0. 07, -7. 88, -7. 9, 7. 03, -7. 881 is ascending order
Answer:
-7.9, -7.881, -7.88, 0.07, 7.03
Step-by-step explanation:
Numbers provided: 0.07, -7.88, -7.9, 7.03, -7.881
The numbers that are negative are lower on the number line than negative numbers.You look at the digits from left to rightThe bigger the negative number is, the further left it goesa large diamond with a mass of 4289.6 grams was recently discovered in a mine. if the density of the diamond is 3.51 grams over centimeters cubed, what is the volume? round your answer to the nearest hundredth. 142.78 cm3 384.96 cm3 1221.9 cm3 33759.15 cm3
If a large diamond with a mass of 4289.6 grams was recently discovered in a mine and the density of the diamond is 3.51 grams over centimeters cubed, the volume is 1221.9 cm³.
To find the volume of the diamond, we need to use its mass and density. The density of the diamond is given as 3.51 grams per cubic centimeter. This means that every cubic centimeter of diamond has a mass of 3.51 grams.
We can use this information to find the volume of the diamond by dividing its mass by its density. Plugging in the given values, we get:
Volume = Mass / Density
Volume = 4289.6 g / 3.51 g/cm³
Volume = 1221.86 cm³
This means that the diamond has a volume of 1221.86 cubic centimeters. However, the question asks us to round the answer to the nearest hundredth, so we round this value to: Volume = 1221.9 cm³
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Mai is visiting Paris to see the Eiffel Tower. She is 80 feet away when she spots it. To see the top, she has to look up at an angle of 85. 7 degrees. How tall is the Eiffel Tower to the nearest foot?
The Eiffel Tower is approximately 919 feet tall to the nearest foot.
We can use trigonometry to solve this problem.
Let's assume that the height of the Eiffel Tower is h feet.
From the problem, we know that Mai is 80 feet away from the base of the tower and looking up at an angle of 85.7 degrees. We can use the tangent function to relate the height of the tower to the angle and distance:
tan(85.7) = h/80
We can solve for h by multiplying both sides by 80:
h = 80 × tan(85.7)
Using a calculator, we get:
h ≈ 919.4 feet
Therefore, the Eiffel Tower is approximately 919 feet tall to the nearest foot.
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Adam received a bonus of 15% of his weekly wage of $600. How much of a bonus was given to him?
Answer:
90$
Step-by-step explanation:
We need to find 15% of the number 600:
[tex] \frac{600 \times 15\%}{100\%} = 90 [/tex]
So, the answer is 90$
in this question, we will show the existence and uniqueness of solutions to systems of differential equations with inputs in particular,we previously considered the scalar differential equation
Existence and uniqueness of solutions to systems of differential equations depend on the number of equations and the order of each equation. For example, a system of two first-order equations has a unique solution, while a system of three first-order equations may not have a unique solution.
Previously, we considered the scalar differential equation, which is a single differential equation involving only one independent variable. In this case, the solution to the equation is unique. This is because there is only one equation and only one variable, so the solution must be unique for a given set of initial conditions.
For a system of differential equations, the existence and uniqueness of solutions depend on the number of equations and the order of each equation.
Systems of differential equations with higher order equations or more equations than unknowns may not have a unique solution. On the other hand, if there are more unknowns than equations, then there is always a unique solution. To find the solution, the equations must be solved simultaneously.
In conclusion, A scalar differential equation always has a unique solution.
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Help!! I need to find the perimeter
The perimeter of the triangle is 72 √5 / 3 units.
How to find the perimeter of a triangle?The perimeter of a triangle is the sum of the whole three sides of the triangle. The triangle above is an equilateral triangle.
An equilateral triangle has all it sides and angles congruent to each other.
Therefore, the perimeter of the triangle can be found as follows:
Let's find the side of the triangle using trigonometric ratios,
sin 60 = opposite / hypotenuse
sin 60 = 4√15 / h
cross multiply
h = 4√15 ÷ √3 / 2
h = 4√15 × 2 / √3
h = 8√15 / √3
Hence,
hypotenuse side = 8√45 / 3
perimeter of the triangle = 8√45 / 3 + 8√45 / 3 + 8√45 / 3
perimeter of the triangle = 8√45 + 8√45 + 8√45 / 3
perimeter of the triangle = 24√45 / 3
perimeter of the triangle = 72 √5 / 3 units
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Buffalo Wild Wings charges you $22 per guest plus a room rental fee of $450.
