If the soccer team is going to purchase only warm-up pants, then the greatest number of warm-up pants the team can purchase is 42, but if instead the soccer team is going to purchase only duffel bags, then the greatest number of duffel bags the team can purchase is 54.
How do you solve this problem?Inequality, a relationship between two values/expressions that aren't equal to each other, is involved in solving this problem.
The soccer team's got $1,512 to purchase either all warm-up pants or all duffel bags. The cost of the warm-up pants is $36 each and the cost of the duffel bags is $28 each. Since you're asked to find the greatest numbers of each purchase, you'll need to write inequalities to figure out the answer.
The keyword here is "greatest number", so you can use the symbol ≤ for the inequalities. Therefore, 36x ≤ 1,512 is the inequality for finding the greatest number of warm-up pants and 28x ≤ 1,512 is the inequality for finding the greatest number of duffel bags.
The solutions to the first and second inequalities are, consecutively, x ≤ 42 and x ≤ 54, meaning the team can buy at most 42 warm-up pants or 54 duffel bags.
Learn more about inequality here: https://brainly.com/question/25275758
#SPJ4
What is the solution set of the inequality?
Answer:
the fourth one is the right one
Solve x² + 5x - 14 = 0
By solving the equation x² + 5x - 14 = 0 get the value of x is 2 or -7.
Given,
In the question:
To solve the equation:
x² + 5x - 14 = 0
Now, According to the question:
x² + 5x - 14 = 0
Split the middle term into two terms :
x² - 2x + 7x - 14 = 0
Factor the first two terms and the last two terms separately
x(x - 2) + 7 (x -2) = 0
Factor out
(x - 2) (x + 7) = 0
Apply Zero Product Property
x - 2 = 0 or x + 7 = 0
x = 2 or x = -7
Hence, By solving the equation x² + 5x - 14 = 0 get the value of x is 2 or -7.
Learn more about Equation at:
https://brainly.com/question/28261966
#SPJ1
First, complete the story below so that it can be represented by the equation 5000-50x=4800-30x
Pool A started with 5000 liters of water, and 50 liters per minute are being (Drained out or Pumped back in)
Pool B started with 4800 liters of water, and 30 liters per minute are being (Drained out or Pumped back in)
The amount of water after x minutes is more in which pool? Pool A or Pool B?
The amount of water after x minutes is equal in both pools.
What is a Linear equation in one variable?
A univariate linear equation is an equation of the form ax + b = 0, where a and b are two integers, x is a variable, and there is only one solution.
For example, 2x+3=8 is a linear equation in one variable.
The given equation is 5000 - 50x = 4800 - 30x.
solving for 'x',
5000 - 50x = 4800 - 30x
5000 - 4800 = 50x - 30x
200 = 20x
x = 200/20
x = 10
The amount of water after 10 minutes in Pool A will be = 5000 - 50(10)
= 5000 - 500
= 450 liters
The amount of water after 10 minutes in Pool B will be = 4800 - 30(10)
= 4800 - 300
= 450 liters.
Hence, the amount of water will be the same in both pools.
To learn more about the linear equations in one variable, visit:
https://brainly.com/question/10839449
#SPJ13
what is the answer what is the answer what is the step by step answer to learn to do it
Answer: 1.01% sale tax.
Step-by-step explanation:
First you must take your tax price before and the tax price after and divide them. This gets you 1.01.
To be sure this is your answer you can multiply the 1.01% by 53 and it gives you 53.53$ (If you don't understand I suggest looking at a video from khan academy they explain things much better than I do.)
Hope that helped in some way :)
relative maxima and relative minima of the function f(x) = x^5 - 4x^3 + 3x^2 - 8x - 6
The relative maxima and relative minima of the function
f(x) = x^5 - 4x^3 + 3x^2 - 8x - 6
the relative maxima is -1.871the relative minima is 1.518How to fine the relative maxima and minimaThe relative minima and maxima is calculated
by differentiating the given function find the critical values or roots of the equationdifferentiate the second tiesubstitute the critical value that are real numbersthe critical value that gave a negative value is the maximathe critical value that gave a positive value is minimaThe procedure is done as follows
x^5 - 4x^3 + 3x^2 - 8x - 6
differentiating gives
5x^4 - 12x^2 + 6x - 8
solving the equation for the critical values are
x₁ = 0.176 + 0.73i
x₂ = 0.176 - 0.73i
x₃ = 1.518
x₄ = -1.871
The second derivative
5x^4 - 12x^2 + 6x - 8
differentiating gives
20x^3 - 24x + 6
substituting x = 1.58
20 * 1.58^3 - 24 * 1.58 + 6
= 46.966 (positive hence minima)
substituting x = -1.871
20 * -1.871^3 - 24 * -1.871 + 6
= -169.9 (negative hence maxima)
Learn more about relative maxima and minima at:
https://brainly.com/question/6422517
#SPJ1
What is the name of the bolded part of this shape?
Answer:
A right-angled triangle
suppose the insect population doubled after 15 hours. how long (in hours) will it take the insect population to grow to eight times its initial size? (simplify your answer completely.)
Using population growth modeling it is concluded that the population of insects after 1 hour will be about 1.05 times.
What is growth and decay modeling?The method used to calculate the growth and decay of insects or bacteria are called growth and decay modeling.
Let us assume n₀ is the initial population, then the total population n(t) after t time is given by the formula:
n(t) = n₀ [tex]e^{rt}[/tex], where r = the relative rate of growth.
Suppose an initial number of insects is x and after 15 hours it becomes 2x.
2x = x[tex]e^{15r}[/tex]
[tex]e^{15r}[/tex] = 2
Take the log of both sides of the equation
ln [tex]e^{15r}[/tex]= ln 2
15r = ln 2
r = 0.693147/15
Now, population after 1-hour = x [tex]e^{r}[/tex]
= 1.047
≈ 1.05
Hence the population of insects after 1 hour will be about 1.05 times.
To know more about the growth of the population of insects, visit:
https://brainly.com/question/3155351
#SPJ4
Write 95% as a fraction or mixed number in simplest form.
the probability that a visitor to an animal shelter will adopt a dog is 0.10. out of 9 visits, what is the probability that at least (equal to or more than) 1 dog will be adopted?
The probability of having at least one dog adopted is 0.6126
It is given that the probability to adopt a dog is 0.1
The adoption of the dog here clearly follows a Binomial distribution
ⁿCₓ X pˣ X (1 - p)ⁿ⁻ˣ
where,
n = no. os sample
p = probability of success
x = random variable.
Here the success would be the adoption of a dog, We are given here there were 9 visits
Hence,
n = 9
p = 0.1
1 - p = 0.9
we need to find the probability of the adoption of at least one dog
= P(X ≥ 1)
= 1 - P(X = 0)
Hence we get
P(X = 0)
= ⁹C₀ X 0.1⁰ X 0.9⁹
= 0.3874
Hence,
P(X ≥ 1)
= 1 - 0.3874
= 0.6126
Therefore the probability that at least one dog will be adopted is 0.6126
To know more about Probability visit
brainly.com/question/14210034
#SPJ4
Find x and m
Giving brainlist to fastest reply that’s correct! Also liking answers for trying to answer <3
Answer:
x=21, m<s=95
Step-by-step explanation:
85+5x-10=180
75+5x=180
5x=105
x=21
m<S= 5(21)-10
m<S= 105-10
m<s=95
2
Select the correct answer.
Which interval describes where the graph of the function is positive?
-8
O
O
O
B.
A. -∞ <<∞
C.
A
D.
N
-∞ < x < -1
-8∞ < < -2
-2 < < -1
Ň
-6
-8
-N
6 8
Option B is the correct answer, the interval in which the graph of the function is positive is -∞ < x < -1.
What do mean by interval?
In mathematics, a (real) interval is a collection of real numbers that includes all real numbers that fall inside any two of the collection's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 x 1. The set of all real numbers, the set of nonnegative real numbers, the set of positive real numbers, the empty set, and any singleton are additional examples of intervals.
As we can see in the graph provided in the question, the graph of function reach the positive side of the y-axis at x = -1, it means one of the two end point of the interval is going to be -1. And, the graph is constantly and slowing increasing it's value as increase in the x-axis therefore, the other endpoint of the interval cab be considered as negative infinity.
To know more about interval, go to link
https://brainly.com/question/1503051
#SPJ1
Your faucet in your kitchen starts leaking. You put a bucket under it. The faucet is leaking at a constant rate. After 5 minutes, there is 300 mL of water in the bucket. What is the pattern rule?
Answer: 60mL per minute
Step-by-step explanation:
300/5=60
Can I please get brainly?
rearrange the formula below to make 'a' the new subject:
[tex]c + \frac{1}{2}a^{2}b = d[/tex]
is the bottom answer correct for this question? :
[tex]a = \sqrt{2(\frac{d-c}{b} )}[/tex]
Step-by-step explanation:
c + 1/2 × a²b = d | - c on both sides
1/2 × a²b = d - c | ×2 on both sides
a²b = 2(d - c) | /b on both sides
a² = (2/b) × (d - c) | sqrt on both sides
a = sqrt(2(d - c)/b)
yes, the given answer is correct.
The half-life of a substance is the time it takes for half of that substance to break down or decay. The half-life of an unknown element is 1 day.
Write an equation for the amount remaining from a sample of 100 grams of the element after x days. How much of the substance will be left after 3 days? Where is the
asymptote?
Answer:
See below
Step-by-step explanation:
Amount = 100 (1/2)^x
after 3 days
amount = 100 ( 1/2)^3 = 12.5 gm left
Solve for A in terms of I and P.
I=A–P
Answer:
I+P=A
Step-by-step explanation:
isolate a on 1 side
I=A—P
+P. +P
I+P=A
Hopes this helps please mark brainliest
Answer:
A=P+I
Step-by-step explanation:
make A the subject of formula
giving A= P+I
You are asked to write an equation for the line of best fit for the scatter plot shown at the right without the use of a graphing calculator. What should you do first? Explain
Answer:
Find the slope between the points (1,2) and (9,12).
Step-by-step explanation:
If I was going to draw the line of best fit without a calculator, I would draw it including these two points. Once I had these two points, I would find the slope using these points.
Can somebody please answer these 3 questions please and thank you
[tex]\displaystyle \boxed{\text{First Attachment, 14}}[/tex]
Answer:
x = 30
y = 60
Step-by-step explanation:
First, vertical angles are congruent. This helps us fill in more of the angles so we can find x and y.
Next, supplementary angles add up to 180°, aka a line. We can use this to fill out even more of the diagram given.
Lastly, corresponding angles on parallel lines are congruent.
By using the information above, we can decide that x = 30 and y = 60. See the first attachment for all the angle values filled out.
[tex]\displaystyle \boxed{\text{Second Attachment, 12}}[/tex]
Answer:
x = 65
Step-by-step explanation:
From the above explanation, we will be using vertical angles and supplementary angles to solve this question. See the second attachment.
We also know there are 180 degrees in a triangle.
Lastly, we know that alternate interior angles are congruent.
Using this knowledge, we can decide that x = 65.
[tex]\displaystyle \boxed{\text{Third Attachment, 13}}[/tex]
Answer:
x = 30
Step-by-step explanation:
Again, we will be using vertical angles, supplementary angles, and corresponding angles to solve this question. See the third attachment.
After placing vertical angles down from the given information, we can fill in more using corresponding angles.
Lastly, we know there are 360 degrees in a circle. We can create an equation from this and solve.
Using this information, we can decide that x = 30.
(DUE IN 2 HOURS PLEASE HELP) Find an equation for the line that passes through the points (5, 2) and (-4, 5).
Answer:
Y= -1/3x+11/3
Step-by-step explanation:
24.15 as a two significant figures?
24.15 as two significant figures is 24.
What are significant figures?All significant figures are those that enhance the overall worth of the number's meaning. Numbers are frequently rounded to avoid repeating quantities that are not significant. When rounding, one must be careful not to lose precision. Sometimes the purpose of rounding numbers is simply to make them simpler.
What are the significant figure's rules?Use the following guidelines to decide which numbers are important and which are not:
1) A decimal number less than 1 is not affected by the zero to the left of it.
2) The placeholders for all trailing zeros are all insignificant.
3. There should be significance between non-zero numbers.
4) Every non-zero number has meaning.
5) A number is rounded if it has more digits than the necessary number of significant ones. For instance, 432,500 is rounded up to 433,000 to three significant digits using the half-up (regular) method.
6) Zeros at the end of numbers that are not important but are left in because eliminating them would change the number's value. The 000 in 433,000 in the example above cannot be removed without converting the number to scientific notation.
Given the number, 24.15
We have to convert it to two significant figures, so we will consider the only two figures before the decimal point. So, the number up to two significant figures is 24.
To know more about the significant figures, visit:
https://brainly.com/question/29153641
#SPJ1
a line with slope 2 intersects a line with slope 6 at the point (40, 30). what is the distance between the x-intercepts of these two line
The distance between the x-intercepts of these two line is 10 units.
Given that,
These two lines' x-intercepts are separated by 10 units.
Equation of the line with slope 2 is
y-30/x-40 = 2
For x intercept put y = 0,
then
-30/x-40 =2
x =25
Equation of the line with slope 6 is
y-30/x-40 =6
For x intercept put y = 0,
then
-30/x-40 =6
x =35
Distance between x-intercepts of these two lines is difference of the two intercepts i.e,
D = 35-25 = 10.
Thus, the distance between the x-intercepts of these two line is 10 units.
To learn more about x-intercepts click here:
brainly.com/question/14180189
#SPJ4
help
Simplify the ratio of 0,5 kg: 250 g
Answer:
2:1
Step-by-step explanation:
.5 kg : 250g
the units must be same at both sides
500g : 250g
{as 1 kg = 1000g}
by simplifying both sides
10g : 5g
2g : 1g
2:1
What are the like terms in the expression 8 + x squared minus 4 x cubed + 5 x + 2 x squared?
8, 5 x
x squared, 2 x squared
8, 5 x 2 x squared
x squared, Negative 4 x cubed, 2 x squared
In the expression, 8 + x squared minus 4 x cubed + 5 x + 2 x squared.
2x^2 and x^2 are the like terms
How to find the like terms in the expressionThe given expression is 8 + x squared minus 4 x cubed + 5 x + 2 x squared
This is rewritten as
8 + x^2 - 4x^3 + 5x + 2x^2
The terms in the expression are grouped as
constant terms: 8
terms with x variable : 5x
terms with x^2 variables: 2x^2 and x^2
terms with x^3 variables: 4x^3
Like terms refers to terms that are similar either as a constants or have same variables
Hence the like terms in the expression is 2x^2 and x^2
Learn more on like term in equations here:
https://brainly.com/question/29333659
#SPJ1
Solve for n. −2(n − 5.5) > 21 PLEASE HELP MEEEEEEE
Answer:
Step-by-step explanation:
1. Divide by -2 and thus flip the inequality
2. (n-5.5)<21/-2
3. Add 5.5 to both sides
4. n<-5
5.Check by plugging in any number less than -5 and see if the inequality is true
6. Example: plug in -10
Is -2(-10-5.5)>21?
Yes
31>21 your solution is n<-5
On solving the linear inequality −2(n − 5.5) > 21 for n, we get n < -5.
Linear inequalities are the expressions where any two values are compared by the inequality symbols such as, '<', '>', '≤' or '≥'.
Given in the question,
-2(n - 5.5) > 21
Solving the inequality,
-2n + 11 > 21
-2n > 21 - 11
-2n > 10
-n > 5
n < -5
Learn more about linear inequalities here
https://brainly.com/question/31366329
#SPJ2
6) In Jim’s school, there are 3 girls for every 2 boys. There are 800 students in total. Using this information, how many students are girls?
A. 260
B. 320
C. 480
D. 390
Answer:
C) 480
Step-by-step explanation:
Ratio:
[tex]\sf \dfrac{3}{5}*800 = 3 * 160[/tex]
= 480
f(x)=x²-5x - 9
Find f(-9)
Answer:
117
Step-by-step explanation:
f(-9)=-9^2-5(-9)-9
f(-9)=81+45-9
f(-9)=126-9
f(-9)=117
hopes this helps please mark brainliest
reimond needs to order crushed rock for a courtyard what is the cost of 4.5 t at $12.50 per tonne?
The cost of 4.5 tonnes of rock is $56.25
Given,
cost of 1 tonne of rock=$12.50
then
to find cost of 4.5 tonnes of rock, multiply 12.50 with 4.5,
cost of 4.5 tonnes of rock = 4.5* 12.50 = $56.25
Thus ,the cost of 4.5 tonnes of rock is $56.25.
To learn more about cost refer here
https://brainly.com/question/17364893
#SPJ1
I need help me thank you
Step-by-step explanation:
s = 17b
when b =2:
s = 17b
s = 17(2)
s = 34
when b = 4
s = 17b
s = 17(4)
s = 68
HELP ME!!! Need a new answer for this so it’s my “own”!!!
Question 1 (Essay Worth 10 points)
(06.01, 06.02 HC)
Part A: Create a fourth-degree polynomial in standard form. How do you know it is in standard form? (5 points)
Part B: Explain the closure property as it relates to polynomials. Give an example. (5 points)
Part A: polynomial in Standard form;-
bluef(x) = ax⁴ + bx³ + cx²+ dx + e
Part B: Closure property relates to polynomial;-
The polynomial's closer property for subtraction. When two polynomials of identical degrees with different leading coefficients are subtracted, a polynomial of the same degree is produced.
What is Polynomial?
A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x2 4x + 7 is an illustration of a polynomial with a single indeterminate x.
A.
Any of the following can be the fourth degree polynomial with two terms:
f1(x) = ax⁴ + bx³
f2(x) = ax⁴ + cx²
f3(x) = ax⁴ + dx
f4(x) = ax⁴ + e
a ≠ 0 in all four instances.
Explanation. Because each of the aforementioned polynomials fi(x)-s can be written in the form of f(x) by setting blue0 equal to (c,d,e), (b,d,e), (b,c,e), and (b,c,d), respectively, each of the aforementioned polynomials is in standard form.
B.
The polynomial's closer property for subtraction. When two polynomials of identical degrees with different leading coefficients are subtracted, a polynomial of the same degree is produced.
Example.
Let r(x) be defined as a₁x³ + a₂x² + a₃x + a₄
s(x) is equal to b₁x³ + b₂x² + b₃x + b₄
where a ≠ 0 ≠ b and a ≠ b both belong to a set of real or complex numbers called ai and bi.
If this is how subtraction is defined, then
r(x) - s(x) = [a₁x³ + a₂x² + a₃x + a₄] - [b₁x³ + b₂x² + b₃x + b₄]
r(x) - s(x) = (a₁ - b₁)x³ + (a₂ - b₂)x² + (a₃ - b₃)x + (a₄ - b₄)
Given that (a₁ - b₁) ≠ 0, r(x) - s(x) is similarly a polynomial of fourth degree in this situation.
To learn more about Polynomial click on the link
https://brainly.com/question/2833285
#SPJ13
Are you local grocery store? You can buy 3 pounds of rice for 9 dollars use this information to fill in the missing parts
The proportional relationship that gives the cost of x pounds of rice is given as follows:
y = 3x.
What is a proportional relationship?A proportional relationship is a special case of a linear function, with slope represented by k and intercept of 0, hence the output variable y is obtained with the multiplication of the input variable x and the slope k, as follows:
y = kx.
In this problem, the input and the output are given as follows:
Input: pounds of rice.Output: cost.You can buy 3 pounds of rice for 9 dollars use, hence the constant representing the cost per pound is given as follows:
k = 9/3 = 3.
Hence the equation is:
y = 3x.
Missing InformationThis problem is incomplete but we suppose that it asks for a proportional relationship giving the cost of x pounds of rice.
More can be learned about proportional relationships at brainly.com/question/10424180
#SPJ1
Please Help!
Solve for x:
-18x = 108
Show your work
Answer:
x=-6
Step-by-step explanation:
-18x=108
/-18. /-18
x=-6
Hopes this helps please mark brainliest
Divide both sides by −18.
x = 108/-18Divide 108 by −18 to get −6.
x=−6