To turn a number into scientific notation, move the decimal point so that there is only 1 number to the left of the decimal point.
Count the number of spaces you moved the decimal point.
If you move the decimal point to the right, the exponent is negative, if you move it to the left the exponent is positive.
0.000075
You need to move the decimal point 5 places to the right to get 7.5
Because it was moved to the right, the exponent is negative 5
The answer would be 7.5 x 10^-5 which is B.
The scientific notation of 0.000075 is 7.5 x [tex]10^{-5[/tex]. This is because in converting to scientific notation, the goal is to have a number >=1 but <10 multiplied by 10 raised to an exponent. In this case, the decimal was moved 5 places to the right to result in a number <10.
Explanation:In mathematics, scientific notation is used to express very large or very small numbers in a simpler way by using powers of ten. In this case, you're trying to represent the number 0.000075. To do this accurately in scientific notation, we would write it as 7.5 x [tex]10^{-5[/tex]. This is because the exponent of the 10 represents how many places the decimal point was moved to convert the number to a new form where a number greater than or equal to 1 but less than 10 is multiplied by 10 raised to an exponent.
In the case of option D - 75 x [tex]10^{-6[/tex], it's suggesting we moved the decimal place 6 places to the right to a number that's >= 10, which is incorrect. The decimal is moved 5 places to the right to get a number that's less than 10. Thus, the correct answer is B - 7.5 x [tex]10^{-5[/tex].
Learn more about Scientific Notation here:https://brainly.com/question/16936662
#SPJ3
I need help with a calculus 2 exercise, with a good explanation to what I'm trying to figure out.
The problem involves finding the arc length when y = (x^2)/2 - (lnx/4) given 2≤ x ≤ 4
So I know the formula involves L = Integral from a to b of sqrt(1+(f'(x))^2)dx
And I took the the derivative of y = (x^2)/2 - (lnx/4)
And got = x - (1/4x)
I then kept reducing it to suit the formula
1 + ( x - 1/4x)^2
I added the alike terms
1 + x^2 - 1/2 + 1/16x^2
x^2 + 1/2 + 1/16x^2
AND then comes my question!
So it is supposed to become this afterwards: (x + 1/4x) ^ 2
But how did that happen, I don't understand how I can reduce it to a square, please help me figure it out.
When writing rational expressions, you need to be aware that ...
1/4x = (1/4)x ≠ 1/(4x)
Parentheses around the denominator are required, unless you're typesetting the expression and can use a fraction bar for grouping.
The derivative of the curve expression is ...
y' = x - 1/(4x) . . . . . parentheses added to what you wrote
and the expression (1 -(y')^2) can be written ...
1 -(y')^2 = x^2 +1/2 +1/(16x^2) . . . . . parentheses added to what you wrote
The first and last terms of this trinomial are both perfect squares, so you might suspect the whole trinomial is a perfect square. You recall that ...
(a +b)^2 = a^2 + 2ab + b^2
This is a good "pattern" to remember. Using it is a matter of pattern recognition, as is the case with a lot of math.
Here, you have ...
a = x
b = 1/(4x)
In order for your trinomial to be a perfect square, the product 2ab must equal the middle term of your trinomial. (Spoiler: it does.)
2ab = 2(x)(1/(4x)) = (2x)/(4x) = 1/2 . . . . . matches the middle term of 1 -(y')^2
Hence your trinomial can be written as the square ...
1 -(y')^2 = (x +1/(4x))^2
_____
This is convenient because you want to integrate the square root of this. Your integral then becomes ...
[tex]\displaystyle\int\limits_{2}^{4}{\left(x+\frac{1}{4x}\right)\,dx[/tex]
Find the value of x....
Answer:
x = 7.5
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that the relationship between the angle and the sides of interest is ...
