations using tangent function:
tan(5) = 119/x
tan(18) = 119/y
We can solve for x and y by isolating them in each equation:
x = 119/tan(5) ≈ 1343.44 feet
y = 119/tan(18) ≈ 370.79 feet
Therefore, the distance from point A to point B is approximately 1343.44 - 370.79 = 972.65 feet.
We rounded the final answer to the nearest foot, which is 973 feet.
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Jacob is building a square pyramid for a class project. He needs to cover the entire pyramid in aluminum foil. The base of the pyramid has a perimeter of 76 centimeters. The slant height of each triangular side is 28 centimeters. What is the surface area, in square centimeters, of Jacob’s pyramid?
The surface area of the pyramid is 390.8 cm².
What is the surface area of the triangular pyramid?The surface area of the triangular pyramid is calculated as follows;
S.A = base area + ¹/₂ (perimeter + slant height)
The height of the pyramid is calculated by applying Pythagoras theorem;
h = √ (28² - 14²)
h = 24.2 cm
Area of the base = ¹/₂ x 28 cm x 24.2 cm = 338.8 cm²
The surface area of the pyramid is calculated as follows;
S.A = 338.8 cm² + ¹/₂ (76 cm + 28 cm)
S.A = 390.8 cm²
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Answer:
1,425
Step-by-step explanation:
I got this one correct
Which detail adds tension to the rising action of the story?
Mowgli grows stronger and learns life lessons without knowing it. Mother Wolf tells Mowgli that some day he will have to kill Shere Khan. Mowgli forgets his mother’s advice because he is a young boy. Mowgli would call himself a wolf if he had the ability to speak like a human
The detail that adds tension to the rising action of the story is when Mother Wolf tells Mowgli that some day he will have to kill Shere Khan.
This statement introduces a sense of conflict and foreshadows a significant challenge that Mowgli must face in the future. The idea of Mowgli, a young boy raised by wolves, confronting and defeating the powerful and dangerous Shere Khan adds suspense to the story, as readers anticipate the eventual showdown between these two characters.
Other details, such as Mowgli growing stronger and learning life lessons, or Mowgli forgetting his mother's advice, are relevant to his character development, but do not contribute as directly to the story's tension. Similarly, Mowgli considering himself a wolf and lacking the ability to speak like a human reflects his unique upbringing, but does not add tension in the same way as the impending confrontation with Shere Khan.
In conclusion, Mother Wolf's warning about Mowgli's future encounter with Shere Khan adds tension to the rising action of the story, as it sets up an exciting and challenging conflict for the protagonist to face, capturing the reader's interest and anticipation.
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1. All square, upper triangular matrices are diagonalizable. (T/F)
2. If a matrix is diagonalizable, then it is invertible. (T/F)
1. All square, upper triangular matrices are diagonalizable. (TRUE)
2. If a matrix is diagonalizable, then it is invertible. (FALSE)
Understanding matrix1. True: All square, upper triangular matrices are diagonalizable.
A square matrix is diagonalizable if it can be transformed into a diagonal matrix by a similarity transformation, which means there exists an invertible matrix P such that P^-1 * A * P is a diagonal matrix. Upper triangular matrices have all their elements below the main diagonal equal to zero.
Since the eigenvalues of an upper triangular matrix are equal to its diagonal elements, we can form a diagonal matrix with these eigenvalues. Since there exists such a diagonal matrix, all square, upper triangular matrices are diagonalizable.
2. False: If a matrix is diagonalizable, it is not necessarily invertible
Diagonalizable matrices can be transformed into a diagonal matrix with the eigenvalues along the main diagonal.
However, invertibility requires that the matrix have a nonzero determinant, which means that all of its eigenvalues must be nonzero.
If a diagonalizable matrix has a zero eigenvalue, its determinant will be zero, and it will not be invertible. Therefore, diagonalizability does not guarantee invertibility.
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Which triangle will always have the same area, no matter how it is drawn? A А a right triangle that has two 45° angles an obtuse triangle that has two 30° angles © a right triangle that has two 5-inch-long sides an obtuse triangle that has two 5-inch-long sides
The triangle that will always have the same area, no matter how it is drawn, is a right triangle that has two 45° angles. The correct answer is option A
This is because any right triangle with two 45° angles is a special type of triangle called an isosceles right triangle. In an isosceles right triangle, the two legs are congruent, which means they have the same length. Therefore, no matter how the triangle is drawn, its area will always be the same.
To see why this is true, let's use the formula for the area of a right triangle:
Area = (base x height) / 2
In an isosceles right triangle, the base and height are congruent, so we can write:
Area = (leg x leg) / 2
Simplifying this expression, we get:
Area = (leg^2) / 2
Since the legs of an isosceles right triangle are congruent, we can substitute leg for both legs in the formula:
Area = (leg^2) / 2 = (leg x leg) / 2
No matter how the triangle is drawn, the legs will have the same length, so the area of the triangle will always be the same.
Therefore, the correct answer is option A, a right triangle that has two 45° angles.
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When viewed from a distance of 32 feet from its base the top of the flagpole can be seen from the ground at an angle of elevation of 39° what is the height of the flagpole
The height of the flagpole is approximately 23.7 feet.
We can use the tangent function to solve this problem. Let's call the height of the flagpole "h". From the ground, we have a right triangle with the flagpole height as the opposite side, the distance to the flagpole as the adjacent side, and the angle of elevation as the angle opposite the flagpole height.
Using the tangent function, we can write:
tan(39°) = h/32
Solving for h, we get:
h = 32 * tan(39°)
h ≈ 23.7 feet
Therefore, the height of the flagpole is approximately 23.7 feet when viewed from a distance of 32 feet at an angle of elevation of 39°.
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Find the probability that a point chosen randomly inside the rectangle is in each given shape. Round to the nearest tenth.
(a) Square
(b) Not the triangle
The probabilities are given as follows:
a) Square: 1/6.
b) Not the triangle: 43/48.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The area of the rectangle is given as follows:
A = 12 x 8 = 96.
(area of rectangle, multiply the dimensions).
The areas of each figure are given as follows:
Square: 4² = 16. (area of square is the square of the side length).Triangle: 0.5 x 4 x 5 = 10. (area of right triangle is half the multiplication of the side lengths).Hence the probability of the square is given as follows:
p = 16/96 = 1/6.
(area of square divided by total area).
The probability that the region is not the triangle is given as follows:
p = (96 - 10)/96
p = 86/96
p = 43/48.
(triangle and not triangle are complementary events).
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Write an expression for the nth term of the sequence. (Your formula should work for n=1,2,...) 4 5 6 7 5 6 7 8 Need Help? Watch
The nth term of the sequence 4 5 6 7 5 6 7 8 is given by a_n = 3 + (n-1)/2 for odd n and a_n = 4 + (n-2)/2 for even n.
How to find the nth term of a given sequence?To find the nth term of the given sequence, we need to observe the pattern in the sequence. We can see that the sequence consists of two parts:
the first part is a consecutive sequence of integers starting from 4, and the second part is a consecutive sequence of integers starting from 5, where the second part starts right after the first part ends.
So, we can express the nth term of the sequence as follows:
If n is odd, then the nth term is given by:
a_n = 3 + (n-1)/2
If n is even, then the nth term is given by:
a_n = 4 + (n-2)/2
Using this formula, we can find any term of the given sequence by plugging in the corresponding value of n. For example:
When n=1, the first term is 4: a_1 = 4.
When n=6, the sixth term is 6: a_6 = 6.
When n=7, the seventh term is 7: a_7 = 7.
When n=8, the eighth term is 8: a_8 = 8.
Note that this formula works only for n = 1, 2, 3, 4, 5, 6, 7, 8, ... , since the sequence has only 8 terms.
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Can someone please help me ASAP? It’s due tomorrow. I will give brainliest if it’s correct. Show work.
the probability of choosing H or P in either selection is 0.84
How to find the probability?Two random letters are selected from the word Happy, and we want to find the probability of choosing H or P in either selection.
There are 5 letters, 1 is an H, 2 are P's.
Then the probability of selecting one of these 3 in the first selection is:
p = 3/5 = 0.6
And if we don't chose any of these in the first selection we had the probability:
q = 2/5 = 0.4 (choosing one of the a's)
the probability of choosing one of the p's or the H in the second is again:
q' = 3/5 = 0.6
The joint probability is:
Q = q*q' = 0.4*0.6 = 0.24
Then the total probability is:
p + Q = 0.6 + 0.24 = 0.84
The correct option is the second one.
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John rides his bike 68 km south and then 6 km went. How far is he from his starting point?
John is approximately 68.26 km away from his starting point after riding 68 km south and then 6 km west.
To find out how far John is from his starting point after riding 68 km south and then 6 km west, we will use the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, we will consider the 68 km south as one side, and the 6 km west as the other side, with the distance from the starting point being the hypotenuse.
Step 1: Square the lengths of the two given sides.
68^2 = 4624
6^2 = 36
Step 2: Add the squared values together.
4624 + 36 = 4660
Step 3: Find the square root of the sum to get the length of the hypotenuse (distance from the starting point).
√4660 ≈ 68.26 km
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Flying Home for the Holidays Does the airline you choose affect when you'll arrive at
your destination? The dataset DecemberFlights contains the difference between actual and
scheduled arrival time from 1000 randomly sampled December flights for two of the major North
American airlines, Delta Air Lines and United Air Lines. A negative difference indicates a flight
arrived early. We are interested in testing whether the average difference between actual and
scheduled arrival time is different between the two airlines.
a. Define any relevant parameter(s) and state the null and alternative hypotheses.
b. Find the sample mean of each group, and calculate the difference in sample means.
c. Use StatKey or other technology to create a randomization distribution and find the p-value.
d. At a significance level of a = 0. 01, what is the conclusion of the test? Interpret the conclusion in
context.
a
Relevant parameter is the difference between actual and scheduled arrival time. Also the difference in sample means is -1.70 minutes. We get a p-value of 0.017 and the conclusion is that there is evidence to suggest that the average difference between actual and scheduled arrival time is different for Delta Air Lines and United Air Lines.
a. Relevant parameter: the difference between actual and scheduled arrival time.
Null hypothesis: The average difference between actual and scheduled arrival time is the same for Delta Air Lines and United Air Lines.
Alternative hypothesis: The average difference between actual and scheduled arrival time is different for Delta Air Lines and United Air Lines.
b. Sample mean for Delta Air Lines: -2.31 minutes
Sample mean for United Air Lines: -4.01 minutes
Difference in sample means: -1.70 minutes
c. To create a randomization distribution, we can pool the data from both airlines and randomly assign them to two groups with the same sample sizes as Delta Air Lines and United Air Lines. We then calculate the difference in sample means for each random assignment. Repeating this process many times gives us a randomization distribution. Using StatKey with 10,000 iterations, we get a p-value of 0.017, which is less than 0.01.
d. At a significance level of 0.01, we reject the null hypothesis and conclude that there is evidence to suggest that the average difference between actual and scheduled arrival time is different for Delta Air Lines and United Air Lines. Specifically, the average difference for United Air Lines is greater than that of Delta Air Lines. This could have implications for travelers who prioritize arriving on time, as they may wish to consider
Delta over United.
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I’m having trouble with this
CAN SOMEONE SHOW ME STEP BY STEP ON HOW TO DO THIS
A city just opened a new playground for children in the community. An image of the land that the playground is on is shown.
A polygon with a horizontal top side labeled 45 yards. The left vertical side is 20 yards. There is a dashed vertical line segment drawn from the right vertex of the top to the bottom right vertex. There is a dashed horizontal line from the bottom left vertex to the dashed vertical, leaving the length from that intersection to the bottom right vertex as 10 yards. There is another dashed horizontal line that comes from the vertex on the right that intersects the vertical dashed line, and it is labeled 12 yards.
What is the area of the playground?
900 square yards
855 square yards
1,710 square yards
The area of the playground include the following: 900 square yards.
How to calculate the area of a regular polygon?In Mathematics and Geometry, the area of a regular polygon can be calculated by using this formula:
Area = (n × s × a)/2
Where:
n is the number of sides.s is the side length.a is the apothem.In Mathematics and Geometry, the area of a parallelogram can be calculated by using the following formula:
Area of a parallelogram, A = base area × height
Area of playground, A = 45 × 20
Area of a playground, A = 900 square yards.
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Shirts are packed at random in two sizes, regular and extra-large. four shirts are selected from a box of 24 and checked for size. if there are 15 regular shirts in the box, find the probability that all 4 will be regular size.
The probability that all four shirts selected from the box of 24 will be regular size is 0.1367 or 13.67%.
Probability refers to the likelihood or chance of an event occurring. In this scenario, we are interested in finding the probability that all four shirts selected from the box of 24 will be regular size.
To determine this probability, we first need to find the total number of ways in which we can select four shirts from the box. This is known as the sample space and can be calculated using the combination formula, which is nCr = n!/(r!(n-r)!). In this case, we have 24 shirts and are selecting four, so the sample space is 24C4 = (24!)/(4!(24-4)!) = 10,626.
Next, we need to find the number of ways in which we can select four regular shirts from the 15 available. This can be calculated using the same combination formula, which is 15C4 = (15!)/(4!(15-4)!) = 1,455.
Finally, we can calculate the probability of selecting all four regular shirts by dividing the number of favorable outcomes (i.e., selecting four regular shirts) by the total number of possible outcomes (i.e., the sample space). So, the probability of selecting all four regular shirts is 1,455/10,626 = 0.1367 or 13.67%.
Therefore, the probability that all four shirts selected from the box of 24 will be regular size is 0.1367 or 13.67%.
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PLEASE HELP
A survey was done that asked people to indicate whether they prefer saltwater fishing or freshwater fish in the results of the survey are shown in the two way table
complete a relative frequency table from this data.
enter your answer is rounded to the nearest 10th of a percent in the boxes
According to the above, the fishing population is divided into 53% prefer fresh water and 47% prefer salt water.
To find the percentage of people that make up each group, we must find the total number of people who were surveyed:
228 + 245 + 242 + 285 = 1,000
Once we find the total number of people who took the survey, we can find the percentage of each value by making rules of three as shown below:
Age 30 and younger and Saltwater fishing:
1,000 = 100%
228 = ?%
Hence, We get;
228 x 100 / 1,000 = 22.8%
Age 30 and younger and Freshwater fishing:
1,000 = 100%
245 = ?%
245 x 100 / 1,000 = 24.5%
Over 30 years old and Saltwater fishing:
1,000 = 100%
242 = ?%
242 * 100 / 1,000 = 24.2%
Over 30 years old and Freshwater fishing:
1,000 = 100%
285 = ?%
285 * 100 / 1,000 = 28.5%
To find the other percentages we must find the total number of fishermen by age ranges and by fishing preference:
Age ranges
228 + 245 = 473
242 + 285 = 527
1,000 = 100%
473 = ?%
473 * 100 / 1,000 = 47.3%
1,000 = 100%
527 = ?%
527 * 100 / 1,000 = 52.3%
Fishing mode preferences
228 + 242 = 470
245 + 285 = 530
1,000 = 100%
530 = ?%
530 * 100 / 1,000 = 53%
1,000 = 100%
547 = ?%
470 * 100 / 1,000 = 47%
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Your doing practice 6
The union set of A and B is A∪B={1, 2, 3, 4, 5, 6, 7, 9}.
Given that, A={x|x is an odd number greater than 0 and less than 10} and B={2, 3, 4, 5, 6}.
Here, set A={1, 3, 5, 7, 9}
Now, A∪B = {1, 3, 5, 7, 9}∪{2, 3, 4, 5, 6}
= {1, 2, 3, 4, 5, 6, 7, 9}
Therefore, the union set of A and B is A∪B={1, 2, 3, 4, 5, 6, 7, 9}.
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5.
Sarah deposited $800 in an account that earns
2% interest compounded annually. Claire deposited
$800 in an account that earns 2% simple interest.
How much will each girl have in their account at the
end of 8 years if they do not make any deposits or
withdrawals?
Answer:
Sarah will have $937.28 and Claire will have $928.
Step-by-step explanation:
All my work is provided in the screenshots that are attached to my answer! Drop questions in the comments and I'll try to respond if I remember/see them lol.
Have a great day!
The amount of a popular drink in bottles has the normal distribution with the mean = 101. 5 milliliters (mL) and the standard deviation = 1. 6 milliliters (mL). If n = 36 bottles are randomly selected, find the probability that the average content in these selected bottles is smaller than 102. 1 milliliters (mL)
The probability of the normal distribution with given mean and standard deviation representing average content in the selected bottles is smaller than 102.1 mL is equal to 0.9878.
Distribution of the sample means of a normal distribution ,
Mean μ = 101.5 mL
Standard deviationσ = 1.6 mL
sample size n = 36
For normal distribution,
Standard deviation of the sample means is,
σ/√n
= 1.6/√36
= 0.2667 mL
Probability that the average content in the selected bottles is smaller than 102.1 mL,
Standardize the sample mean using the formula,
z = (X- μ) / (σ/√n)
where X is the sample mean.
Substituting the values, we get,
⇒z = (102.1 - 101.5) / (0.2667)
⇒ z = 2.25
Using a standard normal distribution table ,
Probability of a z-score being less than 2.25 is approximately 0.9878.
Therefore, the probability that the average content in the selected bottles is smaller than 102.1 mL is approximately 0.9878.
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Qn in attachment. ..
Answer:
pls mrk me brainliest (・(ｪ)・）
Suppose that a report by a leading medical organization claims that the healthy human heart beats an average of 72 times per minute. Advances in science have led some researchers to question if the healthy human heart beats an entirely different amount of time, on average, per minute. They obtain pulse rate data from a sample of 85 healthy adults and find the average number of heart beats per minute to be 76, with a standard deviation of 13. Before conducting a statistical test of significance, this outcome needs to be converted to a standard score, or a test statistic. What would that test statistic be
The test statistic (or standard score) would be 1.72.
To convert the outcome of the pulse rate data to a standard score, we would need to calculate the z-score. The formula for the z-score is: (sample mean - population mean) / (standard deviation / square root of sample size).
In this case, the sample mean is 76, the population mean (according to the report) is 72, the standard deviation is 13, and the sample size is 85. Plugging these values into the formula, we get:
(76 - 72) / (13 / sqrt(85)) = 1.72.
Therefore, the test statistic (or standard score) is 1.72. This indicates that the sample mean of 76 is 1.72 standard deviations above the population mean of 72. This information can be used to conduct a statistical test of significance and determine whether the difference between the sample mean and population mean is statistically significant.
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a pet store has 115 fish and each tank can hold six fish how many tanks do you nedd
Answer:
20 tanks
Step-by-step explanation:
if each tank holds 6 fish and there are 115 fish, you need to divide the amount of fish total by amount that go in 1 tank:
115/6 = 19.1666666667
Now we round up bc we cant leave any fish out right?
So your answer is 20 tanks will be needed to hold 115 fish if it’s 6 fish per tank.
Check this by multiplying the tanks and fish in every tank:
20 x 6 = 120
Meaning that 115 fish go into 20 tanks, one of the tanks just having 1 fish :D
Answer: 20 is the correct option.
Step-by-step explanation:Given that a pet store has 115 fish that need to be placed into fish tanks and each tank hold 6 fish.
We are to find the number of tanks that the store need.
We will be using the UNITARY method to solve the given problem.
Number of tanks needed to store 6 fishes = 1.
So, number of tanks needed to store 1 fish will be [tex]\frac{1}{6}[/tex]
Therefore, number of tanks needed to store 115 fishes is given by
[tex]\frac{1}{6}[/tex] × 155 =[tex]\frac{115}{6}[/tex]= 19 [tex]\frac{1}{6}[/tex] = 19.16.
Since we cannot have 0.16 tank, so we need one tank more than 19 to store all fishes.
Thus, the store needs 20 tanks for 115 fishes.
Hope this helps :)
17. Determine whether the two figures are similar. If so, give the similarity ratio of *
the smaller figure to the larger figure. The figures are not drawn to scale.
6 ft
8 ft
6 ft
Yes; 3:5
Yes; 2:3
OYes; 2:5
10 ft
12 ft
10 ft
No they are not similar
The answer is "No they are not similar". The correct option is D.
To determine if the two cuboids are similar, we need to check if their corresponding sides are proportional.
If we compare the corresponding sides of the first cuboid and the second cuboid, we get:
6/10 = 0.6
8/12 = 0.666...
6/10 = 0.6
Since these ratios are not equal, the corresponding sides are not proportional, and therefore the two cuboids are not similar.
Therefore, the answer is "No they are not similar".
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Let D(x) be the demand (in units) for a new product when the price is x dollars (a) Write sentences interpreting the following D (9,25) = 200 When the price is__________- the demand is ______-units
When the price of the new product is $9.25, the demand for the product is 200 units.
What is demand?The quantity of a specific commodity or service that consumers are willing and able to buy at a specific price and time is referred to as demand. It stands for consumers' willingness and capacity to pay for a good or service.
According to question:The demand for a new product at a price of x dollars is denoted by the notation D(x). So, the notation D(9.25) represents the demand for the new product when the price is $9.25. According to the given information, D(9.25) = 200.
Therefore, we can interpret this as: when the price of the new product is $9.25, the demand for the product is 200 units.
D(9.25) = 200
where D(x) represents the demand for the new product when the price is x dollars. We substitute x = 9.25 into the equation to find the demand when the price is $9.25, which is 200 units.
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Find the radius of the circle with equation x² + y² = 12²
Answer:
The equation of a circle with center (a,b) and radius r is given by:
(x - a)² + (y - b)² = r²
Comparing this to the equation x² + y² = 12², we can see that the center of the circle is (0,0) and the radius is 12. Therefore, the radius of the circle is 12 units.
Whats 4x + 5 = 6 (x + 3) - 20 - 2x
To solve this equation, we first simplify both sides of the equation by using the distributive property to expand the right-hand side:
4x + 5 = 6(x + 3) - 20 - 2x
4x + 5 = 6x + 18 - 20 - 2x
Next, we can combine like terms on the right-hand side:
4x + 5 = 4x - 2
Now, we can subtract 4x from both sides to isolate the variable on one side of the equation:
4x - 4x + 5 = 4x - 4x - 2
5 = -2
This is a contradiction since 5 cannot be equal to -2. Therefore, there is no solution to this equation.
In other words, the equation is inconsistent and there is no value of x that can make it true.