An inequality for each of the constraints (one for frames, one for hours for assembly, and 2 non-negative inequalities describing the products is:
x + y ≤ 300
x1 + y3 ≤ 360
What is an inequality?Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal.
Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.
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Would like answers for both, thanks in advance :D
Answer:
Number three is D.
Step-by-step explanation:
NO LINKS!! URGENT HELP PLEASE!!!
Determine the equation of the circle graphed below. Part 2c^2
Answer: [tex](x+7)^2 + (y+1)^2 = 9[/tex]
center = (-7, -1)
radius = 3
======================================================
Explanation:
The highest point on the circle is at (-7,2)
The lowest point is at (-7, -4)
Connecting these endpoints gets us one diameter of this circle.
Apply the midpoint formula to these endpoints.
[tex]\text{Endpoints: }(x_1,y_1) = (-7,2) \text{ and } (x_2,y_2) = (-7,-4)\\\\\text{Midpoint} = (x_m, y_m)\\\\\begin{array}{|l|l|}\cline{1-2}x_m = \frac{x_1 + x_2}{2} & y_m = \frac{y_1 + y_2}{2}\\ & \\x_m = \frac{-7 +(-7)}{2} & y_m = \frac{2 +(-4)}{2}\\ & \\x_m = \frac{-14}{2} & y_m = \frac{-2}{2}\\ & \\x_m = -7 & y_m = -1\\\cline{1-2}\end{array}\\\\\text{The midpoint is located at }(-7, -1)\\\\[/tex]
This midpoint of a diameter is also the location of the center of the circle. Recall that all diameters are a special type of chord that pass through the center of a circle.
The circle is centered at (-7, -1)
---------
Now compute the distance from the center (-7,-1) to a point on the circle's edge. Let's say we picked (-7,2)
The distance between these points is 3 units, which we can find by subtracting the y coordinates and using absolute value
distance = |2 -(-1)| = |2+1| = |3| = 3
You could use the distance formula, but it's probably easier to subtract and then use absolute value.
The distance of 3 units represents the radius of the circle. It's how far you need to go from the center to get to the circle's edge.
Circle radius = 3
---------
Summary
(h,k) = (-7,-1) = centerr = 3 = radiusWe plug those items into the circle template equation.
[tex](x-h)^2 + (y-k)^2 = r^2\\\\(x-(-7))^2 + (y-(-1))^2 = 3^2\\\\(x+7)^2 + (y+1)^2 = 9[/tex]
That last equation is the final answer.
Sue likes to skate at a skate park that is due south of her school and due west of her favorite ice cream parlor. If the skate park is 4 miles from her school and the straight-line distance between the school and the ice cream parlor is 5 miles, how far is the skate park from the ice cream parlor?
The skate park is approximately 6.4 miles from the ice cream parlor.
We can use the Pythagorean theorem to find the distance between the skate park and the ice cream parlor.
As per the information, we can see that the distance we're looking for is the hypotenuse of a right triangle with legs of length 4 miles (distance from school to skate park) and 5 miles (distance from school to ice cream parlor).
Using the Pythagorean theorem, we get:
c² = a² + b²
where c is the distance between the skate park and the ice cream parlor, and a and b are the distances from the school to the skate park and ice cream parlor, respectively.
Substituting the values we know, we get:
c² = 4² + 5²
c² = 16 + 25
c² = 41
Taking the square root of both sides, we get:
c = √41
c ≈ 6.4
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The cost of a first-class postage in 1970 was $0.06 and in year 2013 was $0.46. Determine the average annual rate of increase in the price of postage stamps during the
years 1970 to 2013.
A. 18.47%
B. 4.851%
C. 6.63%
D. 4.84%
From 1970 to 2013, the price of postal stamps increased at an average yearly rate of 4.851%.
The formula for compound interest is:
[tex]A = P(1 + r/n)^{(nt)[/tex]
where A represents the total sum, P represents the beginning sum, r represents the yearly interest rate, n is the number of times the interest is compounded annually, and t represents the number of years.
In this instance, we may consider the initial cost of postal stamps in 1970 as the principal and the rise in price as the interest. The yearly rate of rise, r, may be calculated using the formula.
Let P represent the price in 1970 ($0.06) and A represent the price in 2013 ($0.46). Let t be the duration, or 43 years, from 1970 to 2013.
Then, we can write:
[tex]A = P(1 + r)^t[/tex]
Substituting the values, we get:
[tex]0.46 = 0.06(1 + r)^{43[/tex]
Dividing both sides by 0.06, we get:
[tex]7.67 = (1 + r)^{43[/tex]
Taking the 43rd root of both sides, we get:
[tex](1 + r) = 7.67^{1/43}\\(1 + r) = 1.04851[/tex]
Subtracting 1 from both sides, we get:
r = 0.04851 = 4.851%
Therefore, the average annual rate of increase in the price of postage stamps from 1970 to 2013 is 4.851%.
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lina bought two patio chairs that cost $ 37 each and a table that cost $ 58. what is the total cost of these items?
answer 95 I think that is the answer do you know it it is hard
Answer:
Total cost = $132
Step-by-step explanation:
We can find the total cost using the formula
total cost = (item 1 quantity * cost) + (item 2 quantity * cost)
We essentially find the sum of the product of item quantity and cost for each item:
Thus, for 2 chairs costing $37/chair and 1 table costing $58/table, the total cost is:
Total cost = (2 * $37) + (1 * $58)
Total cost = $74 + $58
Total cost = $132
What is the measure of y (angle AXB)?
1. 90°
2. 60°
3. 45°
4. 30°
Answer:
4. 30°
Step-by-step explanation:
Sum of interior angles of a triangle = 180
y° + ∠XYZ + ∠YZX = 180
y° = 180 - 90 - 60 = 30°
Write your answer has a fraction in the simplest form
We can see here that the probability that it is yellow is: 2.4.
What is probability?Probability is a way to gauge how likely something is to happen. It is stated as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty of the event.
Probability that the marble is yellow:
Total marbles = 12
Yellow marbles = 5
Probability that the marble is yellow: 12/5 = 2.4
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When graphing an equation on graph paper I have to have all of these but....
O label numbers and x/y axis
O work shown
O t-chart or slope intercept form explaned
at least 4 points on the graph
When graphing an equation on graph paper I have to have all of these but: B. work shown.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.What is a graph?In Mathematics and Geometry, a graph is a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis) respectively.
In conclusion, you do not need to have your algebraic work shown when graphing an equation on graph paper.
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A circular arc has measure 6cm and is intercepted by a central angle of 40° . Find the radius r of the circle
The radius of the circle with central angle θ = 40° is r = 8.594 cm
Given data ,
A circular arc has measure 6cm and is intercepted by a central angle of 40°
Now , the radius r of the circle is given by
r = L / θ
where θ is in radians
So , 40° = 0.6981317007977318 radians
On simplifying , we get
r = 40 / 0.6981317007977318
Now , the measure of r = 8.594 cm
Hence , the radius is r = 8.594 cm
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Two train tracks run parallel leaving a station. Train A leaves the station heading east at 55 mph. Train B leaves the station 2 hrs and 15 minutes later also traveling east but at 120 mph. The equation below gives the distance, D, between the two trains as a function of the number of hours, T, that have passed since train B left the station.
For which two values of T will D = 40? Round to the nearest tenth.
A.
0.1 and 0.3
B.
12.9 and 25.2
C.
-1.3 and 1.3
D.
1.3 and 2.5
Answer: Answer choice C: -1.3 and 1.3.
Step-by-step explanation:
We can start by using the formula for the distance, D, between the two trains as a function of time, T:
D = 55(T + 2.25) - 120T
Simplifying this equation, we get:
D = 55T + 123.75 - 120T
D = -65T + 123.75
To find the two values of T for which D = 40, we can set this equation equal to 40 and solve for T:
40 = -65T + 123.75
-85 = -65T
T = 1.31
Plugging this value back into the original equation, we can see that D is equal to 40:
D = -65(1.31) + 123.75
D = 40.0375
Therefore, one solution is T = 1.31. To find the other solution, we can plug D = 40 into the equation and solve for T:
40 = -65T + 123.75
-83.75 = -65T
T = 1.29
Plugging this value back into the original equation, we can see that D is equal to 40:
D = -65(1.29) + 123.75
D = 40.0375
Therefore, the two values of T for which D = 40 are approximately 1.3 and 1.3, which rounds to answer choice C: -1.3 and 1.3.
A recycling bin contained 40 pounds of plastic in October and 50 pounds of plastic in
November. By what percentage did the amount of plastic increase from October to
November?
The percentage increase by the given data is 25%.
We are given that;
Weight of plastic in october= 40
Weight of plastic in november= 50
Now,
To find the percentage increase of the amount of plastic from October to November, we need to find the absolute increase and divide it by the original amount, then multiply by 100 to get the percentage.
The absolute increase is the difference between the final amount and the initial amount, which is 50 - 40 = 10 pounds.
The original amount is the initial amount, which is 40 pounds.
10/40×100=25%.
Therefore, by the percentage the answer will be 25%.
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Jacob is standing 112 m from a building. The angle of elevation from where he is standing on the ground to the top of the building is 62°.
How tall is the building?
