Answer:
The formula for an exponential decay problem is: y = x (1 - r)^x
Where x = initial amount, r = rate of decay and x = # time periods
So, x = $258, r = 8% = .08 and x = 11 years
y = 258 (1 - 0.08)^11 = 258 (0.92)^11 = 258 * 0.3996 = $103.10
Step-by-step explanation:
Sketch each angle in standard position.
-75°
That angles in standard position are always measured from the positive x-axis in a counterclockwise direction for positive angles, and in a clockwise direction for negative angles.
To sketch the angle -75° in standard position, follow these steps:
1. Start by drawing the initial arm, which is the positive x-axis. This arm should be horizontal, extending to the right.
2. Since the angle is negative, we need to rotate clockwise. To do this, measure 75° clockwise from the initial arm and draw the terminal arm.
3. The terminal arm should be in the fourth quadrant, as it is rotating clockwise. It will extend downwards to form an angle of 75° with the positive x-axis.
4. Label the angle as -75°.
Remember that angles in standard position are always measured from the positive x-axis in a counterclockwise direction for positive angles, and in a clockwise direction for negative angles.
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Convert 27/4 into a mixed number.
Answer:
\(6 \times \frac{3}{4} \)
Step-by-step explanation:
4 in 27 is 6 and it remains 3.
In a certain city the temperature (in degrees Fahrenheit) t hours after 9 am was approximated by the function T(t)=60+19sin( 12πt) Determine the temperature at 9am. Determine the temperature at 3pm. Find the average temperature during the period from 9 am to 9pm.
The average temperature during the period from 9 am to 9 pm is approximately equal to 64.5 degrees Fahrenheit.
The temperature at 9 am can be determined by substituting t=0 in the given function T(t). Therefore, T(0) = 60 + 19sin(0) = 60. Hence, the temperature at 9 am is 60 degrees Fahrenheit.
To determine the temperature at 3 pm, we need to substitute t=6 in the given function T(t). Therefore, T(6) = 60 + 19sin(72π) ≈ 60 - 19 = 41 degrees Fahrenheit.
To find the average temperature during the period from 9 am to 9 pm, we need to calculate the definite integral of T(t) from t=0 to t=12 and divide it by 12. Therefore,
Average temperature = (1/12) * ∫[0,12] (60 + 19sin(12πt)) dt
Using integration by substitution, we get
Average temperature = (1/12) * [(60t - (19/12π)cos(12πt))] [0,12]
Simplifying this expression, we get
Average temperature = (1/12) * [720 + (19/12π)]
Therefore, the average temperature is approximately 64.5 degrees Fahrenheit.
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The length of sides of triangular fields are 10m, 24m and 26m. A farmer grows flowers in this field. If 5kg flowers can be obtained in 1 Sq metre area, then find the area of field and quantity of flowers that can be grown.
Answer:
Area: 120m²
Flowers: 600kg
Step-by-step explanation:
we can use Heron's formula to solve for the area.
Heron's formula:
Area of triangle = \(\sqrt{ s(s-a)(s-b)(s-c)}\)
s = 1/2 (a+b+c)
s = 1/2 (10 +24+26)
s = 30
Area of triangle
\(=\sqrt{30(30-10)(30-24)(30-26)} \\=120m^{2}\)
Since every 1 m² of area can grow 5kg of flowers,
the yield of flowers will be:
120 x 5
=600kg
Your company wants to purchase some equipment for recycling metals. Machine A costs $323,000 and has a useful life of 10 years. Its operating costs are $2.40 per ton of metal processed. Machine B costs $178,000 and has a useful life of 6 years. Its operating costs are $8.00 per ton of metal processed. How many tons of metal per year must your company process to favor Machine A over Machine B? Assume an MARR of 18% per year.
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To determine the number of tons of metal per year needed for Machine A to be favored over Machine B, we compare their costs. Machine A costs $323,000 with an annual operating cost of $2.40/ton, while Machine B costs $178,000 with an annual operating cost of $8.00/ton. The machines have useful lives of 10 years and 6 years, respectively, and the minimum attractive rate of return (MARR) is 18% per year.
By calculating the equivalent annual costs (EAC) for each machine using the given formula and comparing them, we can determine the point at which Machine A becomes more favorable. However, specific values for the discounting factors and the tons per year needed are missing, making it impossible to provide an exact answer.
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8. P(-3, -7) and (3,-5) fine the midpoint
Answer: 0,-6
Step-by-step explanation:
Midpoint Formula x1+x2/2, y1+y2/2
-3+3= 0/2=0 -7+(-5)= -12/2 = -6
0,-6
Many families in California are using backyard structures for home offices, art studios, and hobby areas as well as for additional storage. Suppose that the mean price for a customized wooden, shingled backyard structure is $3100. Assume that the standard deviation is $1200.
a. What is the z-score for a backyard structure costing $2300?
b. What is the z-score for a backyard structure costing $4900?
c. Interpret the z-scores in parts (a) and (b). Comment on whether either should be considered an outlier.
d. If the cost for a backyard shed-office combination built in Albany, California, is $13,000, should this structure be considered an outlier? Explain.
