Answer: Sarah is correct
Step-by-step explanation:
A composite number is referred to as a positive integer which is gotten when someone multiplies two positive integers that are smaller than the number. We should note that we should not use one while multiplying.
A prime number is a number that can only be divided when the number is being divided by one and itself. Examples are 2, 3, 7, 11 etc.
Based on the above analysis, 2 is a prime number while 4 is a composite number. Therefore, Sarah is correct.
Mo has a bag of sweets she has 3 chews and2 mints left Seh picks out a sweet what is the probability that she picks a mint
Answer:
2/5
Step-by-step explanation:
If she has 3 chews and 2 mints left, the probability that she picks a mint is 2/5 as they are only 2 mints and 3 chews and 2+3 = 5. So the awnser is 2/5.
PLEASE EXPLAIN!!!
You are planning to use a ceramic tile design in your new bathroom. The tiles are equilateral triangles. You decide to arrange the tiles in a hexagonal shape as shown. If the side of each tile measures 11cm, what will be the exact area of each hexagonal shape?
A: 3,993 cm^2
B: 181.5√3 cm^2
C: 132√3 cm^2
D: 33cm^2
The exact area of each hexagonal shape is 181.5sqrt(3) cm^2. Option B
To determine the exact area of each hexagonal shape formed by the equilateral triangles, we need to calculate the area of one equilateral triangle and then multiply it by the number of triangles that make up the hexagon.
The formula to calculate the area of an equilateral triangle is:
Area = (sqrt(3) / 4) * side^2
Given that the side of each tile measures 11 cm, we can substitute this value into the formula to find the area of one equilateral triangle:
Area = (sqrt(3) / 4) * (11 cm)^2
= (sqrt(3) / 4) * 121 cm^2
= 121sqrt(3) / 4 cm^2
Now, since the hexagon is formed by six equilateral triangles, we can multiply the area of one triangle by 6 to find the total area of the hexagon:
Hexagon Area = 6 * (121sqrt(3) / 4 cm^2)
= 726sqrt(3) / 4 cm^2
= 181.5sqrt(3) cm^2
Therefore, the exact area of each hexagonal shape is 181.5sqrt(3) cm^2.
The correct answer is B: 181.5√3 cm^2.
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he following problems add in a minimal threshold value for the species to survive, T, which changes the differential equation to
P't = rp(1-P/K) (1-T/P)
Bengal tigers in a conservation park have a carrying capacity of 100 and need a minimum of 10 to survive. If they grow in population at a rate of 1% per year, with an initial population of 15 tigers, solve for the number of tigers present.
the solution for the number of tigers present over time is given by:
P - (P^2)/(2K) - (T/K)P + (T/K)ln(P) = rt + 11.375 + 0.1ln(15)
To solve the given differential equation for the population of Bengal tigers in the conservation park, we'll use the given parameters and initial conditions.
The differential equation for the population (P) is:
P't = rp(1 - P/K)(1 - T/P)
Given:
Carrying capacity (K) = 100
Minimum threshold value for survival (T) = 10
Population growth rate (r) = 1% = 0.01 (per year)
Initial population (P0) = 15
Now, let's solve the differential equation to find the number of tigers present over time.
Separating variables, we have:
(1 - P/K)(1 - T/P) dP = rp dt
Integrating both sides:
∫ (1 - P/K)(1 - T/P) dP = ∫ rp dt
Let's evaluate the integral on the left side:
∫ (1 - P/K)(1 - T/P) dP = ∫ (1 - P/K - T/K + T/(KP)) dP
= ∫ (1 - P/K) - (T/K) + (T/PK) dP
= P - (P^2)/(2K) - (T/K)P + (T/K)ln(P) + C1
On the right side, we have:
∫ rp dt = rt + C2
Combining both sides and simplifying, we have:
P - (P²2)/(2K) - (T/K)P + (T/K)ln(P) + C1 = rt + C2
To solve for the constants C1 and C2, we use the initial condition P(0) = P0:
P0 - (P0²2)/(2K) - (T/K)P0 + (T/K)ln(P0) + C1 = r(0) + C2
P0 - (P0²2)/(2K) - (T/K)P0 + (T/K)ln(P0) + C1 = C2
Substituting the given values:
15 - (15²2)/(2×100) - (10/100)×15 + (10/100)ln(15) + C1 = C2
15 - (225/200) - (150/100) + (10/100)ln(15) + C1 = C2
15 - 1.125 - 1.5 + 0.1ln(15) + C1 = C2
Simplifying further, we have:
12.375 + 0.1ln(15) + C1 = C2
Now we have the general solution:
P - (P²2)/(2K) - (T/K)P + (T/K)ln(P) = rt + C
Using the initial condition P(0) = 15, we can solve for C:
15 - (15²2)/(2×100) - (10/100)×15 + (10/100)ln(15) = r(0) + C
15 - 1.125 - 1.5 + 0.1ln(15) = C
11.375 + 0.1ln(15) = C
Therefore, the solution for the number of tigers present over time is given by:
P - (P²2)/(2K) - (T/K)P + (T/K)ln(P) = rt + 11.375 + 0.1ln(15)
This is the general solution for the population of Bengal tigers in the conservation park.
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Question 4 of 10
Which of the following could be the ratio between the lengths of the two legs
of a 30-60-90 triangle?
Check all that apply.
□A. √2:√2
B. 15
□ C. √√√√5
□ D. 12
DE √3:3
OF. √2:√5
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SUBMIT
The ratios that could be the lengths of the two legs in a 30-60-90 triangle are √3:3 (option E) and 12√3 (option D).
In a 30-60-90 triangle, the angles are in the ratio of 1:2:3. The sides of this triangle are in a specific ratio that is consistent for all triangles with these angles. Let's analyze the given options to determine which ones could be the ratio between the lengths of the two legs.
A. √2:√2
The ratio √2:√2 simplifies to 1:1, which is not the correct ratio for a 30-60-90 triangle. Therefore, option A is not applicable.
B. 15
This is a specific value and not a ratio. Therefore, option B is not applicable.
C. √√√√5
The expression √√√√5 is not a well-defined mathematical operation. Therefore, option C is not applicable.
D. 12√3
This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which simplifies to √3:3. Therefore, option D is applicable.
E. √3:3
This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which is equivalent to √3:3. Therefore, option E is applicable.
F. √2:√5
This ratio does not match the ratio of the sides in a 30-60-90 triangle. Therefore, option F is not applicable. So, the correct option is D. 1 √2.
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Q.No.4. Calculate the cube root of 64.
Answer:
\(\huge\boxed{\sqrt[3]{64}=4}\)
Step-by-step explanation:
We know:
\(\sqrt{a}=b\iff b^2=a\qquad\text{for}\ a\geq0\\\\\sqrt[3]{a}=b\iff b^3=a\)
We have:
\(\sqrt[3]{64}=4\ \text{because}\ 4^3=4\cdot4\cdot4=64\)
A power line is to be constructed from a power station at point A to an island at point C, which is 1 mi directly out in the water from a point B on the shore. Point B is 4 mi down shore from the power station at A. It costs $5000 per mile to lay the power line under water and $3000 per mile to lay the line underground. At what point S down shores from A between the cities?
Answer:
Given :
length offshore = CS=√(1+X^2)
Cable charged = 5000√(1+X^2)
onshore length = 4-X
laying cost = 3000(4-X)
total cost:
C=5000√(1+X^2) +3000(4-X)
DC/DX
= [5000*(0.5)*2X/{√(1+X^2)}]-3000=0... for optimum
5000X=3000√(1+X^2)
25X^2=3+3X^2
22X^2=3
X=√(3/22)
= 0.3693 miles
So, it would be laid offshore to S in a manner that
BS=X=0.3693 miles
Onshore=4-0.3693
=3.6307 miles
Please HELP ME!!! due at 8pm tonight 10/12/22
Answer:
y=2x+4
Step-by-step explanation:
get x is get two point let’s say (-2,0) and (0,4)
The 4-0/0-(-2)=4/2=2 so 2 is x and (0,4) is where it hit the y axis so 4 is b plug in
Y=2x+2
A clay specimen, 25 mm thick, has been tested in an oedometer apparatus with two way rainage, and it is observed that 50% of the consolidation settlement occurs in 1 hour. A ayer of the same clay is observed to settle 10 mm in 10 years and after many years to settle (total primary consolidation) by 35 mm. Determine the thickness of the clay layer if it drains only from upper surface
The thickness of the clay layer, which drains only from the upper surface, can be determined based on the consolidation settlement observations. With 50% of consolidation settlement occurring in 1 hour for a 25 mm thick specimen, and a total primary consolidation settlement of 35 mm occurring over many years, the thickness of the clay layer is approximately 87.5 mm.
The consolidation settlement of a clay specimen can be used to estimate the thickness of a clay layer that drains only from the upper surface. In this case, the observed settlement data provides valuable information.
Firstly, we know that 50% of the consolidation settlement occurs in 1 hour for a 25 mm thick clay specimen. This is an important parameter for calculating the coefficient of consolidation (Cv) using Terzaghi's theory. From the Cv value, we can estimate the time required for full consolidation settlement.
Secondly, we are given that the same clay settles 10 mm over 10 years and eventually settles a total of 35 mm over a longer period. This long-term settlement is known as the total primary consolidation settlement. By comparing this settlement value with the settlement data from the oedometer test, we can determine the thickness of the clay layer.
To calculate the thickness, we can use the concept of the consolidation settlement ratio. The ratio of the total primary consolidation settlement to the consolidation settlement at 50% completion is equal to the ratio of the total thickness to the thickness at 50% completion. Applying this ratio, we can determine that the thickness of the clay layer, which drains only from the upper surface, is approximately 87.5 mm.
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if r(t) = (4t, 3tยฒ, 4tยณ) , find r'(t), T(1), r''(t), and r'(t) ร r ''(t).
The value of the expression is r'(t) = (4, 6t, 12t²), T(1) = (2/7, 3/7, 6/7), r''(t) = (0, 6, 24t), r'(t) ร r''(t) = 144t³.
We are given the vector-valued function r(t) = (4t, 3t², 4t³).
To find r'(t), we need to take the derivative of each component of r(t) with respect to t:
r'(t) = (d/dt)(4t), (d/dt)(3t²), (d/dt)(4t³)
r'(t) = (4, 6t, 12t²)
To find T(1), we need to evaluate r'(t) at t = 1 and then divide by the magnitude of r'(1):
r'(1) = (4, 6(1), 12(1)²) = (4, 6, 12)
| r'(1) | = sqrt(4² + 6² + 12²) = sqrt(196) = 14
T(1) = r'(1) / | r'(1) | = (4/14, 6/14, 12/14) = (2/7, 3/7, 6/7)
To find r''(t), we need to take the derivative of each component of r'(t) with respect to t:
r''(t) = (d/dt)(4), (d/dt)(6t), (d/dt)(12t²)
r''(t) = (0, 6, 24t)
Finally, to find r'(t) ร r''(t), we need to take the dot product of r'(t) and r''(t):
r'(t) ร r''(t) = (4, 6t, 12t²) ร (0, 6, 24t)
r'(t) ร r''(t) = 0 + 6t(6t) + 12t²(24t)
r'(t) ร r''(t) = 144t³
Therefore, we have:
r'(t) = (4, 6t, 12t²)
T(1) = (2/7, 3/7, 6/7)
r''(t) = (0, 6, 24t)
r'(t) ร r''(t) = 144t³
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Graph the solution to this inequality on the number line.
−4m+3>11
Answer: The person above me is correct. Here is a picture if you still dont get it..
Step-by-step explanation:
The following table shows the number of pieces of junk mail that arrives in my mailbox each day. What is the probability that 3 or fewer pieces of junk mail will be received today? Please show steps with the formula used.Number of Pieces of Junk Mail Frequency
2 2
3 14
4 6
5 16
6 12
The probability of receiving 3 or fewer pieces of junk mail is 0.44 or 44%.
Probability is a measure of how likely an event is to occur.
Total number of pieces of junk mail that could be received = 2 + 14 + 6 + 16 + 12 = 50
Total number of pieces of junk mail that correspond to receiving 3 or fewer pieces = 2 + 14 + 6 = 22
Now calculate the probability by dividing the number of pieces of junk mail that correspond to receiving 3 or fewer pieces by the total number of pieces of junk mail:
P(3 or fewer pieces) = 22/50 = 0.44
So the probability of receiving 3 or fewer pieces of junk mail is 0.44 or 44%.