Tan = Opposite/Adjacent
tan(37°) = x/10 . . . . fill in given values
Multiplying by 10, we get ...
x = 10·tan(37°) ≈ 7.5
5x-3y=18
3x+3y=30
Please help
Solve for x in 5x - 3y = 18
x = 3(6 + y)/5
Substitute x = 3(6 + y)/5 into 3x + 3y = 30
9(6 + y)/5 + 3y = 30
Solve for y in 9(6 + y)/5 + 3y = 30
y = 4
Substitute y = 4 into x = 3(6 + y)/5
x = 6
Therefore,
x = 6
y = 4
The solution to the system of equations is x = 6 and y = 4.
Step 1: Add the two equations.
5x - 3y = 18
3x + 3y = 30
8x = 48
Step 2: Solve for x.
8x = 48
x = 6
Step 3: Substitute x = 6 into one of the original equations to solve for y.
5(6) - 3y = 18
30 - 3y = 18
-3y = -12
y = 4
Grace and her brother Sid want to raise money to go to band camp. Their parents have agreed to help them earn up to $400 by paying them $25 when one of them mows the lawn and $10 for each hour that one of them babysits their younger brother. They will have to do a combination of both chores in order to earn the money. Select the equation that represents the number of lawns they can mow, m, and hours they can babysit, b, to earn $400.
Answer:
25m + 10b = 400
Step-by-step explanation:
Total amount that can be earned = $ 400
Amount earned on mowing a lawn = $ 25
Amount earned per hour on babysitting = $10
Amount earned for mowing one lawn is $ 25, so amount earned for mowing m lawns will be $ 25m
Amount earned for one hour of babysitting is $ 10, so amount earned for babysitting for b hours will be $ 10b
Total amount earned = Amount earned from mowing m lawns + Amount earned from babysitting for b hours
Using the values from above, we can set up the equation as:
400 = 25m + 10b
or
25m + 10b = 400
This equation represents the number of lawns they can mow, m, and hours they can babysit, b, to earn $400.
One hundred people were surveyed about their favorite kind of yogurt. How many more people prefer chocolate than vanilla?
(vanilla- 25%)
(swirl-35%)
(chocolate- 40%)
a. 10
b. 15
c. 25
d. 40
Answer:
b) 15
Step-by-step explanation:
Given that,
Total people = 100
% of people prefer vanilla = 25%
Number of people prefer vanilla out of 100 = 25% of 100
=> 25/100 * 100 = 25
% of people prefer swirl = 35%
Number of people prefer swirl out of 100 = 35% of 100
=> 35/100 * 100 = 35
% of people prefer chocolate = 40%
Number of people prefer chocolate out of 100 = 40% of 100
=> 40/100 * 100 = 40
The number of more people preferring chocolate over vanilla = 40 - 25
=> 15 so option b is correct
Answer:
The answer is B (15)
Step-by-step explanation:
I need help with 2.4
Answer:
A and D
Step-by-step explanation:
ΔACD is 3 times the size of ΔABE, so the dilation uses a scale factor of 3. That only leaves choices A, D, and E.
Dilation about point A leaves point A in the same place, so choice E can be eliminated on that basis. (There is only one point A, and not a translated version, consistent with choice A.)
Point C in the larger triangle corresponds to point B in the smaller triangle, and is 4 units down from it. Hence the description of D makes sense.
___
We hope you can see that choosing correct answers in multiple-choice questions is as much about consistency and reasonableness as it is about knowing how to work the problem. You do have to understand what the problem is asking and what the answers are saying about it.
Point M is located at (3, 7). If point M is translated 2 units to the left and 4 units down, what are the coordinates of M’?
It would be located at (1, 3). Hope this helps!
Answer:
1,3
Step-by-step explanation:
A math test is to have 20 questions the test format uses multiple choice worth five points each and problem-solving worth six points which the test has a total of 100 point write a system to determine how many of each type of questions are used
To determine the number of each type of question on the math test, set up a system of equations. Solve the system of equations using substitution or elimination method. The math test consists of 5 multiple-choice questions and 15 problem-solving questions.
Explanation:To determine how many of each type of questions are used on the math test, we can set up a system of equations. Let's use x to represent the number of multiple-choice questions and y to represent the number of problem-solving questions. Since there are 20 questions in total, we have the equation x + y = 20. Each multiple-choice question is worth 5 points and each problem-solving question is worth 6 points, so we also have the equation 5x + 6y = 100.
