To get from 1.098 to 1,098,000, Brian would need to multiply by 1,000,000 that is 10 raised to the power 6.
What is scientific notation?Powers of 10 are used in scientific notation to indicate extremely big or extremely tiny quantities. A number is written as the result of a coefficient (a number between 1 and 10) and a power of 10 when it is expressed in scientific notation. The number represented by the power of 10 is the distance the decimal point must be moved to convert a number to standard form (i.e., a number without exponents).
To get from 1.098 to 1,098,000, Brian would need to multiply by 1,000,000 that is 10 raised to 6.
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Select the expression that represents this real-world situation.
Josie has 12 yards of fabric. She is making identical dresses for d dolls. What is the length of fabric used for each doll?
12 + d
12 − d
12 x d
12 ÷ d
It takes 4 people 8 days to paint a wall. How long will it take for 8 people to finish the same wall?
Answer: 4 days
Step-by-step explanation:
If it takes 4 people 8 days to paint a wall. We can only assume that doubling the number of people would be 2 times as fast. So divide 8/2=4.
Is △ABC ≅ △DEF? Explain. Options - AAS, NO, HL, ASA, Are, Are not, SAS, Yes
________; the triangles __________ congruent by ___________
No; the triangles are not congruent by any of the congruence criteria.
To determine if two triangles are congruent, we must use one of the five congruence criteria: Side-Angle-Side (SAS), Angle-Angle-Side (AAS), Angle-Side-Angle (ASA), Side-Side-Side (SSS), and Hypotenuse-Leg (HL). To be congruent, the triangles must have three pairs of congruent sides and three pairs of congruent angles.
In the case of △ABC and △DEF, we can compare their sides and angles to determine if they are congruent. We can see that the sides of the two triangles are not equal in length, nor do the angles have the same measure. Therefore, △ABC is not congruent to △DEF.
In order to prove that the two triangles are not congruent, we can use the formula for determining the measure of the angles in a triangle, known as the Law of Cosines. This formula states that c² = a² + b² - 2ab cos γ, where c is the length of the longest side of the triangle, a and b are the lengths of the other sides of the triangle, and γ is the measure of the angle opposite the side c.
Using this formula, we can calculate the measure of the angles in both triangles. For △ABC we have angle A = arccos ( (b² + c² - a²) / 2bc ) and for △DEF we have angle D = arccos ( (e² + f² - d²) / 2ef ). The measure of angle A is not equal to the measure of angle D, so we can conclude that △ABC ≠ △DEF
Therefore, based on the calculation of the angles and the lengths of the sides, it can be concluded that △ABC is not congruent to △DEF.
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The most important condition for making an inference about a population mean from a significance test is that the data contain no outliers. the data come from a random sample. the sample size is at least 30. the sample size is less than 10% of the population size. the population distribution is exactly Normal.
The most important condition for making an inference about a population mean from a significance test is that option (b) the data come from a random sample
A random sample is essential to ensure that the sample is representative of the population and that the statistical inference is valid. Other conditions, such as the absence of outliers, sample size, or population distribution, may also affect the validity of the inference, but they are not as crucial as the random sampling condition.
In practice, it is recommended to check for outliers, assess the sample size and the population distribution, and ensure other assumptions of the statistical test are met, such as the normality of the sampling distribution or the equal variance assumption, depending on the test used. However, the random sampling condition remains the most fundamental requirement.
Therefore, the correct option is (b) the data come from a random sample
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Scale factors,
For 19 would it be 5/4 since the polygon is free trying bigger and for 20 would it be 4/5 since it is getting smaller?
All my friends are writing it the other way around but I’m confused because how can it get bigger if it’s less than 1?
The answers of the following questions are mentioned below respectively.
What is scale factor?Scale factor is the ratio of the lengths of corresponding sides of two similar figures. Two figures are considered similar if they have the same shape, but not necessarily the same size.
