Answers
7. 13.2 m
8. 44 in
9. 50.3 cm
Related Questions
Solve the equation -2/3d - 1/4d = -22 for d.
Answers
Answer:
d=24
Step-by-step explanation:
create a common denominator of 12
\(\frac{-2}{3}\)d-\(\frac{1}{4}\)d=\(\frac{-22}{1}\)
\(\frac{-2}{3}\)*4 \(\frac{1}{4}\)*3 \(\frac{-22}{1}\)*12
\(\frac{-8}{12}\)d - \(\frac{3}{12}\)d = \(\frac{-264}{12}\)
\(\frac{-11}{12}\)d=\(\frac{-264}{12}\)
multiple each side by reciprocal (\(\frac{12}{-11}\)) and simplify
d=24
The value of d from the given equation is 24.
The given equation is \(-\frac{2}{3}d - \frac{1}{4}d=-22\).
We need to solve the given equation for d.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation can be solved for d as follows:
Take LCM of denominators
LCM of denominators 3 and 4 is 12
Now equate denominators to LCM, that is
\(d(-\frac{2}{3} - \frac{1}{4})=-22\)
⇒ \(d(-\frac{8}{12} - \frac{3}{12})=-22\)
⇒ \(d(\frac{-8-3}{12} )=-22\)
⇒ \(d(\frac{-11}{12} )=-22\)
⇒ d=24
Therefore, the value of d from the given equation is 24.
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calculate vred, the speed of red light in the diamond. to four significant figures, c=2.998×108m/s.
Answers
The speed of red light in a diamond, denoted as vred, is approximately equal to the speed of light in a vacuum, c, which is 2.998 × 10^8 m/s, rounded to four significant figures.
According to the principles of optics and the refractive index of a material, the speed of light in a medium is generally lower than its speed in a vacuum. The refractive index of a diamond is approximately 2.42.
To calculate the speed of red light in a diamond, we can use the formula vred = c / n, where c represents the speed of light in a vacuum and n represents the refractive index of the diamond.
Substituting the given values, we have vred = (2.998 × 10^8 m/s) / 2.42. Evaluating this expression yields a result of approximately 1.239 × 10^8 m/s.
Rounding this value to four significant figures, we obtain the speed of red light in a diamond, vred, as approximately 1.239 × 10^8 m/s.
Therefore, the speed of red light in a diamond, rounded to four significant figures, is approximately 1.239 × 10^8 m/s, which is slightly lower than the speed of light in a vacuum, c.
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When you see two equations exactly the same, how many answers will there be in the system of equations?
Answers
Answer:
infinite number of solutions
Step-by-step explanation:
If both sides of an equation are exactly the same.
then any value of the variable will make the equation true.
Thus there is an infinite number of solutions
If y − 3 = 3x, which of the following sets represents possible inputs and outputs of the function, represented as ordered pairs?
{(0, 3), (1, 6), (2, 9)}
{(3, 0), (6, 1), (9, 2)}
{(1, 3), (2, 6), (3, 9)}
{(3, 1), (6, 2), (9, 3)}
Answers
Answer:
A. {(0, 3), (1, 6), (2, 9)}Step-by-step explanation:
Rewrite the function in the slope-intercept form:
y - 3 = 3xy = 3x + 3The ordered pairs:
x = 0 ⇒ y = 3 ⇒ (0, 3)x = 1 ⇒ y = 6 ⇒ (1, 6)x = 2⇒ y = 9 ⇒ (2, 9)x = 3 ⇒ y = 12 ⇒ (3, 12)Correct set is A
{(3,0),(6,1),(9,2)}
because when you plug in the values you get
3-3=3(0) = 0=0
6-3=3(1) = 3=3
9-3=3(2) = 6=6
how to determine if a linear transformation is an isomorphism
Answers
Therefore, to determine if a linear transformation is an isomorphism, we can check if the determinant is non-zero or if the kernel is only the zero vector.
An isomorphism is a bijective linear transformation, that is both one-to-one and onto. The determinant of a linear transformation can help determine if it is an isomorphism. If the determinant is non-zero, the linear transformation is invertible, and therefore an isomorphism. A linear transformation is an isomorphism if and only if its determinant is nonzero.
Additionally, another way to check if a linear transformation is an isomorphism is to check if the kernel, which is the set of all vectors that get mapped to zero, is equal to only the zero vector. If the kernel is only the zero vector, then the linear transformation is one-to-one and therefore an isomorphism.
