The question is about finding the total count of possible 5-digit numbers that either has identical adjacent digits or differ from its neighbor digits by exactly 1 and containing at least one 5. Providing an exact solution without knowing students' pre-existing knowledge on the subject can be difficult. This kind of problem typically involves methodologies like recursive relationships.
Explanation:This question pertains to combinatorics, a topic in mathematics that deals with countable structures. Specifically, the question is asking how many five-digit numbers are there that follows the conditions given in the question.
The condition that the number contains the digit 5 is applicable for both the cases where the digit is the same as or differs by 1 from its neighbors. This is because 5 is a middle digit from 0 to 9, and it can satisfy both conditions.
The problem can be approached by finding the total count of five digit numbers that satisfy just the adjacent difference conditions, and then subtracting the count of such numbers that do not contain the digit 5.
However, providing a step-by-step solution to this problem would be complex and lengthy, especially without the proper context of the student's pre-existing knowledge. The method to solve it would involve recursive relationships and possibly programming or usage of a suitable mathematical software.
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7x - 7 = 126 what is x
Answer:
19
Step-by-step explanation:
7x-7=126
add+7 to 126 and you will get 133
7x/133
x=19
Answer:
x = 19
Step-by-step explanation:
7x - 7 = 126
Add 7 to each side
7x - 7+7 = 126+7
7x = 133
Divide each side by 7 to isolate x
7x/7 = 133/7
x = 19
Casie jumped off of a cliff into the ocean while on vacation. Her height as a function of time is modeled by the equation h = −16t2 +16t + 140, where t is the time in seconds and h is the height in feet. How long does it take Casie to hit the water?
Find the volume of the rectangular prism. Use the dimensions shown.
NEED HELP ASAP!!!!!
Answer:
The Volume is 660^3.
Step-by-step explanation:
The formula is Length * Width * Height.
22 * 5 * 6 = 660 and its volumed so the units is cubed.
Hence volume of rectangular prism is 660[tex]cm^{2}[/tex]
What is Rectangular prism?A hexahedron? rectangular prism, or six-faced solid, is a cuboid in geometry. It has quadrilateral faces. "Cuboid" implies "like a cube," in the sense that a cuboid can be turned into a cube by altering the length of the edges or the angles between edges and faces.
How to solve?Volume of cuboid =LBH
where L= length, B=breadth, H=Height
Hence volume = 22*5*6
=660[tex]cm^{2}[/tex]
Hence volume of rectangular prism is 660[tex]cm^{2}[/tex]
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What is the common difference between the elements of the arithmetic sequence below?
–18, –22.5, –27, –31.5, –36
Answer:
-4.5Step-by-step explanation:
-22.5-(-18)=-4.5
-27-(-22.5)=-4.5
-31.5-(-27)=-4.5
then the common difference is -4.5
Answer: -4.5
Step-by-step explanation:
It is the most common difference.
The expected rainfall, in inches, for a city for the month of July is given by the inequality |x − 4.25| ≤ 0.15. Find the city’s expected maximum and minimum rainfall amounts.
The minimum rainfall expected is ______
inches, and the maximum rainfall expected is ______
inches.
Answer:
4.1 ; 4.4
Step-by-step explanation:
For min:
x - 4.25 = -0.15
x = 4.1
For max:
x - 4.25 = 0.15
x = 4.4
Answer:
The minimum rainfall expected is 4.1 inches, and the maximum rainfall expected is 4.4 inches.
Step-by-step explanation:
#platofam
How do you find the equality of 4/12=A/3
Answer:
A = 1
Step-by-step explanation:
[tex] frac. \: \frac{4}{12} = \frac{a}{3} [/tex]
[tex] \frac{ \: \: \: 4 \: \div \: x \: = \: a}{12 \: \div \: x \: = \: 3} [/tex]
[tex] \frac{ \: \: 4 \: \div \: x \: = \: a}{12 \: \div \: 4 \: = \: 3} [/tex]
[tex] \frac{ \: \: 4 \: \div \: 4 \: = \: a}{12 \: \div \: 4 \: = \: 3} [/tex]
[tex] \frac{ \: \: 4 \: \div \: 4 \: = \: 1}{12 \: \div \: 4 \: = \: 3} [/tex]
[tex] a= 1[/tex]
Given that the volume of a cylinder is 720 pi m^3, find the radius of the cylinder if the height is 5 m. What is the radius?
Answer:
12m
Step-by-step explanation:
720 pi = pi × r² × 5
720 = 5r²
r² = 144
r = 12 meters
19. 54 is what percent of 135
Answer:
Step-by-step explanation:
Solve for x. x^2−9=16
Answer:
x=5 or x=-5
Step-by-step explanation:
either one of those
x2−9=16
Step 1: Add 9 to both sides.
x2−9+9=16+9
x2=25
Step 2: Take square root.
x=±25
x=5 or x=−5
Find the value of each trigonometric ratio
The value of each trigonometric ratio is
[tex]$\sin A=\frac{15}{17}, \ \cos A=\frac{8}{17}, \ \tan A =\frac{15}{8}[/tex]
[tex]$\csc A=\frac{17}{15}, \ \sec A=\frac{17}{8}, \ \cot A =\frac{8}{15}[/tex]
Solution:
The given triangle is right triangle.
AC (hypotenuse) = 34, AB (adjacent) = 16, BC (opposite) = 30
To find the trigonometric ratios:
Using trigonometric formulas for right triangle,
[tex]$\sin \theta=\frac{\text { opposite }}{\text { hypotenuse }}[/tex]
[tex]$\sin A=\frac{BC}{AC}[/tex]
[tex]$\sin A=\frac{30}{34}=\frac{15}{17}[/tex]
[tex]$\cos \theta=\frac{\text { adjacent }}{\text { hypotenuse }}[/tex]
[tex]$\cos A=\frac{AB}{AC}[/tex]
[tex]$\cos A=\frac{16}{34}=\frac{8}{17}[/tex]
[tex]$\tan \theta=\frac{\text { opposite }}{\text { adjacent }}[/tex]
[tex]$\tan A=\frac{BC}{AB}[/tex]
[tex]$\tan A=\frac{30}{16}=\frac{15}{8}[/tex]
[tex]$\csc A =\frac{1}{\sin A}[/tex]
[tex]$\csc A =\frac{17}{15}[/tex]
[tex]$\sec A =\frac{1}{\cos A}[/tex]
[tex]$\sec A =\frac{17}{8}[/tex]
[tex]$\cot A =\frac{1}{\tan A}[/tex]
[tex]$\cot A =\frac{8}{15}[/tex]
Hence the value of each trigonometric ratio is
[tex]$\sin A=\frac{15}{17}, \ \cos A=\frac{8}{17}, \ \tan A =\frac{15}{8}[/tex]
[tex]$\csc A=\frac{17}{15}, \ \sec A=\frac{17}{8}, \ \cot A =\frac{8}{15}[/tex]
Four times What divided by two equals 5.2
My answer was wrong sorry
Answer:
Step-by-step explanation:
2.6 becuase 4a/2= 5.2
4a=10.4
a=2.6
If x^2 = 7, what is the value of x?
Step-by-step explanation:
[tex] {x}^{2} = 7 \\ \\ \implies \: x = \sqrt{7} \\ \\ \implies \: x = 2.65[/tex]
What is the slope of the line.
Answer:
The slope is 2
Step-by-step explanation:
The slope of the line is change in y over change in x.
The formula is: [tex]\frac{y2-y1}{x2-x1}[/tex]
Step 1: Identify the two points
(x1, y1) -> (0, 0)
(x2, y2) -> (1, 2)
Step 2: Plug into the equation
The formula is: [tex]\frac{y2-y1}{x2-x1}[/tex]
Slope = [tex]\frac{2 - 0}{1-0}[/tex]
Slope = 2/1
Slope = 2
Answer: The slope is 2
Translate the sentence into an inequality.
The sum of a number times 9 and 30 is at least - 15
Use the variable c for the unknown number.
[tex]9x +30\geq 30[/tex]
Solution:
Given that,
Translate the sentence into an inequality
The sum of a number times 9 and 30 is at least - 15
Let "c" be the unknown variable
"at least" means "greater than or equal to"
From given,
sum of a number times 9 and 30 = 9x + 30
Which means,
[tex]9x +30\geq 30[/tex]
Thus the given sentence is translated into inequality
The sentence 'The sum of a number times 9 and 30 is at least - 15' can be translated into the inequality
[tex]9c + 30 \geq -15[/tex]Explanation:The sentence 'The sum of a number times 9 and 30 is at least - 15' can be translated into an inequality by first recognizing the mathematical operations being described. The phrase 'a number times 9' is multiplication, so let's represent this number with the variable c. Thus, this part is 9c. The word 'sum' represents addition. Finally, 'is at least' indicates that the sum is greater than or equal to a particular value (-15 in this case).
Putting these elements together, we get the inequality
[tex]9c+30\geq -15[/tex]This is the inequality that represents the sentence.
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A plastic storage bin is shaped like a rectangle or prism. The height of the band is 9 inches. The bottom of the band has an area of 180 in.². What is the volume of the storage bin
Answer:
v = 1620 ^3
Step-by-step explanation:
If the area of the bottom is 180 sq in and the height is 9 in then this is how you would solve the problem.
To get area of the volume is l * w * h
Because of the associative property we can do this in any order we want
If we know that l * w is 180, then all we have to do is multiply 180 by 9
180 * 9 = 1620
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Answer:
Part 1) The volume of the storage body is 576 cubic feet
Part 2) To find out how many boxes can she fit in the storage body, divide the volume of the storage body by the volume of each box
Part 3) Sheila can fit 64 boxes into the truck
Step-by-step explanation:
step 1
Find the volume of the storage body
we know that
The volume of the of the storage body is equal to the volume of two rectangular prism
The volume of a rectangular prism is equal to
[tex]V=LWH[/tex]
First rectangular prism (top)
[tex]V=(15)(6)(8-6)=180\ ft^3[/tex]
Second rectangular prism (bottom)
[tex]V=(15-4)(6)(6)=396\ ft^3[/tex]
The volume of the storage body is
[tex]V=180+396=576\ ft^3[/tex]
step 2
we know that
To find out how many boxes can she fit in the storage body, divide the volume of the storage body by the volume of each box
step 3
substitute the given values
[tex]\frac{576}{9}= 64\ boxes[/tex]
therefore
Sheila can fit 64 boxes into the truck
Solve the equation:-|b+4|-1=10
Step-by-step explanation:
[tex]|b + 4| - 1 = 10 \\ \\ \therefore \:|b + 4| = 10 + 1 \\ \\ \therefore \:|b + 4| = 11 \\ \\ \therefore \:b + 4 = \pm \: 11 \\ \\ \therefore \:b + 4 = 11 \: \: or \: \: b + 4 = - 11 \\ \\ \therefore \:b = 11 - 4 \: \: or \: \: b = - 11 - 4 \\ \\ \therefore \:b = 7 \: \: or \: \: b = - 15 \\ \\ \therefore \:b = \{ - 15, \: \: 7 \}[/tex]
what is -2 3/4 divided by -1 1/2
Exact Form:
−11/6
Decimal Form:
−1.83
Mixed Number Form:
−1 5/6
If h hours and 30 minutes is equal to 450 minutes,
what is the value of h?
Answer:
h = 7
Step-by-step explanation:
1 hour = 60 mins
h hours = 60h mins
60h + 30 = 450
60h = 420
h = 7
Answer:7
Step-by-step explanation:
h+30=450
h=450-30
h=420minutes
But 1hour=60minutes
Therefore 420minutes=420/60 hour =7hours
at age 27, jill deposited $4,000 into an ira, where it earns 9.8% interest compounded monthly. what will it be worth when she is thirty-five?
The amount when she is 35 is $8,733.01221.
Given that,
The deposited amount is $4,000.The rate of interest is 9.8%.The time is 8 years.Based on the above information, the calculation is as follows:
[tex]= \$4,000 \times (1 + 9.8\%\div 12)^{8\times 12}\\\\= \$4,000 \times (12.098\div 12)^{96}[/tex]
= $8,733.01221
Therefore we can conclude that The amount when she is 35 is $8,733.01221.
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Final answer:
At age 35, Jill's IRA investment, which started with a $4,000 deposit at age 27 and earns 9.8% interest compounded monthly, will be worth approximately $8,159.55.
Explanation:
To determine the future value of Jill's IRA investment, we will use the formula for compound interest, which is A = [tex]P(1 + \(\frac{r}{n}\))^n^t[/tex], where:
P is the principal amount (the initial amount of money)
r is the annual interest rate (decimal)
n is the number of times that interest is compounded per year
t is the time the money is invested for in years
A is the amount of money accumulated after n years, including interest.
In Jill's case, she deposited $4,000 into an IRA at age 27, and we want to find out what it will be worth when she is 35. The annual interest rate is 9.8%, but since it is compounded monthly, we will have to convert this to a monthly rate and adjust the time accordingly
The steps to solve for the amount A are as follows:
Convert the annual interest rate to a decimal: 9.8% = 0.098
Find the monthly interest rate by dividing the annual rate by 12: \[tex](\frac{0.098}{12}\)[/tex]
Calculate the number of years money is invested: 35 - 27 = 8 years
Find the number of times interest is compounded: 12 months/year × 8 years
Use the compound interest formula to calculate A.
Now, let's do the math:
P = $4,000
r = 0.098 / 12
n = 12
t = 8
A = 4000(1 + [tex]\(\frac{0.098}{12}\))^(12\(\times\)8)[/tex]
Using a calculator we get:
A = $4000(1 + 0.0081667)⁹⁶
A = $4000(1.0081667)⁹⁶
A = $4000 [tex]\(\times\)[/tex] 2.0398873
A ≈ $8,159.55
Therefore, at age 35, Jill's IRA investment will be worth approximately $8,159.55.
To the nearest tenth, find the area of
a circle with d= 8 km. Use 3.14 for pi
Answer:
25.1
Step-by-step explanation:
the formula for the area of a circle is A=3.14(pi)r² or A=3.14(pi)d
r = radius d = diameter
so
a = 3.14d
a= (3.14)(8)
a= (25.12) rounded to the nearest tenth = 25.1
hope this helps
welppp fastttt!!!!!!!!!!!!!!!!!!
Answer: B
Step-by-step explanation:
Grade must be greater than or equal to 88
Answer:
The answer for this is B
What is this limit? Without using lopital rule
Answer:
60.
Step-by-step explanation:
(x^2 - 25) / (√(x + 4) - 3).
We rationalise the expression by multiplying top and bottom of the fraction by the complement of the denominator.
That is by (√(x + 4) + 3):
(x^2 - 25)(√(x + 4) + 3)
= ------------------------------------
(√(x + 4) - 3)(√(x + 4) + 3)
= (x + 5)(x - 5)(√(x + 4) + 3)
----------------------------------
(x - 5)
= (x + 5)(√(x + 4) + 3).
The limit as this---> 5
is (5 + 5)(√(5 + 4) + 3)
= 10 * 6
= 60.
please help me again
Answer:
y = 10
Step-by-step explanation:
Since all sides are equal, that means all angles are 60 degrees. 60 + 60 + 60 = 180
5y + 10 - 10 = 60 - 10
5y / 5 = 50 / 5
y = 10
Answer: y = 10
can somebody tell me the answer to -5/8 - 3/4
Step-by-step explanation:
= -5/8-3/4
= -5-6/8
= -11/8
Answer:-11/8
Step-by-step explanation:
HELP PLEASEEE I really need it I’m stuck and don’t know the answer
Answer:
.3-.6 ; 0-.6 ; .1-.3 ; 0-.3 ; 0-.1
Step-by-step explanation:
The "points" are:
(0,96.44), (.1,97.6), (.3, 98.57), and (.6, 98.3)
The "rate of change" is the slope. This means that the change from...
0-.1 is (97.6-96.44)/.1 = 1.16/.1= 11.6
0-.3 is (98.57-96.44)/.3 = 2.13/.3 = 7.1
0-.6 is (98.3-96.44)/.6 = 1.86/.6 = 3.1
.1-.3 is (98.57-97.6)/.2 = .97/.2 = 4.85
.3-.6 is (98.3-98.57)/.3 = -.27/.3 = -.9
Which equation demonstrates the multiplicative identity property?
O (-3+5)+1=-3+57
O (-3+5)(1)=-3+5;
O (-3+5)(-3+5)=-16-30;
(-3+5)(3-5) = 16+30;
Answer:
(-3+5)(1)=-3+5
Step-by-step explanation:
The multiplicative identity is 1.
The multiplicative identity property days that, if you multiply a real number by 1, that result is the same real number.
This is demonstrated in option B of the given alternatives, where we have:
[tex]( - 3 + 5)(1) = - 3 + 5[/tex]
The multiplication by did not change b the value.
Anyone knows how to do this
Answer:
length = x - 2
Step-by-step explanation:
The area (A) of a rectangle is calculated as
A = length × width
Here A = x² - 7x + 10 and width = x - 5
x² - 7x + 10 = length × (x - 5) ← divide both sides by (x - 5)
length = [tex]\frac{x^2-7x+10}{x-5}[/tex] ← factor the numerator
= [tex]\frac{(x-5)(x-2)}{x-5}[/tex] ← cancel common factor (x - 5) on numerator/ denominator
= x - 2
Thus length = x - 2 metres
Find the equation of the axis of symmetry for this function
F(x)= 5x^2 - 3x + 5
Answer:
x = [tex]\frac{3}{10}[/tex]
Step-by-step explanation:
Given a quadratic in standard form, ax² + bx + c : a ≠ 0
Then the axis of symmetry is a vertical line with equation x = h
where h is the x- coordinate of the vertex.
The x- coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
f(x) = 5x² - 3x + 5 ← is in standard form
with a = 5 and b = - 3, thus
[tex]x_{vertex}[/tex] = - [tex]\frac{-3}{10}[/tex] = [tex]\frac{3}{10}[/tex]
Thus the equation of the axis of symmetry is x = [tex]\frac{3}{10}[/tex]
what is a reflex angle
Answer:
an angle that is larger than 180 degrees but is smaller than 360 degrees
Answer:
A reflex angle is any angle larger than 180 degrees and smaller than 360 degrees.
Step-by-step explanation:
Angle one is the Angle of incidence, Angle two is the Angle of reflection, and Angle one is equal to Angle two.