19.To find the scale factor of PQRS to JKLM, we can use the fact that the corresponding sides of similar figures are proportional. Thus, we have:
PQ/JK = QR/KL = RS/LM
Substituting the given values, we get:
w/25 = 12/15 = 10/x
Simplifying, we get:
w = 5/3 * 25 = 41.67 (approx)
x = 15/2 = 7.5
y = 25 * 7.5 / 15 = 12.5
Therefore, the scale factor of PQRS to JKLM is PQ/JK = w/25 = 41.67/25 = 1.6667 (approx).
20. To find the scale factor of JKLM to PQRS, we can take the reciprocal of the scale factor of PQRS to JKLM. Thus, we have:
JK/PQ = 1/(PQ/JK) = 1/1.6667 = 0.6 (approx)
Therefore, the scale factor of JKLM to PQRS is JK/PQ = 0.6 (approx).
21. To find the values of ti.. .r. and v, we need more information or equations.
22. To find the perimeter of each polygon, we can add up the lengths of the sides. Thus, we have:
Perimeter of JKLM = KJ + JM + ML + LK = 25 + y + x + 15 = y + x + 40 = 20 + 7.5 + 40 = 67.5
Perimeter of PQRS = PQ + QR + RS + SP = w + 12 + 10 + 16 = w + 38 = 41.67 + 38 = 79.67 (approx)
Therefore, the perimeter of JKLM is 67.5 and the perimeter of PQRS is 79.67 (approx).
23. To find the ratio of the perimeter of PQRS to the perimeter of JKLM, we can divide the perimeter of PQRS by the perimeter of JKLM. Thus, we have:
Ratio of perimeter of PQRS to perimeter of JKLM = Perimeter of PQRS / Perimeter of JKLM = 79.67 / 67.5 = 1.18 (approx)
Therefore, the ratio of the perimeter of PQRS to the perimeter of JKLM is 1.18 (approx).
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19. The scale ratio of PQRS to JKLM is PQ/JK = 1.6667. (approx).
20. JK/PQ is the scale factor of JKLM to PQRS is = 0.6 (approx).
22. The JKLM perimeter is 67.5 and the PQRS perimeter is 79.67 (approx).
23. The PQRS perimeter's ratio to the JKLM perimeter is 1.18. (approx).
What is scale factor?The ratio of the lengths of the respective sides of two similar figures is known as the scale factor. When two figures share the same shape but not necessarily the same height, they are said to be similar.
19. We can use the knowledge that the corresponding sides of comparable figures are proportional to determine the scale factor of PQRS to JKLM.
So, here we are:
[tex]\frac{PQ}{JK}=\frac{QR}{KL}=\frac{RS}{LM}[/tex]
Replace the specified numbers in the aforementioned equation,
[tex]\frac{w}{25}=\frac{12}{25}=\frac{10}{x}[/tex]
Simplifying, we get:
w = 5/3 * 25
= 41.67 (approx)
x = 15/2 = 7.5
y = 25 * 7.5 / 15
= 12.5
As a result, PQ/JK = w/25 is the scale factor for PQRS to JKLM.
= 41.67/25
= 1.6667 (approx).
20. We can take the inverse of the scale factor of PQRS to JKLM to determine the scale factor of JKLM to PQRS. So, here we are:
JK/PQ = 1/(PQ/JK)
= 1/1.6667
= 0.6 (approx)
As a result, JK/PQ is equal to 0.6 when converting JKLM to PQRS. (approx).
21. To find the values of ti.. .r. and v, additional details or formulae are required.
22. We can sum up the side lengths of each polygon to determine its perimeter. So, here we are:
Perimeter of JKLM = KJ + JM + ML + LK
= 25 + y + x + 15
= y + x + 40
= 20 + 7.5 + 40
= 67.5
Perimeter of PQRS = PQ + QR + RS + SP
= w + 12 + 10 + 16
= w + 38
= 41.67 + 38
= 79.67 (approx)
As a result, the JKLM perimeter is 67.5 and the PQRS perimeter is 79.67 (approx).
23. By dividing the perimeters of the two systems, we can determine the percentage of the perimeters of PQRS and JKLM. So, here we are:
Ratio of the PQRS periphery to the JKLM perimeter = Perimeter of PQRS / Perimeter of JKLM = 79.67 / 67.5 = 1.18 (approx)
As a result, the PQRS perimeter's relationship to the JKLM perimeter is 1.18. (approx).
