The unit circle's radius is 1, that is 1 is the radius of the circle.
45 degrees' sine, cosine, and tan values are
[tex]sin \ 45^0=\frac{1}{\sqrt{2} }[/tex]
[tex]cos\ 45^0=\frac{1}{\sqrt{2 } }[/tex]
[tex]tan \ 45^0 =1[/tex]
Due to the fact that all angles are smaller than,
the reference angle coincides with the specified angle. In the first quadrant, 45 degrees is the reference angle, and sine, cosine, and tangent are all positive trigonometric functions.
In the second quadrant, sine is positive, cosine is negative, and tan is positive. In the fourth quadrant, sine and tan are negative, cosine is positive.
In the case of a unit circle, the cosine sine of the angle formed by the horizontal line is used to represent the unit circle's coordinates.
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Write 98 as a product of prime factors.
HELP?
Answer:
2*7*7
Step-by-step explanation:
Answer: 2*7^2
Step-by-step explanation:
98=2*49
and 49=7^2
so 98=2*7^2
write an equation for the line with the following slop and y-intercept
slope=-6; y-intercept =1
Answer: y = -6x + 1
Step-by-step explanation:
An equation for a line written in slope-intercept form is written as y = mx + b, with m being the slope and b being the y-intercept.
How to graph f(x)=1/x
Answer: ill explain
Step-by-step explanation:
the form for linear equations are f(x) = mx+b
b is the y-intercept (otherwise known as the place where the line crossed the y-axis)
since there is no b, the y-intercept is 0. The line with cross the point (0,0)
your problem is f(x) = x/1
x/1 is equal to 1x/1.
to graph linear functions, you do rise over run (rise/run)
in this case, you rise (go up) one unit, and run (go right) one unit since your digits are 1 and 1
the sample space contains 9 as and 5 bs. what is the probablity that a randomly selected set of 3 will include 1 a and 2 bs?
The probability that a randomly selected set of 3 will include 1 a and 2 b is 45/182.
Probability
The probability is equal to the variety of possible outcomes.
For instance, there is only one way to get a head and there are a total of two possible outcomes, so the probability of flipping a coin and getting heads is 1 in 2. Writing P(heads) = 12.
the total number of outcomes that could occur.
there are total 4 types of probability,
1- Classical
2- Empirical
3- Subjective.
4- Axiomatic
There are 66 equally likely outcomes, or C(9+5,3) =C(14,3)= 364 possible outcomes.
Only C(9,1) * C(5,2)= 90 of these contain 1A and 2B. thus, the likelihood is 90/364.
The value of the solution is 90/364 or 45/182.
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Roots of quadratic functions. For which value(s) of b does the function f(z) = x² + bx +1 have (a) two real roots? (b) only one real root?(c) no real roots?
The values of b for the function f(x) = x² + bx + 1 has
(a) two real roots is |b| > 2 .
(b) has only one real roots is b = ±2 .
(c) has no real roots is b < -2 or b > 2.
A Quadratic Function of the form f(x) = x² + bx + 1 has two real roots if and only if its discriminant (b² - 4ac) is positive, where a = 1, c = 1 .
So ,the discriminant can be written as ⇒ b² - 4 × 1 × 1
⇒ b² - 4.
Part (a) ; the two roots are real if and only if b² - 4 > 0,
⇒ b² > 4.
⇒ |b| > 2 .
Part (b) : function has only one real root if and only if its discriminant =0 .
⇒ b² - 4 = 0 ;
⇒ b² = 4 ;
which implies ⇒ b = ±2 .
Part (c) : function has no real root if and only if its discriminant < 0 .
⇒ b² - 4 < 0 ;
⇒ b² < 4 ;
which implies ⇒ b < -2 or b > 2.
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What is the average of the 3-day simply moving averages for these five days to the nearest $0.01?
The table shows the closing price of a stock over 5 days.
Check the picture below.
Evaluate the expression 42+6⋅52−33÷32 4 2 + 6 · 5 2 - 3 3 ÷ 3 2 .
The value of the expression 42+6⋅52−33÷32 is 352.96
What is Expression?An expression is combination of variables, numbers and operators.
Remember the order of operations rules.BODMAS: parentheses first, then exponents, then multiplication, then division, then addition and subtraction is last.
= 42+6⋅52−33÷32
multiply first
= 42 + (6*52) - 33 ÷ 32
= 42 + 312 - 33 ÷ 32
division second
= 42 + 312 - 1.03125
addition next
= 354 - 1.03125
subtraction last
= 352.96875
Hence, the value of the expression 42+6⋅52−33÷32 is 352.96
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tabria buys a bag of cookies that contains 8 chocolate chip cookies, 8 peanut butter cookies, 5 sugar cookies and 8 oatmeal cookies. what is the probability that tabria randomly selects a peanut butter cookie from the bag, eats it, then randomly selects an oatmeal cookie? express you answer as a reduced fraction.