Champs Bar and Grill charges you $210 for a room and $30 per guest.
How many guests can you invite so that the cost of the two restaurants will be equal?
You could invite
That equal cost is equal to
guests at an equal cost.
dollars.
Answer: 30
Step-by-step explanation: TRUSy
Stated here are some claims or research hypotheses that are to be substantiated by sample data. In each case, identify the nulll hypothesis H0 and the alternative hypothesis H1 in terms of the population mean %u03BC
a) The mean time a health insurance company takes to pay claims is less than 14 working days.
b) the average person watching a movie at a local multiplex theater send over $4.50 on refreshments.
c) The mean hospital bill for birth in the city is less than $5000.
d) The mean time between purchases of a brand of mouthwash by loyal customers is different from 60 days.
The null hypothesis and alternative hypothesis for the population mean µ are identified for the given research hypotheses.
The null hypothesis and alternative hypothesis for the population mean µ are as follows:a) H0: µ ≥ 14; H1: µ < 14b) H0: µ ≤ $4.50; H1: µ > $4.50c) H0: µ ≥ $5000; H1: µ < $5000d) H0: µ = 60; H1: µ ≠ 60 Research hypotheses that are to be substantiated by sample data are as follows:a) The mean time a health insurance company takes to pay claims is less than 14 working days.Null hypothesis H0: µ ≥ 14 Alternative hypothesis H1: µ < 14b) The average person watching a movie at a local multiplex theater send over $4.50 on refreshments.
Null hypothesis H0: µ ≤ $4.50 Alternative hypothesis H1: µ > $4.50c) The mean hospital bill for birth in the city is less than $5000.Null hypothesis H0: µ ≥ $5000 Alternative hypothesis H1: µ < $5000d) The mean time between purchases of a brand of mouthwash by loyal customers is different from 60 days.Null hypothesis H0: µ = 60 Alternative hypothesis H1: µ ≠ 60 Hence, the null hypothesis and alternative hypothesis for the population mean µ are identified for the given research hypotheses.
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Marrero spotted an exclamation point on a billboard in Little Havana. This exclamation point consists of a circle sector and circle. Marrero measured the radius of the sector to be 9 ft, and the radius of the circle to be 1. 5 ft. At the end, he found out that the angle of the sector is 24°. What is the total area of the exclamation point on this Little Havana billboard? Round to the nearest square foot
The overall area of the exclamation point at the Little Havana billboard is about 24 square ft while rounded to the nearest square foot.
To discover the total area of the exclamation point, we need to calculate the area of the sector and the area of the circle, after which add them collectively.
First, let's find the area of the sector. The formula for the area of a circle area is:
Area of sector = (angle/360) x π x radius^2
Substituting the given values, we get:
Area of sector = [tex](24/360) x π x 9^2 = 16.62 ft²[/tex]
Next, let's find the area of the circle. The components for the area of a circle is:
Area of circle = π x radius^2
Substituting the given value, we get:
Area of circle [tex]= π x 1.5^2 = 7.07 ft²[/tex]
Now, we are able to add the areas of the sector and the circle to get the whole area of the exclamation point:
[tex]6.62 feet² + 7.07 feet² = 23.69 ft²[/tex]
Therefore, the overall area of the exclamation point at the Little Havana billboard is about 24 square ft while rounded to the nearest square foot.
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How do you write 10/100 as a percentage?
Answer: [tex]\frac{10}{100}[/tex]× 100
Step-by-step explanation:
Answer:
10/100 = 10%
Step-by-step explanation:
10/100 = 0.1
0.1 * 100 = 10%
ASAP!! ITS URGENT
Solve these problems. (Use a calculator with a square root function, and round off answers to two decimal places.)
Answer:
10. To find the area of rhombus ABCD, we can use the formula:
Area = (diagonal 1 x diagonal 2) / 2
We need to find the length of both diagonals. Since the diagonals of a rhombus are perpendicular and bisect each other, we can use the Pythagorean theorem to find the length of each diagonal.