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What does the three lined equal sign mean
Answer: identical to/same as
Step-by-step explanation:
Answer:
The ≡ sign means identical to, similar but not exactly the same as, equals
Step-by-step explanation:
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What is the gradient of the blue line?
The blue line is the tangent line that passes through the point (0.75, 0.25). The point on the tangent line is (3, 4). The gradient of the curve is approximately 0.6.
Answer:
gradient = [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
calculate the gradient m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (4, 2) and (x₂, y₂ ) = (8, 3) ← 2 points on the line
m = [tex]\frac{3-2}{8-4}[/tex] = [tex]\frac{1}{4}[/tex]
Ms. Mazzei has a farm on 12 acres of land. She wants to create animal pens that are each 3/11 of an acre. How many pens can Ms. Mazzei have in the 12 acres?
Ms. Mazzei can have 44 animal pens in her 12 acres of land.
Describe Algebra?Algebra is a branch of mathematics that deals with the manipulation and properties of mathematical expressions, including variables and symbols representing numbers, as well as the rules governing their relationships and operations.
Algebraic equations typically involve variables, which are represented by letters or symbols, and are used to express relationships between different quantities or unknowns. These equations can be manipulated using algebraic operations such as addition, subtraction, multiplication, division, and exponentiation to solve for the value of the variables.
The study of algebra includes a wide range of topics, including linear algebra, abstract algebra, number theory, and algebraic geometry. It is a fundamental part of mathematics and plays a crucial role in many areas of modern science and technology.
To find the number of animal pens Ms. Mazzei can have in 12 acres of land, we need to divide the total area by the area of each pen:
Number of pens = Total area / Area of each pen
Total area = 12 acres
Area of each pen = 3/11 acres
Number of pens = 12 / (3/11)
Number of pens = 44
Therefore, Ms. Mazzei can have 44 animal pens in her 12 acres of land.
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About 61% of students at a certain high school take the SATs. What is the probability of sampling five successive students at random until you find the first student to take the SATs?
Answer: The probability of a student taking the SATs is p = 0.61. Let's consider the first student we sample. The probability that this student does not take the SATs is q = 1 - p = 0.39.
If the first student does not take the SATs, we need to sample another student. The probability that the second student does not take the SATs, given that the first student did not take the SATs, is still q = 0.39.
Similarly, if the second student also does not take the SATs, we need to sample a third student. The probability that the third student does not take the SATs, given that the first two students did not take the SATs, is still q = 0.39.
We continue this process until we find the first student who takes the SATs. Let X be the number of students we sample until we find the first student who takes the SATs. Then X can take on the values 1, 2, 3, and so on.
The probability that we find the first student who takes the SATs on the first try is p = 0.61. The probability that we find the first student who takes the SATs on the second try is (q)(p) = (0.39)(0.61) = 0.238.
Similarly, the probability that we find the first student who takes the SATs on the third try is (q)(q)(p) = (0.39)(0.39)(0.61) = 0.147.
In general, the probability that we find the first student who takes the SATs on the kth try is (q)^(k-1)(p).
Therefore, the probability that we find the first student who takes the SATs in exactly k tries is:
P(X=k) = (q)^(k-1)(p)
We want to find the probability of sampling five successive students at random until we find the first student to take the SATs. So we want to find:
P(X=1) ∗ P(X=2) ∗ P(X=3) ∗ P(X=4) ∗ P(X=5)
= p ∗ (q)(p) ∗ (q)(q)(p) ∗ (q)(q)(q)(p) ∗ (q)(q)(q)(q)(p)
= (0.61) ∗ (0.39)(0.61) ∗ (0.39)(0.39)(0.61) ∗ (0.39)(0.39)(0.39)(0.61) ∗ (0.39)(0.39)(0.39)(0.39)(0.61)
= 0.61 ∗ 0.238 ∗ 0.147 ∗ 0.0905 ∗ 0.0554
≈ 0.00028
Therefore, the probability of sampling five successive students at random until you find the first student to take the SATs is approximately 0.00028 or 0.028%.
Step-by-step explanation:
Question 2(Multiple Choice Worth 2 points)
(Comparing Data MC)
The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4,6,14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9,18, 20, and 22. There are two dots above 6, 10, 12,14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of variability to determine which bus is the most consistent. Explain your answer.
Bus 18, with an IQR of 16
Bus 47, with an IQR of 24
Bus 18, with a range of 16
Bus 47, with a range of 24
The correct answer is: Bus 18, with an IQR of 9
How to solveTo determine the most consistent bus, we need to calculate the measure of variability, which gives us an idea of the spread of the data.
In this case, we'll use the Interquartile Range (IQR) as the measure of variability.
The IQR is the range between the first quartile (Q1, the 25th percentile) and the third quartile (Q3, the 75th percentile) of the data.
A smaller IQR indicates more consistency in travel times.
Bus 47 Travel Times: 4, 6, 10, 10, 12, 12, 14, 16, 16, 16, 18, 18, 22, 22, 28
Q1 (25th percentile): 10
Q3 (75th percentile): 22
IQR: 22 - 10 = 12
Bus 18 Travel Times: 6, 6, 8, 9, 10, 10, 12, 12, 14, 14, 16, 16, 18, 20, 22
Q1 (25th percentile): 9
Q3 (75th percentile): 18
IQR: 18 - 9 = 9
Comparing the IQRs, we can see that Bus 18 has a smaller IQR (9) compared to Bus 47 (12).
This means that Bus 18 has more consistent travel times than Bus 47.
So, the correct answer is:
Bus 18, with an IQR of 9
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A small restaurant has a grease recycling tank in the shape of a cylinder. How much grease measured in cubic centimeters can the restaurant store if the tank has a diameter of 197.2 cm and a height of 223.7 cm? Use 3.14 for `pi`.
The restaurant can store approximately [tex]6.864 * 10^6[/tex] cubic centimeters of grease in the recycling tank in the shape of a cylinder.
The formula for the volume of a cylinder is V = π[tex]r^2[/tex]h, where V is the volume, r is the radius of the circular base, and h is the height of the cylinder.
To use this formula, we need to know the values of r and h for the grease recycling tank. The problem tells us that the diameter of the tank is 197.2 cm, which means the radius is half of the diameter:
r = d/2 = 197.2 cm / 2 = 98.6 cm.
The problem also tells us that the height of the tank is 223.7 cm.
Now we can plug in the values of r and h into the formula for the volume of a cylinder:
V = π[tex]r^2[/tex]h
V = π[tex](98.6 cm)^2(223.7 cm)[/tex]
V = [tex]3.14 * (98.6 cm)^2 * (223.7 cm)[/tex]
V ≈ [tex]6.864 * 10^6 cm^3[/tex]
Therefore, the volume of the grease recycling tank is approximately [tex]6.864 * 10^6[/tex] cubic centimeters, which means that the restaurant can store that amount of grease in the tank.
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. A pile of bottle caps is located at (4, -10). find the length of the most direct path between Ann and the bottle caps?
Thus, the most direct path between the bottle caps and Ann is found as:
d = 10.63 units.
Define about the distance formula:The algebraic phrase known as the distance formula, which provides the distances between two places in terms of respective coordinates (in coordinate system).
The distance formulas with points in rectangular coordinates in two- through three-dimensional Euclidean space are based here on Pythagorean theorem.
The formula used to calculate the distance between both the points (x1, y1) and ((x2, y2)
d = √[(x2 - x1)² + (y2 - y1)²]
Coordinates of pile of bottle caps -:(x1, y1) = (4, -10).
Coordinates of ANN - (x2, y2) = (-4, 3).
Using the distance formula:
d = √[(x2 - x1)² + (y2 - y1)²]
d = √[(-4 - 4)² + (-3 + 10)²]
d = √[(64) + 49]
d = 10.63 units
Thus, the most direct path between the bottle caps and Ann is found as:
d = 10.63 units.
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complete question
A pile of bottle caps is located at (4, -10). find the length of the most direct path between Ann and the bottle caps?
The graph for the question is given.
please help me!!!!!!!!
