Answer:43/50
Step-by-step explanation:
you must divide both the numerator and denominator by 2
86/100 can be simplified to 43/50 by dividing both the numerator and denominator by 2, which is the greatest common factor. 86/100 can also be written as 0.86 or 86%.
If 0 < x < 2π, find the sum of all solutions to the equation 2cos^2(x)-7 cos(x)-4=0.
Show how to do it on a ti-84 if possible.
The sum of all solutions to the equation 2cos²(x) - 7cos(x) - 4 = 0 for 0 < x < 2π is approximately 9.425 + 2π.
What is quadratic equation?In mathematics, a quadratic is a polynomial expression of the second degree, meaning it contains one or more terms that are squared but no terms that are cubed or higher. Quadratic functions are typically written in the form ax² + bx + c, where a, b, and c are constants and x is the variable.
To find the sum of all solutions to the equation 2cos²(x) - 7cos(x) - 4 = 0 for 0 < x < 2π, we can first use the quadratic formula to solve for cos(x):
cos(x) = [7 ± √(7² - 4(2)(-4))] / (2(2))
cos(x) = [7 ± √89] / 4
The two possible solutions for cos(x) are:
cos(x) = (7 + √89) / 4
cos(x) = (7 - √89) / 4
Note that for 0 < x < 2π, the cosine function has values between -1 and 1. Therefore, the first solution cos(x) = (7 + √89) / 4 is not valid, since it is greater than 1.
The second solution cos(x) = (7 - √89) / 4 is valid, since it is between -1 and 1. Therefore, the sum of all solutions to the equation is:
x = cos⁻¹[(7 - √89) / 4] + 2πn, where n is an integer.
We need to find the sum of all possible values of x for 0 < x < 2π. We can do this by finding the smallest and largest values of n that give valid solutions, and then summing the corresponding values of x.
The smallest value of n that gives a valid solution is n = 0, since cos⁻¹[(7 - √89) / 4] is already between 0 and 2π. The largest value of n that gives a valid solution is n = -1, since adding 2π to cos^(-1)[(7 - √89) / 4] gives a value greater than 2π.
Therefore, the sum of all solutions to the equation is:
89) / 4 - 2π]
x = cos⁻¹[(7 - √89) / 4] + cos⁻¹[(7 - √
x ≈ 6.2832 + 0.8429 + 2π
x ≈ 9.425 + 2π
The sum of all solutions to the equation 2cos²(x) - 7cos(x) - 4 = 0 for 0 < x < 2π is approximately 9.425 + 2π.
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An angle measures 50° more than the measure of its complementary angle. What is the measure of each angle?
The measure of the angle x is 70°, and the measure of its complementary angle is (90 - x) = (90 - 70) = 20°.
What is complementary angle?When two angles in geometry add up to 90°, they are said to be complimentary.
Right triangles frequently include complementary angles, where one angle is a right angle (measured 90 degrees), while the other two angles are mutually exclusive.
If two angles add up to 90 degrees, they are complimentary.
If one of the angles has a measure of x, then the complementary angle's measure is (90 - x).
We are told that the angle x measures 50° more than its complementary angle, which can be written as:
x = (90 - x) + 50
Simplifying and solving for x, we have:
2x = 140
x = 70
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An airplane over the ocean sights an island at an angle of depression of 45. At this time, the
distance from the airplane to the island is 15,000 meters. What is the height of the plane to
the nearest meter?
Type your answer...
The height of the plane above the ocean is approximately 15,000 meters to the nearest meter.
What is the angle of depression?The angle of depression is an angle formed between a horizontal line (such as the ground, ocean surface, or any other reference plane) and a line of sight from an observer looking downward towards an object or point of interest that is located below the observer's line of sight.
According to the given information:
The angle of depression is the angle formed between the horizontal line (such as the ocean's surface) and the line of sight from an observer looking downward to an object (such as the island). In this case, the angle of depression is given as 45 degrees.
Given:
Angle of depression = 45 degrees.
Distance from airplane to island = 15,000 meters.
