Answers
Answer:
B
Step-by-step explanation:
Using the rule of logarithms
\(log_{b}\) x = n ⇒ x = \(b^{n}\)
Given
\(log_{10}\) 50 = 1.70 , then
\(10^{1.70}\) = 50 → B
Related Questions
(x+4)
Solve for x:
= 2. (1 point)
3
O x = 2
O
x= 10
3
2
X =
O x= -2
Answers
Answer:
x = 2
Step-by-step explanation:
\( \frac{x + 4}{3} = 2\)
\(x + 4 = 6\)
\(x = 6 - 4 = 2\)
A die is rolled 200 times with the following results.
Outcome
1
2
3
4
5
6
Frequency
32
36
44
20
30
38
What is the theoretical probability of the given event?
P(even)
a.
One-third
c.
1
b.
One-half
d.
StartFraction 3 Over 7 EndFraction
Answers
Answer:
Step-by-step explanation:
it is about the probability to land on it so you probably got it wrong (pun)
What is the final sale price of a $140 dollar jacket after a 35% discount
Answers
Answer:
$91
Step-by-step explanation:
Replacing the given values in formula (a) we have:
Amount Saved = Original Price x Discount in Percent / 100. So,
Amount Saved = 140 x 35 / 100
Amount Saved = 4900 / 100
Amount Saved = $49 (answer).
In other words, a 35% discount for a item with original price of $140 is equal to $49
Answer:
$91
Step-by-step explanation:
• To answer this, we can first calculate how much was discounted by calculating the value of 35% of $140:
⇒ 35% of $140
⇒ \(\frac{35}{100} \times \$ \space\ 140\)
⇒ $49
• Now that we we know that $49 was discounted from the original price, we can find the final sale price simply by subtracting $49 from the original price:
final sale price = $140 - $49
= $91
Two-fifths of your yard is covered with grass. This is equal to what decimal?
Answers
Answer: 0.4
Step-by-step explanation:
Two-fifths is 2/5
If you were to put this into a calculator, you would get 0.4.
If this were to come up in a non-calculator test, I would mentally multiply both the numerator and denominator by 2 to get 4/10, which you can then divide quickly to get 0.4. :)
A triangle has vertices at L:(4, 4), M:(7, 4), and N:(5, 2).
The triangle is translated 7 units down and reflected across the y-axis.
What are the coordinates of L'? Write your answer as an ordered pair for full credit.
Answers
Answer:
A triangle has vertices at L:(4, 4), M:(7, 4), and N:(5, 2).
The triangle is translated 7 units down and reflected across the y-axis.
What are the coordinates of L'? Write your answer as an ordered pair for full credit.
Step-by-step explanation:
An investor invested a total of $1,200 in two mutual funds. One fund earned a 5% profit while the other earned a 2% profit. If the investor’s total profit was $39, how much was invested in each mutual fund?
Answers
Answer:
So $700 was invested in the mutual fund that earned a 2% profit, and $500 was invested in the mutual fund that earned a 5% profit.
Step-by-step explanation:
Let x be the amount invested in the mutual fund that earned a 5% profit, and let y be the amount invested in the mutual fund that earned a 2% profit. We know that the total investment was $1,200, so:
x + y = 1200
We also know that the total profit was $39, which can be expressed as a decimal as 0.39 (since profit is calculated as a percentage of the initial investment). The amount of profit earned on the first fund is 5% of x, or 0.05x, and the amount of profit earned on the second fund is 2% of y, or 0.02y. So:
0.05x + 0.02y = 0.39
We now have two equations with two variables:
x + y = 1200
0.05x + 0.02y = 0.39
We can solve for one variable in terms of the other in the first equation, and substitute into the second equation:
x = 1200 - y
0.05(1200 - y) + 0.02y = 0.39
Simplifying and solving for y:
60 - 0.05y + 0.02y = 0.39
0.03y = 0.39 - 60
0.03y = -59.61
y = -59.61 / 0.03
y = 1987
This tells us that $1,987 was invested in the mutual fund that earned a 2% profit. To find the amount invested in the mutual fund that earned a 5% profit, we can substitute into the first equation:
x + y = 1200
x + 1987 = 1200
x = 1200 - 1987
x = -787
This doesn't make sense, since we can't have a negative investment amount. It means that we made a mistake somewhere. Checking our work, we can see that the equation 0.05x + 0.02y = 0.39 should actually be:
0.05x + 0.02y = 39
(without the decimal point). With this correction, we can solve as before:
x + y = 1200
0.05x + 0.02y = 39
x = 1200 - y
0.05(1200 - y) + 0.02y = 39
60 - 0.05y + 0.02y = 39
0.03y = 21
y = 700
So $700 was invested in the mutual fund that earned a 2% profit, and $500 was invested in the mutual fund that earned a 5% profit.