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A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 47.0 and 52.0 minutes. Find the probability that a given class period runs between 50.25 and 51.0 minutes.
Answer:
0.15 or 15%
Step-by-step explanation:
Since lengths are uniformly distributed, the probability that a class period runs between a two exact times is:
\(P(x_1\leq x \leq x_2)=\frac{x_2-x_1}{b-a}\)
In this case, a = 47.0 and b = 52.0 minutes.
The probability that a given class period runs between 50.25 and 51.0 minutes is:
\(P(50.25\leq x \leq 51.0)=\frac{51.0-50.25}{52-47} \\P(50.25\leq x \leq 51.0)=0.15=15\%\)
The probability is 0.15 or 15%.
each of the faces of a fair six-sided die is numbered 1 through 6. two dice will be tossed, and the sum of the numbers appearing on the faces that land up will be recorded. what is the probability that the sum will be 4, given that the sum is less than or equal to 6? write your answer as a decimal.
The probability of getting a sum of 4 given that the sum is less than or equal to 6 is 2/5.
To find the outcomes where the sum is less than or equal to 6. From the table, we can see that there are five such outcomes: (1,1), (1,2), (2,1), (1,3), and (2,2). Therefore, the probability of getting a sum less than or equal to 6 is:
P(sum ≤ 6) = 5/36
To find the outcomes where the sum is 4 given that the sum is less than or equal to 6, we can look at the table again and identify the outcomes where the sum is 4. We can see that there are only two such outcomes: (1,3) and (2,2). Therefore, the probability of getting a sum of 4 given that the sum is less than or equal to 6 is:
P(sum = 4 | sum ≤ 6) = 2/5
The notation "P(A | B)" denotes the probability of event A given that event B has occurred. In this case, event B is "the sum is less than or equal to 6", and event A is "the sum is 4".
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a circle is inside a square. the radius of the circle is increasing at a rate of 2 meters per hour and the sides of the square are decreasing at a rate of 1 meter per hour. when the radius is 5 meters, and the sides are 23 meters, then how fast is the area outside the circle but inside the square changing? the rate of change of the area enclosed between the circle and the square is square meters per hour.
For the radius of the circle 5 meters and sides 23meters the rate of change of area which is enclosed between the circle and the square is equal to -42.9 square meters per hour.
Let us consider radius of the circle be r.
And each side of the square be x.
As radius of the circle is increasing at a rate of 2 m/hour.
⇒ dr/dt = 2.
Sides of the square are decreasing at the rate of 1meter per hour
⇒ dx/dt = -1
Area outside the circle and inside the square given by :
A(t) = x² - πr²
Here x(t) and r(t) both are functions of time;
Derivative with respect to 't' we get,
⇒ A'(t) = 2x (dx/dt ) - π( 2r × dr/dt)
Here radius 'r' = 5 meters
And x = 23/4 sides
= 5.75m
Substitute the value we get,
⇒A'(t) = 2 × 5.75 × (-1 ) - π × 5 × 2
⇒A'(t) = - 11.5 - 10π
⇒A'(t) = -11.5 - 10 × 3.14
⇒A'(t) = -11.5 - 31.4
⇒A'(t) = -42.9 square meters per hour.
Therefore, the rate of change of the area enclosed between the square and the circle is equal to -42.9 square meters per hour.
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Technology required. Jada is visiting New York City to see the Empire State building. She is100 feet away when she spots it. To see the top, she has to look up at an angle of86.1 degrees. How tall is the Empire State building?
Lets draw a picture of our problem
then, we have a right triangle
we can relate such quantities by means of the tangent function, that is,
\(\tan 86.1=\frac{h}{100}\)by moving 100 to the left hand side, we have
\(\begin{gathered} 100\times\tan 86.1=h \\ or\text{ equivalently} \\ h=100\times\tan 86.1 \end{gathered}\)therefore, the answer is
\(h=1466.85\text{ ft}\)that is,by rounding up, the height is 1467 feets
A silo is constructed using a cylinder with a hemisphere on top. The circumference of the hemisphere and the circumference of the cylinder are equal. The diameter of the circular base of the cylinder is 10 feet. The cylinder is 40 feet tall. One of the circular bases on the cylinder is in contact with the ground.
