Miranda needs to work 50 hours at her job in order to purchase the computer.
What is amount?Amount is a term generally used to refer to a numerical value which represents a quantity of something. It can be used to describe the size, magnitude, or total of an object, event, or concept. Amount is often used to refer to money, but it can also be used to refer to other elements such as time, energy, weight, and volume. Amount can also be used to refer to a certain degree or level, such as a certain amount of effort or a certain amount of progress.
To find the amount of hours Miranda needs to work in order to purchase the computer, the following equation can be used:
12 x = Computer Price x 0.6
Where 12 is the hourly wage Miranda earns, x is the amount of hours Miranda needs to work, and 0.6 is the percentage (60%) of Miranda’s earnings that will be used to purchase the computer.
The computer price is not given, so let’s assume it to be $1000. Plugging in the values, the equation becomes:
12 x = 1000 x 0.6
Simplifying the equation, we have:
12 x = 600
Dividing both sides by 12, we get:
x = 600/12
x = 50
Therefore, Miranda needs to work 50 hours at her job in order to purchase the computer.
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Find the equation of the tangent line to the graph of y = xlnx at the point (2,2ln2).
The equation of the tangent line to the graph of y = xlnx at the point (2,2ln2) is y = (ln(2) + 1)x - 2ln2 - 2.
What is tangent?A tangent is a straight line or plane that touches a curve or curved surface at a single point, but does not intersect it at that point. The tangent line can be thought of as the instantaneous rate of change of the curve at that point. In calculus, the slope of the tangent line at a point on a curve is defined as the derivative of the curve at that point. The tangent line is often used to approximate the behavior of the curve near the point of tangency.
To find the equation of the tangent line to the graph of y = xlnx at the point (2,2ln2), we need to use the slope-point form of the equation of a line.
First, we find the slope of the tangent line by taking the derivative of the function y = xlnx:
y = xlnx
y' = ln(x) + 1
At x = 2, we have:
y' = ln(2) + 1
So the slope of the tangent line at (2,2ln2) is ln(2) + 1.
Next, we use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
where (x1, y1) is the given point, and m is the slope we just found.
Substituting x1 = 2, y1 = 2ln2, and m = ln(2) + 1, we get:
y - 2ln2 = (ln(2) + 1)(x - 2)
Expanding and simplifying, we get the equation of the tangent line:
y = (ln(2) + 1)x - 2ln2 - 2
So the equation of the tangent line to the graph of y = xlnx at the point (2,2ln2) is y = (ln(2) + 1)x - 2ln2 - 2.
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Can you solve this question?
f'(x)=?
The length of the missing leg of the triangle is 8 units. We have a right triangle ABC with angle BAC equal to 90 degrees. The length of one of the legs is 6 units, and the length of the hypotenuse is 10 units.
We are asked to find the length of the other leg of the triangle.
[tex]That is, a^2 + b^2 = c^2[/tex]
In this case, we know that the length of one leg is 6 units, and the length of the hypotenuse is 10 units. We can substitute these values into the Pythagorean theorem and solve for the missing leg:
[tex]a^2 + b^2 = c^2[/tex]
[tex]6^2 + b^2 = 10^2[/tex]
[tex]36 + b^2 = 100[/tex]
[tex]b^2 = 100 - 36[/tex]
[tex]b^2 = 64[/tex]
Taking the square root of both sides, we get:
b = 8
Therefore, the length of the missing leg of the triangle is 8 units.
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Sergey is solving 5x2 + 20x – 7 = 0. Which steps could he use to solve the quadratic equation by completing the square? Select three options. 5(x2 + 4x + 4) = –7 + 20 x + 2 = Plus or minus StartRoot StartFraction 27 Over 5 EndFraction EndRoot 5(x2 + 4x) = 7 5(x2 + 4x + 4) = 7 + 20 5(x2 + 4x) = –7
The solutions to the quadratic equation [tex]5x^2 + 20x - 7 = 0[/tex] are[tex]x = -2 + \sqrt{(23/5)[/tex] and [tex]x = -2 - \sqrt{(23/5)[/tex].
A quadratic equation is a second-degree polynomial equation of the form [tex]ax^2 + bx + c = 0[/tex], where x is the variable, and a, b, and c are coefficients, where a is non-zero.
The square root is an important mathematical concept that arises in many areas of mathematics and science, such as geometry, algebra, and physics. It is used to calculate the length of sides of a right triangle, to solve quadratic equations, and to model the behavior of physical systems
The three steps Sergey could use to solve the quadratic equation by completing the square are:
Rewrite the equation in the form [tex]ax^2 + bx + c = 0[/tex].
Add and subtract [tex](b/2a)^2[/tex] to complete the square:
[tex]5(x^2 + 4x + 4 - 4) = 7[/tex]
Simplify the left side and solve for x by taking the square root:
[tex]5(x + 2)^2 = 11[/tex]
[tex](x + 2)^2 = 11/5[/tex]
[tex]x + 2 = \pm \sqrt{(11/5)[/tex]
[tex]x = -2 \pm \sqrt{(11/5)[/tex]
Therefore, the three correct options are:
[tex]5(x^2 + 4x + 4 - 4) = 7[/tex]
[tex]5(x + 2)^2 = 11[/tex]
[tex](x + 2)^2 = 11/5, x = -2 \pm \sqrt{(11/5)[/tex]
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The points (-5, 6) and (x, 3) are elements of an inverse variation.
What is the value of X?
X=-10 when the points (-5, 6) and (x, 3) are elements of an inverse variation.
What is inverse variation?A relationship between two variables known as an inverse variation occurs when one variable increases while the other decreases, resulting in a constant product. Y = k/x, where k is a constant of variation, can be used to explain the relationship between two variables x and y if they are inversely proportional in mathematics.
The fact that their product must be constant allows us to determine the value of x because the points (-5, 6) and (x, 3) are components of an inverse variation.
As a result, x must be 10 to provide the elements of an inverse variation (-5, 6) and (x, 3).
x * 3 = -5 * 6
x = -30/3
x = -10
In conclusion, an inverse variation is a mathematical connection where the product of two variables stays constant.
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help i only need 8 show work
The height of the flagpole is approximately 68.53 feet.
What is trigonometric equations ?Trigonometric equations are equations that involve trigonometric functions such as sine, cosine, tangent, and their reciprocals. These equations typically involve finding the values of the angles or sides of a right-angled triangle or periodic functions that repeat themselves after certain intervals.
According to given information:This problem involves finding the height of a flagpole using trigonometry. The surveyor measures the angle of elevation from the tripod to the top of the pole and knows the distance from the base of the pole to the tripod. By using the tangent function and the given angle, we can set up an equation that relates the height of the pole to the distance and the angle. We simplify the equation and solve for the unknown height, which gives us an approximate value of 68.53 feet.
the height of the flagpole, we can use trigonometry. Let's call the height of the flagpole "h".
Using the tangent function, we can set up the following equation:
tan(26) = h / (150 + 3)
The 3 feet is added to the distance because the tripod is 3 feet tall.
Simplifying this equation, we get:
tan(26) = h / 153
To solve for "h", we can multiply both sides by 153:
h = tan(26) * 153
Using a calculator, we can evaluate the right side of the equation to get:
h ≈ 68.53
Therefore, the height of the flagpole is approximately 68.53 feet.
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Solve. (Easy 10 points)
Answer:
A) -3
Step-by-step explanation:
To remove the radical on the left side of the equation, cube both sides of the equation.
[tex]\sqrt[3]{4x + 4}^{3}[/tex] = (-2)³
Simplify each side of the equation.
4x + 4 = -8
4x = -12
x = -3
So, the answer is A) -3
answer this please as i do not get this question thank you
Step-by-step explanation:
The number line is GREATER than but does not INCLUDE -4 ( due to the hollow dot) and is less than or EQUAL to 5 (solid dot)
-4 < n ≤ 5
Bilquis is deciding between two different movie streaming sites to subscribe to. Plan A costs $22 per month plus $1 per movie watched. Plan B costs $14 per month plus $3 per movie watched. Let A represent the monthly cost of Plan A if Bilquis watches x per month, and let B represent the monthly cost of Plan B if Bilquis watches x movies per month. Graph each function and determine the interval of movies watched, x, for which Plan A is cheaper than Plan B.
We can express this interval using set-builder notation as: {x | x > 4}
What is expression?
An expression consists of one or more numbers or variables along with one more operation.
The monthly costs of each plan as functions of the number of movies watched:
A(x) = 22 + x
B(x) = 14 + 3x
To graph these functions, we can plot several points for each one, as shown in follow fig.
