One-third of a number is at least four less than the number. Which inequality represents the number?
Answers
When one-third of a number is at least four less than the number, the inequality to represent the information is C. n ≥ 6.
What is an inequality?It should be noted that an inequality is simply used to illustrate the expressions that aren't equal.
Let the number be n.
This will be illustrated as:
1/3n ≥ n - 4
Collect like terms
1/3n - n ≥ -4
-2/3n ≥ -4
Multiply through by -3/2
n ≥ -4 × -3/2
n ≥ 6
The value is n ≥ 6.
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Related Questions
Use the point-slope formula to write an equation of the line that passes through (0,6) and (-2,0) write answer in slope intercept form
Answers
Equation using slope intercept form is 3y = x + 18
What is slope intercept form?An intercept in mathematics is a location on the y-axis through which the line's slope passes. It is a place on the y-axis where a straight line or a curve crosses. This is reflected in the equation for a line, which is written as y = mx + b, where m denotes slope and c denotes the y-intercept. Y = mx + b is the general formula for the slope-intercept form, where m stands for the line's slope and b for the y-value of the line's y-intercept. We may more easily determine a line's slope and its y-axis intersection using the slope-intercept form of a linear equation.
Given Data
Points(0,6) and (-2,0)
The slope formula = [tex]\frac{y_{2}-y_{1 } }{x_{2}-x_{1} }[/tex]
y₂= 0
y₁=6
x₂=-2
x₁=0
Slope = (-2-0)/(0-6)
Slope = -2/ -6
Slope = 1/3
Slope intercept form
y = mx + b
y = (1/3)x + 6
y = (x+18)/3
3y = x + 18
Equation using slope intercept form is 3y = x + 18
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Identify the zeros of the funtion using a graphing calculator.
2
f(x)=x(squared) - 9
enter your answer in {brackets} from least to greatest
Answers
The zeros of the function are x = 3 and x = -3
How to determine the zeros of the function?The equation of the function is given as
f(x) = x(squared) - 9
Rewrite the equation properly
So, we have the following equation
f(x) = x^2 - 9
Express the equation as a difference of two squares
So, we have the following equation
f(x) = (x - 3)(x + 3)
Set the equation to 0
(x - 3)(x + 3) = 0
Split
x - 3 = 0 and x + 3 = 0
Solve for x
x = 3 and x = -3
Hence, the solutions are -3 and 3
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How many solutions does -14 + 6b + 7 - 2b = 1 + 5b have
Answers
The number of solutions that -14 + 6b + 7 - 2b = 1 + 5b has is 1 solution.
How to illustrate the information?It should be noted a equation is important to illustrate the relationship between the variables. In this case, the equation given is illustrated as:
-14 + 6b + 7 - 2b = 1 + 5b
Collect like terms
-8 + 6b - 2b = 5b
b = -8
Therefore, it has only one solution.
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Solve the inequality.16-x^=0
Answers
Inequalities
Solve:
[tex]16-x^2\le0[/tex]For a better understanding, we first multiply the inequality by -1. Recall by doing so, the sign must be flipped:
[tex]x^2-16\ge0[/tex]Factor the binomial:
[tex](x-4)(x+4)\ge0[/tex]We have a product of two variable expressions and it must be positive or zero. That can only be possible if:
* Both factors are positive or zero
* Both factors are negative or zero
The answer can come from any of the conditions stated above, so the solution is the OR combination of the individual solutions.
The first condition states:
x - 4 ≥ 0 AND x + 4 ≥ 0
This leads to the solution:
x ≥ 4 AND x ≥ -4
If x must be greater or equal to 4 and greater or equal to -4, then the AND combination gives the solution: x ≥ 4
The second condition states:
x - 4 ≤ 0 AND x + 4 ≤ 0
This leads to:
x ≤ 4 AND x ≤ -4
The AND combination gives the second solution x ≤ -4
The final solution is the first solution OR the second solution, that is:
x ≤ -4 or x ≥ 4
Representing the solution in the number line, we get the graph below:
Expressed in interval form: (-∞ , -4] U [4, +∞)
A test was given to a group of students. The grades and gender are summarized below A B C TotalMale4192043Female1116532Total15352575If one student is chosen at random from those who took the test,Find the probability that the student got a 'B' GIVEN they are male.
Answers
What is the answer to m
Answers
the sum of the internal angles of a quadrilateral is 360, therefore:
[tex]\begin{gathered} m\angle A+m\angle B+m\angle C+m\angle D=360 \\ \text{and} \\ m\angle A+m\angle C=180 \\ m\angle B+m\angle D=180 \end{gathered}[/tex]so
[tex]\begin{gathered} a+5+a-25=180 \\ 2a-20=180 \\ 2a-20+20=180+20 \\ 2a=200 \\ \frac{2a}{2}=\frac{200}{2} \\ a=100 \end{gathered}[/tex]mm
mm
the phone sells Jan a bicycle for $175 and a helmet for $17. The total cost for Jin is 160% of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin
Answers
Jin
The bicycle selling price was : $175
The helmet was for : $17
Jin total cost was 160% of what Stefan spent originally to buy the two items
This means ; 160/100 * x = { 175+17} -----where x is the original amount stefan spent to buy the two items
1.6 x = 192
x = 192 /1.6
x=120
Stefan originally spent $120
The money he made after the sell is: $192-$120 =$72
Answer
a) $120
b) $72
Determine whether the point (4,2) is in the solution set of the system of inequalities below. 4x + y < 2, y > -2
Answers
The point (4,2) is not in the solution set as it do not satisfy the first inequality 4x+y<2.
To be in the solution set of the system of inequalities the point (4.2) must satisfy both the given linear inequalities.
So, 4x + y < 2
when x = 4, y = 2
4(4) + 2 = 18 which is not less than 2
So, point do not satisfies this linear inequality
Now, for y>-2,
y = 2 which satisfies the inequality
Therefore, we say that the point (4,2) is not in the solution set of the system of inequalities.
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Help with this problem
Answers
I₃ indifference curve represents the highest utility
What is an indifference curve?
An indifference curve is a graph that illustrates numerous pairings of two goods or commodities that leave the customer equally well off or satisfied—hence indifferent—when it comes to owning any pairing of the two items that is represented along the curve.
A consumer must give up more of one good in order to buy more of another, hence an indifference curve will always have a negative slope.
The given indifference map is a fast food meals per week vs movie tickets per week graph .
In which I₃ yields more than I₂ .
And I₂ yields more than I₁.
Thus, I₃ curve represents the highest utility.
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Mary sold 192 worth of greeting cards if she received 25% Commission on all sales how much commission did she receive
Answers
25% of 192 = 192 * 25/100 = 192 * 0.25 = 48
Answer:
Mary received $48
Question:
Find all critical points of the function g(x)=sin^2(11x). Express your answer in terms of pi.
(Use symbolic notation and fractions where needed. Use n for all integer values.)
Answers
Critical points are the points where the slope of the function is zero thus at θ = 0,π/22,π11,3π/22 ... will be the critical points of function g(θ) = sin²(11θ).
What is the slope?A slope is a tangent or angle at a point and a slope is the intensity of inclination of any geometrical lines.
Slope = Tanx where x will be the angle from the positive x-axis at that point.
As per the given function,g(θ) = sin²(11θ).
The critical points are the points where the slope of the tangent of the function is zero.
The slope of the tangent of a function is the first derivative thus,
g'(θ) = 0 ⇒ 2× 11 sin(11θ)cos(11θ) = 0
Sin(11θ) = 0 ⇒ θ = 0
Cos(11θ) = 0 ⇒ 11θ = π/2
θ = π/22
Since, sinusoidal functions are repeating thus,
Next critical point = π/22 + π/22 = π/11 and so on.
Hence "Critical points are the points where the slope of the function is zero thus at θ = 0,π/22,π11,3π/22 ... will be the critical points of function g(θ) = sin²(11θ)".
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The measures of the angles of a triangle are shown in the figure below. Solve
for x.
62⁰
82⁰
(x+12)
Answers
Answer: 24
Step-by-step explanation:
The angles of a triangle add to 180 degrees, so:
[tex]62+82+x+12=180\\\\156+x=180\\\\x=24[/tex]
I need help
There are 3 consecutive even integers with a sum of 72. Which equation can be used to find such integers?
x + 2 = 24
x + 2 = 12
x + 1 = 12
x + 1 = 24
Answers
The equation used to find the 3 consecutive even integers with a sum of 72 is x + 2 = 24.
What is defined as the even integers?An even integer is one that is divisible by two, i.e. a multiple of two.For eg:- 2,4,6,... and −2,−4,−6,.... are divided by twoAs a result, the integers 2,4,6,... and −2,−4,−6,.... are all even integersThus, the integer of a form 2k is a even integer, in which k is an integer.For the given data in question.
Let the first even integer be 'x'.
Second even integer will be 'x + 2'.
Thirst even integer will be 'x + 4'.
The sum is 72
x + x + 2 + x + 4 = 72
Simplifying;
3x + 6 = 72
Divide whole equation by 3.
x + 2 = 24
Thus, the equation used to find the 3 consecutive even integers with a sum of 72 is x + 2 = 24.
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Mei and Dennis compare the numbers graphed on the number line below. Mei writes theinequality -9 <-3. Dennis writes the inequality -3 <-9. Which statement is true?FILE-10 -9 -8 -7 -6 -5 -4 -3 -2 -10A)Mei is correct because -9 is greater than 3.B)Mei is correct because -9 is to the left of -3 onthe number line.C)Dennis is correct because 3 is less than 9.D)Dennis is correct because -3 is to the right of--9 on the number line.
Answers
The correct answer is:
Mei statement that the inequality is -9 < -3 is True.
Mei is correct because -9 is to the left of -3 on the number line. ( first option in the picture).
Suppose a hospital would like to estimate the proportion of patients who feel that physicians who care for them always communicated effectively when discussing their medical care. A pilot sample of 40 patients found that 28 reported that their physician communicated effectively. Determine the additional number of patients that need to be sampled to construct a 90% confidence interval with a margin of error equal to 2% to estimate this proportion.
Part 1
The additional number of patients that need to be sampled is
(Round up to the nearest integer.)
Answers
174 more patients need to have their samples taken than were originally anticipated. This is further explained below.
What is a Marginal error?Generally, the equation for the margin of error is mathematically given as
[tex]{Margin\ of \ error } & \ amp;=Z_{o \text { it }} \text { at } 5 \% \text { lo.s } \times S E(p)[/tex]
Where
Z is the distributionSE is the standard deviationGiven that the margin of error should be 7%, or 0.07, the total number of extra patients is denoted by n.
sample proportion = 11/20 = 0.55
q =0.45
Margin of error = Zo at 5% lo.s * S E(p)
To solve for the 0.07amp
[tex]\\\\0.07 =1.96 \times \sqrt{\frac{p q}{n}}[/tex]
[tex]\\\\&0.07=1.96 \sqrt{\frac{0.55 \times 0.45}{20+n}} \\\\0.07 =\frac{0.97508}{\sqrt{20+n}} \\\\\sqrt{20+n} =\frac{0.97508}{0.07} \\\\\end{aligned}[/tex]
20+n =194.04
n =174.04
n=174
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The measures of the angles of a triangle are shown in the figure below. Solve for x.
50°
(6x-18)°
70°
Answers
Answer:
x=13
Step-by-step explanation:
We add all the numbers together, and all the variables
6x-78
We move all terms containing x to the left, and all other terms to the right
6x=78
x=78/6
which should equal 13
A DVD is available at a store for $16.99. The list price of this DVD was $18.75. What was the percent discount? % (Round to the nearest tenth as needed.)
Answers
The cost of DVD = $16.99
The list price of this DVD was $18.75
So, the discount =
[tex]18.75-16.99=1.76[/tex]And the percent discount =
[tex]\frac{1.76}{18.75}\cdot100=9.3866\%[/tex]Rounding the answer to the nearest tenth
So, the answer will be : the percent discount = 9.4%
What can be concluded from the statement ∠1+∠2m∠1+m∠2 = 90°?
Answers
When two angles add to 90º they are called complementary angles.
Then, if in the given statement the sum of angles 1 and 2 is equal to 90º, angles 1 angle 2 are complementary.
Answer: <1 and <2 and <1and <2 are complementary
There are 500 fish in a pond, to 1sf. What is the least possible number of fish that could be taken from
the pond so that there are 400 fish in the pond to 1sf
Answers
Answer:
one
Step-by-step explanation:
The least number of fish COULD be 450 ....this would be 500 to 1 S.F.
if you take ONE fish away there are then 449 which would be 400 to 1 S.F
write an equivalent expression for (925x to the 3rd times y to the negative 4th times z to the second) 0
Answers
Answer:
1
Step-by-step explanation:
Anything to the power of 0 is 1.
Ex:
[tex]x^{0} =1\\3643737737^{0} =1\\[/tex]
The circumference of a circle is 12.56 miles. What is the circle's diameter?
Answers
Answer:
d= 4 miles
Step-by-step explanation:
C=2πr
d=2r
d=C
π=12.56
π≈3.99797mi
Albert is taking a 60 item multiple choice test. He knows the correct answers to all,except 1/5 of the items.If he guesses correctly on 3/4 of these questions,how many items correctly?
Answers
57 items are correct.
What is an item?
Items are a fundamental component of an OracleAS Portal page. Item types are used to categorize items. Item types determine the contents of an item as well as the information kept about it. Users with the necessary permissions can add an item or create an item type. The properties of an object type define the information stored about it. The item types that you can add to a page differ depending on whatever item types the page group administrator has included in the page group. If the built-in item types are insufficiently flexible, users with proper access can develop new custom item kinds to fulfill their needs.
1/5 of 60 items = 60/5 = 12 items
3/4 of 12 items = 12x3/4 = 9 items
Total no. of correct items = 60 - 12 + 9 = 57 items
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The surface area S of a cylinder is
S
=
2
π
r
2
+
2
π
r
h
where r is the base radius and h is the height. What is h, in inches, when S is 175 square inches and r is 6 inches?
Answers
The value of height (h) will be 1.35 inches.
What is Surface area?
The space occupied by a plat surface is called Surface area.
Given that;
Surface area (S) = 2πr² + 2πrh
Where, r is the base radius and h is the height.
Now, When Surface area = 175 square inches
Radius (r) = 6 inches.
Then, We can calculate height as;
Since,
Surface area (S) = 2πr² + 2πrh
175 = 2 × 3.14 × (6)² + 2 × 3.14 × 6 h
175 = 226.08 + 37.68h
175 - 226.08 = 37.68 h
- 51.08 = 37.68 h
h = - 51.08 / 37.68
h = - 1.35
Thus, The value of height (h) will be 1.35 inches.
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Sue used 4 ounces of dark chocolate chips for every 3 ounces of white chocolate chips if she uses 21 ounces of chips altogether how many ounces of dark chocolate chips did she use
Answers
Answer: 12 oz
Step-by-step explanation:
Answer: 12
Step-by-step explanation:
Find 98.6% of 343.7. Round to the nearest thousandth.
Answers
Percentage, a relative value indicating hundredth parts of any quantity.
98.6% of 343.7 is in nearest thousandth 338.888
What is Percentage?Percentage, a relative value indicating hundredth parts of any quantity.
We need to find 98.6% of 343.7.
Ninty eight point six percentage of three hundred forty three point seven.
Ninty eight point six percentage we need to convert into decimal number this can be achieved by dividing with 100.
98.6% =98.6/100
When ninty eight point six is divided by hundred we get zero point nine eight six.
=0.986
We need to find what is 98.6% of 343.7.
To find ninty eight point six percentage of three hundred forty three point seven. we are required to multiply the converted value of 98.6% with three hundred forty three point seven.
Simply we need to multiply 0.986 with 343.7.
=0.986×343.7
=338.888
Hence 98.6% of 343.7 is 338.888
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A baker has a bag with 20 cups of flour. The baker plans to use the flour to make 4 loaves of bread. Each loaf of
bread uses 3 cups of flour.
How many cups of flour will remain in the bag when the baker has finished making the bread?
Enter your answer in the space provided.
Answers
Explanation:
4 x 3 is = 12
20 - 12 = 8
8 cups of flour will remain in the bag.
Diego's current ago is five times Martina's age ten years ago. If Martina is currently m years old, what is Diego's current age in terms of m?
Answers
Given that Diego's current age is five times Martina's age ten years ago.
Martin is currently m years old.
Ten years ago, Martin's age was (m-10) yers.
Since, Diego's current age is five times Martina's age ten years ago., therefore, Diego's current age is
5(m-10).
So, Diego's current age is 5(m-10).
3. Compute the derivatives of the following functions. Do not simplify.
a) f(x)=tanx/e^3
b) f(x)= tan -¹(x³)(x^5)(ln x) c) f(x)=^7√x^5+ 5^x d) g(x)=x^sec(x)
Answers
Answer:
A im sure
Example
hope itz helpppp
Which statement is true of the graphed function? (PICTURE OF GRAPH BELOW)a) More information is needed to determine whether the graphed function is even, odd, or neither.b)The function is neither an even nor an odd function.c) The function is an even function.d) the function is an odd function
Answers
To determine if a function is even or odd, we start from its definition.
While for an EVEN FUNCTION we have: F(x) = F(-X), for an ODD FUNCTION we have F(-X) = -F(X)
Now, from this, we can check that all the values the function achiever for any X value, the -X has same height. The function presents a symmetry over the Y-axis, and this implies in a function to be an EVEN FUNCTION.
And from the solution developed above, the only statement that is true is the
C) The function is an even function.
Find the area of the circle A) 12.56 mm^2B) 25.12 mm^2C) 37.17 mm^2D) 50.24 mm^2
Answers
The formula in getting the area of the circle is:
[tex]A=\pi r^2[/tex]where r = the radius of the circle and the value of π = 3.14
In the diagram, the radius of the circle is 4 mm. Let's replace the "r" in the formula with 4 mm and "π" with 3.14
[tex]A=(3.14)(4mm)^2[/tex]Then, simplify.
[tex]\begin{gathered} A=(3.14)(16mm^2) \\ A=50.24\text{ }mm^2 \end{gathered}[/tex]Therefore, the area of the circle is 50.24 mm². (Option D)
We have π = 3.14 and the radius is 4 mm. Therefore we apply the following formula:
A = π * r²Replacing values in the equation.
A = 3.14 * (4 mm)²We calculate potentiation.
A = 3.14 * 16 mm²We multiply
A = 50.24 mm²
Answer: The circle area is 50.24 mm^2 (option D)✅ .
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