Answer:
[tex]5.3044992\times 10^{10}[/tex]
Step-by-step explanation:
We are given that a license plate consist of 5 digits and 5 uppercase letters
Digits used=0,1,2,..9
Total number of letters=26
Repetition is not allowed
Total number of odd digits=(1,3,5,7,9)=5
The first place filled by 5
Second place filled by 4
Third place filled by 8
Fourth place filled by 7
Fifth place filled by 6
Sixth place filled by 26
Seventh place filled by 25
Eighth place filled by 24
Ninth place filled by 23
Tenth place filled by 22
Total number of possible different license plates =[tex]5\times 4\times 8\times 7\times 6\times 26\times 25\times 24\times 23\times 22[/tex]=[tex]5.3044992\times 10^{10}[/tex]
The number of possible license plates, considering the restrictions on the first and second odd digits and no repetition, is 53,144,832,000. This was determined by systematically calculating the choices for each digit and letter and then multiplying them together.
Calculating the Number of Different License Plates
To determine the number of different license plates possible, we need to consider two sections: the digits and the letters. The first and second digits must be odd, and repetition of digits and letters is not permitted.
Step-by-Step Calculation:
→ First digit: Since it must be odd (1, 3, 5, 7, 9), there are 5 choices.
→ Second digit: Also must be odd but different from the first, so there are 4 remaining choices.
→ Third digit: Any digit except the first two, leaving 8 choices.
→ Fourth digit: Any remaining digit, leaving 7 choices.
→ Fifth digit: Any remaining digit, leaving 6 choices.
→ First letter: Any uppercase letter, 26 choices.
→ Second letter: Any remaining uppercase letter, 25 choices.
→ Third letter: Any remaining uppercase letter, 24 choices.
→ Fourth letter: Any remaining uppercase letter, 23 choices.
→ Fifth letter: Any remaining uppercase letter, 22 choices.
→ Multiply these choices together:
5 × 4 × 8 × 7 × 6 × 26 × 25 × 24 × 23 × 22
→ Calculate the total:
5 × 4 × 8 × 7 × 6 = 6720
26 × 25 × 24 × 23 × 22 = 7893600
6720 × 7893600 = 53,144,832,000
Therefore, the number of different license plates possible is 53,144,832,000.
GEOMETRY! Show your work, please.
Answer:
90°
Step-by-step explanation:
By inscribed angle theorem:
[tex]m\angle STU = \frac{1}{2} \times 180 \degree = 90 \degree[/tex]
A motorboat takes 5 hours to travel 200 miles going upstream. The return trip takes 4 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
Answer:
rate of motorboat: b
rate of current: c
So the rate the boat travels upstream is $b - c$, and the rate it travels downstream is $b + c$
Step-by-step explanation:
d = rt
200 = (b - c)\cdot 5
200 = (b + c)\cdot 4
b - c = 40
b + c = 50
Adding these equations, we get:
2b = 90
b = 45
So
c = 50 - 45 = 5
Therefore the rate of the boat is 45kph, and the rate of the current is 5kph
Hope this helps :)
Final answer:
The boat has a speed of 45 mph in still water, and the current runs at 5 mph. By using the given times and distances for upstream and downstream travel, we can set up equations to solve for the boat's speed and the current's speed.
Explanation:
To find the rate of the boat in still water and the rate of the current, let's denote the boat's speed in still water as b and the speed of the current as c. When the boat goes upstream, its effective speed is b - c, and when it goes downstream, its effective speed is b + c. We can translate this into two equations based on the information given:
(b - c) × 5 hours = 200 miles (upstream)
(b + c) × 4 hours = 200 miles (downstream)
By dividing the distance by the time, we can solve for the effective speeds upstream and downstream.
b - c = 200 miles / 5 hours = 40 mph
b + c = 200 miles / 4 hours = 50 mph
Add these two equations:
2b = 90 mph
b = 45 mph (boat's speed in still water)
Next, subtract the first equation from the second:
2c = 10 mph
c = 5 mph (current's speed)
So, the boat has a speed of 45 mph in still water, and the current has a speed of 5 mph.
Abigail has a cylindrical candle mold with the dimensions shown. If Abigail has a rectangular block of wax measuring 15 cm by 12 cm by 18 cm, about how many candles can she make after melting the block of wax? Round to the nearest tenth.
Find the volume of the candle using the formula for volume of a cylinder:
V = PI x r^2 x h = 3.14 x 3.4^2 x 6 = 217.79 cubic cm. Round to 217.8
Find the volume of the block: V = l x w x h = 15 x 12 x 18 = 3,240 cubic cm.
Now divide the volume of the block by the volume of a candle:
3240 / 217.8 = 14.88
Round to the nearest tenth = 14.9 candles.
Number of cylindrical candles after melting the rectangular block is 14.9.
What is cylinder?" Cylinder is a three dimensional surface formed by two parallel lines and two parallel circular base."
What is volume?" Volume is the total amount of space occupied by any 3 dimensional body."
Formula used
Volume of a cylinder = π r²h
Volume of a rectangular block = length × width ×height
According to the question,
Height of a cylinder = 6cm
radius of cylinder = 3.4cm
Length of a block = 15cm
width of a block = 12cm
height of a block = 18cm
Volume of a cylinder = [tex]3.14[/tex]× [tex](3.4)^{2}[/tex]×[tex]6[/tex]
=217.8 cubic cm
Volume of rectangular block = [tex]15[/tex] × [tex]12[/tex] × [tex]18[/tex]
= 3240 cubic cm
Number of candles = Volume of rectangular block / volume of cylinder
= [tex]\frac{3240}{217.8}[/tex]
= 14.88
= 14.9 (nearest tenth)
Hence the Number of cylindrical candles after melting the rectangular block is 14.9.
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What is the value of a?
Answer:
a = 13
Step-by-step explanation:
The three angles of any triangle MUST add up to 180°. Thus, 3a + 8a + 37 = 180, and 11a = 180 - 37 = 143.
If 11a = 143, then a = 143/11 = 13
a = 13
Answer:
a = 13
Step-by-step explanation:
8a + 3a + 37° = 180°
11a + 37° = 180°
11a = 180° - 37°
11a = 143°
a = 143/11
a = 13
I need help with this I don’t understand what it’s asking.
Answer:
20
Step-by-step explanation:
Because it is a square table, that means all the sides are even. And to find the area, we do Height * Base. But again, because they're even, we would just need to find 2 numbers that multiply to be 400. And that number, is 20. 20 * 20 = 400. So the length of one side is 20.
a loaded truck is traveling 20 mph faster than a freight train. In the time it takes the train to travel 160 miles, the truck travels 240 miles. find the speed of the truck
To find the speed of the truck, start by assigning the speed of the train as 'x', then the truck's speed is 'x + 20'. Set up an equation based on the principle of time = distance/speed, make them equal to each other then solve for 'x'. The truck's speed will be 'x + 20'.
Explanation:Let's call the speed of the freight train 'x' (in mph). We know from the question, that the loaded truck is traveling 20 mph faster than the train, so the truck's speed is 'x + 20' mph.
Given that the time it takes for the train to travel 160 miles is the same time it takes the truck to travel 240 miles, we can write an equation based on the principle that time equals distance divided by speed.
For the train, time = 160/x and for the truck, time = 240/(x+20). As both times are equal, we can write the equation as:
160/x = 240/(x + 20).
Solving this equation for 'x' will give us the speed of the freight train in mph. Then, by adding 20 to 'x', we can find the speed of the truck.
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A dealer sold a car to a man and made
a propit of 15%. The man then sold it
to a woman for 120,175 at a loss of 5%. How much did the dealer buy the car
Answer:
110.000
Step-by-step explanation:
Selling at a loss of 5% means it was sold for 95% of its purchase value.
If 120.175 equals to 95% then 100%(the purchase value) is 126.500.
