Answer:
17%
Step-by-step explanation:
change in temprature=100-120=-20
% chsnge in temp.=-20/120 ×100=-50/3 %=-16.66666...≈-17%
negative sign shows temperature is coming down.
the poultry farmer decided to make his own chicken scratch by combining alfalfa and corn in rail car quantities.A rail car of corn costs $400 and a rail car of alfalfa costs $200. The farmer's chickens have a minimum daily requirement of vitamin K (500 milligrams) and iron (400 milligrams), but it doesn't matter whether those elements come from corn, alfalfa, or some other grain. A unit of corn contains 150 milligrams of vitamin K and 75 milligrams of iron. A unit of alfalfa contains 250 milligrams of vitamin K and 50 milligrams of iron.Formulate the linear programming model for this situation.
Answer:
- Min Z = $400C + $200A
Step-by-step explanation:
The linear programming model deals with the minimization or maximization of a linear function of several variables and inequalities. This method assists the industries in minimizing costs and maximizing production.
In the given situation,
The Linear programming model would be:
Min Z = $400C + $200 A
which is based on:
150 mg of vitamin K in corn C + 250 mg of vitamin K in AlfaAlfa ≥ 500
75 mg of iron in Corn + 50 mg of iron in AlfaAlfa ≥ 400
∵ C, A ≥ 0
Thus, the equation would be,
Min Z = $400C + $200 A
The width of a rectangular slab of concrete is 7 m less than the length. The area is 98 m squared. Find the dimensions
Answer:
Length = 14 m, Width = 7 m
Step-by-step explanation:
Let the length is l and width is b.
Width, b = l-7
Area of the rectangle, A = 98 m²
We know that, the area of a rectangle is as follow :
[tex]A=lb[/tex]
So,
[tex]98=l(l-7)\\\\98=l^2-7l\\\\l^2-7l-98=0\\\\l^2+7l-14l-98=0\\\\l(l+7)-14(l+7)=0\\\\l=14,-7[/tex]
Length can't be negative. So,
Width, b = 14-7 = 7 m
So, the dimensions of the rectangle are 14 m and 7 m respectively.
What is the following product?(2square root 7 +3square root 6)(5square root2+4square root3)
Answer:
[tex]10\sqrt{14} + 8\sqrt{21} + 30 \sqrt{3} +36\sqrt{2}\\\\[/tex]
Step-by-step explanation:
[tex]( 2 \sqrt7 + 3 \sqrt6)(5\sqrt2 + 4\sqrt3)\\\\= 2\sqrt7(5\sqrt2 + 4\sqrt3) + 3\sqrt6 ( 5\sqrt2 + 4\sqrt3)\\\\=10\sqrt{7 \times 2} + 8\sqrt{7 \times 3} + 15\sqrt{6 \times 2} + 12\sqrt{ 6\times 3}\\\\=10\sqrt{14} + 8\sqrt{21} + 15 \sqrt{12} +12\sqrt{18}\\\\= 10\sqrt{14} + 8\sqrt{21} + 15 \sqrt{4 \times 3 } +12\sqrt{9 \times 2}\\\\= 10\sqrt{14} + 8\sqrt{21} + 15 \sqrt{2^2 \times 3} +12\sqrt{3^2 \times 2}\\\\= 10\sqrt{14} + 8\sqrt{21} + 30 \sqrt{3} +36\sqrt{2}\\\\[/tex]
Please answer & number. Thank you! <33
Answer:
2）=2
4）=3
5）=5
8）=-1
Step-by-step explanation:
just divide the number by the number with variable
Find the slope of the line y= -3x+7
Answer:
If you had a line of x = 7, (or any time you have an equation where x equals a number) then you would have a vertical line. In every vertical line, the slope is undefined. In equations of lines that are in the format of y = mx + b, the slope is represented by the "m".Answer:
-3
Explanation:
The given equation is in slope-intercept form. The format of slope-intercept is y = mx + b, where m is the slope and b is the y-intercept.
The slope is the coefficient of x.
