A store has two types of animal feed available. Type A contains 3 pounds of oats and 3 pounds of corn per bag. Type B contains 1 pound of oats and 7 pounds of
corn per bag. A farmer wants to combine the two types so that the resulting mixture has at least 18 pounds of oats and at least 54 pounds of corn. The store
only has 11 bags of type A feed and 12 bags of type B feed in stock. Type A costs $4 per bag, and type B costs $1 per bag. How many bags of each type should
the farmer buy to minimize her cost?
Note that the ALEKS graphing calculator can be used to make computations easier.
Type A feed:
Type B feed:
bag(s)
bag(s)
The farmer will purchase five bags of kind A and six bags of type B.
Per bag, Type A includes 9 pounds of oats and 3 pounds of maize.
Per bag, Type B includes 2 pounds of oats and 10 pounds of maize.
The farmer is looking for a blend that comprises at least 57 pounds of oats and 75 pounds of maize.
Allow the farmer to mix type A feed = x pounds.
and feed type B = y pounds
(9x + 2y) pounds of oats when blended
Corn amount when combined: (3x + 10y) pounds
Oats equation: 9x + 2y = 57 ———— (1)
Corn equation: 3x + 10y = 75 ————- (2)
Subtract equation (2) from equation (2) by multiplying it by three (1)
3(3x + 10y) - (9x + 2y) = 75×3 - 57
9x + 30y - 9x - 2y = 225 - 57
28y = 168
y = 6 bags
derived from the equation (1)
9x + 2×6 = 57
9x + 12 = 57
9x = 57 - 12
9x = 45
x = 5 bags
Because the business has 15 bags of each sort, each bag costs $4.
As a result, the cost of 5 bags of type A and 6 bags of type B is = (54) + (64)
= 20 + 24
= $44
The farmer intends to buy five bags of kind A and six bags of type B.
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Find all of the numbers less than100 that have at least 2 and at least one 5 in their prime factorization
Answer: [tex]10, 20, 30, 40, 50, 60, 70, 80, 90[/tex]
Step-by-step explanation:
If the numbers have at least one 2 and at least one 5, then they are multiples of 10 (since [tex]10=2 \times 5[/tex]).
So, these numbers are [tex]10, 20, 30, 40, 50, 60, 70, 80, 90[/tex].
Question 4 options:
Premises:
If I'm a student, then I go to school. If I go to school, then I learn.
Conclusion:
If I'm a student, then I learn.
This is an example of the Law of
The law of mathematical logic that was used to derive the given conclusion is; Law of Syllogism
What is the Law of Syllogism?The law of syllogism is defined as a type of logical argument using deductive reasoning.
Now, In mathematical logic, the Law of Syllogism states that if the following two statements are true:
(1) If a , then b .
(2) If b , then c .
Then we can derive a third true statement:
(3) If a , then c .
Now, applying that law to our question, we see that;
1) If I'm a student, then I go to school.
2) If I go to school, then I learn.
Then we can derive a third true statement:
3) If I'm a student, then I learn.
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Use the numbers 5, 6, and 7 and the operations of addition, subtraction, multiplication, and/or division to create three different number expressions with three different values. One of the expressions should have a value of 37.
The use the numbers 5, 6, and 7 and the operations of addition, subtraction, multiplication, and/or division to create three different number expressions with three different values will be:
1. 5 × 6 + 7 = 37
2. 5 + 6 - 7 = 4
3. 5 + 6 + 7 = 18
What is addition?Addition simply means the sum of the numbers that are given. It should be noted that addition is represented by the sign +.
In this case, we are told to use 5, 6 and 7 to create different values. These are represented above. The addition of 5, 6, and 7 gives 18.
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Find the equation of the tangent at f(x) at x=0
Given:
The function
[tex]f(x)=\frac{2x}{x^2+1}[/tex]Required:
Find the equation of the tangent at f(x) at x=0.
Explanation:
The slope of f(x),
[tex]f^{\prime}(x)=\frac{2(-x^2+1)}{(x^2+1)^2}[/tex]Now, the slope of function at x = 0 is f'(x) = 2.
The line with slope m = 2 and passing through (0, 0).
[tex]f(x)=2x[/tex]Answer:
Equation of tangent of the function at x = 0, f(x) = 2x.
Part 1
Tell whether the sequence is arithmetic. If it is, identify the common difference.