AC is one diagonal, AB is a side of the rhombus, and BD is the other diagonal divided by 2 (since BD bisects AC):
BD = AC/2 = 10/2 = 5 cm
Using the Pythagorean theorem with AC and BD:
AC^2 = AB^2 + BD^2
AC^2 = 13^2 + 5^2
AC^2 = 169 + 25
AC^2 = 194
AC = sqrt(194) ≈ 13.93 cm
Now that we have the lengths of both diagonals:
Area = (AC x BD) / 2
= (13.93 x 5) / 2
≈ 34.83 cm^2
Therefore, the area of rhombus ABCD is approximately 34.83 cm^2.
11. We know that the area of rhombus ABCD is 96 cm^2, and that BD is 8 cm. To find the length of AC, we can use the formula:
Area = (diagonal 1 x diagonal 2) / 2
Solving for diagonal 1 (AC):
AC = (2 x Area) / BD
= (2 x 96) / 8
= 24 cm
Therefore, the length of AC is 24 cm.
12. We know that AB is a side of the rhombus and that AB = 16 m. We also know that mZABD = 60 degrees. We can use trigonometry to find the length of the diagonals.
First, we can find the length of AD using the law of cosines:
AD^2 = AB^2 + BD^2 - 2(AB)(BD)cos(mZABD)
AD^2 = 16^2 + (2x)^2 - 2(16)(2x)cos(60)
AD^2 = 256 + 4 - 32x
AD^2 = 260 - 32x
AD = sqrt(260 - 32x)
Then, we can find the length of AC using the law of sines:
AC / sin(mZBAD) = AD / sin(mZABD)
AC / sin(120) = AD / sin(60)
AC = (AD x sin(120)) / sin(60)
AC = (sqrt(260 - 32x) x sqrt(3)) / 2
Now that we have the lengths of both diagonals:
Area = (AC x BD) / 2
= [(sqrt(260 - 32x) x sqrt(3)) / 2] x 8 / 2
= 2(sqrt(260 - 32x) x sqrt(3))
≈ 67.29 m^2
Therefore, the area of rhombus ABCD is approximately 67.29 square meters.
13. We know that the perimeter of the rhombus is 20 mm, so each side is 5 mm. We also know that AC is one of the diagonals. To find the length of the other diagonal, we can use the Pythagorean theorem.
Let x be half the length of the other diagonal:
AC^2 = (2x)^2 + 5^2
x^2 = (AC^2 - 25) / 4
x = sqrt((AC^2 - 25) / 4)
Now that we have the lengths of both diagonals:
Area = (AC x BD) / 2
= (AC x 2x) / 2
= xAC
= sqrt((AC^2 - 25) / 4) x AC
≈ 19.80 mm^2
Therefore, the area of rhombus ABCD is approximately 19.80 square millimeters.
The length and width of a rectangle are consecutive integers. The area of the
rectangle is 56 square centimeters. Find the length and width of the rectangle.
The length and width of the rectangle are 7 cm and 8 cm
How to find the length and width of the rectangle.From the question, we have the following parameters that can be used in our computation:
The length and width of a rectangle are consecutive integers
This means that
Length = x
Width = x + 1
So, we have
Area = x * (x + 1)
Substitute the known values in the above equation, so, we have the following representation
x * (x + 1) = 56
Express 56 as 7 * 8
So, we have
x * (x + 1) = 7 * 8
This means that
x = 7
So, we have
Length = 7
Width = 7 + 1
Length = 7
Width = 8
Hence, the length is 7 cm
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\begin{tabular}{cc} \hline Number of Hours & Frequency \\ \hline 0 & 127 \\ 1 & 176 \\ 2 & 348 \\ 3 & 252 \\ 4 & 328 \\ 5 & 239 \\ 6 & 139 \\ 7 & 27 \\ 8 & 60 \\ \hline Total & 1696 \end{tabular} (b) Compute the standard deviationσX. Round the answer to at least three decimal places.σX=
The standard deviation is σX ≈ 1.936 (rounded to at least three decimal places).