What is the area of the surface of the silo that will be exposed to rain, wind, and sun?
450π square feet
475π square feet
500π square feet
525π square feet
Answer:
The answer is 450 pi square feet
Step-by-step explanation:
The area of the surface of the silo is 450π square feet.
What is surface area?Surface area is the amount of space covering the outside of a three-dimensional shape.
Given that a silo is constructed using a cylinder with a hemisphere on top.
Both are having equal circumference.
The diameter of the circular base of the cylinder is 10 feet. The cylinder is 40 feet tall.
The surface that will be exposed to the rain is the lateral surface of the cylinder and the hemisphere.
The lateral area of the cylinder is a rectangle with height equal to the height of the cylinder and width equal to the circumference of the base of the cylinder.
Circumference of the base = 2πr = 10π ft
The lateral area = 400π ft²
The surface area of a hemisphere is = 2πr² = 50π ft²
Total surface area = 450π ft²
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sin theta + cos theta
cos theta (1-cos theta)
Given the initial expression sin(θ) + cos(θ) * cos(θ) * (1 - cos(θ)), we simplified it to sin(θ) + cos²(θ) - cos³(θ).
Given the expression:
sin(θ) + cos(θ) * cos(θ) * (1 - cos(θ))
Let's simplify this expression step by step:
1. First, recognize that cos(θ) * cos(θ) can be written as cos²(θ). So, the expression becomes:
sin(θ) + cos²(θ) * (1 - cos(θ))
2. Next, we'll distribute cos²(θ) to both terms inside the parentheses:
sin(θ) + cos²(θ) - cos³(θ)
At this point, we have simplified the expression as much as possible. The final expression is:
sin(θ) + cos²(θ) - cos³(θ)
In summary, given the initial expression sin(θ) + cos(θ) * cos(θ) * (1 - cos(θ)), we simplified it to sin(θ) + cos²(θ) - cos³(θ). Remember that this is a general expression and its specific value depends on the angle θ.
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Х
According to a Nielsen survey, radio reaches 88% of children each week. Suppose we took weekly random
samples of n = 125 children from this population and computed the proportion of children in each sample
whom radio reaches.
What will be the shape of the sampling distribution of the proportions of children the radio reaches?
Choose 1 answer:
A. Skewed to the left
B. Skewed to the right
C. Approximately normal
D. Uniform
Answer:
C. Approximately normal
Step-by-step explanation:
We know that when we have, np≥10, and n(1−p)≥10, and both of these are true, where n is the sample size, and p is the sample of proportions, the sampling proportions of sample distributions, will be normal in shape.
Expected successes : np=125(0.88)=110≥10
Expected failures : n(1−p)=125(1−0.88)=15≥10
the equilibrium price is the price at which the quantity
The equilibrium price is the price at the equilibrium price is the price that brings supply and demand into balance, ensuring that the market clears and there is neither a shortage nor a surplus of goods.
The equilibrium price is the price at which the quantity demanded by consumers equals the quantity supplied by producers in a market. It is the point of balance between supply and demand.
At the equilibrium price, there is no shortage or surplus of goods in the market. The quantity demanded by consumers at that price matches the quantity supplied by producers, resulting in a state of market equilibrium.
If the price is set above the equilibrium price, there will be a surplus of goods because the quantity supplied exceeds the quantity demanded. Producers will be left with excess inventory, and they may need to lower the price to sell their goods.
On the other hand, if the price is set below the equilibrium price, there will be a shortage of goods because the quantity demanded exceeds the quantity supplied. Consumers will be willing to buy more goods at the lower price, and producers may need to raise the price to meet the increased demand.
Therefore, the equilibrium price is the price that brings supply and demand into balance, ensuring that the market clears and there is neither a shortage nor a surplus of goods.