-1,4,9,14
PLEASE HURRY
Answer:
It is arithmetic, the common difference is 5
Step-by-step explanation:
What an arithmetic sequence has to have is a common difference meaning you are adding or subtracting the same number each time, in this case you are adding 5 every time so it is arithmetic
A shirt that normally costs $30 is on sale for
$21.75. What percent of the regular price is
the sale price?
Answer:
72.5%
Step-by-step explanation:
Hello!
We can find the percentage by dividing the sale price by the original price, then multiplying that by 100.
Find the Percentage[tex]\frac{21.75}{30} * 100[/tex]0.725 * 10072.5The percentage is 72.5%.
find the area of the circle. Use 3.14 for pie. Do not round your answer.
Answer: A = 452.16 ft²
Step-by-step explanation:
This gives us the formula to solve for the area.
A = πr²
The radius (r) is the same as the diameter divided by 2.
24 ft / 2 = 12 ft
We will input these given values and solve.
A = πr²
A = (3.14)(12)²
A = 452.16 ft²
Answer:
452.16 ft²
Step-by-step explanation:
To find the radius, you divide the diameter (24) by 2, which equals 12. The area of a circle formula is πr². To find area, you do 12² * 3.14. That equals 144 * 3.14, which equals 452.16.
Use the intersect method to solve the equation. x^2 - 3x = x^2 -1
The coordinate that represent the solution of the equation -
x² - 3x = x² - 1 is (0.333, -0.8889).
What is equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given is the following equation -
x² - 3x = x² - 1
In order to solve it using intersect method, we will plot the graphs of both functions and find the point of intersection of graphs of both the equations.
Assume -
f(x) = x² - 3x
g(x) = x² - 1
Now, the point of intersection of both the graphs will be the solution to the equation given by -
f(x) = g(x)
It can be seen from the graph that, both the graphs intersect at the coordinate (0.333, -0.8889). This coordinate will be the solution set of the equation -
f(x) = g(x)
Therefore, the coordinate that represent the solution of the equation -
x² - 3x = x² - 1 is (0.333, -0.8889).
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question is in the picture
Wilbur landed his plane.
The plane's elevation relative to the ground
(in meters) as a function of time (in seconds)
is graphed.
How high was the plane after 1000 seconds?
At 1000 seconds the graph shows the height of 3500 meter.
what is graph?The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.
Following the creation of a research question, data is continuously gathered through observation. The information is subsequently arranged, condensed, categorised, and visually portrayed.
In a line graph, the information or data is represented as a series of markers, or dots, and is then connected to one another by a straight line.
Usually, data that varies over time is represented with a line graph.
Given:
The graph gives the relation between Elevation and Time.
As, if at 400 seconds the height is 6500 meters.
and, at 800 seconds the height is 4500 meters.
Thus, at 1000 seconds the graph shows the height of 3500 meter.
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Reflect the given triangle over the y - axis [[3,6,3],[-3,3,3]]
By using a reflection over the y-axis, the coordinates of the image of the triangle are (- 3, - 3), (- 6, 3) and C'(x, y) = (- 3, 3).
How to determine the coordinates of the vertices of a triangle by rigid transformations
Rigid transformations are transformations applied on geometric loci such that the form of the construction is not altered. Reflections over the y-axis are examples of rigid transformations. In this problem we need to apply this kind of transformation on the three vertices of the triangle: A(x, y) = (3, - 3), B(x, y) = (6, 3), C(x, y) = (3, 3).
The reflection over the y-axis is described by the following formula:
P'(x, y) = P(x, y) + (- 2 · p, 0)
Where:
P(x, y) - Original pointP'(x, y) - Resulting pointp - x-Component of P(x, y).If we know that A(x, y) = (3, - 3), B(x, y) = (6, 3) and C(x, y) = (3, 3), then the image of the vertices of the triangle:
A'(x, y) = (3, - 3) + (- 6, 0)
A'(x, y) = (- 3, - 3)
B'(x, y) = (6, 3) + (- 12, 0)
B'(x, y) = (- 6, 3)
C'(x, y) = (3, 3) + (- 6, 0)
C'(x, y) = (- 3, 3)
Now we present the picture of the two triangles.
The coordinates of the image of the triangle are A'(x, y) = (- 3, - 3), B'(x, y) = (- 6, 3) and C'(x, y) = (- 3, 3).
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1/16 - ( -7/16)
Write your answer as a fraction in simplest form.
The product of -2 and a number is at most 10.
Find the possible numbers.
On<-5
Ons-5
Onz-5
On>-5
Answer:
n ≥ -5
Step-by-step explanation:
-2n ≤ 10
Divide both sides by -2. Remember to flip ≤ to ≥.
-2n/(-2) ≥ 10/(-2)
n ≥ -5
If a fraction has a numerator of 2, then the fraction can be reduced. A counter example is ____ option below.
a) 10/15
b) 11/22
c) 1/10
d) 2/11
Answer:
The answer is d
Step-by-step explanation:
2/11 has a numerator of 2 but cant be reduced
Answer:
Step-by-step explanation:
I misunderstood the question. So, please disregard this answer. Thank you.
PLEASE HELP ME ILL LITERALLY AND I PROMISE ON GOD TO RATE YOU 5 STARS AND GIVE U POINTS
Answer:
1. 12hrs
2. 2hrs
Step-by-step explanation:
4:00pm is 2 hrs from 6:00pm
5:00am is 12hrs from 5:00pm
Choose two statements that are true for this expression
For this exponential function,
what is the output value (y),
when the input value (x) is 3?
y = 5.2x
(3, [?])
Enter
Answer:
40
Step-by-step explanation:
5*(2^3)=40
find the area under the standard normal distribution curve to the right of . use a ti-83 plus/ti-84 plus calculator and round the answer to at least four decimal places.
using calculator
Area right to the right of the 2=2.12
P(Z > 2.12)
• P(Z < -2.12)
= 0.0170
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You take a $4,500 loan to pay for a trip
to the Amazon rainforest to photograph
wild animals. If the loan's interest rate is
8% for 1 year, what is the interest for the
first payment?
A $12.58
C $30.00
Vincent Fal
B $26.00
D $80.99
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$4500\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years\dotfill &1 \end{cases} \\\\\\ I = (4500)(0.08)(1) \implies I = 360~\hfill \underset{monthly~payment}{\stackrel{360 ~~ \div ~~ 12}{\text{\LARGE 30}}}[/tex]
c.
PRT/100
4500×8×1/100=360
per month=360÷12
=30
write and solve a real world problem in which you find the commission
A car salesman earns a 3% commission on sales. If he sells a car for $27,990, how much commission will he earn?
($27,990)*(0.03) = $839.70
The Jones family will pay their insurance broker a commission of $1,750.00.
Commission is an amount of money paid to an employee or company as an incentive to sell more. A straight commission is a percentage of sales.
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ANSWER QUICK I WILL GIVE BRAINLIEST!
Solve k over negative 1.8 is less than negative 4.9 for k.
k < −8.82
k > 8.82
k < −6.7
k > −6.7
Answer:
k<-8.82
Step-by-step explanation:
k/1.8<-4.9
k<-8.82
Answer:k<-8.82
Step-by-step explanation:
If triangle LMN has an obtuse angle at vertex M, which statements could be true? Check all that apply.
Triangle LMN is an obtuse angle then, the angle at vertex L is acute, the angle at vertex N is acute.
The triangle LMN is an obtuse angle at the vertex M. So by the definition of obtuse angle triangle LMN is an obtuse angle.
As ∠M is an obtuse angle
So 90° < m∠M < 180°
By the property of a triangle,
m∠L + m∠M + m∠N = 180°
m∠M = 180° - (m∠L + m∠N)
90° < 180° - (m∠L + m∠N) < 180°
90° - 180° < -(m∠L + m∠N) < 0
-90° < -(m∠L + m∠N) < 0
90° >(m∠L + m∠N) > 0
90° > m∠L and 90° > m∠N
Therefore both angles L and N are acute angles.
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Answer:
1, 2 and 5
Step-by-step explanation:
see picture
What are three pairs of corresponding angles?
A house has decreased in value by 35% since it was purchased. If the current value is $78,000, what was the value when it was purchased?
Answer: The value of the house when it was purchased was 120,000
Step-by-step explanation:
1) Set up the equation. Let x be the house.
x-x*35%= 78,000
First, the house decreases 35% of the cost of the original house. It now costs 78,000.
2) Solve the equation.
x-x*0.35 = 78,000
x-0.35x=78,000
0.65x = 78,000
x= 120,000
Create three probability application problems of your own. Solve your problems. Explain your answers.
