The value of the expression l/2 when l=50 is 25.
Given information:
The expression l/2 means "half of l".
The expression is l/2 where l is variable.
In this case, the value of l is given as 50. So to calculate the expression, you just need to substitute 50 for l in the expression and simplify:
If l = 50, then
l/2 = 50/2 = 25
Therefore, the value of the expression l/2 when l=50 is 25.
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Sue likes to skate at a skate park that is due south of her school and due west of her favorite ice cream parlor. If the skate park is 4 miles from her school and the straight-line distance between the school and the ice cream parlor is 5 miles, how far is the skate park from the ice cream parlor?
The skate park is approximately 6.4 miles from the ice cream parlor.
We can use the Pythagorean theorem to find the distance between the skate park and the ice cream parlor.
As per the information, we can see that the distance we're looking for is the hypotenuse of a right triangle with legs of length 4 miles (distance from school to skate park) and 5 miles (distance from school to ice cream parlor).
Using the Pythagorean theorem, we get:
c² = a² + b²
where c is the distance between the skate park and the ice cream parlor, and a and b are the distances from the school to the skate park and ice cream parlor, respectively.
Substituting the values we know, we get:
c² = 4² + 5²
c² = 16 + 25
c² = 41
Taking the square root of both sides, we get:
c = √41
c ≈ 6.4
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Let h(x) = x² - 8x.
(a) Find the average rate of change from 3 to 9.
(b) Find an equation of the secant line containing (3,h(3)) and (9, h(9))
A recycling bin contained 40 pounds of plastic in October and 50 pounds of plastic in
November. By what percentage did the amount of plastic increase from October to
November?
The percentage increase by the given data is 25%.
We are given that;
Weight of plastic in october= 40
Weight of plastic in november= 50
Now,
To find the percentage increase of the amount of plastic from October to November, we need to find the absolute increase and divide it by the original amount, then multiply by 100 to get the percentage.
The absolute increase is the difference between the final amount and the initial amount, which is 50 - 40 = 10 pounds.
The original amount is the initial amount, which is 40 pounds.
10/40×100=25%.
Therefore, by the percentage the answer will be 25%.
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You currently have $6,500 that you would plan to deposit into an investment account that has an anticipated growth factor of 1.03 per year. Use guess and check to estimate the number of years that it will take for this investment to grow to $10,000. Show your work.
Answer:
Using guess and check, we can estimate the number of years it will take for the investment to grow to $10,000 as follows:
First, we'll assume that it will take 5 years for the investment to grow to $10,000.
After 5 years, the investment would grow to:
$6,500 x 1.03^5 = $7,960.35
Since this is still less than $10,000, we need to increase the number of years.
Next, we'll assume that it will take 10 years for the investment to grow to $10,000.
After 10 years, the investment would grow to:
$6,500 x 1.03^10 = $9,020.14
Since this is still less than $10,000, we need to increase the number of years again.
Finally, we'll assume that it will take 15 years for the investment to grow to $10,000.
After 15 years, the investment would grow to:
$6,500 x 1.03^15 = $10,005.58
Since this is slightly more than $10,000, we can estimate that it will take around 15 years for the investment to grow to $10,000.
Therefore, the estimated number of years it will take for the investment to grow to $10,000 is about 15 years.
Write the standard form of the equation of the circle with radius 7 and center at (0, 0).
The standard form of the equation of the circle with a radius of 7 and center at (0, 0) will be x² + y² = 49.
Given that:
The center is at the origin.
Radius, r = 7
Let r be the radius of the circle and the location of the center of the circle be (h, k). Then the equation of the circle is given as,
(x - h)² + (y - k)² = r²
Substitute h = 0, k = 0, and r = 7, then we have
(x - 0)² + (y - 0)² = 7²
x² + y² = 49
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When graphing an equation on graph paper I have to have all of these but....
O label numbers and x/y axis
O work shown
O t-chart or slope intercept form explaned
at least 4 points on the graph
When graphing an equation on graph paper I have to have all of these but: B. work shown.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.What is a graph?In Mathematics and Geometry, a graph is a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis) respectively.
In conclusion, you do not need to have your algebraic work shown when graphing an equation on graph paper.