Standard deviation (σX) is a measure that is used to quantify the amount of variation or dispersion of a set of data values. Here is how to compute it from the given data:\begin{tabular}{cc} \hline Number of Hours & Frequency \\ \hline 0 & 127 \\ 1 & 176 \\ 2 & 348 \\ 3 & 252 \\ 4 & 328 \\ 5 & 239 \\ 6 & 139 \\ 7 & 27 \\ 8 & 60 \\ \hline Total & 1696 \end{tabular}(b) Compute the standard deviation σX. Round the answer to at least three decimal places.The formula to use is:\[\sigma_X = \sqrt{\frac{\sum f(x_i - \overline{x})^2}{n}}\]where:σX = standard deviation∑ = sum off = frequencyxi = value of i-th datan = total number of data\[\overline{x} = \frac{\sum fx}{n}\]is the sample mean, which we must calculate first.\[\overline{x} = \frac{\sum fx}{n} = \frac{0\cdot127 + 1\cdot176 + 2\cdot348 + 3\cdot252 + 4\cdot328 + 5\cdot239 + 6\cdot139 + 7\cdot27 + 8\cdot60}{1696} \approx 2.7875\]Substituting into the standard deviation formula:\[\sigma_X = \sqrt{\frac{\sum f(x_i - \overline{x})^2}{n}} = \sqrt{\frac{0\cdot(127 - 2.7875)^2 + 1\cdot(176 - 2.7875)^2 + 2\cdot(348 - 2.7875)^2 + 3\cdot(252 - 2.7875)^2 + 4\cdot(328 - 2.7875)^2 + 5\cdot(239 - 2.7875)^2 + 6\cdot(139 - 2.7875)^2 + 7\cdot(27 - 2.7875)^2 + 8\cdot(60 - 2.7875)^2}{1696}} \approx 1.936\]Therefore, the standard deviation is σX ≈ 1.936 (rounded to at least three decimal places).
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how much pure alcohol must a pharmacist add to 10cm^3 of an 8% alcohol solution to strengthen it to an 80% solution
[tex]36 cm^3[/tex] of pure alcoh ol must be added to the [tex]10 cm^3[/tex] of the 8% solution to obtain [tex]10 + 36 = 46 cm^3[/tex] of an 80% solution.
What is Algebraic expression ?
Algebraic expression can be defined as combination οf variables and constants
Let's first calculate the amount of pure alcohol in the 8% solution:
Amount of pure alcohol = 8% of [tex]10 cm^3 = 0.08 x 10 cm^3 = 0.8 cm^3[/tex]
N ow, let's assume [tex]x cm^3[/tex]of pure alcohol must be added to the 10 cm^3 of the 8% solution to obtain a total volume of [tex]10 + x cm^3[/tex] of an 80% solution. The amount of pure alcohol in the final solution would be:
ο[tex](10 + x) cm^3 = 0.8 (10 + x) cm^3[/tex]
Since we started with [tex]0.8 cm^3[/tex]of pure alcohol and we want to end up with
[tex]0.8 (10 + x) cm^3[/tex], we can set up the following equation:
[tex]0.8 + x = 0.8 (10 + x)[/tex]ο
Simplifying and solving for x, we get:
[tex]0.8 + x = 8 + 0.8x[/tex]
[tex]0.2x = 7.2[/tex]
[tex]x = 36[/tex]
Therefore, [tex]36 cm^3[/tex] of pure alcohol must be added to the [tex]10 cm^3[/tex]of the 8% solution to obtain [tex]10 + 36 = 46 cm^3[/tex] of an 80% solution.
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Answer:
36cm^3
Step-by-step explanation:
Determine the intercepts of the line.
Do not round your answers
Lewis wants to play several games of paintball with his friends. At the park, it costs $19.31 for admission and paintballs, and $6.71 for each game he plays. Which of the following equations could be used to determine Lewis's total cost for several games of paintball?(Let x represent the number of games Lewis plays and y represent his total cost.)
A.
y = $6.71x
B.
$19.31y = $6.71x
C.
y = $19.31x + $6.71
D.
y = $6.71x + $19.31
Find the exact value of sin−1(cos(1013π)).
The exact value of sin−1(cos(1013π)) is sin−1(1 / (2sin(1013π) - cos(1013π) + 1)).
To find the exact value of sin−1(cos(1013π)), we need to use the identity sin^2(x) + cos^2(x) = 1. Since sin−1(cos(1013π)) is an angle whose sine is cos(1013π), we can let that angle be x: sin(x) = cos(1013π).Let's find the sine of x using the identity sin^2(x) + cos^2(x) = 1:sin^2(x) + cos^2(x) = 1sin^2(x) + (cos(1013π))^2 = 1sin^2(x) + cos^2(1013π) = 1sin^2(x) + sin^2(π/2 - 1013π) = 1Now we need to simplify sin^2(π/2 - 1013π):sin^2(π/2 - 1013π) = sin^2(π/2)cos^2(1013π) - 2sin(π/2)cos(1013π)sin(1013π/2) + sin^2(1013π/2)= 1(cos(1013π))^2 - 2sin(1013π/2)cos(1013π) + 0= cos^2(1013π) - 2sin(1013π)cos(1013π)= cos(1013π)(cos(1013π) - 2sin(1013π))Using the identity sin^2(x) + cos^2(x) = 1, we can rewrite sin^2(x) as 1 - cos^2(x):sin^2(x) + cos^2(x) = 11 - cos^2(x) + cos^2(1013π) = 11 - cos(1013π)(cos(1013π) - 2sin(1013π)) + cos^2(1013π) = 1cos(1013π) - cos(1013π)^2 + 2sin(1013π)cos(1013π) = 1cos(1013π) + cos(1013π)(2sin(1013π) - cos(1013π)) = 1cos(1013π)(2sin(1013π) - cos(1013π) + 1) = 1cos(1013π) = 1 / (2sin(1013π) - cos(1013π) + 1)Therefore, the exact value of sin−1(cos(1013π)) is sin−1(1 / (2sin(1013π) - cos(1013π) + 1)).
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Use synthetic division and the Remainder Theorem to evaluate P(c). P(x)=3x^(2)+10x+1,c=-1 P(-1)
By answering the abοve questiοn, we may state that Hence, using divide synthetic divisiοn and the Remainder Theοrem, we have established that P(-1) = -1.
What is divide?Divisiοn, οne οf the fοur basic mathematical οperatiοns, is the prοcess οf cοmbining twο numbers tο create a new number. Other οperatiοns include additiοn, subtractiοn, and multiplicatiοn. Divisiοn is the reverse οf multiplicatiοn.
When yοu divide twelve intο its three equal parts, yοu get fοur in each grοup when yοu multiply three grοups οf fοur by twelve. Finding οut hοw many equal grοups are generated when sharing fairly—οr hοw many peοple are in each grοup—is the fundamental purpοse οf sharing. Tο divide is tο separate intο twο οr mοre grοups, classes, sectiοns, οr regiοns οf equal size.
In οrder tο evaluate P(c) using synthetic divisiοn and the Remainder Theοrem, we take the fοllοwing actiοns:
[tex]-1 | 3 10 1\s|_______[/tex]
[tex]-1 | 3 10 1\s| \s3[/tex]
[tex]-1 | 3 10 1\s| \s3\s-13[/tex]
Write the sum οf the twο numbers yοu just nοted dοwn underneath the fοllοwing cοefficient, 1:
[tex]-1 | 3 10 1\s| \s3\s-13\s-1[/tex]
The divisiοn's final value is the leftοver amοunt. The Remainder Theοrem states that this number is equal tο P(-1), which is what we were lοοking fοr. Hence, P(-1) equals 1.
Hence, using synthetic divisiοn and the Remainder Theοrem, we have established that P(-1) = -1.
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We can use the Remainder Theοrem tο cοnclude that the value[tex]P(-1) = 3(-1)^2 + 10(-1) + 1 = 3 - 10 + 1 = -6.[/tex]
What is synthetic divisiοn?Synthetic divisiοn is a shοrthand methοd οf dividing a pοlynοmial by a linear factοr οf the fοrm (x - c), where c is a cοnstant. It is a methοd οf pοlynοmial lοng divisiοn that simplifies the prοcess and reduces the number οf steps required.
Tο evaluate P(-1) using synthetic divisiοn and the Remainder Theοrem, we can fοllοw these steps:
Step 1: Write the cοefficients οf the pοlynοmial P(x) in οrder οf decreasing degree, including any missing terms with a cοefficient οf 0. In this case,
[tex]P(x) = 3x^2 + 10x + 1[/tex]
Step 2: Set up the synthetic divisiοn table by placing the value οf c, which is -1 in this case, in the leftmοst cοlumn and writing the cοefficients οf the pοlynοmial in the secοnd cοlumn:
-1 | 3 10 1
Step 3: Bring dοwn the first cοefficient, which is 3, intο the third cοlumn:
-1 | 3 10 1
---------
3
Step 4: Multiply the value in the third cοlumn by the value οf c, which is -1, and write the result in the fοurth cοlumn:
-1 | 3 10 1
---------
3 -3
Step 5: Add the values in the secοnd and fοurth cοlumns and write the result in the fifth cοlumn:
-1 | 3 10 1
---------
3 -3 0
Step 6: The value in the last cοlumn, 0, is the remainder when P(x) is divided by x + c, which is x + 1 in this case. Therefοre, we can use the Remainder Theοrem tο cοnclude that P(-1) = 0.
