Answer: a) The profit function can be written as:
P(x) = 5x - 400x + 600
To find the asymptotes, we can look at the denominator of the second term, which is (x - 3). This means that there is a vertical asymptote at x = 3. To find the intercepts, we can set P(x) = 0:
5x - 400x + 600 = 0
Solving for x, we get:
x = 1.5 and x = 2.5
Therefore, there are x-intercepts at (1.5, 0) and (2.5, 0). To sketch the graph, we can also note that the coefficient of x^2 is negative, which means that the graph is a downward-facing parabola.
b) The domain of the function is the set of all possible values of x, which in this context represents the amount of coffee sold. Since we cannot sell a negative amount of coffee, the domain is x ≥ 0.
The range of the function is the set of all possible values of P(x), which represents the profit. Since the coefficient of x^2 is negative, the maximum profit occurs at the vertex of the parabola. The vertex has x-coordinate:
x = -b/(2a) = -(-400)/(2(-200)) = 1
Therefore, the maximum profit occurs when x = 1. The vertex has y-coordinate:
P(1) = 5(1) - 400(1) + 600 = 205
Since the coefficient of x^2 is negative, the range is (-∞, 205].
c) The horizontal asymptote of the function is y = -400, which represents the long-term average profit per kilogram of coffee sold. This means that as x gets very large, the profit per kilogram approaches -400. This could happen, for example, if the cost of producing the coffee increased significantly while the price remained the same.
d) To find the amount of coffee that must be sold to make a profit of $4000, we can set P(x) = 4000 and solve for x:
5x - 400x + 600 = 4000
Simplifying, we get:
-395x = -3400
Dividing both sides by -395, we get:
x ≈ 8.61
Therefore, approximately 8.61 kg of coffee must be sold to make a profit of $4000.
Step-by-step explanation:
savvas realize topic 5 assesment
Finally, express the solution as an interval of real numbers or as a set of values that make the inequality. x<10.4, x>3.3, x≥32 and x≤-15.
How to solve inequality?To solve an inequality, you need to find the set of values that make the inequality true. The process for solving an inequality depends on the type of inequality and the variables involved. Here are the general steps:
Determine the type of inequality: Is it a greater than (>), less than (<), greater than or equal to (≥), or less than or equal to (≤) inequality?Simplify both sides of the inequality as much as possible using algebraic operations such as addition, subtraction, multiplication, and division. Remember to apply the same operation to both sides of the inequality.If you multiplied or divided both sides of the inequality by a negative number, you need to reverse the direction of the inequality. For example, if you multiplied both sides of x < 3 by -1, you would get -x > -3.If there are variables on both sides of the inequality, move them all to one side of the inequality and simplify.If there are absolute values in the inequality, you may need to split the inequality into two separate cases, one for when the quantity inside the absolute value is positive, and one for when it is negative.Finally, express the solution as an interval of real numbers or as a set of values that make the inequality true. If the inequality is strict (> or <), use an open interval (e.g., (a, b)). If the inequality includes equality (≥ or ≤), use a closed interval (e.g., [a, b]).
by the question.
a. x-3.5>6.9
x>6.9+3.5
x>10.4
b. 6.4>x+3.1
x[tex]\geq 32[/tex]
c. x/4≤8
x≤32
d. 2/3x≤-10
x≤-15
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what is the answer of 10.9% of $8.85
Answer:
To find 10.9% of $8.85 we can convert the percentage into a decimal:
10.9% = 0.109
0.109x8.85 = $0.964
=$0.96 (Rounded to 2 decimal places)
Are quadrilaterals LMNO and PQRS similar?
Yes, quadrilaterals LMNO and PQRS are similar because a translation and a dilation map quadrilateral LMNO onto PQRS.
Yes, quadrilaterals LMNO and PQRS are similar because a rotation and a dilation map quadrilateral LMNO onto PQRS.
Yes, quadrilaterals LMNO and PQRS are similar because a reflection and a dilation map quadrilateral LMNO onto PQRS.
No, quadrilaterals LMNO and PQRS are not similar because their corresponding segments are not proportional.
The correct answer is (d) No, quadrilaterals LMNO and PQRS are not similar because their corresponding sides are not proportional.
What are quadrilaterals?A quadrilateral is a geometric shape with four sides and four corners.
To be classified as a quadrilateral, its shape must be a closed figure with four straight sides and four interior angles.
To determine quadrilaterals are similar, we need to check if corresponding angles are congruent and corresponding sides are proportional.
Checking corresponding angles are congruent:
∠ L to ∠P.
∠M to ∠Q.
∠ N to ∠ R.
∠O to ∠S.
All corresponding angles are congruent. Therefore, quadrilaterals have the same shape.
Check if corresponding sides are proportional.
LM =√((-1 - (-2))² + (4 - 2)²) = √(2² + 2²) = 2√2
MN = √((3 - (-1))² + (4 - 4)²) = √(4²) = 4
NO = √((4 - 3)² + (2 - 4)²) = √(2² + 2²) = 2√(2)
OL = √((-2 - 4)² + (2 - (-6))²) = √(6² + 8²) = 10
PQ = √((4 - 2)² + (-2 - (-6))²) = √(2² + 4²) = 2√5
QR = √((12 - 4)² + (-2 - (-2))²) = √(8²) = 8
RS = √((15 - 12)² + (-6 - (-2))²) = √(3² + 4²) = 5
SP = √((2 - 15)² + (-6 - (-6))²) = √(13²) = 13
LM / PQ = (2√2) / (2√5) = √(8/5)
MN / QR = 4 / 8 = 1/2
NO / RS = (2√(2)) / 5√(1) = (2/5)√(2)
OL / SP = 10 / 13
The corresponding sides are not proportional because they are not all equal or proportional to each other. Therefore, we can conclude that the quadrilaterals LMNO and PQRS are not similar.
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Your tank has a volume of 10 L at the surface (1 atm pressure). You reach a depth of 66 ft. What is the
pressure? What is the volume?
the pressure at a depth of 66 ft is 197,580 Pa, and the volume of the tank at this depth is 0.000505 L.
EquationsTo find the pressure at a depth of 66 ft in a liquid, we can use the formula:
pressure = density x gravity x depth
Assuming the liquid in the tank is water, the density is 1000 kg/m³, and gravity is 9.81 m/s².
First, we need to convert 66 ft to meters:
66 ft x 0.3048 m/ft = 20.1168 m
Then, we can find the pressure at this depth:
pressure = 1000 kg/m³ x 9.81 m/s² x 20.1168 m = 197,580 Pa
To find the volume of the tank at this depth, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at a constant temperature:
P₁V₁ = P₂V₂
where P₁ and V₁ are the initial pressure and volume (1 atm and 10 L, respectively), and P₂ and V₂ are the final pressure and volume.
We can rearrange this equation to solve for V₂:
V₂ = (P₁ x V₁) / P₂
Substituting the values, we get:
V₂ = (1 atm x 10 L) / (197,580 Pa / 1 atm) = 0.000505 L
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A line has a slope of 5/6
and passes through the point (7,6). Write its equation in slope-intercept form.
Answer:
y = 5/6x + 1/6
Step-by-step explanation:
m = 5/6, x = 7, y = 6
y = mx + b
6 = 5/6(7) + b
b = 6 - 35/6
b = 36/6 - 35/6 = 1/6
y = 5/6x + 1/6
Answer:
Below
Step-by-step explanation:
Here is another way:
Start with point ( 7,6) slope ( m= 5/6) form :
(y-6) = 5/6 ( x-7) expand
y-6 = 5/6 x - 35/6 add 6 to both sides
y = 5/6 x + 1/6 Done.
the length of a rectangle is 9 centimeters less than its width. what are the rectangles dimension if its area is 90.
Length of rectangle in cm:
Width of rectangle in cm:
Let the width of the rectangle be "X". Then the length of the rectangle will be (X-9).
Formula to find the area of a rectangle is given by-
[tex] \small \underline{ \boxed{ \sf{ \pmb{Area_{(rectangle)} = Length\times Width }}}}\\[/tex]
On substituting the values-
[tex] \:\:\:\:\:\:\longrightarrow \sf {Area_{(rectangle)} = X \times \bigg(X-9\bigg)}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf {90 = X^2 -9X}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf {X^2-9X =90}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf {X^2-9X -90=0}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf {X^2-15X+6X -90=0}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf {X\bigg(X-15\bigg) +6\times \bigg(X-15\bigg)=0}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf {\bigg(X-15\bigg) \times \bigg(X+6\bigg) =0}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \boxed{ \tt{ \pmb{ \red{X = 15\: Or,\: -6}}}}\\[/tex]
Since,width cannot be (Negative) , so the width will be 15cm.And the length will be (X-9)= (15-9)=6cm.
