A lumber company sells two types of wood: mahogany and black walnut. The company has 260 boards of mahogany and 320 boards of black walnut. The lumber company expects to sell at most 380 boards of wood. The profit for selling the wood is $20 per board for mahogany and $6 per board for black walnut.Write and graph a system of inequalities to represent the constraints of this problem situation.
Answers
The system of equation are
x ≤ 260 y ≤ 320 x + y ≤ 380The profit function is = 20x + 6y
How to write the system of equationsLet's define the following variables:
x: the number of boards of mahogany sold
y: the number of boards of black walnut sold
Based on the problem statement, we can write the following system of inequalities to represent the constraints:.
x ≤ 260 (there are only 260 boards of mahogany available)
y ≤ 320 (there are only 320 boards of black walnut available)
x + y ≤ 380 (the total number of boards sold can't exceed 380)
The profit function is:
P(x, y) = 20x + 6y
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Related Questions
What was the total number of hours worked by the 15 employees? Write the expression of total number he total number of hours worked by the 15 employees and solve it.
Answers
The expression of total number of hours worked by the 15 employees is 505 .
What is an expression?An expression is a mathematical statement that combines numbers, variables, and/or operators to represent a quantity or relationship. It can be evaluated or simplified, but does not have an equals sign and is not a complete equation.
To find the total number of hours worked by the 15 employees, we need to add up the hours worked by each individual employee.
Let's say that employee 1 worked x1 hours, employee 2 worked x2 hours, and so on, up to employee 15 who worked x15 hours. Then, the total number of hours worked by the 15 employees can be expressed as:
Total number of hours = x1 + x2 + ... + x15
To solve this expression, we need to know the specific number of hours worked by each employee. If we are given this information, we can simply substitute the values into the expression and add them up to find the total number of hours.
we can calculate the total number of hours worked as:
Total number of hours = 40 + 30 + 35 + ... + 20
= 505
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If a certain apple tree grew 2 feet and then tripled its height, it would become 4 feet
shorter than the pine tree that grows on the other end of the street. Which
of the formulas below describes the relation between the height of the apple tree a
and the height of the pine tree p?
A) P-4=3a+2
B) P=2(a+3)+4
C) P=3(a+2)-4
D) P=3a+10
Answers
Answer:
Step-by-step explanation:
C.) P = 3(a+2)-4
The formula which describes the relation between the height of the apple tree and the height of the pine tree p is P=3(a+2)-4, the correct option is C.
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.
We are given that;
Growth of apple tree= 2feet
Now,
Let's call the original height of the apple tree "h". According to the problem, if the apple tree grew 2 feet and then tripled its height, it would become 4 feet shorter than the pine tree. So we can write:
3(h+2) - 4 = p
Simplifying, we get:
3h + 2 = p
Now we can see that option (D) P=3a+10 is very similar to our expression, but it has a constant term of 10 instead of 2. This constant term does not match the problem statement, which says that the apple tree would be 4 feet shorter than the pine tree, not taller. Therefore, option (D) is not the correct answer.
Option (A) P-4=3a+2 also does not match the problem statement. If we solve for p, we get:
P = 3a + 6
This means that the apple tree would be 6 feet shorter than the pine tree, not 4 feet shorter as stated in the problem.
Option (B) P=2(a+3)+4 also does not match the problem statement. If we solve for p, we get:
P = 2a + 10
This means that the apple tree would be 10 feet shorter than the pine tree, not 4 feet shorter as stated in the problem.
Option (C) P=3(a+2)-4 matches our expression from earlier. If we solve for p, we get:
P = 3a + 2
Therefore, by equation the answer will be P=3(a+2)-4.
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Mark wants to buy a new pair of sneakers that cost 215. His aunt gave him 100 for the sneakers. Market also lnow sthat he can esrn 16 for each hour that he works at his aunts store how many full hours must mark work to buy the sneakers
Answers
Mark needs a total amount of 215 to buy sneakers and we know that his aunt gave him 100 for the same, he also know that he can earn 16 for each hour that he works at his aunt's store, therefore he needs to work 8 hours.
