Answers
your answer is A
Related Questions
What number is 1/10 greater than 7962
Answers
just divide the number by 1/10
792.6
just divide the number by 1/10
cory earns 52.50 in 7 hours. find the unit rate
Answers
divide the two:
52.50 / 7 = 7.50 per hour
What is the meaning of the function of h = f(50, t)? describe the behavior of this function?
Answers
Suppose that h = f(x,t) = 2x - 1/t. This is my invention.
Then f(50,t) would come out as 2(50) - 1/t, which is a function of just 1 variable.
Matrix's van holds 14 gallons of gas and can be driven 25 miles per gallon. His next road trip is 1,050 miles away. How many times will his ban need to be filled up to make the trip?
Answers
On his next trip, he'll be driving it for 1050 miles, how many tanks is that?
well, how many times does (14*25) go into 1050? 1050/(14*25) that many.
Under what conditions can the t-distribution be correctly employed to test the difference between two population means?
Answers
Final answer:
The t-distribution is employed when testing the difference between two population means if the data come from a simple random sample and the population is approximately normally distributed or the sample size is large. It is also used when the population standard deviation is unknown, and a one-tailed or two-tailed test is conducted based on expectations about the direction of the mean difference.
Explanation:
Conditions for Using the t-Distribution to Test Differences Between Two Means
The t-distribution is appropriately used to test the difference between two population means under specific conditions. Firstly, your data must be obtained from a simple random sample. Secondly, the sample should come from a population that is approximately normally distributed, or the sample size should be large enough to compensate for non-normality. This is because the t-test relies on the assumption of normality, especially with smaller sample sizes (<30). If the sample size is small and the population distribution is unknown or not normal, the use of a t-test may not be appropriate without transformation or other techniques to meet the assumptions.
It is also essential to use the t-distribution when the population standard deviation is unknown, and as a result, the sample standard deviation is used as an estimate. Moreover, the t-test can adapt to various research scenarios, considering that it is designed to handle different levels of variability and data types. This flexibility makes the t-distribution a key tool for many scientific studies where the variance is not known ahead of time.
In hypothesis testing, the direction of the mean difference is considered, such as when conducting a one-tailed test or a two-tailed test. A one-tailed test is conducted when an expectation about the direction of the difference exists, while a two-tailed test is used to determine if there is any statistically significant difference between group means without a predefined direction. Lastly, when employing the t-test for paired data, the assumption is that the population from which the differences are drawn is normally distributed.
I need help with this question... phenobarbital elixir contains 2 grams in 1 liter of elixir. How many milligrams of phenobarbital are contained in 1 teaspoon of elixir?
Answers
Answer:
9.86 milligrams
Step-by-step explanation:
It is given that 1 liter f elixir contains 2 grams of phenobarbital elixir.
Since 202.884 teaspoons = 1 liter
so 1 teaspoon of elixir = [tex]\frac{1}{202.884}[/tex] liter
∵ 1 liter of elixir contains phenobarbital = 2 gms.
∴ [tex]\frac{1}{202.884}[/tex] liter of elixir contains phenobarbital = [tex]\frac{2*1}{202.884}[/tex] = 0.009858 grams
or 0.009858 × 10³ milligrams
= 9.86 milligrams.
Therefore, 9.86 milligrams of phenobarbital will be required.
Final answer:
The milligrams of phenobarbital in one teaspoon of elixir, multiply the milligrams per milliliter (2 mg/mL) by the volume of one teaspoon (5 mL), resulting in 10 milligrams per teaspoon.
Explanation:
The milligrams of phenobarbital in one teaspoon of elixir by first understanding the concentration of the solution and then using the volume conversion. Since 1 liter of the phenobarbital elixir contains 2 grams (2000 mg), we need to find out how many milligrams are contained in a smaller volume, specifically in one teaspoon, which is 5 milliliters. milligrams, so 2 grams = 2000 milligrams.
Next, consider the volume conversion: There are 1000 milliliters in 1 liter. So if 2000 mg is in 1000 milliliters, there would be 2 mg in 1 milliliter (since 2000 ÷ 1000 = 2).
Finally, since 1 teaspoon equals 5 milliliters, we multiply the amount of milligrams in 1 milliliter by 5.
Mathematically: 2 mg/mL * 5 mL = 10 mg
Therefore, there are 10 milligrams of phenobarbital in 1 teaspoon of elixir.
Kristina invests $5,000 at 15% simple interest for 2 years.How much interest did Kristina earn over the 2 years?
Answers
SI = PRT/100
=( 5000 × 15 × 2)/100
= 50×15×2= 1500$
Simplyfy (x - 5 / x^3 + 27) + (2 / x^2 - 9)
Answers
[tex]\bf \cfrac{x-5}{x^3+27}+\cfrac{2}{x^2-9}\implies \cfrac{x-5}{x^3+3^3}+\cfrac{2}{x^2-3^2} \\\\\\ \cfrac{x-5}{(x+3)(x^2-3x+3^2)}+\cfrac{2}{(x-3)(x+3)}\\\\\\ \cfrac{x-5}{(x+3)(x^2-3x+9)}+\cfrac{2}{(x-3)(x+3)} \\\\\\ \textit{so, we'll use the LCD of }(x-3)(x+3)(x^2-3x+9) \\\\\\ \cfrac{(x-3)(x-5)~~+~~(x^2-3x+9)2}{(x-3)(x+3)(x^2-3x+9)} \\\\\\ \cfrac{x^2-8x+15~~+~~2x^2-6x+18}{(x-3)(x+3)(x^2-3x+9)}\implies \cfrac{3x^2-14x+33}{(x-3)(x+3)(x^2-3x+9)}[/tex]
n=6x35+4 what does n represent in a division problem
Answers
At a speed of 45 yards per minute, a 120 pound swimmer burns 420 calories per hour and a 172 pound swimmer burns 600 calories per hour. write an equation that models the number of calories burned per hour as a function of the swimmer's weight.
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−4x−y+4 when x=−1/4 and y=3 .
Answers
1 - 3 + 4
-2 + 4
2
What is the area of 30 X 40 rectangle in square units
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this is because 30x40= 1,200.
The area of the given rectangle is 1200 square units.
Given that, width = 30 units and length = 40 units.
What is the area of a rectangle?The formula of the area of a rectangle is used to find the area occupied by the rectangle within its boundary. The area of a rectangle is obtained by multiplying its length and width. Thus, the formula for the area, 'A' of a rectangle whose length and width are 'l' and 'w' respectively is the product "l × w".
Now, the area of a rectangle = 40 × 30
= 1200 square units
Therefore, the area of the given rectangle is 1200 square units.
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Help with Precalc Vectors? Medal and fan v = (-7,8) Find the magnitude of vector v. Express your answer in radical form sqrt of 113 is what I got for that. second part: use the magnitude and the angle of vector v to write it in the form (lvlcostheta, lvl sin theta). I don't know how to determine the single angle for one vector. Earlier in a different part of the problem, I was asked to find the angle between two vectors, but I don't think you use that here since no second vector is provided. So how would I answer the second part? Thanks(:
Answers
Lets find the mag of v = (-7,8). Since we have one order pair we are finding the mag from the origin.
Yes we are using Pythagorean Theorem to calculate the magnitude
[tex]a^2 + b^2 = c^2[/tex]
[tex]\sqrt{v^2} = \sqrt{(-7)^2 + (8)^2}[/tex]
[tex]v = \sqrt{(-7)^2 + (8)^2}[/tex]
[tex]v = \sqrt{49 + 64}[/tex]
[tex]v = \sqrt{113}[/tex]
[tex]v = \sqrt{113} = 10.6301458[/tex]
Now we use
[tex]\theta = tan^{-1} (\frac{b}{a})[/tex]
[tex]\theta = tan^{-1} (\frac{8}{-7})= 48.8[/tex]
[tex](\sqrt{113} \times cos(48.8) , \sqrt{113} \times sin(48.8) )[/tex]
To express the vector v = (-7,8) in the form (|v|cosθ, |v|sinθ), you first correctly found the magnitude |v| using the Pythagorean theorem. Then, to find the angle θ, use the arctangent function applied to the y/x components of your vector. Ensure the angle is in the correct quadrant by modifying it if necessary.
Explanation:To find the magnitude of the vector v = (-7,8), you've correctly done the Pythagorean theorem and found sqrt(113), which is the absolute value of your vector, written as |v|. Now, to express the vector in the form (|v|cosθ, |v|sinθ), we need to find the angle θ. This is found using the arctangent function (also known as the inverse tangent or atan). θ = atan(y/x), where x and y are the x and y components of your vector respectively. Be careful with the sign as atan can only return values from -π/2 to π/2.
In your case θ = atan(8/-7), but since this gives a negative answer and the vector is in the second quadrant where angles are positive, you should add π to your result to get the correct angle. Then you can substitute |v| and θ into the expressions for the x and y components.
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√10, π, 3.5
order least to greatest
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3.14, 3.16, 3.5
___________________________________
" π , √10 , 3.5 " .
___________________________________
We have: "3.5" (given) ;
" π " = 3.14159...
"√10" = 3.162277660168379
___________________________________
So, from least to gretest, we have:
___________________________________
" π , √10 , 3.5 " .
___________________________________
then difference between the cubes of two numbers is twice the value of the perfect square of a possitive Intiger
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For example, the difference between 2² and 4² = 12, which is twice the number 6, which is √36
The difference between 2² and 6² = 32, which is twice the number 16, which is a perfect square.
So choose depending on your interpretation of the question... ;-)
Jasmine finished the bike trail in 2.5 hours at an average rate of 2.5 miles per hour.Lucy biked the same trail at a rate of 6 1/5 mile per hour.How long did it take lucy to bike the trail?
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2.5 hours at a rate of 2.5 miles per hour = 2.5 * 2.5 = 6.25 miles
the trail was 6.25 miles long
Lucy rode at 6 1/5 mile per hour
so 6.25 / 6 1/5 = 1.008 = 1.01 hours
Write twelve and sixteen thousand as a mixed decimal
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hope this helps
he bought 8 pizzas to be shared equally among 40 people. what is the equivalent representation
Answers
If the test for a disease is accurate 65% of the time, how often will it come back positive if a patient doesn't have the disease?
Answers
Answer:
35% of the time
Step-by-step explanation:
A P E X
two pounds of peaches cost 4.50 5 pounds cost 11.25and 10 pounds cost 22.50 what is the constant of proportionality
Answers
4.50 /2 = 2.25
11.25/5 = 2.25
22.50/10 = 2.25
the constant is the price per pound which is 2.25
Answer:
c
Step-by-step explanation:
What are 5 numbers that have 3,5, and 7 as prime factors
Answers
What two consecutive whole numbers that square root of 86 lies between
Answers
sqrt(86) = 9.273
which is between 9 & 10
What is the area of a triangle with verticies at (-2,1), (2,1) and (3,4)
Answers
notice, is just a triangle with a base of 4, and an altitude of 3.
Describe the set of all points p(x,y) in a coordinate plane that satisfy the given condition
Answers
The line x = -2 is a vertical line passing through point (-2, 0) on the x axis.
The set of points satisfying x = -2 are all the points on the coordinate plane which lies on the vertical line crossing point -2 on the x-axis.
Part B:
The line y = 5 is a horizontal line passing through point (0, 5) on the y axis.
The set of points satisfying y = 5 are all the points on the coordinate plane which lies on the horizontal line crossing point 5 on the y-axis.
Part C:
The line x = 0 is the y axis.
The set of points satisfying x ≥ 0 are all the points on the coordinate plane to the right of the y-axis.
Part D:
The set of points satisfying xy > 0 are all the points on the coordinate plane which lies on the 1st quadrant and all the points on the coordinate plane which lies on the 3rd quadrant.
Part E:
The line y = 0 is the x axis.
The set of points satisfying y < 0 are all the points on the coordinate plane that are below the x-axis.
Part F:
The line x = 0 is the y axis.
The set of points satisfying x = 0 are all the points on the coordinate plane that lie on the y-axis.
Part G:
The line y = -2 is a horizontal line passing through point (0, -2) on the x axis.
The set of points satisfying y = -2 are all the points on the coordinate plane which lies on the horizontal line crossing point -2 on the y-axis.
Part H:
The line x = 4 is a vertical line passing through point (4, 0) on the x axis.
The set of points satisfying x = 4 are all the points on the coordinate plane which lies on the vertical line crossing point 4 on the x-axis.
Part I:
The set of points satisfying x / y < 0 are all the points on the coordinate plane which lies on the 2nd quadrant and all the points on the coordinate plane which lies on the 4th quadrant.
Part J:
The line xy = 0 are the x-axis and the y-axis.
Therefore, the set of points satisfying xy = 0 are all the points on the coordinate plane which lies on the x-axis and all the points on the coordinate plane which lies on the y-axis.
Part K:
The line y = 1 is a horizontal line passing through point (0, 1) on the y axis.
The set of points satisfying y > 1 are all the points on the coordinate plane which lies above the horizontal line crossing point 1 on the y-axis.
Part L:
The line y = 0 is the x axis.
The set of points satisfying y = 0 are all the points on the coordinate plane that lie on the x-axis.
The set of all points p(x,y) in a coordinate plane that satisfy the given condition refers to the graph that represents the change of y as a function of x.
Explanation:In a rectangular (Cartesian) xy-coordinate system, a point in a plane is described by a pair of coordinates (x, y). The set of all points p(x,y) that satisfy the given condition refers to the plotted or sketched graph that represents the change of y as a function of x. Using the given table of points (1,5), (2,10), (3,7), and (4,14), we can plot these points on a graph and connect them to see how y values change with different x values.
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Find the gradient of the function at the given point. function point f(x, y, z) = x2 + y2 + z2 (3, 9, 8)
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Answer:
[tex]\displaystyle \nabla f(3, 9, 8) = 6 \hat{\i} + 18 \hat{\j} + 16 \hat{\text{k}}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Rule [Basic Power Rule]:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Multivariable Calculus
Differentiation
Partial DerivativesDerivative NotationGradient: [tex]\displaystyle \nabla f(x, y, z) = \frac{\partial f}{\partial x} \hat{\i} + \frac{\partial f}{\partial y} \hat{\j} + \frac{\partial f}{\partial z} \hat{\text{k}}[/tex]
Gradient Property [Addition/Subtraction]: [tex]\displaystyle \nabla \big[ f(x) + g(x) \big] = \nabla f(x) + \nabla g(x)[/tex]
Gradient Property [Multiplied Constant]: [tex]\displaystyle \nabla \big[ \alpha f(x) \big] = \alpha \nabla f(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle f(x, y, z) = x^2 + y^2 + z^2[/tex]
[tex]\displaystyle P(3, 9, 8)[/tex]
Step 2: Find Gradient
[Function] Differentiate [Gradient]: [tex]\displaystyle \nabla f = \frac{\partial}{\partial x} \Big( x^2 + y^2 + z^2 \Big) \hat{\i} + \frac{\partial}{\partial y} \Big( x^2 + y^2 + z^2 \Big) \hat{\j} + \frac{\partial}{\partial z} \Big( x^2 + y^2 + z^2 \Big) \hat{\text{k}}[/tex][Gradient] Rewrite [Gradient Property - Addition/Subtraction]: [tex]\displaystyle \nabla f = \bigg[ \frac{\partial}{\partial x}(x^2) + \frac{\partial}{\partial x}(y^2) + \frac{\partial}{\partial x}(z^2) \bigg] \hat{\i} + \bigg[ \frac{\partial}{\partial y}(x^2) + \frac{\partial}{\partial y}(y^2) + \frac{\partial}{\partial y}(z^2) \bigg] \hat{\j} + \bigg[ \frac{\partial}{\partial z}(x^2) + \frac{\partial}{\partial z}(y^2) + \frac{\partial}{\partial z}(z^2) \bigg] \hat{\text{k}}[/tex][Gradient] Differentiate [Derivative Rule - Basic Power Rule]: [tex]\displaystyle \nabla f = 2x \hat{\i} + 2y \hat{\j} + 2z \hat{\text{k}}[/tex][Gradient] Substitute in point: [tex]\displaystyle \nabla f(3, 9, 8) = 2(3) \hat{\i} + 2(9) \hat{\j} + 2(8) \hat{\text{k}}[/tex][Gradient] Evaluate: [tex]\displaystyle \nabla f(3, 9, 8) = 6 \hat{\i} + 18 \hat{\j} + 16 \hat{\text{k}}[/tex]∴ the gradient of the function at the given point is <6, 18, 16>.
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Topic: Multivariable Calculus
Unit: Directional Derivatives
Which expression is equivalent to 18a+12b+9a+24b ?
Answer Choices
* 63ab
* 30a+33b
* 27a+36b
* 21a+42b
Answers
27a+36b, Because 18a+9a=27a 12b+24b=36b,so the correct answer is 27a+36b.
The correct expression is equivalent to 18a+12b+9a+24b is,
⇒ 27a + 36b
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 18a + 12b + 9a + 24b
Now, We can simplify as;
⇒ 18a + 12b + 9a + 24b
⇒ 18a + 9a + 12b + 24b
⇒ 27a + 36b
Thus, The correct expression is equivalent to 18a+12b+9a+24b is,
⇒ 27a + 36b
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what 3 digits are in the units period?
Answers
When the expression -5x^2+20x-17 is written in the form $a(x+d)^2+e$, where a, d, and e are constants, then what is the sum a+d+e?
PLEEEASE HELP
Answers
-5x^2+20x-17
=-5(x^2-4x)-17
=(-5(x-2)^2+20) -17
=-5(x-2)^2+3
So a=-5, d=-2, e=+3
a+d+e=-5-2+3=-4
equivalent ratios number 1 to 50
Answers
Which of the following symbols correctly completes this comparison? 5 + 10 + 13 ? 13 + 10 + 5 = < > ≠
Answers
The correct symbol to complete the expression is,
⇒ 5 + 10 + 13 = 13 + 10 + 5
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The expression is,
⇒ 5 + 10 + 13 ? 13 + 10 + 5
Now,
Since, The expression is,
⇒ 5 + 10 + 13 ? 13 + 10 + 5
From LHS;
⇒ 5 + 10 + 13 = 28
From RHS;
⇒ 13 + 10 + 5 = 28
So, We get;
The correct symbol to use is,
⇒ 5 + 10 + 13 = 13 + 10 + 5
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