In one town 44% of voters are democrats if two voters are randomly selected for a survey find the probability that they are both Democrats assume events are independent round to the nearest thousand if necessary
the probability that they are both Democrats. round to the nearest thousandth if necessary is 0.194
The probability that BOTH is democrats means the probability of "one being democrat" AND "another also being democrat".
The AND means we need to MULTIPLY the individual probability of a person being a democrat.
The probability that a voter is democrat is 44% (0.44) -- stated in the problem
Now, the Probability of BOTH being Democrats is simply MULTIPLYING 0.44 with 0.44
Rounded to the nearest thousandth, 0.194
The last answer choice is correct.
the complete question is-
In one town 44% of all voters are Democrats if two voters are randomly selected for a survey find the probability that they are both Democrats. round to the nearest thousandth if necessary.
0.189
0.880
0.440
0.194
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please help immediately
please go to my profile and answer the other I need them asap.
10³•10⁵•10³
Step-by-step explanation:
10³means 10×3,10⁵means 10×5and 10³means 10×3 30+50+30=110
video
Let the region R be the area enclosed by the function f(x) = ln (x) + 1 and
g(x)=x-1. If the region R is the base of a solid such that each cross section
perpendicular to the a-axis is a semi-circle with diameters extending through the
region R, find the volume of the solid. You may use a calculator and round to the
nearest thousandth.
The volume of the solid is approximately 0.558 cubic units.
To find the volume of the solid, we need to integrate the area of the semi-circles along the a-axis.
We know that the diameter of each semi-circle is the distance between the functions f(x) and g(x), which is:
d(a) = f(a) - g(a) = ln(a) + 1 - (a-1) = ln(a) - a + 2
The radius of each semi-circle is half of the diameter, which is:
r(a) = (ln(a) - a + 2) / 2
The area of each semi-circle is π times the square of its radius, which is:
[tex]A(a) = πr(a)^2 = π/4 (ln(a) - a + 2)^2[/tex]
To find the volume of the solid, we integrate the area of each semi-circle along the a-axis, from a = e to a = 2:
V = ∫[e,2] A(a) da
V = ∫[e,2] π/4 [tex](ln(a) - a + 2)^2 da[/tex]
V ≈ 0.558 (rounded to the nearest thousandth)
Therefore, the volume of the solid is approximately 0.558 cubic units.
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If i have a 97% grade and i get a 75% on a quiz that counts 7% of my grade, how much is my grade? (37 points)
Answer: 90.32%
Step-by-step explanation:
To calculate your updated grade after receiving a 75% on a quiz that counts 7% of your overall grade, you can use the following formula:
New grade = (Old grade * (100 - weight of quiz)) + (Quiz grade * weight of quiz)
Plugging in your values, we get:
New grade = (97 * (100 - 7)) + (75 * 7)
New grade = (97 * 93) + (5.25)
New grade = 903.16
Therefore, your new grade is 90.32%.
Answer: The sum of the weight of all your coursework plus your final is equal to 14.00
Step-by-step explanation:
not sure
rx+sy=24
4x+16y=120
In the system of equations above, r and s are
constants. If the system has an infinite number of
solutions, what is the value of rs
?
The values of r and s, considering that the system has an infinite number of solutions, are given as follows:
r = 4/5.s = 16/5.How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the rate of change.b is the y-intercept of the function, which is the initial value.The number of solutions of a system of two linear functions is given as follows:
Infinity solutions: same slope and intercept.Zero solutions: same slope, difference intercepts.One solution: different slopes.For this problem, the system has an infinite number of solutions, meaning that the equations are multiples, thus the values of r and s are given as follows:
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ALGEBRA 1 HW!! I WILL GIVE BRAINLYEST
A) The completed table is given as follows:
L D(L)
0 0
3 1
4 1
6.5 2
10 2
11.9 2
15 3
B) the graph is attached accordingly.
C) In the context of the given problem, to store 43 liters of coffee, she needs at least 8 dispensers, as given by the function D(L).
What is the explanation for the above response?a) To complete the table, we need to use the given function D(L) to determine the number of beverage dispensers needed to hold different amounts of coffee.
We know that each beverage dispenser can hold 6 liters of coffee, so we can start by dividing the amount of coffee needed by 6 and rounding up to the nearest integer to get the number of dispensers needed.
