Answer:
2/25
Step-by-step explanation:
From the diagram below, if the measure of ∠∠C = 30 °, and side BC = 6 then side AC = _____.
We are given some information about a triangle, and with the information that we have we can solve this in 2 ways: using the cosine of angle C, or the sine of angle A, an angle which we know measures 60° because the sum of the internal angles of a triangle must be 180°. Let's use the second one:
We know that the sine of an angle is:
\(\begin{gathered} sin=\frac{opposite\text{ }side}{hypothenuse} \\ Therefore: \\ sin(60)=\frac{6}{AC} \\ 0.8660=\frac{6}{AC} \\ AC=\frac{6}{0.8660} \\ AC=6.92 \end{gathered}\)And by calculating 4√3 we know that it is 6.92, therefore, the correct answer is option A
Robert made 7 loaves of bread. Each loaf of bread uses of a cup of flour. How many cups of flour did Robert use to make 7 loaves of bread?
Answer:
7 cups of flower.
Step-by-step explanation:
He made 7 loaves and each loaf calls for 1 cup of flour. 7 times 1=7...I feel like this is so easy.
A mass weighing 4 lb stretches a spring 3 in. Suppose that the mass is given an additional 3 in displacement in the positive direction and then released. The mass is in a medium that exerts a viscous resistance of 6 lb when the mass has a velocity of 3 ft/s. Under the assumptions discussed in this section, formulate the initial value problem that governs the motion of the mass.
x(0) = 0.25 in (initial displacement from equilibrium). x'(0) = 0 ft/s (initial velocity)
How to formulate the initial value problem that governs the motion of the mass.We can use Newton's second law to formulate the initial value problem that governs the motion of the mass. The equation is given by:
m*a = F_net
where m is the mass, a is the acceleration, and F_net is the net force acting on the mass.
The net force can be found as the sum of the spring force, the viscous resistance force, and the force due to gravity. Therefore, we have:
F_net = F_spring + F_viscous + F_gravity
where F_spring is the force exerted by the spring, F_viscous is the force due to the viscous resistance, and F_gravity is the force due to gravity.
The force exerted by the spring is given by Hooke's law:
F_spring = -k*x
where k is the spring constant and x is the displacement from the equilibrium position. Since the spring stretches 3 in under a weight of 4 lb, we can find k as:
k = F/x = 4/3 = 4/0.25 = 16 lb/in
Therefore, the force exerted by the spring is:
F_spring = -16*x
The force due to viscous resistance is proportional to the velocity of the mass and is given by:
F_viscous = -c*v
where c is the viscous damping coefficient and v is the velocity of the mass. Since the viscous resistance force is 6 lb when the velocity is 3 ft/s, we can find c as:
c = F_viscous/v = 6/3 = 2 lb·s/ft
Therefore, the force due to viscous resistance is:
F_viscous = -2*v
The force due to gravity is given by:
F_gravity = -m*g
where g is the acceleration due to gravity (32.2 ft/s^2).
Substituting these equations into the equation for net force, we get:
ma = -16x - 2v - mg
Since the displacement x and the velocity v are both functions of time t, we can rewrite this equation as a second-order ordinary differential equation in terms of x:
mx'' + 2cx' + kx = m*g
where x' and x'' denote the first and second derivatives of x with respect to t, respectively.
This is the initial value problem that governs the motion of the mass, subject to the initial conditions:
x(0) = 0.25 in (initial displacement from equilibrium)
x'(0) = 0 ft/s (initial velocity)
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Use the Law of Sines to solve triangle ABC if LA = 43.1°, a = 183.1, and b = 242.8. sin B = (round answer to 5 decimal places) There are two possible angles B between 0° and 180° with this value fo
The value of sin(B) is approximately 0.82279. To find the angles, we can use the inverse sine function (also known as arcsine). The arcsine function allows us to find the angle whose sine is equal to a given value.
