[tex]\dfrac{x!-(x-3)!}{23}=1\\x!-(x-3)!=23\\(x-3)!((x-2)(x-1)x-1)=23\\(x-3)!((x^3-x^2-2x^2+2x)-1)=23\\(x-3)!((x^3-3x^2+2x)-1)=23[/tex]
23 is a prime number, therefore there are two possibilities:
[tex]\text{I.}\, (x-3)!=1 \wedge x^3-3x^2+2x-1=23[/tex]
or
[tex]\text{II.}\, (x-3)!=23 \wedge x^3-3x^2+2x-1=1[/tex]
[tex]\text{I.}\\(x-3)!=1\\x-3=0 \vee x-3=1\\x=3 \vee x=4[/tex]
Now, we check if any of these solutions is also a solution to the second equation:
[tex]3^3-3\cdot3^2+2\cdot3-1=23\\27-27+6-1-23=0\\ -18=0[/tex]
Therefore, 3 is not a solution.
[tex]4^3-3\cdot4^2+2\cdot4-1=23\\64-48+8-1-23=0\\0=0[/tex]
Therefore, 4 is a solution.
[tex]\text{II.}[/tex]
[tex](x-3)!=23[/tex]
We know that [tex]3!=6[/tex] and [tex]4!=24[/tex], therefore there isn't any [tex]n\in\mathbb{N}[/tex], for which [tex]n!=23[/tex], so there's no solution.
So, the only solution is [tex]x=4[/tex].
NEED HELP!!!!!!!!!!!!!!!!!!!!!!
Answer:
The third answer
Step-by-step explanation:
if p is equivalent to q then q must be equivalent to p. I’m not 100% sure but that’s my best guess. I hope this helps :)
What is the product of (x² + x + 2) and (x² − 2x + 3)
Answer:
[tex]x^4-x^3+3x^2-x+6[/tex]
Step-by-step explanation:
Multiply each term in the first equation by all the terms in the second and add them together.
help awdaWdawdadawdaWDaSwdaWDawdas
Answer:maybe c or d??
Step-by-step explanation:
3. Measure the length of each leg and
the hypotenuse of this triangle:
AD =
units
AE=
units
DE=
units
Correct!
Check
The length of each leg and the hypotenuse of this triangle will be:
AD = 2 units.
AE = 2 units.
DE = 2.8 units
How to compute the hypotenuse?From the information given and the attached diagram, the value or AD and AE are 2 units respectively.
The value of DE will be calculated as the square root of 2² + 2². This will be:
= 2² + 2² = 8
= ✓8 = 2.8
Therefore, the correct options are 2, 2, and 2.8 units.
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Solve the compound inequality. Graph the solution set and write it in interval notation. x<2 and x>-3
Answer:
Answer is (-3, 2)
Two numbers are in the ratio 3:8.
The larger number is 96, find the
sum of the numbers
Answer:
The sum of the numbers is 132
Step-by-step explanation:
First find the smallest number
3/8=x/96 2(96)=8x 288=8x x=36Thus, you found the smallest number
then there sum given as 96+36=132
Use the given sample data to find Q3.
49 52 52 52 74 67 55 55
The given sample data the Q3=61
We begin by ordering the data from smallest to largest.
Next, find the median of the data.
The data set has 8 values, so the two middle values are 52 and 55.
49 52 52 52 55 55 67 74
What is the formula for the median?Median = (52 + 55) / 2
Median= 53.5
The third quartile (Q3) is the 25th percentile or the median of the upper half of the data.
To find the median of all the values that lie above 53.5.
Q3 = (55 + 67)/ 2
Therefore the Q3=61
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2x-3<1 or 3x-1<17
Solve compound inequality
The union consists of all of the elements that are contained in each interval.
Inequality Form:
x<6
Interval Notation:
(−∞,6)
Pleas help me please i dont know what this question is
Answer:
A = 6
B = 1
C = 14
Step-by-step explanation:
A = 25 - 19 = 6
B = 6 - 5 = 1
C = 19 - 5 = 14
give brainliest please! <3
Given: angle 2 and angle 4 are vertical. Prove angle 2 congruent to angle 4
Need help quick!
The diagram shows that ∠2 and ∠4 are the vertical angles.
What are vertical angles?Vertical angles are the angles that are opposite of each other when two lines cross.
The statements are:
1. < 2 & < 4 are vert. angles
2. Lines M & N intersect at P
3. < 2 & < 3 are a linear pair
4. m < 2 + m < 3 = 180
5. <3 and < 4 are a linear pair
6. m < 3 + m <4 =180
7. m < 2 + m < 3 = m < 3 + m < 4
8. m < 2 = m < 4
9. < 2 =~ <4
Here are the reasons:
1. Given
2. Def of vertical angles.
3. Def of. Linear pair
4. Angle addition postulate
5. Def of a linear pair
6. Angle addition postulate
7. Substitution property
8. Subtraction property
9. Def of =~ angles.
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Answer: View the picture below!
Step-by-step explanation: Just did the assignment!
the density of some steel is7.98gm/cc.how much does 60cc weigh?
Substituting into the formula d=m/v,
[tex]7.98=\frac{m}{60}\\\\m=\boxed{478.8 \text{ gm}}[/tex]
Of all awarded prizes, 10% are worth $1000, 20% are worth $100, and 70% are worth $10. Find the expected winnings if you purchase a single ticke
Answer:
$127
Step-by-step explanation:
[tex](.10 \times 1000) + (.20 \times 100) + (.70 \times 10) = 100 + 20 + 7 = 127[/tex]
Make d the subject of the formula h=d/3+2
Which represents a quadratic function?
f(x) = 2x³ + 2x² - 4
f(x) = -7x²-x+2
f(x)=-3x + 2
f(x) = 0x² + 3x-3
Option B is correct, the function f(x) = -7x² - x + 2 represents a quadratic function
What is quadratic equation?A quadratic function is a polynomial function of the form f(x) = ax² + bx + c, where a, b, and c are constants and a is not equal to zero.
f(x) = -7x² - x + 2 is a quadratic function because it is of the required form.
Specifically, it has a quadratic term (-7x²), a linear term (-x), and a constant term (2).
The other three functions do not have a quadratic term and thus are not quadratic functions.
f(x) = 2x³ + 2x² - 4 is a cubic function because it has a cubic term (2x³).
f(x) = -3x + 2 is a linear function because it has only a linear term (-3x) and a constant term (2).
f(x) = 0x² + 3x - 3 is also a linear function because it has no quadratic term and only a linear term (3x) and a constant term (-3).
Hence, the function f(x) = -7x² - x + 2 represents a quadratic function
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Michael went to the game store there was so much games he wanted and if one of them was $42.29 and the other one was $87.99 and he had $142 how much would he have left
Answer:
$11.72
Step-by-step explanation:
Add: $42.29 + $87.99 = $130.28
Subtract: $142 - $130.28 = $11.72
Answer:
he would have spent 131.08 dollars meaning he has 11.72 dollars left.
Step-by-step explanation:
what is the simplified equivalent of the terminating
The simplified fractional equivalent of 0.25 is 1/4 .
The complete question is
What is the simplified fractional equivalent of the terminating decimal 0.25?
What is simplified equivalent ?When a number is solved to a state where it cannot be further simplified , but can be written in a different format , the two numbers are then called the simplified equivalent of each other.
The given number is decimal 0.25
So this number is in its simplified state but can also be written as
0.25 * 1
= 0.25 * 100 /100
= 25/100
= 1/4
Therefore 1/4 is the simplified fractional equivalent of 0.25.
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Homework:Section 5.3 Homework
Question 5, 5.3.21
Part 1 of 2
HW Score: 50%, 4 of 8 points
Points: 0 of 1
Question content area top
Part 1
In airline applications, failure of a component can result in catastrophe. As a result, many airline components utilize something called triple modular redundancy. This means that a critical component has two backup components that may be utilized should the initial component fail. Suppose a certain critical airline component has a probability of failure of 0.0056 and the system that utilizes the component is part of a triple modular redundancy.
(a) Assuming each component's failure/success is independent of the others, what is the probability all three components fail, resulting in disaster for the flight?
(b) What is the probability at least one of the components does not fail?
The probability that all three components fail is 1.756 × 10⁻⁷. The probability of at least one of the components does not fail 0.9999998244.
What is a Probability?Probability is the likelihood for an event to occur. In a given statistical distribution, the probability explains the range of values and probabilities that a randomized variable could have.
From the given information;
Assuming each component's failure/success is independent of the others: the probability that all three components fail is:
P(three components fail) = (0.0056)^3
P(three components fail) = 1.756 × 10⁻⁷
The probability that at least one does not fail is:
P(at least one does not fail) = 1 - P(all three components fail)
P(at least one does not fail) = 1 - 1.756 × 10⁻⁷
P(at least one does not fail) = 0.9999998244
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How does understanding of 5 x 12 = 60 help to solve for the product of 5
x 120? Explain in words
Answer:
c6
Step-by-step explanation:
justjustcancacanjustadda0totheproduct of5cxwewtogetthesameresultasx1totoandtimes
3) Number: 640,700
the value of 4 in this number is 40,000
Number: 64,070
the value of 4 in this number is 4,000
So, times greater: 40,000 ÷ 4,000 = 10 times greater.
4)
The multiplication, 5 × 12 = 60. So, 5 × 120 = 600.
There is an extra zero at the very last of the result as '120' was multiplied with 5 instead of '12' which does not have zero at last which changes the result.
Similar cases with: 5 × 10 = 50. So, 5 × 100 = 500.
Inside the box of every cereal box contains a surprise gift. The store manager assures employees that 18 of the 48 boxes on the shelf have a secret decoder ring and inside the other 30 boxes on the shelf contain a different gift. If two cereal boxes are randomly selected from the shelf to purchase, what is the probability that both of them have the secret decoder ring? (Give answer as a decimal correct to least three decimal places.)
The probability that both of them have the secret decoder ring will be 0.1356.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
Inside the box of every cereal box contains a surprise gift.
The store manager assures employees that 18 of the 48 boxes on the shelf have a secret decoder ring.
And inside the other 30 boxes on the shelf contain a different gift.
If two cereal boxes are randomly selected from the shelf to purchase.
Then the probability that both of them have the secret decoder ring will be
The total events will be
Total event = ⁴⁸C₂
Total event = 1128
The favorable events will be
Favorable event = ¹⁸C₂
Favorable event = 153
Then the probability will be
P = 153 / 1128
P = 0.1356
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which system of the equation is represents by the graph?
Graph the equation.
Y= - 3/2x
Answer:
Step-by-step explanation:
(1)
Mrs Tan had $3756 to spend on furniture. She bought a sofa set for $1195 and 6 chairs at $128 each.
(a) How much did she spend altogether?
(b) How much money did she have left?
(Marshall Cavendish/ Pupil's book My Pals Are Here! Maths 4A 3rd Edition)
HELP!Which linear function represents the line given by the point-slope equation y - 2 = 4(x − 3)? Of(x) = 6x-1 Of(x) = 8x-6 Of(x) = 4x - 14 Ofix) = 4x - 10 Which linear function represents the line given by the point - slope equation y - 2 = 4 ( x − 3 ) ? Of ( x ) = 6x - 1 Of ( x ) = 8x - 6 Of ( x ) = 4x - 14 Ofix ) = 4x - 10
[tex]y-2=4(x-3)\\\\y-2=4x-12\\\\y=4x-10\\\\\boxed{f(x)=4x-10}[/tex]
Large eggs weigh 1/1/2 pounds per dozen. Dawn bought eight large eggs. How much did the eggs weigh
Answer: 1 pound
Step-by-step explanation:
Because 12 eggs= 1.5 pounds. So, you divide 1.5/12 = 0.125. And the 0.125 times 8 = 1 pound
Answer:
1 lb
Step-by-step explanation:
Since 1 dozen(12) eggs weigh 1 1/2 or 3/2 lbs, each egg weights 3/2 ÷ 12 = 3/24 lb
So 8 eggs would weight 8 x 3/24 = 1 lb
Translate to an equation then solve the equation. Seven times the difference of some number and 2 amounts to the quotient of 196 and 14. (Type the question using x as the variable. Do not simplify.) x= ____
Answer:
x = 4
Step-by-step explanation:
7 * ( x-2) = 196/14
7x -14 = 14
7x = 28
x = 4
solve the following inequality:
ALGEBRA 1
Answer:
[tex]m \leqslant 10 \: or \: m > 4[/tex]
Step-by-step explanation:
[tex] \frac{m - 2}{3} \leqslant - 4 \\ \frac{m - 2}{3} \times 3 \leqslant - 4 \times 3 \\ m - 2 \leqslant - 12 \\ m - 2 + 2 \leqslant - 12 + 2 \\ m \leqslant 10[/tex]
OR
[tex]3m - 8 > 4 \\ 3m - 8 + 8 > 4 + 8 \\ 3m > 12 \\ \frac{3m}{3} > \frac{12}{3} \\ m > 4 [/tex]
Solve the quadratic equation numerically (using tables of x- and y- values). x squared + 7 x + 12 = 0 a. x = -1 or x = -1 c. x = -3 or x = -3 b. x = -4 or x = -3 d. x = 2 or x = -1 Please select the best answer from the choices provided
Answer:
b. x = -4 or x = -3
Step-by-step explanation:
[tex]x^{2} +7x+12[/tex]
To factor this, come up with two numbers that can be multiplied together to get 12, but add to get 7.
We get 4 and 3.
4 + 3 = 7
4 x 3 = 12
Now we can factor with these two numbers:
[tex](x+4)(x+3) = 0[/tex]
Now, solve for x by separating the factors:
[tex]x + 4 = 0[/tex]
[tex]x = -4[/tex]
And,
[tex]x + 3 = 0[/tex]
[tex]x = -3[/tex]
So, the answers are -4 and -3.
Describe the graph of a quadratic function below given in table form
3 is less than w and 9 is greater than w
The complete question is
"Write the inequality when 3 is less than w and 9 is greater than w."
The inequality become as 3 < w < 9.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
Given information ;
when 3 is less than w and 9 is greater than w.
Thus, the inequality will be ;
3 < w < 9
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A triangle with side lengths a, b, and c is shown below.
Which statement about the side lengths must be true?
A a+b>c
B b+c
C a+b
D a+c
The statement about the sides must respect to represent a triangle is given as follows:
A. a + b > c.
What is the condition for 3 lengths to represent a triangle?In a triangle, the sum of the lengths of the two smaller sides has to be greater than the length of the greater side.
The smaller sides for the triangle are given as follows:
a and b.
Hence the statement is:
a + b > c.
(as the sum of the lengths of the smaller sides a and b must be greater than the length of the larger side, which is of c).
Hence the correct statement is given by option A.
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