To solve the inequality, multiply both sides by (-5). The solution is b ≤ 30 or (∞, 30]
Tips to solve linear inequalities:
Isolate the variable on one side by using subtraction or addition. Subtraction and addition will not change the inequality.Use division or multiplication to find the solution. Multiplication and division by a positive number will not the inequality. However, if we multiply or divide both sides with a negative number, we need to flip the inequality direction.Interval notation is often used for the solution(s). Recall the differences between a bracket [ or ], and a parenthesis ( or ). A bracket means the endpoint is included in the solution while a parenthesis means the endpoint is not included in the solution. Remember, infinity ∞ always use a parenthesis.
Example: x ≥ 2 can be written as [2, ∞), while
x > 0 is written as (2, ∞)
The given problem:
-b/5 ≥ -6
Notice that the variable, b, is already isolated on the left side. Multiply both sides by (-5) and flip the sign of the inequality ( since we multiply it by a negative number):
-b/5 . (-5) ≤ -6 . (-5)
b ≤ 30
Using the interval notation, the solution is (∞, 30]
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84
12
+(5-7²)-72+6-2
Answer:
8300
Step-by-step explanation:
First, do parenthesis
Then, do the rest of the PEMDAS
Last, you're done!
he larger of two numbers is 15 more than three times the smaller number. If the sum of the two numbers is 63, find the numbers.
Answer:
51 and 12
Step-by-step explanation:
Solve➲ Let a be the bigger number
➲ Let b be the smaller number
[tex]a = 3b + 15\\a = 3 \cdot b + 15\\a + b = 63\\\bold{Solve:b}\\3b + 15 + b = 63\\3b + b = 4b\\4b + 15 = 63\\4b = 63 - 15\\4b = 48\\b = 12\\\\\bold{Solve:a}\\a = 3b + 15 \rightarrow a = 3 \cdot 12 + 15 = 51[/tex]
Thus,
b = 12, a = 51
_______________________________
Wrapping up:
➲ Hope this helps.
➲ Address concerns if needed.
➲ Have a great day!
Knowledge Check
Question 10
Keith purchased a prepaid phone card for $50.75. Calls cost 8 cents a minute using this card. The credit, C (in dollars), left on the card after it is used for x
minutes of calls is given by the following
C=50.75-0.08x
How much credit is left on the card after Keith uses it for 30 minutes of calls
The credit that is left on the card after Keith uses it for 30 minutes of calls is $48.35.
How to calculate the cost?From the information given, Keith purchased a prepaid phone card for $50.75. Calls cost 8 cents a minute using this card
The equation was given as C=50.75-0.08x
Therefore, the credit that is left on the card after Keith uses it for 30 minutes of calls will be:
C=50.75-0.08x
C = 50.75 - 0.08(30)
C = 50.75 - 2.40
C = $48.35
The credit is $48.35.
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Write a sentence for this equation.
2+3n=4n
Answer: 4 times a number equals 2 plus 3 times a number
Step-by-step explanation: (NMA)
Question 1 (Multiple Choice Worth 5 points)
(01.06 LC)
Which statement shows that money is a "measure of value?"
This bill is worth twenty dollars.
My phone is worth eight hundred dollars.
The dollar I just found in my drawer is still worth a dollar.
The more features it has, the more it is worth.
Answer: My phone is worth eight hundred dollars.
Step-by-step explanation:
The correct statements are:
This bill is worth twenty dollars.
My phone is worth eight hundred dollars.
What is an equation?Two algebraic expressions having the same value and symbol '=' in between are called an equation.
Given statements:
This bill is worth twenty dollars.
My phone is worth eight hundred dollars.
The dollar I just found in my drawer is still worth a dollar.
The more features it has, the more it is worth.
From the given statements:
This bill is worth twenty dollars.
Here, the measure of the value is n = $20.
My phone is worth eight hundred dollars.
Here, the measure of the value is m = $800.
Therefore, the correct explanation is given above.
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0.1x+ 3x/5+ 20/ 5 =0.5
Answer:
x = -5
Step-by-step explanation:
Im not very sure but here it is. =D
Tell me if it helps you.
Estimate the bending strength of beams by bending 10 beams untll they break and recording the force at which the beams broke.
The bending strength of beams by bending 10 beams untll they break will be estimated as-
The ten beams that were evaluated.The breaking force of each beam. It is quantitative.What is bending strength?Flexural strength is a material property that refers to the highest stress in a material well before yielding in a bending test. It is also recognized as bending strength or transverse rupture strength.
Some key features regarding the bending strength are-
When a specimen, typically a beam or rod, is bent, it is subjected to a variety of stresses throughout its depth. The stress will be at the maximum compressive stress on the inside of the bend, while it will be at its maximum tensile stress on the opposite side.The extreme fibres are the specimen's inner and outer edges. Tensile stress is what causes most materials to fail before compressive stress. This is caused by small surface defects of varying sizes that grow under tensile stress.Flexural strength is defined as the maximum tensile stress value under bending before the beam and rod fails.
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which city has a greater percentage of households with annual incomes between 50,000 dollars and 80,000 dollars?
The typical household income in both cities is $80,000.
The distribution is more evenly distributed in Statstown . At least 25% of the total values in Medianville are between $60,000 and $80,000, as can be shown. As a result, more than 25% of people have annual incomes between $50,000 and $80,000. 25% of people in Statstown make between $40,000 and $80,000 per year. Therefore, less than 25% of people have annual salaries between $50,000 and $80,000.
What proportion of Americans earn more than $100,000 annually?
In 2020, 24% of Americans had a yearly salary of over $100,000. 34% of American households have a yearly income of $100,000 or more. American households making over $100,000 annually climbed by 4.1% in the five years leading up to 2022.
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The distance between the points (3,-6) and (3,4)
Answer:
10 units
Step-by-step explanation:
calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (3, - 6 ) and (x₂, y₂ ) = (3, 4 )
d = [tex]\sqrt{(3-3)^2+(4-(-6))^2}[/tex]
= [tex]\sqrt{0^2+(4+6)^2}[/tex]
= [tex]\sqrt{0+10^2}[/tex]
= [tex]\sqrt{0+100}[/tex]
= [tex]\sqrt{100}[/tex]
= 10
evaluate write your answer as a whole number or as a simplified fraction
Answer: The answer is 27
Step-by-step explanation: 6 x 6 x 6 = 216. 216 is the numerator. 2 x 2 x 2 = 8. 8 is the denominator.
216 / 8 = 216 '/. 8 = 27
What is meant by the phrase degrees of freedom as it pertains to the computation of the sample standard deviation?.
The phrase "Degrees of Freedom" in the computation of sample standard deviation is, n - 1.
Degrees of freedom:
Degrees of freedom refers to the maximum number of logically independent values, which are values that have the freedom to vary, in the data sample.
Degrees of freedom is calculated by subtracting one from the number of items within the data sample.
Given,
Here we need to find the meaning for the phrase degrees of freedom as it pertains to the computation of the sample standard deviation
It means, There are n-1 degrees of freedom in the computation of s because an unknown parameter is estimated by the sample mean.
For each parameter estimated, 1 degree of freedom is lost.
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What is a polynomial function in standard form with zeros 1,-1, 2, and 4?
○_A. y = x¹ − 6x³ + 7x² + 6x − 8
O B. y = x² - 6x³ + 9x² + 6x-8
OC. y = x³ + 7x² + 6x - 8
OD. y = x - x³ + x²+x-8
The equation using the polynomial function is a x⁴ - 6x³ + 7x² + 6x - 8.
According to the statement
We have to find that the equation using the polynomial function.
So, For this purpose, we know that the
A polynomial function is a function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation
From the given information:
The standard form with zeros 1,-1, 2, and 4:
Polynomial with Zeros 1, - 1, 2 and 4 can be expressed thus :
x = 1 : x - 1
x = - 1 :x + 1
x = 2 :x - 2
x = 4 :x - 4
Hence, we have :
(x - 1)(x + 1)(x - 2)(x - 4) = 0
We can then expand ;
(x - 1)(x + 1) = x² + x - x - 1 = x² - 1
(x² - 1)(x - 2) = x³ - 2x²-x + 2
(x³ - 2x² - x + 2)(x - 4)
x⁴ - 4x³ - 2x³ + 8x² - x² + 4x + 2x - 8
x⁴ - 6x³ + 7x² + 6x - 8.
So, The equation using the polynomial function is a x⁴ - 6x³ + 7x² + 6x - 8.
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Tom keeps all of his marbles in a bag. 5 red marbles. 4 blue marbles. and three yellow are in the bag. if he randomly chooses one marble what is the probability it is blue?
If Tom choose one marble then the probability that it will blue is 1/3.
According to the given question.
Total number of red marbles in a bag = 5
Total number of blue marbles in a bag = 4
Total number of yellow marbles in a bag = 3
So, the total number of marbles in a bag = 5 + 4 + 3 = 12
As we know that, the probability is the measure of the likelihood of an event to happen. It measures the certainty of the event.
Therefore, if Tom choose one marble then the probability that it will blue
= 4/12
= 1/3
Hence, if Tom choose one marble then the probability that it will blue is 1/3.
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Is -1/3 - 4/5 positive, negative, or zero?
The given expression is negative as after the solving fraction the value is: -17/15
What is the fraction addition formula?Examine the fractions' denominators. Find the LCM of the denominators and rationalize them to make the denominators of both fractions the same. Add the fraction numerators while keeping the denominator constant. To find the final sum, simplify the fraction.
According to the given data:Given fraction are : -1/3 , -4/5
Applying the fraction addition formula:
by calculating and reasoning the LCM of denominators Add the fraction numerators while keeping the denominator constant. To find the final sum, simplify the fraction.
= (-1/3)+( -4/5)
Applying the fraction addition rule:
= [tex]\frac{-1}{3}[/tex] - [tex]\frac{-4}{5}[/tex]
Finding the LCM of the denominators:
= [tex]\frac{-5}{15} - \frac{12}{15}[/tex]
= -17/15
The given expression is negative as after the solving fraction the value is: -17/15
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Is the number 6.2 x 10^(-3) greater than 1 or smaller than 1?
The word geometry comes from the Greek words geo, which means "earth," and metron, which means "a measuring
of." Given this information, how do you think the study of geometry developed?
The study of geometry developed from. measuring the Earth.
What is geometry about?Geometry has its roots in issues that people face on a daily basis. According to the conventional myth, which was preserved in Herodotus' History (5th century bce), the Egyptians invented surveying to restore property values following the yearly Nile flood.
One of the first areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects. A geometer is a mathematician who specializes in geometry.
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A machine that originally cost $15,600 has a value of $7500 at the end of 3 years. the same machine has a value of $2800 at the end of 8 years. find the average rate of change in value (depreciation) of the machine between its purchase and the end of 3 years. a. -$3200 per year c. $-5400 per year b. -$2700 per year d. $2700 per year
A) The rate for the first 3 years :
15,600 - 7500 = 8100
8100/3 years = 2,700 per year depreciation.
B) The rate between 3 and 8 years:
7500 - 2800 = 4700
4700 / 5 year = 940 per year depreciation.
C) the value of the machine depreciated at a higher rate in the first 3 years. After the first 3 years, the depreciation rate decreased.
(-2, 8), (r, 4), m = -1/2
A nature specialist tagged 1000 rabbits in the County Park. At a later date, they found 10 tagged rabbits when they caught 200 rabbits. Find the estimate of the total number of rabbits in the County Park.
Answer:
20000 rabbits
Step-by-step explanation:
Explain the difference between partitioning a directed line segment MN in a 2:7 ratio
versus a 7:2 ratio. Include a specific example as part of your explanation.
The difference between partitioning a directed line segment MN in a 2:7 ratio versus a 7:2ratio because of following
To understand this let us take the line segment MN which is of a length is divided into 9 equal parts. Here, we are dividing it into nine parts because the proportions 2 and 7 make a sum of 9.
When we divide the line segment MN in the ratio 2:7, the first two parts out of the nine from the left side are separated from the rest 7. This means that the first proportion from the left hand side of the line is smaller than the other.
Now, when we divide the line segment MN in the ratio7:2, the first seven parts out of the nine from the left side are separated from the rest two. This means that the first proportion from the left hand side of the line is larger than the other.
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what is 16 divided by 2 2/3 pls help
It should be noted that 16 divided by 2 2/3 is 6.
How to compute the value?It should be noted that the information is to compute 16 divided by 2 2/3.
Therefore, this will be:
16 ÷ 2 2/3
= 16 ÷ 8/3
= 16 × 3/8
= 2 × 3
= 6
Therefore, the value is 6.
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A small model car is 12 inches long and the actual car is 132 inches long. what is the scale factor of the model to the actual car?
Help please
Answer: 11
Step-by-step explanation: 132/12 = 11
You divide the actual car length by the model and you get the scale factor.
The scale factor of the model to the actual car is 1/11 inches.
What is a scale factor?The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).
Given:
A small model car is 12 inches long and the actual car is 132 inches long.
To find the scale factor:
When both the original dimensions and the new dimensions are known, the scale factor may be determined.
The following is a basic formula to determine a figure's scale factor:
Scale factor = Dimension of the new model ÷ Dimension of the actual car
Scale factor = 12 / 132
Scale factor = 1/11
Therefore, the scale factor is 1/11 inches.
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AP stats.
does anyone know how to calculate frequency and divide into classes?
Answer:
I answered you in another answer
Step-by-step explanation:
suppose that 51% of people own dogs. if you pick two people at random, what is the probability that they both own a dog?
If 51% of people owns dogs and you randomly pick two people, then probability that they both own a dog is 0.2601
Given,
The percentage of people own dogs= 51%
We know,
Probability = Number of favorable outcomes / Total outcomes.
If you choose random guy and probability that guy own a dog = 0.51
Here the probability of having a dog is independent events
Then,
Probability that they both own a dog = Probability of first person own a dog × Probability of second person own a dog
= 0.51×0.51
=0.2601
Hence, If 51% of people owns dogs and you randomly pick two people, then probability that they both own a dog is 0.2601
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The fixing of east and west germany's currencies at a 1:1 ratio to each other during the german unification in 1990 is an example of a _____.
The fixing of east and west Germany's currencies at a 1:1 ratio to each other during the German unification in 1990 is an example of a fixed exchange rate policy
We know
The fixed exchange rate policy is the rule to ties the country's official currency exchange rate to another country's currency which set by the central bank or government.
Here,
The fixing of east and west Germany's currencies at a 1:1 ratio to each other during the German unification in 1990. The fixed exchange policy is used here
Hence, The fixing of east and west Germany's currencies at a 1:1 ratio to each other during the German unification in 1990 is an example of a fixed exchange rate policy
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i need help how to solve this
The answer is 23
Step-by-step explanation:
7 + 2^4 ÷ 4 + 2(3² × 2 ÷ 6 + √9)
7 + 16 ÷ 4 + 2(9 × 2 ÷ 6 + √9)
7 + 4 + 2(3 + 3)
11 + 2(6)
11 + 12
= 23
what is the mean (average) rate that the grand canyon has been eroded into the colorado plateau during the past 6 million years, expressed in millimeters per year? show your work below.
The mean rate the Grand Canyon has been eroded into the Colorado plateau within the past 6 million years is [tex] \frac{4 }{15} \: mm/year [/tex]
What is the average or mean of the given data?The possible part of the question as obtained from a similar question includes;
The time at which the western Grand Canyon began to be evacuated by river erosion = 6 million years ago
The depth of the Grand Canyon = 1.6 km
(a) The average value or the mean is given by the formula;
[tex]Average = \frac{Depth \: of \: erosion }{Time \: taken } [/tex]
The depth of erosion = 1.6 km
Time of erosion = 6 million years
The average rate at which the Grand Canyon has been eroded into the Colorado plateau is therefore;
[tex]Average = \frac{1.6 \: km }{6 \times {10}^{6} \: years} [/tex]
1.6 km = 1,600,000 mm
Therefore;
[tex]Average = \frac{1600000 \: mm }{6 \times {10}^{6} \: years} = \frac{4 }{15} \: mm/year [/tex]
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I need help please !!
Step-by-step explanation:
A has no solution.
15x - 45 = 15x + 75
-45 = 75
is false for every value of x.
in other words, when you add to the same thing different amounts, the result cannot be identical ever.
B has a solution
-45x - 45 = -75x + 75
-120x = 120
-x = 1
x = -1
C has a solution
45x - 45 = -15x + 75
60x = 120
x = 2
D has a solution
15x - 45 = 75x + 75
-120 = 60x
-2 = x
a is 60 miles from b. an automobile at a starts for b at the rate of 20 miles an hour at the same time that an automobile at b starts for a at the rate of 25 miles an hour. how long will it be before the automobiles meet?
The time taken before the two automobiles meet is determined as 1.33 hours.
Time taken before the two automobiles meetApply the principle of relative velocity as shown below;
Vat + Vbt = D
(Va + Vb)t = D
where;
D is the distance between the two automobilest is the time when they meetVa is velocity of automobile aVb is velocity of automobile b(20 + 25)t = 60
45t = 60
t = 60/45
t = 1.33 hours
Thus, the time taken before the two automobiles meet is determined as 1.33 hours.
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evaluate the expression if a=3/4, b=-8, c=-2, and d=3
Answer: 206
Step-by-step explanation:
a=3/4, b=-8, c=-2, d=3
-b[a+(c-d)^2]=
-(-8)[3/4+(-2-3)^2]=
8[3/4+(-5)^2]=
8[3/4+25]=
8*3/4 + 200=
24/4 + 200=
6+200=206