To find the height of the plane, we can use trigonometry. The tangent function is commonly used to relate angles of depression to the height of an object above the horizontal.
In a right triangle, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. In this case, the side opposite the angle of depression is the height of the plane, and the side adjacent to the angle is the distance from the airplane to the island.
Using the tangent function:
tan(angle of depression) = height of plane/distance to the island
Plugging in the given values:
tan(45 degrees) = height of plane / 15,000 meters
We can now solve for the height of the plane:
height of plane = tan(45 degrees) * 15,000 meters
Using a calculator, we find:
height of plane = 15000 * tan(45 degrees) ≈ 15000 meters (rounded to the nearest meter)
So, the height of the plane above the ocean is approximately 15,000 meters to the nearest meter.
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Describe fully the single transformation which takes shape A to shape B
The transformation that took place from shape A to shape B is that there was a 180° turn around at point 0,2 on the graph.
How to determine the transformation of a shape?On the graph, the shape A is the same size as the shape B but with different angles of transformation.
For shape A,
The width at x-axis = -4,-2
length at y-axis = 1,4
For shape B;
The width at x-axis = 2,4
length at y-axis = 0,3
Therefore, transformation that took place from shape A to shape B is that there was a 180° turn around at point 0,2 on the graph.
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what is the side length of the dilated square?
The side length of the dilated side would be 3 cm.
How to find the side length ?The area of the original square is 16 cm ², so its side length is √ 16 = 4 cm.
When the square is dilated by a factor of 0. 75, its area will be reduced to ( 0. 75 ) ² times the original area , which would then be:
= ( 0.75 ) ² x 16 cm ² = 9 cm²
Therefore, the area of the scaled square is 9 cm². The area of a square equals to the size of its side duration, thus we can locate the side length of the magnified square by extracting the square root of its area:
√ 9 cm = 3 cm
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An ice cream container is 20 cm long, 10 cm wide and 6 cm high. How many liters of ice cream can it hold?
The Ice Cream container will hold 1.2 liters of Ice Cream.
The Volume of Ice Cream can be calculated by Cubical Volume Equation V=l*b*h _______(1). We Have the data : Length = 0.2 meters, Width = 0.1 meters, Height = 0.06 meters
Now Having the Values of Length, Height & Width. Putting these Values in The Equation (1),
Volume = 0.2*0.1*0.06 m³
Volume = 0.0012 m³
We have got the Volume of Ice Cream that can be contained by the Container in m³. To Convert into Liters, we have equation 1 m³=1000 Liters. According to this, The Volume of Ice Cream Contained in The Container will be 1.2 Liters.
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Need help asap it’s 8th grade math
Answer:
B.
Step-by-step explanation:
x + 3x + 6 = 6 + 4x
Add like terms.4x + 6 = 6 + 4x
Transfer like terms to the same side of the equation.4x - 4x = 6 - 6
When we add and subtract like expressions, the result will be 0 = 0.This means, whatever value we pick in place of x, there will always be a solution therefore, the equation in option B has infinitely many solutions.
Jim is making smoothies for his friends. If 5 ounces of fruit is needed for each smoothie, how many pounds of fruit would he need to make 12 smoothies?
Answer:
Jim would need 3.75 pounds of fruit to make 12 smoothies.
Step-by-step explanation:
Since 1 pound = 16 ounces, 12 smoothies will require:
12 x 5 = 60 ounces of fruit
To convert this to pounds, we divide by 16:
60 / 16 = 3.75 pounds of fruit
Therefore, Jim would need 3.75 pounds of fruit to make 12 smoothies.
Below is the graph of equation y=|x+2|-1. Use this graph to find all values of x such that y>0, y<0
Note that all values of y > 0 at x = (0, 1, 2, 3, 4)
How is this so?As seen from the graph attached in answer area as well, The graph is above x-axis (i.e. y value of equation) only when x has values {0, 1, 2, 3, 4}.
At x = 0:
y = - | 0-2| + 2
⇒ - 2+ 2
y = 0
At x = 1:
y = - | 0-1| + 2
⇒ 0+ 2
y = 1
At x = 2:
y = - | 2-2| + 2
⇒ - 1+ 2
y = 1
At x = 3:
y = - | 3-2| + 2
⇒ - 1+ 2
y = 1
At x = 4:
y = - | 4-2| + 2
⇒ - 2+ 2
y = 0
Thus, all values of y > 0 at x = (0, 1, 2, 3, 4)
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A patient weighs 258 pounds. What is the patients weight in kilograms? Round to the nearest tenth
Answer:
Step-by-step explanation:
well 2.20 (ronded) pounds is one kilogram so multiply 258 by 2.20 then divide by two to get 117.03
Payout on homeowner's insurance policy. Ivy Gordon's home in Charleston was recently gutted in a fire. Her living and dining rooms were destroyed completely, and the damaged personal property had a replacement price of $32,000. The average age of the damaged personal property was 5 years, and its useful life was estimated to be 15 years. What is the maximum amount the insurance company would pay Ivy, assuming that it reimburses losses on an actual cash-value
basis?
Therefore, if the insurance provider reimburses damages on a real cash-value basis, the most the insurer could possibly pay Cornell for the destroyed personal goods is $21,333.33.
What Does Percent Mean?The fraction or proportion can be expressed as a percentage as a number out of 100. Latin's translation of the term "percent" is "per hundred". The part (numerical number) is divided by the total (numerical value) to determine the percentage, which is then multiplied by 100.
If Ivy's losses are covered on a true cash-value basis, her insurer would be required to pay the following maximum amount:
The depreciated worth of the destroyed personal property must be determined first. Given that the expected 15-year useful life and the average age of the product
Given that its expected usable life is 15 years and that its average age is 5 years, the amount of its usefulness that has already been used up is:
5 years / a fifteen-year period equals a third, or 33.33%
As a result, the depreciated worth of the personal property damaged is:
$32,000 x (100% - 33.33%) = $21,333.33
Therefore, if the insurance provider reimburses damages on a genuine cash-value basis, the most the insurer could possibly pay Harvard for the destroyed personal goods is $21,333.33. This is due to the insurance provider's refusal to pay Ivy the full cost of replacement of what was damaged, but only the diminished worth of it.
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The maximum amount the insurance company would pay Ivy on an actual cash-value basis is $21,338.68.
what is percentage?
Percentage is a way of expressing a number or proportion as a fraction of 100. It is represented by the symbol "%".
To determine the maximum amount the insurance company would pay Ivy on an actual cash-value basis, we need to calculate the depreciated value of the damaged personal property.
First, we can calculate the percentage of the useful life that the damaged personal property had been used up to the time of the fire:
Percentage of useful life used = (age of damaged property / useful life) x 100%
Percentage of useful life used = (5 / 15) x 100%
Percentage of useful life used = 33.33%
Next, we can calculate the depreciation percentage based on the percentage of useful life used:
Depreciation percentage = Percentage of useful life used x 1/100
Depreciation percentage = 33.33% x 1/100
Depreciation percentage = 0.3333
Finally, we can calculate the depreciated value of the damaged personal property:
Depreciated value = Replacement price x (1 - Depreciation percentage)
Depreciated value = $32,000 x (1 - 0.3333)
Depreciated value = $21,338.68
Therefore, the maximum amount the insurance company would pay Ivy on an actual cash-value basis is $21,338.68.
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find two numbers who’s product is -10
Answer:
One possible pair of numbers whose product is -10 is 2 and -5. Another possible pair of numbers whose product is -10 is -2 and 5.
What is a coterminal angle of pi/4?
9pi/4 pi/2 3pi/4
The angle 9pi/4 is a positive coterminal angle of pi/4.
What is a coterminal angle?
Two angles are called coterminal if they have the same initial and terminal sides. In other words, two angles are coterminal if they differ by a multiple of 360 degrees or 2π radians. For example, 30 degrees and 390 degrees are coterminal angles, as are π/4 and 9π/4.
A coterminal angle of pi/4 can be found by adding or subtracting any multiple of 2pi until we get an angle between 0 and 2pi that is equivalent to pi/4.