The probability of Tabria randomly selecting a peanut butter cookie and then an oatmeal cookie is 8/35 or 8 in 35 chance
The probability of selecting a peanut butter cookie first is 8/29, since there are 8 peanut butter cookies and 29 total cookies of all variety in the bag. Then, the probability of selecting an oatmeal cookie after eating a peanut butter cookie is 8/28, since there are now only 28 cookies remaining in the bag and 8 of them are oatmeal cookies. To find the combined probability, we multiply the individual probabilities:
8/29 × 8/28 = 8/35.
This means there is an 8 in 35 chance that Tabria will randomly select a peanut butter cookie and then an oatmeal cookie.
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3/5 intoconvert to decimal
Answer: 0.6
Step-by-step explanation:
3 divided by 5 is 0.6
0.6 x 5 = 3
3/5 = 0.6
Solve the equation.
P = _
After solving the equation P = [tex]$ \frac{ry}{r+y}[/tex], y is equal to [tex]\dfrac{rp}{(r- p)}[/tex].
What is equation?
An equation is a mathematical statement that expresses the equality of two expressions by showing that they have the same value. Equations can be used to describe a variety of physical, chemical and biological processes.
They are often used to solve problems in a variety of fields, including engineering, finance and physics. Equations are typically written in standard form, with the equal sign being used to indicate the equality of two expressions.
The two expressions can be written in a variety of forms, including algebraic equations, differential equations, calculus equations and trigonometric equations. The solutions to equations can be found by using a variety of techniques, including solving equations graphically or analytically.
Given
P = [tex]$ \frac{ry}{r+y}[/tex]
Solve for y
⇒ pr + py = ry
⇒ pr = y(r−p)
⇒ y = [tex]\dfrac{rp}{(r- p)}[/tex]
Thus, after solving the equation P = [tex]$ \frac{ry}{r+y}[/tex],y is equal to [tex]\dfrac{rp}{(r- p)}[/tex].
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Complete question:
Find the volume of the solid obtained by rotating the region enclosed by the graphs x=y^4 and x= y^1/4 about the y-axis over the interval [0,1].
The volume of the solid obtained by rotating the region enclosed by the graphs [tex]x=y^4[/tex] and [tex]x= y^1/4[/tex] about the y-axis over the interval [0,1] is 4π/7.
[tex]V = π ∫y^4 - y^1/4 dy[/tex]
= π ∫[tex]y^7/4 dy[/tex]
=[tex][4π/7*y^(7/4+1)]_0^1[/tex]
= [tex]4π/7[/tex]
To find the volume of the solid obtained by rotating the region enclosed by the graphs[tex]x=y^4[/tex] and [tex]x= y^1/4[/tex] about the y-axis over the interval [0,1], we first use the formula for the volume of a solid of revolution: V = π ∫[tex]y^2 - y^1/4 dy.[/tex] Then, we rewrite the upper limit of the integral as [tex]y^7/4[/tex]and evaluate the integral from 0 to 1. This gives us the volume as 4π/7.
The volume of the solid obtained by rotating the region enclosed by the graphs [tex]x=y^4[/tex] and [tex]x= y^1/4[/tex] about the y-axis over the interval [0,1] is 4π/7.
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find the value of k for which the constant function x(t) = k is a solution of the differential equation . 4t^3 dx/dt + 2x - 2 =0
As per the differential equation, the value of k for which the constant function is 1.
The term called differential equation in math is defined as an equation which contains one or more terms and the derivatives of one variable
Here we know that the differential equation is
=> 4t³ dx/dt + 2x - 2 = 0
Here we have also know that x(t) = k is a solution of the differential equation.
Which means the t the value of x' = 0.
Then the value of 4t³ dx/dt = 0.
So, here we have rewritten the equation like the following,
=> 0 + 2x - 2 = 0
Here we know that the value of x = k, then we get the equation like the following,
=> 2k - 2 = 0
=> k = 1
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A textbook tore old a combined total of 251 biology and ociology textbook in a week. The number of ociology textbook old wa 67 le than the number of biology textbook old. How many textbook of each type were old?
From the combination of 251 textbook, 92 sociology and 159 biology textbook were sold.
Let the number of biology textbook be x. So, the number of sociology textbook = 251 - x. The difference between the number of two books is 67. Representing this as equation.