120.175/95*100 = 126.500 (plenty of other ways to calculate this, but this is one of the easiest)
So now we change to the dealer's perspective, he sold the car for 126.500 and for him that meant a 15% profit. If the purchase value is 100%, then the sale value is 115% (purchase value+15% profit)
Calculate the purchase value:
126.500/115*100 = 110.000
The dealer bought the car for 110.000, sold it for 126.500, so he made a profit of 16.500 (126.500-110.000) which is a 15% profit (15% of 110.000 is 16.500).
The point (−7, -24) is on the terminal side of angle θ, in standard position. What are the values of sine, cosine, and tangent of θ? Make sure to show all work.
Answer:
[tex]\sin 253.740^{\textdegree} = -\frac{24}{25} = -0.960[/tex]
[tex]\cos 253.740^{\textdegree} = -\frac{7}{25} = -0.280[/tex]
[tex]\tan 253.340^{\textdegree} = \frac{24}{7} = 3.429[/tex]
Step-by-step explanation:
The point is in the 3rd Quadrant of the Cartesian Plane. Therefore, angle must be between 180° and 270° with respect to the horizontal.
The angle is:
[tex]\theta = 180^{\textdegree}+\tan^{-1}\left(\frac{24}{7} \right)[/tex]
[tex]\theta \approx 253.740^{\textdegree}[/tex]
The values of the trigonometrical functions are computed below:
[tex]\sin 253.740^{\textdegree} = -\frac{24}{25} = -0.960[/tex]
[tex]\cos 253.740^{\textdegree} = -\frac{7}{25} = -0.280[/tex]
[tex]\tan 253.340^{\textdegree} = \frac{24}{7} = 3.429[/tex]
Last fall, a middle school took a group of students on a trip to Space Camp, which is 360 miles away. The bus that they took to Space Camp traveled at a constant speed, and it took them 6 hours to get from the school to the camp. How many miles did the bus travel in 1 hour?
Answer:
The bus travelled 60 miles in 1 hour.
Step-by-step explanation:
To solve this problem we need to calculate the average speed at which the bus travelled. This is given by the distance travelled divided by the time that they took to get there. So we have:
average speed = distance/time
average speed = 360/6
average speed = 60 miles/h
Therefore in 1 hour they travelled 60 miles.
The stopping distance of a car is modeled by the function d = 0.05r(r + 2) where d is the stopping distance of the car measured in feet and r is the speed of the car in miles per hour. If skid marks left on the road are 75 feet long, how fast was the car traveling?
Answer:
The car was moving approximately at a speed of 37.74 miles per hour.
Step-by-step explanation:
We are given the following in the question:
The stopping distance of a car is given by
[tex]d = 0.05r(r + 2)[/tex]
where d is the stopping distance in feet and r is speed of the car in miles per hour.
The stopping distance is 75 feet, we have to find the speed of the car,
Putting d = 75 in the equation, we get,
[tex]75 = 0.05r(r + 2)\\r^2 + 2r = 1500\\r^2 + 2r-1500 = 0\\\\r =\dfrac{-2\pm \sqrt{4-(4)(1)(-1500)}}{2}\\\\r\approx -39.74,37.74[/tex]
Thus, the car was moving approximately at a speed of 37.74 miles per hour.
Which statement is true of triangles QRS and MNP?
EMERGENCY momoninos operations 1.) 2a-3b divided by 6 2.) 4m+5n divided by 12 3.) 5m-4x divided by -3 4.) 4x+8y-3z divided by 9 5.) 5a+3b+12c divided by -8
Answer:
1) (a/3) - (b/2)
2) (m/3) + (5n/12)
3) (-5m/3) + (4x/3)
4) (4x/9) + (8y/9) - (z/3)
5) (-5a/8) + (-3b/8) + (-3c/2)
Step-by-step explanation:
1) 2a-3b divided by 6
(2a-3b)/6 = (2a/6) - (3b)/6 = (a/3) - (b/2)
2) 4m+5n divided by 12
(4m+5n)/12 = (4m/12) + (5n/12) = (m/3) + (5n/12)
3) 5m-4x divided by -3
(5m-4x)/(-3) = (-5m/3) + (4x/3)
4) 4x+8y-3z divided by 9
(4x+8y-3z)/9 = (4x/9) + (8y/9) - (3z/9) = (4x/9) + (8y/9) - (z/3)
5) 5a+3b+12c divided by -8
(5a+3b+12c)/(-8) = (-5a/8) + (-3b/8) + (-12c/8) = (-5a/8) + (-3b/8) + (-3c/2)
abby has 10 apples, she gives away 5 how many does she have left
Answer:
5 apples
Step-by-step explanation:
brainliest?
5 Apples Are Left
Step-by-step explanation:Simply subtract the initial total and the apples given away.
10 - 5 = 5 left
What numbers would be needed to complete another bottom row in the pyramid below? I need help fast!
Answer:
Step-by-step explanation:
the second option
Graph the integer 6 and its opposite on the number line. Graph the integer 0 and its opposite on the number line.
Graph the integer 6 and its opposite
Plot -6 and 6 <- the opposite of 6 is -6
Graph the integer 0 and its opposite on the number line
0 and 0 <- The opposite of 0 is itself as it has no negative value
Step-by-step explanation:
Graph the integers between 2 and 6 on a number line
Solve for x if 2(5x+2)2=48
Answer:
x =(-4-√96)/10=(-2-2√ 6 )/5= -1.380
x =(-4+√96)/10=(-2+2√ 6 )/5= 0.580
Step-by-step explanation:
Answer: cccccccccccccc
Step-by-step explanation: <3
A toy soldier set a selection of 6 weapons for 3 soldiers.
How many different ways can the 3 soldiers be assigned weapons if each soldier is to be assigned only one weapon?
Answer:
2
Step-by-step explanation:
There are 120 different ways to assign 6 weapons to 3 soldiers, each receiving one weapon, calculated using permutations.
Calculating Permutations for Weapons Assignment
To determine how many different ways 3 soldiers can be assigned weapons from a selection of 6, we need to calculate the permutations of 6 objects taken 3 at a time. We use the permutation formula, which is expressed as P(n, k) = n! / (n-k)!, where n is the total number of items, and k is the number of items to choose. In this case, n is 6 (the total number of weapons), and k is 3 (the total number of soldiers).
We calculate the permutations as follows:
6! / (6-3)! = (6 * 5 * 4) / (3 * 2 * 1) = 120 ways.
Therefore, there are 120 different ways to assign the weapons to the soldiers, with each soldier getting one weapon.
A laundry detergent is sold at four stores.
Size (ounces)
60
54
48
40
Store
Hawkin's Store
Don's Store
Allen's Market
Value Market
Price
$6.50
$5.50
$5.61
$4.50
Which store has the lowest price per ounce?
Hawkin's Store
Answer:
Hawkins's Store = 60 ounces for 6.50
Don's Store = 54 ounces for 5.50
Allen's Market = 48 ounces for 5.61
Value Market = 40 ounces for 4.50
6.50/60=.10833333
5.50/54=.10185 smallest decimal
5.61/48 = .116875
4.50/40=.1125
Step-by-step explanation:
the answer is Don's Store
hope this helps(:
The store Don's has the lowest price per ounce is $0.10.
What is the unit rate?Unit rate can be defined as the ratio between two measurements with the second term as 1. It is considered to be different from a rate, in which a certain number of units of the first quantity is compared to one unit of the second quantity.
Here,
In Hawkin's Store:
The cost of 1 ounce is 6.50/60
= $0.11
In Don's Store:
The cost of 1 ounce is 5.50/54
= $0.10
In Allen's Market
The cost of 1 ounce is 5.61/48
= $0.12
In Value Market:
The cost of 1 ounce is 4.50/40
= $0.1125
Therefore, the store Don's has the lowest price per ounce is $0.10.
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If you flip a coin 300 times how many times would you expect the coin to lands head up ? Explain your reasoning (write in complete, mathematically precise sentences).
Answer: you would expect it to flip about 150 times heads.
Step-by-step explanation: A coin has two sides. There's an equal chance for each side. So 50-50 chance.
300 divided by 2 is 150
(Sorry if it's not the best mathematical way to say it)
How do you get area from a triangle
Answer:
1/2 bh
Step-by-step explanation:
Multiply the base by the height then multiply by 1/2, or divide by 2
Answer:
A=hbb
2
Step-by-step explanation:
Identify the equation that represents the line of best fit on this scatter plot.
Answery
y= 2x+2
Step-by-step explanation:
The area of a rectangle is 8x^2 +14x + 3. the width is 2x +3. What is the length?
Answer:
4x+1
Step-by-step explanation:
Please see attached image.
The temperature inside a freezer was –18 °C when the freezer was accidentally unplugged. After that, the temperature increased by 2 °C per hour. This situation can be modeled by an equation of the form y = mx + b , where x = the time in hours that the freezer was been unplugged and y = the temperature in degrees Celsius. What is the value of b in this equation?
Answer:
-18
Step-by-step explanation:
b is where the line crosses the y-axis, or where x=0. Since it starts at -18, then that would be the b.
in the adjoining figure P A and PB are tangents from P to a circle with Centre O if angle APB is equal to 40 degree then find angle ACB
Step-by-step explanation:
40° + 90° + 90° + angle ACB = 360°
220° + angle ACB = 360°
angle ACB = 360° - 220°
Therefore angle ACB = 140°
Hope it will help :)
Final answer:
To find angle ACB, determine angle AOB by subtracting the tangents' right angles and angle APB from 360 degrees, which results in 140 degrees. Then, using the Inscribed Angle Theorem, angle ACB is half the measure of angle AOB, yielding 70 degrees.
Explanation:
The student is asking how to find the angle ACB when given that PA and PB are tangents to a circle with centre O, and angle APB is 40 degrees. To find angle ACB, which is the angle at the circle subtended by the chord AB, we first determine the measure of angle AOB, which is central and subtended by AB as well. Since the tangents from a point outside a circle form a right angle with the radius at the point of contact, we have two right triangles OAP and OBP, each with an angle of 90 degrees. These right angles add to the given angle APB to form a full angle around point P which is 360 degrees. Knowing angle APB is 40 degrees, we can find angle AOB by subtracting the sum of the two right angles and angle APB from 360 degrees.
Angle AOB = 360 degrees - (90 degrees + 90 degrees + 40 degrees) = 360 degrees - 220 degrees = 140 degrees
Finally, since angle ACB is inscribed and angle AOB is central, both subtended by the same chord AB, angle ACB is half the measure of angle AOB by the Inscribed Angle Theorem. Therefore, angle ACB is 70 degrees.
Angle ACB = ½ * Angle AOB = ½ * 140 degrees = 70 degrees
A triangle has one angle that measures 35º. Which values could be the measures of the other two angles?
Answer:
See below.
Step-by-step explanation:
The 3 angles in a triangle add up to 180 degrees, so the sum of the other 2 angles is 180 - 35 = 145 degrees.
So, for example the other 2 angles could be 60 and 85 degrees.
Answer:
75° and 70°
25° and 120°
90° and 55°
Step-by-step explanation:
I got it right
A right triangle has a side with length 20 meters, hypotenuse with length 25 meters, and side labeled b. StartRoot 5 EndRoot m 5 m StartRoot 45 EndRoot m 15 m
Answer:
15 m
Step-by-step explanation:
25² = 20² + b²
625 = 400 + b²
b² = 225
b = 15
it is 15 hope this helped and good luck...