One way to find a positive coterminal angle is to add 2pi:
pi/4 + 2pi = 9pi/4
So, The angle 9pi/4 is a positive coterminal angle of pi/4.
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The principal at Carr Elementary and Middle School bought candy bars to be given to
teachers for Teacher Appreciation Week. Her first order was for 36 candy bars and
she paid $27. The second order was for 24 candy bars and she paid $18. The
relationship between candy bars and the amount paid is proportional, Write an
equation to represent the relationship, where y is the number of candy bars and * is
the cost, in dollars.
The equation that represents the relationship between x and y, where y is the number of candy bars and x is the cost in dollars, is x = 0.75y.
What is an equation?An equation is a mathematical statement showing the equality or equivalence of two or more mathematical expressions.
Equations contain mathematical expressions with the equal symbol (=).
First Order Second Order
The number of candy bars 36 24
The total cost of order $27 $18
The unit cost per candy bar = $0.75 $0.75
($27 ÷ 36) ($18 ÷ 24)
Let the number of candy bars bought = y
Let the cost of the candy bars = x
Equation:36x = $27
x = $0.75
Similarly, 24x = $18
x = $0.75
Therefore, the equation representing the relationship is:
x = 0.75y
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Polygon JKLM is drawn with vertices J(−4, −4), K(−4, −6), L(−1, −6), M (−1, −4). Determine the image coordinates of L′ if the preimage is reflected across y = −2.
L′(−3, 6)
L′(−1, 6)
L′(−1, 2)
L′(1, 2)
The image coordinates of L′ are L′(-1, 2).
What are Transformation and Reflection?
Single or multiple changes in a geometrical shape or figure are called Geometrical Transformation.
A geometrical transformation in which a geometrical figure changes his position to his mirror image about some point or line or axis is called Reflection.
To reflect the preimage of point L across the line y = -2, we need to find the distance between L and the line y = -2 and then move that same distance above the line to get the image L′.
The distance between point L and the line y = -2 is 4 units (since the y-coordinate of point L is -6 and the y-coordinate of the line y = -2 is -2).
So, to get the image L′, we move 4 units above the line y = -2 starting from the x-coordinate of L, which is -1. This gives us the coordinates (-1, 2).
Therefore, the image coordinates of L′ are L′(-1, 2).
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what is the volume of this figure?
The volume of the hexagonal prism is 374.13 cubic inches.
What is apothem of a polygon?The distance from a regular polygon's centre to one of its sides' midpoints is known as the apothem. In other terms, it is the greatest circle whose radius fits inside the polygon. The apothem runs through the middle of the polygon and is perpendicular to the side it touches. All apothems are equivalent in a regular polygon.
For regular polygons, the apothem is a crucial quantity because it is used to determine the polygon's area. The formula: can be used to determine the area of a regular polygon.
A = apothem x perimeter x (1/2)
The volume of the hexagonal prism is given by the formula:
V = B x h
Here, B is the base area thus,
Given the base area = 41.57 sq. in and height = 9 in we have:
V = (41.57)(9) = 374.13 cubic inches.
Hence, the volume of the hexagonal prism is 374.13 cubic inches.
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NEED HELP NOW DUE TODAY
Warren is building shelves for his 3-D printed model collection. He has a piece of wood that is 4.5 feet long. After cutting five equal pieces of wood from it, he has 0.7 feet of wood left over.
Part A: Write an equation that could be used to determine the length of each of the five pieces of wood he cut. (1 point)
Part B: Explain how you know the equation from Part A is correct. (1 point)
Part C: Solve the equation from Part A. Show every step of your work. (2 points)
Part A: The equation that could be used to determine the length of each of the five pieces of wood cut by Warren is: x + 0.7 = 4.5
Part B: The equation from Part A is correct because it takes into account the total length of the wood (4.5 feet), as well as the amount of wood that is left over (0.7 feet).
Part C: the length of each of the five pieces of wood cut by Warren is 3.8 feet.
What is equation?It is made up of two mathematical objects, with an equals sign (=) between them. Equations are used to represent relationships between unknown variables and can be solved to find their values.