We can solve this system of equations using substitution or elimination method. Let's solve it using elimination:
Multiply the first equation by 5 to make the coefficients of x the same in both equations: 5x + 5y = 100.Subtract the new equation from the second equation to eliminate x: (5x + 6y) - (5x + 5y) = 100 - 100. Simplifying, we get y = 20 - 5 = 15.Substitute y = 15 into the first equation to solve for x: x + 15 = 20. Subtracting 15 from both sides, we find x = 5.Therefore, the math test consists of 5 multiple-choice questions and 15 problem-solving questions.
Learn more about Determining the number of each type of question on a math test here:https://brainly.com/question/11879419
#SPJ2
15 points!!!
kinda rusty with triangles. scratch that. really rusty.
Consider the attached figure. The height CD cuts the triangle exactly in half. This means that
[tex]\overline{AD}=\overline{BD}=\dfrac{1}{2}\overline{AB}=10[/tex]
Moreover, since CD is the height of the triangle, we know that ACD is a right triangle. We know the hypothenuse AC to be 20 feet because it is a side of the triangle, and we just found out that AD is 10. We can use the pythagorean theorem to deduce
[tex]\overline{CD}=\sqrt{\overline{AC}^2-\overline{AD}^2}=\sqrt{400-100}=\sqrt{300}[/tex]
So, the area is
[tex]A=\dfrac{bh}{2}=\dfrac{\overline{AB}\cdot\overline{CD}}{2} = \dfrac{20\cdot\sqrt{300}}{2}=10\sqrt{300}\approx 173[/tex]
Well to start off all sides are gonna be 20. To find area it’s lxw so 20•20=400
Dives 400 by 12 and you get 33.333333333 so you round that to the nearest whole foot and you get 33 feet
solve for x; ax=7 I can find 1x or x by __________________ on both sides of the equation
You can solve for 'x' in the equation 'ax = 7' by dividing both sides of the equation by 'a'. The result is 'x = 7/a'. This is based on the principle of maintaining equation equality through similar operations on both sides.
Explanation:To solve for
x
in the equation
ax = 7
, you need to isolate the variable, x. This is done by
dividing
both sides of the equation by 'a'. This leaves x = 7/a. Therefore, you can find 'x' by dividing both sides of the equation by 'a'.
This process is based on the principle of equality.
You can maintain the equality of the equation by doing the same mathematical operation to both sides. Consequently, by dividing both sides by 'a', you successfully solve for x without disrupting the balance of the equation.
Learn more about solving equation here:https://brainly.com/question/18322830
#SPJ2
Given: Circumscribed polygon ELPJ
K, U, V, S -points of tangency
EK=2, LU=4, PV=1, JS=2
Find: Perimeter of ELPJ
[tex]P_{ELPJ} = EK+ES+LU+LK+PV+PU JS+JV \\ \Leftrightarrow P_{ELPJ} = 2EK + 2LU + 2PV + 2JS = 2 \times 2 + 2 \times 4 + 2 \times 1 + 2 \times 2 = 18[/tex]
Find the value of x in the triangle above Thank you to whoever helps
this is an isosceles triangle two sides are the same
so there are 180° in a triangle
180-58= 122 now divide this by two because the last two angles are equal
122/2=61° =x°
Leo wants to paint a mural that covers a wall of an area of 600 square feet. The height of the wall is 2/3 of its lengtht. What is the lenght and the height of the wall?
To determine the dimensions of the wall, we set up an equation using the given area and the fact that the wall's height is 2/3 of its length. Solving for length and height, we find that the length is 30 feet and the height is 20 feet.
The question asks to determine the length and height of a wall that Leo wants to paint, given that the area of the wall is 600 square feet, and the height is 2/3 of its length. To solve this, we will set up an equation to represent the relationship between the length and height and use the area to find the specific dimensions.