Round the final answer to the nearest tenth
Answer:
Step-by-step explanation:
twice the sum of a number and 5 is equal to three times the difference of the number and 4
Answer:
2(x + 5) = 3(x - 4)
2x + 10 = 3x - 12
x = 22
PLS HELP ME OUT! A sporting event has a promotion in which the first 1,000 fans to enter the arena receive either a blue cap or a red cap. A random number generator is used to simulate the color of a cap given to a person where indicates a blue cap and indicates a red cap. Ten simulations, each consisting of ten random numbers, are conducted, and the results are shown in the following table:
Based on the simulations, what is the probability that ten hats given to ten people will consist of more blue caps than red caps? a. 0.20
b. 0.40 c. 0.60 d. 0.80
The probability that ten hats given to ten people will consist of more blue caps than red caps is given as follows:
a. 0.2.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The outcomes in which there are more blue than red caps are those in which the number of zeros is greater than the number of ones, hence the number of desired outcomes is of:
2. (simulation number 7 and simulation number 10).
Hence the probability is of:
p = 2/10
p = 0.2.
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Two ramps are placed back to back as shown. What is the length of the ramp labeled x?
The value of the x as shown in the graph will be 16.61 ft.
From the sine rule in the triangle,
In a triangle ABC, where a, b, and c are the side lengths opposite to the angles A, B, and C respectively, and where the opposite angles A, B, and C are opposite to sides a, b, and c respectively, the Sine Rule states:
[tex]\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}[/tex]
Use the Law Of Sines to solve this:
(Sin 7)/9 = (Sin 13)/x
Cross multiply...
x(Sin 7) = 9(Sin 13)
Divide both sides by Sin 7
x = [9(Sin 13)]/(Sin 7)
x = 16.61254121
therefore, for the ramp, the value of the x will be 16.612 ft.
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A right prism with a triangular base has a volume of 195 mm3 . The right prism is 13 mm tall. The triangular base of the prism has a base length of 5 mm .
What is the base height of the triangular base of the right prism? Round your answer to the nearest whole millimeter, if necessary.
A data set contains three points, and two of the residuals are-7 and 4. What is the third residual?
A. 7
B. -3
C. -4
D. 3
Answer:
D
Step-by-step explanation:
We know that the residual is the difference between the observed value and the predicted value for a given point. Let's assume that the predicted values for the three points in the data set are denoted by ŷ₁, ŷ₂, and ŷ₃, and the observed values are denoted by y₁, y₂, and y₃.
We can write the residuals as:
e₁ = y₁ - ŷ₁
e₂ = y₂ - ŷ₂
e₃ = y₃ - ŷ₃
We are given that two of the residuals are -7 and 4.
Let's assume that e₁ = -7 and e₂ = 4.
We can use these values to find the third residual e₃.Since the sum of residuals is always equal to zero, we have:
e₁ + e₂ + e₃ = 0
Substituting the values of e₁ and e₂, we get
:-7 + 4 + e₃ = 0
Simplifying, we get:
e₃ = 3
Therefore, the third residual is 3, which is option D.
Justify Results Hector was asked to simplify the expression (5^-3/5^-1) He gave the answer 1/25 Did Hector give the correct answer? Explain.
Answer:
To simplify the expression (5^-3/5^-1), we need to use the rule of exponents that states when dividing two powers with the same base, we can subtract the exponents.
Using this rule, we get:
(5^-3/5^-1) = 5^-3 ÷ 5^-1 = 5^-3 × 5^1 = 5^-2 = 1/25
Therefore, Hector gave the correct answer.
Sydney started with no money in her piggy bank and adds $3.50 each day. Destiny started with $50 in her piggy bank and spends $5 of her money each day. Which equation or inequality represents the number of days, x, needed for Destiny and Sydney to have the same amount of money in their piggy banks?
The inequality represents the number of days, x, needed for Destiny and Sydney to have the same amount of money in their piggy banks is 50 ≥ 3.5x + 5
We are given that Sydney started with no money in her piggy bank and adds $3.50 each day. Destiny started with $50 in her piggy bank and spends $5 of her money each day.
We need to find the equation or inequality that represents the number of days, x, needed for Destiny and Sydney to have the same amount of money in their piggy banks.
Sydney started with zero money in her piggy bank and adds $3.50 each day means 0 + 3.50 and Destiny started with $50 in her piggy bank and spends $5 of her money each day then
the inequality becomes as ;
50 ≥ 3.5x + 5
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A moving company offers two sizes of moving trucks. Truck G can fit 20 boxes that measure 1 cubic yard. Truck H is twice as large.
Which measurement can be used to determine the amount of boxes that can fit into Truck H?
Responses?
Measurement can be used to determine the amount of boxes that can fit into Truck H is 2(20 boxes) = 2 cubic yards
What are algebraic expressions?Algebraic expressions are defined as those mathematical expressions that consists of variables, terms, coefficients, constants and factors.