Part A:
The equation that could be used to determine the length of each of the five pieces of wood cut by Warren is: x + 0.7 = 4.5, where x is the length of each piece of wood.
Part B:
The equation from Part A is correct because it takes into account the total length of the wood (4.5 feet), as well as the amount of wood that is left over (0.7 feet).
This equation can be used to calculate how much wood Warren has cut off from the original 4.5 feet of wood, which is the length of each of the five pieces of wood.
Part C:
Solving the equation from Part A:
x + 0.7 = 4.5
Subtract 0.7 from both sides:
x + 0.7 - 0.7 = 4.5 - 0.7
x = 3.8
Therefore, the length of each of the five pieces of wood cut by Warren is 3.8 feet.
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A student needs to decorate a box as part of a project for her history class. A model of the box is shown.
A rectangular prism with dimensions of 22 inches by 14 inches by 3 inches.
What is the surface area of the box?
416 in2
232 in2
832 in2
616 in2
After answering the query, we may state that Therefore, the surface area of the box is 832 in².
what is surface area ?An object's surface area is a measure of how much space it takes up overall. The entire amount of space around a three-dimensional form is its surface area. The total surface area of a three-dimensional form is referred to as its surface area. By summing the areas of each face, one may get the surface area of a cuboid with six rectangular faces. Alternatively, you may identify the box's dimensions using the following formula: Surface (SA) equals 2lh, 2lw, and 2hw. A three-dimensional form's surface area is a measurement of how much space it takes up overall on the surface (a three-dimensional shape has a height, breadth, and depth).
To find the surface area of the rectangular prism, we need to find the area of each of its six faces and then add them up.
The top and bottom faces each have an area of 22 inches by 14 inches = 308 square inches.
The front and back faces each have an area of 22 inches by 3 inches = 66 square inches.
The left and right faces each have an area of 14 inches by 3 inches = 42 square inches.
2(308) + 2(66) + 2(42) = 616 + 132 + 84 = 832 square inches.
Therefore, the surface area of the box is 832 in².
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Is the following function one to one? f(x) = (x + 2)²
Yes No
Answer:
Yes, the function f(x) = (x + 2)² is one-to-one.
45 POINTS! Three balls are packaged in a cylindrical container. The balls just touch the
top, bottom, and sides of the cylinder. The diameter of each ball is 13 cm.
a. What is the volume of the cylinder rounded to the nearest cubed centimeter
b. What is the total volume of the three balls rounded to the nearest cubed centimeter?
c. What percent of the volume of the container is occupied by the three balls?
Answer:
a) 5177 cubic centimeters
b) 3451 cubic centimeters
c) 66.66% (67%)
Step-by-step explanation:
a) V=pi*r2*h
V=pi*6.5^2*39
V=5176.5593
b) V=4/3*pi*r^3
V=4/3*pi*6.5^3
V=1150.34651
remember we have to multiply by 3 since there are 3 balls:
V=3451.03953
c) 3451/5177=0.66660*100=66.66%
Each spinner below is spun one time. X represents that number of spins that land on 2. Which table correctly displays the probability distribution?
The probability distribution for the number of spins that land on two is given as follows:
P(X = 0) = 0.5625.P(X = 1) = 0.375.P(X = 2) = 0.0625.How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
Each spinner has a 3/4 probability of not landing on two, hence the probability of landing on two zero times is given as follows:
P(X = 0) = 3/4 x 3/4
P(X = 0) = 9/16
P(X = 0) = 0.5625.
For two times, the probability is given as follows:
P(X = 2) = 1/4 x 1/4
P(X = 2) = 1/16
P(X = 2) = 0.0625.
Hence the probability of one landing is given as follows:
P(X = 1) = 1 - (0.5625 + 0.0625)
P(X = 1) = 0.375.
(considering complementary events)
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Carlos has been collecting baseball cards for the past few years. The number of total cards in his collection each year is as follows. • 50 cards the first year • 100 cards the second year • 150 cards the third year • 200 cards the fourth year
Write a function that represents the number of cards as a function of the number of years, t .