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PLSSSS HELPPPPP REWARDD BRAINLIESTT
Answer:
12 m wide
Step-by-step explanation:
12 * 16 =192
Express irrational solutions in exact form. log 3(x + 4) + log 3(x+1)= 2 Rewrite the given equation without logarithms. Do not solve for x. (Do not simplify. Type your answer in factored form. Use integers or fractions for any numbers in the equation.) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. of 5-8x5} The solution set is 2 (Simplify your answer. Use a comma to separate answers as needed. Use integers or fractions for any numbers in the expression. Type an exact answer, using radicals as needed.) OB. There is no solution.
The solution set is {(-5 + 3√5)/2, (-5 - 3√5)/2}. These are exact, irrational solutions.
Using the product rule of logarithms, we can combine the two logarithms into a single logarithm:
log3[(x + 4)(x + 1)] = 2
Now, we can rewrite this equation without logarithms:
3^2 = (x + 4)(x + 1)
Expanding the right side:
9 = x^2 + 5x + 4
Bringing everything to one side:
x^2 + 5x - 5 = 0
Using the quadratic formula:
x = (-5 ± √(5^2 - 4(1)(-5))) / (2(1))
x = (-5 ± √45) / 2
Simplifying the radical:
x = (-5 ± 3√5) / 2
So, the solution set is {(-5 + 3√5)/2, (-5 - 3√5)/2}. These are exact, irrational solutions.
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There are two unit rates for every rate, true or false?
Answer:
True
Step-by-step explanation:
A rate is a special ratio in which the two terms are in different units. For example, if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces. This is not a ratio of two like units, such as shirts. This is a ratio of two unlike units: cents and ounces
it should be true. Let me know if I'm incorrect.
Rewrite 26/9 as a mixed number. help me
The required mixed number of 26/9 is given as 2 8/9.
What is a mixed number?A mixed number is a number that consists of a whole number and a proper fraction. It is written in the form "a b/c", where "a" is the whole number, "b" is the numerator of the proper fraction, and "c" is the denominator of the proper fraction.
Here,
To rewrite 26/9 as a mixed number, we need to divide the numerator (26) by the denominator (9) and express the result as a whole number and a proper fraction.
26 ÷ 9 = 2 with a remainder of 8
The whole number part is 2, and the proper fraction part is 8/9, since 8 is the remainder and 9 is the denominator.
Therefore, 26/9 as a mixed number is 2 8/9.
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does applying gradient boosting linear regressor multiple times give the same result as linear regression
No, applying gradient boosting linear regressor multiple times does not necessarily give the same result as linear regression.
Gradient boosting is an iterative machine learning algorithm that involves combining multiple weak models, such as decision trees, to create a strong predictive model. In each iteration of the algorithm, a new model is trained to predict the errors of the previous models, and the final prediction is the sum of the predictions of all the models.
On the other hand, linear regression is a parametric method that involves fitting a linear equation to the data, where the coefficients of the equation are estimated using the least squares method. While gradient boosting linear regression and linear regression both aim to predict a target variable based on a set of input variables, they use different approaches and assumptions, and their results may not be the same.
In particular, gradient boosting can be more effective than linear regression when the relationship between the input variables and the target variable is nonlinear or when there are complex interactions between the input variables. However, linear regression can be more interpretable and easier to implement than gradient boosting in some cases.
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Number 8 please thanks!
\(4b(b+2)=16+4b^2\\4b^2+8b=16+4b^2\\8b = 16 + 4b^2-4b^2\\8b = 16\\b = 2\)
Hope that helps!
Solve the following system of equations:
2x + 4y = 18
-3x + 2 = y
A.(-1, 4)
B.(1, 4)
C.(-1, 5)
D.(1, -1)
Answer:
Option C
Step-by-step explanation:
Given the following question:
\(2x+4y=18\)
\(-3x+2=y\)
To find the answer we need to find the values of each of the variables by solving one equation at a time, and then substitute those answers into each equation in till we have our answers.