In the equation y = -3x + 7, the slope is -3, because -3 is the coefficient of x.
Hence, the slope is -3.How much fabric is needed to make a tent in the shape of a triangular prism with the following measures?
Answer:
The fabric needs 196.4 ft²
Step-by-step explanation:
∵ The tent formed formed from 4 faces
two equilateral triangles with side length 7 ft
two rectangles with dimensions 11 ft and 7 ft
∵ Area equilateral Δ = 1/4 S²√3
∵ Area rectangle = L × W
∴ The area of the prism = 2 × 1/4 × (7)²√3 + 2 × 7 × 11
= 196.4 ft²
Note:
If you find the area of the triangle by the rule 1/2 × base × height
∴ Area Δ = 1/2 × (7) × 6 = 21 ft²
∴ Area tent = 2 × 21 + 2 × 77 = 196 ft²
Two answer very closed
Answer:
273 ft^2 (apparently you have to cover the ground)
Step-by-step explanation:
You want to put a 5 inch thick layer of topsoil for a new 23 ft by 27 ft garden. The dirt store sells by the cubic yard. How many cubic yards will you need to order?
Answer:
9.5833333333 yd³
9 7/12 yd³
Step-by-step explanation:
23 * 27 * 5/12 = 258.75 ft³
1 yd³ = 3ft * 3ft * 3ft
1 yd³ = 27 ft³
258.75 ft³ * 1 yd³/27 ft³ = 9.5833333333 yd³
9.5833333333 yd³
9 7/12 yd³
Your grandma recently moved to Hawaii (Hawaiian Standard Time Zone). You always call her at 8:00pm on her birthday (November 6th). You are at home in Southern California. What time do you need to call her to reach her at 8:00pm Hawaiian Time
What are the domain and range of the function represented by the set of
ordered pairs?
{(-16, 0), (-8, -11), (0, 12), (12,4)}
Answer:
domain:-16,-8,0,12
range:0,-11,12,14
Reflections were shown across the x- and y-axes but reflections can occur across any line. The figure above shows quadrilateral EFGH reflected about the line y=x. Which best describes what happens to the ordered pair for this reflection?
1. (x,y) → (y,x)
2. (x,y) → (-x,-y)
3. (x,y) → (-y,-x)
4. There is no relationship between the points.
Answer:
1. (x,y) → (y,x)
Step-by-step explanation:
Coordinate of point E:
Before the transformation, the coordinate of point E was given by (3,-6).
After the transformation, we have E'(-6,3), which eliminates options 2 and 3.
For the other points, we will also get, (x,y) -> (y,x), which is the rule given when the original figure is reflected over the line y = x, and thus, the correct answer is given by option 1.
How many digit numbers with all ranging from to have at least of their digits equal. How many have exactly equal digits
Answer:
Step-by-step explanation:
Please can you re-write your question, the question is incomplete and difficult to understand.
Thanks.
The shaded region R in diagram below is enclosed by y-axis, y = x^2 - 1 and y = 3.
Determine the volume of the solid generated when the shaded region R is revolved
about x = -1 by using Disk method.
Cross sections of the volume are washers or annuli with outer radii x(y) + 1, where
y = x(y) ² - 1 ==> x(y) = √(y + 1)
and inner radii 1. The distance between the outermost edge of each shell to the axis of revolution is then 1 + √(y + 1), and the distance between the innermost edge of R on the y-axis to the axis of revolution is 1.
For each value of y in the interval [-1, 3], the corresponding cross section has an area of
π (1 + √(y + 1))² - π (1)² = π (2√(y + 1) + y + 1)
Then the volume of the solid is the integral of this area over [-1, 3]:
[tex]\displaystyle\int_{-1}^3\pi y\,\mathrm dy = \frac{\pi y^2}2\bigg|_{-1}^3 = \boxed{4\pi}[/tex]
[tex]\displaystyle\int_{-1}^3 \pi\left(2\sqrt{y+1}+y+1\right)\,\mathrm dy = \pi\left(\frac43(y+1)^{3/2}+\frac{y^2}2+y\right)\bigg|_{-1}^3 = \boxed{\frac{56\pi}3}[/tex]
Help. Does anyone know the answer. Pls help!
