The police must check 2600 possible license plates, calculated by multiplying 26 possibilities for the third letter not seen by the witness with 100 possibilities for the two digits also not seen.
To determine how many license plates the police must check to find the culprit, we consider the information that the witness saw the first two letters and the last digit. Since letters can be repeated, there are 26 possibilities for each of the two letters the witness saw. For the last digit, which the witness also saw, there are 10 possibilities (0 through 9). The third letter and the other two digits, which the witness did not see, each have the following number of possibilities: 26 for the third letter, and 10 for each of the two remaining digits.
Calculating the number of possible combinations:
First two letters (seen by the witness): 26 * 26 = 676 possibilitiesLast digit (seen by the witness): 10 possibilitiesThird letter (not seen by the witness): 26 possibilitiesThe two remaining digits (not seen by the witness): 10 * 10 = 100 possibilitiesTherefore, the total number of license plates the police must check is the product of the possibilities for the parts the witness did not see:
26 (third letter) * 100 (two remaining digits) = 2600 possible license plates.
(Financial Algebra workbook 10-3)
Under his "Household expenses" Budget category, Mark has allocated $60 per month for pet food. He can purchase "wet food" for $1.50 per can or "dry food" for $3 per bag.
E). Name a combination of bags and cans that will cause him to be over budget.
Which points in the scatter plot are outliers?
Select EACH CORRECT ANSWER
point A
point F
point H
point K
point M
A 15 sector in a circle has an area of 11.9 m2 What is the area of the circle?
Please help with geometry
Elly buys 75 shares of stock in a mutual fund for a total investment of $450. She sells 50 shares of her stock for total proceeds of $400. Determine if Elly made a profit or loss, and how much per share.
a.
loss of $0.67 per share
b.
loss of $2 per share
c.
profit of $0.67 per share
d.
profit of $2 per share
We have been given that Elly buys 75 shares of stock in a mutual fund for a total investment of $450.
It means the cost of 1 share is given by
[tex]\frac{450}{75}\\ \\ =\$6[/tex]
Now, we have been given that she sells 50 shares of her stock for total proceeds of $400.
It means the cost of 1 share is given by
[tex]\frac{400}{50} \\ \\ \$8[/tex]
She purchased per share at $6 and sold per share at $8.
It means that she made a profit of [tex]8-6=\$2[/tex] per share.
Therefore, d is the correct option.
(d) profit of $2 per share
Elly made a profit of $2 per share.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
First, we can determine the average cost per share of the 75 shares of stock that Elly bought:
Average cost per share = Total investment / Number of shares
= $450 / 75 shares
= $6 per share
Next, we can determine the total proceeds from the sale of 50 shares:
Total proceeds = Number of shares sold x Price per share
= 50 shares x ($400 / 50 shares)
= $400
Elly paid $6 per share for the 75 shares she bought, and she sold 50 shares for $8 per share.
The difference between these prices will determine whether she made a profit or loss per share:
Profit or loss per share = Selling price per share - Average cost per share
= $8 per share - $6 per share
= $2 per share
Since the profit per share is positive, Elly made a profit.
Therefore,
Elly made a profit of $2 per share.
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A local company manufactures netbook computers. Their profit function is given by this equation: y equal minus x to the power of 2 plus 120 x plus 3000 where x is the number of netbooks produced in one day and y is the profit (in dollars) the company makes that day. What is the maximum profit that the company can make? (Hint: Find the vertex of the parabola.)
Answer: $6,600
Step-by-step explanation:
Given: The profit function is given by the equation:
[tex]y=-x^2+120x+3000[/tex],where x is the number of netbooks produced in one day and y is the profit (in dollars) the company makes that day.
To find the maximum profit, first we need to find critical point of the function.
For that, first differentiate the above function w.r.t. x, we get
[tex]y'=-2x+120[/tex]
Now, Put [tex]y'=0[/tex], we get
[tex]-2x+120=0\\\\\Rightarrow\ x=60[/tex]
Again differentiate the above function w.r.t. x, we get
[tex]y"=-2<0[/tex]
By second derivative test, at x=60 , attains its maximum value.