A(x) - B(x) < 0
(22 + x) - (14 + 3x) < 0
22 + x - 14 - 3x < 0
-2x + 8 < 0
-2x < -8
x > 4
Therefore, Plan A is cheaper than Plan B for any number of movies watched greater than 4. We can express this interval using set-builder notation as: {x | x > 4}
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The Question is in the picture
Using compound interest, we can find that at age 59 retirement option 1 will be better than retirement option 2.
Define compound interest?Compound interest is computed on the principal and the accrued interest for a given time period. The interest that has accumulated on the principal over time is added to it, and the combined amount acts as the new principal for the subsequent time period. Once more, the interest for the following period is calculated using the total cumulative principal amount.
Compound interest is the term used to describe the method of computing interest employed in all financial and business transactions globally. The benefit of compounding is that it is consistently better than or comparable to other strategies, such simple interest.
At age 59,
Option 1 = 30000 × 34
= $1020000
Option 2 = 15000 (1+12/408) ^34
= 15000 × (1.02) ^34
= 15000 × 1.9606
= $29409.
So, when you retire at 59, option 1 is better than option 2.
At age 69,
Option 1 = 30000 × 44
= $1,320,000
Option 2 = 15000 (1+12/528) ^44
= 15000 × (1.02) ^44
= 15000 × 2.390
= $35,850.
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At age 59, retirement option 1 will outperform retirement option 2, according to compound interest.
Define compound interest?On the principal and the interest that has accrued over a specific length of time, compound interest is calculated. The principal is increased by the interest that has accrued on it over time, and the combined sum serves as the new principal for the term that follows. Once more, the entire cumulative principal amount is used to determine the interest for the upcoming period.
The term "compound interest" refers to the technique of calculating interest used in all financial and commercial transactions worldwide. Compounding has the advantage of constantly outperforming or being on par with other approaches, like simple interest.
At age 59,
Option 1:
= 30000 × 34
= $1020000
Option 2:
[tex]=15000(\frac{1+12}{408} )^{34} \\\\=15000\times 1.02^{34}[/tex]
= 15000 × 1.9606
= $29409.
So, when you retire at 59, option 1 is better than option 2.
At age 69,
Option 1:
= 30000 × 44
= $1,320,000
Option 2:
[tex]=15000(\frac{1+12}{528} )^{44} \\\\=15000\times 1.02^{44}[/tex]
= 15000 × 2.390
= $35,850.
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(SBAC Performance Task Practice Test Question) Label the dimensions of the net for the current cereal box with dimensions of 12 inches high, 8 inches wide, and 2 inches deep. (Please show how to do it because im at a loss at the time this is being asked)
The dimensions of the net will be the same as the dimensions of the rectangular prism, since the net is just a flattened version of the 3D shape.
What is Rectangular prism ?
A rectangular prism is a three-dimensional geometric shape that has six faces, all of which are rectangles.
To label the dimensions of the net for the current cereal box, you need to identify the six faces of the rectangular prism that makes up the cereal box.
Start by drawing a rectangular prism with the given dimensions (12 inches high, 8 inches wide, and 2 inches deep).
Then, label each face with its dimensions, as follows:
The top face (which will be the same size as the bottom face) has dimensions 8 inches by 2 inches.
The front and back faces have dimensions 12 inches by 8 inches.
The left and right faces have dimensions 12 inches by 2 inches.
Top face: 8 in. x 2 in.
Front and back faces: 12 in. x 8 in.
Left and right faces: 12 in. x 2 in.
Therefore, Note that the dimensions of the net will be the same as the dimensions of the rectangular prism, since the net is just a flattened version of the 3D shape.
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The Uintah High School band program sold cookies to raise money for their band trip. They charged $3 for each cookie and $4 for each large cookie. They raised $880 from cookie sales. We know that they sold 2 times as many cookies as small cookies. How many small cookies did they sell?
147
$3 x 147 cookies = (approximately) $440
$440 x 2 = 880
find the number which's arithmetic square root is 10
Answer: The square root of 10 is 3.162
PLS SOMEONE HELP MEEEEE
In conclusion MN is approximately 8.73.
How to solve?
In triangle MNK, we know that MN = NK and the angle between them is 110 degrees. Let's call the third angle in this triangle A.
We also know that MK = 5.
Since the sum of the angles in a triangle is always 180 degrees, we can find angle A:
A + 110 + A = 180
2A = 70
A = 35
Now we can use the Law of Sines to find MN:
MN/sin(110) = MK/sin(A)
MN/sin(110) = 5/sin(35)
MN = 5×sin(110)/sin(35)
MN ≈ 8.73
Therefore, MN is approximately 8.73.
