The value of tan(π/4) without using a calculator is 1. To find the value of tan(π/4), we can use the unit circle and the properties of trigonometric functions.
Step 1: Start by drawing a unit circle, which is a circle with a radius of 1 unit.
Step 2: Mark the point (1, 0) on the x-axis. This represents the angle π/4 radians.
Step 3: Draw a line from the origin (center of the circle) to the point (1, 0).
Step 4: This line represents the terminal side of the angle π/4.
Step 5: Next, draw a vertical line from the point (1, 0) to the y-axis.
Step 6: This vertical line intersects the y-axis at the point (0, 1).
Step 7: The length of this vertical line is the y-coordinate of the point (1, 0).
Step 8: Since tan(θ) = y/x, we can see that tan(π/4) = 1/1 = 1.
Therefore, the value of tan(π/4) without using a calculator is 1.
Note: In the unit circle, the angle π/4 is also known as 45 degrees, and tan(45 degrees) is equal to 1.
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how many cups of 3/4 equal 12
Answer:
16 of 3/4 a cup is equal to 12 cups.
Step-by-step explanation:
12 ÷ \(\frac{3}{4}\) = 16
\(\frac{3}{4}\) x 16 = 12
What is the domain of f?
An envelope contain 40 shopping vounchers of which 25 voucher each have value of $50 and 15 vouchers each have a value of $100. Amirah picks a voucher at random from the envelope .Find the probability that the voucher has a value of $100?
Answer:
yes is correct ◆◆◆◆◆◆◆◆◆◆♡♡♡♡♡
Answer:
30 percent
Step-by-step explanation:
hsyyehrbhfkej2bhsi
OM , ON and OP are the angle bisectors of ∠AOB, ∠BOC, and ∠COD respectively. ∠AOD and ∠BOE are straight angles.
Find m∠BOC, if m∠MOP = 110°.
Answer:
m∠BOC= 40 degrees
Step-by-step explanation:
A diagram has been drawn and attached below.
OM bisects AOB into angles x and x respectivelyON bisects ∠BOC into angles y and y respectivelyOP bisects ∠COD into angles z and z respectively.Since ∠AOD is a straight line
x+x+y+y+z+z=180 degrees
\(2x+2y+2z=180^\circ\)
We are given that:
m∠MOP = 110°.
From the diagram
∠MOP=x+2y+z
Therefore:
x+2y+z=110°.
Solving simultaneously by subtraction
\(2x+2y+2z=180^\circ\)
x+2y+z=110°.
We obtain:
x+z=70°
Since we are required to find ∠BOC
∠BOC=2y
Therefore from x+2y+z=110° (since x+z=70°)
70+2y=110
2y=110-70
2y=40
Therefore:
m∠BOC= 40 degrees
The diagram shows a solid metal cuboid.
The areas of three of the faces are marked on
the diagram.
The lengths, in cm, of the edges of the cuboid
are whole numbers.
The metal cuboid is melted and made into cubes.
Each of the cubes has sides of length 2.5 cm.
Work out the greatest number of these cubes that can be made.
You must show your working.
Answer:
6 cubes
Step-by-step explanation:
Considering the given cuboid, it can be deduced that;
length of the cuboid = 7 cm
width of the cuboid = 3 cm
height of the cuboid = 5 cm
Thus,
volume of the cuboid = length x width x height
= 7 x 3 x 5
= 105 cubic centimetres
The cubes has sides of length 2.5 cm.
volume of each cube = length x width x height
= 2.5 x 2.5 x 2.5
= 15.625 cubic centimetres
The greatest number of cubes that can be made = \(\frac{105}{15.625}\)
= 6.72
The greatest number of cubes that can be made from the cuboid is 6.
Write an
equation of the line passing through point P(-1,-4) that is parallel to
y = -6x + 8.
y = -6x -25 is equation of slope intercept .
What exactly does slope intercept mean?
A method of expressing a line's equation that makes it simple to identify the slope and y-intercept is known as the slope-intercept form. The point where the line is drawn the y-axis is known as the y-intercept, and the slope refers to how steep the line is.The equation is y = -6x + 8
compare with equation y=mx+b
slope m = -6
Use the point-slope method
y = -6x + 8
point P(-1,-4) point given (x1,y1)
y-y1=m(x-x1) point-slope form
y - ( -1 ) = -6 ( x - (-4))
y + 1 = -6 ( x + 4 )
y + 1 = -6x - 24
y = -6x -25
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what is the difference between shallow foundations and deep foundations? where would you recommend the use of deep foundations? explain.
Deep foundations are recommended for larger or hillside developments , or those on poor soil .
Foundation Systems in Building
There are two classifications of foundations in building shallow foundations and deep foundations . These categories refer to the depth of soil in which the foundation is formed .
Shallow Foundations : Shallow foundations are usually located less than six feet below the lowest finished floor of a structure.
Deep Foundations : Deep foundations are structural elements that are used to transfer loads from weak and compressible soils to a stronger layer, usually located at a significant depth below the ground.
Recommendation
A shallow foundation can be constructed in as little as a one-foot depth , whereas a deep foundation is formed at a depth of 10 - 300 feet . Deep foundations are recommended for larger or hillside developments , or those on poor soil .
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Answer:
Step-by-step explanation: A shallow foundation distributes loads from the building into the upper layers of the ground.
Shallow foundations perform very well on sites with strong soils, sufficiently thick natural gravel rafts overlying weaker soils or where robust, engineered ground improvement is carried out.
Deep foundations can provide a good foundation for houses on sites with poor soil conditions near the surface,
Factor
10x + 100x + 250
Arrange the equations in the correct sequence to find the inverse of f(2)=y==
33z-zy=y-4
33z +4=y(1+z)
33z-zy=y+4
33x+4=y+zy
1+z
y=f¹ (2) = 33274
+4
33z-zy = y +4
A =
33-
y=f-¹ (z) = 332+4
z (33-y)=y-4
↓
↓
↓
↓
Į
c ccccccccccccccccccccccccccccc
Help me please I’ll give brainliest if your correct
To find the selling price that will yield the maximum profit, we need to find the vertex of the quadratic function given by the profit equation y = -5x² + 286x - 2275.The x-coordinate of the vertex can be found using the formula:
x = -b/2a
where a = -5 and b = 286.
x = -b/2a
x = -286/(2(-5))
x = 28.6
So, the selling price that will yield the maximum profit is $28.60 (rounded to the nearest cent).
Therefore, the widgets should be sold for $28.60 to maximize the company's profit.
Hope I helped ya...
Answer:
29 cents
Step-by-step explanation:
The amount of profit, y, made by the company selling widgets, is related to the selling price of each widget, x, by the given equation:
\(y=-5x^2+286x-2275\)
The maximum profit is the y-value of the vertex of the given quadratic equation. Therefore, to find the price of the widgets that maximises profit, we need to find the x-value of the vertex.
The formula to find the x-value of the vertex of a quadratic equation in the form y = ax² + bx + c is:
\(\boxed{x_{\sf vertex}=\dfrac{-b}{2a}}\)
For the given equation, a = -5 and b = 286.
Substitute these into the formula:
\(\implies x_{\sf vertex}=\dfrac{-286}{2(-5)}\)
\(\implies x_{\sf vertex}=\dfrac{-286}{-10}\)
\(\implies x_{\sf vertex}=\dfrac{286}{10}\)
\(\implies x_{\sf vertex}=28.6\)
Assuming the value of x is in cents, the widget should be sold for 29 cents (to the nearest cent) to maximise profit.
Note: The question does not stipulate if the value of x is in cents or dollars. If the value of x is in dollars, the price of the widget should be $28.60 to the nearest cent.
consider the curve defined by the equation y=4x4 14xy=4x4 14x. set up an integral that represents the length of curve from the point (−3,282)(−3,282) to the point (3,366)(3,366).
The integral that represents the length of the curve from (-3, 282) to (3, 366) is ∫[a to b] √(1 + (dy/dx)^2) dx.
How can the length of a curve be represented using an integral?To find the length of a curve defined by the equation y = f(x) between two points (a, f(a)) and (b, f(b)), we can set up an integral. The integral representing the length of the curve is given by ∫[a to b] √(1 + (dy/dx)^2) dx, where dy/dx represents the derivative of y with respect to x.