Number of biology textbook = number of sociology textbook + 67
Keep the values in formula -
x = 251 - x + 67
Rewriting the equation
x + x = 251 + 67
Performing addition on both sides of the equation
2x = 318
x = 318/2
Performing division
x = 159
Number of biology textbook = 159
Number of sociology textbook = 251 - 159
Number of sociology textbook = 92
Thus, 92 sociology and 159 biology textbook 1ere sold.
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The complete question is -
A textbook store sold a combined total of 251 biology and sociology textbook in a week. The number of sociology textbook old was 67 less than the number of biology textbook sold. How many textbook of each type were sold?
The box plots show theo’s math scores and language arts scores. math 2 box plots. the number line goes from 50 to 100. for math, the whiskers range from 55 to 90, and the box ranges from 60 to 85. a line divides the box at 80. for language arts, the whiskers range from 50 to 90, and the box ranges from 60 to 80. a line divides the box at 70. language arts about 50% of theo’s scores are in which range for each subject? 60 to 85 for math; 60 to 80 for language arts 55 to 90 for math; 50 to 90 for language arts 55 to 60 for math; 50 to 60 for language arts 85 to 90 for math; 80 to 90 for language arts
Answer:The box plots for Theo’s math scores and language arts scores.
2 box plots. The number line goes from 50 to 100.
For math, the whiskers range from 55 to 90, and the box ranges from 60 to 85. A line divides the box at 80.
For language arts, the whiskers range from 50 to 90, and the box ranges from 60 to 80. A line divides the box at 70.
About 50% of Theo’s scores are in which range for each subject?
60 to 85 for math; 60 to 80 for language arts
55 to 90 for math; 50 to 90 for language arts
55 to 60 for math; 50 to 60 for language arts
85 to 90 for math; 80 to 90 for language arts
Step-by-step explanation:
the whiskers range from 55 to 90 => ( min 55 , max 90 , range = 90-55 = 45)
the box ranges from 60 to 85. => (Q₁ = 60 and Q₃ = 85)
A line divides the box at 80 => (Q₂ = Median = 80)
For language arts,
the whiskers range from 50 to 90 => ( min 50 , max 90 , range = 90-50 = 40)
the box ranges from 60 to 80. => (Q₁ = 60 and Q₃ = 80)
A line divides the box at 70. => (Q₂ = Median = 70)
50% of Theo’s scores lies between Q₁ and Q₃
find all points on the curve defined by the equations x(t)=2sin(8t) and y(t)=−9cos(8t) with a slope of −93–√2 when 0≤t<π8
The point on the curve with a slope of −93–√2 is (2, 0.43)
Given x(t) = 2 sin(8t) and y(t) = −9 cos(8t)
We are asked to determine the points on the curve with a slope of −93–√2.
Now, x/2 = sin(8t) --(1)
-y/9 = cos(8t) --(2)
Squaring and adding equations (1) and (2)
(x/2)² + (-y/9)² = sin²(8t) + cos²(8t)
x²/4 + y²/81 = 1
Differentiating both sides
x/2 + (2y/81) (dy/dx) = 0
Given slope = dy/dx = −93–√2
(2sin(8t))/2 + (2(−9 cos(8t))/81)(-93 - √2) = 0
sin(8t) + (2/9)cos(8t)(93 + √2) = 0
Solving for t and taking care of 0 ≤ t <π/8
we get t = 11.59°, 34.09°, 79.09°......
But only t within the given range is t = 11.59°.
Now, x = 2sin(8 x 11.59°) = 2
and y = -9 cos(8 x 11.59°) = 0.43
Hence, the point on the curve with a slope of −93–√2 is (2, 0.43)
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State the value of h for which y = -x + 6 will be a tangent to the curve y = 5x^2 + 6x - 3h
what percent of the days did it rain in april
Can someone please help me with this aleks question
Answer: [tex]ST=27[/tex]
Step-by-step explanation:
[tex]RU=\sqrt{29^2 -21^2}=20\\\\SU=\sqrt{52^2 -20^2} \implies ST=\sqrt{52^2 -20^2}-21 =27[/tex]
An architect is designing a rectangular pavilion that has a length of x + 8 units and a width of x - 4 units. Write an expression representing the area covered by the pavilion.
Answer:
Step-by-step explanation:
The expression representing the area covered by the pavilion can be found by multiplying the length by the width:
A = (x + 8) * (x - 4)
where A represents the area and x is the length of one of the sides.
How can 0.5 be expressed as fraction?
Step-by-step explanation:
changing 0.5 to fraction is 1/2
0.5 is equal to 1/2 as a fraction.
What is 0.5 as a fraction?Being able to quickly translate fractions between different forms, such as decimals and percentages, is a useful talent. You may learn how to change 0.5 from a decimal to a fraction by following the instructions in this guide.The first step in changing 0.5 into a fraction is to rewrite it as p/q, where p and q are both positive integers. To begin with, the fraction 0.5 might be represented as simply 0.5/1 in order to be considered one.The next thing we'll do is count how many fractional digits there are in 0.5 after the decimal point, which in this case is 1. The numerator and denominator of 0.5/1 are multiplied by 10 to the power of the number of digits after the decimal point, depending on how many digits are present. For example, we would multiply by 100 for 0.45 because it has two fractional digits, and by 1000 for 0.324 because it has three fractional digits. We will therefore in this instance multiply the numerator and denominator of 0.5/1 each by 10:0.5×10 /1×10=5 / 10
Finally, discover related factors and eliminate them to simplify the fraction, if possible:5 /1 0 = 1 /2 .
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If a right triangle is formed when three squares are joined at their vertices, the area of the largest square is the same as the combined area of the two smaller squares.
in option A and B a right triangle is formed when three squares are joined at their vertices, the area of the largest square is the same as the combined area of the two smaller squares.
What is the Pythagoras theorem?The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
A) From the given figure, side of a largest square is 17 inches, side of a larger square is 15 inches and the area of a smaller square is 64 square inches.
We know that, the area of a square is side².
The side(c) of a smaller square is side²=64
Then, c=8 units
By using Pythagoras theorem, we get
17²=15²+c²
289=225+8²
289=289
B) From the given figure, area of a largest square is 169 square inches, area of a larger square is 144 square inches and the side of a smaller square is 5 inches.
We know that, the area of a square is side².
The side(a) of a largest square is side²=169
Then, a=13 inches
The side(b) of a larger square is side²=144
Then, b=12 inches
By using Pythagoras theorem, we get
13²=12²+5²
169=144+25
169=169
Therefore, in option A and B a right triangle is formed when three squares are joined at their vertices, the area of the largest square is the same as the combined area of the two smaller squares.
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Find the area of the figure.
(Sides meet at right angles.)
3 cm
2 cm
2 cm
2 cm
1 cm
2 cm
2 cm
6 cm
And then what is the square centimeters?
The area of the given figure in square centimeters would be = 45cm².
How to calculate the area of the given figure?Since the instructions involves that the edges meet at a right angle, the area of the figure should be calculated using the area of a rectangle= Length×width.
The length of the figure= 2+3= 5cm
The width of the figure= 2+2+5= 9cm
Therefore the area of the figure= 9×5= 45cm²
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When preparing to measure the height and weight of a newly admitted patient, why would the nurse ask about the patient's ability to stand?
To determine if the patient is steady enough to stand without assistance
The nurse asks the patient about their ability to stand when preparing to measure their height and weight because it is the most accurate way to measure these physical characteristics. By asking about their ability to stand, the nurse can determine if alternative methods of measurement need to be used, and can also identify any underlying health issues that need to be addressed
When a patient is admitted to a healthcare facility, one of the first things the healthcare provider does is gather information about the patient's physical characteristics. This includes measuring the patient's height and weight.
As part of the preparation process for measuring height and weight, the nurse may ask the patient about their ability to stand. There are several reasons why this is important.
First, the most accurate way to measure height is to have the patient stand upright, with their head facing forward and their feet together. If the patient is unable to stand, the nurse may have to use alternative methods to measure height, such as a measuring tape, which may not be as accurate.
Second, standing is also the most accurate way to measure weight. If the patient is unable to stand, the nurse may have to use a bed scale, which may not provide an accurate measurement of the patient's weight.
Finally, asking the patient about their ability to stand helps the nurse to determine if there are any underlying health issues that need to be addressed. For example, if the patient is unable to stand, it may indicate that they have a mobility issue that needs to be addressed.
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Tiana' laptop originally cot $250, but the tore offered a 20% off dicount. If Tiana alo paid alo paid 8% ale tax. What i the final place of the laptop?
Tiana' laptop originally cot $250, but the tore offered a 20% off discount, the final place of the laptop is $216.
Let the Laptops original price be $250
But he tore the offer of 20% discount, after getting a 20% discount,
(100 - 20)% x 250
= 200
Tiana then paid also a 8% tax on this price so,
= (100+8)% x 0.8(250)
=1.08 x 200
=216
So final price be ,
P = L (0.8)(1.08)
P = 250 x 0.8 x 1.08
P = $216
A tax is a mandatory financial charge or other type of levy imposed by a government organization on a taxpayer (an individual or legal entity) to cover costs associated with running the country and other public expenditures.