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Complete Quedtion:
In triangle AMNK, we have MN = NK, angle M/N = 110 degrees, and MK = 5. What is the length of MN?
A regular tube of toothpaste costs $2.50 for 3.2 ounces. A travel-size tube costs $1.00 for 1.2 ounces. Compare the prices and weights using percent to decide which is the better buy.
Answer: The regular tube is the better buy
Step-by-step explanation: $2.50/3.2 ounces equals $.78 per ounce. $1.00/1.2 ounces equals $.83 per ounce. Therefore, the regular tube is the better buy.
Find the common difference:
10,8,6,4,2
Answer: The common difference of the arithmetic sequence 10, 8, 6, 4, 2,… is -2. Note: By considering the formula of arithmetic sequence we verify the common difference which we obtained.
Answer:
-2
Step-by-step explanation:
In the sequence we have three kinds of sequence namely, arithmetic sequence, geometric sequence and harmonic sequence. In arithmetic sequence we the common difference between the two terms, In geometric sequence we the common ratio between the two terms, In harmonic sequence it is a ratio of arithmetic sequence to geometric sequence.
Open the image and answer the question
Answer:
[tex] {≈225.4 \: m}^{2} [/tex]
[tex] {≈248.2 \: m}^{2} [/tex]
Step-by-step explanation:
(My first few steps are in the photo I've added)
Now, we can find the area of the first cutout:
[tex]s(cutout1) = \frac{\pi \times {r}^{2} \times \alpha }{360°} = \frac{\pi \times {18}^{2} \times 114°}{360°} = \frac{36963\pi}{360°} = 102.6\pi[/tex]
We can also find the altitude of the first triangle using trigonometry:
[tex] \sin(∠obd) = \frac{od}{ob} [/tex]
We also need to find AB by using the Pythagorean theorem:
[tex] {ad}^{2} = {ao}^{2} - {od}^{2} = {18}^{2} - {5.56}^{2} = 293.0864[/tex]
[tex]ad > 0[/tex]
[tex]ad = \sqrt{293.0864} ≈ 17.12[/tex]
[tex]ab = 2 \times 17.12 = 34.24[/tex]
[tex]h1 = od = ob \times \sin(∠obd) = 18 \times \sin(18°)≈5.56[/tex]
Then, we can find the area of the 1st triangle:
[tex]s (1triangle)= \frac{1}{2} \times 5.56 \times 34.24 ≈95.19[/tex]
And we can also find the area 1:
[tex]area1 = s(cutout1) - s(triangle1) = 102.6\pi - 95.19≈225.25[/tex]
Now let's do the same thing with the second area:
[tex]s(cutout2) = \frac{\pi \times {r}^{2} \times \alpha }{360°} = \frac{\pi \times {18}^{2} \times 131°}{360°} = \frac{42444\pi}{360°} =117.9 \pi[/tex]
[tex] \sin(∠obe) = \frac{oe}{oc} [/tex]
[tex]h2 = oe = oc \times \sin(∠obe) = 18 \times \sin(24.5°)≈7.46[/tex]
[tex] {be}^{2} = {bo}^{2} - {oe}^{2} = {18}^{2} - {7.46}^{2} = 268.3484[/tex]
[tex]be > 0[/tex]
[tex]be = \sqrt{268.3484} ≈16.38[/tex]
[tex]bc = 2 \times 16.38 = 32.76[/tex]
[tex]s(triangle2) = \frac{1}{2} \times 7.46 \times 32.76 = 122.19[/tex]
[tex]area2 = s(cutout2) - s(triangle2) = 117.9\pi - 122.19≈248.2[/tex]
I don't know if I got this right, though...
The area of the shaded segments in the circle is 422.5 square meters
Calculating the area of the shaded segmentsGiven that
Radius = 18 meters
Angles = 114 degrees and 131 degrees
The area of the shaded segments is the sum of the area of the individual segments and this is calculated as
Segment area = (½) × r² × [(π/180) θ – sin θ]
Using the above, we have
Shaded segments = (½) × 18² × [(114π/180) – sin (114)] + (½) × 18² × [(131π/180) – sin (131)]
Evaluate
Shaded segments = 422.5 square meters
Hence, the shaded segments is 422.5 square meters
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Find the area of the shaded triangle or quadrilateral.
What is the area of the WAVE
Answer:
Step-by-step explanation:
What is a rectangular prism?
A right rectangular prism is a box-shaped object, that is, a 3-dimensional solid which has six rectangular faces. Rectangular prisms can also be oblique - leaning to one side - but the side faces are parallelograms, not rectangles. A right rectangular prismz is also called a cuboid, box, or rectangular hexahedron. Moreover, "rectangular prism" and "right rectangular prism" are often used interchangeably.
The most common math problems related to this solid are of the type right rectangular prism calc find V or find A, where the letters stand for the Volume and Area, respectively. Let's see the necessary rectangular prism formula and learn how to solve those problems quickly and easily.
How do I find the volume of a rectangular prism?
The rectangular prism volume formula is:
volume = h × w × l,
where h is prism height, w is its width, and l is its length. To calculate the volume of a cardboard box:
Find the box length. For example, it can be equal to 18 in.
Determine its width. Let's say you measured 12 in.
Find out the rectangular prism height. Assume it's 15 in.
Calculate the cuboid volume. Using the rectangular prism volume formula above, we get volume = (18 × 12 × 15) in = 3240 in³.
How do I find the area of a rectangular prism?
The surface area of the cuboid consists of 6 faces - three pairs of parallel rectangles. To find the rectangular prism surface area, add the areas of all faces:
surface_area = 2 × (h × w) + 2 × (h × l) + 2 × (l × w) = 2 × (h × w + h × l + l × w),
where h is prism height, w is its width, and l is its length.
Let's see an example of how to solve the right rectangular prism calc - find A problem. We'll come back to our example with the box and calculate its surface area:
Calculate the rectangular prism surface area. First rectangle area is 15in × 12in = 180in², second 15in × 18in = 270in² and third one 18in × 12in = 216in². Add all three rectangles' areas - it's equal to 666 in² (what a number!) - and finally multiply by 2. The surface area of our cardboard box is 1332in².
Or save yourself some time and use our rectangular prism calculator.
Finally, let's attack the right rectangular prism calc find d (that is, the diagonal) type of problem.
How do I calculate the diagonal of a rectangular prism?
To determine the diagonal of a rectangular prism, apply the formula:
diagonal = √(l² + h² + w²)
where h is prism height, w is its width, and l is its length.
A 56° B D M E What is the value of y? needs an answer asap
Step-by-step explanation:
The inscribed angle BAD = 1/2 arc BD
56° = 1/2 BD
arc BD = 112°
and arc BAD would then be 360 - 112 = 248°
For the EXTERNAL angle y
y = 1/2 ( difference of intercepted arcs ) = 1/2 ( 248 -112)° = 68°
explain how you can use log(3)7=1.7712 to approximate the value of log(3)15309
To approximate the value of log(3)15309 using log(3)7 = 1.7712, we can use the following steps:
Express 15309 as a power of 3:
15309 = 3^x
Take the logarithm base 3 of both sides:
log(3)15309 = x
Use log rules to simplify the expression:
log(3)15309 = log(3)(3^x)
log(3)15309 = x * log(3)3
log(3)15309 = x * 1
log(3)15309 = x
Substitute the value of x by using log(3)7 = 1.7712:
log(3)15309 ≈ 1.7712 * log(3)81 (since 81 is the largest power of 3 that is less than 15309)
log(3)15309 ≈ 1.7712 * 4
log(3)15309 ≈ 7.0848
Therefore, log(3)15309 ≈ 7.0848.
3000 meters is what in kilometers.
Answer:
3 km
Step-by-step explanation:
3000 m = x km
1000 m = 1 km
Form a proportion to represent the situtation based on a conversion.
[tex]\frac{3000}{x} = \frac{1000}{1}[/tex]
Cross multiply.
1000x = 3000
x = 3 km
To calculate 3000 Meters to the corresponding value in Kilometers, multiply the quantity in Meters by 0.001 (conversion factor). In this case we should multiply 3000 Meters by 0.001 to get the equivalent result in Kilometers:
3000 Meters x 0.001 = 3 Kilometers
Therefore, 3000 Meters is equivalent to 3 Kilometers.
r=-0.49 and the margin of error for 95% confidence is 0.10
Answer:
Step-by-step explanation:
um
baseball cards a baseball card collection contains five times as many national league players as American league players card. express the number of national league players cards in the collections in terms of the number of American league players card.
The number of National League players cards in the card collection in terms of the number of American League players cards can be expressed as 5x.
Let's start with the information given in the problem:
The baseball card collection contains five times as many National League players as American League players.
Let's use x to represent the number of American League players cards in the collection.
Since the collection contains five times as many National League players as American League players, we can express the number of National League players cards in terms of x as follows:
Number of National League players cards = 5 times the number of American League players cards
Number of National League players cards = 5x
So, if the number of American League players cards in the collection is x, then the number of National League players cards would be 5x, according to the problem statement.
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The volume of a cone is equal to the volume of a sphere.
The radius of the cone is four times the radius of the sphere.
Write down an expression for h
in terms of r.
You must simplify your answer.
h=
an expression for height h in terms of radius r, h=r/4
Definition of VolumeThe quantity of space a three-dimensional solid shape takes up is measured by its volume. Although it is hard to conceive in any shape, it may be likened to shapes. A compass box, for instance, has a bigger volume than an eraser inserted inside of it.
Volume of Sphere=4/3πr³
Volume of Cone=1/3πR²h
Given:
A cone's volume is equal to a sphere's volume. The cone's radius is four times greater than the sphere's radius.R=4r
4/3πr³=1/3πR²h
4r³=R²h
4r³=(4r)²h
r=4h
an expression for height h in terms of radius r, h=r/4.
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NO LINKS!!! URGENT HELP PLEASE!!!
Please help me with 1 and 2
Answer:
1. 33 foot
2. 6.2 foot
Step-by-step explanation:
1.
Let's denote the height of the tree by "h". We can use the tangent function to solve the problem:
tangent of the angle of elevation = opposite / adjacent
In this case, the opposite side is the height of the tree, and the adjacent side is the distance from the tree to the point on the ground where the angle of elevation is measured. So we have:
tan(35) = h / 47
To solve for "h", we can multiply both sides by 47:
h = 47 tan(35)
Using a calculator, we get:
h ≈ 32.9 feet
So the height of the tree to the nearest foot is 33 feet.
2.
Let's call the distance we're trying to find "x". We can use trigonometry to relate the angle and the length of the guy wire to the distance "x". Specifically, we can use the sine function:
sine of the angle = opposite / hypotenuse
In this case, the opposite side is the distance "x", and the hypotenuse is the length of the guy wire, which is 8 feet. So we have:
sin(51) = x / 8
To solve for "x", we can multiply both sides by 8:
x = 8 sin(51)
Using a calculator, we get:
x ≈ 6.2 feet
So the stake is about 6.2 feet from the foot of the stop sign, to the nearest tenth of a foot.
there us 40 pens 9 out of 10 r black wats the fraction an the percentage
Answer:
White
Step-by-step explanation:
Number of favorable outcomes/Number of trails =4/20 or 1/5
Please help me solve the question!
The probability of winning the minimum award in the lottery is 0.00185%.
What is probability?The possibility of an event occurring is expressed in terms of probability and odds. Probability is often stated as a decimal or percentage and represents the ratio of the number of likely outcomes to all conceivable possibilities. Conversely, odds are often stated as a ratio or fraction and are the ratio of the number of favourable events to the number of negative outcomes.
The probability of correctly matching two out of five white balls is given by the combination formula:
C(5,2) = 5! / (2! * (5-2)!) = 10
The probability of matching the gold ball is = 1/44.
Multiplying we have:
P(win minimum award) = (10 / C(54,5)) * (1 / 44) = 0.0000185, or approximately 0.00185%
Hence, the probability of winning the minimum award in the lottery is 0.00185%.
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While on vacation at the beach, Eleanor drew the figure shown. In Eleanor’s drawing, the measure of ∠FMD is 15°, and the measure of ∠BMC is 30°. Which equations can be used to find the measure m of ∠CMD? Angle AMB and BMF is right angles with common side BM. Seg MC and MD divides angle BMF into 3 angles those are angle BMC, angle CMD and angle DMF. A. 15° + 30° = a; a + 90° = m B. 15° + 90° = a; 180° – a = m C. 15° + 30° = a; 90° – a = m D. 30° – 15° = a; 90° – a = m
The correct equation to find the measure of ∠CMD is C. 15° + 30° = a; 90° – a = m.
What is right angle?It is formed when two straight lines intersect at a single point, creating two equal and opposite angles.
This is because the angles in a triangle must add up to 180°.
In this case, ∠FMD and ∠BMC are the two angles of the triangle, and the third angle is a right angle.
Therefore, the measure of ∠CMD must be 90°.
To find the measure of ∠CMD, we must first find the sum of ∠FMD and ∠BMC.
This can be done by setting up the equation 15° + 30° = a.
We then subtract this sum from 90° to get the measure of ∠CMD, which gives us the equation 90° – a = m.
Therefore, the correct equation to find the measure of ∠CMD is
15° + 30° = a; 90° – a = m.
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Los 1600 euros de alquiler de un terreno se reparten entre tres ganaderos que llevan alli a pastar sus ovejas. Como no tienen el mismo número de ovejas, deciden pagar proporcionalmente al número de ovejas de cada uno. Si el primero tiene 120 Ovejas,el segundo 72 y el tercero 68. ¿ Cuánto paga cada uno?
So, each farmer pays the following amounts: The first farmer pays 738.40 euros. The second farmer pays 443.04 euros. The third farmer pays 418.56 euros
What is proportion?Proportion refers to the equality of two ratios. In other words, when two ratios are set equal to each other, they form a proportion. A proportion is typically written in the form of two fractions separated by an equals sign, such as a/b = c/d. Proportions are commonly used in mathematics to solve problems involving ratios and proportions, such as finding missing values or scaling up or down a given quantity.
Here,
To find out how much each farmer pays, we need to determine the proportion of the total rent that each farmer owes based on the number of sheep they have. First, we need to find the total number of sheep:
120 + 72 + 68 = 260
The first farmer has 120 sheep, which is 46.15% of the total number of sheep (120/260). Therefore, the first farmer owes 46.15% of the rent:
0.4615 x 1600 = 738.40 euros
Similarly, the second farmer has 72 sheep, which is 27.69% of the total number of sheep (72/260). Therefore, the second farmer owes 27.69% of the rent:
0.2769 x 1600 = 443.04 euros
The third farmer has 68 sheep, which is 26.15% of the total number of sheep (68/260). Therefore, the third farmer owes 26.15% of the rent:
0.2615 x 1600 = 418.56 euros
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Complete question:
The rent of 1600 euros for a piece of land is divided among three farmers who graze their sheep there. As they do not have the same number of sheep, they decide to pay proportionally according to the number of sheep each has. If the first one has 120 sheep, the second 72, and the third 68. How much does each one pay?
Curious about people's recycling behaviors, Sandra put on some gloves and sifted through some recycling and trash bins. She kept count of the plastic type of each bottle and which bottles are properly dispensed.
What is the probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle?
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On solving the provided question we can say that Based on Sandra's research, there is a 15% probability that a randomly picked bottle is appropriately put AND is a Plastic #4 bottle.
What is probability?Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% since there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many disciplines, including statistics, economics, science, and engineering.
Therefore there are 15 bottles that match both requirements (well arranged and Plastic #4).
The sample has 100 bottles in total.
As a result, the likelihood that a randomly chosen bottle is appropriately put AND is a Plastic #4 bottle is:
P(properly positioned and Plastic #4) = the number of bottles that match both requirements. / The sample's total number of bottles
P(properly positioned and Plastic #4) = 15 / 100
P(properly positioned and Plastic #4) = 0.15 or 15%
Based on Sandra's research, there is a 15% probability that a randomly picked bottle is appropriately put AND is a Plastic #4 bottle.
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Rewrite each equation without absolute value for the given conditions.
y = |x3| + x +2|-|x - 5| if 3
Rewriting the absolute value problems gives us: y = |x − 3| + |x + 2| − |x − 5| = 3 - x + x + 2 - (5 - x) = x
How to write Absolute Value equations?The absolute value is simply defined as the distance from zero.
The equation we are to rewrite is:
y = |x − 3| + |x + 2| − |x − 5|, if -2 < x < 3
Modulus value means that it always gives positive value. Thus:
if x < a, then |x - a| is positive when |x - a | = a -x, which is positive as a is larger than x.
and if x >a, then |x-a| is positive when |x-a| = x - a, which is positive as a is smaller than x.
Applying the same,
For -2 < x < 3,
|x - 3 | = 3 - x, as x <3
| x + 2 | = | x - (-2)| = x - (-2) = x+2 as x> -2
| x - 5 | = 5 -x , as x < 5
Therefore, y = |x − 3| + |x + 2| − |x − 5| = 3 - x + x + 2 - (5 - x) = x
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