The z-score is a measure of how many standard deviations a data point is from the mean. It can be calculated using the formula
z = (x - μ) / σ,
where x is the data point, μ is the mean, and σ is the standard deviation.
a. The z-score for a backyard structure costing $2300 can be calculated as follows:
z = (2300 - 3100) / 1200 = -800 / 1200 = -0.67
b. The z-score for a backyard structure costing $4900 can be calculated as follows:
z = (4900 - 3100) / 1200 = 1800 / 1200 = 1.
c. The z-score in part (a) is -0.67, which means that the backyard structure costing $2300 is 0.67 standard deviations below the mean. The z-score in part (b) is 1.5, which means that the backyard structure costing $4900 is 1.5 standard deviations above the mean. Neither of these z-scores are extreme enough to be considered outliers, as they are both within 2 standard deviations of the mean.
d. The z-score for the backyard shed-office combination costing $13,000 can be calculated as follows:
z = (13000 - 3100) / 1200 = 9900 / 1200 = 8.25
This z-score is much larger than 2, which means that the structure costing $13,000 is more than 8 standard deviations above the mean. This is an extreme value and should be considered an outlier.
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Help with math hw please
Answer:
27.2
Step-by-step explanation:
x is the hypotenuse.
For the 54-deg angle, 22 is the opposite leg.
The trig ratio that relates the opposite leg to the hypotenuse is the sine.
In general:
sin A = opp/hyp
We have:
sin 54 = 22/x
x sin 54 = 22
x = 22/sin 54
x = 27.193
Answer: 27.2
Help Wanted! ♀️ Solve for X, Leave answer in simplest radical form. (Multistep Pythagorean Theorem)
Answer:
x = √39
Step-by-step explanation:
both triangles have one same side, which can be called y
so y^2 = 10^2 - 6^2
and y^2 = x^2 + 5^2
then x^2 + 5^2 = 10^2 - 6^2
x^2 = 100 - 36 - 25 = 39
x = √39
patrick wants to estimate the percentage of companies that use video ads. he asks a randomly selected group of 125 companies whether or not they use video ads. what is the statistic?
The percentage of companies that use video ads in the sample is the statistic.
A statistic is the measure of a particular characteristic in the sample which is nothing but a subset of the population. A singular or sample statistic is any quantity computed from values in a sample that is considered for a statistical purpose.Here, the concern is to estimate the percentage of companies that use video ads.
He took a sample of 125 companies to inquire whether or not they use video ads.
So, the percentage of companies that use video ads in the sample is the statistic.
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Based on this analysis, we can determine which statements are true:
The radius of the circle is 3 units.
The center of the circle lies on the x-axis.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
What is equation?A mathematical statement proving the equality of two expressions is known as an equation. It consists of an equal sign placed between two expressions, referred to as the equation's left-hand side (LHS) and right-hand side (RHS). The equal sign indicates that the values on the two sides of the equation are equal.
Here,
x² + y² – 2x – 8 = 0
We can complete the square for the x terms by adding (–2/2)² = 1 to both sides:
x² – 2x + 1 + y² – 8 = 1
(x – 1)² + y² = 9
Comparing this equation to the standard form of a circle, (x – h)² + (y – k)² = r², we see that the center of this circle is (h, k) = (1, 0), and the radius = 3.
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Please help! I will give brainlist
The required Rebecca can pack a maximum of 300 supply boxes in this crate. Option B is correct.
What is volume?Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
Here,
The crate can be thought of as a rectangular prism with dimensions:
Height = 9 feet
Width = 10 feet
Depth = 10 feet
The supply boxes can be thought of as smaller rectangular prisms with dimensions,
Height = 1.5 feet
Width = 1 foot
Depth = 2 feet
In the height dimension, we can fit 6 boxes since 9 feet divided by 1.5 feet per box equals 6.
In the width dimension, we can fit 10 boxes since 10 feet divided by 1 foot per box equals 10.
In the depth dimension, we can fit 5 boxes since 10 feet divided by 2 feet per box equals 5.
Therefore, the maximum number of supply boxes that can be packed in this crate is,
6 boxes (height) x 10 boxes (width) x 5 boxes (depth) = 300 boxes.
So, Rebecca can pack a maximum of 300 supply boxes in this crate.
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I have a picture of the question
Given in the question:
a.)
Multiplying by which conversion factor would allow you to convert 35 liters to milliliters?.
Therefore, the formula for converting 35 liters to milliliters is 35000, with a conversion factor of 1000.
This is further explained below.
What is the conversion factor?Generally, The amount that is supplied in liters must be multiplied by 1000 in order to be converted to milliliters.
A conversion factor is a number that may be multiplied or divided to shift the units of measurement used for one set to another.
In situations when a conversion is required, the correct conversion factor that results in the same value must be used. For the purpose of converting inches to feet, for instance, the correct value for the conversion is 12 inches equaling 1 foot.
In conclusion, Therefore 35 liters to milliliters is given as 35000, conversion factor of 1000
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Answer:
1000ml and 1 liter
Step-by-step explanation:
What is the average monthly rate?
Answer:
47
Step-by-step explanation:
I WILL GIVE
Create an equivalent expression for this
Answer: C
Step-by-step explanation:
Answer: I think the answer is A.
Step-by-step explanation:
The value of a certain collectible card in dollars from January 2020 to May 2021 can be modeled by the function V(m)=250m2 – 3,500m + 18,000, where m is the approximate number of months since the start of 2020.
Over what period was the value of the card declining?
The value of the card was declining over the period is from the month of January 2020 to July 2020.
To determine the period over which the value of the card was declining,
Identify the range of values for which the derivative of the function V(m) is negative.
Let's find the derivative of the function V(m),
V'(m)
= dV(m)/dm
= 500m - 3500
To determine when the value of the card is declining, find when V'(m) is less than zero.
Setting V'(m) < 0,
⇒500m - 3500 < 0
Solving for m,
⇒500m < 3500
⇒m < 7
The value of the card is declining for values of m less than 7.
Since m represents the approximate number of months since the start of 2020,
The declining period can be determined as the time from the start of 2020 to the 7th month.
Hence, the period over which the value of the card was declining is from January 2020 to July 2020.
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Which category in the Excel Options dialog box contains the option to change the user name? Advanced ○General ○ Account Setings ○Trust Center
The category in the Excel Options dialog box that contains the option to change the user name is "General".
In the Excel Options dialog box, the category that contains the option to change the user name is the General category.
Excel graphing methods, Go to Insert > Line after selecting the data. The type of line chart you want may be chosen from a dropdown menu that appears when you click the icon.
We'll use the fourth 2-D line graph (Line with Markers) for this illustration. Your line graph for the chosen data series will be added by Excel.
What are the primary three graphs?
How to Use Graphs in Science
Bar, circle, and line graphs are the three most often utilized graph kinds. Each form of graph may be used to display a certain kind of data.
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Lines CE and AD intersect at B.
What is the measure of angle DBE?
Group of answer choices
37∘
143∘
53∘
127∘
Answer:
The measure of angle DBE is 37° ⇒ (A)
Step-by-step explanation:
If two lines are intersecting at a point, then every two vertically opposite angles are equal in measure
Example:
If line XY intersects line MN at point Z, then angle MZX, angle NZY are vertically opposite angles, and angle MZY, angle NZX are vertically opposite angles
Let us use this fact to solve the question
∵ Line CE intersects line AD at point B
∴ ∠ ABC and angle ∠DBE are vertically opposite angles
∴ m∠ABC = m∠DBE
∵ m∠ABC = 37°
∴ m∠DBE = 37°
The measure of angle DBE is 37°
Solve for x. Round to the nearest tenth of a degree, if necessary.
2.1
D
4
to
E
Answer:
\(31.7^\circ\)
Step-by-step explanation:
We use the property that the sin of the angle of a right triangle is the ratio of the side opposite that angle divided by the hypotenus
Therefore
\(\begin{aligned}\sin x & = \dfrac{2.1}{4}\\& = 0.525\\\end{aligned}\\\begin{aligned}x &= sin^{-1}(0.525)\\& = 31.7^\circ \end{aligned}\)
The height, s of a ball (in feet) thrown with an initial velocity of 80 feet per second from an initial height of 6 feet is given as a function of the time t (in seconds) by s(t)=-16t^2 +80t+6. Explain in detail how you could find the maximum height of the ball. Now, explain, in detail, a second method of finding the maximum height. Using one of these two methods, determine the time at which height is a maximum and find that maximum height. Be sure to use units in your answer and explain your methods thoroughly.
if the z transform of a function f(k) is 2z/[(z^2 0.2z 0.06)(z-1)], assuming f(infinity) is bounded, the limit of f(k) when k goes to infinity is
Factorize the polynomial to obtain the roots of the equation, which are z=0.2, z=0.06, and z=1.
The z-transform is a mathematical tool that is commonly used to analyze discrete-time signals and systems. In this case, we are given the z-transform of a function f(k) and we are asked to determine the limit of f(k) as k approaches infinity.
From the given expression of the z-transform, we can see that the denominator is a polynomial of degree 3 in z. We can factorize the polynomial to obtain the roots of the equation, which are z=0.2, z=0.06, and z=1.