Algebraic expressions are also known to be composed of arithmetic operations, such as;
MultiplicationDivisionFloor divisionAdditionSubtractionBracketParenthesesFrom the information given, we have that;
For Truck G = 20 boxes
And 20 boxes = 1 cubic yard
Then,
Truck H = 2(Truck B)
Truck H = 2(20 boxes)
Truck H = 40 boxes
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a student in a foreign language progam learns 15 new word each week which graph best represents the relationship between x the number of weeks the student has been in the progam and y the total number of new words the student has learned
The proportional relationship y = 15x represents the relationship between the variables, and it's graph is given by the image presented at the end of the answer.
What is a proportional relationship?A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.
The equation that defines the proportional relationship is given as follows:
y = kx.
In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.
A student in a foreign language program learns 15 new word each week, hence the constant is given as follows:
k = 15.
Meaning that the equation is:
y = 15x.
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Let h(x) = x² - 8x.
(a) Find the average rate of change from 3 to 9.
(b) Find an equation of the secant line containing (3,h(3)) and (9, h(9))
How many centimeters are in x meters
Answer:
multiply the number of meters by 100
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Answer:
Step-by-step explanation:
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5
Select the correct answer.
If the domain of the function, f, is restricted to x 20, which function is the inverse off?
f(x) = 91² - 12, 20
O A. q(z) = √2+1
√√2-12
3
OB. h(z)
OC. p(z) = √2-12
c.
9
√2+12
D. g(x)
O D.
The inverse of the function f(x) = 9x²- 12 is p(x) = √(x + 12)/9
How to find the inverse of the function?Given that the domain of a function f is restricted to x ≥ 0, we need to find the inverse of the function
f(x) = 9x²- 12 for x ≥ 0.
To find the inverse of the function, we proceed as follows.
f(x) = 9x²- 12
Let f(x) = y
So, we have that
y = 9x²- 12
Adding 12 to both sides of the equation, we have that
y + 12 = 9x²- 12 + 12
y + 12 = 9x²
Dividing both sides by 9, we have that
(y + 12)/9 = 9x²/9
(y + 12)/9 = x²
Taking square root of both sides, we have that
√x² = √(y + 12)/9
x = √(y + 12)/9
Now, replacing x with y, we have that
x = √(y + 12)/9
y = √(x + 12)/9
Replacing y with f⁻¹(x), we have that
f⁻¹(x) = √(x + 12)/9
So, the inverse is p(x) = √(x + 12)/9
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Pls help
Here is a figure made of two circles inside of one circle.
Answer:
(a) Area of the big circle
= π(9^2) = 81π square cm
(b) Area of both little circles
= 2π(4.5^2) = 40.5π square cm
= 81π/2 square cm
(c) Area of the blue section
= 81π - 40.5π = 40.5π square cm
= 81π/2 square cm
Help!
The surface area of this rectangular prism is __ square centimeters.
The surface area of the rectangular prism is 216 square cm
What is the surface area of the rectangular prism?From the question, we have the following parameters that can be used in our computation:
10 cm by 3 cm by 6 cm
The surface area of the rectangular prism is calculated as
Area = 2 * (3 * 10 + 3 * 6 + 10 * 6)
Evaluate
Area = 216
Hence, the area is 216 square cm
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I need help with this problem.
According to the information, the elasticity is 0.619, suggests that the demand is relatively insensitive to price changes.
How to calculate the elasticity?To evaluate the elasticity at $p=2$, we need to use the formula for price elasticity of demand:
E = (dQ/Q) / (dP/P)
where:
E = price elasticity of demand
dQ = change in quantity demanded
Q = quantity demanded
dP = change in price
P = price
We are given the equation for the demand function:
x = 15000 - 3535√p
So, the quantity demanded at price $p$ is $Q = x(p) = 15000 - 3535\sqrt{p}$.
Taking the derivative of Q with respect to p:
dQ/dp = -3535/(2√p)
Now we can calculate the elasticity at $p=2$:
Q = 15000 - 3535√2
dQ/dp = -3535/(2√2)
P = 2
dP = 0
E = (dQ/Q) / (dP/P)
E = (-3535/(2√2)) / [(15000 - 3535√2)/2]
E ≈ -0.619
According to the above, the elasticity is 0.619, suggests that the demand is relatively insensitive to price changes.
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how to do I solve this
Answer:
the answer is 80
Step-by-step explanation:
1pound=16ounces
What is the value of x?
34°
(-1/2 x) °
Answer:
The expression "34° (-1/2 x) °" can be simplified by multiplying 34° by the quantity (-1/2 x):
34° (-1/2 x) ° = (34°) * (-1/2 x)
To multiply two values with units, we can simply multiply the numerical parts and keep the units. Therefore, we get:
(34°) * (-1/2 x) = -17x°
So the value of "34° (-1/2 x) °" is simply -17x°.