Answer:
Step-by-step explanation:
the first and last choices look good
Badluckville had been expecting a $50 million investment for a new golf resort, but the contract was cancelled.
Badluckville's mayor estimates that this will cost the city $300 million in total economic activity. What is the mayor's
estimate of the multiplier and marginal propensity to consume?
Answer:
multiplier = 6
marginal propensity to consume = .83
Step-by-step explanation:
/ means divided by
1 .
300,000,000 / 50,000,000 =
multiplier =
6
2.
300,000,000 - 50,000,000 =
250,000,000
250,000,000/300,000,000 =
marginal propensity to consume =
0.83333333333
or
.83
quizlet
marginal propensity to consume is equal to ΔC / ΔY, where ΔC is the change in consumption, and ΔY is the change in income
investopedia
(3k + 5)(2k2 – 5k – 3)
Someone please help me !!
Answer:
6(x-1)(x+1)(6x-1)/6(x-1)
6(x+1)(6x-1)/6
(x+1)(6x-1)
How do I solve this?
Answer:
Step-by-step explanation:
4x+3y=13
5x-4y=-7
find the measure of angle BAC
Answer:
a= 26
Step-by-step explanation:
180-130=50
total angle in triangle =180
4a+a+50=180
then proceed like norma algebra
What is the place value of the 4 in 4.09?
Choose 1 answer:
(Choice A)
Tens
(Choice B)
Ones
(Choice C)
Tenths
(Choice D)
Hundredths
Answer:
B: Ones.
Step-by-step explanation:
Because this number is 4.09, and the decimal is right next to the 4, that means that it is in the ones place. Decimals are always adjacent on the right to the ones place.
Divide the following complex numbers:
[tex](2 + i) \div (1 - 4i)[/tex]
Answer:
[tex]-\dfrac{2}{17} + \dfrac{9}{17}i[/tex]
Step-by-step explanation:
[tex] (2 + i) \div (1 - 4i) = [/tex]
[tex] = \dfrac{2 + i}{1 - 4i} [/tex]
[tex] = \dfrac{2 + i}{1 - 4i} \times \dfrac{1 + 4i}{1 + 4i} [/tex]
[tex] = \dfrac{(2 + i)(1 + 4i)}{(1 - 4i)(1 + 4i)} [/tex]
[tex] = \dfrac{2 + 8i + i + 4i^2}{1 + 16} [/tex]
[tex] = \dfrac{2 + 9i - 4}{17} [/tex]
[tex] = \dfrac{-2 + 9i}{17} [/tex]
[tex]= -\dfrac{2}{17} + \dfrac{9}{17}i[/tex]
NEED ANSWER QUICK
Timmy and Tommy are two boys whose ages add up to 23. Timmy is 5
years older than Tommy. How old are they?
Answer:
Tommy's age is 9 years old.
Timmy's age is 14 years old.
Step-by-step explanation:
Take Tommy's age to be x and Timmy's age to be x+5
x+x+5=23
2x+5=23
2x=23-5=18
x=18÷2=9
x+5=9+5=14
pls help
With a coupon you can buy up to 4 medium pizzas at $6 each. What is the
domain of this graph?
Answer:
Domain: {1, 2, 3, 4}
Step-by-step explanation:
The domain of the graph (input values) is the number of pizzas which are plotted on the x-axis while the range (output values) is the cost of pizza, plotted on the y-axis (vertical axis)
The domain therefore would consists of each x-coordinate that represent each point on the graph, which are {1, 2, 3, 4}
Lindsay is checking out books at the library, and she is primarily interested in mysteries and nonfiction. She has narrowed her selection down to ten mysteries and twelve Nonfiction books. If she randomly chooses four books fro her selections, what’s the probability that they will all be nonfiction?
twelve nonfiction books. If she randomly chooses four books
answer to 4 decimal places, if necessary.
