Which answer includes the intervals that contain the solution to the inequality?
Answers
The correct option is D (-∞,-3)∪(-1,1)
Step-by-step explanation:
Given,
[tex]\frac{x^{2}-1 }{3x+9}[/tex] ≤ 0
To find the solution.
The solution could be found if
[tex]x^{2} -1[/tex] ≤ 0 and
3x+9 ≠ 0 [if the denominator is 0, it gives ∞ as solution]
Now,
[tex]x^{2} -1[/tex] ≤ 0
or, (x+1)(x-1) ≤0
or, x ≤1 and x≤-1
Both of the above condition holds is x≤1
Again,
3x+9≠0
or, x≠-3
All the conditions gold for the values (-∞,-3)∪(-1,1)
Hence the correct option is D.
Related Questions
Manuela and Stephen survey 250 people at a sporting event and ask if they prefer hamburgers or hot dogs, and if they prefer regular or diet soda.
Regular Soda Diet Soda Total
Hamburgers 90 40 130
Hot Dogs 70 50 120
Total 160 90 250
a. What is the probability that someone who prefers diet soda will also prefer hamburgers?
b. What is the probability that someone who prefers hot dogs will also prefer regular soda?
c. Are preferring diet soda and preferring hamburgers independent events? Explain.
d. Are preferring regular soda and preferring hot dogs independent events? Explain.
Answers
Answer:
a. 40/250
b. 70/250
c. Preferring diet soda and preferring hamburgers are not independent events
d. Preferring regular soda and preferring hot dogs are not independent events
Step-by-step explanation:
We are given:
Regular Soda Diet Soda Total
Hamburgers 90 40 130
Hot Dogs 70 50 120
Total 160 90 250
a. The probability that someone who prefers diet soda will also prefer hamburgers can be calculated as:
No. of people who prefer hamburgers and diet soda / Total no. of people
40/250
b. The probability that someone who prefers hot dogs will also prefer regular soda can be calculated as:
No. of people who prefer hot dogs and regular soda/Total no. of people
70/250
c. For two events to be independent, they must fulfill the condition:
P(A and B) = P(A) * P(B)
P(Diet Soda) = No. of people who prefer diet soda/total no. of people
= 90/250
P(Hamburgers) = No. of people who prefer hamburgers/total no. of people
= 130/250
P(Diet Soda and Hamburgers) = 40/250
Now, we need to check:
P(Diet Soda and Hamburgers) = P(Diet Soda) * P(Hamburgers)
40/250 = 90/250 * 130/250
40/250 ≠ 11700/62500
So, we can conclude that these two events are not independent events.
d. P(Regular Soda) = No. of people who prefer regular soda/total no. of people
= 160/250
P(Hot dogs) = No. of people who prefer hot dogs/total no. of people
= 120/250
P(Regular Soda and Hot Dogs) = 70/250
Now, we need to check if:
P(Regular Soda and Hot Dogs) = P(Regular Soda) * P(Hot dogs)
70/250 ≠ 160/250 * 120/250
So, these two events are not independent.
The solutions obtained are Part (a): The probability is 0.444, Part (b): The probability is 0.583, Part (c): Preferring diet soda and preferring hamburgers are not independent and Part (d): Preferring regular soda and preferring hot dogs are not independent.
Probability and Independence Analysis
Let's analyze the data provided from Manuela and Stephen's survey:
Regular Soda Diet Soda Total
Hamburgers 90 40 130
Hot Dogs 70 50 120
Total 160 90 250
→ Part A: Probability that Someone Who Prefers Diet Soda Also Prefers Hamburgers
The number of people who prefer diet soda is 90, and among them, 40 prefer hamburgers. Therefore, the probability is calculated as follows:
P(Hamburgers|Diet Soda) = 40 / 90
≈ 0.444
→ Part B: Probability that Someone Who Prefers Hot Dogs Also Prefers Regular Soda
The number of people who prefer hot dogs is 120, and among them, 70 prefer regular soda. Therefore, the probability is:
P(Regular Soda|Hot Dogs) = 70 / 120
≈ 0.583
→ Part C: Independence of Preferring Diet Soda and Preferring Hamburgers
To determine if these events are independent, we check if:
P(Diet Soda AND Hamburgers) = P(Diet Soda) * P(Hamburgers)
Calculations:
→ P(Diet Soda AND Hamburgers) = 40 / 250
→ P(Diet Soda) = 90 / 250
→ P(Hamburgers) = 130 / 250
→ P(Diet Soda AND Hamburgers) ≠ P(Diet Soda) * P(Hamburgers)
Since the equality does not hold, these events are not independent.
Part D: Independence of Preferring Regular Soda and Preferring Hot Dogs
We test the same independence condition for regular soda and hot dogs:
→ P(Regular Soda AND Hot Dogs) = P(Regular Soda) * P(Hot Dogs)
Calculations:
→ P(Regular Soda AND Hot Dogs) = 70 / 250
→ P(Regular Soda) = 160 / 250
→ P(Hot Dogs) = 120 / 250
→ P(Regular Soda AND Hot Dogs) ≠ P(Regular Soda) * P(Hot Dogs)
Therefore, these events are also not independent.
(True or False) The Long Division symbol is the same as the Radical (Root) symbol?
Answers
Answer:
false
Step-by-step explanation:
Answer:
FALSE
Step-by-step explanation:
the radical root symbol and long division symbol look different, and have different purposes. radical root symbol - √. the long division has so less angles.
Rewrite without parentheses.
- 2x² (5x² – 9x-2)
Answers
Answer: without parentheses it'll be : -2x square 2 2x square 2 9x-2!
Step-by-step explanation: well to start with,Nothing will change when you solve it just rember the PEMDAS and you'll be fine! Good luck :3
What 3 ratios are equivalent to 5:15? pls help me ASAP! ʕ •ᴥ•ʔ
Answers
Answer: 13:65, 8:40, 18:90
Answer:
First of all that bear is adorable second 1:3, 10:30, and 15:45
Step-by-step explanation:
To do this you have to figure out if the ratios equal the fraction 1/3 which is the fraction for the ratio 5:15 all of those equal 1/3
I know I didn't explain that well but I still hope that this helps you :)
What is the coefficient of the variable in the expression 6 − 4x − 8 + 2?
a. 6
b. 2
c. −4
d. −8
Answers
Answer:
-4
Step-by-step explanation:
Really need help on this problem
Answers
Answer:
7
Step-by-step explanation:
Answer:
7kg
Step-by-step explanation:
4. Wanda lives in the same state as Reese (ex 4 p 313). Her weekly unemployment
compensation is $360. What were the total 26-week earnings for her highest two consecutive
quarters of employment?
Answers
Final answer:
To find the total earnings for Wanda's highest two consecutive quarters of employment, multiply her weekly unemployment compensation by the number of weeks in two quarters.
Explanation:
To find the total earnings for Wanda's highest two consecutive quarters of employment, we need to compare the given state and weekly unemployment compensation with the table provided. According to the table, the maximum weekly unemployment compensation for Oregon is $330. Since Wanda's weekly compensation is $360, it means that her state is Oregon. Now, we can find the total earnings for her highest two consecutive quarters by multiplying her weekly compensation by the number of weeks in two quarters (26 weeks).
$360 times 26 (*) = $9360
Therefore, the total 26-week earnings for Wanda's highest two consecutive quarters of employment is $9360.
What is the value of the discriminant for the quadratic equation 0 = x + 2 + x^2?
Discriminant = b^2— Час
Answers
Answer:
The discriminant of the quadratic equation is -7.
Step-by-step explanation:
We are given the following quadratic equation in the question:
[tex]x^2+x+2 = 0[/tex]
Comparing to general quadratic equation:
[tex]ax^2+bx+c = 0\\a = 1\\b = 1\\c = 2[/tex]
We have to find the discriminant of the quadratic equation.
Formula:
[tex]d = b^2-4ac[/tex]
Putting values, we get,
[tex]d = (1)^2 - 4(1)(2) = 1 - 8 = -7[/tex]
Thus, the discriminant of the quadratic equation is -7.
Help me Please! Find the volume and surface area for all.
Answers
Answer:
V =41.41³
A = 94.41²
----
V =225.16³
SA =283.25²
----
V = 64³
SA =113.32²
----
V =433.33³
SA = 378.57²
Step-by-step explanation:
Picture 2 = a = 1/2 base = 3.5 x 3.5 = 12.25 b= 5 x 5 = 25
c²= a² + b² = 3.5² + 5²
c ²= √12.25 + √25
c ²= √ 37.5 = 6.12372435696
c ² = 6.1237 missing side
Picture 1 + 2 formula SA = bh + (s1 + s2 + s3)H
V = V= 1/2 b x h h x SA
Picture 3 + 4 formula SA= a²+ 2a a² / 4 + h² V= a² h/3
What is the midpoint of segment JK shown in the graph
Answers
Answer:
b. 1/2, -1/2
Step-by-step explanation:
[tex]\frac{-4+5}{2}, \frac{2+(-3)}{2} =(\frac{1}{2} ,\frac{-1}{2}[/tex] )
What is the circumference of a circle with a diameter of 8 feet?Use 3.14 for π.
Answers
Answer:
c=25.12
Step-by-step explanation:
C=πd
C=3.14*8
C=25.12
Answer:
25.12ft
Step-by-step explanation:
take 8 and times that by 3.14, and you get:
25.12
Where will the different sections of the box plot be located? The box will go from 27. A line dividing the box will go at. The left whisker will go from 11 to. The right whisker will go from 33.
The five values for a data set are:
minimum = 11
lower quartile = 12
median = 23.5
upper quartile = 27
maximum = 33
A number line going from 0 to 40 in increments of 5.
Answers
Answer:
12 to 27
a long dividing the box will go at 23.5
11 to 12
the right whisker will go from 27 to 33
Step-by-step explanation: ^^^
The given sections of the box plot will be located, at the following places:
The box will go from 12 to 27 (IQR).
A line dividing the box will go at 23.5 (median).
The left whisker will go from 11 to 12.
The right whisker will go from 27 to 33 (see box plot in the image attached below).
What is a Boxplot?A boxplot shows the following values:
Minimum - which is located at the beginning of the left whiskerLower Quarter (Q1) - which is located at the beginning of the edge of the rectangular box.Median - the value at the point where a vertical line divides the boxUpper Quarter (Q3) - which is located at the end of the edge of the rectangular box.Maximum - which is located at the end of the right whisker.Therefore, the given sections of the box plot will be located, at the following places:
The box will go from 12 to 27 (IQR).
A line dividing the box will go at 23.5 (median).
The left whisker will go from 11 to 12.
The right whisker will go from 27 to 33 (see box plot in the image attached below).
Learn more about box plot on:
https://brainly.com/question/24335827
the coat of a customers smartphone bill can be modeled by the equation C=10g+50 where g is the number of gigabits of data the customer per month.Factor this cost polynomial
Answers
Answer:
[tex]C=10(g+5)[/tex]
Step-by-step explanation:
Given the cost of a customers smartphone bill,
C=10g+50
We are required to factor the polynomial.
First, determine the G.C.D of both terms
The GCD of 10g and 50 is 10Next, we divide each of the term by 10 and balance it by multiplying the expression by 10.
[tex]C=10g+50\\=10(\frac{10g}{10}+\frac{50}{10})\\C=10(g+5)[/tex]
The cost polynomial factored is C=10(g+5).
Answer:
10g+60=10(g+6)
Step-by-step explanation:
thats the answer
9. ten times the minutes spent exercising? this is algebra you have to write it in expression
Answers
Answer:
Ten times the minutes spent exercising is 10t.
Step-by-step explanation:
Given : Expression 'ten times the minutes spent exercising'.
To find : Write the expression in algebraic form ?
Solution :
Let t represent the number of minutes spent exercising.
Here, "ten times the minutes spent exercising "
Ten time means multiplying value by 10,
So the algebraic expression is '10t'.
Therefore, ten times the minutes spent exercising is 10t.
Simplify the expression. 18a + 12x − 12a + 15x A) 6a + 27x B) 6a − 3x C) 30a − 18x D) −30 −3x
Answers
Answer:
18a + 12x - 12a + 15x
6a + 27x
the answer is a
Step-by-step explanation:
Which is the solution to the inequality?
2 and three-fifths less-than b minus StartFraction 8 over 15 EndFraction
b less-than 2 and StartFraction 1 over 15 EndFraction
b greater-than 2 and StartFraction 1 over 15 EndFraction
b less-than 3 and StartFraction 2 over 15 EndFraction
b greater-than 3 and StartFraction 2 over 15 EndFraction
Mark this and return
Answers
Answer:
[tex]b>3\frac{2}{15}[/tex]
Step-by-step explanation:
You can multiply by 15, add 8, divide by 15. (Or, you could get there directly by adding 8/15 to both sides.)
[tex]2\frac{3}{5}<b-\frac{8}{15}\\\\39<15b-8\\\\47<15b\\\\\boxed{3\frac{2}{15}<b}[/tex]
Answer:
D; b > 3 2/15
Step-by-step explanation:
If a pair of standard dice are rolled, what is the probability that the sum will be less than 5?
The answer is [tex]1/?[/tex] I just need the denominator
Answers
Answer:
Probability= No. of favorable outcomes/ total no. of outcomes
= 4/6 Since below 5 will be 4
and we need to simplify= 2/3
Step-by-step explanation:
Answer: the answer is 1/6
Step-by-step explanation:
PLEASE HELP I WILL MARK YOU AS BRAINLIEST!
Answers
Answer:
12 units²
Step-by-step explanation:
Area = ½ × base × height
= ½ × 4 × 6
= 12 units²
8-6 divided by j-k
j = 2 and k = 3
Answers
(8-6)/(2-3)=2/-1=-2 as the answer
Step-by-step explanation:
[tex] \frac{8 - 6}{j - k} = \frac{2}{2 - 3} = \frac{2}{ - 1} = - 2 \\ [/tex]
Find the area of figure above. Use 3.14 for pi.
Answers
Answer:
139.26990817 m² is the exact answer.
10*10=100
5²*pi + 100= 139.26990817
Hope this helped!! :)
Semicircle: 3.14*5^2 = 78.5
100 + 78.5 = 178.5m^2
HELP ASAP !!!!!!!!!! nnnnn
Answers
Answer:
45.8
Step-by-step explanation:
We can use the Pythagorean theorem with legs 3x and 4x+7
a^2+ b^2 = c^2
(3x^2) +(4x+7)^2 = c^2
Let x = 8
(3*8)^2 + (4*8+7)^2 = c^2
24^2+ 39^2 = c^2
576+1521 = c^2
2097 = c^2
Take the square root of each side
sqrt(2097) = sqrt(c^2)
45.79301257 =c
Rounding to the nearest tenth
45.8 =c
Answer:
45.8
Step-by-step explanation:
First solve for the other two sides by replacing x with 8
4(8)+7 = 39
3(8) = 24
Then use the pythagorean theorem ([tex]a^{2} + b^{2} = c^{2}[/tex]) to solve for the hypotenuse, c being the hypotenuse
[tex]39^{2} + 24^{2} = c^{2}[/tex]
1521 + 576 = [tex]c^{2}[/tex]
2097 = [tex]c^{2}[/tex]
[tex]\sqrt{2097} = \sqrt{c^{2} }[/tex]
45.8
Solve the equation -2c=-18
Answers
Answer:
c = 9
Step-by-step explanation:
-2c = -18
/-2 /-2 (Divide both sides by -2)
_______
c = 9
Answer:
c=-9
Step-by-step explanation:
-2c=18
divide the whole thing by -2
c=-9
BRAINLIST pls Answer
Juanita shares 4 pounds of kibble equally in 3 dog bowls. How many pounds of kibble are in each bowl?
Answers
Answer:
1 1/3 pound (1 pound and 1/3)
Step-by-step explanation:
u just but it in a fraction
4/3
and simplify to mixed number
1 1/3
Answer:
4/3 = 1.33
Step-by-step explanation:
Since you will be dividing the amount of kibble, the equation is 4 pounds / 3 bowls. 3/4 would be dividing the bowls and that would make no sense at all. Therefore the answer is 1.33 pounds per bowl.
Need help will mark brainiest
Answers
Answer:
a) 19
b) 3
Step-by-step explanation:
They are adding 3 sticks each time so n=3
I hope this helps
Micah paid $45 for 14.5 gallons of gas. What is the estimated cost of one gallon of gas?
Answers
Answer:
$3.00/ gallon
Step-by-step explanation:
Take the amount paid and divide by the number of gallons
We are estimating so round 14.5 gallons to 15
$45/15 gallons
$3.00/ gallon
Solve the equation. Then check your solution.
-16-10.2g = -14.7g + 16.85
a. 147.825
b. -7.3
c. 3.65
d. 7.3
Please select the best answer from the choices provided
Answers
Answer:
d. 7.3
Step-by-step explanation:
-16-10.2g = -14.7g + 16.85
4.5g = 32.85
g = 7.3
The solution for the equation -16 - 10.2g = -14.7g + 16.85 is g = 7.3. You can verify it by substituting the solution back into the original equation.
Explanation:To solve the given equation, -16 - 10.2g = -14.7g + 16.85, we must first isolate the variable, g, by moving all terms involving g to one side of the equation and constant terms to the other side. Add 10.2g to both sides of the equation, giving, -16 = -4.5g + 16.85. To further isolate g, subtract 16.85 from both sides resulting in -32.85 = -4.5g. Finally, divide by -4.5 to solve for g. Thus, g = -32.85 / -4.5 = 7.3. We verify our solution by substituting 7.3 back into the original equation and confirming that the equality holds true.
Learn more about Equation Solving here:https://brainly.com/question/18262581
#SPJ2
54 1/3 in simplified radical form
Answers
PLEASE ANSWER TO BE NAMED BRAINLIEST GET A THANK YOU AND A FRIEND REQUEST AND 10 P
If x = time, and y = the number of problems in the set, which equation models the relationship?
Question 3 options:
y = 12x
y = x + 12
y = 1.2x
y = x + 1.2
Answers
Answer:
C, y = 1.2x
Step-by-step explanation:
Notice that x, representing time, is multiplied by 1.2 each time to get y, representing the number of problems. You can find this out by dividing y by x. 36/30 = 1.2.
48/40 = 1.2.
And so on...
P.S.: If you ever come across a problem like this, subtract one y value by another y value, then subtract the corresponding x values from eachother, then make both numbers into one fraction with y as the numerator and x as the denominator. In this problem, that would look like this:
48 and 36 are both y values: 48 - 36 = 12
40 and 30 are the corresponding x values: 40 - 30 = 10
We get 12/10, which can be simplified to 1.2. The slope is 1.2.
This method will always work for a straight line and will be taught to you soon if you haven't learned it already.
find the gcf and lcm of 20 and 12
Answers
Answer:
GCF: 4 LCM:60
Step-by-step explanation:
Answer:
gcf-6, lcm-60
Step-by-step explanation:
factors of 20: 1, 2, 4, 5, 10, 20
factors of 12: 1, 2, 3, 4, 6, 12
multiples of 20: 20, 40, 60, 80, 100
multiples of 12: 12, 24, 36, 48, 60, 72
An 6-sided die is rolled four times. What is the probability of rolling a six on all four rolls?
Answers
Answer:
4/6
Step-by-step explanation: