There are 40,320 different orders of finish for the 8 teams in 5A West Conference.
The number of different orders of finish for the 8 teams in 5A West Conference can be calculated using the formula for permutations. The formula for permutations is n!/(n-r)! where n is the total number of items and r is the number of items being arranged.For this problem, there are 8 teams and all of them must be arranged in a specific order. Therefore, we need to calculate the permutation of all 8 teams.Using the permutation formula, we have:n!/(n-r)! = 8!/(8-8)! = 8!/(0!) = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320
Therefore, there are 40,320 different orders of finish for the 8 teams in 5A West Conference.
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A grocer has two kinds of candy, one selling for 40 cents a pound and the other for $1.40 per pound. How many pounds of each kind must he use to make 100 pounds worth 85 cents a pound?
Answer:The quantity of grocer of price $1.40 is 45 pounds
The quantity of grocer of price 40 cents is 55 pounds
Step-by-step explanation:
Let The quantity of one grocer = x pound
Let The quantity of other grocer = y pound
The selling price of x grocer = 40 cents per pound
The selling price of y grocer = $ 1.40 per pound = 1.40 × 100 = 140 cents
Total quantity = 100 pounds
Total price of both grocer = 85 cents
According to question
x + y = 100 .........A
And
40 × x + 140 y = 85 × 100
Or, 40 x + 140 y = 8500 ........B
Solving eq A and eq b
(40 x + 140 y) - 40 × ( x + y ) = 8500 - 40 × 100
Or, (40 x - 40 x) + (140 y - 40 y) = 8500 - 4000
or, 0 + 100 y = 4500
∴ y =
i.e y = 45 pounds
So, The quantity of grocer of price $1.40 = y = 45 pounds
Again
Put the vaue of y in eq A
x + y = 100
i.e x = 100 - y
or, x = 100 - 45
∴ x = 55 pounds
So, The quantity of grocer of price 40 cents = x = 55 pounds
Hence, The quantity of grocer of price $1.40 is 45 pounds
And The quantity of grocer of price 40 cents is 55 pounds Answer
Use a system of equations to find the cubic function f(x)=ax3+bx2+cx+d that satisfies the equations. Solve the system using matrices. f(−2)=−7; f(−1)=2; f(1)=−4; f(2)=−7
The solution of the system is a = -1, b = 1, c = 0, and d = -3.
To find the cubic function f(x) = ax³ + bx² + cx + d that satisfies the given equations by using a system of equations and solving the system using matrices, we proceed as follows:Equations for the given cubic function:f(-2) = a(-2)³ + b(-2)² + c(-2) + d = -7 ...(1)f(-1) = a(-1)³ + b(-1)² + c(-1) + d = 2 ...(2)f(1) = a(1)³ + b(1)² + c(1) + d = -4 ...(3)f(2) = a(2)³ + b(2)² + c(2) + d = -7 ...(4)The matrix form of the system of equations is given by AX = B, whereA = [(-2)³ (-2)² -2 1; (-1)³ (-1)² -1 1; (1)³ (1)² 1 1; (2)³ (2)² 2 1],X = [a; b; c; d], andB = [-7; 2; -4; -7].The augmented matrix form of the system of equations is given by [A|B] = [(-2)³ (-2)² -2 1 -7; (-1)³ (-1)² -1 1 2; (1)³ (1)² 1 1 -4; (2)³ (2)² 2 1 -7].Performing the row operations, we get the row echelon form of the augmented matrix as follows:[A|B] = [1 0 0 0 -1; 0 1 0 0 1; 0 0 1 0 0; 0 0 0 1 -3].Therefore, the solution of the system is a = -1, b = 1, c = 0, and d = -3.Hence, the cubic function f(x) = ax³ + bx² + cx + d that satisfies the given equations is given by f(x) = -x³ + x² - 3.
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write an equation in slope-intercept form of the line that passes through the given points
[tex]\left[\begin{array}{ccc}x&y\\-4&9\\-2&4\\0&-1\\2&-6\end{array}\right][/tex]
Answer:
y = - [tex]\frac{5}{2}[/tex] x - 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 4, 9) and (x₂, y₂ ) = (2, - 6) ← 2 ordered pairs from the table
m = [tex]\frac{-6-9}{2-(-4)}[/tex] = [tex]\frac{-15}{2+4}[/tex] = [tex]\frac{-15}{6}[/tex] = - [tex]\frac{5}{2}[/tex]
the line crosses the y- axis at point (0, - 1 ), ordered pair from table, then
c = - 1
y = - [tex]\frac{5}{2}[/tex] x - 1 ← equation of line
In an elementary chemical reaction, single molecules of two reactants A and B form a molecule of the product C: A+B - C. The law of mass action states that the rate of reaction is proportional to the product of the concentrations of A and B: dc dt = k[A]B] (See Example 3.7.4.) Thus, if the initial concentrations are [A] = a moles/Land (B] = b moles/L and we write r = (C), then we have do dt ka - x)( - ) a. Assuming that a b, find as a function of t. Use the fact that the initial concentration of C is o. b. Find (t) assuming that a = b. How does this expression for a(t) simplify if it is known that 1 [C] - a after 20 seconds?
For the given elementary chemical reaction, the solution to the question is: C = a^2 * (1-t^2/400(1-a))
The question asks about calculating the concentration of C in a chemical reaction. Given that the reaction equation is as follows: A + B → C The rate of reaction can be expressed as: dc/dt = k[A][B] Where, k is the rate constant[A] is the concentration of reactant A in moles/L[B] is the concentration of reactant B in moles/L, c is the concentration of product C in moles/L
The initial concentration of A and B is [A] = a moles/L, [B] = b moles/L Let r be the rate of reaction, i.e. r = dc/dt Thus, using the equation r = k[A][B], we get r = k(a)(b)Now, we can write a differential equation for the concentration of C as follows: dc/dt = r, with initial concentration of C as 0 moles/L∴ dc/dt = kab
Substituting r = k(a)(b) in the equation, we get dc/dt = kabdc/db = kab*dt Differentiating both sides, we get, ln(C) = kab*t + C where C is a constant, ln(C) = ln(a^2) = 2ln(a) = C When a = b, the concentration of C will be maximum at t = (1/k)(ln(a)).
Thus the concentration of C as a function of time (when a = b) is given by C = a^2 * (1-t^2/2)If [C] = a after 20 seconds, then using the equation, we get a = a^2 * (1 - 20^2 * k^2/2)Therefore, 1 = a * (1 - 200k^2) Solving this equation for k, we get, k = ± sqrt[(1-a)/200a^2] For the positive value of k, the concentration of C as a function of time is given by C = a^2 * (1-t^2/400(1-a)).
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A catapult launches a pumpkin from the base of a hill. The hill follows an incline with the
height in meters, y, in terms of horizontal distance in meters, x, given by the equation
y=0. 9x. The height of the pumpkin, as it is launched uphill, is given by the function
y = -0. 1x² +4. 9x
What is the height, in meters, where the pumpkin lands on the hill?
The height, in meters, where the pumpkin lands on the hill is 4.9 meters.The equation for the height of the hill is y = 0.9x.
This equation can be rearranged to solve for x, giving x = y/0.9. The equation for the height of the pumpkin is y = -0.1x² + 4.9x. Substituting the x value from the previous equation into the equation for the height of the pumpkin gives y = -0.1(y/0.9)² + 4.9(y/0.9). Simplifying this equation gives y = 4.9, which is the height, in meters, where the pumpkin lands on the hill.
The equation for the height of the hill is y = 0.9x, which describes the incline of the hill. This equation can be rearranged to solve for x, giving x = y/0.9. This equation can then be used to substitute into the equation for the height of the pumpkin, which is y = -0.1x² + 4.9x. When the x value from the previous equation is substituted into the equation for the height of the pumpkin, the equation simplifies to y = -0.1(y/0.9)² + 4.9(y/0.9). Simplifying further gives y = 4.9, which is the height, in meters, where the pumpkin lands on the hill. This can be verified by substituting 4.9 for y in the equation for the height of the hill, which gives x = 4.9/0.9 = 5.4. This value can be substituted into the equation for the height of the pumpkin, which gives y = -0.1(5.4)² + 4.9(5.4) = 4.9, verifying the result.