Now, the Maximum profit will be :
[tex]y=-(60)^2+120(60)+3,000=6,600[/tex]
Hence, the maximum profit that the company can make = $6,600
Compute the area of a triangle with sides. 15 × 15 × 18
Iridium -192 has a half life of 74 days after 148 days, how many milligrams of 900 mg sample will remain?
The amount that remained out of the 900 mg sample after 148 days is 225 milligrams.
Given,
Iridium -192 has a half-life of 74 days.
We need to find out after 148 days how many milligrams of the 900 mg sample will remain.
Here the initial amount is 900mg.
What is half life?It is the time at which the initial amount of a substance is reduced to half its amount.
The formula used with half-life:
[tex]N_{t} =N_{0} (\frac{1}{2})^\frac{t}{t_\frac{1}{2} }[/tex]
Where
N_t = Amount after time t
N_0 = initial amount
t_1/2 = half-life value of the substance.
t = time.
We have,
N_0 = 900 mg
t_1/2 = 74 days.
t = 148 days.
Substituting the values in the formula,
We get,
N_t = 900 ( 1/2 ) ^148/74
N_t = 900 ( 1/2 )^2
N_t = 900/4
N_t = 225 mg
We see that the amount that remains after 148 days is 225 milligrams.
Thus the amount that remained out of the 900 mg sample after 148 days is 225 milligrams.
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CDs and DVDs Solve by setting up a system of linear equations with 2 variables and 2 unknowns. CDs cost $5.96 more than DVDs at All Bets Are Off Electronics. How much would 6 CDs and 2 DVDs cost if 5 CDs and 2 DVDs cost $127.73?
The relationship between the total cost and the costs of CDs and DVDs are represented by a linear function.
The cost of 6 CDs and 2 DVDs is $147.68
Let:
[tex]C \to CDs[/tex]
[tex]D \to DVDs[/tex]
From the question, we have:
[tex]C = D + 5.96[/tex]
[tex]5C + 2D = 127.73[/tex]
Substitute [tex]C = D + 5.96[/tex] in [tex]5C + 2D = 127.73[/tex]
[tex]5 \times (D + 5.96) + 2D = 127.73[/tex]
[tex]5D + 29.8 + 2D = 127.73[/tex]
Collect like terms
[tex]5D + 2D = 127.73 - 29.8[/tex]
[tex]7D = 97.93[/tex]
Divide both sides by 7
[tex]D = 13.99[/tex]
Substitute [tex]D = 13.99[/tex] in [tex]C = D + 5.96[/tex]
[tex]C = 13.99 + 5.96[/tex]
[tex]C = 19.95[/tex]
The cost of 6 CDs & 2 DVDs is represented as:
[tex]Cost =6C + 2D[/tex]
So, we have:
[tex]Cost =6 \times 19.95 + 2 \times 13.99[/tex]
[tex]Cost =147.68[/tex]
Hence, the cost of 6 CDs & 2 DVDs is $147.68
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What is the y-intercept of the equation 5x - 6y = 18?
A.-6
B. -3
C .5
D. 18
The y-intercept is for x = 0.
Put the value of x = 0 to the equation 5x - 6y = 18:
5(0) - 6y = 18
0 - 6y = 18
-6y = 18 divide both sides by (-6)
y = -3 → B.Please help me with a simple math problem.
What is the value of b?
A. 1.5
B. 3
C. 3.75
D. 4.5
Which story problems could be solved using the given equation? 6 divided by 1/2 = ? Choose exactly two answers that are correct.
A.
Mike spends a hour reading every night before bed. How many hours does Mike spend reading before bed in 6 days?
B.
Alice has 6 yards of ribbon. She uses yard of ribbon for each package she’s wrapping. How many packages can Alice wrap?
C.
A cup of milk is used for every serving in a recipe. How many servings can be made with 6 cups of milk?
D.
Charlie spent of his savings on 6 equally priced admission tickets to the zoo. What fraction of his savings did Charlie spend on each ticket?
TON OF FREE POINTS FOR THE SMARTEST FINANCE PERSON! EASY PEASY, JUST NEED HELP TO DO IT THE RIGHT WAY ASAP!!! WHO SHALL WIN? Do not answer incorrectly or to get free points please, or you will be reported, and not smart.
David buys a home for $278,640. His home is predicted to increase in value 4% each year. What is the predicted value of David's home in 18 years? Round your answer to the nearest dollar.
Options:
$542,638
$564,474
$576,284
$580,122
Thanks in advance, you guys truly rock.
564474 is the correct answer
Hope this helps...
Three numbers are in the ratio of 6:5:1. What are the numbers if the difference between the smallest and largest is 30?
a.48, 40, 18B.36, 30, 6
c.24, 20, 4D.180, 150, 30
which of the points satisfy the linear inequality graphed here?
a)(0,0)
b)(10,0)
c)(-10,0)
d)(10,10)
A toy manufacturer makes a toy truck, a toy car, and a toy boat. The production spreadsheet is:
Toy Time to Produce Cost to Produce Profit for Each Truck 10 minutes $1.00 $1.00 Car 12 minutes $0.75 $1.50 Boat 8 minutes $0.80 $0.60
After accounting for breaks, a worker actually works 400 minutes each day. The manufacturer needs each worker to generate a potential profit of $35 each day. Write a system of inequalities that expresses these constraints.
Answer:
[tex]\left\{\begin{array}{l}10x+12y+8z\le 400\\x+1.5y+0.6z\ge 35\end{array}\right.[/tex]
Step-by-step explanation:
Let x be the number of toy trucks, y be the number of toy cars and z be the number of toy boats a worker makes each day.
1. If a worker spends 10 minutes to make one toy truck, then he spends 10x minutes to make x toy trucks. If a worker spends 12 minutes to make one toy car, then he spends 12y minutes to make y toy cars. If a worker spends 8 minutes to make one toy boat, then he spends 8z minutes to make z toy boats. In total he can spend at most 400 minutes each day, then
[tex]10x+12y+8z\le 400.[/tex]
2. If a worker generates profit of $1.00 per one toy truck, then he generates profit of $x per x toy trucks. If a worker generates profit of $1.50 per one toy car, then he generates profit of $1.50y per y toy cars. If a worker generates profit of $0.60 per one toy boat, then he generates profit of $0.60z per z toy boats. The manufacturer needs each worker to generate a potential profit of $35 each day, then
[tex]x+1.5y+0.6z\ge 35.[/tex]
Thus, the system of two inequalities is
[tex]\left\{\begin{array}{l}10x+12y+8z\le 400\\x+1.5y+0.6z\ge 35\end{array}\right.[/tex]
Explain how the discriminant b squared minus 4 ac can be used to determine the number of solutions to a quadratic equation
Select the factors of x2 − 14x + 49.
(x + 49)(x + 1)
(x + 7)(x + 7)
(x − 7)(x − 7)
(x − 49)(x − 1)
Answer:
The factors of the expression x² - 14x + 49 are (x - 7) (x - 7) .
Step-by-step explanation:
As given the expression in the question be as follow .
= x² - 14x + 49
This is also written as
= x² - 7x - 7x + 49
= x (x - 7)-7 (x - 7)
= (x - 7) (x - 7)
Therefore the factors of the expression x² - 14x + 49 are (x - 7) (x - 7) .
The radius of a circular clock face is 13 centimeters. how do i find the circumfrence
Hence, the circumfrence is [tex]81.64[/tex].
What is the circumference?
Circumference is the distance around a circle. We can find the circumference using either the diameter or radius of a circle. For shapes made of straight lines, we say they have a perimeter.
Here given that,
The radius of a circular clock face is [tex]13[/tex] centimeters.
The general formula of circumference of a circle is [tex]2\pi r[/tex].
As, [tex]r=13cm[/tex]
Substitue these values in the general formula then,
[tex]2\pi r=2(3.14)(13)\\\\=81.64[/tex]
Hence, the circumfrence is [tex]81.64[/tex].
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What is the equation of the line that passes through the points (–12, –8) and (–17, –16)?
A.
-17=-8/5(x-16)
B.
-16=8/5(x-17)
C.
+16=-4/5(x+10)
D.
y+16=8/5(x+17)
If a pizza is sliced into 6 even slices, what is the angle of rotational symmetry?