Mark needs a total amount of 215 to buy sneakers and we know that his aunt gave him 100 for the same,
therefore, we can say that 215 - 100 = 115
therefore, Mark now needs only 115 for him to buy sneakers and now we need to find how many full hours do Mark need to work to buy sneakers:
therefore, we need to divide 115 by 16 to find out the hours he needs to work at his aunt's store:
115/16 = 7.2
we get 7.2 which also means 7 hours 20 mins but we need to find full hours Mark needs to work, that will be:
8 hours.
Therefore, we know that Mark needs to work 8 full hours for him to buy sneakers.
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Marty graphs the hyperbola (y+2)236−(x+5)264=1 . How does he proceed? Drag a value, phrase, equation, or coordinates in the boxes to correctly complete the statements. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Answers
To construct the graph of the hyperbola, the procedure is as follows:
Marty first identifies the center of the hyperbola as (-5,2), and that the hyperbola opens up and down. Since a = 6, the coordinates of the vertices are (-5, -4) and (-5, 8).The slopes of the asymptotes of this parabola are a = ± 3/4, and the asymptotes pass through the center of the hyperbola. The equations of the asymptotes are y - 2 = ± 3/4(x + 5).Equation of an hyperbolaThe equation of a vertical hyperbola with center (x*, y*) is given according to the following equation:
(y - y*)²/a² - (x - x*)²/b² = 1.
A vertical hyperbola opens up and down.
In this problem, the equation is:
(y + 2)²/36 - (x + 5)²/64 = 1.
Hence the center is:
(-5, 2).
The value of coefficient a is:
a² = 36 -> a = 6.
Then the vertices of the hyperbola are:
(-5, 2 - 6) = (-5,-4).(-5, 2 + 6) = (-5,8).The slopes of the asymptotes of the parabola are given as follows:
±a/b.
Hence:
a/b = 6/8 = 3/4.-a/b = -6/8 = -3/4.Since the asymptotes pass through the center, the equation is:
y - 2 = ± 3/4(x + 5).
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Sunflower canola oil is a cooking oil sold in south african supermarkets a 750ml bottle cost R28 and a 2litre bottle cost R63 evaluate which option will be the most cost effective option
Answers
A 2-liter container costs R0.032 per milliliter, which is less than a 750-milliliter bottle, which costs R0.037 per milliliter.
A milliliter is it an ML?a volumetric measurement using the metric system. One litre is equivalent to 1,000 milliliters. Additionally known as cc, mL, and cubic centimetre.
To evaluate which option is the most cost-effective, we need to calculate the cost per milliliter of each bottle of cooking oil.
For the 750ml bottle, the cost per milliliter is:
R28 / 750ml = R0.037 per ml
For the 2-liter bottle, the cost per milliliter is:
R63 / 2000ml = R0.032 per ml
Therefore, the 2-liter bottle is the more cost-effective option, as it has a lower cost per milliliter than the 750ml bottle. The cost per milliliter of the 2-liter bottle is R0.032, which is cheaper than the cost per milliliter of the 750ml bottle, which is R0.037.
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An appliance dealer sells three different models of upright freezers having 13.4, 15.8, and 19.3 cubic feet of storage space. Consider the random variable x - the amount of storage space purchased by the next customer to buy a freezer. Suppose that x has the following probability distribution. x P(x) 13.4 0.2 15.8 0.5 19.3 0.3 (a) Calculate the mean and standard deviation of x (in cubic feet). (Hint: See Example 6.15. Round your standard deviation to four decimal places.) μx = _____ cubic ft
θx = _____ cubic ft
Answers
(a) μx 15.55 cubic feet. The standard deviation is the square root of the variance, i.e., θx = 1.881 cubic feet
The mean, or expected value, of x can be calculated as μx = Σ(xi * P(xi)) where xi are the possible values of x and P(xi) are their corresponding probabilities. Thus, μx = (13.40.2) + (15.80.5) + (19.3*0.3) = 15.55 cubic feet.
To calculate the standard deviation, we first need to calculate the variance, which can be obtained as θ²x = Σ((xi-μx)² * P(xi)). Thus, θ²x = ((13.4-15.55)²0.2) + ((15.8-15.55)²0.5) + ((19.3-15.55)²*0.3) = 3.54.
Therefore, the standard deviation is the square root of the variance, i.e., θx = √3.54 = 1.881 cubic feet (rounded to four decimal places).
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The speed s (in miles per hour) of a car can be given by s = √(30fg), where fis the
coefficient of friction and d is the stopping distance (in feet). The table shows the
coefficient of friction for different surfaces. You are driving 35 miles per hour on an
icy road when a deer jumps in front of your car. How far away must you begin to
brake to avoid hitting the deer? Round your answer to the nearest whole integer. NO
UNITS NEEDED
Answers
Answer:
Step-by-step explanation:
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Answer:
s= 6
Step-by-step explanation:
The speed s (in miles per hour) of a car can be given by s = √(30fg), where fis the
coefficient of friction and d is the stopping distance (in feet). The table shows the
coefficient of friction for different surfaces. You are driving 35 miles per hour on an
icy road when a deer jumps in front of your car. How far away must you begin to
brake to avoid hitting the deer? Round your answer to the nearest whole integer. NO
UNITS NEEDED
A simplified carbon cycle with aerobic and anaerobic processes is depicted here. Although much of the emphasis on global climate change has been on increasing carbon dioxide levels, methane is also a greenhouse gas whose levels are increasing due to human and other activity. Which of these actions would increase methane levels in the atmosphere and potentially affect global climate change? Select ALL that apply.
--------------------------------------------------------------------------------------------------------------------------------
A Agricultural practices in rice cultivation releases methane.Agricultural practices in rice cultivation releases methane.
B Anaerobic digestion of cellulose by cows produces methane.Anaerobic digestion of cellulose by cows produces methane.
C Photosynthesis by phytoplankton converts carbon dioxide into the atmosphere.Photosynthesis by phytoplankton converts carbon dioxide into the atmosphere.
D Industrial combustion of fossil fuels releases methane into the atmosphere.Industrial combustion of fossil fuels releases methane into the atmosphere.
E Anaerobic decomposition of landfill material releases methane into the atmosphere.
Answers
In attempts to reduce greenhouse gas emissions and the effects of climate change, these sources must be taken into account.
what is equation ?A mathematical equation is a claim that two expressions are equal, typically represented with an equal sign (=) between them. The terms "left hand side" (LHS) and "right hand side" (RHS) of the equation, respectively, refer to the expressions on either side of the equal sign. Equations are a common tool for problem solving because they may be used to depict relationships between variables or quantities and to determine the value(s) of the unknown variable(s) that satisfies the equation. For instance, the link between the variables x and the integers 2, 5, and 11 is represented by the equation 2x + 5 = 11. Finding the value of x that makes the left and right sides of the equation equal is necessary to solve this equation.
given
A) Rice farming operations release methane into the atmosphere.
B) Methane is created when cows break down cellulose anaerobically.
E) Methane is released into the atmosphere when landfill material decomposes anaerobically.
Any of the aforementioned behaviours would raise the atmospheric methane concentrations and may have an impact on climate change globally.
Methane is a greenhouse gas that causes the atmosphere of the Earth to warm.
It is produced by both natural and artificial processes. Examples of human activities that contribute to methane emissions into the atmosphere include the production of rice, cattle digestion, and landfill decomposition.
In attempts to reduce greenhouse gas emissions and the effects of climate change, these sources must be taken into account.
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25. Students in a class took an algebra test if 15 students passed the test what percent pass the test
Answers
Answer:
15/x * 100 %
Step-by-step explanation:
Since we don't know the total, we have 15/x * 100 % as the percent of how many people passed the test. (x is amount of people, 15 or greater.)
In a recent election 65% of eligible voters actually voted. A simple random sample of 1000 people is taken from the population of eligible voters. Which of the following represents the probability that less than 70% of the people sampled voted?
Answers
The probability that less than 70% of the people sampled voted is 0.9992.
Step 1: Calculate the mean of the sample. µ = p = 0.65 (since the percentage of eligible voters who actually voted in the recent election is 65%).
Step 2: Calculate the standard deviation of the sample.σ = sqrt{[p(1 - p)]/n} = sqrt{[(0.65)(0.35)]/1000} = 0.01578
Step 3: Calculate the z-score for the given probability. z = (0.7 - 0.65)/0.01578 = 3.16Step 4: Use the standard normal distribution table to find the area to the left of the z-score (since we want to find the probability that less than 70% of the people sampled voted).P(z < 3.16) ≈ 0.9992Therefore, the probability that less than 70% of the people sampled voted is approximately 0.9992 (or 99.92%).
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Of first-time college students who matriculate to a certain university, the odds in favor of having graduated in the top 25 percent of their high school class are 2.06 to 1. Of transfer students who matriculate to the same university, 0.666666666666667 proportion graduated in the top 25 percent of their high school class.
(a) For first-time college students, what is the proportion who graduated in the top 25 percent of their high school class (rounded to three decimal places)?
(b) For transfer students, what is the ratio in favor of having graduated in the top 25 percent of their high school class?
Odds and Probability:
Odds in favor of an event is expressed as a ratio:
O
(
f
)
=
favorable cases
:
unfavourable cases
Similarly odds against are expressed as:
O
(
a
)
=
unfavorable cases
:
favourable cases
.
Odds and probability are closely related, as the probability in favor of an even is computed as:
P
=
favorable cases
favorable cases+unfavorable cases
Answers
The answers to the questions (a) the proportion who graduated in the top 25 percent of their high school class will be 0.672 and (b) the ratio in favor of having graduated in the top 25 percent of their high school class is 2:3.
(a) For first-time college students, the proportion who graduated in the top 25 percent of their high school class (rounded to three decimal places) is 0.672.
(b) For transfer students, the ratio in favor of having graduated in the top 25 percent of their high school class is 0.67:1. It is said that 0.666666666666667 proportion graduated in the top 25 percent of their high school class. This can be simplified as follows:0.666666666666667=20/30=10/15=2/3. Therefore, the ratio in favor of having graduated in the top 25 percent of their high school class is 2:3.
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which degenerate conic is formed when a double cone is sliced at the apex by a plane perpendicular to the base of the cone?
Answers
When a double cone is sliced at the apex by a plane perpendicular to the base of the cone, the resulting conic section is a parabola.
Option B is the correct answer.
We have,
A parabola is a type of conic sect ion that can be defined as the locus of points equidistant from a fixed point (the focus) and a fixed line (the directrix).
In the case of slicing a double cone at the apex, the resulting conic section will have the characteristic shape of a parabola.
The slicing plane intersects both sides of the double cone, creating a curved shape that opens upward or downward, depending on the orientation of the cone.
The vertex of the parabola corresponds to the point of intersection of the slicing plane with the double cone.
Therefore,
When a double cone is sliced at the apex by a plane perpendicular to the base, a parabola is formed.
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The complete question:
Which degenerate conic is formed when a double cone is sliced at the apex by a plane perpendicular to the base of the cone?
