Answer: b
Step-by-step explanation:
ok, lets see the answers one for one.
a) in this case, t can be 4, if t= 4 then t + 1 = 5 and the inequality is false.
b) in this case, the maximum vale of t is 2, then 2 + 1 = 3, the inequality is true here, and all the other numbers in the set is smaller than 2, then all this set keeps the inequality true.
c and d) both sets allow to take, for example, t= 10, wich makes the inequality false.
now in this type of exercises, you should se the biggest and lowest number that keeps the inequality true, in this case the biggest is 2, because 2 + 1 = 3, and there is no lowest limit because any negative number + 1 will be less than 3. With those limits then you can figure the set of valid solutions with all the numbers in between.
Final answer:
The solution to the inequality 3 ">=" t + 1 is option b) {t | t ">=" 2}, which means that t is any number less than or equal to 2.
Explanation:
Before solving the inequality 3 ">=" t + 1, first, let's isolate the variable t. To do that, we subtract 1 from both sides of the inequality:
3 - 1 ">=" t + 1 - 1
2 ">=" t
This can be read as 't is less than or equal to 2' or 't must be any number that is 2 or smaller.' Therefore, the correct answer is:
{t | t ">=" 2}
When comparing with the question options, it is clear that option b) matches our solution.
Thus, option b) {t | t ">=" 2} is the correct answer to the inequality given in the question.
Evaluate. -1/2y + 3 = -12
Answer:
Y = 30
Step-by-step explanation:
hope this helps u out :)
A train leaves the station at 6 pm traveling west at 80 mph. On a parallel track, a second train leaves the station 3 hours later traveling west at 100 mph. At what time will the second train catch up with the first?
Answer:
Step-by-step explanation:
Start train 1 at 6 pm an train 2 at 9pm
Rob purchased a rug for his apartment the rug is 72 inches by 96 inches . Calculate the area of the rug in square inches
Answer:
Area of the rug will be 6912 square inches.
Step-by-step explanation:
Rob has purchased a rug having measurement 72 inches by 98 inches for his apartment.
Since the rug will be in the shape of a rectangle, area will be represented by the formula,
Area = Length × width
= 72 × 96
= 6912 square inches.
Therefore, area of the rug will be 6912 square inches.
To calculate the area of Rob's rug, multiply the length of 96 inches by the width of 72 inches, resulting in an area of 6,912 square inches. Thus, the area of the rug is 6,912 square inches.
To find the area of Rob's rug, you need to multiply the length and the width of the rug.
Length = 96 inchesWidth = 72 inchesThe formula for area is:
Area = Length × Width
Using the given dimensions:
Area = 96 inches × 72 inches = 6,912 square inches
Therefore, the area of the rug is 6,912 square inches.
Find the greatest comman factor of 15 and 20
Answer:
GCF(15,20) = 5
Step-by-step explanation:
Prime Factorization of 15
Prime factors of 15 are 3, 5. Prime factorization of 15 in exponential form is:
15 = 31 × 51
Prime Factorization of 20
Prime factors of 20 are 2, 5. Prime factorization of 20 in exponential form is:
20 = 22 × 51
Factors of 15
List of positive integer factors of 15 that divides 15 without a remainder.
1, 3, 5
Factors of 20
List of positive integer factors of 20 that divides 15 without a remainder.
1, 2, 4, 5, 10
Greatest Common Factor
We found the factors and prime factorization of 15 and 20. The biggest common factor number is the GCF number.
So the greatest common factor 15 and 20 is 5.
How do you simplify 5 (3t) - 7 (2t)
Answer:
3t-2
Step-by-step explanation:
Multiply the terms 3t and 2t. You should get 5t.Subtract 7 from 5; you should get -2.Now, your equation is 3t-2, you're done!Paulo ran a marathon in about 1.56 × 10^4 s. A) Write Paulo's time in standard notation. B) Miguel ran a marathon in 4 h and 16 min. Who ran the race in the shorter amount of time? Show your work. (Question 2) Solve each given equation and show your work. Tell whether each equation has one solution, an Infinite number of solutions, or no solution. Explain your answers. A) 2x+4(x-1)=2+4x , (B) 25-x=15-(3x+10) , (C) 4x=2x+2x+5(x-x). (I posted a picture of question 3).
Paulo's time in standard notation is 15,600 seconds. Miguel ran the marathon in a shorter time of 15,360 seconds. For the given equations, A) and B) each have one solution (x=3 and x=10, respectively), while C) has an infinite number of solutions.
Explanation:To convert Paulo's time from scientific to standard notation, we multiply 1.56 by 10 to the power of 4. This equals 15,600 seconds. Next, we need to convert Miguel's time to seconds to directly compare the two durations. Miguel ran for 4 hours and 16 minutes, which is equal to (4 × 3600) + (16 × 60) = 14,400 + 960 = 15,360 seconds. Therefore, Miguel ran the race in a shorter amount of time by 240 seconds.
For question 2, we solve the following equations:
For equation A) 2x + 4(x - 1) = 2 + 4x, after simplifying we get 2x + 4x - 4 = 2 + 4x. The 4x terms cancel out and we are left with 2x - 4 = 2. Solving for x gives x = 3. This equation has one solution.
For equation B) 25 - x = 15 - (3x + 10), simplifying gives 25 - x = 5 - 3x. Solving for x yields x = 10, so this equation also has one solution.
For equation C) 4x = 2x + 2x + 5(x - x), simplifying results in 4x = 4x, which is true for all values of x. Therefore, this equation has an infinite number of solutions.
As question 3 involves an image that we cannot see here, this part of the student's question has been left unanswered.
If m∠EBD = 36° and m∠DBC = 108° find m∠EBC
Check the picture below.
The measure of m∠EBC if m∠EBD = 36° and m∠DBC = 108° is 144degrees
The point where two lines intersect is known as the angle.
From the diagram shown:
m∠EBC = m∠EBD + m∠DBC
Given the following:
m∠EBD = 36degrees
m∠DBC = 108degrees
Substitute the given values into the expression as shown:
m∠EBC = 36 + 108
m∠EBC = 144degrees
Hence the measure of m∠EBC is 144degrees
Learn more here: https://brainly.com/question/13250148
Eight years from now , Bianca will be 50% older than she is now . How old is Bianca
Answer:
16
Step-by-step explanation:
because eight is 50% of 16
Answer: She will be 16
Step-by-step explanation:
Dave is driving to Gilmore to visit his friend. If he wants to stop for lunch when he is about halfway there, in which town should he plan to stop?
Answer:
Dave should stop at Springfield.
Step-by-step explanation:
As shown, Gilmore is 26 miles away.
And Dave is driving to Gilmore but he wants to stop for lunch when he is about halfway there.
That means he wants to stop around [tex]\frac{26}{2}=13[/tex] miles.
And Springfield is 15 miles away that is nearest to 13 miles.
Hence, Dave should stop at Springfield.
i need the answers for 11-13 please and thank you is you can only do one of them that’s okay with me
Answer:
Step-by-step explanation:
11. I can't see the full problem statement, so I'm unable to answer the question.
12. Answer below:
"one half" = [tex]\frac{1}{2}[/tex]
"negative five eighths" = [tex]\frac{-5}{8}[/tex]
To evaluate the expression, you multiply the two numbers together:
[tex]\frac{1}{2} * \frac{-5}{8} = \frac{1 * -5}{2 * 8} = \frac{-5}{16}[/tex]
13. Answer below:
"one third" = [tex]\frac{1}{3}[/tex]
"eleven sixteenths" = [tex]\frac{11}{16}[/tex]
To evaluate the expression, you multiply the two numbers together
[tex]\frac{1}{3} * \frac{11}{16} = \frac{1 * 11}{3 * 16} = \frac{11}{48}[/tex]
Write each fraction as a desimol 29/1000
Fraction Decimal Percentage
30/1000 0.03 3%
29/1000 0.029 2.9%
28/1000 0.028 2.8%
29/997 0.02909 2.909%
Answer:
0.029
Step-by-step explanation:
When is a linear model not a good fit for a set of data?
When there is not a constant rate of change.
When each input value has only one output value.
When the data set does not go through the origin.
When the data set does not increase.
ANSWER: when there is not a constant rate of change
Answer:
When there is not a constant rate of change
Step-by-step explanation:
A linear model shows a continuous response variable as a function of one or more predictor variables.
A linear model is a good fit for a set of data when the plotted points show a constant rate of change.
When a plot of values form a scatter plot, it is difficult to identify a linear model because the points will not appear to follow a trend.
To come up with a linear function in this case will require you to identify the line of best fit then extending the line to y-axis intercept so as to be able to find the slope.
Question is provided in the image attached.
25 points!
Hey!
-------------------------------
Find the zero term:
Plug in 0 for n.
a = 8 + 3(0 - 1)
a = 8 + 3(-1)
a = 8 + (-3)
a = 5
Answer: 5
-------------------------------
Find the first term:
Plug in 1 for n.
a = 8 + 3(1 - 1)
a = 8 + 3(0)
a = 8 + 0
a = 8
Answer: 8
-------------------------------
Find the 40th term:
Plug in 40 for n.
a = 8 + 3(40 - 1)
a = 8 + 3(39)
a = 8 + 117
a = 125
Answer: 125
-------------------------------
Hope This Helped! Good Luck!
If 7+√5 is equal to √5 plus a number, what do you know about the number? Why?
Answer:
7.
Step-by-step explanation:
Let the number be n, then
7 + √5 = n + √5
As the 2 sides are equal in value, n must be 7.
Weight (g)
words, not numbers, deso
1-14.
k (For example, write, "Double the previo
vious number
Copy and complete each sequence below. Using we
how the patterns work. (For example, write. “T
a.
1,3,6, 10,-
-
b. 1, 2, 3, 5,
d. 8,7,5,2,_
c.
e.
1,3,9, 27, -,-
49, 47, 52, 50, 55, —,—
12
Core Connections, Course
Answer: a) add n+1 to the previous term
b) add the previous two terms
d) subtract n+1 from the previous term
e) multiply the previous term by 3
f) subtract 2 from previous term then add 5 to the next term
Step-by-step explanation:
a) 1, 3, 6, 10
∨ ∨ ∨
+2 +3 +4 The next term is 10 +5 = 15
b) 1, 2, 3, 5
∨ ∨ ∨
=3 =5 =8 The next term is 5 + 8 = 13
d) 8, 7, 5, 2
∨ ∨ ∨
-1 -2 -3 zThe next term is 2 - 4 = -2
e) 1, 3, 9, 27
∨ ∨ ∨
×3 ×3 ×3 The next term is 27 × 3 = 81
f) 49, 47, 52, 50, 55
∨ ∨ ∨ ∨
-2 +5 -2 +5 The next term is 55 - 2 = 53
The following term is 53 + 5 = 58
a. Add the next consecutive natural number to the previous term.
b. Divide the previous term by 2.
c. Multiply the previous term by 3.
d. Subtract the next consecutive natural number from the previous term.
e. Alternate between subtracting 2 and adding 5.
a. 1, 3, 6, 10, __, __
Pattern Description: This sequence is created by adding consecutive natural numbers to the previous term.
Start with 1.Add 2 (1 + 2 = 3).Add 3 (3 + 3 = 6).Add 4 (6 + 4 = 10).The next term is (10 + 5 = 15).
The term after that is (15 + 6 = 21).
So the pattern is: Add the next consecutive natural number to the previous term.
Next two terms: 15, 21
b. 1, 1/2, 1/4, 1/8, __, __
Pattern Description: This sequence is created by dividing the previous term by 2.
Start with 1.Divide by 2 (1 / 2 = 1/2).Divide by 2 (1/2 / 2 = 1/4).Divide by 2 (1/4 / 2 = 1/8).The next term is (1/8 / 2 = 1/16).
The term after that is (1/16 / 2 = 1/32).
So the pattern is: Divide the previous term by 2.
Next two terms: 1/16, 1/32
c. 1, 3, 9, 27, _, __
Pattern Description: This sequence is created by multiplying the previous term by 3.
Start with 1.Multiply by 3 (1 × 3 = 3).Multiply by 3 (3 × 3 = 9).Multiply by 3 (9 × 3 = 27).The next term is (27 × 3 = 81).
The term after that is (81 × 3 = 243).
So the pattern is: Multiply the previous term by 3.
Next two terms: 81, 243
d. 8, 7, 5, 2, _, __
Pattern Description: This sequence is created by subtracting consecutive natural numbers starting from 1.
Start with 8.Subtract 1 (8 - 1 = 7).Subtract 2 (7 - 2 = 5).Subtract 3 (5 - 3 = 2).The next term is (2 - 4 = -2).
The term after that is (-2 - 5 = -7).
So the pattern is: Subtract the next consecutive natural number from the previous term.
Next two terms: -2, -7
e. 49, 47, 52, 50, 55, _, __
Pattern Description: This sequence alternates between subtracting 2 and adding 5.
Start with 49.Subtract 2 (49 - 2 = 47).Add 5 (47 + 5 = 52).Subtract 2 (52 - 2 = 50).Add 5 (50 + 5 = 55).The next term is (55 - 2 = 53).
The term after that is (53 + 5 = 58).
So the pattern is: Alternate between subtracting 2 and adding 5.
Next two terms: 53, 58
Complete question:
Copy and complete each sequence below. Using words, not numbers, describe how the patterns work. (For example, write, “Double the previous number.”)
a. 1, 3, 6, 10,__, __
b. 1, 1/2 1/4 1/8 , __ , __
c. 1, 3, 9, 27,__, __
d. 8, 7, 5, 2,___, __
e. 49, 47, 52, 50, 55, __, __
Kim biked 43.6 kilometers on
Monday, 37.5 kilometers on Tuesday
and 46.2 kilometers on Wednesday.
How many kilometers did she bike in
the three days?
Answer:
127.3
Step-by-step explanation:
A nurse mixes 60cc of a 50% saline solution with a 30% saline solution to produce a 35% saline solution. How much of the 30% solution should he use?
Final answer:
To create a 35% saline solution by mixing a 50% and a 30% solution, the nurse needs to use 6000cc of the 30% solution.
Explanation:
The question asks how much of a 30% saline solution a nurse needs to mix with 60cc of a 50% saline solution to achieve a final solution concentration of 35%. To solve this problem, let's denote the volume of the 30% solution needed as x cc. Using the concept of weighted averages for concentrations, we can set up the following equation:
(60cc × 50%) + (x cc × 30%) = (60cc + x cc) × 35%
Solving this equation, we get:
3000 + 0.3x = 0.35(60 + x)
3000 + 0.3x = 21 + 0.35x
Subtracting 0.3x from both sides:
3000 = 21 + 0.05x
Subtracting 21 from both sides and dividing by 0.05:
x = 6000 cc
Therefore, the nurse should use 6000cc of the 30% saline solution to achieve the desired concentration.
Louie needs to add 2/3 of a cup of chocolate to his cupcakes. He only has a 1/3-cup measuring cup. How many scoops of chocolate does Louie need to add?
Answer:
2 Scoops
Step-by-step explanation:
1/3 plus 1/3 equals 2/3, so he would need two 1/3 scoops.
What is the domain of f(x)= x-4/square root x
Answer:
Step-by-step explanation:
f(x)= x-4/√x
f exist for : x > 0
so the domain is : D= ]0 ; + ∞[
Which equation could be solved using the graph above?
X^2+4x+3=0
X^2-4x+3=0
X^2-6x+9=0
X^2-1=0
Answer:
X²+4x+3=0
Step-by-step explanation:
y = X² + 4x + 3
y = 0
Solution:
x = -3, x² = -1
Steps:
X² + 4x + 3 = 0
write 4x as a sum
X²+ 3x + x + 3 = 0
Factor out x from expression
X (x + 3) + x + 3 = 0
Factor out x + 3 from expression
(x + 3) x (x + 1) = 0
When the product of factors equals 0, at least one factor is 0
x + 3 = 0
x + 1 = 0
solve for x
x = -3
x + 1 = 0
solve for x
x = -3
x = -1
The final solutions are
X = -3, X² = -1
Answer:
Option A.
Step-by-step explanation:
The vertex form of a parabola is
[tex]y=a(x-h)^2+k[/tex]
where, (h,k) is vertex and a is a constant.
The vertex of the parabola is (-2,-1).
Substitute h=-2 and k=-1 in the above equation.
[tex]y=a(x-(-2))^2+(-1)[/tex]
[tex]y=a(x+2)^2-1[/tex] .... (1)
The parabola passes through the point (0,3). So, it must be satisfy by the point (0,3).
[tex]3=a(0+2)^2-1[/tex]
[tex]3+1=4a[/tex]
[tex]a=1[/tex]
Substiturte a=1 in equation (1).
[tex]y=1(x+2)^2-1[/tex]
On simplification we get
[tex]y=x^2+4x+4-1[/tex]
[tex]y=x^2+4x+3[/tex]
It means the equation [tex]x^2+4x+3=0[/tex] could be solved using the given graph.
Therefore, the correct option is A.
IIIIIII NNNNNNEEEDDDDD AAAANNNNSSSWWEERR NNNNOOOOOWWWW plz
James wants to carpet the room shown in the diagram. If he uses 12 ft wide carpet strips, how many linear feet will he need to buy?
A) 11
B) 12
C) 20
D) 60
The area of the room = (40 x 24) - (20 x 12)
Area = 960 - 240 = 720 square feet
Divide square feet by width of a strip:
720 / 12 = 60 linear feet.
The answer is D.
Answer : The correct option is, (D) 60
Step-by-step explanation :
First we have to calculate the area of room.
Area of room = Area of big rectangle + Area of small rectangle
Area of rectangle = Length × Width
Area of room = (40 × 12) + (20 × 12)
Area of room = 720 square feet
Now we have to calculate the number of linear feet will he need to buy.
Number of linear feet = [tex]\frac{\text{Area of room}}{\text{Width of carpet strips}}[/tex]
Number of linear feet = [tex]\frac{720}{12}=60[/tex]
Thus, the number of linear feet will he need to buy is, 60
I need help simplifying this
Answer:
x^(1/12).
Step-by-step explanation:
By the laws of indices:
(x ^ 1/2)^1/6)
= x ^(1/2*1/6)
= x^(1/12).
A lawyer has an annual income of $173,482 and will pay a 5.5% income tax rate. What is the amount of income tax in dollars and cents that the lawyer will have to pay?
Answer:
173,482-5.5=173,476.5
Answer:
$9,541.51
Step-by-step explanation:
assume that an avarage cell has a diameter of 7 micrometers (7x10^10 meter) which means it has a volume of 200 cubic micrometers. How many cells are ther in a cubic centimeter
Answer:
5x10⁸
Step-by-step explanation:
Cell = 200 cubic micrometers.
Te question is, how many 200 cubic micrometers are there in a cubic centimeter. 1st, we have to convert 200 cubic centimeter into cubic centimeter:
1cm = 1x10⁴micro, which is the same to:
1x10⁻⁴ cm = 1micro
Now, we have to cube both sides, to "equal the volumes"
(1x10⁻⁴cm)³ = (1micro)³
1x10⁻¹²cm = 1micro³
Multiple both sides by 200:
200 x 1x10⁻¹²cm = 1micro³ x 200
2x10⁻¹⁰cm³ = 200micro³
Finally, 1 cubic cm / 2x10⁻¹⁰cm³ = 5x10⁸
Final answer:
Explaining the number of cells in a cubic centimeter based on the volume of a 10 μm cell.
Explanation:
For a 10 μm cell:
Calculate the volume: V = (4/3)πr³
Convert diameter to radius: r = 5 μm
Substitute and calculate volume: V = (4/3)π(5)³ = 524 μm³
Convert to cubic centimeters: 1 μm³ = 10^-9 cm³, so 524 μm³ = 5.24 x 10^-7 cm³
Calculate the number of cells in 1 cm³: 1 cm³ / 5.24 x 10^-7 cm³ = 1.91 x 10^6 cells
Jabari is thinking of three numbers. The greatest number is twice as large as the least number. The middle number is three more than the least number. The sum of the three numbers is
75
. Find the numbers.
Answer:
18,21,36
Step-by-step explanation:
You can use Algebra to solve it x+x+3+2x=75 or 4x+3=75 will give you the answer 1818 then plus 3 is 21so 18 plus 21 is 39Then the greatest number is 18x2=3639+36=75this is really hard and I need help
Answer:
No solution
Step-by-step explanation:
Subtract 5k from both sides
Simplify
No solution
What 21 over 40 divided by
I’m
Answer:
if you're asking what 21 divided by 40 is then it's 0.525
Step-by-step explanation:
What is 18/27 simplify?
Answer:
The answer is 2/3 okay? Pls thx me!
Evaluate ab for a = -2 3/4 and b= - 4/6
Answer:
1 5/6
Step-by-step explanation:
ab = (-2 3/4) * (-4/6)
= ( -11/4) * ( -4/6)
= (11 * 4) / (4 * 6 )
= 11/6
= 1 5/6
Write 230.071 in expanded form
The third number to the left of the decimal is the hundreds, so you have 200.
The 2nd number to the left of the decimal is the tens, so you have 30.
The first number to the left of the decimal is the ones, and you have 0 ones, so you have 0.
The first number to the right of the decimal is the tenths place, which is 0 so it is 0.0
The second number to the right is the hundredths place, which is 0.07
The third number is the thousandths place, which is 0.001
The expanded form becomes:
200 + 30 + 0 + 0.0 + 0.07 + 0.001
Answer:
230.071 = 200 + 30 + 0.07 + 0.001
Step-by-step explanation:
First, make the following table.
Hundreds: 2
Tens: 3
Ones: 0
Decimal: .
Tenths: 0
Hundredths: 7
Thousandths: 1
With the help of this table, now it is easy to write the expanded form as follows
230.071 = 200 + 30 + 0.07 + 0.001