Can someone help me with this?
Answers
Explanation: combine -F and -3F makes -4F and 14 - 11 = 3
-f + (-3f)= -4f
14-11= 3
Therefore, -4f+3
In a basketball free-throw shooting contest shots made by Sam and Wil were in the ratio 7:9.Wil made 6 more shots than Sam. Find the number of shots made by each of them.
Answers
Will = 9(3) = 27
Answer:
Sam made 21 shots, and Wil made 27 shots.
The amount of chlorine in a swimming pool varies directly with the volume of water. The pool has 2.5 milligrams of chlorine per liter of water. There are 8000 gallons of water in the swimming pool. How much chlorine is in the pool? Round to the nearest thousand milligrams.
There are
milligrams of chlorine in the pool.
Answers
The solution is, 76,000 mg chlorine is in the pool.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
The pool has 2.5 milligrams of chlorine per liter of water.
There are 8000 gallons of water in the swimming pool.
we know,
1 gallon = 3.785 liters
Water in pool = 8000 x 3.785
Water in pool = 30,280 liters
so, we get,
Chlorine dosage = 2.5 mg / liter
Chlorine = 2.5 x 30,280
Chlorine = 75,700 mg
To the nearest thousand milligram:
Chlorine = 76,000 mg
Hence, The solution is, 76,000 mg chlorine is in the pool.
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A manufacturer has a steady annual demand for 15,000 cases of sugar. It costs $10 to store 1 case for 1 year, $30 in set up cost to produce each batch, and $16 to produce each case. Find the number of cases per batch that should be produced to minimize cost.
Answers
The number of cases per batch that should be produced to minimize cost is: 300 units
How to find the economic order quantity?The number of cases per batch that should be produced to minimize cost can be found by using the Economic Order Quantity.
The Economic Order Quantity (EOQ) is a calculation performed by a business that represents the ideal order size that allows the business to meet demand without overspending. The inventory manager calculates her EOQ to minimize storage costs and excess inventory.
Thus:
Number of cases per batch = √((2 * Setup costs * annual demand)/ holding costs for the year)
Solving gives:
√((2 * 30 * 15000)/10)
= √90000
= 300 units
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regularization parameters in an estimation procedure. what is regularization?
Answers
Regularization is a process of adding a penalty term to the error function in order to avoid overfitting in an estimation process.
The addition of a penalty term can prevent model overfitting and improve model generalization. Regularization is a technique that is used in many machine learning models, including regression, neural networks, and SVMs (Support Vector Machines).The regularization parameter, also known as the tuning parameter, controls the extent of the penalty added to the error function. A larger regularization parameter results in more aggressive regularization and a simpler model, while a smaller regularization parameter results in less aggressive regularization and a more complex model. The regularization parameter should be selected carefully to achieve a balance between model complexity and model performance.
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*WILL GIVE BRAINLIEST* the following function represents the production cost f(x), in dollars, for x number of units produced by company 1:
f(x)=0.05x^2-7x+300
The following table represents the production cost g(x), in dollars, for x number of units produced by company 2:
x g(x)
0.6 899.58
0.8 899.52
1 899.50
1.2 899.52
1.4 899.58
Based on the given information, determine which company has a lower minimum and find the minimum value.
a.) f(x) at (1, 899.50)
b.) g(x) at (70, 55)
c.) f(x) at (70, 55)
d.) g(x) at (1, 899.50)
Answers
Answer:
C.
Step-by-step explanation:
By analyzing the functions f(x) and g(x), we can see that they are both quadratic relations.
To find the minimum value, we want to find the y-coordinate of the vertex.
In f(x), by using the formula (-b/2a), we get the x-coordinate of the vertex, 70. When we substitute 70 into the function, we get 55 as our minimum.
In h(x), we can see that the lowest y-coordinate in the given points is 899.52. So (1, 899.50) is our vertex.
This means that in f(x), the minimum production cost is $70. In contrast, in h(x), the minimum production cost is $899.50. Therefore f(x) has a lower minimum, with its minimum value at (70, 55), our vertex.
Answer:
The Answer is C. f(x) at (70, 55)
Hope This Helps!