Since f(infinity) is bounded, it means that the function f(k) approaches a finite value as k goes to infinity. In other words, the limit of f(k) as k approaches infinity exists.
To determine the limit, we need to use the partial fraction decomposition method to express the z-transform as a sum of simpler fractions. Then, we can use the inverse z-transform to obtain the original function f(k).
Once we have the original function, we can evaluate the limit as k approaches infinity by analyzing the behavior of the function at the poles and zeros of the z-transform.
In conclusion, the limit of f(k) when k goes to infinity can be determined by using the partial fraction decomposition and inverse z-transform methods. The behavior of the function at the poles and zeros of the z-transform will determine whether the limit exists and what its value is.
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please help! What is the product in the form ax^2+bx+c
Answer:
a=2, b=2, c=-12
Step-by-step explanation:
Since it's in factor form, you would first distribute using foil to get \(2x^{2} -4x+6x-12\) and then combine like terms when necessary. In this case, the fully simplified version is \(2x^{2} +2x-12\). Therefore your a is 2, b is 2, and c is -12.
5 7/8 + 1 1/3 =
Im confused
please help!!
-2x + 2y=-4 x-4y=-10 solve by elimination
Step-by-step explanation:
To solve by elimination, we need to get the coefficients of either x or y the same for both equations.
Let's first multiply the second equation by 2, so that the coefficients of x become opposite in sign:
-2x + 2y = -4
2x - 8y = -20
Now, we can add the two equations together to eliminate x:
(2x - 8y = -20)
(-2x + 2y = -4)
-6y = -24
Dividing both sides by -6, we get:
y = 4
Now, we can substitute this value of y into either of the original equations to solve for x. Let's use the first equation:
-2x + 2y = -4
-2x + 2(4) = -4
-2x + 8 = -4
-2x = -12
x = 6
Therefore, the solution is (x, y) = (6, 4).
Answer:
To solve this system of equations by elimination, we need to eliminate one of the variables, either x or y. Let's choose to eliminate y:
-2x + 2y = -4
x - 4y = -10
Multiplying the second equation by 2, we get:
-2x + 2y = -4
2x - 8y = -20
Now we can add the two equations to eliminate y:
-2x + 2y + 2x - 8y = -4 - 20
Simplifying, we get:
-6y = -24
Dividing both sides by -6, we get:
y = 4
Now we can substitute y = 4 into one of the equations to solve for x. Let's use the first equation:
-2x + 2y = -4
-2x + 2(4) = -4
Simplifying, we get:
-2x + 8 = -4
Subtracting 8 from both sides, we get:
-2x = -12
Dividing both sides by -2, we get:
x = 6
Therefore, the solution to the system of equations is (x, y) = (6, 4).
im confused please help
Answer:
its a
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Jenna and Becca were both selling cookies door to door. Jenna sold 8 boxes of cookies for every 3 boxes of cookies Becca sold. Combined, they sold a total of 385 boxes of cookies. How many boxes did each girl sell
Answer: Jenna sold 280 and Becca sold 105 boxes.
Step-by-step explanation:
Let 3x be the number of cookies Becca sold.
Then, the number of cookies Jenna sold = 8x
Since Combined, they sold a total of 385 boxes of cookies.
So, \(3x+8x=385\)
\(\Rightarrow\ 11x=385\\\\\Rightarrow\ x=\dfrac{385}{11}\\\\\Rightarrow\ x=35\)
So, Jenna sold 8(35) = 280 boxes
and Becca sold 3(35)= 105 boxes
Hence, Jenna sold 280 and Becca sold 105 boxes.
The price of a television is $245. The sales tax rate is 8%. What is the amount of sales tax?
Answer:
$19.60
Step-by-step explanation:
245 is 100% of the total.
x is 108% of the total.
245/100 = x/108
245(108) = 26460
26460/100 = 264.6
264.6 - 245 = 19.6
A n s w e r :
$ 1 9 . 6 0
E x p l a n a t i o n
T a k e t h e a m o u n t a n d m u l t i p l y b y t h e t a x r a t e t o
d e t e r m i n e t h e s a l e s t a x
t a x = 2 4 5 * 8 %
C h a n g e t o d e c i m a l f o r m
t a x = 2 4 5 * . 0 8
= 1 9 . 6 0
Estimate:
11 is 50% of what number?
A 20
B 40
C 60
D 5
Answer:
50% of a number means that we are taking half of a number. Since 11 is 50% of a number that means that we need to multiply 11 by 2 to get the original number. When we multiply 11 by 2 we get 22 and that is closest to option A which is 20.
Answer: Option A, \(20\)
Please ignore what was already selected
Answer: Option 4
CE/DE
Explanation:
Sin = Opposite/Hypotenuse
In triangle DCE the opposite ( angle D ) is CE and the hypotenuse is DE
so sinD = CE/DE
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