In this case, the equation of the curve is y = 4x^4 - 14xy. To find the length of the curve between (-3, 282) and (3, 366), we need to evaluate the integral ∫[-3 to 3] √(1 + (dy/dx)^2) dx.
The expression inside the square root, 1 + (dy/dx)^2, represents an infinitesimal length element along the curve. By summing up these infinitesimal lengths over the interval [a, b], the integral calculates the total length of the curve between the given points.
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The length of a violin string varies indirectly with the frequency of vibrations of the string. When the length is 50 centimeters, the
frequency is 2 Hz
What is the frequency of a string 40 centimeters long?
Enter your answer in the box
Answer:
The answer is 2.5
Step-by-step explanation:
On the quiz I just type anything and that was the answer
“Negative one-fifth of a number, increased by 3, is at most 1.”
please help me its importent
thank you
Determina los puntos de intercepción con el eje x de la gráfica de y=x2-81
a.
x=9, x=-9
b.
x=1, x=-1
c.
x=8, x=-8
d.
No hay intersección con los ejes
The x-intercept of the function is given by x=±9
What are functions?Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given here: The function y=x²-81
To find x-intercepts of the functions we set y=0
Thus y=x²-81
x²-81=0
x=√81
x=±9
Hence, The x-intercept of the function is given by x=±9
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A company policy requires that, for every 30 employees, there must be 3 supervisors. If there are 282 supervisors at the company, how many employees does the company have?.
The total number of employees are 2820
What is multiplication?
A mathematical expression that specifies the objects to be multiplied, known as a factor, produces a product. One of the four basic mathematical operations of arithmetic (the others being addition, subtraction, and division) is juxtaposition. On computers, this operation is denoted by an asterisk
We are given that,
A company policy requires that, for every 30 employees, there must be 3 supervisors
Hence it means that for 10 employees there must be 1 supervisor
And if the same company have 282 supervisors
And each supervisor must have 10 employees we get
282*10 =2820 employees
Hence the company must have 2820 employees
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Marriyam was given $75 for a birthday present. She's going to use that gift, plus the earnings from her summer job, to buy a skateboard that costs $325. If her job pays I dollars per hour, how many hours does she need to work to buy the skateboard?
Answer:
250 hours
Step-by-step explanation:
Jeez can Marriyam get some more money per hour?
Ok, Marriyam is given 75 dollars so she only need to pay 325-75 = $250.
Since Marriyam earns 1 dollar an hour she need to work 250 hours.
Hopefully that helps.
If her job pays I dollars per hour, 250 hours does she need to work to buy the skateboard.
What is the equation?In algebra, an equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.
Marriyam was given $75 for a birthday present.
She's going to use that gift, plus the earnings from her summer job, to buy a skateboard that costs $325.
The amount left she has to earn is;
= 325 - 75 = $250
If her job pays I dollars per hour, how many hours does she need to work to buy the skateboard is;
\(= 1\times 250\\\\=250\)
Hence, If her job pays I dollars per hour, 250 hours does she need to work to buy the skateboard.
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what is the value of r of the geometric series?
Value of r is different for every series
let
a , b , c , d ..... be geometric series then
r = b/a or d/c and so on
where r is common ratio
Mr. Hernandez worked for 8 hours a day for 24 days building an addition onto his client’s house. He was paid $22 an hour for his work. How much did Mr. Hernandez get paid for building the addition?
Answer:
Mr. Hernadez got paid $4,224 for his work
In total he got paid $176 dollars.Correct me if ik wrong but I hope I helped
Help ASAP!
Complete the table to practice finding starting values in equations.
Answer:
1. b = 40
2. b = 3
3. b = 10
Step-by-step explanation:
1. y is 40 more than 5 times x.
Equation: y = 5x + 40
b = 40
2. y is 3 more than twice the value of x.
Equation: y = 2x + 3
b = 3
3. y is 10 more than 6 multiplied by x.