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Select the graph that would represent the best presentation of the solution set for |x| < 5.
Based on the principle of Inequality, Attached image is a graph of the inequality for |x| < 5. The red region is the solution set.
What is the graph equation?A mathematical statement known as an equation demonstrates the relationship between two or more numbers and variables by utilizing mathematical operations such as addition, subtraction, multiplication, division, exponents, and so forth.
Therefore, An expression that demonstrates a non-equal comparison of numbers and variables is called an inequality. So, the graph that best represents this solution set is a number line with open circles at x = -5 and x = 5 and a shaded region in between, indicating that all values of x within this range satisfy the inequality.
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An object is dropped from a small plane. As the object falls, its distance, d, above the ground after t seconds, is
given by the formula d = -16² +1,000. Which inequality can be used to find the interval of time taken by the object
to reach the height greater than 300 feet above the ground?
-16² +1,000 <300
-16² +1,000 ≤300
-16² +1,000 ≥ 300
-16f²+1,000 > 300
Answer:
-16²+1,000 > 300 [After an edit in the original expression, as noted below).
Step-by-step explanation:
The equation d = -16² +1,000 tells us the height above ground, d, of the object after t seconds. When t = 0 seconds, the ball has not been dropped yet, but the equation tells us that d = 1,000 at t = 0. That means the object starts at 1,000 feet above ground.
We want the time it takes for the object to reach any height greater than 300 feet above ground. This is a tad (metric for just a tiny bit) unexpected, since even at time of 0 the object is greater than 1,000 feet.
Looking at the answer options, note that the left side of the inequalities is -16^2+100. I will assume the 4th option has a typo: the f^2. It should read the same as the others.
-16^2+100 is the distance, d. So to help us think this through, let's rephrase the answer options in terms of distance, d:
1) d<300
2) d≤300
3) d≥300
4) d>300
The question asks "We want the time it takes for the object to reach any height greater than 300 feet above ground."
Option 4 says d>300, or height greater than 300. That is the inequality that matches the question. [Note: It did not say greater than or equal to (option 3).]
what is the result of substituting for y in the bottom equation?
Answer:
A. y=(x-3)^2+2(x-3)-4
B. x-3=x^2+2x-4
C. y=x^2+2x-4-(x-3)
D. (x-3)=x^2
Optiοn B. is cοrrect, the result οf substituting fοr y in the given equatiοns is x - 3 =x² + 2x - 4.
What is the equivalent expression?Equivalent expressiοns are expressiοns that wοrk the same even thοugh they lοοk different. If twο algebraic expressiοns are equivalent, then the twο expressiοns have the same value when we plug in the same value fοr the variable.
Tο substitute fοr y in the secοnd equatiοn, we can replace y with its equivalent expressiοn in terms οf x frοm the first equatiοn, which gives us:
x - 3 = x² + 2x - 4
This is option B.
Optiοn A is incοrrect because it substitutes y fοr its expressiοn in terms οf x in the wrοng equatiοn.
Optiοn C is incοrrect because it subtracts (x-3) instead οf adding it tο the secοnd equatiοn.
Optiοn D is incοrrect because it sets the expressiοn fοr y in the first equatiοn equal tο x² instead οf the expressiοn fοr y in the secοnd equatiοn.
Hence, οptiοn B. is cοrrect, the result οf substituting fοr y in the given equatiοns is x - 3 = x² + 2x - 4.
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Complete question:
What is result of substituting for y in the bottom equation?
y = x – 3,
y = x² + 2x – 4
A. y=(x-3)²+2(x-3)-4
B. x-3=x²+2x-4
C. y=x²+2x-4-(x-3)
D. (x-3)=x²
When asked to draw a quadrilateral with all four sides measuring 5 cm, Jada drew a square.
5 cm
15 cm
5 cm
1. Do you agree with Jada's answer?
2. Is there a different shape Jada could have drawn that would answer the question? Explain your
reasoning
Absolutely, Jada's response is right. A square is a quadrilateral with four equal-length sides. A quadrilateral is a square if all four sides measure 5 cm.
Unfortunately, there is no alternative form Jada could have drawn that meets the requirement of all four sides measuring 5 cm. Every other quadrilateral with four equal-length sides is likewise a square. If Jada had drawn a quadrilateral with one or more sides of varying lengths, the specified criterion would not have been met. As a result, the only design Jada could have sketched that meets the requirement of having all four sides measure 5 cm is a square. It is worthwhile to investigate the properties of quadrilaterals and how they connect to the conditions presented in the problem. A quadrilateral is a four-sided polygon. Quadrilaterals come in a variety of shapes, including squares, rectangles, parallelograms, trapezoids, and kites. Certain quadrilaterals have unique qualities, such as opposing sides that are parallel or all angles that are right angles. The criterion in the provided problem is that all four sides of the quadrilateral measure 5 cm.
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A. What is the magnitude of an earthquake with amplitude 100,000? How
do you know?
The magnitude of the earthquake with an amplitude of 100,000 is 2 on the Richter scale
What do you mean by Magnitude and amplitude in term of Earthquake ?Magnitude: The magnitude of an earthquake is a measure of the amount of energy released during the earthquake. It is typically determined using a logarithmic scale called the Richter scale or other similar scales like the moment magnitude scale (MMS), surface wave magnitude (Ms), or body wave magnitude (Mb). The Richter scale is based on the amplitude of the largest seismic wave recorded on a seismographs, and each increase of one unit on the scale corresponds to a ten-fold increase in the amplitude of the seismic waves and a 32-fold increase in the amount of energy released.
Amplitude: The amplitude of an earthquake is the size of the seismic waves that are generated by the earthquake. It is measured in microns (millionths of a meter) and is recorded on a seismographs. The amplitude of seismic waves can vary greatly depending on the distance from the earthquake's epicenter and the geological structure of the surrounding area.
The magnitude of an earthquake is a measure of the amount of energy released during the earthquake, and is typically determined using a logarithmic scale called the Richter scale.
The formula for calculating the magnitude of an earthquake based on its amplitude is:
Magnitude = log10 (Amplitude) - 3
where the amplitude is measured in microns.
Assuming the amplitude of the earthquake is 100,000 microns, we can calculate its magnitude as:
Magnitude = log10 (100,000) - 3
Magnitude = 5 - 3
Magnitude = 2
Therefore, the magnitude of the earthquake with an amplitude of 100,000 is 2 on the Richter scale.
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Question 2
1 pts
At a community event, a vendor lets attendees spin their prize wheel. The wheel consists of 5
colored sections that the vendor claims to be equally likely. One of the sections is labeled "winner!"
A diligent observer records the outcomes of 75 spins. Let X = the number of spins that resulted in a
win.
Use this normal distribution to calculate the probability that AT MOST 10 of the spins result in a
win. Use up to 4 decimal places for the final answer. Use Table A for this one. Stapplet will give a
different value.
Next ▸
Please ASAP Help
Will mark brainlest due at 12:00
Answer:
plot the point at 1
Step-by-step explanation:
Do the Ratios 6/5 and 4/3 fit a Proportion
Answer:
No
Step-by-step explanation:
[tex]\frac{6}{5}=1.2[/tex]
[tex]\frac{4}{3} =1.33[/tex]
[tex]\frac{6}{5} < \frac{4}{3}[/tex]
Hope this helps.
Answer:
No
Step-by-step explanation:
6/5=4/3
18=20
9≠10
Calculate the following without using a calculator -5×(-3+7)+20÷(-4)
Answer:
-25
Step-by-step explanation:
simplification using BODMAS
[tex]-5 * 4 + -5[/tex]
-20 - 5
= -25
The graph shows a two-dimensional side view of a
satellite dish and the small reflector inside it. The vertex
of the small reflector is 6 in. from focus F₁ and 20 in. from
focus F2. What equation best models the small reflector?
Picture of graph attached !!! please help
The equation is -7x+y=0.
What is an equation?A mathematical statement known as an equation consists of two algebraic expressions separated by equal signs (=) on either side.
It demonstrates the equality of the relationship between the printed statements on the left and right.
Left side equals right side in all formulas.
To find the values of unknowable variables, which stand in for unknowable quantities, you can solve equations.
A statement is not an equation if it lacks the equals sign. When two expressions have the same value, a mathematical statement known as an equation will include the symbol "equal to" between them.
Hence, The equation is -7x+y=0.
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A bookstore sells 7 books for $89.25. Which table represents the relationship between number of books and the total price?
Answer: C is our answer.
The first thing that we can do is divide the known number of books into the price that they sold for.
Our equation would be 89.25 divided by 7, which is 12.75. This means that one single book is 12.75. We can look at the charts and point out where one book is 12.75, that is both A and D. While Chart B and C have 7 books for 89.25 which we know is correct.
Lets look at chart D.The next part we can solve is the price of 2 books. 12.75 x 2 is 25.50, so we can mark question B incorrect since two books are 25.50 not 13.75.Chart B is incorrect because 14 books is double 7, so it should be twice as much as 89.25, which we should know 90 dollars is not two times as much 80. Chart A is incorrect because 11 x 12.75 is 140.25, while the chart reads as 22.75.
Now lets look at chart C. Next we can solve the price of 8 books. 8 x 12.75 is 102. Then we solve for 9 books. 12.75 x 9 is 114.75, which means that C is correct.
I hope this helped & Good Luck <3!!
Given the expression
Choose all the equivalent expressions as your answer.
The equivalent expressions of [tex]x^3[/tex] are[tex]\frac{(x ^ 6)}{(x ^ 3)}[/tex]and [tex]\frac{(x^{-3}) }{(x^{-6}) }[/tex], the expressions [tex]\frac{(x^{30}) }{(x^{10})}[/tex] and [tex]\frac{(x ^ 4) ^ 2)}{x ^ 2}[/tex] are not equivalent to [tex]x^3[/tex].
What are equivalent expressions?
Equivalent expressions are different algebraic expressions that have the same value when evaluated for a particular set of variables.
The equivalent expressions [tex]x^3[/tex] are:
[tex]\frac{(x ^ 4) ^ 2)}{x ^ 2}[/tex] : This expression can be simplified as follows:
=[tex]\frac{(x ^ 4) ^ 2)}{x ^ 2}[/tex]
= [tex]\frac{(x ^ 8)}{(x ^ 2) }[/tex]
=[tex]x^{8-2}[/tex]
= [tex]x^6[/tex]
[tex]\frac{(x ^ 6)}{(x ^ 3)}[/tex] : This expression can be simplified as follows:
=[tex]\frac{(x ^ 6)}{(x ^ 3)}[/tex]
= [tex]x^{6-3}[/tex]
=[tex]x^3[/tex]
[tex]\frac{(x^{30}) }{(x^{10})}[/tex] : This expression can be simplified as follows:
=[tex]\frac{(x^{30}) }{(x^{10})}[/tex]
=[tex]x^{30-10}[/tex]
=[tex]x^{20}[/tex]
[tex]\frac{(x^{-3}) }{(x^{-6}) }[/tex] : This expression can be simplified as follows:
=[tex]\frac{(x^{-3}) }{(x^{-6}) }[/tex]
=[tex]x^{-3-(-6)}[/tex]
=[tex]x^{-3+6}[/tex]
=[tex]x^{3}[/tex]
Therefore, the equivalent expressions of [tex]x^3[/tex] are[tex]\frac{(x ^ 6)}{(x ^ 3)}[/tex]and [tex]\frac{(x^{-3}) }{(x^{-6}) }[/tex] , the expressions [tex]\frac{(x^{30}) }{(x^{10})}[/tex] and [tex]\frac{(x ^ 4) ^ 2)}{x ^ 2}[/tex] are not equivalent to [tex]x^3[/tex].
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Cumulative distribution function for a continuous random variable x
The cumulative distribution function gives us the probability that the random variable is less than or equal to a given value.
The cumulative distribution function (CDF) of a continuous random variable x is a function which gives the probability that the random variable x is less than or equal to a given value x. Mathematically it is expressed as:
[tex]F(x) = P(X ≤ x)[/tex]
The calculation of the cumulative distribution function is done by integrating the probability density function (PDF) from the lower limit to the given value x. Thus,
[tex]F(x) = ∫-∞ x f(u) du[/tex]
Where f(u) is the probability density function.
For example, if we have a continuous random variable x with probability density function f(x) = x2, then the cumulative distribution function [tex]F(x) = ∫-∞ x x2 du = 1/3x3 + c.[/tex]
Thus, It is a powerful tool for analysing the probability distribution of a continuous random variable.
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Complete question:
What is the cumulative distribution function for a continuous random variable x?
What is the answer to this question?
Answer:
Step-by-step explanation:
The domain is found by setting the denominator equal to 0 and solving for y. This value of y gives you the values that cause the denominator to go to 0, which is a problem. In this rational expression, there are no real numbers that cause the denominator to go to 0, so the domain is all real numbers.
A population has a standard deviation of sigma = 24. a. On average, how much difference should exist between the population mean and the sample mean for n = 4 scores randomly selected from the population? b. On average, how much difference should exist for a sample of n = 9 scores? c. On average, how much difference should exist for a sample of n = 16 scores?
Therefore , the solution of the given problem of standard deviation comes out to be he average difference between the population mean and the sample mean is 6.
What is standard deviation?Variance is a measure of variation used in statistics. The average difference between the gathering and the mean is calculated using the photo of that figure. By comparing each number to the mean, it incorporates those data points into the calculations on their own, in contrast to many other legitimate measures of variable. Variations could result from deliberate errors, unrealistic expectations, or changing economic or commercial circumstances.
Here,
For a group of n = 4, the standard error of the mean (SEM) is as follows:
=> SEM = α/√(n)
=> 24/√(4) = 12
Therefore, for n = 4 scores drawn at random from the population, the average difference between the population mean and the sample mean is 12.
b. The SEM for a group of n = 9 is:
=> α/√(n) = 24/√(9)
=> 8; SEM = α
Therefore, for n = 9 scores drawn at random from the population, the average difference between the population mean and the sample mean is 8.
c. The SEM for a sample of 16 is as follows:
=> α / √(n) = 24 / √(16) = 6;
=> SEM =α
Therefore, for n = 16 scores drawn at random from the population, the average difference between the population mean and the sample mean is 6.
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(Helpppp)Write slope-intercept form of the line which is perpendicular bisector to
a segment with endpoints A(5,9), B(7,13).
Answer:
the slope-intercept form of the line which is perpendicular bisector to the segment with endpoints A(5,9), B(7,13) is y = (-1/2)x + 14
An iPhone costs £800 in London, €880 in Paris and $850 in New York. Using £1 = €1.16 and £1 = $1.41, state the lowest price of the iPhone in £. Give your answer to 2 dp.
Answer:
£602.84 in New York
Step-by-step explanation:
London Cost:
Converting pound to dollars:
£800 * 1.41 = $1128
Paris cost:
Converting euro to pounds:
€880/1.16 = £759
Converting pound to dollars again:
£759 * 1.41 = $1070
New york cost:
$850
The lowest price is in new york which is:
$850/1.41 = £602.84
Feel free to mark this as brainliest (I'm one brainliest off 50 so please help out
PLEASE HELP WITH THIS PROBLEM ASAP
16. The base side y = 10.565 and altitude x = 22.657
17. The hypotenuse c = 49.70 and base y = 46.70.
18. The value of AB = 30√3 and AC = 45
19. The value of AB = 36√3 and BC = 18√3.
What is a hypotenuse?In geοmetry, a hypοtenuse is the lοngest side οf a right-angled triangle, the side οppοsite the right angle. The length οf the hypοtenuse can be fοund using the Pythagοrean theοrem, which states that the square οf the length οf the hypοtenuse equals the sum οf the squares οf the lengths οf the οther twο sides.
16. Given hypotenuse = 25
θ = 25°
Sin θ = opposite/hypotenuse
Sin 25° = y/25
y = Sin 25° × 25
y = 10.565
Given hypotenuse = 25
θ = 25°
Cos θ = adjacent/hypotenuse
Cos 25° = x/25
x = Cos 25° × 25
x = 22.657
17. Given Side = 17
θ = 20°
Sin 20° = 17/c
c = 17/Sin 20°
c = 49.70
Cos θ = adjacent/hypotenuse
Cos 20° = y/49.70
y = Cos 20° × 49.70
y = 46.70
18. Given BC = 15√3
In a 30°−60°−90° triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is 3√ times the length of the shorter leg.