A. Circle
B. Parabola
C. Ellipse
D. Hyperbola
50 POINTS!!!!! NEED HELP ASAP!!!!! RUNNING OUT OF TIME!!!!!
Answers
Answer:17.6 cm
Step-by-step explanation:
if you can see the graph it can be seen as 17.6 cm.
if you zoom in on the graph and look at the squares that are shaded in you roughly get 17.6
ANSWER ASAP
Find the length of the hypotenuse in a right triangle with the following two side lengths.
a = 12, b = 16, c = ?
A. c = 17
B. c = 18
C. c = 19
D. c = 20
Answers
Answer: 20
Step-by-step explanation:
Using the Pythagorean theorem, we know that:
c² = a² + b²
Substituting the given values, we get:
c² = 12² + 16²
c² = 144 + 256
c² = 400
Taking the square root of both sides, we get:
c = √400
c = 20
Therefore, the length of the hypotenuse in the right triangle is 20.
explanation:
hypotenuse aka c^2 = a^2 + b^2
c^2 = (12x12)+(16x16) = (144) + (256)
c^2 = 400
*square root both sides to remove the square in c*
c = 20
the number of minutes needed to complete a job, m, varies inversely with the number of workers, w. three workers can complete a job in 30 minutes. how many minutes would it take 6 workers to complete the job?
Answers
The number of minutes needed to complete a job, m, varies inversely with the number of workers, w.
Three workers can complete a job in 30 minutes.
To find, out how many minutes would it take 6 workers to complete the job.
The formula used for inverse variation is, m1w1 = m2w2
Where, m1 = 30,
w1 = 3,
m2 = ?
and w2 = 6
Substitute the given values in the above formula, 30 × 3 = m2 × 6
Simplify the above expression,90 = 6m2
Divide both sides by 6,90 / 6 = m2m2 = 15
Hence, it will take 15 minutes for 6 workers to complete the job.
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A barista mixes 12lb of his secret-formula coffee beans with 15lb of another bean that sells for $18 per lb. The resulting mix costs $20 per lb. How much does the barista's secret-forumula means cost per pound?
Answers
Answer:
The baristas secret formula beans cost per pound is $19.2.
Step-by-step explanation:
Given is that a barista mixes 12 lb of his secret-formula coffee beans with 15 lb of another bean that sells for $18 per lb.The cost of 1 pound of another bean as -$(15/18) = $(5/6)Assume that 1 pound of secret coffee costs ${x}. So, we can write -x + 5/6 = 20x = 20 - 5/6x = 19.2Therefore, the baristas secret formula beans cost per pound is $19.2.
Answer:
Find 5 rational numbers between 4/5 - and * 3/7
Operación de vectores
Answers
Answer:
operaciones vectoriales, Extensión de las leyes del álgebra elemental a los vectores. Incluyen suma, resta y tres tipos de multiplicación. La suma de dos vectores es un tercer vector, representado como la diagonal del paralelogramo construido con los dos vectores originales como lados.
Answer:
operaciones vectoriales, Extensión de las leyes del álgebra elemental a los vectores. Incluyen suma, resta y tres tipos de multiplicación. La suma de dos vectores es un tercer vector, representado como la diagonal del paralelogramo construido con los dos vectores originales como lados.
Step-by-step explanation:
Find the outer perimeter.
10 ft
8 ft
P = [?] ft
Round to the nearest
hundredth.
Answers
The outer perimeter is 76.12 ft according to given question.
what is perimeter?
Perimeter is a term used in geometry to refer to the total distance around the outside of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape. For example, in a rectangle, the perimeter is calculated by adding the length of all four sides. In a circle, the perimeter is called the circumference and is calculated as the distance around the edge of the circle.
The perimeter of a semicircle is the sum of the length of its straight edge and half the circumference of the circle.
In this case, the radius of the semicircle is given as 8 units, so the circumference of the corresponding full circle is 2πr = 2π(8) = 16π units.
Half the circumference of the circle is therefore 8π units.
The straight edge of the semicircle is simply the diameter of the circle, which is twice the radius, or 2(8) = 16 units.