The angle of rotational symmetry of a pizza sliced into 6 even slices is 60 degrees, which is the angle required to rotate each slice to coincide with the next, demonstrating six-fold rotational symmetry.
Explanation:The angle of rotational symmetry for a pizza sliced into 6 even slices can be calculated based on the fact that a complete rotation is 360 degrees.
Since the pizza is divided into 6 slices, the angle to rotate each slice to coincide with the next is 360 degrees divided by 6.
Step-by-Step Explanation
Start with the full rotation angle, which is 360 degrees.Divide 360 by the number of slices, which is 6.The angle of rotational symmetry is therefore 360 ÷ 6 = 60 degrees.Each 60-degree turn will align the pizza with itself, showing that it has rotational symmetry at this angle.
Since the pizza can be rotated 6 times and each time result in the same shape positioned identically, it demonstrates six-fold rotational symmetry.
The ratio between the volumes of two cubes is 125 to 216. what is the ratio between their respective surface areas?
The local grocery store wants to know if the shoppers prefer Crest or Colgate toothpaste. The store gives all of its shoppers a value saver card, then uses a random number generator to select 30 card numbers and surveys those shoppers. Is this sampling method representative of the entire population and explain?
A. No, some shoppers may not buy toothpaste there.
B. Yes, all shoppers have a value card and the shoppers interviewed were chosen by a random number generator.
C. No, need a bigger sample.
D. No, the store should only ask women.
No, some shoppers may not buy toothpaste there.
The answer is option A.
What is an example of a word problem?Word problems normally include mathematical modeling questions, where records and information approximately a positive machine is given and a student is needed to expand a model. For example, Jane had $5.00, then spent $2.00. How much does she have now?
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I need your help here! 15 pointa and brainliest. If you cant do it, at least give me the formula to this so I can solve it.
Answer:
0.40 formula x3.9 standardwise. Sorry if this doesnt help. I tried.
Step-by-step explanation:
What is the answer? (384 ft is wrong)
The perimeter of a square window is 360 cm find the length of one side
To find the length of one side of a square window with a perimeter of 360 cm, we use the formula for the perimeter of a square, resulting in each side being 90 cm long.
Explanation:To find the length of one side of a square window when the perimeter is 360 cm, we can use the formula for the perimeter of a square, which is P = 4s, where P represents the perimeter and s represents the length of one side. Given that the perimeter is 360 cm, we can set up the equation 360 = 4s. Dividing both sides of the equation by 4 gives us s = 90 cm.
Therefore, the length of one side of the square window is 90 cm.
can someone please help ill try to add the picture
giving away all these points to the lucky person who can explain how to get the answer (Law of Cosines) !!!
According to Newton's Law of Cooling, if a body with temperature T 1 is placed in surroundings with temperature T 0, different from that of T 1, the body will either cool or warm to temperature T(t) after t minutes, where: T(t) = T 0 + (T 1 - T 0)e kt and k is a constant. A cup of coffee with temperature 140°F is placed in a freezer with temperature 0°F. The constant k ≈ -0.0815. Use Newton's Law of Cooling to find the coffee's temperature, to the nearest degree Fahrenheit, after 15 minutes. The temperature is about a0degrees Fahrenheit.
Using Newton's Law of Cooling, the coffee's temperature after 15 minutes when placed in a freezer with a temperature of 0°F is approximately 76°F.
Explanation:According to Newton's Law of Cooling, the temperature of an object changes at a rate proportional to the difference between its temperature and the temperature of its surroundings. In the given problem, we have a cup of coffee initially at 140°F placed in a freezer at 0°F, aimed to find the coffee's temperature after 15 minutes. The constant k is given as -0.0815.
We can plug these values into the equation T(t) = T0 + (T1 - T0)ekt. Therefore, the temperature of the coffee after 15 minutes can be calculated as T(15) = 0 + (140 - 0)e-0.0815*15.
Computing this gives us a value of approximately 76°F. Thus, after 15 minutes, the coffee's temperature, to the nearest degree Fahrenheit, is 76°F when placed in a freezer with a temperature of 0°F according to Newton's Law of Cooling.
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A circle has a circumference of 144\pi144π144, pi. what is the radius of the circle?