Therefore, to determine if a linear transformation is an isomorphism, we can check if the determinant is non-zero or if the kernel is only the zero vector.
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Solve for x:
-3x +5 = 17
Answers
Answer:
x=-4
Step-by-step explanation:
-3x +5 = 17
-3x+5-5=17-5
-3x=12
-3x/3 = 12/-3
x=-4
6.
Write the linear inequality shown in the graph. The gray area represents the shaded region.
A. y ≥ –3x + 4
B. y ≥ –3x – 4
C. y ≤ –3x – 4
D. y ≤ –3x + 4
Answers
Answer:
D. y ≤ –3x + 4
Step-by-step explanation:
IfA={1,2,3,4} B={2,4,6} C={1,3,5,7} andU={1,2,3,4,5,6,7} then B−C
Answers
Answer:
\(B-C=\{2,4,6\}\)
Step-by-step explanation:
We are given the following sets:
\(A=\{1,2,3,4\}\\ B=\{2,4,6\}\\ C=\{1,3,5,7\}\\ and\\U=\{1,2,3,4,5,6,7\}\)
To find: \(B-C = ?\)
Solution:
Here, we are given 4 sets,
The universal set, U and its 3 proper subsets A,B and C.
Proper subsets are the subsets which have at least one element which is extra in the super set.
Now, let us have a look at the definition of 'minus' in terms of sets.
Minus is defined as the set of elements which contains the elements of first set which are not present in the other set.
OR
The common elements are not written.
For example:
P = {10,20,30}
Q = {10,40,70}
P - Q = {20,30}
Common element(s) of P \(\cap\) Q = {10} is/are not written in P-Q.
Here, there are no common elements in B and C.
\(\therefore B-C = B\)
OR
\(B-C=\{2,4,6\}\) is the correct answer.
Simplify:3^0-3^4x3^-5
Answers
Answer:
\(3 {}^{0} - 3 {}^{4} \times 3 {}^{ - 5} \)
\( = 1 - 3 {}^{ - 1} \)
\( = 1 - \frac{1}{3} \)
\( = \frac{2}{3} \)
round to the nearest tenth
Answers
Volume of sphere = 4/3*pi*r^3
Let the radius and height be 2
Cylinder = pi * 2^2 * 2 = 8pi = 25.1
Volume = 4/3 * pi * 2^3 = 32/3pi = 33.5
33.5 / 25.1 = 1.33
32/3 pi / 8 pi = 4/3
Four thirds of the cylinder’s volume is the sphere’s volume
Question 2 (2 points)A triangle has vertices at F(8,3), G (3,5), and H (1,7). What are the coordinates of each vertex if the triangle isrotated 180° about the origin counterclockwise?OF"-8, 3), G'(-3,5), F'(-1,7)OF"(8,3), G(-3,5), H'(-1, -7)OF"(8.–3), G:(3,-5), H' (1, -1)OF"(-8, -3), G'(-3,-5), H (-1, -7)
Answers
You have the following points that form a triangle in the coordinate system:
F(8,3)
G (3,5)
H (1,7)
If the traingle is rotated by 180° around the origin of coordinates you have:
F'(-8,-3)
G'(-3,-5)
H'(-1,-7)
without importance of the sense of the rotation, if it is 180°, each coordinate of each point will have the opposite sign bu the same coefficient.
find the $1314^{\text{th}}$ digit past the decimal point in the decimal expansion of $\dfrac{5}{14}$.
Answers
The $1314^\text{th}$ digit past the decimal point is 2.
To find the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$, we can use long division to compute the decimal expansion of the fraction.
The long division of $\frac{5}{14}$ is as follows:
```
0.35 <-- Quotient
-----
14 | 5.00
4.2 <-- Subtract: 5 - (14 * 0.3)
-----
80 <-- Bring down the 0
70 <-- Subtract: 80 - (14 * 5)
-----
100 <-- Bring down the 0
98 <-- Subtract: 100 - (14 * 7)
-----
20 <-- Bring down the 0
14 <-- Subtract: 20 - (14 * 1)
-----
60 <-- Bring down the 0
56 <-- Subtract: 60 - (14 * 4)
-----
40 <-- Bring down the 0
28 <-- Subtract: 40 - (14 * 2)
-----
120 <-- Bring down the 0
112 <-- Subtract: 120 - (14 * 8)
-----
80 <-- Bring down the 0
70 <-- Subtract: 80 - (14 * 5)
-----
...
