Mathematics College

How many four​-digit even numbers are possible if the leftmost digit cannot be​ zero

Answers

Answer 1
Final answer:

There are 4500 four-digit even numbers possible when the leftmost digit cannot be a zero.

Explanation:

The question is about finding out the number of four-digit even numbers possible given that the first or leftmost digit cannot be a zero. In a four-digit even number, the last digit (rightmost) should be an even number, i.e., 0, 2, 4, 6, or 8. Hence, there are 5 possibilities for the last digit.

Next, since the leftmost digit cannot be a zero, it leaves us with 9 possibilities (1-9). Lastly, the middle two digits can be any digit from 0 to 9, so there are 10 possibilities each for the second and third digits.

Therefore, the total number of four-digit even numbers under the given conditions is found by multiplying these possibilities: 9 (for the first digit) * 10 (for the second digit) * 10 (for the third digit) * 5 (for the last digit) = 4500.

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Answer 2
Final answer:

To find the number of four-digit even numbers where the leftmost digit cannot be zero, there are 9000 possibilities.

Explanation:

To find the number of four-digit even numbers where the leftmost digit cannot be zero, we need to consider the following:

Choose the digit for the leftmost position (excluding zero). This can be done in 9 ways.Choose the digits for the other three positions (including zero for even numbers) in 10 ways each (0-9).

By multiplying the number of choices for each position, we get the total number of four-digit even numbers without leading zeros: 9 * 10 * 10 * 10 = 9000.

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Related Questions

Two identical twins can only be distinguished by the characteristic that one always tells the truth and the other always lies. One twin tells you of a lucky number pair: "When I multiply my first lucky number by 3 and my second lucky number by 6, the addition of the resulting numbers produce a sum of 12. When I add my first lucky number and twice my second lucky number, the sum is 5." Which twin is talking? How do you know?

Answers

To get a sum of 12, you know that the lucky numbers must be pretty small.  The first lucky number is 2, multiplied by 3 gets us 6.  The second lucky number is 1, multiplied by 6 gets us 6.  6 + 6 = 12.
The solve the next problem, the second lucky number (1) twice is 2.  When added to the first lucky number, the sum is 4.  This is tricky, because if the first lucky number was multiplied by 2 and added to the second lucky number, the sum would be 5.
In this case, the twin that lies is talking. 

write each fraction as a sum or difference
2m-5/9

Answers

This is a fraction that has a linear expression as the numerator and a constant number in denominator.
So we can simply divide each term of numerator by denominator because we can write [tex] \frac{a+b}{c} = \frac{a}{c}+ \frac{b}{c} [/tex]
So we can write given fraction as
[tex] \frac{2m-5}{9} = \frac{2m}{9} - \frac{5}{9} [/tex] which is expressed as a difference.

What statement regarding the diagram is true?

Answers

I believe the second one right, because if I remember two opposite angles of an outside angle = the outside angle.

A rug is shaped like a rectangle who's per Perimeter there's 192 feet the length is five times longer with find the length and the width

Answers

P = Perimeter = 2(length) + 2(width).  Let the width be x; then if the length is 5 times longer than the width, the length is 5x.

Plug these values into the Perimeter equation P = 2(length) + 2(width):

P = 2(5x) + 2(x), or P = 12x, and this is known to have the value 192 units.  Solve for the width, x:

(192 units) = 12x gives us x = 16 units.  Then the length is 5(16 units) = 80 units.

Check:  Does   2(80 units) + 2(16 units) = 192 units?  If so, then our width (16) and length (80) are correct.

You deposit $5000 in an account earning 2% interest compounded continuously. How much will you have in the account in 15 years?

Answers

The compound interest is given by:
A=p(1+r/100)^n
where:
A=future amount
p=principle
r=rate
n=time in years
Therefore given that, p=$5000, r=2% and n=15 years, the amount after 15 years will be:
A=5000(1+2/100)^15
A=5000(1+0.02)^15
A=5000(1.02)^15
A=6,729.34
We conclude that the amount after 15 years will be $6,729.34

What's the answer to the equation;
√2y+3=11

Answers

y=59 that should be the correct answer 

The answer should be Y=32 should be it
 




The course for a walkathon is 6 miles long. If Chloe wants to walk 50 miles during the walkathon, how many times must she walk the course?

Answers

she should walk the course about 8 or 9 times

divide 50 by 6

50/6 = 8.333

 so she has to walk it 8.33 times

 round answer as needed.

Evaluate the limit, if it exists. (if an answer does not exist, enter dne.) lim h→0 (5 + h)−1 − 5−1 h

Answers

[tex]\displaystyle\lim_{h\to0}\frac{(5+h)^{-1}-5^{-1}}h=\lim_{h\to0}\frac{\frac5{5(5+h)}-\frac{5+h}{5(5+h)}}h[/tex]
[tex]\displaystyle=-\lim_{h\to0}\frac h{5(5+h)h}[/tex]
[tex]\displaystyle=-\lim_{h\to0}\frac1{5(5+h)}=-\frac1{25}[/tex]

Alternatively, recall that if [tex]f(x)=\dfrac1x[/tex], then [tex]f'(x)=-\dfrac1{x^2}[/tex], and so

[tex]f'(5)=\displaystyle\lim_{x\to5}\frac{\frac1x-\frac15}{x-5}[/tex]

Take [tex]h=x-5[/tex], so that [tex]x=h+5[/tex], and we have the original limit. So the limit is equivalent to the value of [tex]f'(5)[/tex], i.e.

[tex]f'(5)=-\dfrac1{5^2}=-\dfrac1{25}[/tex]

A wheelchair access ramp has an angle of elevation of 20°. If the ramp reaches to the top of a 33 inch high porch, how long is the ramp?

Answers

sinα=height/length

length=height/sinα, we are given that α=20° and h=33 in

length=33/sin20° in

length≈96.49 in (to nearest hundredth of an inch)
This is a sin operation, Sin is the relationship between the opposite (height) and the hypotenuse (length of ramp). Plugging in: Sin(20deg) = 33/x

Sin(20) = 33/x

x*Sin(20) = 33

x = 33/Sin(20)

x = 96.49in long.

*This answer is the length of the SLOPE of the ramp.

a car dealership has 55 cars and 11 vans.what is the ratio of cars to vans? wriiten as a fraction in simplest form?

Answers

55/1 ratio is 5 to 1 or 5/1.   55 divided by 11 is 5 and 11 divided by 11 is 1, so the ratio is 5 to 1.

Out of 30 students surveyed 17 have a dog based on these results predict how many of the 300 students in the school have a dog

Answers

17/30 = 0.5666 so about 57% of the sample had dogs

 300 x 0.57 = 171 would have dogs

 

A small company repairs home computers. In the past 200 days, it has been quite busy, taking in and repairing 2 computers on 52 of those days; 3 computers on 84 of those days; 4 computers on 40 of those days; and 5 computers on 24 of those days. Build a probability distribution for the number of computers repaired on any given day, show it is a valid distribution, and calculate its mean and variance.

Answers

The probability distribution is shown in the table below

The value of [tex]x[/tex]: 2, 3, 4, and 5 shows the number of computers repaired and [tex]P(X=x)[/tex] shows the probability

Mean = (2×0.26×) + (3×0.42) + (4×0.2) + (5×0.12) 
Mean = 0.52+1.26+0.80+0.6
Mean = 3.18

Variance = [(2²×0.26)+(3²×0.42)+(4²×0.2)+(5²×0.12)] - (3.18)²
Variance = 0.9076

Which of the following gives all of the sets that contain -1/2?

A.the set of all rational numbers and the set of all real numbers
B.the set of all natural numbers and the set of all irrational numbers
C.the set of all integers and the set of rational numbers
D.the set of all natural numbers, the set of rational numbers, and the set of all real numbers

Answers

i think it might be.... A.the set of all rational numbers and the set of all real numbers

Answer:

Option A is Correct Option.

Step-by-step explanation:

Given: [tex]\frac{-1}{2}[/tex]

[tex]\frac{-1}{2}[/tex]  is a rational no.

Option A:

Given no is a rational no.

⇒ Both Set of rational no and real nos. contain rational nos..

Thus, Correct Option.

Option B:

set of natural nos and irrational nos does not contain rational nos.

Thus, Not correct option.

Option C:

Set of integers does not contain rational numbers.

Thus, Incorrect Option.

Option D:

Set of all Natural Nos. does not contain rational nos.

Thus, This option is not correct option

Therefore, Option A is Correct Option.

The axis of symmetry for a quadratic equation can be found using the formula x =-b/2a , where a and b are coefficients in the quadratic equation and x represents the values along a vertical line on the coordinate plane. When the equation is solved for a, such that b is the numerator of the resulting fraction, what is the denominator of the fraction?

2x

–2x

1/2x

–1/2x

Answers

if x = -b/2a, then 2a = -b / x so a = -b / 2x or a = b / -2x

So the denominator is -2x because it has to take the minus sign that the numerator refused to take ;-)

The answer is B on edgen.

Kathy walked 3 1/2 miles per hour for 1 1/4 hours. During 1/2 of her walking time it rained. How many miles did she walk while it was raining?

Answers

I think it's 2.2 miles walking in the rain

1 1/4 = 5/4 * 1/2 = 5/8


3 1/2 = 7/2 * 5/8 = 35/16 =  2 3/16 miles

PLEASE help me...Suck at math. find the following using the given triangle.

Answers

To find the perimeter just add the sides

5+5+6 = 16

To find the area, you need to use the following formula

[tex] area = \frac{1}{2}bh[/tex]
we know b but we need to find the height. We can find the heigh by using pythagorean theorem [tex]a^2 + b^2 = c^2[/tex]

height = [tex] a^2 + 3^2 = 5^2 [/tex]
             [tex] a^2 + 9 = 25 [/tex]
             [tex] a^2  = 25 - 9[/tex]
             [tex] a^2 = 16 [/tex] 
            [tex] a = \sqrt{16} = 4 [/tex] 
            h = height = 4

[tex] area = \frac{1}{2}\times 6\times 4 = 12cm^2[/tex]

Cost:

6.00 per cm^2 = 6.00 x 12 =  $72.00 dollars
check the picture below.

what's the cost? well is $6 per square foot, what area did you get? well, say you got A, so the cost is just  A * 6.

Translate this sentence into an equation; 14 less than Julie's score is 62. Use the variable m to represent Julie's score.

Answers

First, when we hear "less than" we should think of subtraction. Since Julie's score is represented by m, 14 less than her score would be the same as m-14 because we need to use subtraction. Then since 14 less than her score is equal to 62, we can set m-14 equal to 62 to get our final answer which is m-14=62.

I hope this helps!
To solve problems like these, we must break it down for each term.

"14 less than Julie's score"
This implies that we are going to have 14 less than the variable that represents Julie's score (which in this case, is m).

m-14

"is 62"
"Is" is almost always used as a way of saying "=," and 62 is the value that it equals.

m-14=62

Using the reasoning above, we can see that an equation to represent this scenario is m-14=62. 

Suppose an isosceles triangle ABC has A = 45° and b = c = 4. What is the length of a2?

Answers

You can use the Law of Cosines (a^2=b^2+c^2-2bc cosA)

a^2=4^2+4^2-2*4*4*cos45°

a^2=32-32cos45°

a^2=32(1-cos45°)

a=√(32(1-cos45°))

a≈3.06 units (to nearest hundredth of a unit)

What is the height of a cylinder with a volume of 315 pi cubic meters and a radius of 6 meters?  8.75 meters 12.25 meters 26.25 meters 52.5 meters

Answers

check the picture below.

simplify away.

Since this cylinder has a radius of 6 meters, its height is equal to 8.75 meters.

Given the following data:

Radius of cylinder = 6 m.

Volume of cylinder = 315π m.

How to calculate the height of this cylinder?

Mathematically, the volume of a cylinder is calculated by using this formula:

V = πr²h

Where:

h is the height.r is the radius.

Substituting the given parameters into the formula, we have;

315π = π × 6² × h

315π = 36πh

h = 315/36

Height, h = 8.75 meters.

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A math teacher gave her class two tests. 76% of the class passed the first test. 58% of the class passed both tests. What is the approximate probability that a student who passed the second test, given that he passed the first test.

Answers

P(test 2 | test 1) = P(test 2∩test 1) ÷ P(test 1)
P(test 2 | test 1) = 0.58 ÷ 0.76
P(test 2 | test 1) = 0.76 ≈ rounded to two decimal places


Keeping in mind that a functions rate of change is measure of how fast the function is increasing or decreasing what does the slope of a linear function indicate?

Answers

When a linear function is graphed, a line will drawn on the plot. If we analyze this, this means that the two variables are related by a constant of proportionality. That constant is called the slope. Since the slope is constant, that means that the rate of change is also constant. It would only differ if the rate is increasing or decreasing. It would be increasing if its magnitude is positive which will be graphed as a diagonal to the right. Otherwise, it is decreasing whose magnitude is negative which will be graphed as a diagonal to the left.

Answer: A linear function is represented as a straight line. The slope of the line gives the function’s rate of change.

Step-by-step explanation: Plato sample answer

What property describes the number sentence? 6+0=6

Answers

hello : 
the property describes the number sentence 6+0=6 is : " 0 Neutral element for addtion"

Matthew currently has enough money to buy 45 toy cars. If the cost of each car was 10 cents less, Matthew could buy 5 more cars. How much money does Matthew have to spend on toy cars?

Answers

 x=price per toy car 
45x = money Matt has 
45x =50(x-.1) 
45x =50x -5 
5 =5x 
x=$1 
45x= $45
the cost of each car is $1

The total ages of 2 buildings is 201 years. if one building is twice as old as the other, what are the ages of 2 buildings?

Answers

Answer: 67 years and 134 years

In this case, you are given the buildings sum ages ( building A ages+ building B ages = 201 years) and the building ratio ( Building A ages= 2x Building B ages).
To answer the question, you simply need to insert the second equation into the first. It would be:

building A ages + building B ages= 201
2x building B ages + building B ages= 201
building B ages= 67 years.

Then building A ages= 2x 67 years= 134 years.

The ages of the two buildings are 67 and 134 years. This is found by setting up an algebraic equation where the sum of their ages is 201, and one is twice as old as the other.

Finding the Ages of Two Buildings

If the total ages of two buildings is 201 years and one building is twice as old as the other, then we can express the ages of the buildings using algebra. Let's denote the age of the younger building as y years. The older building is twice as old, so its age would be 2y years. The equation based on their total ages would be:

y + 2y = 201 years

Solving this equation:

Combine like terms: 3y = 201.

Divide both sides by 3 to isolate y: y = 201 / 3.

Calculate the exact value: y = 67 years.

So, the younger building is 67 years old, and the older building, being twice as old, is 134 years old.

Atmospheric pressure decreases by about 11.8% for every 1000 meters you climb. The pressure at sea level is 1013 millibars (a unit of pressure). Construct an exponential model to represent the atmospheric pressure at a given altitude in thousands of meters. Use your model to determine the atmospheric pressure at an altitude of 4000 meters.
(Express your answer in millibars rounded correctly to the nearest tenth.)

Answers

at sea level, the pressure is 1013, that's when the altitude is at 0, sea level, let's see

[tex]\bf \textit{Periodic Exponential Decay}\\\\ A=I(1 - r)^{\frac{t}{p}}\qquad \begin{cases} A=\textit{accumulated amount}\to &1013\\ I=\textit{initial amount}\\ r=rate\to 11.8\%\to \frac{11.8}{100}\to &0.118\\ t=\textit{meters climbed}\to &0\\ p=period\to &1000 \end{cases} \\\\\\ 1013=I(1-0.118)^{\frac{0}{1000}}\implies 1013=I\cdot 1\implies 1013=I[/tex]

so, the inital amount is 1013, when t = 0,

[tex]\bf \textit{Periodic Exponential Decay}\\\\ A=I(1- r)^{\frac{t}{p}}\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\to &1013\\ r=rate\to 11.8\%\to \frac{11.8}{100}\to &0.118\\ t=\textit{meters climbed}\to &t\\ p=period\to &1000 \end{cases} \\\\\\ A=1013(1-0.118)^{\frac{t}{1000}}\implies A=1013(0.882)^{\frac{t}{1000}}[/tex]

now, to check the atmospheric pressure at 4000, simply set t = 4000, to get A.


how many miles can you drive with 13.2 gallons of gasoline

Answers

286.44 I multiplied the numbers together
This depends on how large your car is and how fast you drive.
Certain cars burn more gasoline than others. You also may burn more or less gasoline depending on your speed. Slower speeds burn less, whereas faster speeds burn more.

The perimeter of a rectangular field is 168 feet. The field is 36 feet wide. How long is the field

Answers

To find the length, divide the peremiter by 2 and then subtract the width.

Length= Peremiter/2 - width
L = P/2 - W
L = 168/2 - 36
L = 84 - 36
L = 48

The length is 48

The extreme rock climbing club planned a climbing expedition. The total cost was $5000, which was to be divided equally among the members going. Prior to the trip, 3 members decided not to go. If the cost per person increases by $375, how many people went on the expedition?

Answers

Most useful original number of planned climbers were 687 members .hope i helped
687 I am pretty sure hope it helps,,,,,,,,,,m,,,,

The volume of the Moon is about 2.18×10102 cubic kilometers. The volume of Earth is about 1.09×10121 cubic kilometers. The number of Moons that can fit inside Earth can be found by dividing Earth's volume by the Moon's volume. About how many Moons can fit inside Earth?

Answers

Volume of Earth is 1.09×1012 cubic kilometers

Volume of Moon is 2.18×1010 cubic kilometers

Hence number of Moons that can fit in Earth is

1.09×10122.18×1010

= 1012−102   as  2.18=1.09×2

= 1022

= 1002=50

Answer:

50 moons

Step-by-step explanation:

cause i got it right on the test

a triangular prism has height of 10cm and a base area of 12cm. a rectangular prism has height of 10cm and base dimensions of 3 cm and 4 cm. do the solids have the same volume?

Answers

check the picture below.

notice, the base area of the rectangular prism is just 3x4.
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