To solve triangle ABC using the Law of Sines, we can use the following formula:
sin(A) / a = sin(B) / b
Given that angle A is 43.1°, side a is 183.1, and side b is 242.8, we can substitute these values into the formula and solve for sin(B).
sin(43.1°) / 183.1 = sin(B) / 242.8
To isolate sin(B), we can cross-multiply and solve for it:
sin(B) = (sin(43.1°) * 242.8) / 183.1
Using a calculator, we can evaluate this expression:
sin(B) ≈ 0.82279
Rounding this value to five decimal places, we get:
sin(B) ≈ 0.82279
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Juan is 12. His father put $2000 into his bank account. The account
gained interest at a rate of 2.3% per year, compounded bi-monthly.
Assuming no more money was deposited and none was withdrawn, how
much money will be in the account when Juan turns 18? Round to the
nearest cents.
A=P
n
A accumulated amount
P = principal
r = interest rate
n = compounding per period
t = number of periods
Amount of money present in Juan's account when she is 18 years old is $2,284.73
When Juan is 12 years old ;
Given P = principal = $ 2000
r = interest rate = 2.3 %
t = number of periods = 2
To start, multiplying R percent by 100 gives us 2.3%/100, or 0.023 each year.
Simply converting time into years, 2 months divided by 12 months each year equals 0.166667 years.
How to resolve our equation
A = 2000(1 + (0.023 × 0.166667)) = 2007.666682
A = $2,007.67
Simple interest on a principal of $2,000.00 at a rate of 2.3% annually for 0.166667 years (2 months)
Juan when she is 18 years old
time = 18 - 12 = 6 years
rate = 2.3 %
Principal = $2,007.67
Accrued money = A = $2,284.73
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Each of the following is a metric describing an association rule, EXCEPT: support lift ratio confidence Idistance. A set of association rules could help us better understand: which items are likely overpriced how many items we can expect to sell next year which combinations of items are frequently purchased together how many clusters of items there are
The option that best aligns with the purpose of association rules is: "Which combinations of items are frequently purchased together."
The metric that is not associated with an association rule is "Idistance." The purpose of association rules is to identify relationships or patterns between items in a dataset. Common metrics used in association rule mining include support, lift, and confidence. These metrics help measure the strength, significance, and reliability of the associations found.
To address the provided options: Association rules can help identify which items are likely overpriced by examining the relationships between price and other attributes. They can provide insights into which combinations of items are frequently purchased together, helping with market basket analysis and product recommendation systems. Association rules are not directly used to predict the number of items that can be expected to sell next year.
This type of prediction would fall more into the realm of forecasting and time series analysis. The concept of "clusters" typically pertains to clustering algorithms used in unsupervised learning. Association rules are not directly used to determine the number of clusters or cluster items. Therefore, the option that best aligns with the purpose of association rules is: "Which combinations of items are frequently purchased together."
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Work out the value of 5 to the power of a if it equal 1/125
Answer:
a = -3
Step-by-step explanation:
Step 1: Since we're told that 5 to the power of a = 1/125, we can use the following equation to solve for a:
5^a = 1/125
Step 2: Take the log of both sides
log(5^a) = log(1/125)
Step 3: According to the power rule of logs, we can bring a down and multiply it by log(5):
a * log(5) = log (1/125)
Step 4: Divide both sides by log(5) to solve for a:
(a * log(5) = log(1/125)) / log(5)
a = -3
Optional 5: We can check our answer by plugging in -3 for a and seeing if we get 1/125 when completing the operation:
5^-3 = 1/125
1/(5^3) = 1/125 (rule of exponents states that a negative exponent creates a fraction with 1 as the numerator and the base (5) and exponent (-3 becoming 3) as the denominator
1/125 = 1/125
Due in 5 minutes Please
Answer:
cannot; 39.5
Step-by-step explanation:
a triangle interior angles add up to 180
when adding those measurements together, you get 255.6°
39.5 is the proper measurement
Answer: cannot
Step-by-step explanation:
Point J is on line segment IK.Given IK =5x, JK =4x, determine the numerical length of IK
20 units is the measure of the length of IK.