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A circular arc has measure 6cm and is intercepted by a central angle of 40° . Find the radius r of the circle
The radius of the circle with central angle θ = 40° is r = 8.594 cm
Given data ,
A circular arc has measure 6cm and is intercepted by a central angle of 40°
Now , the radius r of the circle is given by
r = L / θ
where θ is in radians
So , 40° = 0.6981317007977318 radians
On simplifying , we get
r = 40 / 0.6981317007977318
Now , the measure of r = 8.594 cm
Hence , the radius is r = 8.594 cm
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What is the measure of y (angle AXB)?
1. 90°
2. 60°
3. 45°
4. 30°
Answer:
4. 30°
Step-by-step explanation:
Sum of interior angles of a triangle = 180
y° + ∠XYZ + ∠YZX = 180
y° = 180 - 90 - 60 = 30°
A moving company offers two sizes of moving trucks. Truck G can fit 20 boxes that measure 1 cubic yard. Truck H is twice as large.
Which measurement can be used to determine the amount of boxes that can fit into Truck H?
Responses?
Measurement can be used to determine the amount of boxes that can fit into Truck H is 2(20 boxes) = 2 cubic yards
What are algebraic expressions?Algebraic expressions are defined as those mathematical expressions that consists of variables, terms, coefficients, constants and factors.
Algebraic expressions are also known to be composed of arithmetic operations, such as;
MultiplicationDivisionFloor divisionAdditionSubtractionBracketParenthesesFrom the information given, we have that;
For Truck G = 20 boxes
And 20 boxes = 1 cubic yard
Then,
Truck H = 2(Truck B)
Truck H = 2(20 boxes)
Truck H = 40 boxes
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Complete the ratio table
Answer: do u need help
Step-by-step explanation: ask a teacher dont cheat
6+3(-2x - 3y). Please help mee
A data set contains three points, and two of the residuals are-7 and 4. What is the third residual?
A. 7
B. -3
C. -4
D. 3
Answer:
D
Step-by-step explanation:
We know that the residual is the difference between the observed value and the predicted value for a given point. Let's assume that the predicted values for the three points in the data set are denoted by ŷ₁, ŷ₂, and ŷ₃, and the observed values are denoted by y₁, y₂, and y₃.
We can write the residuals as:
e₁ = y₁ - ŷ₁
e₂ = y₂ - ŷ₂
e₃ = y₃ - ŷ₃
We are given that two of the residuals are -7 and 4.
Let's assume that e₁ = -7 and e₂ = 4.
We can use these values to find the third residual e₃.Since the sum of residuals is always equal to zero, we have:
e₁ + e₂ + e₃ = 0
Substituting the values of e₁ and e₂, we get
:-7 + 4 + e₃ = 0
Simplifying, we get:
e₃ = 3
Therefore, the third residual is 3, which is option D.
How many centimeters are in x meters
Answer:
multiply the number of meters by 100
Write your answer has a fraction in the simplest form
We can see here that the probability that it is yellow is: 2.4.
What is probability?Probability is a way to gauge how likely something is to happen. It is stated as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty of the event.
Probability that the marble is yellow:
Total marbles = 12
Yellow marbles = 5
Probability that the marble is yellow: 12/5 = 2.4
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the diagram shows a right angled triangle
Answer:
34.8°
Step-by-step explanation:
You want the angle opposite a side of length 8 cm in a right triangle with hypotenuse 14 cm.
SineThe sine relation is the one of interest in this geometry:
Sin = Opposite/Hypotenuse
sin(x°) = (8 cm)/(14 cm)
The angle can be found using the inverse sine function:
x° = arcsin(8/14) ≈ 34.8°
The size of the angle x° is 34.8°.
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Two ramps are placed back to back as shown. What is the length of the ramp labeled x?
The value of the x as shown in the graph will be 16.61 ft.
From the sine rule in the triangle,
In a triangle ABC, where a, b, and c are the side lengths opposite to the angles A, B, and C respectively, and where the opposite angles A, B, and C are opposite to sides a, b, and c respectively, the Sine Rule states:
[tex]\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}[/tex]
Use the Law Of Sines to solve this:
(Sin 7)/9 = (Sin 13)/x
Cross multiply...
x(Sin 7) = 9(Sin 13)
Divide both sides by Sin 7
x = [9(Sin 13)]/(Sin 7)
x = 16.61254121
therefore, for the ramp, the value of the x will be 16.612 ft.
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5
Select the correct answer.
If the domain of the function, f, is restricted to x 20, which function is the inverse off?
f(x) = 91² - 12, 20
O A. q(z) = √2+1
√√2-12
3
OB. h(z)
OC. p(z) = √2-12
c.
9
√2+12
D. g(x)
O D.
The inverse of the function f(x) = 9x²- 12 is p(x) = √(x + 12)/9
How to find the inverse of the function?Given that the domain of a function f is restricted to x ≥ 0, we need to find the inverse of the function
f(x) = 9x²- 12 for x ≥ 0.
To find the inverse of the function, we proceed as follows.
f(x) = 9x²- 12
Let f(x) = y
So, we have that
y = 9x²- 12
Adding 12 to both sides of the equation, we have that
y + 12 = 9x²- 12 + 12
y + 12 = 9x²
Dividing both sides by 9, we have that
(y + 12)/9 = 9x²/9
(y + 12)/9 = x²
Taking square root of both sides, we have that
√x² = √(y + 12)/9
x = √(y + 12)/9
Now, replacing x with y, we have that
x = √(y + 12)/9
y = √(x + 12)/9
Replacing y with f⁻¹(x), we have that
f⁻¹(x) = √(x + 12)/9
So, the inverse is p(x) = √(x + 12)/9
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Help!
The surface area of this rectangular prism is __ square centimeters.
The surface area of the rectangular prism is 216 square cm
What is the surface area of the rectangular prism?From the question, we have the following parameters that can be used in our computation:
10 cm by 3 cm by 6 cm
The surface area of the rectangular prism is calculated as
Area = 2 * (3 * 10 + 3 * 6 + 10 * 6)
Evaluate
Area = 216
Hence, the area is 216 square cm
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Question 10: The graph below shows a company's profits f(x), in dollars, depending on the price of 8.01 & 8.04
pens x, in dollars, sold by the company.
Part A (2pts): Highlight your answer below
150
90
00
30
f(x)
What does the maximum value represent?
A The point where no profit is made
B.
C.
D.
The point where the most profit is made
The point where the most pens are made
The point where no pens are made.
Part B (2 pts) Highlight/circle your answer What do the x-intercepts represent?
A.
The price per pen where the most profit is made
B.
The price per pen where no profit is made.
C.
D.
The point where the most pens are made.
The point where no pens are made.
Part C (3 pts): What is an approximate average rate of change of the graph from
x=3 to x = 6? Show your work.
Part D (3 pts) Drag & Drop into the blanks to describe the constraints of the
domain.
The domain of this graph given the situation is
because
beyond those points.
+
Z
The x-intercepts represent a zero profit, the maximum value of the graph represents the maximum profit, An approximate average rate of change of the graph from x=3 to x=5 represents the reduction in profit from 3 to 5 and the domain is constrained by x=0.
Part A:
The x-intercepts represent a zero profit.
The maximum value of the graph represents the maximum profit.
The function increases up till the vertex and decreases after it.
This means that the profit increases as it reaches the peak at the vertex.
It decreases after the vertex up till it reaches zero.
On the left of the first zero and on the right of the second zero, the profits are negative.
Part B:
An approximate average rate of change of the graph from x=3 to x=5 represents the reduction in profit from 3 to 5.
Part C:
Simply, the domain is constrained by x=0.
We are obliged at x=6 .
This is because we have to avoid a negative profit.
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how to do I solve this
Answer:
the answer is 80
Step-by-step explanation:
1pound=16ounces
What is the value of x?
34°
(-1/2 x) °
Answer:
The expression "34° (-1/2 x) °" can be simplified by multiplying 34° by the quantity (-1/2 x):
34° (-1/2 x) ° = (34°) * (-1/2 x)
To multiply two values with units, we can simply multiply the numerical parts and keep the units. Therefore, we get:
(34°) * (-1/2 x) = -17x°
So the value of "34° (-1/2 x) °" is simply -17x°.
a student in a foreign language progam learns 15 new word each week which graph best represents the relationship between x the number of weeks the student has been in the progam and y the total number of new words the student has learned
The proportional relationship y = 15x represents the relationship between the variables, and it's graph is given by the image presented at the end of the answer.
What is a proportional relationship?A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.
The equation that defines the proportional relationship is given as follows:
y = kx.
In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.
A student in a foreign language program learns 15 new word each week, hence the constant is given as follows:
k = 15.
Meaning that the equation is:
y = 15x.
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Pls help
Here is a figure made of two circles inside of one circle.
Answer:
(a) Area of the big circle
= π(9^2) = 81π square cm
(b) Area of both little circles
= 2π(4.5^2) = 40.5π square cm
= 81π/2 square cm
(c) Area of the blue section
= 81π - 40.5π = 40.5π square cm
= 81π/2 square cm
A right prism with a triangular base has a volume of 195 mm3 . The right prism is 13 mm tall. The triangular base of the prism has a base length of 5 mm .
What is the base height of the triangular base of the right prism? Round your answer to the nearest whole millimeter, if necessary.
Jacob is standing 112 m from a building. The angle of elevation from where he is standing on the ground to the top of the building is 62°.
How tall is the building?
Round the final answer to the nearest tenth
Answer:
Step-by-step explanation:
Two train tracks run parallel leaving a station. Train A leaves the station heading east at 55 mph. Train B leaves the station 2 hrs and 15 minutes later also traveling east but at 120 mph. The equation below gives the distance, D, between the two trains as a function of the number of hours, T, that have passed since train B left the station.
For which two values of T will D = 40? Round to the nearest tenth.
A.
0.1 and 0.3
B.
12.9 and 25.2
C.
-1.3 and 1.3
D.
1.3 and 2.5
Answer: Answer choice C: -1.3 and 1.3.
Step-by-step explanation:
We can start by using the formula for the distance, D, between the two trains as a function of time, T:
D = 55(T + 2.25) - 120T
Simplifying this equation, we get:
D = 55T + 123.75 - 120T
D = -65T + 123.75
To find the two values of T for which D = 40, we can set this equation equal to 40 and solve for T:
40 = -65T + 123.75
-85 = -65T
T = 1.31
Plugging this value back into the original equation, we can see that D is equal to 40:
D = -65(1.31) + 123.75
D = 40.0375
Therefore, one solution is T = 1.31. To find the other solution, we can plug D = 40 into the equation and solve for T:
40 = -65T + 123.75
-83.75 = -65T
T = 1.29
Plugging this value back into the original equation, we can see that D is equal to 40:
D = -65(1.29) + 123.75
D = 40.0375
Therefore, the two values of T for which D = 40 are approximately 1.3 and 1.3, which rounds to answer choice C: -1.3 and 1.3.
1. Define, compare and contrast common stock and preferred stock.
2. Define, compare and contrast dividends and dividends in arrears.
3. Define, compare and contrast bond premium and discount.
4. What are the 3 main fee structures of mutual funds?
5. What is NAV and how is it calculated?
Common Stock:
- Represents ownership in a company and a claim on a portion of the company's assets and earnings.- Has voting rights, allowing shareholders to participate in corporate decision-making.- Dividends are not guaranteed and can fluctuate.- In the event of liquidation, common stockholders are paid after preferred stockholders.Preferred Stock:
- Represents partial ownership in a company but typically does not carry voting rights.- Typically has a fixed dividend rate, which is paid before dividends to common stockholders.- In the event of liquidation, preferred stockholders have priority over common stockholders.- Can be converted to common stock or have a callable feature, allowing the company to redeem shares at a predetermined price.Comparison:
- Common stockholders have voting rights, while preferred stockholders generally do not.- Preferred stock usually has a fixed dividend rate, while common stock dividends can fluctuate.- Preferred stockholders have priority in receiving dividends and in the event of liquidation.2. Dividends vs Dividends in Arrears:Dividends:
- Payments made by a corporation to its shareholders, usually in the form of cash or additional shares.- Typically paid from a company's profits or retained earnings.- Can be regular (e.g., quarterly) or special (one-time) dividends.Dividends in Arrears:
- Unpaid dividends owed to preferred stockholders.- Occur when a company does not pay the full dividend amount it has committed to for preferred stockholders.- Must be paid before any dividends can be paid to common stockholders.Comparison:
- Dividends are regular or special payments to shareholders, while dividends in arrears are unpaid dividends owed to preferred stockholders.- Dividends in arrears must be paid before any dividends can be paid to common stockholders.3. Bond Premium vs Bond Discount:Bond Premium:
- Occurs when a bond's market price is higher than its face value.- Usually results from a decrease in market interest rates, making the bond's fixed interest payments more attractive to investors.- Bond premium is amortized over the life of the bond, reducing the bond's book value.Bond Discount:
- Occurs when a bond's market price is lower than its face value.- Usually results from an increase in market interest rates, making the bond's fixed interest payments less attractive to investors.- Bond discount is amortized over the life of the bond, increasing the bond's book value.Comparison:
- A bond premium represents a bond selling for more than its face value, while a bond discount represents a bond selling for less than its face value.- Bond premiums typically occur when market interest rates decrease, while bond discounts occur when market interest rates increase.4. 3 Main Fee Structures of Mutual Funds:1. Sales Loads: Fees paid when buying or selling shares of a mutual fund. They can be front-end loads (charged when buying shares) or back-end loads (charged when selling shares).
2. Expense Ratio: The annual fee that covers the fund's operating expenses, including management fees, administrative fees, and other costs. It is expressed as a percentage of the fund's average net assets.
3. 12b-1 Fees: Annual fees charged by some mutual funds to cover marketing and distribution expenses. These fees are included in the fund's expense ratio.
5. NAV (Net Asset Value):- NAV represents the per-share value of a mutual fund, calculated by dividing the fund's total net assets by the number of outstanding shares.- Total net assets are calculated by subtracting the fund's liabilities from its total assets.- NAV is typically calculated at the end of each trading day and is the price at which investors can buy or sell shares of the mutual fund.Justify Results Hector was asked to simplify the expression (5^-3/5^-1) He gave the answer 1/25 Did Hector give the correct answer? Explain.
Answer:
To simplify the expression (5^-3/5^-1), we need to use the rule of exponents that states when dividing two powers with the same base, we can subtract the exponents.
Using this rule, we get:
(5^-3/5^-1) = 5^-3 ÷ 5^-1 = 5^-3 × 5^1 = 5^-2 = 1/25
Therefore, Hector gave the correct answer.
PLS HELP ME OUT! A sporting event has a promotion in which the first 1,000 fans to enter the arena receive either a blue cap or a red cap. A random number generator is used to simulate the color of a cap given to a person where indicates a blue cap and indicates a red cap. Ten simulations, each consisting of ten random numbers, are conducted, and the results are shown in the following table:
Based on the simulations, what is the probability that ten hats given to ten people will consist of more blue caps than red caps? a. 0.20
b. 0.40 c. 0.60 d. 0.80
The probability that ten hats given to ten people will consist of more blue caps than red caps is given as follows:
a. 0.2.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The outcomes in which there are more blue than red caps are those in which the number of zeros is greater than the number of ones, hence the number of desired outcomes is of:
2. (simulation number 7 and simulation number 10).
Hence the probability is of:
p = 2/10
p = 0.2.
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I need help with this problem.
According to the information, the elasticity is 0.619, suggests that the demand is relatively insensitive to price changes.
How to calculate the elasticity?To evaluate the elasticity at $p=2$, we need to use the formula for price elasticity of demand:
E = (dQ/Q) / (dP/P)
where:
E = price elasticity of demand
dQ = change in quantity demanded
Q = quantity demanded
dP = change in price
P = price
We are given the equation for the demand function:
x = 15000 - 3535√p
So, the quantity demanded at price $p$ is $Q = x(p) = 15000 - 3535\sqrt{p}$.
Taking the derivative of Q with respect to p:
dQ/dp = -3535/(2√p)
Now we can calculate the elasticity at $p=2$:
Q = 15000 - 3535√2
dQ/dp = -3535/(2√2)
P = 2
dP = 0
E = (dQ/Q) / (dP/P)
E = (-3535/(2√2)) / [(15000 - 3535√2)/2]
E ≈ -0.619
According to the above, the elasticity is 0.619, suggests that the demand is relatively insensitive to price changes.
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