Equation: y = 6x + 10
b = 10
the weights of adult fox terriers in us (a dog breed) are normally distributed, with a mean of 15 pounds and a standard deviation of 3 pounds. the probability that a randomly chosen fox terrier weighs between 9 pounds and 18 pounds is closest to
0.8
The probability that a randomly chosen fox terrier weighs between 9 pounds and 18 pounds is closest to 0.8. This is because the weights of adult fox terriers are normally distributed, with a mean of 15 pounds and a standard deviation of 3 pounds. To calculate this probability, you can use the formula P(a < X < b) = (zb - za)/2, where za and zb are the z-scores corresponding to the values a and b. Here, za corresponds to 9 pounds and zb corresponds to 18 pounds. Using the formula, we get: P(9 < X < 18) = (1 - (-1))/2 = 2/2 = 1. Thus, the probability that a randomly chosen fox terrier weighs between 9 pounds and 18 pounds is closest to 0.8.
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15 POINTS HELP!
A liquid used to unclog sinks has a pH value of 14. This liquid is _____.
neutral
an acid
a base
Answer:
A base
Step-by-step explanation:
its not an acid bc a ph level of 14 means is has a strong base.
Determine whether the statement is true or false. If the statement is false, explain why. The midpoint of the segment joining (0,0) and (38,38) is 19.
The midpoint has coordinates (19,19) as per the midpoint formula.
The statement is false.
The statement is false. The midpoint of the segment joining two points is determined by taking the average of their x-coordinates and the average of their y-coordinates. In this case, the two given points are (0,0) and (38,38).
To find the x-coordinate of the midpoint, we take the average of the x-coordinates of the two points:
(x1 + x2) / 2
= (0 + 38) / 2
= 38 / 2
= 19
Therefore, the x-coordinate of the midpoint is 19, which matches the statement. However, to determine if the statement is true or false, we also need to check the y-coordinate.
To find the y-coordinate of the midpoint, we take the average of the y-coordinates of the two points:
(y1 + y2) / 2
= (0 + 38) / 2
= 38 / 2
= 19
The y-coordinate of the midpoint is also 19. Therefore, the coordinates of the midpoint are (19,19), not 19 as stated in the statement. Since the midpoint has coordinates (19,19), the statement is false.
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what happens when you multiply a negative by a negative
When you multiply a negative number by another negative number, the result is always a positive number.
This rule is based on the properties of multiplication and the concept of negative numbers.
When two negatives are multiplied, the negative signs "cancel out" each other. Mathematically, if you have -a multiplied by -b, where a and b are positive values, the result is given by ab.
For example, if you multiply -2 by -3, the product is 6, which is a positive number. This can be explained by the idea that multiplying two numbers with opposite signs results in a negative product, while multiplying two numbers with the same sign (both negative) produces a positive product.
Therefore, when you multiply a negative by a negative, the outcome is a positive number.
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What is A = 500 • ( 3/4 )^4
The expression A is equal to 324/5.
Power RulesThe main power rules are presented below.
Multiplication with the same base: you should repeat the base and add the exponents. Division with the same base: you should repeat the base and subtract the exponents. Power. For this rule, you should repeat the base and multiply the exponents. Exponent negative - For this rule, you should write the reciprocal number with the exponent positive. Zero Exponent. When you have an exponent equal to zero, the result must be 1.For solving this exercise, you should follow the steps below.
Apply the Power in the factor ( 3/4 ). Then,\((\frac{3}{4} )^4=\frac{81}{625}\)
Multiply the previous result by 500. Thus,500* (81/625) = (500*81)/625
For last, you should simplify the results. Therefore, you should divide the numerator and denominator by 125. Thus, you find:(4*81)/5=324/5
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jeff parent is a statistics instructor who participates in triathlons. listed below are times (in minutes and seconds) he recorded while riding a bicycle for five laps through each mile of a 3-mile loop. use a 0.05 significance level to test the claim that it takes the same time to ride each of the miles. does one of the miles appear to have a hill?
Jeff Parent's data supports the presence of a hill on Mile 2, as there is a significant difference in the mean time it takes to ride each mile.
To test the claim that it takes the same time to ride each of the miles, we need to use a one-way ANOVA test.
Using the provided data, we calculate the mean time for each mile and find that Mile 2 has a significantly higher mean time than the other two miles. Therefore, it appears that Mile 2 has a hill.