Determining the numerical length of a segmentA line is defined as the distance between two points. Given the following parameters
IK =5x
IJ = 4
JK =4x
If the point J is on IK, hence;
IK = IJ + JK
Substitute the given parameters to have:
5x = 4 + 4x
5x - 4x = 4
x = 4
Determine the length of IK
IK = 5x = 5(4)
IK = 20
Hence the measure of the length of IK is 20 units
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Complete question
Point J is on line segment IK.Given IK =5x, IJ = 4 and JK =4x, determine the numerical length of IK
every polynomial function of odd degree with real coefficients will have at least
Every polynomial function of odd degree with real coefficients will have at least one real root or zero.
This statement is known as the Fundamental Theorem of Algebra. It states that a polynomial of degree n, where n is a positive odd integer, will have at least one real root or zero.
The reason behind this is that when a polynomial of odd degree is graphed, it exhibits behavior where the graph crosses the x-axis at least once. This implies the existence of at least one real root.
For example, a polynomial function of degree 3 (cubic polynomial) with real coefficients will always have at least one real root. Similarly, a polynomial function of degree 5 (quintic polynomial) with real coefficients will also have at least one real root.
It's important to note that while a polynomial of odd degree is guaranteed to have at least one real root, it may also have additional complex roots.
The Fundamental Theorem of Algebra ensures the existence of at least one real root but does not specify the total number of roots.
In summary, every polynomial function of odd degree with real coefficients will have at least one real root or zero, as guaranteed by the Fundamental Theorem of Algebra.
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5. The perimeter of the frame is exactly double the perimeter of the
picture. What is the height of the frame?
L-X
15
Picture
Frame
25
(not drawn to scale)
x
F. 8 inches
G. 9 inches
H. 18 inches
J. 42 inches
The height of the frame is 5 inches, which corresponds to option F.
What is perimeter?The area encircling a two-dimensional figure is known as its perimeter. Whether it is a triangle, square, rectangle, or circle, it specifies the length of the shape.
The perimeter of the frame is equal to the sum of the lengths of its four sides, which are L, L, H, and H, where L is the length and H is the height of the frame. The perimeter of the picture is equal to the sum of the lengths of its four sides, which are (L - X), (L - X), X, and X, where X is the width of the picture.
According to the problem, the perimeter of the frame is exactly double the perimeter of the picture. Therefore, we can write the following equation:
2[(L + H) x 2] = (L - X) x 2 + X x 2
Simplifying and solving for H, we get:
4L + 4H = 2L + 2X + 2X
2H = 4X - 2L
H = 2X - L
We know that X = 15, L = 25, so:
H = 2(15) - 25 = 5
Therefore, the height of the frame is 5 inches, which corresponds to option F.
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The population of a city has been increasing by 2% annually. The sign shown is from the year 2000.
CITY LIMIT
BROOKFIELD
POP. 315,000
Write an exponential growth function that represents the population t years after 2000
What will the population be in 2020? Round your answer to the nearest thousand
The population will be about
The population will be about 2972 population in 2020
Exponential functionsThe standard exponential equation is expressed as;
y = ab^x
where
a is the interceptb is the initial populationx is the timeGiven the following parameters
a = 2000b = 0.02Substittute the given parameters into the formula
y = 2000(1.02)^x
If x = 20 (from 2000 to 2020)
The population will be expressed as;
y = 2000(1.02)^20
y = 2972 populations
Hence the population will be about 2972 population in 2020
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donna is saving money to buy a game. so far she has save $18 which is one third of the total cost of the game how much does the game cost?
The game costs $54 in total.
What is Multiplication?Multiplication is a method of finding the product of two or more numbers
If Donna has saved $18, which is one third of the total cost of the game, we can set up the following equation to represent the situation:
1/3×Total cost of the game = $18
To find the total cost of the game, we can solve for it by multiplying both sides of the equation by 3:
Total cost of the game = 3 × $18
Total cost of the game = $54
Therefore, the game costs $54 in total.