So, the perimeter of the semicircle is the sum of the straight edge and half the circumference:
Perimeter = 16 + 8π
Using approximate value for pi (π = 3.14), the perimeter can be expressed as:
Perimeter ≈ 16 + 8(3.14) ≈ 40.12 units.
The perimeter of a rectangle is given by the sum of the lengths of its four sides.
In this case, the length of the rectangle is given as 10 units and its width is given as 8 units.
Therefore, the perimeter of the rectangle is:
Perimeter = 2(Length + Width) = 2(10 + 8) = 2(18) = 36 units.
So, the perimeter of the rectangle with length 10 units and width 8 units is 36 units.
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Martina made $60 for 5 hours of work. At the same rate, how many hours would she have to work to make $204 ?
Answers
Answer:
WELL 17
Step-by-step explanation:
60 DIVED BY 5 IS 12
SO 12 DIVIDED BY 204 IS 17 SOOOOOO 17 IS THE ANS
a different pattern is made using 20 straight lines and 14 arcs
Answers
The total cost of metal in the pattern would be £24.6.
What is the total cost of the pattern?
Let's assume that the cost of one arc is 3x, then the cost of one straight line would be 2x.
The total number of lines and arcs is given as 20 + 14 = 34.
Since 20 straight lines cost £12, the cost of one straight line is £12/20 = £0.6.
Therefore, the cost of one arc is (3/2) * £0.6 = £0.9.
The total cost of the 20 straight lines would be 20 x £0.6 = £12.
The total cost of the 14 arcs would be 14 x £0.9 = £12.6.
So, the total cost of metal in the pattern would be £12 + £12.6 = £24.6.
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The complete question is below:
A different pattern is made using 20 straight lines
and 14 arcs.
The straight lines and arcs are made from metal.
20 straight lines cost £12
cost of one straight line : cost of one arc = 2 : 3
Work out the total cost of metal in the pattern.
A cylindrical garbage can has the dimensions shown.
A cylinder has a diameter labeled twelve inches and height labeled fifteen inches.
Question 1
Part A
What is the area of the horizontal cross section of the cylinder? Use 3.14
for π
.
Enter the correct answer in the box.
about
square inches
Question 2
Part B
What is the area of the vertical cross section of the cylinder through the centers of the bases?
Enter the correct answer in the box.
Answers
Check the picture below.
so the horizontal cross-section is simply the area of a circle with a radius of 6, and the vertical cross-section is simply a 12x15 rectangle.
[tex]\stackrel{ \textit{\LARGE horizontal cross-section} }{\pi (6)^2\implies 36\pi \implies 36(3.14)\implies \text{\LARGE 113.04}~in^2} \\\\\\ \stackrel{ \textit{\LARGE vertical cross-section} }{(12)(15)\implies \text{\LARGE 180}~in^2}[/tex]
A linear function maps input numbers to output numbers.
Complete the input-output table for this function.
Input
1
2
5
10
Output
4
10
28
n
Answers
Step-by-step explanation:
after a little bit of thinking and experimenting we find that the function multiplied x by 6 and subtracts 2.
y = 6x - 2
formally, we find this by using the normal linear form
y = ax + b
and we use the given data points to find a and b.
4 = a×1 + b = a + b
10 = a×2 + b = 2a + b
so, by adding a on one side and adding 6 on the other side, we keep the balance.
therefore, a = 6
the first equation gives us then
4 = 6 + b
b = -2
and that's it.
so,
for x = 10 we get as output (y)
6×10 - 2 = 58
for x = n we get as output (y)
6n - 2
Work out the fraction and ratio that
complete the equations below.
Give each answer in its simplest form.
a) h:k=5:6
h =
k
b) 2x=9y
x:y
=
:
Answers
The fraction and ratio that complete the equations in its simplest term is 5/6k and 2 : 9 respectively.