\(2x+4y=18\)
\(-3x+2=y\)
\(y-y=0\)
\(-3x+2+ -y=0\)
\(2-2=0\)
\(-3x+-y=0+-2\)
\(-3x+3x=0\)
\(-y=3x-2\)
\(-y\div-1=y\)
\(3x+2\div-1=-3x+2\)
\(y=-3x+2\)
Substitute y for -3x + 2:
\(2x+4y=18\)
\(y=-3x+2\)
\(2x+4(-3x+2)=18\)
\(2x+4(-3x+2)=18=-10x+8=18\)
\(-10x+8=18\)
\(8-8=0\)
\(18-8=10\)
\(-10x=10\)
\(-10x\div10=x\)
\(10\div-10=-1\)
\(x=-1\)
Substitute x for -1:
\(y=-3x+2\)
\(x=-1\)
\(y=-3(-1)+2\)
\(-3\times-1=3\)
\(y=3+2\)
\(3+2=5\)
\(y=5\)
\(x=-1\)
\(y=5\)
Your answer is "(-1, 5)" or option C.
Hope this helps.
im struggling a lot with this question have good day
well, 2 and 1/2 is just 2 + 1/2 or just 2.5, so 2.5%.
\(~~~~~~ \stackrel{ \textit{\LARGE 8 years} }{\textit{Simple Interest Earned}} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$250\\ r=rate\to 2.5\%\to \frac{2.5}{100}\dotfill &0.025\\ t=years\dotfill &8 \end{cases} \\\\\\ I = (250)(0.025)(8) \implies I = 50\)
how about after 1 year? well, we simply set t = 1, so (250)(0.025)(1) = 6.25.
would the interest for t = 2 be the same as for t = 1, if t = 2 is calculated, anyhow, the wording is a bit poor, let me reword it.
after the 1st year, she has an accumulated amount of 250 + 6.25 = 256.25.
now, if for the 2nd year we use the same 2.5% rate BUT we use the accumulated amount of $256.25 to get the interest, instead of the initial $250, will they be the same?
well, hell no, because (250)(0.025)(2) using the inital amount
is not the same as (256.25)(0.025)(2).
bear in mind that simple interest is calculated for each year using the initial amount or deposit, not the accumulated amount thus far.
the ratio of dividends to the average number of common shares outstanding is:
The ratio of dividends to the average number of common shares outstanding is known as the dividend yield. It is a measure of the return on an investment in the form of dividends received relative to the number of shares held.
To calculate the dividend yield, you need to divide the annual dividends per share by the average number of common shares outstanding during a specific period. The annual dividends per share can be obtained by dividing the total dividends paid by the number of outstanding shares. The average number of common shares outstanding can be calculated by adding the beginning and ending shares outstanding and dividing by 2.
For example, let's say a company paid total dividends of $10,000 and had 1,000 common shares outstanding at the beginning of the year and 1,500 shares at the end. The average number of common shares outstanding would be (1,000 + 1,500) / 2 = 1,250. If the annual dividends per share is $2, the dividend yield would be $2 / 1,250 = 0.0016 or 0.16%.
In summary, the ratio of dividends to the average number of common shares outstanding is the dividend yield, which measures the return on an investment in terms of dividends received per share held.
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Directions: calculate the following simple interest problems. write your answers in the space provided. use the formula I = Px R xT and round your answers to the nearest cent
a. P =$500
R = 8% T = 3 years
I = ____ ?
b. P =$50
R = 12% T = 1 years
I = ____ ?
a. P =$1000
R = 18% T = 24 years
I = ____ ?
The simple interests are:
a)$120 b)$6 c)$4320
a. To calculate the simple interest for P = $500, R = 8%, and T = 3 years, use the formula S.I = P x R x T:
S.I = $500 x 0.08 x 3
S.I = $500 x 0.24
S.I = $120
So the simple interest for the first problem is $120.
b. To calculate the simple interest for P = $50, R = 12%, and T = 1 year, use the formula S.I = P x R x T:
S.I = $50 x 0.12 x 1
S.I = $50 x 0.12
S.I = $6
So the simple interest for the second problem is $6.
c. To calculate the simple interest for P = $1000, R = 18%, and T = 24 years, use the formula S. I = P x R x T:
S.I = $1000 x 0.18 x 24
S.I = $1000 x 4.32
S.I = $4320
So the simple interest for the third problem is $4320.
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which one is greater -8.652 or -7.045
Answer:
-7.045 is greater
Step-by-step explanation:
Because -7.045 is closer to 0
Answer:
-7.045
Step-by-step explanation: