Answer:
The state can issue 456,976,000 license plates.
Step-by-step explanation:
For digits, it is assumed that we can use 0-9. Thus, there are 10 options for each slot with a digit.
For letters, it is assumed that we can use the 26 letters of the alphabet (i.e. A through Z). Thus, there are 26 options for each slot with a letter.
For this particular problem, the slot method can be used. Assuming that repetition of letters/digits is allowed:
[tex]\frac{10}[/tex] [tex]\frac{26}[/tex] [tex]\frac{26}[/tex] [tex]\frac{26}[/tex] [tex]\frac{26}[/tex] [tex]\frac{10}[/tex] [tex]\frac{10}[/tex]
= 10*26*26*26*26*10*10
=456,976,000.
Therefore, the state can issue 456,976,000 license plates.
3y+5 < 10
solve for y
Answer:
y>3/5
Step-by-step explanation:
3y+5 <10
3y<5
y>3/5
Answer:
[tex]\:3y+5<10\\3y+5-5<10-5\\3y<5\\\frac{3y}{3}<\frac{5}{3}\\y<\frac{5}{3}[/tex]
OAmalOHopeO
Consider the equation 2x-8=10-x. Why can't you determine whether this equation is true or false?
Answer:
False
Step-by-step explanation:
If we consider x=1 then
2*1-8 = 10-1
2-8 =9
6 = 9 (which is impossible)
so false
We can determine that the original equation 2x - 8 = 10 - x is true when x = 6.
We have,
Simplify the equation:
2x - 8 = 10 - x
Combining like terms by adding x to both sides:
3x - 8 = 10
Now, to isolate the variable x, add 8 to both sides:
3x = 18
Finally, divide both sides of the equation by 3:
x = 6
By solving the equation, x = 6.
Therefore,
We can determine that the original equation 2x - 8 = 10 - x is true when x = 6.
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Josue leans a 26-foot ladder against a wall so that it forms an
angle of 80° with the ground. How high up the wall does the
ladder reach? Round your answer to the nearest hundredth of a
foot if necessary.
Answer:
25.61 feet
Step-by-step explanation:
First, we can draw a picture (see attached picture). With the wall representing the rightmost line, and the ground representing the bottom line, the ladder (the hypotenuse) forms a 80 degree angle with the ground and the wall and ground form a 90 degree angle.
Without solving for other angles, we know one angle and the hypotenuse, and want to find the opposite side of the angle.
One formula that encompasses this is sin(x) = opposite/hypotenuse, with x being 80 degrees and the hypotenuse being 26 feet. We thus have
sin(80°) = opposite / 26 feet
multiply both sides by 26 feet
sin(80°) * 26 feet = opposite
= 25.61 feet as the height of the wall the ladder reaches
The height of the wall does the ladder reach to the nearest hundredth of the foot is 25.61 feet.
What is a right-angle triangle?It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function. The Pythagoras is the sum of the square of two sides is equal to the square of the longest side.
Josue leans a 26 feet ladder against a wall so that it forms an angle of 80° with the ground.
The condition is shown in the diagram.
Then the height of the wall will be
[tex]\rm \dfrac{h }{26 } = sin 80 \\\\h \ \ = 26 \times sin 80\\\\h \ \ = 25.61 \ ft[/tex]
More about the right-angle triangle link is given below.
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In forming a confidence interval for μ1 - μ2, only two assumptions are required: independent samples and sample sizes of at least 30.
a. True
b. False
Зу = -2 - 6
3y = 2z - 6
Answer:
y = -8/3, z = -1
the length of a rectangle is twice its width the perimeter is 48 cm what are the dimensions of the rectangle
Answer:
The length=16cm and the width=8cm.
Step-by-step explanation:
Given that the length is twice the breadth or width of the rectangle
Let's assume that the breadth of the rectangle is x.
Thus the length is 2x.
Given perimeter=48cm
The formula for the perimeter of a rectangle is 2(l+b) where l is length and b is breadth.
2(x+2x)=48
(3x)=48/2
3x=24
x=8cm
2x=16cm
Step-by-step explanation:
length=2x
width=x
2x+x+2x+x=48
6x=48
6x÷6=48÷6
x=8
length=16
width=8
Miller's Steakhouse offers 8 side dishes, 5 types of steak, and 4 toppings. How many different smothered steak dinners can be made if a smothered steak dinner consists of the customer's choice of steak served with 3 different toppings and 3 different side dishes?
Answer:
1120
Step-by-step explanation:
To find the possible number of steak dinners, you would multiply the number of choices for each part of the dinner. You would used combinations instead of permutations since the order of the toppings chosen or side dishes chosen do not matter. There are 5 choose 1 choices for types of steak, which is just 5. There are 8 choose 3 choices for side dishes, which is 56. There are 4 choose 3 choices for toppings, which is 4. 5*56*4 is 1120, so there are 1120 possible steak dinners.
Each spring, Bill's yard has about 950 square feet of space to cover with mulch. One year, trying to save some cash, Bill bought cheapo overseas mulch from a gas station, and the packaging said that each bag covered 1.8 square meters. How many bags did Bill need
Answer:
161 bags
Step-by-step explanation:
Since we need to know how many square feet a bag can cover, we need to convert the 1.8 square meters to feet. A meter is about 3 feet and 3.5 inches, so to find how many bags he needs we need to convert the bag into feet. First lets convert the meter into inches:
[tex](3*12)+3.5\\(36)+3.5 = 39.5[/tex]
Remember that a foot is 12 inches. Now, we need to multiply the 39.5 inches by 1.8 to find out how many square inches a bag holds.
[tex]39.5*1.8 = 71.1[/tex]
We need square feet though, so let's divide our 71.1 inches by 12 to get a foot measurement.
[tex]71.1/12=5.93[/tex]
A bag holds 5.93 square feet of mulch. Now, to figure out how many bags he needs, we need to divide 950 (total area to cover) by 5.93 (area each bag covers).
[tex]950/5.93=160.2[/tex]
Since Bill cant buy a fifth of a bag, we need to round up so he has enough. So, Bill needs 161 bags of mulch to cover his yard.
The surface area of a melting snowball decreases at a rate of3.8cm2/min. Find the rate at which its diameter decreases when the diameter is13cm. (Round your answer to three decimal places if required)
Answer:
Step-by-step explanation:
This is a pretty basic related rates problem. I'm going to go through this just like I do in class when I'm teaching it to my students.
We see we have a snowball, which is a sphere. We are talking about the surface area of this sphere which has a formula of
[tex]S=4\pi r^2[/tex]
In the problem we are given diameter, not radius. What we know about the relationship between a radius and a diameter is that
d = 2r so
[tex]\frac{d}{2}=r[/tex] Now we can have the equation in terms of diameter instead of radius. Rewriting:
[tex]S=4\pi(\frac{d}{2})^2[/tex] which simplifies to
[tex]S=4\pi(\frac{d^2}{4})[/tex] and a bit more to
[tex]S=\pi d^2[/tex] (the 4's cancel out by division). Now that is a simple equation for which we have to find the derivative with respect to time.
[tex]\frac{dS}{dt}=\pi*2d\frac{dD}{dt}[/tex] Now let's look at the problem and see what we are given as far as information.
The rate at which the surface area changes is -3.8, and we are looking for [tex]\frac{dD}{dt}[/tex], the rate at which the diameter is changing, when the diameter is 13. Filling in:
[tex]-3.8=\pi(2)(13)\frac{dD}{dt}[/tex] and solving for the rate at which the diameter is changing:
[tex]-\frac{3.8}{26\pi}=\frac{dD}{dt}[/tex] and divide to get
[tex]\frac{dD}{dt}=-.459\frac{cm}{min}[/tex] Obviously, the negative means that the diameter is decreasing.
What is the value of x in the equation
-%y = 30, when y = 15?
Answer:
x not given
therefore no answer for x
G. Find the ratio between a pen and pencil if ten pens cost $22.5 and a dozen pencils cost $18.
Answer:
Cost ratio of pens:pencils = 9 : 4
Step-by-step explanation:
Pen : Pencil
10/10 : 12/12
22.5 / 10 : 18 / 12
2.25 : 1.5 cost per pen : pencil
HC of 0.25 and 0.5 is 8
8 x 2.25 = 18:
1.5 x 8 = 12
Then place them under their denominator x 10 x 12
pens = 18/10 = 1.8
pencils = 12/12 = 1
HC of 1.8 and 1 is 5
1.8 x 5 = 9
1 x 5 = 5
Answer = 9 : 4
Combine the expressions below
4x+(-2x)+6+(-9)
=4x-2x=2x
=6-9=-3
=2x-3
Which of the following is equal to -18
Step-by-step explanation:
9i√2
-18
so therefore the answer is 9i√2
Coefficient of y in the equation: 3(2x -1/3y) = 0 is equal to a) 3 b) 1 c)-3 d)-1
Answer:
d is the right answer because the coefficient of y is 3*(-1/3) which results -1 so d is the right answer
The coefficient of y in the given equation is 1. Therefore, option B is the correct answer.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is 3(2x -1/3y)=0.
Now, 6x-1/y=0
A numerical or constant quantity placed before and multiplying the variable in an algebraic expression.
Here, coefficient of y is 1.
Therefore, option B is the correct answer.
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Engineering
When p= 3, q. I and r. 2, the
expression 2p² q3 is equal to
Answer:
[tex]{ \tt{2 {p}^{2} {q}^{3} }} \\ = { \tt{ {2(3)}^{2} . {(1)}^{3} }} \\ = 18[/tex]
Each pizza shown is broken up into different sized slices, but they are all equivalent.
Come up with another ratio of pizza slices that is equivalent to all of these pizzas.
!!! I need help with this question !!! I tried using the standard deviation formula but my answers are wrong. Can someone please help me! Thank you for your help!
Answer:
Step-by-step explanation:
I need help with this
bing jhwwjwiwisisuwuwywywywfsfsahajai
JK=8x+6 KL=6x+20 find JL
Answer:
14x + 26
Step-by-step explanation:
JL = JK + KL
= 8x + 6 + 6x + 20
= 8x + 6x + 6 + 20
JL = 14x + 26
Solve the following equation. for x
7x - 2 < 10
Step-by-step explanation:
7x < 10+2
7x<12
x < 12/7
Hope this helps!
Answer:
[tex]7x-2<10[/tex][tex]7x-2+2<10+2[/tex][tex]7x<12[/tex][tex]\frac{7x}{7}<\frac{12}{7}[/tex][tex]x<\frac{12}{7}[/tex]OAmalOHopeO
Help ASPPP!!!
Name a point that is represented on this graph. Use an ordered pair to give your answer. (Hint:
Look at the shaded region)
Answer:
(-5, -9)
Step-by-step explanation:
From the graph shown, the perfect ordered pair represented on the graph occurs when x = -5, y = -9. Therefore the required coordinate could be (-5, -9)
Dutchess County, New York, has been experiencing a mean of 35.4 motor vehicle deaths each year. If D = the number of vehicle deaths in Dutchess County in a year, what is the distribution for D (Binomial or Poisson) Explain.
Answer:
Poisson, as we have the mean number and not a proportion.
Step-by-step explanation:
We have the mean number of vehicle deaths per year, thus, since it is a mean and not a proportion, we use the Poisson distribution.
If we were working with the proportion of accidents that end in death for example, or any other proportion, it would be a binomial random variable.
please help me its timed -H.M
Answer:
f(3) = g(3)
General Formulas and Concepts:
Algebra I
Functions
Function NotationGraphingStep-by-step explanation:
We can see from the graph that the lines intersect at (3, 6). If this is the case, then that means that when x = 3 for both functions, it outputs f(x) = 6.
Rewriting this in terms of function notation:
f(3) = 6, g(3) = 6
∴ f(3) = g(3)
The mortgage on your new house is $180,000. Your monthly mortgage payment is $839 for 30 years. How much interest will be paid if the house is kept for the full 30 years?
9514 1404 393
Answer:
$122,040
Step-by-step explanation:
The interest is the difference between the mortgage value and the total amount paid.
($839/mo)×(12 mo/yr)×(30 yr) -180,000 = $302,400 -180,000 = $122,040
$122,040 will be paid in interest.
Find the mean for the data items
Answer:
4.5
Step-by-step explanation:
Given the data :
Score, x ____: 1, 2, 3, 4, 5, 6, 7, 8
Frequency, F : 1, 5, 1, 4, 4, 1, 5, 1
This is a grouped data: The mean of a grouped data is given as :
Mean (xbar) = ΣFx / ΣF
ΣFx = (1*1)+(2*5)+(3*1)+(4*4)+(5*4)+(6*1)+(7*5)+(8*1) = 99
ΣF = (1+5+1+4+4+1+5+1) = 22
Mean (xbar) = ΣFx / ΣF = 99 / 22 = 4.5
Consider a uniform density curve defined from x = 0 to x = 8. What percent of observations fall between 1 and 5?
a) 0.20
b) 0.50
c) 0.62
d) 0.13
e) 0.63
f) None of the above
Answer: 0.50, which is choice b
Explanation:
The interval [tex]1 \le x \le 5[/tex] covers 5-1 = 4 units in the horizontal direction.
This is out of 8 units that span from x = 0 to x = 8 (we could say 8-0 = 8).
So we get the final result of 4/8 = 0.50
In other words, the interval from x = 1 to x = 5 covers exactly half of the interval from x = 0 to x = 8.
Which is the graph of the following inequality
Answer:
graph a is the correct answer
Step-by-step explanation:
The width of a rectangle measures (7k-2m)(7k−2m) centimeters, and its length measures (5k-m)(5k−m) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
Answer:
[tex]P = 24k-6m[/tex]
Step-by-step explanation:
The correct expressions are:
[tex]W = 7k - 2m[/tex]
[tex]L = 5k - m[/tex]
Required
The perimeter (P)
This is calculated as:
[tex]P = 2 *(L + W)[/tex]
So, we have:
[tex]P = 2 *(5k - m + 7k -2m)[/tex]
Collect like terms
[tex]P = 2 *(5k + 7k- m -2m)[/tex]
[tex]P = 2 *(12k-3m)[/tex]
Open bracket
[tex]P = 24k-6m[/tex]
The height of Mt.Whitney is approximately 14,490 feet. What is a rounded form of this number written in scientific notation?
Which of the following is graphed below?