Let's use L to represent the length of the wall and H to represent the height. According to the given information, H = (2/3)L. The area of a rectangle is calculated by multiplying its length by its height, so we can set up the equation:
Area = L \H = 600 sq ft
Substituting the height with its relation to length, we get:
600 = L \(2/3)L
Dividing both sides by L and then by 2/3, we find that:
L² = 600 \(3/2)
L² = 900
L = 30 ft (since length must be positive)
Now, to find the height:
H = (2/3)\L = (2/3) \ 30 = 20 ft
So, the length of the wall is 30 feet and the height is 20 feet.
Jacob made a banner for a sporting event in the shape of a parallelogram. The area of the banner is 127 1/2 square centimeters. The height of the banner is 4 1/4 centimeters. What is the base of the banner?
Answer:30
Step-by-step explanation: its 30 because you divide 127 1/2 or 127.5 by 4.25 or 4 1/4.
Can someone please give me a helping hand and help me answer this question
Answer:
see attached
Step-by-step explanation:
The chart shows you that w=2 when z=0. That's the point on the w-axis at lower left. Only one equation gives those results.
5 friends share 3 bags of trail mix equally. What fraction of a bag of trail mix does each friend get?
Answer
the answer is 6/10 or 0.6
Step-by-step explanation:
6/10 (3/5) because you have to share the amount of bags into the ratio of friends which would give you 0.6 or 6/10 simplified to 3/5
Suppose that 2 were subtracted from each of the values in a data set that originally had a standard deviation of 3.5. What would be the standard deviation of the resulting data?
Answer:
standard deviation will remain unchanged at 3.5
Step-by-step explanation:
Subtracting 2 from each of the values in the data set will only change the origin of the data set. The mean of the values will change but the variance and consequently the standard deviation will remain unchanged
Answer:
standard deviation of the resulting data will be 3.5
Step-by-step explanation:
When we add or subtract each values of the data set by some constant then the mean will change by the same amount whereas the there is no change in the standard deviation.
So, when we subtract 2 from each values of the data set, the standard deviation of the resulting data will be also 3.5.
Need the answer to #3
Answer:
3. P(R1|Q) = 3/19 ≈ 0.16
Step-by-step explanation:
The desired probability is the ratio of P(Q·R1) to P(Q). The probability P(Q) is not given, but there is sufficient information to find it.
P(Q·R1) = P(Q|R1)·P(R1) = 0.40·0.15 = 0.06
P(Q·R2) = P(Q|R2)·P(R2) = 0.20·0.55 = 0.11
P(Q·R3) = P(Q|R3)·P(R3) = 0.70·0.30 = 0.21
Since R1 and R2 and R3 are mutually exclusive and have a joint probability of 1, this means ...
P(Q) = P(Q·R1) +P(Q·R2) +P(Q·R3) = 0.06 +0.11 +0.21 = 0.38
Then the desired probability is ...
P(R1|Q) = P(Q·R1)/P(Q) = 0.06/0.38
P(R1|Q) = 3/19 ≈ 0.16
The answer to this equation
Answer:
a = 12
Step-by-step explanation:
Multiply the equation by the inverse of the coefficient of "a".
4·(1/4)a = 4·3
1·a = 12 . . . . . . simplify
a = 12
If the first step in the solution of the equation -9 + x = 5x - 7 is "subtract x," then what would the next step be ?
Answer:
-1/2=x
Step-by-step explanation:
-9 + x = 5x - 7
-x -x
-9=4x-7
+7 +7
-2=4x
-2/4 =4x/4
-1/2=x
Find the volume of a cube whose sides are each 6 centimeters long.
A. 216 cm3
B. 360 cm3
C. 644 cm3
D. 1,028 cm3
Answer:
A. 216 cm³
Step-by-step explanation:
The volume of a cube is the cube of the side length:
V = s³ = (6 cm)³ = 216 cm³
How would you find the volume of a rectangular prism with length of 1/4 inches, a width of 1 1/4 inches, and height of 4
Answer:
The volume would be 1 1/4 cubic inches.
Step-by-step explanation:
To find this, multiply all three numbers together because the formula for volume is length multiplied by width multiplied by height.
V = lwh
V = (1/4)(1 1/4)(4)
V = 1 1/4
help please
problem 8 and fix problem 10
Answer:
8. A'(-1/2, 1), B'(0, 0), C'(1, 1 1/2)
10. 20°, 60°, 100°
Step-by-step explanation:
8. Point B is at the origin, the center of dilation, so its coordinates remain unchanged. The coordinates of A and C are each multiplied by the scale factor, 1/2.
A' = (1/2)A = (1/2)(-1, 2) = (-1/2, 1)
C' = (1/2)C = (1/2)(2, 3) = (1, 3/2)
__
10. The total number of ratio units is 1+3+5 = 9. The total of angle measures in any triangle is 180°. So, each of the "ratio units" must stand for 180°/9 = 20°. Then the angles are ...
1 · 20° = 20°
3 · 20° = 60°
5 · 20° = 100°
figure WXYZ is shown below. Figure WXYZ is translated up 3 units and 4 units to the right to create WXYZ. What is the measure of angle Z after this transformation? A.) 58 B.) 77 C.) 96 D.) 103
If I'm not wrong, there's no change in the measurement... I think it's D. since there's no visible change in the angle measurement. If it asked the coordinates then maybe I could elaborate. This question is confusing though. :/
The measure of angle Z after the transformation is D) 103°.Therefore , D.) 103 is correct .
A translation does not change the measure of angles, so the measure of angle Z after the transformation is the same as the measure of angle Z before the transformation, which is 103°.
Image verification:
The image you sent shows a kite with the following angle measures:
Angle W = 96°
Angle X = 58°
Angle Y = 103°
Angle Z = 103°
The kite is translated up 3 units and 4 units to the right, which does not change the measure of any of the angles.
Therefore, the measure of angle Z after the transformation is still 103°.
Pascal wanted the area of the floor to be 54 square feet and the width still be 2/3 the length.What would the dimensions of the floor be?
PLZ HELP ME QUICKLY
The dimensions should be 6ft by 9ft.
Final answer:
The dimensions of the floor with an area of 54 square feet, where the width is 2/3 of the length, are 9 feet in length and 6 feet in width.
Explanation:
Pascal wants to find the dimensions of a floor where the area is 54 square feet and the width is 2/3 the length. To find the dimensions, we set up an equation where the length is L and the width is W, with W = (2/3)L. Since area is calculated by the formula Area = length times width, we get 54 = L times (2/3)L. Solving this equation by multiplying the length terms and then dividing both sides by 2/3, we get L² = 54 times (3/2), which simplifies to L² = 81. Taking the square root of both sides gives us L = 9 feet. Consequently, the width would be W = (2/3) times 9 = 6 feet. Therefore, the dimensions of the floor are 9 feet by 6 feet.
what is tan(sin^-1(x/2))
Let
[tex]\theta=\sin^{-1}\dfrac x2\implies\sin\theta=\dfrac x2[/tex]
Recall that
[tex]\cos\theta=\sqrt{1-\sin^2\theta}=\sqrt{1-\dfrac{x^2}4}[/tex]
Then
[tex]\tan\theta=\dfrac{\sin\theta}{\cos\theta}\implies\tan\left(\sin^{-1}\dfrac x2\right)=\dfrac{\frac x2}{\sqrt{1-\frac{x^2}4}}[/tex]
[tex]\implies\tan\left(\sin^{-1}\dfrac x2\right)=\dfrac x{\sqrt{4-x^2}}[/tex]
Final answer:
To find tan(sin⁻¹(x/2)), we use the relationship between the sides of a right triangle, leading to the solution tan(θ) = x/√(4 - x²).
Explanation:
The question "what is tan(sin-1(x/2))" involves understanding inverse trigonometric functions and their properties. To solve this, we can create a right-angled triangle where the angle θ has a sine value of x/2. According to the Pythagorean theorem, if one side (opposite) is x and the hypotenuse is 2, the adjacent side can be calculated as √(4 - x²). Thus, tan(θ) = opposite/adjacent = x/√(4 - x²).
The figure is made up of 2 hemispheres and a cylinder.
What is the exact volume of this figure?