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you have added the fractions 2/5 and 4/10 by converting 2/5 into 4/10 so the denominators are the same. your addition has given you the total of 8/10. now what must you do?
Answer: Reduce the fraction to the simplest form.
Hope this helps :)
Step-by-step explanation:
8/10
/ 2
4/5
An automobile purchaed for $25 comma 000
i worth $2600
after 7
year. Auming that the car' value depreciated teadily from year to year, what wa it worth at the end of the third year?
The worth at the end of the third year is 15,400.
Depreciation:
The purchase value of an asset is the amount that it is purchased for. The value of the asset after a certain number of years is the difference between the purchase value and the accumulated depreciation.
There is a general formula to calculate Depreciation:
Depreciation Method = (Cost of an Asset – Residual Value)/Useful life of an Asset.
Given that Cost of an Asset=25000
Residual Value=2600
The useful life of an Asset=7
Now plug the given values in the above formula:
(25,000-2,600)/7=22,400/7=3,200
DM=3,200 which is calculated annually.
For the 3 years worth:
25,000-3,200*3
25,000-9,600=15,400.
At the end of the third year, the worth is 15,400.
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Can someone please please help mke i was suppose to finnish this at least 4 weeks ago please can someone answer these 3 question for at leat 150 or 200 points.
The missing values in the ratio table are:
1/12,3/2, and1/48The equivalent ratios in the order they appear in the table are:
1/24 : 1/21/12 : 11/8 : 3/2, and1/48 : 1/4What are equivalent ratios?Ratios that are the same when compared are referred to as equivalent ratios. To determine whether two or more ratios are equivalent, they can be put side by side.
An equivalent ratio is, for instance, 1 : 2 and 2:4.
Divide or multiply both amounts by the same number to arrive at an equivalent ratio. The method is the same as determining equivalent fractions.
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where does the dependance of experience is reflected in prior proability syntactic distinction semantic distinction both a & b none of the mentioned
The dependance on experience is reflected in the syntactic distinction between prior probability statements.
syntax refers to alphabet, while semantics refers to meaning. Syntax is the set of rules demanded to insure a judgment is grammatically correct; semantics is how one's wordbook, grammatical structure, tone, and other rudiments of a judgment coalesce to communicate its meaning. syntax is the arrangement or order of words, determined by both the pen's style and alphabet rules. consisting of or noting coinages that are combined in the same order as they would be if they were separate words in a corresponding construction The word blackberry, which consists of an adjective followed by a noun, is a syntactic emulsion.
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1. on a two-lane, two-way road you cannot pass or overtake another vehicle within how many feet of a bridge, viaduct, tunnel, intersection, or railroad grade crossing?
Within 100 feet of a bridge, viaduct, tunnel, intersection, or railroad grade crossing.
In contrast to crossing over or under using an overpass or tunnel, a level crossing is an intersection where a railway line crosses a road, path, or (in rare circumstances) an airport runway at the same level. The phrase also applies when a light rail line crosses a road in a similar manner but has a separate right-of-way or reserved track.
Other terms include road through railroad, criss-cross, train crossing, and RXR. They also include railway level crossing, railroad crossing (mostly international), grade crossing, or railroad crossing (primarily American) (abbreviated).
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To estimate the height of a building, two students find
the angle of elevation from a point (at ground level)
down the street from the building to the top of the
building is 40°. From a point that is 250 feet closer to
the building, the angle of elevation (at ground level) to
the top of the building is 46°. If we assume that the
street is level, use this information to estimate the
height of the building.
The height of the building is
feet.
When the angle of elevation from a point on the structure to its top is 40°, the building has a height to the nearest foot of 758 feet.
what is triangle ?Offered that it has sides and three vertices, a triangle qualifies as a polygon. It belongs to the fundamental geometric shapes. Triangle ABC is the term used to refer to a triangle with the endpoints A, B, and C. When the three points are not collinear, a unique rectangle and triangle in Trigonometry are discovered. Triangles are polygons because they have three sections and three corners. The points where the four sides of the triangle converge are referred to as the triangle's corners. Three triangle angles are multiplied to yield 180 degrees.
given
Using the triangles OBD and OAD and the SOH CAH TOA identity
OAD in triangle
Divide the two resulting equations to obtain the value of "x" for the triangle OBD.
The building's height must then be determined to the closest foot.
Just to refresh your memory, H = xtan50 H = 636tan50
H = 636(1.1918)
H = 757.96 feet.
Consequently, the building is 758 feet tall to the nearest foot.
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