A linear function representing the number of cards as a function of the number of years, t is y = 50 + 50t.
What is a linear function?A linear function is a mathematical or algebraic equation of a straight line in the slope-intercept form.
Linear functions are written as f(x) = mx + b, where m is the slope and b is the y-intercept of the line.
Number of Total Cards in Carlos' Collection
Year Total Cards
Year 1 50
Year 2 100
Year 3 150
Year 4 200
Slope = Rise/Run = (100 - 50)/(2 - 1)
= 50
Initial value in the first year = 50
Let the number of years involved = t
Let the value in year t = y
Linear Equation:y = 50 + 50t
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What is the difference between saving and
investing? Provide examples.
Answer:
What is Saving?
Saving means to keep money aside, not using it for any purpose at all, until in reach of desired goal. While some save for emergencies, others save for family or materials.
Example: My father is saving for a really nice vacation trip to Canada. He needs enough money to pay for gas, the hotel rooms, food and other necessities.
What is Investing?
Investing is the practice of putting interest into something. Investing involves paying for something in increments while also having flowy income. You could invest in almost anything.
Example: My mother and I are investing into a large, family-sized, RV. We are making custom arrangements and changes while we are still living in, and keeping our tiny-home.
What is the value of x?
sin(x+16)°=cos(2x+14)°
Enter your answer in the box.
The value of x for which sin(x+16)°=cos(2x+14)° is 20
How to determine the value?Trigonometry is a branch of mathematics concerned with relationships between angles and ratios of lengths
The given equation says:
sin(x+16)°=cos(2x+14)°
Remember that sin(90-x) = cos x
Applying this formula we have
So comparing we have,
sin(x+16)°=cos(2x+14)°
90 - (x + 16) = 2x +14
distributing - over the bracket
90 -x - 16 = 2x + 14
bringing like terms together,
90-16-14 = 2x +x
60 = 3x
Dividing both sides by 3,
x =20
Therefore the value of sin(x+16)°=cos(2x+14)° is 20⁰
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Boris's gas tank is 1/2 full. After he buys 3 gallons of gas, it is 2/3 full. How many gallons can Boris's tank hold?
Boris's gas tank can hold 18 gallons of gas.
What are gallons?Gallons are a unit of volume commonly used to measure liquids, particularly in the United States. One gallon is equivalent to 128 fluid ounces or 3.785 liters. It is often used to measure the amount of gasoline or other fuels used in vehicles, as well as the amount of water in swimming pools or storage tanks.
Let's assume that the tank can hold "x" gallons of gas.
According to the problem, Boris's gas tank is initially half full, which means that it contains:
[tex]1/2 * x = x/2[/tex] gallons of gas
After he buys 3 gallons of gas, the tank is 2/3 full, which means it contains:
[tex]2/3 * x = 2x/3[/tex]gallons of gas
We can set up an equation based on the given information:
[tex]x/2 + 3 = 2x/3[/tex]
Multiplying both sides by 6 to eliminate the fractions:
[tex]3x + 18 = 4x[/tex]
Subtracting 3x from both sides:
[tex]18 = x[/tex]
Therefore, Boris's gas tank can hold 18 gallons of gas.
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Boris's gas tank can hold 18 gallons of gas.
What are gallons?
Gallons are a unit of volume commonly used to measure liquids, particularly in the United States. One gallon is equivalent to 128 fluid ounces or 3.785 liters. It is often used to measure the amount of gasoline or other fuels used in vehicles, as well as the amount of water in swimming pools or storage tanks.
Let's call the total capacity of Boris's gas tank "x". We know that when the tank is half full, it contains 1/2x gallons of gas. After Boris buys 3 gallons of gas, the tank is 2/3 full, which means it contains 2/3x gallons of gas. We can set up an equation to solve for x:
1/2x + 3 = 2/3x
To solve for x, we need to isolate it on one side of the equation. We can do this by first subtracting 1/2*x from both sides:
3 = 2/3x - 1/2x
To simplify the right side, we need to find a common denominator. The smallest common denominator of 2 and 3 is 6, so we can rewrite the fractions as:
3 = (4/6)*x - (3/6)*x
Now we can combine the terms on the right side:
3 = (1/6)*x
To solve for x, we can multiply both sides by 6:
x = 18
Therefore, Boris's gas tank can hold 18 gallons of gas.
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Find the value of angle c. Give your answer
in degrees (°).
65°
127⁰°
140°
Not drawn accurately
Answer:
65° + 127° + 140° = 332°
360° - 332° = 28° (measure of missing interior angle)
28° + c = 180°, so c = 152°.
The value of angle C is 152°
What is Quadrilateral:A quadrilateral is a four-sided polygon, which means it is a closed shape with four straight sides. The sum of the angles in a quadrilateral is always 360 degrees.
To solve the given problem, find the missing angle using the sum of angles and find the angle C with the 4th angle of the Quadrilateral.
Here we have
A quadrilateral with angles 65°, 140°, 127°
Let 'x' be the missing angle
As we know the sum of angles in a quadrilateral is 360°
=> 65° + 140° + 127° + x = 360°
=> 332° + x = 360°
=> x = 28°
Here ∠C + 28° = 180° [ Sum of Linear angles ]
=> ∠C = 180° - 28°
=> ∠C = 152°
Therefore,
The value of angle C is 152°
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how do i put this into desmos calculator?
The height of the air plane is obtained as 10503 ft.
What is the height?We know that we can be able able to use the principles that can apply to the right triangle so as to be able to obtain the height that the triangle has been able to attain.
We know that in working with the right triangle, we have to look out for the ratio that we can be able to use to obtain the height that the problem in this case requires that we should find and as such we have that;
Tan 35 = H/15000
H = height of the airplane
H = 15000 Tan35
H = 10503 ft
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ridgette brings a bag of 100 assorted candies in different flavors to her swim meet. She randomly grabs some candies out of the bag and hands them out to her teammates. The table below shows the flavors she has handed out. Flavor Number of candies lemon 6 orange 5 grape 8 cherry 13 Based on the data, estimate how many lemon candies were in the bag of 100 candies
Based on the data, the estimated number of lemon candies in the bag of 100 assorted candies is about 19.
What is proportion?In mathematics, proportion refers to the relationship between two quantities that are equivalent or have a constant ratio. It is usually expressed as a fraction or a ratio. For example, if a recipe calls for 2 cups of flour and 1 cup of water, the proportion of flour to water is 2:1 or 2/1. Proportions are used in a variety of mathematical and real-world situations, such as solving problems involving ratios, rates, and percentages.
In the given question,
We can use a simple proportion to estimate the number of lemon candies in the bag. We know that Ridgette handed out a total of 6 lemon candies out of a total of candies. Therefore, the proportion of lemon candies in the bag is:
6/total candies = number of lemon candies/100
We can cross-multiply to solve for the number of lemon candies:
number of lemon candies = 6 x 100 / total candies
We can also use the information about the other flavors to estimate the total number of candies in the bag. The total number of candies is:
total candies = lemon + orange + grape + cherry
Using the information from the table, we can estimate the total number of candies:
total candies = 6 + 5 + 8 + 13 = 32
Therefore, the estimated number of lemon candies in the bag is:
number of lemon candies = 6 x 100 / 32 = 18.75
We can round this to the nearest whole number to estimate that there were about 19 lemon candies in the bag of 100 assorted candies.
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You are a researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 25 bacteria reveals a sample mean of
¯x=64 hours with a standard deviation of s=4.2 hours. You would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.6 hours at a 95% level of confidence.
What sample size should you gather to achieve a 0.6 hour margin of error? Round your answer up to the nearest whole number.
n = bacteria
Answer:
567
Step-by-step explanation:
n
x is atleast 12 inequality
The statement can be written as the inequality:
x ≥ 12
How to write that as an inequality?We know that x is at least 12, so x can be equal to 12, or larger. We want to write that as an inequality, and it can be written as:
x ≥ 12
The symbol:
"≥"
Means that the thing in the left is larger or equal than the thing in the right, so that inequlity represents the given statement.
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