The inequality that represents the velocity of an object that has mass of 30 Kg and creates a momentum of at least 15 Kg(m/s) is 15 ≥ 30×v .
The relation between the mass(m) of an object with momentum(p) and velocity(v) is given by the equation
p=m × v .
In the question,
it is given that
the mass of the object = 30 Kg
the momentum required is at least 15 Kg(m/s).
let the velocity of the object " v " .
Substituting values in the formula ,
we get ,
15 = 30×v
the word at least in inequality is represented by " ≥ " .
So , the inequality becomes
15 ≥ 30×v
Therefore , the inequality that represents the velocity of an object that has mass of 30 Kg and creates a momentum of at least 15 Kg(m/s) is 15 ≥ 30×v .
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A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). The one-time fixed costs will total $24,149. The variable costs will be $11.50 per book. The publisher will sell the finished product to bookstores at a price of $21.75 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?
The publisher should produce and sell 2356 books so that the production costs will equal the money from sales.
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is a small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). The one-time fixed costs will total $24,149. The variable costs will be $11.50 per book. The publisher will sell the finished product to bookstores at a price of $21.75 per book.
Assume the number of books to be printed be [x].
Then, we can write -
24149 + 11.50x = 21.75x
21.75x - 11.5x = 24149
10.25x = 24149
x = 2356 books
Therefore, the publisher should produce and sell 2356 books so that the production costs will equal the money from sales.
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V : 33= 7 : 11 what is the answer to this please
The value of V illustrated in the ratio V : 33= 7 : 11 is 21.
What is a ratio?It should be noted that a ratio is simply used to show the relationship between the variables and illustrate the comparison.
In this case, the value of V can be illustrated as:.
V/33 = 7/11
Cross multiply
11V = 33 × 7
V = (33 × 7) / 11
V = 21
Therefore, V is 21.
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Rewrite as a simplified fraction 3.16
Answer: 3 4/25
Step-by-step explanation:
a drawing of a surboard in a catalog shows it's length as 8 1/2 inches. find the actual length of surfboard if 1/2 inch length on the drawing correspond to 3/8 foot of actual length.
The actual length of surfboard based on the information is 6 3/8 feet.
How to calculate the length?From the information illustrated, the drawing of a surboard in a catalog shows it's length as 8 1/2 inches.
The actual length of surfboard if 1/2 inch length on the drawing correspond to 3/8 foot of actual length will be illustrated thus:
Let the actual length be x.
1/2 / 3/8 = 8 1/2 / x
0.5 / 0.375 = 8.5 / x
Cross multiply
0.375 × 8.5 = 0.5x
x = (0.375 × 8.5) / 0.5
x = 6.375 = 6 3/8 feet
The length is 6 3/8 feet.
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please tell me what is 9 divided by 7
3
Answer: 3.86
Step-by-step explanation:
Here we will show you how to calculate 9 divided by 7/3. We will give you the answer in fraction form and decimal form.
Here is 9 divided by 7/3 displayed mathematically:
9
÷
7
3
The numbers in 9 divided by 7/3 are labelled below:
9 = whole number
7 = numerator
3 = denominator
To make it a fraction form answer, you multiply the whole number by the denominator and make the result the new numerator. The old numerator becomes the new denominator:
9 x 3
7
=
27
÷
7
Thus, the answer to 9 divided by 7/3 in fraction form is:
27
÷
7
To make the answer to 9 divided by 7/3 in decimal form, you simply divide the numerator by the denominator from the fraction answer above:
27 / 7 = 3.86
The answer is rounded to the nearest two decimal points if necessary.
27/7 is an improper fraction and should be written as 3 6/7.
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9 divided by 7/3 is equal to 27/7 or 3 6/7.
To divide 9 by 7/3, we can rewrite the division as a multiplication by the reciprocal of the divisor.
The reciprocal of 7/3 is obtained by flipping the fraction, which means interchanging the numerator and denominator.
Therefore, the reciprocal of 7/3 is 3/7.
So, we can rewrite the division as:
9 ÷ (7/3) = 9 × (3/7)
To multiply fractions, we simply multiply the numerators together and the denominators together.
So, multiplying 9 and 3 gives us 27, and multiplying 7 and 1 gives us 7.
Therefore:
9 ÷ (7/3) = 27/7
The result, 27/7, is an improper fraction. It means we have 27 parts divided into 7 equal parts.
However, if you prefer, we can also express the result as a mixed number, which consists of a whole number and a proper fraction.
To convert 27/7 into a mixed number, we divide the numerator (27) by the denominator (7).
The quotient is the whole number part, and the remainder becomes the numerator of the proper fraction.
27 ÷ 7 = 3 remainder 6
So, the mixed number representation of 27/7 is:
27/7 = 3 6/7
Therefore, 9 divided by 7/3 is equal to 27/7 or 3 6/7.
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In a blueprint of a building, a conference room is 6 inches long and 4 inches wide. The scale factor is 2 inches: 7 feet.
What are the dimensions of the conference room? Enter the answer in each box.
The conference room is
feet long and
feet wide.
The conference room is 21 feet long and 14 feet wide.
Given that, in a blueprint of a building, a conference room is 6 inches long and 4 inches wide.
What is the scale factor?Scale factor is a number by which the size of any geometrical figure or shape can be changed with respect to its original size. It is used to draw the enlarged or reduced shape of any given figure and to find the missing length, area, or volume of an enlarged or reduced figure.
Here, the scale factor is 2 inches : 7 feet.
Now, length = 6 inches
= 2 inches + 2 inches + 2 inches
= 7 feet + 7 feet + 7 feet
= 21 feet
Width = 4 inches
= 2 inches + 2 inches
= 7 feet + 7 feet
= 14 feet
Therefore, the conference room is 21 feet long and 14 feet wide.
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Find the perimeter.
15 24/14
14
10/
12²/
12/3/1
10/1/
35 -/-/
Perimeter = 119
Simplify your answer completely.
?
[tex]\displaystyle\\Answer:\ 119\ \boxed{\frac{4}{7} }[/tex]
Step-by-step explanation:
[tex]\displaystyle\\P=10\frac{1}{7}+12\frac{2}{7}+15\frac{3}{14} +24\frac{1}{14} +12\frac{2}{7} +10\frac{1}{7}+35\frac{3}{7} \\\\P=(10\frac{1}{7}+12\frac{2}{7}+12\frac{2}{7} +10\frac{1}{7}+35\frac{3}{7})+(15\frac{3}{14} +24\frac{1}{14}) \\\\P=(\frac{71}{7} +\frac{86}{7} +\frac{86}{7}+\frac{71}{7} +\frac{248}{7} )+(\frac{213}{14}+\frac{337}{14})\\\\[/tex]
[tex]\displaystyle\\ P=\frac{71+86+86+71+248}{7} +\frac{213+337}{14} \\\\P=\frac{562}{7} +\frac{550}{14} \\\\P=\frac{562}{7}+\frac{2(275)}{2(7)} \\\\P=\frac{562}{7} +\frac{275}{7}\\\\P=\frac{562+275}{7} \\\\P=\frac{837}{7}\\\\P=119\frac{4}{7}[/tex]
let's firstly convert the mixed fractions to improper fractions and then add them up.
[tex]\stackrel{mixed}{10\frac{1}{7}}\implies \cfrac{10\cdot 7+1}{7}\implies \stackrel{improper}{\cfrac{71}{7}} ~\hfill \stackrel{mixed}{12\frac{2}{7}}\implies \cfrac{12\cdot 7+2}{7}\implies \stackrel{improper}{\cfrac{86}{7}} \\\\\\ \stackrel{mixed}{15\frac{3}{14}}\implies \cfrac{15\cdot 14+3}{14}\implies \stackrel{improper}{\cfrac{213}{14}} ~\hfill \stackrel{mixed}{24\frac{1}{14}}\implies \cfrac{24\cdot 14+1}{14}\implies \stackrel{improper}{\cfrac{337}{14}}[/tex]
[tex]\stackrel{mixed}{35\frac{3}{7}}\implies \cfrac{35\cdot 7+3}{7}\implies \stackrel{improper}{\cfrac{248}{7}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{71}{7}+\cfrac{71}{7}+\cfrac{86}{7}+\cfrac{86}{7}+\cfrac{213}{14}+\cfrac{337}{14}+\cfrac{248}{7}\hspace{5em}\textit{so we have an LCD of 14} \\\\\\ \cfrac{(2)71+(2)71+2(86)+2(86)+(1)213+(1)337+2(248)}{14} \\\\\\ \cfrac{1674}{14}\implies \cfrac{837}{7}\implies 119\frac{4}{7}[/tex]
C1 Determine the Greatest Common Factor of polynomials
To find the greatest common factor of a polynomial, find a number that all of its coefficients are divisible by, for example, the GCF of an 8x 2 + 4x + 2 is 2 because all of the coefficients (8, 4, 2) are divisible by 2 and the expression simplifies to 2(4x2 + 2x + 1).
What is the Greatest Common Factor?A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, the numbers 12, 20, and 24 share the components 2 and 4. The GCF of 12, 20, and 24 is 4 because it is the largest.
To find the greatest common factor of a polynomial, find a number that all the coefficients of the polynomial are divisible by i.e. the GCF of a 8x^2 + 4x + 2 is 2 because all the coefficients (8, 4, 2) are divisible by 2 and the expression simplifies to 2(4x^2 + 2x + 1).
The GCF can be smaller than the smallest coefficient, for example 20x^2 + 15x + 10 (GCF is 5, smallest coefficient is 10) and 5 < 10. However it cannot be larger than the smallest coefficient.
Therefore the smallest coefficient should be larger than or equal to the GCF in order to be divisible.
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Which statement describes when the plans are based on the same number of aerobic exercise sessions?
Each plan utilizes a combination of 2 strength-training sessions and 2 aerobic exercise sessions per week.
Each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week.
Each plan utilizes a combination of 3 strength-training sessions and 2 aerobic exercise sessions per week.
Each plan utilizes a combination of 3 strength-training sessions and 3 aerobic exercise sessions per week.
From the statements that are provided in the question, the statement that best describes when the plans is Each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week.
What is word problem?A word problem are sentences describing a real-life scenario where a problem needs to be solved by mathematical calculation.
Ideally, for the best health benefits, such as increasing strength and aerobic and reduction in heart diseases, it is suggested to do a combination of strength training and aerobic training for at least five times a week.
Each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week. is the correct statement
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PLEASE HELP ASAP!! THANKS IN ADVANCE! :)
Simplify.
Answer:
[tex]\frac{(x+3)(x-1)}{x}[/tex]
Step-by-step explanation:
So the first thing you want to do is factor out the polynomials.
[tex]x^2+4x+3 ; (x+3)(x+1)[/tex]
[tex]x^2+x; x(x+1)[/tex]
[tex]2x^2-3x+1; (2x-1)(x-1)[/tex]
Once you have factored these out, you can write out the division using keep-change-flip;
[tex]\frac{(x+3)(x+1)}{2x-1}*\frac{(2x-1)(x-1}{x(x+1)}[/tex]
Before trying to multiply all of the factors, rule out factors that appear both in the numerator and the denominator;
[tex]\frac{(x+3)}{1}*\frac{(x-1)}{x}[/tex]
Now you can multiply the fractions and receive [tex]\frac{(x+3)(x-1)}{x}[/tex]
a cowboy agreed to work for one year for plus a horse. he quit after 7 months and was paid plus a horse. how many dollars was the horse worth, if the paid salary reflects the fair proportion of his yearly salary?
The worth of the horse is 1800 dollars
Given that a cowboy worked for one year for 19,200 plus a horse.
After 7 months, he quit and was paid 10,450 but got to keep the horse.
We need to find the worth of the horse.
Here, the horse is part of the payment in total, so it has to be used as a variable when setting up the proportion.
Let us consider the net worth of the horse to be H
solving for H,
[19,200 + H] / 12 = [10,450 + H] / 7
Now, cross multiply
134,400 + 7H = 125,400 + 12H
134,400 - 125,400 = 12H - 7H
9,000 = 5H
H = 9,000 / 5
H = $1,800
Hence, the net worth of the horse, H is $1,800.
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5. Find the selling Price of an item that originally cost a store $70 was marked up20% and then after no selling for 6 months was discounted 10%?
Answer:
$75.6
Explanation:
If the original cost was $70 and it was marked up 20%, the price after this is calculated as:
$70 + $70(0.2) = $70 + $14 = $84
Where $70(0.2) = $14 is the amount added to the original when it is marked up 20%.
Then, it was discounted 10%, we get that the selling price is
$84 - $84(0.1) = $84 - $8.4 = $75.6
Where $84(0.1) = $8.4 is the discount made on the initial price.
Therefore, the answer is $75.6
(-1,4) -3
in slope intercept form and how to do it
The equation of line that passes through the point (-1,4) and slope = -3 , in slope intercept form is y = (-3)x + 1 .
The Slope Intercept Form of the line is represented by
y=mx+c
where , m is the slope
and
c is the y-intercept
In the question ,
it is given that
the slope of the line is = -3 .
So, the equation of line becomes
y = (-3)x+c ...(i)
As this line passes through (-1,4) , it will satisfy the equation of line
Substituting the values x as -1 , y as 4 , in equation(i) ,
we get
4 = (-1)(-3) + c
4 = 3 + c
c = 4-3
c = 1
So, the y intercept(c) is 1 .
Hence the equation of line becomes y = (-3)x + 1 .
Therefore , the equation of line that passes through the point (-1,4) and slope = -3 , in slope intercept form is y = (-3)x + 1 .
The given question is incomplete , the complete question is
write the equation of line in slope intercept form that passes through the point (-1,4) and has slope as -3 .
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last week the springville nursery sales at the farmers market were 2,375.24. The expenses were $1,593.08 for the items sold how much profit did they make ?
please help asap tysm
last one im asking i swear
Your test scores are 85 and 89 what possible scores can you earn on your next test to average between 87 and 91 inclusive?
Answer:
85,100
Step-by-step explanation:
85 <= (81 + 89 + x) / 3 <=90
255 <= 81 + 89 + x <=270
255 <= 81 + 89 + x <=270
174 <= 89 + x <= 189
85 <= x <= 100
x = 85, 100
Find JKL and LKM if JKM = 140.
The measure of angles JKL and LKM are 100° and 40° respectively.
What is a supplementary angle?A supplementary angle simply refers to two (2) angles or arc whose sum is equal to 180 degrees.
Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can logically deduce that the sum of angles JKL, LKM and JKM are not supplementary angles:
m∠JKL + m∠LKM = m∠JKM
Substituting the given parameters into the formula, we have;
4x° + (2x − 10)° = 140°
6x° − 10 = 140°
6x° = 140° + 10°
6x° = 150°
x° = 150/6
x = 25°
For angle JKL, we have:
m∠JKL = 4x
m∠JKL = 4(25)
m∠JKL = 100°.
For angle LKM, we have:
m∠LKM = 2x − 10
m∠LKM = 2(25) − 10
m∠LKM = 50 − 10
m∠LKM = 40°
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138×14÷28+209
A)278
B)288
C)298
D)388
Answer: A
Step-by-step explanation:
First you multiply 138 x 14 =1932 then divide 28 then you have 69 then add 209 then you have 278.
sorry if its wrong.
Answer:
A) 278
Step-by-step explanation:
Use PEMDAS for order of operations:
Start with anything in parentheses, and then operations are performed on any exponents (also called powers). Next, perform operations on multiplication or division from left to right. Finally, operations on addition or subtraction are performed from left to right.
which equation has no solution?
13y + 2 - 2y = 10y + 3 - y
9(3y + 7) - 2 = 3(-9y + 9)
32.1y + 3.1 + 2.4y - 8.2 = 34.5y - 5.1
5(2.2y + 3.4) = 5(y - 2) + 6y
find the area of a circle
Answer: 3.14 * 3^2 = 28.26
Answer:28.26
Step-by-step explanation:
An inspector examines items coming from an assembly line. A review of her record reveals that she accepts only 8% of all defective items. It was also found that 1% of all items from the assembly line are both defective and accepted by the inspector. What is the probability that a randomly chosen item from this assembly line is defective? write your answer in decimals, not percentage. Do not round your answer.
The probability that a randomly chosen item from this assembly line is defective is 0.125.
How to calculate the probability?Probability simply means the likelihood of the occurence of an event.
From the information, the review of her record reveals that she accepts only 8% of all defective items and it was also found that 1% of all items from the assembly line are both defective and accepted by the inspector.
Therefore, the probability will be:
= Percentage of detectives / Percentage of defective accepted
= 1% / 8%
= 0.01 / 0.08
= 0.125
The probability is 0.125.
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the graph of y equals negative x - 4 shown below use the grass seeds form in which the ordered pair is a solution of the equation select all correct answers
The solution are
[tex]\begin{gathered} y=-1-4=-5 \\ (1,-5) \end{gathered}[/tex][tex]\begin{gathered} y=4-4=0 \\ (-4,0) \end{gathered}[/tex]The answer is B and D.
david and daniel were given the same number of dollars by their father. david earned money doing chores until he had twice as much as he started with. daniel didn't earn any more, but he reciaved $12 for his birthday. if the boys still have the same amount of money, how much did their father give each one?
David and Daniel were given $12 each in the beginning as the given condition.
What are conditions?
A condition that must be met in order for the given statement or theorem to hold. also known as a problem.A necessary condition is one that must exist in order for the given statement to be true (if satisfied it maybe true as there maybe more than one necessary conditions). On the other hand, a sufficient condition is one that, even if it is satisfied, does not automatically imply that the proposition is true.Let david and daniel were given = $x each as per statement.
at the end david had = 2x
and daniel had= x+12
Condition is given that : in the end, the boys still have the same amount of money.
Therefore, equating both what David and Daniel had
2x=x+12
x=12
David and Daniel were given $12 each in the beginning as the given condition.
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Can someone please help me with these asap and show a step by step?
The width of prism is 9yards.
What is volume?Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity. The capacity of an object is measured by its volume. For instance, a cup's capacity is stated to be 100 ml if it can hold 100 ml of water in its brim. The quantity of space occupied by a three-dimensional object can also be used to describe volume.
Given Data
Rectangular prism:
Volume = 990 yd³
Length = 10 yards
Height = 11 yards
Volume of rectangular prism = Length× Height× Width
990 = 10 ×11× width
Width = [tex]\frac{990}{10(11)}[/tex]
Width = 9
The width of prism is 9yards.
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Volume of a conical heap of salt that is 3.5 meters in diameters high
No height value is given, thus the volume cannot be found. The equation is:
1/3πr²h, r = d/2
1/3π(d/2)²h
1/3(3.14)(3.5/2)²h
1/3(3.14)(1.75)²h
1/3(3.14)(3.0625)h
1.053(3.0625)h
3.22h
The volume of the cone is approximately 3.22h.
write an inequality to represent the following problem:
6 less than a number greater than four
The inequality that represents the problem "6 less than a number greater than four" is x - 6 > 4.
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.
Consider the statement,
6 less than a number greater than four.
Let x be the number.
The symbol " > " can be represented as a number greater than another.
Then 6 less than a number greater than 4 can be represented as:
x - 6 > 4
The inequality x - 6 > 4 can be represented for the problem " 6 less than a number greater than four".
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Work out the area of this triangle. 11 cm 4 cm 6 cm
Answer: 22, 12 or 33
Step-by-step explanation:
11cm is the base and 4 is the height your answer is 22 if 6cm is the base and 4 is the height your answer is 12 and if 6 is your height and 11 is your base your answer is 33
Define the domain of the followingA) {-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8}B) {3, -1, 2, 0, -2}C) {-3, -1, 1, 3, 6}D All real Numbers
The domain is a set tht contains all possible x-values in a relataion or a function. In this problem, we just need to know what the x-coordinates are to be able to identify the domain.
Let us first list down the coordinates of the given points. We have:
The x-coordinates are: -3, -1, 1, 3, and 6.
So the domain is: {-3, -1, 1, 3, 6}. The answer is option C.
Write the equation in slope intercept form. -5y + 10x = 20 help meeee
Daniel earned $18 at his job when he worked for 2 hours. Fill out a table of equivalent ratios and plot the points on the coordinate axes provided.
H E
2 18
4 36
6 54
8 72
10 90
H = Hours
E = Earned
These are all equivalent.
If you want to do this on your own, write out the multiplication then remove odd ones, that's exactly what I did.