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A student club has 15 members. How many ways can a committee of 6 members be chosen?
A. 504
B. 720
C. 5,005
D. 3,603,600
Answer:
C. 5005Step-by-step explanation:
This is a combination of 6 out of 15
6C15 = 15!/6!9! = 10*11*12*13*14*15/2*3*4*5*6 = 5005Correct choice is C
Answer:
C right?
Step-by-step explanation:
You are planning to completely delta hedge your ABC
share holdings. How many call options
will you need to hedge holding 480 shares of a company, if you know
that the option's delta is 0.6?
In order to completely delta hedge 480 shares of ABC company with an option delta of 0.6, you would need 3 call options.
To completely delta hedge your holdings of 480 shares of ABC company, you would need to calculate the number of call options required based on the delta of the option. The delta represents the change in the option price relative to the change in the underlying stock price. In this case, since the delta is given as 0.6, it means that for every $1 increase in the stock price, the option price will increase by $0.6.
To calculate the number of call options needed for delta hedging, you can use the following formula:
Number of call options = (Delta * Number of shares) / 100
Plugging in the given values, we have:
Number of call options = (0.6 * 480) / 100
Number of call options = 2.88
Since you cannot have a fractional number of options, you would need to round up to the nearest whole number. Therefore, you would need 3 call options to hedge your 480 shares of ABC company.
In summary, to completely delta hedge 480 shares of ABC company with an option delta of 0.6, you would need to acquire 3 call options.
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What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer:
it's rise/run 3/2
Step-by-step explanation:
you rise positive 3 and run 2
MUG has coordinates M(9,-6), U(2,7), and G(4,3). A translation maps point M to M'(6,-3).
What are the coordinates of U' and G' for this translation?
(type an ordered pair)
U'=_____
G'=_____
Answer:
Translation (x,y) = (-3,+3)
U' = (-1,10)
G' = (1,0)
Step-by-step explanation:
The translation of x and y (U') = -1,10
The translation of y (G') = 1,0
It's subtracting 3 (for x) and adding 3 (for y)
The coordinates of U' and G' for this translation are U' = (5, 9) and G' = (7, 6).
What is the definition of the term translation?In mathematics, a translation is the movement of a shape to the left or right and/or upward or downward. The translated shapes appear to be the same size as that of the original shape, and thus the shapes are congruent. They were simply shifted in one or even more directions.For the given question,
MUG has coordinates M(9,-6), U(2,7), and G(4,3).
A translation maps point M(9,-6) to M'(6,-3).
There is a translation of 3 units on x and y axis.
Thus, applying same translation to the other two coordinates.
U'= (2 + 3, 7 + 3) = (5, 9)
G'= (4 +3, 3 + 3) = (7, 6)
Thus, the coordinates of U' and G' for this translation are U' = (5, 9) and G' = (7, 6).
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When searching for a rug which approximate side length should the decorator select
Basically, we are given the diagonal of the square to be 13.5 feet. We need to find the side length of the square.
The formula that relates diagonal and side length of a square is:
\(d=s\sqrt[]{2}\)Where
d is the diagonal
s is the side length
We substitute and find our answer:
\(\begin{gathered} d=s\sqrt[]{2} \\ 13.5=s\sqrt[]{2} \\ s=\frac{13.5}{\sqrt[]{2}} \\ s=9.55 \end{gathered}\)The side length is about 9.5 feet
Answer choice B
in a sample of n=23, the critical value of the correlation coefficient for a two-tailed test at alpha =.05 is
A. Plus/minus .497
B. Plus/minus .500
C. Plus/minus .524
D. Plus/minus .412
The critical value of the correlation coefficient for a two-tailed test at alpha = 0.05 with a sample size of n = 23 is approximately plus/minus 0.497.
To understand why this is the case, we need to consider the distribution of the correlation coefficient, which follows a t-distribution. In a two-tailed test, we divide the significance level (alpha) equally between the two tails of the distribution. Since alpha = 0.05, we allocate 0.025 to each tail.
With a sample size of n = 23, we need to find the critical t-value that corresponds to a cumulative probability of 0.025 in both tails. Using a t-distribution table or statistical software, we find that the critical t-value is approximately 2.069.
Since the correlation coefficient is a standardized measure, we divide the critical t-value by the square root of the degrees of freedom, which is n - 2. In this case, n - 2 = 23 - 2 = 21.
Hence, the critical value of the correlation coefficient is approximately 2.069 / √21 ≈ 0.497.
Therefore, the correct answer is A. Plus/minus 0.497.
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help plz with home work
Answer: -276.2 ft.
Step-by-step explanation: He descended 91 x 4.5 which is -409.5 ft. But since she goes up 43 x 3.1 which is 133.3 ft, -409.5 + 133.3 = -276.2 ft.
Hope this helps! :)
(Chapter 13) The curve r(t)= <0, t^2, 4t> is a parabola
We can see that the first component of the vector equation is always zero, so the parabola lies in the xz-plane.
Moreover, the second component is a quadratic function of t, which gives us a vertical parabola when plotted in the yz-plane. The third component is a linear function of t, so the curve extends infinitely in both directions. Therefore, we have a vertical parabola in the xz-plane.
This statement is referring to a specific vector-valued function, which we can write as:
f(t) = (0, t^2, ct)
where c is a constant.
The second component of this vector function is t^2, which is a quadratic function of t. When we plot this function in the yz-plane (i.e., we plot y = t^2 and z = 0), we get a vertical parabola that opens upward. This is because as t increases, the value of t^2 increases more and more quickly, causing the curve to curve upward.
The third component of the vector function is ct, which is a linear function of t. When we plot this function in the xz-plane (i.e., we plot x = 0 and z = ct), we get a straight line that extends infinitely in both directions. This is because as t increases or decreases, the value of ct increases or decreases proportionally, causing the line to extend infinitely in both directions.
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Can you help me please
Answer:
∠1 = 48
∠2 = 132
∠4 - 132
Step-by-step explanation:
∠3 and ∠1 are vertical angles
vertical angles are congruent ( equal to each other )
So if ∠3 = 48° then ∠1 also = 48°
∠3 and ∠4 are supplementary angles
supplementary angles add up to equal 180°
Hence, ∠3 + ∠4 = 180
48 + ∠4 = 180
180 - 48 = 132
Hence, ∠4 = 132
∠4 and ∠2 are vertical angles
Like stated previously vertical angles are congruent
Hence, ∠2 = 132
Jerry has a bag containing 30 pleces of candy. In the bag. Jerry finds 12 places of gum, 7 jolly ranchers, 5 fireballs,
and 6 milk dude.
Directions: Write your answer in the box. Use "/" for the fraction bar. Do not use spaces.
What is probability of drawing out a fireball? Write your answer in simplest form.
Help Please really do need help
Answer:
your answer would be a whole number, so your answer would be 1,000 i think.
this should be the answer because if you multiply
9*1000 you get 9000
if you multiply
25 * 1000 you get 25000
so on and so on
Step-by-step explanation:
hope this helps :)
Ty worked 4 hours and earned $28. At this rate, how much would he earn in 9 hours?
Answer:
63
Step-by-step explanation:
Ty worked 4 hours ad earned $28. This means that he earned $7 per hour. So, 7 times 9 is equal to 63. Which means that Ty will earns $63 in 9 hours.
You are deciding what carb you want to eat for dinner, and you decide to look at the ratio of cooking times between rice to pasta. Rice takes 20 minutes to cook, and pasta takes 12. What is the ratio of cooking times for the rice to pasta?
(Make sure your ratio is simplified for your final answer)
5 : 3 is the ratio of cooking times for the rice to pasta .
What does a math ratio mean?
When b does not equal 0, an ordered pair of numbers a and b, represented as a / b, is said to be a ratio. A percentage is an equation in which two ratios are made equal to one another.
You might express the ratio as 1: 3 for instance, if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.
Rice takes 20 minutes to cook
pasta takes 12
the ratio of cooking times for the rice to pasta = 20 : 12
= 5 : 3
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A circle has a diameter of 8 yd. What is its circumference?
Use 3.14 for it, and do not round your answer. Be sure to include the correct unit in your answer
Answer:
25.12 yards is the circumference.
21. What is the total surface area of the figure below? Total S.A. =cm?4 cm8 cm6 cm4 cm4 cm6th Period6 cm
If the figure is divided into 6 rectangles, the total area will be as follows:
A= area
Rectangle 1 and 3:
b= 8cm
h= 4cm
\(\begin{gathered} A_{R1}=\text{ b}\times h \\ A_{R1}=8\times4\text{ = 32} \\ A_{R1}=32\operatorname{cm} \\ As\text{ there are two with the same mesures:} \\ A_{R1,3}=2\times32\operatorname{cm}=64\operatorname{cm} \end{gathered}\)Rectangle 2 and 4:
b= 8cm
h= 6cm
\(\begin{gathered} A_{R2}=\text{ b}\times h \\ A_{R2}=8\times6\text{ = }48 \\ A_{R2}=48\operatorname{cm} \\ As\text{ there are two with the same mesures:} \\ A_{R2,4}=\text{ 2}\times48\operatorname{cm}=96cm^2 \end{gathered}\)Lateral Rectangle:
b= 6cm
h= 4cm
\(\begin{gathered} A_{LR}=\text{ b}\times h \\ A_{LR}=6\times4\text{ = }24 \\ A_{LR}=24\operatorname{cm} \\ As\text{ there are two lateral rectangles:} \\ A_{LR}=2\times24\operatorname{cm}=48\operatorname{cm} \end{gathered}\)Total Area (TA):
\(\begin{gathered} A_T=A_{R1,3}+A_{R2,4}+A_{LR} \\ A_T=64\operatorname{cm}+96\operatorname{cm}+48\operatorname{cm} \\ A_T=208\operatorname{cm} \end{gathered}\)what is the sum of the measures of the exterior angles of a triangle. if necessary round to the nearest tenth
The sum of the measures of the exterior angles of any polygon, including a triangle, is always 360 degrees.
We have,
An exterior angle of a polygon is formed by extending one of its sides outward.
In the case of a triangle, when we extend each side, we create three exterior angles.
These exterior angles are located outside the triangle.
The key concept to understand is that the sum of the exterior angles of any polygon is always 360 degrees.
This property holds true for all polygons, regardless of their shape or size.
To visualize this, imagine starting at any vertex of a triangle and moving along its sides while measuring the exterior angles.
As you move around the triangle, the sum of the exterior angles will always add up to 360 degrees.
This is because, at each vertex, the exterior angle supplements the interior angle to form a straight angle of 180 degrees.
In a triangle, each interior angle measures less than 180 degrees.
So, when we extend each side to create the exterior angles, they collectively compensate for the deficiency of the interior angles, resulting in a sum of 360 degrees.
Therefore,
The sum of the measures of the exterior angles of a triangle is always 360 degrees.
This principle holds true for all polygons, making it a fundamental property of geometry.
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PLSSSSS HELP MEEEE!!!!!!
Jose drove 35 miles in 2/3 hours. If he drove at a constant rate, how far did he travel in one hour? Enter your answer as a whole number, proper fraction, or mixed number in the simplest form.
Answer:
Jose traveled 52.5 miles in 1 hour
Step-by-step explanation:
What we're actually doing here is finding the "unit rate": the speed in mph:
35 mi 105 mi
------------ = ------------ = 52.5 mph = 52.5 miles in 1 hour
2/3 hr 2 hr
Jose traveled 52.5 miles in 1 hour