What is 1.8-(-3.25)
Answer: [tex]5.05[/tex]
Flip
Keep: 1.8
Change: - into +
Change: -3.25 into 3.25
Your new problem
[tex]1.8+3.25[/tex]
Add
[tex]1.8+3.25=5.05[/tex]
The expression 1.8 minus negative 3.25 simplifies to 1.8 plus 3.25, which equals 5.05.
The question asks you to calculate the result of the expression 1.8 minus negative 3.25. When you have a minus sign followed by a negative sign, they cancel each other out and it becomes an addition problem. Therefore, the expression simplifies to 1.8 + 3.25.
To calculate this, you add the two numbers:
1.8+3.25Adding these numbers together gives you 5.05. So, 1.8 - (-3.25) equals 5.05.
Steve reaches into a bag with 5 red marbles, 3 yellow marbles, and 2 green marbles, and randomly selects one. Then, he puts the marble back, and Sam reaches into the same bag and randomly selects a marble. What is the probability that both guys selected a yellow marble.
You have to answer correctly to recieve all 50 points
5 + 3 + 2 = 10 total marbles.
Steve picking a yellow one would be 3/10 (3 yellow / 10 total)
The marble is put back, so there will still be 7 marbles in the bag.
Sam picking a yellow one would then be the same as Steve: 3/10
The probability of them both picking yellow would be 3/10 x 3/10 = 9/100
Answer:
0.09
Step-by-step explanation:
Total: 5+3+2 = 10
3/10 × 3/10
9/100
0.09
What is the value of n in the equation 1 (n – 4) – 3 = 3 - (2n+3)?
Answer:
n=7/3
Step-by-step explanation:
1 (n – 4) – 3 = 3 - (2n+3)
1. distribute the 1 on the left side and distribute the -1 on the right side
1n-4-3=3-2n-3
2. add like terms
1n-7=-2n
3. move n to one side and by itself
-7=-3n
4. divide -3 to get n alone. Both negatives cancel out each other
7/3=n
Step-by-step explanation:
[tex]1(n-4)-3=3-(2n+3)[/tex]
[tex]n-4-3=3-2n-3\\n+2n=3-3+3+4\\3n=7\\n=\frac{7}{3}[/tex]
Proof
[tex]1(n-4)-3=3-(2n+3)[/tex]
[tex]1(\frac{7}{3} -4)-3=3-[2(\frac{7}{3}) +3]\\1(\frac{7-12}{3} )-3=3-(\frac{14}{3} +3)\\1(\frac{-5}{3} )-3=3-(\frac{14+9}{3})\\\frac{-5}{3} -3=3-(\frac{23}{3})[/tex]
[tex]\frac{-5-9}{3} =\frac{9-23}{3} \\\frac{-14}{3} =\frac{-14}{3}[/tex]
how do i covert a fraction into a decimal.
Answer:
By dividing the top number by the bottom.
Step-by-step explanation:
ummmmm
To convert a fraction into a decimal, divide the fraction's numerator by its denominator. Multiplying a decimal by 100 converts it to a percent, and dividing a percent by 100 converts it back into a decimal. This process is used to manipulate numerical values for various mathematical applications.
Explanation:Converting a Fraction to a Decimal
To convert a fraction into a decimal, you simply divide the numerator (the top number) by the denominator (the bottom number). For example, to convert 3/4 to a decimal, you divide 3 by 4, which equals 0.75. If the fraction is not in simplest form, you may first simplify it before dividing. This is a basic mathematical skill that you will use in many areas of math.
To convert a decimal to a percent, you multiply the decimal by 100. For instance, 0.75 multiplied by 100 equals 75%, because you are essentially finding how many 'parts out of 100' are present in the decimal.
In the case of converting percents, to turn a percent into a decimal, you divide by 100. So, taking 75% and dividing by 100 would give you 0.75, which is the original decimal we started with.
Another example is converting 0.0479 into a decimal that's a number between 1 and 10. To do this, we would move the decimal point to the right two places to get 4.79, as specified by the conversion factor which helps in adjusting units or scaling numbers without changing the value.