Answer:
Hemisphere radius = 3 inch
Sphere volume = 4/3 • π • radius^3
Sphere volume = 4/3 • π • 27
Sphere volume = 113.0973355292 cubic inches
Cylinder Volume = π • radius^2 • height
Cylinder Volume = π • 9 * 10
Cylinder Volume = 282.7433388231 cubic inches
TOTAL VOLUME = 113.10 + 282.74 cubic inches
TOTAL VOLUME = 395.84 cubic inches
Step-by-step explanation:
Answer: 126π in.³
Step-by-step explanation:
Complete the square to determine the minimum or maximum value of the function defined by the expression.
x2 − 12x − 2
A) maximum value at 38 B) minimum value at 38 C) maximum value at −38 D) minimum value at −38
Answer:
Option D. minimum value at −38
Step-by-step explanation:
we have
[tex]x^{2}-12x-2[/tex]
Let
[tex]y=x^{2}-12x-2[/tex]
Complete the square
[tex]y+2=x^{2}-12x[/tex]
[tex]y+2+36=(x^{2}-12x+36)[/tex]
[tex]y+38=(x^{2}-12x+36)[/tex]
[tex]y+38=(x-6)^{2}[/tex]
[tex]y=(x-6)^{2}-38[/tex] ------> equation of a vertical parabola in vertex form
The vertex is the point [tex](6,-38)[/tex]
The parabola open upward-----> the vertex is a minimum
therefore
minimum value at −38
Assume f(x) = -2x + 8 and g(x) = 3x. What is the value of (g o f)(3)
Answer:
6
Step-by-step explanation:
(g o f)(3) = g(f(3))
We can find f(3) using its formula with x=3:
f(3) = -2·3 +8 = -6 +8 = 2
Now, we can find g(2) using its formula with x=2:
g(2) = 3·2 = 6
So, the composition value is ...
(g o f)(3) = 6
For #1 and 2, Find the lateral area and surface area of each prism.
The lateral area and surface area of the cuboid are 72 square feet and 142 square feet, respectively. The lateral area and surface area of the prism are 42 square cm and 62 square cm, respectively.
To find the lateral area and surface area of the given cuboid and prism, we need to use the formulas for each.
For the cuboid:
1. Lateral Area: The lateral area of a cuboid can be found by adding the areas of its four side faces. Since the cuboid has a length of 7 feet, a breadth of 5 feet, and a height of 3 feet, we can calculate the lateral area as follows:
- Side 1: length * height = 7 feet * 3 feet = 21 square feet
- Side 2: breadth * height = 5 feet * 3 feet = 15 square feet
- Side 3: length * height = 7 feet * 3 feet = 21 square feet
- Side 4: breadth * height = 5 feet * 3 feet = 15 square feet
The total lateral area is the sum of these four areas: 21 + 15 + 21 + 15 = 72 square feet.
2. Surface Area: The surface area of a cuboid is found by adding the areas of all six faces. In addition to the lateral area, we need to include the areas of the top and bottom faces. Using the dimensions of the cuboid, we can calculate the surface area as follows:
- Top face: length * breadth = 7 feet * 5 feet = 35 square feet
- Bottom face: length * breadth = 7 feet * 5 feet = 35 square feet
The total surface area is the sum of these six areas: 72 (lateral area) + 35 (top face) + 35 (bottom face) = 142 square feet.
Now, for the prism:
1. Lateral Area: To find the lateral area of the prism, we need to find the perimeter of the base and multiply it by the height of the prism. Since the prism has a base with a length of 5 cm and a breadth of 2 cm, the perimeter is: 2 * (length + breadth) = 2 * (5 cm + 2 cm) = 2 * 7 cm = 14 cm.
The lateral area is obtained by multiplying the perimeter by the height: 14 cm * 3 cm = 42 square cm.
2. Surface Area: The surface area of the prism is the sum of the lateral area and twice the area of the base. Since the base is a rectangle with a length of 5 cm and a breadth of 2 cm, its area is: length * breadth = 5 cm * 2 cm = 10 square cm.
The surface area is then calculated as: 42 (lateral area) + 2 * 10 (area of the base) = 42 + 20 = 62 square cm.