```
We can see that the decimal expansion of $\frac{5}{14}$ is a repeating decimal pattern with a repeating block of digits 285714. Therefore, the $1314^\text{th}$ digit past the decimal point is the same as the $1314 \mod 6 = 0^\text{th}$ digit in the repeating block.
Since $1314 \mod 6 = 0$, the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$ is the first digit of the repeating block, which is 2.
So, the $1314^\text{th}$ digit past the decimal point is 2.
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a background count of 600 was recorded during a 30-minute counting time. how long should a sample be counted in order to have a 5% precision for the net counting rate, if the gross count rate is about 2000 cpm?
Answers
Answer: t ≈ 2,403,603
Step-by-step explanation:
z = the z-score associated with the desired level of confidence (for a 5% precision, z = 1.96)
σ = the standard deviation of the background count rate (which is equal to the square root of the background count rate)
E = the desired level of precision (in this case, 5% or 0.05)
Substituting the given values, we get:
σ = sqrt(600) = 24.49
t = (1.96 * 24.49 / 0.05)^2
100 g of fish cost 70¢.
€
(a) Calculate the cost of 180 g.
(b) Mr Tan paid $2.45 for some fish. How
many grams of fish did he buy?
Answers
Answer:
a) 100/70 = 1.43 cents for 1 g of fish
180 x 1.43 = 257.4 pennies = 2.57 dollars
b) 2.45 dollars = 245 pennies
245/1.43 = 141.33.... = 141 g
Step-by-step explanation:
T/F : Span{a1,a2} contains only the line through a1 and the origin, and the line through the a2 and the origin.
Answers
False.
The span of {a1, a2} is the set of all linear combinations of a1 and a2. A linear combination of two vectors is of the form c1a1 + c2a2, where c1 and c2 are constants.
The span of {a1, a2} is the set of all linear combinations of a1 and a2. A linear combination of two vectors is of the form c1a1 + c2a2, where c1 and c2 are constants.
If a1 and a2 are linearly independent, then the span of {a1, a2} is the plane that contains a1 and a2. If a1 and a2 are linearly dependent, then the span of {a1, a2} is the line that contains a1 and a2.
So, in general, the span of {a1, a2} does not contain only the line through a1 and the origin, and the line through a2 and the origin. It can be a line, a plane, or all of R^3, depending on whether a1 and a2 are linearly dependent or independent.
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The sides of a triangle are 14, 11, and 19. Use the Pythagorean Theorem to determine if the triangle is right, acute, or obtuse.
Answers
Answer:
Pythagorean's theorem is a²+b²=c² with c being the longest sides. If it is true then it is a right triangle.
14^2+11^2=19^2
196+121=361
This is true so the triangle is a right triangle
Solve the following Linear Programming Problem by Graphical Method:
Max z = 15x1 + 20 xz x₁ + 4x₂ ≥ 12 x₁ + x₂ ≤ 6 s.t., and x₁, x₂ ≥ 0
Answers
The solution to the linear programming problem is:
Maximum value of z = 120
x₁ = 0, x₂ = 6
To solve the given linear programming problem using the graphical method, we first need to plot the feasible region determined by the constraints and then identify the optimal solution.
The constraints are:
x₁ + x₂ ≥ 12
x₁ + x₂ ≤ 6
x₁, x₂ ≥ 0
Let's plot these constraints on a graph:
The line x₁ + x₂ = 12:
Plotting this line on the graph, we find that it passes through the points (12, 0) and (0, 12). Shade the region above this line.
The line x₁ + x₂ = 6:
Plotting this line on the graph, we find that it passes through the points (6, 0) and (0, 6). Shade the region below this line.
The x-axis (x₁ ≥ 0) and y-axis (x₂ ≥ 0):
Shade the region in the first quadrant of the graph.
The feasible region is the overlapping shaded region determined by all the constraints.
Next, we need to find the corner points of the feasible region by finding the intersection points of the lines. In this case, the corner points are (6, 0), (4, 2), (0, 6), and (0, 0).
Now, we evaluate the objective function z = 15x₁ + 20x₂ at each corner point:
For (6, 0): z = 15(6) + 20(0) = 90
For (4, 2): z = 15(4) + 20(2) = 100
For (0, 6): z = 15(0) + 20(6) = 120
For (0, 0): z = 15(0) + 20(0) = 0
From the evaluations, we can see that the maximum value of z is 120, which occurs at the corner point (0, 6).
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When a basketball was dropped from a height of 100 inches and left to rebound over time, it bounces back to a height that is 4/7
determine the height in inches after 5 bounces. round your answer correct to the tenths decimal place
a. 10 inches
b. 6.1 inches
c. 5.6 inches
d. 30 inches
Answers
The correct answer is option (b) 6.1 inches, which is the closest rounded value to the calculated height.
To determine the height in inches after 5 bounces, we need to calculate the successive heights of each bounce. Since the basketball rebounds to a height that is 4/7 (or approximately 0.5714) of the previous height, we can use this ratio to find the height after each bounce.
Starting with the initial height of 100 inches, we can calculate the height after each bounce as follows:
1st bounce: 100 inches * 4/7 = 57.14 inches
2nd bounce: 57.14 inches * 4/7 = 32.49 inches
3rd bounce: 32.49 inches * 4/7 = 18.56 inches
4th bounce: 18.56 inches * 4/7 = 10.54 inches
5th bounce: 10.54 inches * 4/7 = 6.01 inches
Therefore, after 5 bounces, the height of the basketball would be approximately 6.01 inches. The correct answer is option (b) 6.1 inches, which is the closest rounded value to the calculated height.
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what is the answer to the picture the two answers on there
Answers
In the expression given as -5 - (-7) = -5 + x, the value of x is 7.
What is the value of the expression?In Mathematics, expression simply means the mathematical statements which have at least two terms which are then related by an operator. It should be noted that they illustrate the relationship between the data given.
In this situation, it should be noted that the expression is given as:
-5 - (-7) = -5 + x
Collect like terms
-5 + 7 = -5 + x
x = -5 + 5 + 7
x = 7
The value of x is 7.
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researchers are investigating whether taking aspirin regularly reduces the risk of heart attacks. four hundred men participate in the study. the men are divided randomly into two groups: one group takes aspirin pills, and the other group takes placebo pills (a pill with no aspirin in it). the men each take one pill a day, and they do not know which group they are in. at the end of the study, researchers will count the number of men in each group who have had heart attacks. identify the explanatory and response variables in this situation.
Answers
Explanatory variable: The type of pill the men took each day.
Response variable: Whether a subject had a heart attack.
We have been given that :
Participated candidates are 400
Men are divided randomly so we find out explanatory and response variable.
The explanatory variable is the variable that is manipulated by the researcher. Explanatory Variable also known as the independent or predictor variable, it explains variations in the response variable; in an experimental study, it is manipulated by the researcher.
Response variable: Response Variable is the result of the experiment where the explanatory variable is manipulated. It is a factor whose variation is explained by the other factors. Response Variable is often referred to as the Dependent Variable or the Outcome Variable.
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Help ASAP
Which of these cylinders has the same volume as one with a radius of 4 ft and a height of 9 ft?
Select one:
a cylinder with a radius of 9 ft and a height of 16 ft
a cylinder with a radius of 3 ft and a height of 4 ft
a cylinder with a radius of 3 ft and a height of 16 ft
a cylinder with a radius of 9 ft and a height of 4 ft
Answers
A cylinder with a radius of 3 ft and a height of 4 ft has the same volume as one with a radius of 4 ft and a height of 9 ft.
Explain about the cylinders:We can determine how much interior room a cylinder has by measuring its volume. The volume would be the same as how much material would fill the full can if you had one.
Volume of cylinder = π*r²*h
r is the radius and h is the height.
For given cylinder:
r = 4 ft and h = 9 ft
Volume of given cylinder = π*4²*9
Volume of given cylinder = 144π cu. ft.
Now, from the options:
As, its is clear from formula of cylinder that there is a square of radius.
Thus,
take radius r = 3 ft such that r² = 9 ft and height h = 4 ft.
These are the same dimensions as the given cylinder.
Thus, a cylinder with a radius of 3 ft and a height of 4 ft has the same volume as one with a radius of 4 ft and a height of 9 ft.
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The average temperature of a week is 33o C. Average of first three days is 30o C while of the last three is 35o C. What is the temperature of the fourth day?
Answers
Answer:
34 degrees C
Step-by-step explanation:
30+30+30+35+35+35+34=229
229/7=32.714
and when you round up you get 33
Write a question that represents the following equation.
22-7= 15
Answers
Answer:
15 + 7= 22
Step-by-step explanation:
Can you combine like terms if one coefficient has a variable of x and the second coefficient has a variable of xy?
Answers
Answer: No, because in order for two or more numbers to combine, both or all of them need to have the same variables, or else they are not like terms and you cannot combine them.
Step-by-step explanation:
hope it helped!!!
a triangle has sides with lengths of 6 kilometers, 7 kilometers, and 10 kilometers. is it a right triangle?
Answers
Answer:
Step-by-step explanation:
no because 6 , 7 and 10 doesn't add up to 180 so it is not
A triangle has sides with lengths of 6 kilometers, 7 kilometers, and 10 kilometers is not a right triangle.
To determine if a triangle is a right triangle, you can use the Pythagorean Theorem. The Pythagorean Theorem states that "In a right-angled triangle, the sum of the square of the two shorter sides is equal to the square of the longest side." It can be written as:
a² + b² = c², where 'a' and 'b' are the lengths of the two legs of a right triangle, and 'c' is the length of the hypotenuse.
In this triangle, the two shorter sides have lengths of 6 kilometers and 7 kilometers and the longest side is 10 kilometers.
The square of 6 kilometers is 36 kilometers and the square of 7 kilometers is 49 kilometers.
The sum of 36 kilometers and 49 kilometers is 85 kilometers.
The longest side of the triangle has a length of 10 kilometers, and the square of 10 kilometers is 100 kilometers.
Since 85 kilometers is not equal to 100 kilometers, this triangle is not a right triangle.
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x-4y=-2
Determine if the given ordered pair, (2, 1), satisfies the given equation.
O YES
O NO
Answers
Answer:
Yes.
Step-by-step explanation:
Replace x with 2 and y with 1 and see if the equation is true
x - 4y = -2
2 - 4(1) = -2
2 - 4 = -2
-2 = -2
The statement is true so the point is on the line.
please please please help asap!! will mark brainlest
Select Is a Function or is not a Function to correctly classify each relation.
Answers
Answer:
1 yes
2 yes
3 yes
4no
Step-by-step explanation:
for every x value you should have a unique y value
the chemical ________ can be used to trace the paths of afferent axons.
Answers
The chemical tracer commonly used to trace the paths of afferent axons is called "biocytin."
Afferent nerve fibers are axons (nerve fibers) of sensory neurons that carry sensory information from sensory receptors to the central nervous system. Many afferent projections arrive at a particular brain region. Afferent nerve fiber.
The chemical tracer commonly used to trace the paths of afferent axons is called "biocytin." Biocytin is a modified form of biotin that can be taken up by neurons and transported along their axons. It is often injected into a specific region of interest and allowed to diffuse throughout the neural tissue. Afferent axons originating from the injected area can then take up and transport the biocytin, allowing researchers to visualize and study their pathways using various histological techniques, such as immunohistochemistry or avidin-biotin complex staining.
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Let f(x) = ax3 . Calculate f(x+h)−f(x) h for h 6= 0. After you obtain your answer, evaluate it again by setting h = 0.
Answers
To calculate \(\frac{{f(x+h) - f(x)}}{h}\) for the function \(f(x) = ax^3\), we need to substitute the expressions into the formula and simplify.
\(f(x+h) = a(x+h)^3\\\\f(x) = ax^3\)
Now we can calculate the difference:
\(f(x+h) - f(x) = a(x+h)^3 - ax^3\)
Expanding \((x+h)^3\):
\(f(x+h) - f(x) = a(x^3 + 3x^2h + 3xh^2 + h^3) - ax^3\)
Simplifying:
\(f(x+h) - f(x) = ax^3 + 3ax^2h + 3axh^2 + ah^3 - ax^3\)
The terms \(ax^3\) cancel out:
\(f(x+h) - f(x) = 3ax^2h + 3axh^2 + ah^3\)
Now we can divide by h:
\(\frac{{f(x+h) - f(x)}}{h} = \frac{{3ax^2h + 3axh^2 + ah^3}}{h}\)
Canceling out the common factor of h:
\(\frac{{f(x+h) - f(x)}}{h} = 3ax^2 + 3axh + ah^2\)
Now, we evaluate this expression again by setting h = 0:
\(\frac{{f(x+h) - f(x)}}{h} = 3ax^2 + 3ax(0) + a(0)^2\)
\(= 3ax^2\)
Therefore, when we evaluate the expression by setting h = 0, we get \(3ax^2\).
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need the steps and anwser to make sure i’m on the right track!
Answers
Answer:
If it's parallel it has to have the same slope
y=-3x-3
The second number is the y intercept. If you enter the x value 1 in the equation and get -6 then the y intercept is correct lets say you have
y=-3x
if you enter 1 you get y = -3
what plus -3 is -6? -3. the y intercept is -3.
Hope its correct and it helps
Step-by-step explanation: