The compound inequality that represents the set of real numbers that are between -4 and 5 inclusive is the option;
D: -4 ≤ n ≤ 5
How can the compound inequality be found?A compound inequality comprises of a sentence that makes two inequality statements that are joined by either the word 'and' or 'or'.
Given that the inequality represents the set of all real numbers that are between -4 and 5, and -4 < 5, the required set of numbers is therefore of the form;
[tex] - 4 \: \leftrightarrow \: 5[/tex]
The expression of the required set of numbers as inequalities is therefore;
-4 ≤ n and n ≤ 5The compound inequality is therefore;
D: -4 ≤ n ≤ 5
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Round 3.691 or the nearest hundredth
Answer:
3.69
Step-by-step explanation:
Answer:
3.69
Step-by-step explanation:
when the nearest number from the right side is lower than 5 it just disappears and all of the numbers after that will disappear as well.
The problem-solving plan identifies the letter W as "What do you need to do to solve the problem?" Which of the following answer choices are included in the problem solving plan for the letter W?
A. Solve the problem and change your strategy if necessary.
B. Did you check the answer and did you answer the question asked.
C. Read the problem carefully, find the question, understand the problem and find out what you know.
D. Organize the problem and find the question.
Answer:
d
Step-by-step explanation:
Answer:The answer would most likely be c Read the problem carefully,find the question,understand the problem and find out what you know.
A mining company owns two mines. These mines produce an ore that can be graded into two classes: regular grade and low grade. The company must produce
at least 420 tons of regular-grade and 480 tons of low-grade ore per week. The first mine produces 6 tons of regular-grade and 16 tons of low-grade ore per
hour. The second mine produces 18 tons of regular-grade and 8 tons of low-grade ore per hour. The operating cost of the first mine is $20,500 per hour, and the
operating cost of the second mine is $10,200 per hour. The first mine can be operated no more than 55 hours a week, and the second mine can be operated no
more than 36 hours a week. How many hours per week should each mine be operated to minimize the cost?
The number of hours to operate the mines to minimize cost are Mine 1 hour = 26.5 hours and Mine 2 hour = 14.5 hours
How to determine the number of hours?The given parameters can be represented using the following table of values
Mine 1 (x) Mine 2 (y) Available
Regular grade 6 18 420
Low grade 16 8 480
Operating cost 20500 10200
Time 55 36
From the table, we understand that we are to minimize cost
This means that:
Objective function: C = 20500x + 10200y
Subject to:
6x + 18y >= 420
16x + 8y >= 540
Next, we plot the constraints on a graph (see attachment)
From the graph, we have
(x, y) = (26.5, 14.5)
This means that
Mine 1 hour = 26.5 hours
Mine 2 hour = 14.5 hours
Hence, the number of hours to operate the mines to minimize cost are Mine 1 hour = 26.5 hours and Mine 2 hour = 14.5 hours
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The Andersons are planning to take a 960-mile trip. They will travel 840 miles by car. What percent of the distance will they not travel by car?
The percent of distance that the Andersons will not travel by car is 12.5%, If they are planning to take a 960-mile trip and they will travel 840 miles by car.
Total distance the Andersons are planning to take is 960-mile
They will travel 840 miles by car
Distance they will not travel by car = total distance - distance travelled by car
= 960 - 840 miles
=120 miles
Percentage formula = (value/ total value) x 100
percent of the distance will they not travel by car =
(total distance - distance travelled by car) x 100/total distance
=((960 - 840)/ 960) x100
=(120/ 960) x 100
12.5
If the Andersons are planning to take a 960-mile trip and they will travel 840 miles by car then the percentage of distance they will not travel by car is 12.5%
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For a normally distributed population with a mean of 150 and standard deviation of 25, approximately what percentage of the observations should we expect to lie between 100 and 200?
The percentage of observations which we expect to lie between 100 and 200 is 3.38%
Given, the mean is 150 and
standard deviation(sd) = 25
what percentage of observation lie between 100 and 200.
x + 1sd = 175
x - 1sd = 125
x + 2sd = 200
x - 2sd = 100
x + 3sd = 225
x - 3sd = 7
observation between 100 and 200 lie from x + 1sd
Therefore P(x) = (100-175)÷25
= -3
=3.38%
Hence the percentage of observations that lie between 100 and 200 is 3.38%
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Two figures are said to be SIMILAR if they are the same shape. In more mathematical language, two figures are similar if their corresponding angles are congruent , and the ratios of the lengths of their corresponding sides are equal. This common ratio is called the scale factor.
This pair of figures is similar. Find the value of the missing side (x).
Answer:
The ratio is 8:1 and it is a rectangle so x is 56
If on the similar image the sides are the same the other image will be aswell
Hope thie helps!
If you have any other question feel free to ask!
If 8 is 40% of N, then what does N equal?
Answer:20
Step-by-step explanation:
n x 40% =8
So n = 8 / 40%
n = 20
rectangle has a length of 35 yards less than 7 times its width. If the area of the rectangle is 6468 square yards, find the length of the rectangle.
Therefore the width of the rectangle is 33 yards
length of the rectangle is 196 yards.
Let the width of the rectangle be 'x'
Given the length of the rectangle = 35 yards less than 7 times the width
= 7x - 35
Given the area of rectangle = 6468 square yards
We know that area of rectangle = length * width
= (7x - 35 ) * x
By comparing both we get,
(7x - 35) * x = 6468
7x² - 35x - 6468 = 0
By dividing the equation by '7' we get
x² - 5x - 924 = 0
Factorize the above equation we get
x² - 33x + 28x - 924 = 0
x ( x - 33) +28 (x - 33 ) = 0
( x - 33 ) ( x + 28 ) = 0
∴ x = 33 , -28
Negative values are not consider
Therefore the width of the rectangle is 33 yards
length of the rectangle = 7(33) - 35
= 231 - 35
= 196 yards
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The circumference of a circle is 14 in. What is the area, in square inches?
Answer:
15.6 in² (nearest tenth)
Step-by-step explanation:
Circumference of a circle
[tex]\large\boxed{C=2\pi r}[/tex]
Where r is the radius of the circle.
Given:
C = 14 inSubstitute the given value into the equation for the circumference and solve for r:
[tex]\begin{aligned}\implies 14 & = 2 \pi r\\\\ r & = \dfrac{14}{2 \pi}\\\\ r & = \dfrac{7}{ \pi}\end{aligned}[/tex]
Area of a circle
[tex]\large\boxed{A=\pi r^2}[/tex]
Where r is the radius.
Substitute the found radius into the equation for area and solve for A:
[tex]\begin{aligned}\implies A&=\pi \left(\dfrac{7}{\pi}\right)^2\\\\ A&=\pi \cdot \dfrac{7^2}{\pi^2}\\\\ A&=\dfrac{49\pi}{\pi^2}\\\\ A&=\dfrac{49}{\pi}\\\\A & = 15.6\;\sf in^2\;(nearest\:tenth)\end{aligned}[/tex]
Therefore, the area of the circle with a circumference of 14 in is 15.6 in².
Can somebody help me if you know what this is
Answer: i think it might be 72
Answer:72
Step-by-step explanation:
The least common multiple is the smallest common(of equal value) number. we get this number by multiplying the two numbers by a number value till we get a common number between the two.
just need help with some of them at least 5 questions please already did the first one. i put 90 points please help.
2. The solution to the given system of equation is x = 1 and y = 6
3. The solution to the given system of equations is x = 1, y = 2
4. The simplified form of the expression is y²
5. The simplified form of the expression is 2
8. the subtraction of the polynomials yields -2x³ + 3x² + 9x - 11
9. The multiplication yields x² - 4x - 96
10. The factored form of the expression is (x + 6)(x- 6)
11. The solutions to the given quadratic equation are x = 5 and x = -6
Solving system of equationsFrom the question, we are to solve the given system of equations
The given system of equation is
y = 10 - 4x --------- (1)
2x + 3y = 20 --------- (2)
Substitute equation (1) into equation (2)
2x + 3y = 20
2x + 3(10 -4x) = 20
2x + 30 - 12x = 20
2x - 12x = 20 - 30
-10x = -10
x = -10/-10
x = 1
Substitute the value of x into equation (1)
y = 10 - 4x
y = 10 - 4(1)
y = 10 - 4
y = 6
Hence, the solution to the given system of equation is x = 1 and y = 6
3.
From the question, we are to solve the system of equations using the elimination method
The given system of equations is
5x + 2y = 9
-5x + 4y = 3
Add the two equations
5x + 2y = 9
-5x + 4y = 3
----------------------
0x + 6y = 12
6y = 12
y = 12/6
y = 2
Substitute the value of y into the first equation
5x + 2y = 9
5x + 2(2) = 9
5x + 4 = 9
5x = 9 - 4
5x = 5
x = 5/5
x = 1
Hence, the solution to the given system of equations is x = 1, y = 2
4. From the question, we are to simplify the expression
y⁻⁴(y³)²
First, multiply the exponents in (y³)²
(y³)² = y ³ ˣ ²
= y⁶
Thus,
The expression becomes y⁻⁴y⁶
Applying the multiplication law of indices
y⁻⁴y⁶ = y⁻⁴ ⁺ ⁶
= y²
Hence, the simplified form of the expression is y²
5.
From the question, we are to simplify
∛8
First, express 8 in exponent form
8 = 2³
Thus,
The expression becomes
∛2³
Applying one of the laws of indices,
∛2³ = (2³)¹/³
Multiplying the exponents, we get
2¹
= 2
8.
From the question, we are to subtract the polynomial
(3x² + 5x - 8) - (2x³ - 4x + 3)
Subtracting
(3x² + 5x - 8) - (2x³ - 4x + 3)
3x² + 5x - 8 -(2x³ - 4x + 3)
Open the parentheses by distributing negative
3x² + 5x - 8 -2x³ + 4x - 3
Collect like terms
-2x³ + 3x² + 5x + 4x - 8 - 3
Simplify
-2x³ + 3x² + 9x - 11
Hence, the subtraction of the polynomials yields -2x³ + 3x² + 9x - 11
9.
From the question we are to multiply
(x + 8)(x - 12)
Applying the distributive property
x(x -12) +8(x -12)
x² - 12x + 8x - 96
Simplifying
x² - 4x - 96
10.
From the question, we are to factor
x² - 36
This can be written as
x² - 6²
From the rule of difference of two squares, we have that
a² - b² = (a + b)(a - b)
Thus,
x² - 6² = (x + 6)(x- 6)
11.
From the question, we are to find the solutions for
x² - x - 30 = 0
Solve by factoring
x² - x - 30 = 0
x² + 6x - 5x - 30 = 0
x(x + 6) -5(x + 6) = 0
(x - 5)(x + 6) = 0
∴ x - 5 = 0 and x + 6 = 0
x = 5 and x = -6
Hence, the solutions to the given quadratic equation are x = 5 and x = -6
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Graph the image of rhombus TUVW after a reflection over the line x = 1.
104
-10 -8 -6
U
-4
T
V
W
22
8
6
4
CN
2
-2
-4
2
4
6
8
00
X
10
Answer:
its c
Step-by-step explanation:
What si the greatest multiple of 60 and 72
The greatest common multiple of 60 and 72 is 6.
The given numbers are 60 and 72.
What is the meaning of greatest common multiple?The greatest common factor (GCF) is a term used to describe the biggest number that can divide evenly into two or more numbers. Sometimes, this is also referred to as the greatest common divisor (GCD) or highest common factor (HCF). A factor is a smaller number that can divide evenly into that number.
Now, 60 = 2×2×3×5 and 72 = 2×2×2×3×3
The common factors are 2 and 3
So, the greatest common factor =2×3=6
Therefore, the greatest common multiple of 60 and 72 is 6.
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-2x + 14y = -29
x-7y=19
elimination process
Answer:
no solution
Step-by-step explanation:
Multiplying the second equation by 2 gives 2x-14y=38.
Adding this to the first equation, we get 0=9, and thus there is no solution.
What is f(3)?
-9
-1
1
9
Answer:
9
Step-by-step explanation:
Edge
slope of (-8,-3) and (-1,-2)
Solution :-
As we know that,
m = y_2 - y_1 / x_2 - x_1Therefore ,
>> m = -2 - (-3) / -1 - (-8)
>> m = -2 + 3 / -1 + 8
>> m = 1 / 7
We have that the data are:
(x₁ = -8, y₁ = -3) and (x₂ = -1, y₂ = -2)
The slope is equal to the change in and with respect to change in X, or what rises when moving forward.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{Change \ in \ y}{Change \ in \ x} \ \longmapsto \ \ m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} } \end{gathered}$}}[/tex]
The change in X is equal to the subtraction in the X coordinate (also called advance), and the change in and is equal to the subtraction in the coordinate and (also called elevation).
Introduce the values of x and y In the equation to find the slope.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{-2-(-3)}{-1-(-8) } } \end{gathered}$}}[/tex]
[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{1}{7} } \end{gathered}$}}}[/tex]
The slope of (-8, -3) and (-1, -2) is 1/7.50 POINTSS Solve for q.
s = 4p + 4q
Can someone help me with this question?
Answer:
A) y = 0.3x+24
B) 283.5 dollars
Step-by-step explanation:
A) To create an equation in slope-intercept form, we can start by using the numbers the problem gave us and represent them as coordinates. Generally, time is always our x-value.
(230,93)
(530,183)
Now that we have our two coordinates, we can plug them into the slope-intercept formula: y₂-y₁/x₂-x₁ to find our slope.
(183-93)/(530-230) = 0.3
Now that we have our slope, we can plug it into our equation.
y = 0.3x + b
To find our y-intercept, we can take either one of our 2 coordinates (x,y) and plug them into the equation to solve for b.
93 = 0.3(230) + b
93 = 69 + b
93 - 69 = b
b = 24
Now that we have found our y-intercept, we can plug it into b to complete the equation.
y = 0.3x +24
B) If 865 minutes are used, we can plug 865 into x in our equation to find the total cost.
0.3(865) + 24 = 283.5
Points P, Q, R, and S are collinear. Point Q is between P and R, R is between Q and S, and PQ =RS. If PS= 23 and PR = 17, what is the value of QR?
QR=
(Simplify your answer.)
Answer:
QR = 11
Step-by-step explanation:
P-Q-R-S
PQ = RS
PS = 23
PR = 17
so RS = PS - PR = 23 - 17 = 6
RS = PQ = 6
QR = PS - (RS + PQ) = 23 - (6 + 6) = 23 - 12 = 11
In cell B16, enter a function to calculate the total attendance for the years 2018 through 2022 using the totals in the range B12:F12
The Excel formulas to enter in cell B16 is = SUM(B12 : F12)
How to determine the Excel function?From the question, we can assume the following:
Range = B12 to F12The sum of entries in cells B12 through F12 represent the required sumUsing the sum function, we have:
Total = SUM(B12 : F12)
So, the formula to enter in cell B16 is:
= SUM(B12 : F12)
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find the prime factors of 6912 and cube root
The prime factors of 6912 are 2 and 3 and the cube root of 6912 is approximately 19.05 (rounded to 2 decimal places) .
Prime numbers are numbers which do not have any factors other than 1 and itself. For example 7 is a prime number, 37 is a prime number as the factors of 7 are 1 and 7 and the factors of 37 are 1 and 37.
Prime factorization of a number is given by writing all the prime factors of as number in multiplication form.
The prime factorization of 6912 gives:
6912 = 2 × 2 × 2 ×2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 = 2⁸ × 3³
Hence the prime factors of 6912 are 2 and 3.
The cube root of 6912 = 19.0488... ≈ 19.05 (rounded to 2 decimal places)
Therefore the cube root of 6912 is approximately 19.05 .
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If y=+3x-2 Complete the following
x=-2
y=
Answer:
-8
Step-by-step explanation:
If x = -2, then plug -2 into the equation where the x is:
y = 3(-2) - 2
Then solve:
3 * -2 = -6
-6 - 2 = -8
So, y = -8
Write the expression (-7) x (-7) x 5 x 5 x 5 x 5 using exponents
Answer: [tex]-7^2 * 5^4[/tex]
Step-by-step explanation:
Problem
Tapiwa raked 5%, percent more leaves than Adam raked. Tapiwa raked 357liters of leaves.
How many liters of leaves did Adam rake?
Answer:
339.15
Step-by-step explanation:
5% is equal to 1/20, so we can use 1/20 in place of 5%. All that needs to be done is to determine 1/20 of 357 and subtract the result (we subtract because Tapiwa raked more than Adam)
357 x 1/20 = 17.85
357 - 17.85
339.15
The doctor has determined that one reason for the sickness is due to Cameron’s diet and that he has a protein deficiency. A change in his diet is necessary. He must increase the amount of protein that Cameron consumes. To begin this process, Cameron has to figure out how much protein he should consume in a day. Assume that he is 25 years old and weighs 132 lbs. According to the Food and Nutrition Board, Institute of Medicine, National Academies website, adults need 0.66 g/kg/d of protein.
How many grams of protein does he need each day?
Using proportions, it is found that he needs 39.5 grams of protein each day.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
First we have to convert his weight to kg. Each lb has 0.453592 kg, hence his weight in kg is given by:
132 x 0.453592 = 59.87 kg.
Each day, he needs to consume 0.66 g for each kilogram in his body, hence the amount of protein that he needs to consume each day is given by:
0.66 x 59.87 = 39.5.
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For the stem-and-leaf plot below, what are the maximum and minimum entries?
1 | 3 4
1 | 6 6 6 7 8 9
2 | 0 1 1 2 3 4 4 5 6 6
2 | 7 7 7 8 8 9 9 9
3 | 0 1 1 2 3 4 4 5 5
3 | 6 6 6 7 8 8 9 9
4 | 1 3
Mr Mathes purchases 4 tickets for his family find the value of the expression when t=4
The value of the expression when t=4 is 16
How to calculate the expression?It should be noted that from the information given, it was stated that Mathes purchases 4 tickets for his family.
Therefore, the value of the expression when t=4 will be:
C = 4t
C = 4(4)
C = 4 × 4.
C = 16
Therefore, the value of the expression when t=4 is 16.
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The electoral college is in place so that states with a greater population have more influence in a presidential election. The higher populated states have more votes. For example, Washington is roughly 3 times as populated as Idaho, so Washigton’s number of electoral college votes is 300% of Idaho’s number. If Idaho has 4 electoral college votes, how many votes does Washington have? Percent formula
Answer: 12 electoral college votes
Step-by-step explanation:
4*100%=
4*100/100=
400/100=4
4*300%=
4*300/100=
1200/100=12 votes
8 classes for
n = 75
measurements; minimum value = 40; maximum value = 195
40,60,80,100,120,140,160,180,200 are the class boundaries.
How to find the class boundaries?The lower class boundary (LCB) is the LCL minus one-half the tolerance, and the upper class boundary (UCB) is the UCL plus one-half the tolerance. Class borders are the end points of an open interval that contains the class interval.
given that
8 classes for n = 75measurements
minimum value = 40
maximum value = 195
from the question
smallest class boundary = (maximum - minimum value) / n classes
= (195 - 40) / 75 = 19.375 = 20
round off the value means 20
using minimum value and smallest class boundary.
Hence, the 40,60,80,100,120,140,160,180,200 are the class boundaries.
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Disclaimer: the question is incomplete on portal. Here is the complete question.
Question: Use the information given to find a convenient class width. Then list the class boundaries that can be used to create a relative frequency histogram. (Round your class width up to the nearest multiple of 5. Use the minimum value as the smallest class boundary. Enter your class boundaries as a comma separated list.)
8 classes for n = 75 measurements; minimum value = 40; maximum value = 195.
Factorize the equation
Answer:
[tex]\sqrt{x^2+2}\left(x^2+x+2\right)^2[/tex]
Step-by-step explanation:
Given equation:
[tex](x^2+2)^{\frac{5}{2}}+2x(x^2+2)^{\frac{3}{2}}+x^2\sqrt{x^2+2}[/tex]
[tex]\textsf{Rewrite the exponents }\frac{5}{2} \textsf{ as } \left(\frac{1}{2} \cdot 5\right)\textsf{ and }\frac{3}{2} \textsf{ as }\left(\frac{1}{2} \cdot 3\right):[/tex]
[tex]\implies (x^2+2)^{\frac{1}{2} \cdot 5}+2x(x^2+2)^{\frac{1}{2}\cdot 3}+x^2\sqrt{x^2+2}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]
[tex]\implies \left((x^2+2)^{\frac{1}{2}}\right)^5+2x\left((x^2+2)^{\frac{1}{2}}\right)^3+x^2\sqrt{x^2+2}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{\frac{1}{2}}=\sqrt{a}:[/tex]
[tex]\implies \left(\sqrt{x^2+2}\right)^5+2x\left(\sqrt{x^2+2}\right)^3+x^2\sqrt{x^2+2}[/tex]
Factor out [tex]\sqrt{x^2+2}[/tex] from each of the three terms:
[tex]\implies \sqrt{x^2+2}\left[\left(\sqrt{x^2+2}\right)^4+2x\left(\sqrt{x^2+2}\right)^2+x^2\right][/tex]
[tex]\textsf{Factor the expression in the parentheses using} \quad a^2+2ab+b^2=(a+b)^2.[/tex]
[tex]\textsf{Let }a=\left(\sqrt{x^2+2}\right)^2 \textsf {and }b=x:[/tex]
[tex]\implies \sqrt{x^2+2}\left(\left(\sqrt{x^2+2}\right)^2+x\right)^2[/tex]
[tex]\textsf{Apply exponent rule} \quad \sqrt{a^2}=a:[/tex]
[tex]\implies \sqrt{x^2+2}\left(x^2+2+x\right)^2[/tex]
[tex]\implies \sqrt{x^2+2}\left(x^2+x+2\right)^2[/tex]