In the above question, we need to from 3 probability questions and then give solutions for them
Example 1 : A coin is tossed three times. What is the probability of getting at least one head?
Solution : A coin is tossed 3 times then
Sample space = [HHH, HHT, HTH, THH, TTH, THT, HTT, TTT]
Total number of ways = 2 × 2 × 2 = 8
Favorable Cases = 7
P (A) = 7/8
OR
Probability (of getting at least one head) = 1 – P (no head)⇒ 1 – (1/8) = 7/8
Example 2 : Three red and four black balls are contained in a bag. Randomly, one ball gets taken out of the bag. Determine the probability that the drawn ball is
(i) black
(ii) not black
Solution :
Total number of balls in the bag are = 3 + 4 = 7 balls
Number of favorable outcomes or number of black balls in the bag = 4
(i) Probability getting black balls = [tex]\frac{number of favorable outcomes}{number of total outcomes}[/tex]
P(black ball) = [tex]\frac{4}{7}[/tex]
(ii) Probability getting no black balls = 1 - P(black ball)
= 1 - [tex]\frac{4}{7}[/tex]
= [tex]\frac{3}{7}[/tex]
Example 3 : Given two dice, what is the likelihood of receiving the number 7?
Mathematical probability - There are 36 ways in all, or 6 times 6. Favorable scenarios are (1, 6) (6, 1) (2, 5) (5, 2) (3, 4) (4, 3), etc., in six different ways. P (A) = 6/36 = 1/6
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Find the values of a,b and c that would make the statements true.
1) (ax+2)(5x+b)=10x^2+bx+c
The values of a, b and c are a = 2, b = -10 and c = -20
How to determine the values of the variables?The equation is given as
(ax + 2)(5x + b) = 10x^2 + bx + c
Open the brackets
So, we have
5ax^2 + 10x + abx + 2b = 10x^2 + bx + c
By comparing the above equation.
We have the following set of equations
5a = 10
10 + ab = b
2b = c
By solving the equations, we have
a = 2
Substitute a = 2 in 10 + ab = b
10 + 2b = b
So, we have
b = -10
Substitute b = -10 in 2b = c
2(-10) = c
Evaluate
c = -20
Hence, the values of the variables are a = 2, b = -10 and c = -20
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A bee flies at 12 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 16 minutes, and then flies directly back to the hive at 8 feet per second. It is away from the hive
for a total of 18 minutes.
a What equation can you use to find the distance of the flowerbed from the hive?
b. How far is the flowerbed from the hive?
In linear equation, 864 is distance the flowerbed from the hive .
What are a definition and an example of a linear equation?
A linear equation with one variable is one that includes just one variable. It has the formula Ax + B = 0, with A and B being any two actual values and x being an ambiguous variable with only one possible value. One such linear equation in one variable is 9x + 78 = 18.a) The equation is so called "time equation"
D%2F12 + 16*60 + D%2F8 = 19*60 seconds
(b) To determine the distance D, solve the equation
D%2F12 + D%2F8 = 19*60 - 16*60 = 3*60,
multiply both sides by 24
2D + 3D = 3*60*24
5D = 4320
D = 4320/5 = 864
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Please help and provide an explanation for why the answer is f(x) = -1/3x - 4
What is the equation of the line that passes through Point (-6, -2) and has a Slope of -1/3.
y=-1/3-4
Step-by-step explanation:
point slope form!
y-y=m(x-x)
with the point (-6,-2) and the slope (-1/3) replace the 2nd variables of each variable and replace m with the slope
y-(-2)=-1/3(x-(-6))
then solve that normally
y-(-2)=-1/3(x-(-6))
y+2=-1/3x -2
y=-1/3x-4
I didnt use officially math symbols but i hope you can still read it!
Givin f(x) = 1/x+5 and g(x)=x-2. What are the restrictions of the domain of f(g(x))?
OX≠ -5
OX≠ -3
OX≠ 2
OThere are no restrictions
Answer:
Step-by-step explanation:
x cannot be -3 or 2
Step-by-step explanation:
f(g(x)) = 1 / (( x-2) +5)
= 1/ (x+3)
g(x) cannot have x=2
The domain is restricted where
f(x) has an restriction that x cannot be 5
so g(x) cannot be -5
-5 = x-2
Add 2 to each side
-5+2 = x
-3