D(L) = ceil(L/6)
Using this formula, we can complete the table as follows:
L D(L)
0 0
3 1
4 1
6.5 2
10 2
11.9 2
15 3
Note that for L=0, we don't need any dispensers, so the value of D(L) is 0. For all other values of L, we divide by 6 and round up to get the corresponding value of D(L).
b) The graph is attached.
c) In the context of the given problem, the function D(L) gives the minimum number of beverage dispensers needed to hold L liters of coffee, assuming each dispenser can hold 6 liters.
So, D(43) = 8 means that if Giada needs to brew and store 43 liters of coffee, she will need at least 8 beverage dispensers. Each dispenser can hold 6 liters, so the first 7 dispensers will be completely filled, and the last dispenser will be partially filled with the remaining coffee.
In other words, if Giada fills 7 dispensers completely, she will have used 42 liters of coffee, and the remaining 1 liter of coffee will be stored in the 8th dispenser. Therefore, to store 43 liters of coffee, she needs at least 8 dispensers, as given by the function D(L).
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PLEASE HELP! Find missing side lengths of B and C. Explain
Answer:
b=7 & c=7√2
Step-by-step explanation:
b=7 as it is an isosceles triangle
now using Pythagoras theorem,
(c)^2= (7)^2+(7)^2
⇒(c)^2= 49+49
⇒(c)^2= 98
⇒c= √98
⇒c=7√2
Answer:
b = 7c = 7√2Step-by-step explanation:
You want the missing side lengths in an isosceles right triangle with one side given as 7.
Isosceles right triangleThe two congruent acute angles tell you this right triangle is isosceles. That means sides 7 and b are the same length:
b = 7
The hypotenuse of an isosceles right triangle is √2 times the side length:
c = 7√2
__
Additional comment
You can figure the hypotenuse using the Pythagorean theorem if you haven't memorized the side relations of this "special" right triangle.
c² = 7² + b²
c² = 7² +7² = 2·7²
c = √(2·7²) = 7√2
The side length ratios for an isosceles right triangle (angles 45°-45°-90°) are 1 : 1 : √2.
The other "special" right triangle is the 30°-60°-90° triangle, which has side length ratios 1 : √3 : 2.
Jen is studying how years of drought conditions have caused the water level of Richland Reservoir to drop. At the start of the study, the water in the reservoir was 65 meters deep. Jen observed that the depth of the water dropped by about 0.8 meters the first month of the study. She wants to know what the depth of the water will be if it continues dropping at the same rate. You can use a function to approximate the depth of the water in the reservoir x months after the start of the study. Write an equation for the function.
The equation for the function is D(x) = 65 - 0.8x. Where 65 is the initial depth of the water and 0.8x is the amount by which the depth drops after x months.
What is a linear function?
A linear function is a mathematical function that has a constant rate of change or slope between the independent variable (x) and the dependent variable (y). It is a function that can be graphically represented as a straight line.
We can use a linear function to approximate the depth of the water in the reservoir x months after the start of the study, since the depth is dropping at a constant rate of 0.8 meters per month. Let D(x) be the depth of the water in meters x months after the start of the study. Then we have:
D(x) = 65 - 0.8x
where 65 is the initial depth of the water and 0.8x is the amount by which the depth drops after x months.
Therefore, the equation for the function is D(x) = 65 - 0.8x.
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is 180. The sum of the measures of the second and third angles is five times the measure of the first angle. The third angle is 26 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.
Answer:
x is first angle
y is second angle
and z is third angle
Step-by-step explanation:
This question is solved by a system of equations. We have that:x is the first angle.y is the second angle.z is the third angle.Doing this, we get that:The first angle measures 30º.The second angle measures 67º.The third angle measures 83º.The sum of the measures of the angles of a triangle is 180. This means that The sum of the measures of the second and third angles is five times the measure of the first angle.This means that:From this, the first angle can be found:The measure of the first angle is of 30º.The third angle is 16 more than the second.This means that:Since We get that the second angle is:The second angle measures 67º.For the third angle:The third angle measures 83º.
Compute the probability that a randomly selected person does not have a birthday on the 1st day of the month.
Answer:
0.9973 or 364/365
Step-by-step explanation:
Assuming that every day of the year is equally likely to be someone's birthday, the probability that a randomly selected person has a birthday on the 1st day of the month is 1/365, since there are 365 possible birthdays in a year.
Therefore, the probability that a randomly selected person does not have a birthday on the 1st day of the month is:
P(not on 1st day) = 1 - P(on 1st day)
P(not on 1st day) = 1 - 1/365
P(not on 1st day) = 364/365
So, the probability that a randomly selected person does not have a birthday on the 1st day of the month is 364/365 or approximately 0.9973.
If the graph of a polynomial function P(x) has -intercepts at x = - 4, x = 0, x * 1 point
= 5, which of the following must be true for P(x)?
• (x + 5) is a factor of the polynomial.
• (x-4) is a factor of the polynomial.
•' The degree of the polynomial is 3.
• The degree of the polynomial is greater than or equal to 3.
(x + 5) is nοt necessarily a factοr οf the pοlynοmial, (x-4) is a factοr οf the pοlynοmial are cοrrect statement.
What is a functiοn ?Functiοn can be define in which it relates an input tο οutput.
If the graph οf a pοlynοmial functiοn P(x) has x-intercepts at x = -4, x = 0, and x = 5, then we knοw that the factοrs οf P(x) are (x + 4), x, and (x - 5). This is because a pοlynοmial has x-intercepts where the value οf P(x) is equal tο zerο, and this οccurs when each factοr is equal tο zerο.
Therefοre, we can cοnclude that (x + 4) and (x - 5) are factοrs οf the pοlynοmial P(x), but x is nοt necessarily a factοr. This is because x is a linear factοr with a zerο intercept, but it cοuld be cancelled οut by anοther factοr in the pοlynοmial.
Thus, the cοrrect statement is:
(x + 5) is nοt necessarily a factοr οf the pοlynοmial.
(x-4) is a factοr οf the pοlynοmial.
The degree οf the pοlynοmial is 3 οr greater since the pοlynοmial has three x-intercepts. Hοwever, we cannοt determine the exact degree οf the pοlynοmial withοut additiοnal infοrmatiοn.
Therefοre, (x + 5) is nοt necessarily a factοr οf the pοlynοmial, (x-4) is a factοr οf the pοlynοmial are cοrrect statement.
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1/4 x5/3 as a fraction
The product of the fraction 1/4 x5/3 is 4/12
What are fractions?Fractions are defined as the part of a whole number, variable or element.
The different types of fractions in mathematics are;
Simple fractions.Proper fractions.Improper fractions.Complex fractions.Mixed fractions.Examples of simple fraction; 1/4, 2/3
Examples of improper fractions; 3/2. 4/3
Examples of proper fractions; 1/2, 2/3
From the information given, we have that;
1/4 x5/3
To determine the product, we need to multiply the numerator, then multiply the denominator
5/12
We can no longer divide the values as there is no common divisor.
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What is the value of x in (x+3)^2=49 show your work
Answer:
x = 4,-10Step-by-step explanation:
(x+3)^2=49
x+3=√(49)
x+3=√(7^2)
x+3=7
x+3-3=7-3
x=4x+3=-√(49)
x+3=-7
x+3-3=-7-3
x=-10x = 4,-10
In western music, an octave is divided into 12 pitches. For the film Close Encounters of the Third Kind, director Steven Spielberg asked composer John Williams to write a five-note theme, which aliens would use to communicate with people on Earth. Disregarding rhythm and octave changes, how many five-note themes are possible if no note is repeated?
Answer:
This should be a permutation
Step-by-step explanation:
P (n, r) = n!/(n-r)!
P (12,5) = 12!/(12-5)!
P (12,5) = 12!/7!
P(12,5) = 95040
Just curious to know
Therefore, if Jane had left a message on every call, you would have gotten 670 voicemails. The solution is 670.
what is percentage ?Since "percent" is a slang term for "per hundred," when we discuss percentages, we are speaking to a fraction of a hundred. In a variety of contexts, including math, science, finance, and daily living, percentages are used. The percent sign (%) is commonly used to denote percentages. As an illustration, to determine what proportion of 50 apples are red, you would split the number of red apples by the total number of apples and multiply the result by 100.
given
If Jane had phoned 1,000 times and you had allowed 67% of those calls to go to voicemail, then 67% of those calls would have left voicemails for you.
You can multiply the overall number of calls by the proportion of calls that went to voicemail to determine how many voicemails you would have received:
1000 x 67% = 670
Therefore, if Jane had left a message on every call, you would have gotten 670 voicemails. The solution is 670.
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The complete question is :-
Jane called one thousand times to tell you she's sorry. If you saw she was calling and let your phone go to voicemail 67% of the time, how many voicemails would you have received if she left one each time?
Possible Answers:
3,700
57,000
67
None of the given answers
670
In a recent survey, 60% of the community favored building a supermarket in their neighborhood. If 25 citizens are chosen, what is the variance of the number favoring the supermarket?
The variance of the number of citizens favoring the supermarket is 6.
To find the variance of the number of citizens favoring the supermarket, we need to use the binomial distribution formula:
Variance = n × p × (1 - p)
where n is the number of trials (25 in this case), p is the probability of success (0.6 in this case), and (1 - p) is the probability of failure.
Plugging in the values, we get:
Variance = 25 × 0.6 × (1 - 0.6)
Variance = 25 × 0.6 × 0.4
Variance = 6
The binomial distribution is a probability distribution that models the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes, success or failure. In this case, the trials are the 25 citizens who were chosen, and the success is the event of favoring the supermarket, which has a probability of 0.6.
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Write a quadratic function for the area of the figure. Then, find the area for the given value of x. x = 20 A quadratic function for the area of the figure is A(x) = (Simplify your answer.) ... X
answer: x= 20x
Step-by-step explanation: 2+2 is 4, 4+4 is 8, quick maths
Find the area of the shaded sector of the circle
Answer:
32.67 square meters
Step-by-step explanation:
finding the area of the shaded region.
area of sector = (θ/360°) x πr²
where "θ" is the central angle of the sector in degrees, "r" is the radius of the sector, and π is a mathematical constant approximately equal to 3.14.
Substituting the given values into the formula, we get:
area of sector = (60°/360°) x π(14m)²
area of sector = (1/6) x 3.14 x 196m²
area of sector = 32.67m² (rounded to two decimal places)
Therefore, the area of the section is 32.67 square meters
(1 − cos 0) (1 + cos 0)= 1/csc²0
Step-by-step explanation:
lol sorry for untidy work
How many feet of fencing will be needed to enclose this dog pen? 4.8ft by 4yd
Answer:
19.2 ft
Step-by-step explanation:
A line has the equation y - 6 = 5x + 9 . work out the gradient and the y intercept of the line.
The gradient of the line is 5, and the y-intercept of the line is 15.
EquationsThe given equation is in the form of y = mx + c, where m is the gradient (slope) of the line and c is the y-intercept of a straight line represented in 2D plane.
Rearranging the given equation, we get:
y - 6 = 5x + 9
Adding 6 to both sides, we get:
y = 5x + 15
Now we can see that the equation is in the required form of y = mx + c. The gradient (slope) of the line is 5, which is the coefficient of x in the equation. The y-intercept is 15, which is the constant term in the equation.
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In PQR, PQ= 5.4, QR= 3.6, and PR=6.2. To the nearest Tenth, what is M∠R
Therefore , the solution of the given problem of angles comes out to be M∠R measured at 45.4 degrees, to the closest tenth.
An angle meaning is what?The intersection of the lines that form a skew's ends determines the size of its biggest and smallest walls. There's a possibility that two paths will intersect at a junction. Angle is another outcome of two things interacting. They mirror dihedral forms the most. A two-dimensional curve can be created by placing two line beams in various configurations between their ends.
Here,
To determine the size of angle R in triangular PQR, we can apply the Law of Cosines:
=> cos(R) = (PQ₂ + PR₂ - QR₂) / (2 * PQ * PR)
=> cos(R) = (5.4₂ + 6.2₂ - 3.6₂) / (2 * 5.4 * 6.2)
=> cos(R) = 0.6960917
When we calculate the inverse cosine of both sides, we obtain:
=> R = cos⁻¹(0.6960917)
=> R equals 45.4 degrees
Angle R in triangle PQR is therefore measured at 45.4 degrees, to the closest tenth.
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An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 29 feet up. The ladder makes an angle of 71 degrees with the ground. Find the length of the ladder. Round your answer to the nearest tenth of a foot if necessary.
Answer:
30.7
Step-by-step explanation:
sin(71) = 29/x
x = 29/sin71
≈ 30.7
Jacque bought 2.5 pounds of dark chocolate covered pecans at $0.30 per ounce. In dollars and cents, what was the cost of these pecans?
Answer:
$12.00
Step-by-step explanation:
We know that 1 pound = 16 oz. Thus, we can create a proportion to find how many ounces (x) is 2.5 pounds:
[tex]\frac{1}{16}=\frac{2.5}{x}\\ x=(2.5*16)\\ x=40[/tex]
Since 2.5 pounds = 40 oz, we can now multiply 40 by 0.30 to find the price of 40 ounces of peacans priced at $0.30/ounce:
40 * 0.30 = $12.00