The mean of the data is X = 85. The variance is 187.5. The standard deviation is σ = 13.7
Describe Standard Deviation?Standard deviation is a measure of the amount of variability or dispersion of a set of data points from the mean value. It is calculated by finding the square root of the variance, which is the average of the squared differences between each data point and the mean. The standard deviation indicates how far the data points are from the mean on average, with larger values indicating greater variability and smaller values indicating less variability. The standard deviation is a commonly used measure of spread in statistics and is often used to describe the distribution of a dataset. It is denoted by the symbol σ (sigma) for a population and s for a sample.
To find the mean of the data, we add up all the values and divide by the total number of values:
X = (90 + 75 + 60 + 85 + 65 + 80 + 70 + 75) / 8
= 680 / 8
= 85
So the mean of the data is X = 85.
To find the variance, we need to first find the deviation of each value from the mean, square each deviation, and then take the average of the squared deviations:
deviation of 90 from mean = 90 - 85 = 5
deviation of 75 from mean = 75 - 85 = -10
deviation of 60 from mean = 60 - 85 = -25
deviation of 85 from mean = 85 - 85 = 0
deviation of 65 from mean = 65 - 85 = -20
deviation of 80 from mean = 80 - 85 = -5
deviation of 70 from mean = 70 - 85 = -15
deviation of 75 from mean = 75 - 85 = -10
Now, we square each deviation and find the average:
variance = [(5)² + (-10)² + (-25)² + (0)² + (-20)² + (-5)² + (-15)² + (-10)²] / 8
= (25 + 100 + 625 + 0 + 400 + 25 + 225 + 100) / 8
= 1500 / 8
= 187.5
So the variance is 187.5.
Finally, the standard deviation is the square root of the variance:
σ = √(187.5)
= 13.7 (rounded to the nearest tenth)
Therefore, the standard deviation is σ = 13.7 (rounded to the nearest tenth).
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Construct a polynomial function of least degree possible using the given information.
Real roots: −1 (with multiplicity 2), 1 and (2,
f(2)) = (2, 7)
The polynomial function of least degree possible using the given information.
Real roots: −1 (with multiplicity 2), 1 and (2,
f(2)) = (2, 7) is f(x) = x³ - 3x² + 3x - 1.
How to explain the polynomialSince the polynomial function has real roots at -1 (with multiplicity 2) and 1, we know that the factors of the polynomial are (x + 1)² and (x - 1).
Let the polynomial be of the form f(x) = ax³ + bx² + cx + d. We know that f(2) = 7, so:
a(2³) + b(2²) + c(2) + d = 7
8a + 4b + 2c + d = 7
Now we need to use the fact that the roots are -1 (with multiplicity 2) and 1. Since the polynomial has factors of (x + 1)² and (x - 1), we can write the polynomial as:
f(x) = a(x + 1)²(x - 1)
Expanding this expression, we get:
f(x) = a(x² - 2x + 1)(x - 1)
f(x) = ax³ - 3ax² + 3ax - a
Now we can equate the coefficients of this expression with the coefficients of our assumed polynomial f(x) = ax³ + bx² + cx + d:
a = a
-3a = b
3a = c
-a = d
Therefore, our polynomial function is:
f(x) = x³ - 3x² + 3x - 1
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you order a cell phone case and 2 screen protectors online for a total of $18.95. your friend orders 2 cell phone cases and 5 screen protectors at the same unit prices for a total of $41.40. what is the cost of each cell phone case? each screen protector?
Answer:
Step-by-step explanation:
The cost of each cell phone case is $7.15, and the cost of each screen protector is $2.25.
To solve this problem, we can create a system of equations.
Let x represent the cost of one cell phone case and y represent the cost of one screen protector.
Then, we can write the following equations:
1x + 2y = 18.95 (equation 1)
2x + 5y = 41.40 (equation 2)
We can solve for x and y by multiplying equation 1 by 2 and subtracting it from equation
2.2x + 5y = 41.40(2 x 1x + 2 x 2y = 2 x 18.95)2x + 5y = 41.4002x + 4y = 37.90
Subtracting equation 1 from equation 2 gives us:
2x + 5y = 41.400- (0.2x + 0.4y = 3.790)
1.8x + 4.6y = 37.61
Now we can solve for y.
