Identify the inequality that represents the following problem. One less than twice a number is no less than five. What is the solution set?
1 - 2n ≥ 5
2n - 1 ≥ 5
2n - 1 > 5
1 - 2n > 5
Answer:
1 - 2n > 5. The solution set is (-∞, -2)
Step-by-step explanation:
We are dealing here with two problems:
First, to determine which mathematical statement represents "One less than twice a number is no less than five".Second, solve n, that is, the solution set for the numbers that solve the inequality.First Part: Identifying the inequality"One less than twice a number" can be written as [tex]\\1 - 2n[/tex], where n is the unknown number.
If it is not less than five, thus it is greater (no less) than five. Then, the symbol here is " > " (greater).
As a result: "One less than twice a number is no less than five" could be rewritten as "One less than twice a number is greater than five", or:
[tex]\\1 - 2n > 5[/tex].
Second Part: Finding the solution setThe solution set for this inequality is as follows:
[tex]\\ 1-2n > 5[/tex] ⇒
Subtract -1 from each member of the inequality:
[tex]\\ 1-1-2n>5-1 [/tex] ⇒ [tex]\\ -2n>5-1[/tex] ⇒ [tex]\\ -2n>4 [/tex]
Multiply each member of the inequality by [tex]\\-\frac{1}{2}[/tex] (or divide each member by -2). We have to remember here that when we multiply or divide an inequality by a negative number (-n), this inverts the inequality, that is:
[tex]\\ -\frac{1}{2}*(-2)*n< -\frac{1}{2}*4 [/tex]
[tex]\\ 1*n< -\frac{1}{2}*4 [/tex]
[tex]\\ n < -2 [/tex]
The solution set is then [tex]\\ n< -2 [/tex], which is any value less than -2 (not including -2, because is < and not ≤), and we have infinite negative numbers with such a characteristic. We can write it mathematically as an interval notation:
Solution set for [tex]\\1 - 2n > 5[/tex] is [tex]\\ (-\infty, -2)[/tex].
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If something starts out costing $500, and then is marked down by 25% on each of three separate occasions,what is the final price
Molly has 24 muffins,18 breakfast bars,and 12 bottles of juice to be distributed evenly among a certain number of welcome baskets she wants to package the maximum number of welcome baskets that will contain the same combination of muffins breakfast bars and bottles of jucie which shows the correct number of muffins breakfast bars and juice bottles among with the proper explanation circle all that apply
Answer: Hello mate!
We want to distribute 24 muffins, 18 breakfast bars and 12 bottles of juice evenly into baskets, and we want to know the maximum amount of baskets that makes this possible.
This means that we are looking for the maximal common factor between 12, 18 and 24.
To find it, you can took the smallest number in the set, in this case, 12, and look at his divisors, then see if these divisors also divide the other numbers in the set.
Let's do it:
The biggest divisor of 12 is 6, because of 12/6 = 2.
Now 18/6 = 3, so 6 is also a divisor of 18.
24/6 = 4, then 6 is also a divisor of 24.
Then the maximal common factor of the numbers 12, 18 and 24 is 6.
This means that the maximum number of baskets that have an even distribution of the things is 6, where each basket has 2 bottles of juice, 3 breakfast bars, and 4 muffins.
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Simona si Andrei au impreuna 648 de lei. Andrei are o suma de trei ori mai mare decat a Simonei. Cei doi copii hotarascsa cumpere un joc Lego care costa 128 de lei. Afla cati bani ii raman fiecarui copil, stiind ca ei au cheltuit sume egale.
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The volume of a cube with a side length of [tex]4r^3s[/tex] is a monomial expressed as[tex]64r^9s^3[/tex], derived by cubing the side length according to the formula for the volume of a cube.
To express the volume of a cube with the side length[tex]4r^3s[/tex] as a monomial, we use the formula for the volume of a cube, which is [tex]Volume = side^3[/tex]. Therefore, for a cube with side length [tex]4r^3s[/tex], the volume V can be calculated as follows:
[tex]V = (4r^3s)^3 = 4^3 \times (r^3)^3 \times s^3 = 64 \times r^9 \times s^3[/tex]
This simplifies to V = 64r^9s^3, which is the monomial representing the volume of the cube.
Three students are arguing over who can run the fastest. Student A says that she can run 2/3 mile in six minutes. Student B says that he can run 1/2 mile in four minutes. Student C says that he can run 4/5 mile in eight minutes. What fraction of a mile can Student C run in one minute?
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−20≤5/9(F−32)≤−15 I don't have a calc. for fractions, its at school
The simplified form of the inequality expression is −4 ≤ F ≤ 5
Using the inequality expression given:
−20≤5/9(F−32)≤−15multiply through by 9
−180 ≤ 5 (F−32) ≤ -135
−180 ≤ 5F - 160 ≤ -135
Add 160 to all sides of the expression
−20 ≤ 5F ≤ 25
divide through by 5 to isolate F
−4 ≤ F ≤ 5
The simplified form of the inequality expression is −4 ≤ F ≤ 5
Complete Question:
Simplify the inequality: −20 ≤ 5/9(F−32) ≤ -15
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The quotient of 25 and t plus 6 is the same as twice t plus 1. Turn into equation!
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how can you compare and order rational and irrational numbers
To compare and order rational and irrational numbers, convert rational numbers to decimals and compare them directly, and for irrational numbers, compare their approximate decimal values.
Comparing and ordering rational and irrational numbers involves understanding their magnitude on the number line.
Let's compare 3 rational and irrational numbers: [tex]\( \frac{5}{3} \), \( \sqrt{2} \), and \( -\frac{4}{7} \).[/tex]
1. [tex]\( \frac{5}{3} \)[/tex] is a rational number, as it can be expressed as a fraction.
2. [tex]\( \sqrt{2} \)[/tex] is an irrational number, as it cannot be expressed as a fraction.
3. [tex]\( -\frac{4}{7} \)[/tex] is a rational number, a negative fraction.
To compare them:
1. [tex]\( \frac{5}{3} = 1.67 \)[/tex]
2. [tex]\( \sqrt{2} = 1.414 \)[/tex]
3. [tex]\( -\frac{4}{7} = -0.57 \)[/tex]
Ordering them:
[tex]\( -\frac{4}{7} < \sqrt{2} < \frac{5}{3} \)[/tex]
Calculation:
1. [tex]\( \frac{5}{3} = 1.67 \)[/tex]
2. [tex]\( \sqrt{2} = 1.414 \)[/tex]
3. [tex]\( -\frac{4}{7} = -0.57 \)[/tex]
Order: [tex]\( -\frac{4}{7} < \sqrt{2} < \frac{5}{3} \)[/tex]
So, [tex]\( -\frac{4}{7} \)[/tex] is the smallest, followed by [tex]\( \sqrt{2} \)[/tex], and [tex]\( \frac{5}{3} \)[/tex] is the largest. This is because irrational numbers lie between rational numbers and have a greater magnitude.
Complete Question:
How can you compare and order rational and irrational numbers ?
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Mrs. Sanchez earns a total of $11,314 in commissions and bonus for the year, calculated by adding her annual net commission of $10,764 to her hiring bonus of $550.
How much Mrs. Sanchez earns in commissions and bonus for the year:
1: Calculate her weekly net commission.
She earns $275 per week in commission.
However, $68 is deducted for taxes and benefits, leaving her with:
Weekly net commission = $275 - $68 = $207
2: Calculate her annual net commission.
Assuming she works 52 weeks a year (standard for full-time employment):
Annual net commission = $207/week * 52 weeks/year = $10,764
3: Add the hiring bonus to her net commission.
Her total earnings from commissions and bonus are:
Total earnings = $10,764 + $550 = $11,314
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Answer:
Find out the how much is his overall budget .
To prove
Let us assume that the overall budget of Mr.Hollins be x.
As given
Mr. Hollins determined that he gives away $800 each month.
If he gives away 16% of his budget.
16% is written in the decimal form.
[tex]= \frac{16}{100}[/tex]
= 0.16
Than the equation becomes
x × 0.16 = 800
[tex]x = \frac{800}{0.16}[/tex]
x = $5000
Therefore the overall budget of Mr.Hollins be $5000 .
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