Thus, [tex]P(-1) = 3(-1)^2 + 10(-1) + 1 = 3 - 10 + 1 = -6.[/tex]
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. A normally distributed data set has a µ = 10, the z score for 10 is ___.
10. To convert a z score into a raw score, we need the population mean and the population standard deviation.
True
False
11. Using the Normal Curve table, what is the total percentage between a standard deviation of -2 and +1?
9. A normally distributed data set has a µ = 10, the z score for 10 is 0.
10. It is true that the standard deviation is needed to convert a raw score to a z-score.
11. The total percentage between a standard deviation of -2 and 1 is given as follows: 81.85%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The z-score for the mean is given as follows:
Z = 0/s
Z = 0.
The p-values relative to z-scores between -2 and 1 are given as follows:
z = 1: 0.8413.z = -2: 0.0228.Hence the percentage is given as follows:
84.13 - 2.28 = 81.85%.
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hello please can you give me the answers
Answer: First 2 questions are 12.5% and the third is 25%
Step-by-step explanation: Add up all the possibilities then take the desired possibility and divide by the total possibilities then multiply by 100
Your monthly bill for machine parts is $2,628. 53. If you pay the bill within 15 days, you'll receive a 2% reduction. What will your bill be if you pay it within the allotted time?
The new amount due, subtract the discount of $52.57 from the original bill of $2,628.53, giving the new amount due of $2,579.06. Therefore, if you pay the bill within 15 days, you will receive a 2% reduction and your bill will be $2,579.06.
To calculate the amount due if paying within 15 days, you would need to apply the 2% discount to the original amount. To do this, first find the amount of the discount by multiplying the original bill of $2,628.53 by 0.02. This gives a discount of $52.57. To calculate the new amount due, subtract the discount of $52.57 from the original bill of $2,628.53, giving the new amount due of $2,579.06. Therefore, if you pay the bill within 15 days, you will receive a 2% reduction and your bill will be $2,579.06.
Original Bill : $2,628.53
Discount (2%) : $2,628.53 x 0.02 = $52.57
Amount Due (after 15 days) : $2,628.53 - $52.57 = $2,579.06
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The options for the drop-down menus are;
1. 0 and -3/ -3, 0, and 3/ 0 and 3/ -3 and 3.
2. no/two/three/four.
3. no/two/three/four.
The graph of the function has zeros of 0 and 3, two distinct real zeros, and no complex zeros.
What is a function?
It is defined as a special type of relationship and they have a predefined domain and range according to the function.
We have a function:
y= x²(x² - 6x + 9)
We can write it as a:
y=x²(x-3)²
To find the zeros equate to the function with the zero.
y = 0
x²(x-3)² =0
First, take x²=0 we get:
x = 0
Now
(x - 3)² =0
x - 3 = 0
x = 3
Thus, the graph of the function has zeros of 0 and 3, two distinct real zeros, and no complex zeros.
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By applying the compound angles and without using a calculator, Determine the value of: 1.7.1 cos 15°
Answer:
this is the answer to that problem
What does the circled part of the picture represent?
a point
a line
line segment
ray
Answer:
What does the circled part of the picture represent?
A) a point
B) a line
C) line segment
D) ray
Step-by-step explanation:
it is a btw
HELP!!! Will mark branliest
By De Moivre's formula, the square roots of the complex number √(i 2) are √z = 1 + i and √z = - 1 - i, respectively.
How to find the square roots of a complex numbers
In this problem we find a complex number, whose square roots can be determined by De Moivre's formula:
For z = a + i b:
√z = √r · [cos [(θ + 2π · k) / 2] + i sin [(θ + 2π · k) / 2]], for k = {0, 1}
Where:
r - Normθ - Direction, in radians.If we know that r = 2 and θ = π / 2, then the root of the complex number is:
k = 0
√z = √2 · [cos (π / 4) + i sin (π / 4)]
√z = 1 + i
k = 1
√z = √2 · [cos (5π / 4) + i sin (5π / 4)]
√z = - 1 - i
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Which question can best be answered by finding the volume of a figure
Finding the volume of a figure is a useful tool for solving practical problems that involve 3D space and quantities, such as capacity, mass, or density.
Finding the volume of a figure is a common mathematical calculation used in various fields, such as architecture, engineering, physics, and chemistry. The volume of a figure is a measure of the amount of space that it occupies in three-dimensional (3D) space, such as a cube, a cylinder, a sphere, or a complex shape.
One example of a question that can be answered by finding the volume of a figure is "How much water can a swimming pool hold?" The swimming pool is a 3D figure that can be approximated as a rectangular prism, with a length, width, and depth. By multiplying these three dimensions, we can find the volume of the swimming pool, which represents the amount of water it can hold. This information is useful for designing and constructing the swimming pool, as well as for filling and maintaining it.
Another example is "How much concrete is needed to build a retaining wall?" The retaining wall is a 3D figure that can be approximated as a trapezoidal prism, with a length, height, and thickness. By multiplying these three dimensions, we can find the volume of the retaining wall, which represents the amount of concrete required. This information is useful for estimating the cost and resources needed for the project.
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Which fractions are equivalent to 49
? Choose Yes or No for each fraction
For the given fraction, "Yes" for 8/18 and 12/27, and "No" for 20/36 and 24/45.
The first step in determining whether fractions are equivalent is to simplify them. This involves finding the greatest common factor (GCF) of the numerator and denominator, and dividing both by it. Simplifying fractions allows us to express them in their simplest form, making it easier to compare them to other fractions.
Let's start by simplifying the given fractions:
20/36 = 5/9
8/18 = 4/9
24/45 = 8/15
12/27 = 4/9
As we can see, two of the fractions simplify to 4/9, while the other two do not.
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10.A trader bought a screwdriver set for R90. He added 20% to the cost price for profit and expenses. Calculate the amount a customer will pay for the screwdriver set. 1000 (3) [9]
The customer will pay R108 for the screwdriver set.The trader bought a screwdriver set for R90 and added 20% to the cost price for profit and expenses. To calculate the amount a customer will pay for the screwdriver set, we need to add the profit and expenses to the cost price.
First, let's calculate the profit and expenses added by the trader. Since the trader added 20% to the cost price, the profit and expenses will be:
20% of R90 = 0.2 x R90 = R18
Now, we can calculate the selling price of the screwdriver set by adding the cost price and the profit and expenses:
Cost price = R90
Profit and expenses = R18
Selling price = Cost price + Profit and expenses = R90 + R18 = R108
Therefore, the customer will pay R108 for the screwdriver set.
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Philip claimed that the expression -p + 5 + p is positive for any value of p. Determine whether Philip's statement is always true, sometimes true, or never true. Provide evidence to support your conclusion
The expression is always positive Philip's statement is always true.
The expression -p + 5 + p can be written as -p + 5 + p = -p + p + 5,
which simplifies to 5, no matter what the value of p is.
An expression is a mathematical phrase that can contain numbers, variables, and operations such as addition, subtraction, multiplication, and division. Expressions may or may not have an equal sign. Expressions can be evaluated by replacing any variables with specific values and then simplifying the resulting expression using the order of operations.
Therefore, the expression is always positive and Philip's statement is correct.
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Edmund had $140. He spent 3 7 of his money on toys and 1 5 of his money on new clothes. How much money did Edmund spend altogether?
Edmund spent $63.50 on toys and $28 on new clothes, for a total cost of $91.50.
Edmund had $140 and he decided to spend some of that money on toys and some on new clothes. To calculate how much he spent altogether, we need to first figure out how much he spent on each item. For toys, he spent 3/7 of his total money, which is equal to $63.50. For new clothes, he spent 1/5 of his total money, which is equal to $28. Now that we know how much he spent on each item, we can add these two numbers together to figure out how much he spent altogether. When we add $63.50 and $28, we get a total of $91.50. This means that Edmund spent $91.50 on toys and new clothes altogether.
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