Answers
Answer:
a) 2x² - x + 3 = x(2x + 1) - 2x
<=> 2x² - x + 3 = 2x² + x - 2x
<=> 3 - x = - x
<=> 3 = 0
=> no solution
b) x/2 - x/3 - x/4 = 1/12
[tex] \frac{6x}{12} - \frac{4x}{12} - \frac{3x}{12} = \frac{1}{12} \\ \\ \frac{ - x}{12} = \frac{1}{12} \\ \\ = > - x = 1 \\ \\ \\ < = > x = 1[/tex]
=> the euqation has the solution x = 1
c) |x - 5| = 2|x|
=> x - 5 = 2x
or x - 5 = -2x
<=> x = -5
or 3x = 5
<=> x = -5
x = -5or x = 5/3
d) defined conditions: 2 - x 》 0
<=> x 《 2
we have:
[tex] \sqrt{x + 4} = 2 - x \\ < = > x + 4 = (2 - x) {}^{2} \\ < = > x + 4 = {x}^{2} - 4x + 4 \\ < = > {x}^{2} - 5x = 0 \\ < = > x(x - 5) = 0 \\ [/tex]
<=> x = 0 (because x 《 2)
e)
[tex] \sqrt{5} = \frac{1}{25 {}^{x} } \\ = > 5 = \frac{1}{25 {}^{2x} } \\ < = > 5.25 {}^{2x} = 1 \\ < = > 5.5 {}^{4x} = 1 \\ < = > 5 {}^{4x + 1} = 1 \\ = > 4x + 1 = 0[/tex]
<=> x = -1/4
Answer:
[tex]a) [x: - \infty < x < \infty ][/tex]
[tex]b)[x: - 1][/tex]
[tex]c) [x:- \frac{5}{3} ][/tex]
[tex]d) [x: 3, 0][/tex]
[tex]e) [x: - \frac{1}{4} ][/tex]
Related Questions
Books are identified by an International Standard Book Number (ISBN), a 10-digit code x1 x2...x10, assigned by the publisher. These 10 digits consist of blocks identifying the language, the publisher, the number assigned to the book by its publishing company, and finally, a 1-digit check digit that is either a digit or the letter X (used to represent 10). This check digit is selected so that \sum_{i=1}^{10} ix_i \equiv 0 \text{ mod } 11 and is used to detect errors in individual digits and transposition of digits.
a. The ISBN for a book is 1-32-794182- Q} where Q is the check digit. What is Q?
b. The ISBN of another book is 2-429-39M18-6. Find the digit M.
Answers
Answer:
[tex]Q = 1[/tex]
[tex]M = 2[/tex]
Step-by-step explanation:
Solving (a):
Given: 1-32-794182- Q
Required: Find Q
To do this, we first multiply each digit in descending order of 10.
So, we have:
[tex]Product = 1 * 10 + 3 * 9 + 2 * 8 + 7 * 7 + 9 * 6 + 4 * 5 + 1 * 4 + 8 * 3 + 2 * 2 + Q * 1[/tex]
[tex]Product = 208 + Q *1[/tex]
[tex]Product = 208 + Q[/tex]
Equate the modulus of the product by 11 to 0
[tex]Product \% 11 = 0[/tex]
[tex](208 + Q) \% 11 = 0[/tex]
The next number greater than 208 divisible by 11 is 209.
So, we have:
[tex](208 + Q) \% 11 = 209 \% 11[/tex]
Express 209 as 208 + 1
[tex](208 + Q) \% 11 = (208 + 1)\% 11[/tex]
By comparison:
[tex]Q = 1[/tex]
Hence, the checksum is 1
Solving (a):
Given: 2-429-39M18-6
Required: Find M
Apply the same step in (a)
So, we have:
[tex]Product = 2 * 10 + 4 * 9 + 2 * 8 + 9 * 7 + 3 * 6 + 9 * 5 + M * 4 + 1 * 3 + 8 * 2 + 6 * 1[/tex]
[tex]Product = 198 + 4M + 25[/tex]
[tex]Product = 223+ 4M[/tex]
Equate the modulus of the product by 11 to 0
[tex]Product \% 11 = 0[/tex]
[tex](223+ 4M) \% 11 = 0[/tex]
The next number greater than 223 divisible by 11 is 231.
So, we have:
[tex](223+ 4M) \% 11 = 231 \% 11[/tex]
Express 231 as 223 + 8
[tex](223+ 4M) \% 11 = (223 + 8) \% 11[/tex]
By comparison:
[tex]4M = 8[/tex]
Divide both sides by 4
[tex]M = 2[/tex]
There are 4 blood types, and not all are equally likely to be in blood banks. 49% of donations are type O blood, 27% of donations are type A blood, 20% of donations are type B blood, and 4% of donations are type AB blood. A person with type A blood can safely receive blood transfusions of type O and type A blood. If three donations are made, what is the probability that at least 1 of them can be safely used in a blood transfusion on someone with type A blood? 0.0138 0.4390 0.5610 0.9862
Answers
Answer:
0.9862.
Step-by-step explanation:
For each donation, there are only two possible outcomes. Either it can be safely used in a blood transfusion on someone with type A blood, or it cannot. The probability of a donation being safely used is independent of other donations, which means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Type A blood:
Can receive from type O(49%) and from type A(27%), which means that:
[tex]p = 0.49 + 0.27 = 0.76[/tex]
If three donations are made, what is the probability that at least 1 of them can be safely used in a blood transfusion on someone with type A blood?
Three donations mean that [tex]n = 3[/tex]
This probability is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{3,0}.(0.76)^{0}.(0.24)^{3} = 0.0138[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0138 = 0.9862[/tex]
The answer is 0.9862.
The probability that at least 1 of them can be safely used in a blood is 0.9862.
Since, A person with type A blood can safely receive blood transfusions of type O and type A blood.
Given that,
49% of donations are type O blood
27% of donations are type A blood
So, [tex]p=0.49+0.27=0.76[/tex] and [tex]q=1-0.76=0.24[/tex]
Where p represent probability of success and q represent probability of unsuccessful.
Now use Binomial distribution,
[tex]P(X=r)=n_{C}_rp^{r} q^{n-r}[/tex]
Here three donations, it means that, n = 3
We have to find that the probability that at least 1 of them can be safely used in a blood.
So, [tex]P(X\geq 1)=1-P(X=0)[/tex]
[tex]P(X=0)=3_{C}_0(0.76)^{0} (0.24)^{3}=0.0138[/tex]
[tex]P(X\geq 1)=1-0.0138=0.9862[/tex]
Thus, The probability that at least 1 of them can be safely used in a blood is 0.9862.
Learn more about Binomial distribution here:
https://brainly.com/question/11388449
Playland Park charges $25 admission plus $2 per ride. Funland Park charges $35 admission plus $1 per ride. For what number of rides is the total cost the same at both parks? Does any body know the answer to this question?
Answers
Answer:
10 rides
Step-by-step explanation:
Make an equation.
25 + 2x = 35 + 1x
Subract 1x from the 2x to get 1.
New Equation: 25 + 1x = 35
Subtract 25 from 35 to get 10.
New Equation: 1x = 10
Divide 1 from both sides.
Answer: 10 rides
An order of jelly beans contains 7,350 jelly beans. If each bag in
the shipment can hold 98 jelly beans, how many bags does the
jelly bean company need to use for the shipment?
Answers
Answer:
75
Step-by-step explanation:
7350/98 = 75
A heavy rope, 50 ft long, weighs 0.6 lb/ft and hangs over the edge of a building 120 ft high. Approximate the required work by a Riemann sum, then express the work as an integral and evaluate it.
Exercise (a)
How much work W is done in pulling the rope to the top of the building?
Exercise (b)
How much work W is done in pulling half the rope to the top of the building?
Answers
Answer:
Exercise (a)
The work done in pulling the rope to the top of the building is 750 lb·ft
Exercise (b)
The work done in pulling half the rope to the top of the building is 562.5 lb·ft
Step-by-step explanation:
Exercise (a)
The given parameters of the rope are;
The length of the rope = 50 ft.
The weight of the rope = 0.6 lb/ft.
The height of the building = 120 ft.
We have;
The work done in pulling a piece of the upper portion, ΔW₁ is given as follows;
ΔW₁ = 0.6Δx·x
The work done for the second half, ΔW₂, is given as follows;
ΔW₂ = 0.6Δx·x + 25×0.6 × 25 = 0.6Δx·x + 375
The total work done, W = W₁ + W₂ = 0.6Δx·x + 0.6Δx·x + 375
∴ We have;
W = [tex]2 \times \int\limits^{25}_0 {0.6 \cdot x} \, dx + 375= 2 \times \left[0.6 \cdot \dfrac{x^2}{2} \right]^{25}_0 + 375 = 750[/tex]
The work done in pulling the rope to the top of the building, W = 750 lb·ft
Exercise (b)
The work done in pulling half the rope is given by W₂ as follows;
[tex]W_2 = \int\limits^{25}_0 {0.6 \cdot x} \, dx + 375= \left[0.6 \cdot \dfrac{x^2}{2} \right]^{25}_0 + 375 = 562.5[/tex]
The work done in pulling half the rope, W₂ = 562.5 lb·ft
3. Classify the triangle with the given side lengths as acute, right, obtuse, 10 points
or not a triangle: 11, 13, 25
Not a triangle
Acute
Right
Obtuse
4. Classify the triangle with the given side lengths as acute, right, obtuse, 10 points
or not a triangle. 21, 28, 35
Not a triangle
Acute
Right
Obtuse
Answers
Answer:
3) Obtuse
4) Right
Step-by-step explanation:
3)
11 + 13 > 25 It is a triangle
11² + 13² = 25²
121 + 169 = 625
290 ≠ 625
Since hypotenuse is larger, the triangle is obtuse
4)
21 + 28 > 35 It is a triangle
21² + 28² = 35²
441 + 784 = 1225
1225 = 1225
Since the hypotenuse is equal to the legs, it's a Right triangle
find the value of x. round to the nearest degree.
Answers
Answer:
What you should do in this case is to use the following trinonometric relationship:
senx = C.O / h
Where
C.O: Opposite leg.
h: hypotenuse.
Substituting:
senx = (7) / (9)
Clearing x:
x = ASIN ((7) / (9))
x = 51.05755873
Answer:
The value of x is
x = 51 degrees.
Step-by-step explanation:
The sum of a number times 8 and 23 is at most 26.
Use the variable b for the unknown number
Answers
Answer:
b ≤ 3/8
Step-by-step explanation:
Let the unknown number be b.
Translating the word problem into an algebraic expression, we have;
8b + 23 ≤ 26
Rearranging the equation, we have;
8b ≤ 26 - 23
8b ≤ 3
Dividing both sides by 8, we have;
b ≤ 3/8
help plz ill give extra points
Answers
Hope this helps
Simplify.
(5+squartrt3)2
25 + sqrtrt10
10 + 28sqrtrt3
28 + 10sqrtrt3
Answers
Answer:
Step-by-step explanation:
If the 2 is an exponent, it needs to be written as ^2.
(5+√3)² = 5² + 10√3 + 3 = 28 + 10√3
Then number of pandas in the world is decreauing at a rate of
about 0.5% every year. If in one year there are 3000 pandas in
the world, how many will be there in 4 years? Round to the
nearest whole number.
Answers
Answer:
2998 Panda's will be left in 4 years.
Step-by-step explanation:
0.5 x 4 =2
3000-2=2998
Marie necklace is 30 inches long. She decided to make it 6 inches shorter. How many feet long is the neck less now?
Answers
Answer:
24 inches
Step-by-step explanation:
Answer:
2 feet long
Step-by-step explanation:
12 inches in a foot
30-6=24
24 inches=2 feet
2. Rewrite the following as mixed fractions in simplest form.
a. 1,75
Answers
Step-by-step explanation:
question is not understandable bro i can't understand
Why are family traditions important? (Please write this essay for me)
Answers
Answer:
talk ab
- Generations
- culture
Samantha is 3 years older than her twin sisters. Next year the sum of age ages of all 3 sisters will be 45. how old is Samantha now?
Answers
2 twin sisters
3 years older
Explanation:
The 2 sisters are 45 years old and Samantha is 3 years older
Therefore, 48 years old
nine times the difference between 4 and a number is24.what is the number.
Answers
Answer:
9×24-4
216-4
212
Step-by-step explanation:
I am not sure, but it might help you
Answer:
n = [tex]\frac{4}{3}[/tex]
or (because the wording is kind of confusing)
n = [tex]\frac{20}{3}[/tex]
Step-by-step explanation:
9(4 - n) = 24
36 - 9n = 24
-9n = -12
n = [tex]\frac{4}{3}[/tex]
or (because the wording is kind of confusing)
9(n - 4) = 24
9n - 36 = 24
9n = 60
n = [tex]\frac{20}{3}[/tex]
The trapzeoids below are congruent figures. What is the value of W
Answers
Answer:
2
Step-by-step explanation:
3w=6
w=6÷3
w=2
Using Postulates and/or Theorems learned in Unit 1, determine whether PRQ MRN.
Show all your work and explain why the triangles are similar or why they are not
Please help and give a good explanation
Answers
Answer:
RM / RP = 10/18 = 5/9
RN/RQ = 7/21 = 1/3
Since the two ratios are not the same, triangle PRQ is not similar to triangle MRN.
Step-by-step explanation:
The triangles PRQ and MRN are not similar.
Similar triangles:Triangles are similar if their corresponding angles are congruent and the corresponding sides are in proportion.
This means the ratio of there corresponding sides must be equal. The corresponding angles must be the same . Therefore, the following rules must apply:
∠R = ∠R
∠Q = ∠N
∠P = ∠M
The following proportion rule must apply below:
PR / MR = RQ / RN = PQ / MN
18 / 10 = 21 / 7
9 : 5 ≠ 3 : 1
Therefore, the triangles are not similar
learn more on similar triangles here: https://brainly.com/question/10810713
Which of the following expressions is equivalent to 32 ÷ 4• 4 ÷ 2 • 2?
Answers
Answer:
128
Step-by-step explanation:
32 ÷ 4• 4 ÷ 2 • 2
8 .4.2.2
128
Kent is 12 4/5 years old. Lane is 1 1/6
Years Older than kent and jane
is 1 1/3 year older than lane
How old is jane?
Answers
Answer:
[tex]Jane = 15\frac{3}{10}[/tex]
Step-by-step explanation:
Given
[tex]Kent = 12\frac{4}{5}[/tex]
[tex]Lane = 1\frac{1}{6} + Kent[/tex]
[tex]Jane = 1\frac{1}{3} + Lane[/tex]
Required
Determine Jane's age
Substitute [tex]Kent = 12\frac{4}{5}[/tex] in [tex]Lane = 1\frac{1}{6} + Kent[/tex]
[tex]Lane = 1\frac{1}{6} + 12\frac{4}{5}[/tex]
[tex]Lane = \frac{7}{6} + \frac{64}{5}[/tex]
Take LCM
[tex]Lane = \frac{45+384}{30}[/tex]
[tex]Lane = \frac{419}{30}[/tex]
Substitute [tex]Lane = \frac{419}{30}[/tex] in [tex]Jane = 1\frac{1}{3} + Lane[/tex]
[tex]Jane = 1\frac{1}{3} + \frac{419}{30}[/tex]
[tex]Jane = \frac{4}{3} + \frac{419}{30}[/tex]
Take LCM
[tex]Jane = \frac{40+419}{30}[/tex]
[tex]Jane = \frac{459}{30}[/tex]
[tex]Jane = 15\frac{3}{10}[/tex]
A motorcycle is 90 inches long. A car is 75% longer than the motorcycle. How long is the car?
Answers
What cube is a unit cube
Answers
SOMEONE PLEASE HELP NO LATE RESPONSES JUST PLEASE ASAP
Answers
Answer:
93.5
Step-by-step explanation:
The radius of a circular disk is given as 26 cm with a maximum error in measurement of 0.2 cm. (a) Use differentials to estimate the maximum error (in cm2) in the calculated area of the disk. (Round your answer to two decimal places.) cm2 (b) What is the relative error
Answers
True or False: To calculate the amount of change, you must find the
difference between the new and original values. *
Answers
Given the graphs of f(x) = 2x + 2 and g(x) = x - 2, find the solution to this system of equations:
Answers
Answer:
(-4,-6)
hope this helps !
Write the equation of a line that
passes through the point (0, 3)
with a slope of -3
.
Answers
Answer:
y = -3x + 3
Step-by-step explanation:
use the formula y - y1 = m ( x - x1)
y - 3 = -3 ( x - 0)
y - 3= -3x
y = -3x + 3
What is the measure of n?
12
4
n
m
Answers
There is no attachment attached.
Are these equivalent the the expression on the top right
Answers
Answer:
No
Yes
No
Yes
(choice 3 is a no)
Simplify 6(4x - 3) show work plz
Answers
Answer:
24x-18
Step-by-step explanation:
To simplify this we will need to use the distributive property
we can start with
6*4x=24x
then we can do
6*3=18
and since their is a negative sign in the middle that is what we do, so it will be
24x-18
Can I please have brainliest :)
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{Simplify 6(4x - 3)}[/tex]
[tex]\large\text{DISTRIBUTE}\downarrow[/tex]
[tex]\large\text{6(4x - 3)}[/tex]
[tex]\large\text{6(4x) + 6(-3)}[/tex]
[tex]\large\text{6(4x) = 24x}[/tex]
[tex]\large\text{6(-3) = -18}[/tex]
[tex]\large\text{\bf = 24x - 18}[/tex]
[tex]\boxed{\boxed{\large\text{Answer: \bf \huge 24x - 18 }}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]