Note: this is a non-linear programming question. this question is taken from a statistics course in third year level at university. two investors, elon musk and jeff bezos, each want help in structuring a portfolio from two investments. investment a produces an average annual return of 25% with a variance of 0.05. investment b produces an average annual investment of 9% with a variance of 0.01. investments a and b have a correlation of -0.3. elon musk tells you that: "i want to get the biggest return i can, but the most risk i can possibly accept is 0.01. how should i invest my money?" while jeff bezos tells you that: "risk minimisation is half as important as maximising return for me. what portfolio would be most appropriate for me?" answer the following questions: (a) formulate elon musk's problem as a non-linear program. (4 marks) (b) calculate the risk aversion coefficient for jeff bezos. (2 marks) (c) formulate elon musk's problem as a non-linear program. (3 marks)
Answers
Elon Musk's problem can be formulated as a non-linear program with maximizing return while limiting risk to 0.01. The constraint equations are: 0.25x + 0.09y, \(0.05x^2 + 0.01y^2\) - 0.03xy ≤ 0.01 (risk constraint), and x + y = 1 .
(a) To formulate Elon Musk's problem as a non-linear program, we need to maximize his return while ensuring that the risk is no more than 0.01. Let's denote the fraction of the investment in investment a as x and the fraction in investment b as y.
The objective function can be expressed as:
Maximize 0.25x + 0.09y (representing the expected return)
The constraint for risk can be expressed as:
\(0.05x^2 + 0.01y^2 + 2*(-0.3)*0.05x*y\)≤ 0.01
Simplifying this constraint, we have:
\(0.05x^2 + 0.01y^2\) - 0.03xy ≤ 0.01
Additionally, we need to add the constraint that the sum of fractions x and y is equal to 1:
x + y = 1
(b) To calculate the risk aversion coefficient for Jeff Bezos, we can use the formula:
Risk aversion coefficient = 0.5 / (Expected return - Minimum return)
Given that Jeff Bezos considers risk minimization half as important as maximizing return, we can calculate the risk aversion coefficient using the given information.
(c) It seems that there is a mistake in the question, as it asks to formulate Elon Musk's problem as a non-linear program again. However, we have already formulated Elon Musk's problem in part (a) as a non-linear program.
(a) Elon Musk's problem can be formulated as a non-linear program with the objective of maximizing return while limiting risk to 0.01. The constraint equations are: 0.25x + 0.09y (expected return), \(0.05x^2 + 0.01y^2\) - 0.03xy ≤ 0.01 (risk constraint), and x + y = 1 (sum constraint).
(b) The risk aversion coefficient for Jeff Bezos can be calculated using the given formula.
(c) The question repeats the formulation of Elon Musk's problem, which has already been answered in part (a).
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Square ABCD has points A(5, 10) and B(-4, 3). What is the slope of line segment BC?
Answers
Given the square ABCD with points A(5, 10) and B(-4, 3), the slope of the line segment BC is 7/9
The formula for calculating the slope of a line is expressed as:
\(m=\frac{y_2-y_1}{x_2-x_1}\)
Given the coordinate point A(5, 10) and B(-4, 3)
Substituting the given coordinate into the formula for slope
\(m=\frac{3-10}{-4-5}\\m=\frac{-7}{-9}\\m=\frac{7}{9}\)
Hence the slope of the line segment BC is 7/9
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measures of central tendency include all except: a. standard deviation b. median c. mean d. mode
Answers
The correct answer is (a) standard deviation. The measure of central tendency that is NOT included among the given options is the standard deviation (a).
Measures of central tendency are statistical measures that represent the central or average value of a dataset. They provide insight into the typical or central value around which the data tends to cluster. The three commonly used measures of central tendency are the mean, median, and mode.
a. Standard deviation is not a measure of central tendency. It is a measure of dispersion or variability in a dataset. It quantifies how spread out the data points are from the mean. Standard deviation provides information about the spread or scatter of the data rather than representing a central value.
b. Median is a measure of central tendency that represents the middle value in a dataset when the data points are arranged in ascending or descending order. It divides the data into two equal halves.
c. Mean is a measure of central tendency that represents the arithmetic average of a dataset. It is calculated by summing all the data points and dividing by the total number of observations.
d. Mode is a measure of central tendency that represents the most frequently occurring value or values in a dataset. It identifies the value(s) that appear(s) with the highest frequency.
Therefore, the standard deviation (a) is the measure of central tendency that is NOT included among the given options.
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Helpppp pleaseeee pleaseee please❤️
Answers
Answer:
Data A - 5
Data B - 5
Data C - 5
Data D - 6
Step-by-step explanation:
Data A,
Graph for the data shows that there is a distinct value of y (output value) for every input value of x.
Therefore, Data A is a function.
Data B,
Each ordered pair shows exactly one output value for each input value.
Therefore, Data B represents a function.
Data C,
For each input value there is exactly one output value.
Therefore, Data C represents a function.
Data D,
From the given table,
For x = -1 there are two output values y = 27, 39
For x = -2 output values are y = 45, 21
Since for these input values there are two output values, Data D will not be a function.
the cover charge for entering mandi's dance hall is $5. drinks are then $6 each. what equation, in point-slope form, will give the total cost for the cover charge and drinks?
Answers
The equation of the total cost for the cover charge and drinks in point-slope form is y = 6x + 5.
The point-slope form of a linear equation is given by -
\(y - y_1 = m(x- x_1)\)
where m is the slope and \((x_1, y_1)\) is a point on the line.
Here, the total cost for the cover charge and drinks can be represented by the equation y = mx + b, where y is the total cost, x is the number of drinks, m is the cost per drink, and b is the cost of the cover charge.
We know that the cover charge is $5 and drinks are $6 each, so, we can find the slope (m) of the equation by using the cost per drink which is m = 6.
We can also find the point \((x_1, y_1)\) by using the cover charge cost which is (0,5).
Therefore, the equation in point-slope form of the total cost for the cover charge and drinks will be -
y - 5 = 6(x-0)
y - 5 = 6x
y = 6x + 5
Where x is the number of drinks and y is the total cost i.e. cover charge + drinks.
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In a sale, the price of a book is reduced by 25%.
The price of the book in the sale is £12
Work out the original price of the book
Answers
Question: In a sale, the price of a book is reduced by 25%. The price of the book in the sale is £12. Work out the original price of the book
Answer: £16
Step-by-step explanation:
To determine the original price of the book, we can use the fact that the sale price is 75% (100% - 25%) of the original price. Let's denote the original price as x.
75% of x = £12
To solve for x, we can set up the equation:
0.75x = £12
To isolate x, we divide both sides of the equation by 0.75:
x = £12 / 0.75
x = £16
Therefore, the original price of the book was £16.
What is the y intercept of the following function f(x) f(x) = (x - 2)(x+1)(x–5)
Answers
Answer:
y-inter10
Explanation:
Given the function f(x) defined below:
\(f\mleft(x\mright)=(x-2)\mleft(x+1\mright)\mleft(x-5\mright)\)The y-intercept of any function is the value of f(x) when x=0.
\(\begin{gathered} \text{When x=0} \\ f\mleft(x\mright)=(x-2)\mleft(x+1\mright)\mleft(x-5\mright) \\ f\mleft(0\mright)=(0-2)\mleft(0+1\mright)\mleft(0-5\mright) \\ =-2\times1\times-5 \\ =10 \end{gathered}\)The y-intercept of f(x) is 10.
A cuboid with a volume of 924cm^3 has dimensions 4cm, (x+1)cm and (x+11). Show clearly that x^2+12x-220=0 solve the equation by factorisation, making sure you show the factorisation. Finally, find the dimensions of the cuboid,
Answers
Answer:
\(x^2+12x-220=0\) -- Proved
\(x = 10\ \ \ x = -22\)
Step-by-step explanation:
Given
\(Volume = 924cm^3\)
\(Dimension: 4cm; (x+1)cm; (x+11)cm\)
Required
Show that \(x^2+12x-220=0\)
The volume is calculated as:
\(4 * (x + 1) * (x + 11) = 924\)
Open the brackets
\((4x + 4) * (x + 11) = 924\)
\(4x^2 + 44x + 4x + 44 = 924\)
\(4x^2 + 48x+ 44 = 924\)
Collect Like Terms
\(4x^2 + 48x+ 44 - 924=0\)
\(4x^2 + 48x -880=0\)
Divide through by 4
\(\frac{4x^2}{4} + \frac{48x}{4} -\frac{880}{4}=0\)
\(x^2+12x-220=0\)
Solving further:
Expand the expression
\(x^2 + 22x - 10x - 220 = 0\)
Factorize:
\(x(x + 22) - 10(x + 22) = 0\)
\((x - 10)(x + 22) = 0\)
Split:
\(x - 10 = 0;\ \ \ x + 22 = 0\)
\(x = 10\ \ \ x = -22\)
Kalleen wants $100 to buy a new pair of sneakers. She decides to tutor some kids at a rate of $7 an hour. What is the minimum number of hours she needs to tutor to reach her goal?
Answers
Answer:
15
Step-by-step explanation:
What is an equation of the line that passes through the point (− 3 , 1) and is parallel to the line 4x + 3y = 15?
Answers
Answer: y= − \(\frac{4x}{3\\}\) −3
Step-by-step explanation:
its right trust me
What are the solutions of 3x² + 14x + 16 = 0?
0 x=-₁-2
0 x = -2₁-²2/
0x = ²,2
0x=-₁2
X
Answers
Answer:
x = -2, -2
Step-by-step explanation:
3x² + 14x + 16 = 0
(3x+8) (x+2)
x = -8/3
x = -2
The solutions of the quadratic equation 3x² + 14x + 16 = 0 are x = -2 and x = -8/3.
To find the solutions of the quadratic equation 3x² + 14x + 16 = 0, we can use the quadratic formula.
The quadratic formula states that for an equation of the form ax² + bx + c = 0
The solutions for x can be found using the formula:
x = (-b ± √(b² - 4ac)) / (2a)
For the given equation 3x² + 14x + 16 = 0,
a = 3, b = 14, and c = 16.
Substituting these values into the quadratic formula, we get:
x = (-14 ± √(14² - 4.3.16)) / (2 × 3)
x = (-14 ± √(196 - 192)) / 6
x = (-14 ± √4) / 6
Now we have two possibilities for x:
x₁ = (-14 + √4) / 6
x₂ = (-14 - √4) / 6
Simplifying each expression:
x₁ = (-14 + 2) / 6
x₁ = -12 / 6
x₁ = -2
x₂ = (-14 - 2) / 6
x₂ = -16 / 6
x₂ = -8 / 3
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A company charges a shipping fee that is 4% of the purchase price for all items
it ships. What is the fee to ship an item that costs $66?
Answers
0.04 = 4 percent
66 * 0.04 = 2.64
The shipping fee is $2.64
a prototype rocket burns 159 gallons of liquid hydrogen fuel each second during a regular launch. Make a table that shows how many gallons of fuel are burned after 2,3,5 and 10 seconds.
Answers
Answer:
Seconds: 2 || 3 || 5 || 10 ||
---------------------||-------||--------||--------||
Gallons: 312 || 486 || 780 || 1560 ||
Write L if it is Likely to happen and Write U if it is unlikely to happen. Topic is probability
1. 2:3 __
2. 4:15 __
3. 3/10__
4. 13/21__
5. 6/16 __
6. 8:11 __
7. 9:20__
8. 11:25__
9. 5/16__
10. 7/12 __
11. 6:13__
12. 4:9__
13. 2:5 __
14. 19/45 __
15. 12/25__
Please make it quick
Answers
Answer:
1h b+h boi gate
Step-by-step explanation:
A square has an area of 49 cm squared what is the length of each side
Answers
Answer:
7
Step-by-step explanation:
\(s = {a}^{2} \: thus \: a = \sqrt{s } = \sqrt{49} = 7\)
as many. How many successful free throws did Priya make today?
free throws
vitamin C (mg)
25%
0
50%
0
75%
2.
A 16-ounce bottle of orange juice says it contains 200 milligrams of vitamin C,
which is 250% of the daily recommended allowance of vitamin C for adults. What is
100% of the daily recommended allowance of vitamin C for adults?
10000
100%
1500
125%
150%
20006
25006
Answers
Answer:
A 16-ounce bottle of orange juice says it contains 200 milligrams of vitamin C, which is 250% of the daily recommended allowance of vitamin C for adults. What is 100% of the daily recommended allowance of vitamin C for adults?
Part B: if D(t)=1200, find the value of t and interpret its meaning in the context of the problem.
Answers
The Chang family has been traveling for 18 hours, thus, t-value is 18.
How should t-test results be interpreted?A significant t-score, also known as a t-value, implies that the groups are distinct, whereas a small t-score suggests that the groups are similar. Degrees of freedom are the values in a study that are open to change and are crucial for determining the significance and reliability of the null hypothesis.
D(t) = 2,280 - 60t
D(t) = 1,200; find t.
D(t) = 2,280 - 60t
1200 = 2280 - 60t
From both sides of the equation, deduct 2280.
1200 - 2,280 = 2280 - 60t - 2,280
- 1080 = - 60t
multiplied by -60 on both sides
- 1080 / -60 = - 60t / -60
18 = t
t = 18
The Chang family had travelled for 18 hours, according to this.
The Chang family has been traveling for 18 hours, t = 18.
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The complete question is,
Having just returned from a cross-country road vacation, the Chang family is traveling back home. They can visualize their distance from home in miles after t hours of travel by using the function D(t) = 2,280 - 60t during the journey. If D(t) = 1,200, what does t represent? That value stands for what?
A.t = 20; the Chang family has been traveling for 20 hours.
B. t = 20, meaning the Chang family will need to travel 20 more hours to reach home.
The Chang family has been traveling for 18 hours, thus c. t = 18.
The Chang family must go home for an additional 18 hours using the formula D. t = 18.
Which figure is a scalene triangle?