Answer
Answer:
0.0677 = 6.77% probability that they will all be nonfiction
Step-by-step explanation:
The books are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
10 + 12 = 22 books.
She chooses 4 books, which means that [tex]n = 4[/tex]
12 nonfiction, which meas that [tex]k = 12[/tex]
What’s the probability that they will all be nonfiction?
This is P(X = 4). So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 4) = h(4,22,4,12) = \frac{C_{12,4}*C_{10,0}}{C_{22,4}} = 0.0677[/tex]
0.0677 = 6.77% probability that they will all be nonfiction
3 folders cost \$2.91, 2, point, 91. Which equation would help determine the cost of 22 folders? Choose 1 answer:
Answer:
Step-by-step explanation:
3=$2.91
22=x
3x=64.02
x=21.34
Find the distance between the points (-5, -4) and (3, 1).
On a coordinate plane, points are at (3, 1), (negative 5, negative 4).
Step-by-step explanation:
it will help u
Find the difference.
(3x3−2x2+4x−8)−(5x3+12x2−3x−4)=
Answer:
-2x³ - 14x² + 7x - 4
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
(3x³ - 2x² + 4x - 8) - (5x³ + 12x² - 3x - 4)
Step 2: Simplify
[Distributive Property] Distribute negative: 3x³ - 2x² + 4x - 8 - 5x³ - 12x² + 3x + 4Combine like terms (x³): -2x³ - 2x² + 4x - 8 - 12x² + 3x + 4Combine like terms (x²): -2x³ - 14x² + 4x - 8 + 3x + 4Combine like terms (x): -2x³ - 14x² + 7x - 8 + 4Combine like terms: -2x³ - 14x² + 7x - 4The sum of two six-digit numbers is a seven-digit number
Answer
500,000 + 500,000 = 1,000,000
Step-by-step explanation:
A test taker gets 70 on 1st exam, 80 on 2nd exam, 2/3 of 4/5 of his 2nd exam on his 3rd test. If the professor gives 5 points extra credit on his 4th exam and his average score is 80, what was his score on the 4th exam
=================================================
Explanation:
The phrasing "2/3 of 4/5 of his 2nd exam on his 3rd test" is a bit clunky in my opinion. It seems more complicated than it has to be.
The student got 80 on the second exam. 4/5 of this is (4/5)*80 = 0.8*80 = 64. Then we take 2/3 of this to get (2/3)*64 = 42.667 approximately. If we assume only whole number scores are given, then this would round to 43.
Let x be the score on the fourth exam. Since 5 points of extra credit are given, the student actually got x+5 points on this exam.
So we have these scores
first exam = 70second exam = 80third exam = 43fourth exam = x+5Adding up these scores and dividing by 4 will get us the average
(sum of scores)/(number of scores) = average
(70+80+43+x+5)/4 = 80
(x+198)/4 = 80
x+198 = 4*80
x+198 = 320
x = 320 - 198
x = 122
So the student got a score of x+5 = 122+5 = 127 on the fourth exam.
Express the radical using the imaginary unit, i.
Express your answer in simplified form.
±sqrt(-35)
Answer:
-7i or 7i
Step-by-step explanation:
You can't take the square root of a negative number, so the value "i" is automatically taken out. You're now left with i +/- sqrt(35). The square root of 35 now can either be -7 or 7 because of the +/-, so the final answer is -7i or 7i.
What is the equation, in the point-slope form, of the line that is parallel to the given and passes through the point (-1,-1)?
Answer:
y + 1 = 3(x+ 1)
Step-by-step explanation:
(2,3) , (0 ,-3)
Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]= \frac{-3-3}{0-2}\\\\=\frac{-6}{-2}\\\\= 3[/tex]
m = 3
Parallel lines have same slope.
m = 3; (-1 , -1)
y -y1 = m (x -x1)
y -[-1] = 3(x -[-1])
y + 1 = 3(x+ 1)
Answer:
D. y+1=3(x+1)