1.8x + 4.6y = 37.61
=> 46y = 46.29
=> y = 1.05
Then we can solve for x using equation
1.1x + 2y = 18.95
=> 1x + 2(1.05) = 18.95
=> x = 7.15
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Question:
You order a cell phone case and 2 screen protectors online for a total of $18.95. Your friend orders 2 cell phone cases and 5 screen protectors at the same unit prices for a total of $41.40. What is the cost of each cell phone case? Each screen protector?
Nora made 3 gallons of lemonade.
Which of the following can be used to find the number of pints of lemonade that Nora made?
A 3x2x2
B 3x4x2
C 3x3x2
D 3x4x3
What is the image of (−5,−9) after a dilation by a scale factor of
3 centered at the origin?
The image of (-5,-9) after dilation by a scale factor of 3 centered at the origin is (-15,-27).
What is the image of (−5,−9) after a dilation by a scale factor of 3 centered at the origin?To find the image of the point (-5,-9) after dilation by a scale factor of 3 centered at the origin.
We can use the following formula:
(x', y') = (kx, ky)
Where (x', y') are the coordinates of the dilated point, (x, y) are the coordinates of the original point, and k is the scale factor.
In this case, k = 3, and the coordinates of the original point are (-5,-9).
So we have:
x' = 3(-5) = -15
y' = 3(-9) = -27
Therefore, the image after dilation is (-15,-27).
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a circle is divided into 5 equal parts what is the measure of the angle that turns through 2 parts
The measure of the angle that turns through 2 parts of a circle divided into 5 equal parts is 144 degrees.
What is the circumference of a circle?
The circumference of a circle is the distance around its outer edge or boundary. It is the total length of the circular arc, which is the curved part of the circle.
The formula for the circumference of a circle is C = 2πr
If a circle is divided into 5 equal parts, each part corresponds to an angle of 360/5 = 72 degrees.
To find the measure of the angle that turns through 2 parts, we need to multiply 2 by 72 degrees:
2 parts x 72 degrees/part = 144 degrees
Hence, the measure of the angle that turns through 2 parts of a circle divided into 5 equal parts is 144 degrees.
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find the slope of a line perpendicular to y=- 1/2x+7
Answer:
perpendicular slope = 2
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 )
y = - [tex]\frac{1}{2}[/tex] x + 7 ← is in slope- intercept form
with slope m = - [tex]\frac{1}{2}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{2} }[/tex] = 2
1874
2365
Fold this paper so that
1 is on top of 2,
2 is on top of 3,
3 is on top of 4, ...
Numbers can
be upside down
or backwards.
1
Answer:
Fold the paper in half lengthwise. Unfold it, then fold it in half again widthwise. Unfold it, then fold it in thirds lengthwise. Unfold it and then fold it in half again widthwise. You should now have a paper with 8 sections, with 1 on top of 2, 2 on top of 3, 3 on top of 4, etc. You can flip the numbers upside down or backwards as desired.
Step-by-step explanation:
Help I’ve tried so hard
Step-by-step explanation:
The points are 15 units apart
the FIRST expression shows this
!!!help please I’ll mark BRAINLIEST!
Shawnee bought a shirt on sale that was 20% off of the original price. The original price was $5 more than the sale price. What was the original price? Use a model and check your work using the 80/20 rule.
Simplify the expression. .
2. 3h( 6 – k)
Step by step please
I need help with number 26 asap! Thank you so much!!
I need help with number 26 asap! Thank you so much!!
Therefore, the only solution to the equation cot² x cos x = cot²x on the interval [0, 2m) is x = 0.
What is equation?An equation is a mathematical statement that shows the equality between two expressions. The expressions on either side of the equals sign are called the left-hand side and the right-hand side of the equation. An equation can be written in many different forms, but the most common form is: Left-hand side = Right-hand side
In the given question,
We start by bringing all the terms to one side of the equation, which gives:cot² x (cos x - 1) = 0
Now, we need to solve for x such that this equation holds on the interval [0, 2m).
First, we consider the case where cot² x = 0. This occurs when cot x = 0, or x = π/2, 3π/2, 5π/2, etc. However, none of these solutions are in the given interval [0, 2m), so we can ignore this case.
Next, we consider the case where cos x - 1 = 0. This occurs when cos x = 1, or x = 2nπ, where n is an integer. The only solution that is in the given interval [0, 2m) is x = 0.
Therefore, the only solution to the equation cot² x cos x = cot² x on the interval [0, 2m) is x = 0.
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The area of a rectangle is found using the formula A=lw
, where l
is the length of the rectangle and w
is the width. Multiply each pair of factors and express the area of each rectangle as a single polynomial in terms of x
.
Question
l=x+14; w=3x+1
Answer:
The area of the rectangle is given by the formula A = lw. Substituting the given values, we get:
A = (x+14)(3x+1)
Expanding the expression, we get:
A = 3x^2 + x + 42x + 14
A = 3x^2 + 43x + 14
Therefore, the area of the rectangle is given by the polynomial expression 3x^2 + 43x + 14.
Q1 The following diagram represents the positions and bearings
of two helicopters. Helicopter B is 1.2km away from
helicopter A on a bearing of 122°. How far north is
helicopter A from helicopter B?
N
Helicopter A1220
1.2km
N
Helicopter B
The distance north of Helicopter A from helicopter B is 1. 03 km.
The shortest distance between the polar bear and the conservationists is 9.36 km.
How to find the distance ?To find the distance from Helicopter A to Helicopter B in the north direction, we can use trigonometry. We can create a right triangle with the north direction as one side, the distance between the helicopters as the hypotenuse, and the angle of 122° between them.
Let N be the north distance between A and B. We can use the sine function:
sin(angle) = opposite side / hypotenuse
sin(122°) = N / 1.2 km
Now, solve for N:
N = 1.2 km x sin (122°) = 1.03 km
The polar bear's position is given as 3 km eastward and on a bearing of 104°. To find the shortest distance between the polar bear and the conservationists, we need to consider the right triangle formed by the eastward direction, the north direction, and the distance between the polar bear and the conservationists as the hypotenuse.
Let D be the shortest distance between the polar bear and the conservationists. We can use the cosine function:
cos(angle) = adjacent side / hypotenuse
cos(104°) = 3 km / D
Now, solve for D:
D = 3 km / cos(104°) = 9.36 km
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The sixth-grade art students are making a mosaic using tiles in the shape of right triangle. The two sides that meet to form a right angle are 7 centimeters and 5 centimeters long. If there are 20 tiles in the mosaic, what is the area of the mosaic ?
Answer: The area of the mosaic is 175 cm². To calculate this, multiply the two sides of each triangle together (7 cm * 5 cm = 35 cm²) and then multiply that by the number of tiles (35 cm² * 20 = 175 cm²).
Step-by-step explanation:
This is a new version of the question. Make sure you start new workings.
Select all of the shapes below that are nets of a pentagonal-based pyramid.
Back to task
A
D
Watch video
B
Answ
The shapes that are nets of a pentagonal-based pyramid are shapes A and D.
What are properties of a pentagonal-based pyramid?A net of a pentagonal-based pyramid is a 2-dimensional pattern that can be folded into a 3-dimensional pentagonal-based pyramid. The net of a pentagonal-based pyramid has the following properties:
It consists of a regular pentagon as the base of the pyramid and five triangles that form the sides of the pyramid.The five triangles are congruent isosceles triangles.The apex of the pyramid is located at the center of the regular pentagon.Each triangle has one vertex at the apex of the pyramid and two vertices on the edges of the regular pentagon.The sum of the angles of each triangle is 180 degrees, and the sum of the angles of the regular pentagon is 540 degrees.The perimeter of the base of the pyramid is equal to five times the length of one side of the regular pentagon.The height of the pyramid is the perpendicular distance from the apex to the base, which can be found using the Pythagorean theorem.Learn more on pentagonal-based pyramid here: https://brainly.com/question/28226952
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