Thus, BC = 15√3
AB = 2(15√3)
= 30√3
and
AC = √3(15√3)
= 15 × 3
= 45
Thus, when BC = 15√3, then AB = 30√3 and AC = 45
19. Given AC = 54
In a 30°−60°−90° triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is 3√ times the length of the shorter leg.
Thus, BC = x and AC = x√3
54 = x√3
54 = x√3
x = 54/√3
x = 18√3
BC = 18√3
AB = 2x = 2(BC) = 2(18√3)
= 36(√3)
Thus, when AC = 54, then AB = 36√3 and BC = 18√3.
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Please help me! A sector has a central angle measure of 90 degrees, and a radius of 8 cm. Which equation shows the correct calculation of the area of the sector?
Therefore , the solution of the given problem of area comes out to be
A = 16 is the equation that accurately depicts how to calculate the sector's area.
What is an area ?Its total size can be determined by figuring out how much space is required to completely cover the outside. The immediate surroundings are taken into consideration when calculating the surface of a trapezoidal shape. The total measurements of something are determined by its surface area. A cuboid's capacity for internal water is determined by the sum of the borders that link all of it's six rectangle edges.
Here,
The formula for calculating a circle's sector's area is:
=> A = (θ/360) x πr²
where A is the sector's area, is its central angle measurement, and r is the circle's radius.
Since the radius is 8 cm and the central angle is 90 degrees in this instance, we can reduce by plugging in these values:
=> A = (90/360) x π(8²)
=> A = (1/4) x π(64)
=> A = π(16)
=> A = 16π
A = 16 is the equation that accurately depicts how to calculate the sector's area.
The answer will be given in radius squared units, in this case, cm2.
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Option D. The correct calculation of the area of the sector is [tex]A=(\frac{90}{360}) * (\pi 8^{2} )[/tex]
What is an area of the sector?An area of the sector is the portion of the area of a circle that is enclosed by two radii and an arc. The area of a sector can be found using the formula:
A = (θ/360)πr²
where A is the area of the sector, θ is the central angle of the sector (in degrees), π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.
Given, the radius is 8 cm and the central angle is 90° in this instance, put all these values:
[tex]A=(\frac{90}{360}) * \pi (8^{2} )[/tex]
or we can write down, [tex]A=(\frac{90}{360}) * (\pi 8^{2} )[/tex]
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The radius of circle B
is 4 centimeters and the circumference of
Circle A is 30 pi
centimeters. Find CD.
Find CD:
Let,
[tex]r_1[/tex] be a radius of Circle A
[tex]r_2[/tex] be a radius of Circle B
Given:
[tex]r=4cm.[/tex]
Circumference: [tex]2\pi r[/tex]
[tex]2\pi r_1=30[/tex]
[tex]r_1=\dfrac{15}{\pi }[/tex]
[tex]CD=D_1+D_2[/tex]
[tex]=2r_1+2rx_2[/tex]
[tex]=2\times(\dfrac{15}{\pi })+2\times4[/tex]
[tex]CD=17.55cm.[/tex]
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A traditional western pack of playing cards consists of four suits. Each suit has 13cards. Find the fraction of the playing cards are:
a)red. B)diamonds
c)face cards. D)black and face cards
a) 1/2, b) 1/4, c) 3/13, d) 7/26 (fraction of black and face cards) in a traditional Western pack of playing cards.
A traditional Western pack of playing cards consists of four suits: Hearts (colored red), Diamonds (colored red), Spades (colored black), and Clubs (colored black). Each suit has 13 cards: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, and King.
a) To find the fraction of the playing cards that are red, we need to add up the number of red cards and divide by the total number of cards in the deck. There are two red suits, Hearts and Diamonds, and each has 13 cards. So there are 26 red cards in total. Since there are 52 cards in a deck, the fraction of red cards is 26/52 or 1/2.
b) To find the fraction of cards that are Diamonds, we simply divide the number of Diamonds (13) by the total number of cards (52). This gives us a fraction of 13/52 or 1/4.
c) To find the fraction of face cards, we need to add up the number of face cards and divide by the total number of cards in the deck. In each suit, there are three face cards: King, Queen, and Jack. So there are 12 face cards in each deck (4 suits x 3 face cards per suit). Therefore, there are 12/52 or 3/13 face cards in the deck.
d) To find the fraction of black and face cards, we need to count the number of black cards and the number of face cards that are also black. There are two black suits, Spades and Clubs, and each has 13 cards. So there are total 26 black cards. Of these 26 cards, there are 12 face cards (King, Queen, and Jack) which are not black, leaving 14 black cards which are face cards. Therefore, the fraction of black and face cards is 14/52 or 7/26.
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HELP PLEASE ASAP!!!!
Triangle PQR with coordinates P(-3,4). Q(-6,1), and R(-6,6) is reflected over the x-axis. List the coordinates of the new image
Answer:
P(0,2), Q(3,5), R(3,0)
Step-by-step explanation:
What is the equation of the graph below?
On a coordinate plane, a curve crosses the y-axis at (0, negative 1). It has a minimum of negative 1 and a maximum of 1. It goes through 1 cycle at 2 pi.
y = cosine (x + StartFraction pi Over 2 EndFraction)
y = cosine (x + 2 pi)
y = cosine (x + StartFraction pi Over 3 EndFraction)
y = cosine (x + pi)
The equation of the given graph is: y = cosine (x + pi)
Equation of cosine graphsBy convention, the cosine function like most other trigonometric functions has a period of 2π.
Since, the parental function is y = cos x, which has y-intercept at y = 1, and x-intercept at π/2.
From observation, the function showed in the graph attached has y-intercept at y = -1 and x-intercept at π/2.
This can be interpreted to mean that the function has been translated leftwards π units.
Ultimately, the function that belongs to this graph is; y = cosine (x + pi)
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Answer: D. y = cosine (x + pi)
Step-by-step explanation:
An investor has an account with stock from two different companies. Last year, her stock in Company A was worth $4500 and her stock in Company B was worth $3900. The stock in Company A has increased 5% since last year and the stock in Company B has increased 11%. What was the total percentage increase in the investor's stock account? Round your answer to the nearest tenth (if necessary).
The total percentage increase in the investor's stock account is 7.95% (rounded to the nearest tenth).
What is the percentage?
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" is also used. A percentage is a dimensionless number; it has no unit of measurement.
To calculate the total percentage increase in the investor's stock account, we first need to calculate the new values of the stocks in Company A and Company B after the increase.
The new value of the stock in Company A is:
[tex]4500 + (5 \times 4500) = $4725[/tex]
The new value of the stock in Company B is:
[tex]3900 + (11 \times 3900) = 4339[/tex]
The total value of the investor's stock account after the increase is:
$4725 + $4339 = $9064
To calculate the percentage increase in the investor's stock account, we need to find the difference between the new total value and the original total value, and then divide that difference by the original total value:
($9064 - $8400) / $8400 = 0.0795
We then multiply this decimal by 100 to get the percentage increase:
0.0795 x 100 = 7.95%
Therefore, the total percentage increase in the investor's stock account is 7.95% (rounded to the nearest tenth).
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A screen door spring has a spring constant of 188 N/m, and stretches 0. 292 m when the door is opened. What force does it exert?
(Unit = N)
If the screen door spring has a spring constant of 188 N/m, then the force it exert is 54.9 N .
The force exerted by the screen door spring can be calculated using Hooke's law,
The Hooke's Law states that the force exerted by a spring is directly proportional to its spring constant and the amount it is stretched.
The formula for "Hooke's-law" is ⇒ F = kx
Where F is = force exerted by spring, k is = spring constant, and x is = amount spring is stretched.
In this case , the spring constant(k) = 188 , the distance stretched(x) = 292m ;
Substituting the values,
We get,
⇒ F = (188 N/m)(0.292 m)
⇒ F = 54.896 N
⇒ F ≈ 54.9N
Therefore, The force exerted by the screen door spring is approximately 54.9 N.
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