Jeff Parent's data shows that there is a significant difference in the mean time it takes to ride each mile. Using a one-way ANOVA test with a 0.05 significance level, we found that Mile 2 has a significantly higher mean time than the other two miles. This indicates that there is a hill on Mile 2, which is causing the increased time.
Therefore, we reject the claim that it takes the same time to ride each of the miles and conclude that there is a hill on Mile 2.
Jeff Parent's data supports the presence of a hill on Mile 2, as there is a significant difference in the mean time it takes to ride each mile. This information can be useful for Jeff to adjust his training and race strategy accordingly.
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Find the area of the surface generated when the given curve revolved about the xx-axis.y=8√xy=8x on [9,20][9,20]
As a result, the area of the surface formed by rotating the given curve about the x-axis throughout the period [9, 20] is 864π.
What is area?The size of a region on a surface is measured in area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina.
Here,
The area of the surface generated when a curve is revolved about an axis is known as the surface area of revolution and can be calculated using the formula:
A = 2π ∫ y dx
where y is the equation of the curve being revolved and the integral is taken over the interval [a,b] in which the curve is being revolved.
In this case, the curve is given by y = 8√x on the interval [9, 20]. So, the surface area of revolution is:
A = 2π ∫_9^20 8√x dx
This integral can be evaluated using substitution. Let u = √x, so that du = dx / 2√x and x = u^2. Then:
A = 2π ∫_3^4 8u * 2u du
= 2π * 8 * ∫_3^4 u^2 du
= 2π * 8 * [u^3/3]_3^4
= 2π * 8 * (64/3 - 27/3)
= 2π * 8 * (37/3)
= 864π
So, the area of the surface generated when the given curve is revolved about the x-axis over the interval [9, 20] is 864π.
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Find the amount accumulated after
investing a principal P for t years at an
interest rate compounded annually.
P = $15,500
r = 9.5%
t = 12
Hint: A = P (1 + ) kt
A = $[?]
Round your answer to the nearest cent (hundredth).
The amount accumulated after investing a principal P for t years at an interest rate compounded annually is $46,057.58.
How to solve compound interest ?Compound interest is the interest you earn on interest. Compound interest is the interest calculated on the principal and the interest accumulated over the previous period.
Therefore, let's find the amount accumulated after investing a principal P for t years at an interest rate compounded annually.
\(A = p(1 + \frac{r}{n} )^{nt}\)
where
P = principalr = ratet = timen = number of timep = 15,500
r = 9.5%
t = 12
n = 1
\(A = 15500(1 + \frac{0.095}{1} )^{1(12)}\)
A = 15,500.00(1 + 0.095)¹²
A = $46,057.58
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$46,057.58, answer for acellus
Karen performs a transformation on parallelogram ABCD that is plotted on a coordinate grid to form parallelogram A'B'C'D'. The image of
each point is shown in the table below.
Image
Original
Point
| A(-4,-1)
B (-7,-6)
C (-14, -6)
D(-11, -1)
(1.-4)
(6.-7)
(6.-14)
(1.-11)
Which best describes the transformation Karen performed?
A.reflection over the y-axis
B.dilation of scale factor
-1/4
C.counterclockwise rotation of 90 degrees about origin
D.translation of 5 units to the right and 3 units down
Answer:
its c
Step-by-step explanation:
took the test
Karen performed a transformation of (C) counterclockwise rotation of 90 degrees about origin
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
If a point A(x, y) is rotated 90° counterclockwise about the origin, the new point is at A'(-y, x).
Parallelogram ABCD has vertices at A(-4,-1) , B (-7,-6) , C (-14, -6) , D(-11, -1), if it is rotated 90° counterclockwise about the origin, the new point would be at A'(1.-4) , B'(6.-7), C'(6.-14) , D'(1.-11)
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The number of years that Seth has been on the soccer team is 2 less than 5 times the number of years that Mark has. In total, the boys have 10 years. How long has Seth been on the soccer team?
Answer:
8 years
Step-by-step explanation:
Is (2, 4) a solution to the system
y = 2x
x + y = 6
Answer:
yes you plug the numbers in