What is the fraction and ratio that complete the equations?h : k = 5 : 6
h/k = 5/6
cross product
h × 6 = k × 5
6h = 5k
divide both sides by 6
h = 5/6k
Then,
2x = 9y
2/9 = x/y
2 : 9 = x : y
Ultimately, the simplest form of fraction and ratio which completes the equation is 5/6k and 2:9.
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Which expression below gives the average rate of change of the function h(x) = 4x+2 +7 on the interval -3 ≤ x ≤ 5?
A. (43+2+7)-(45+2+7)
-3+5
B. (45*2 + 7)-(4+2+7)
5-3
C. (45+2+7)-(43+2+7)
5+3
D. (45+²+7)+(42+7)
5+3
Answers
Answer:
C. (45+2+7)-(43+2+7) / 5+3
Step-by-step explanation:
To find the average rate of change of h(x) on the interval -3 ≤ x ≤ 5, we need to evaluate the following expression:
[h(5) - h(-3)] / (5 - (-3))
We have:
h(5) = 4(5) + 2 + 7 = 29
h(-3) = 4(-3) + 2 + 7 = -5
Substituting into the formula, we get:
[29 - (-5)] / (5 - (-3)) = 34 / 8 = 17 / 4
Therefore, the expression that gives the average rate of change of the function h(x) on the interval -3 ≤ x ≤ 5 is:
C. (45+2+7)-(43+2+7) / 5+3
An Ixl question from sixth grade IXL:FF.15 Rectangles: relationship between perimeter and area
Answers
The dimensions of the gray rectangle are approximately 61.9 km by 218.1 km.
What is perimeter of a rectangle?The distance around a rectangle's outside edge is known as its perimeter. It is computed by summing the measurements of the rectangle's four sides. The perimeter P of a rectangle with sides of length l and width w is given by:
P = 2l + 2w.
By understanding that a rectangle contains two pairs of equal sides (length and breadth), and that the distance around the rectangle is equal to the total of these four sides, one may deduce this formula.
Let us suppose the dimensions of the gray triangle as x and y.
The perimeter of rectangle is given as:
P = 2(1 + b)
For the blue triangle we have:
P = 2(72 + 68)
For the gray triangle we have;
P = 2(x + y)
Equating the two since they are equal we have:
2(72 + 68) = 2(x + y)
280 = x + y
We also know the area of the gray triangle thus:
xy = 3876
Substituting y = 280 - x into the second equation, we get:
x(280 - x) = 3876
x² - 280x + 3876 = 0
x = (280 ± √(280² - 4(1)(3876))) / 2
x ≈ 62.7 or x ≈ 61.9
We may discard the negative answer since a rectangle's dimensions cannot be negative.
Substituting the value of x we have:
y = 280 - 61.9 = 218.1 km.
Hence, the dimensions of the gray rectangle are approximately 61.9 km by 218.1 km.
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Morgan sampled 101 students and calculated an average of 6.5 hours of sleep each night with a standard deviation of 2.14. Using a 90% confidence level, she also found that t* = 1.660.A 90% confidence interval calculates that the average number of hours of sleep for working college students is between __________ hours. Answer choices are rounded to the hundredths place.a.)6.15 and 6.85b.)6.46 and 6.54c.)6.46 and 6.85d.)6.08 and 6.92
Answers
The 90% confidence interval for the average number of hours of sleep for working college students is between 6.15 and 6.85 hours.
Therefore, the answer is option (a) 6.15 and 6.85 hours.
What is confidence interval?A confidence interval is a statistical range of values within which we can be reasonably confident that the true value of a population parameter lies. It is commonly used in inferential statistics to estimate an unknown population parameter, such as a mean or a proportion, based on a sample from that population.
To calculate the 90% confidence interval for the average number of hours of sleep for working college students, we'll use the formula:
Confidence Interval = Sample Mean ± (Critical Value x Standard Error)
Where:
Sample Mean: 6.5 hours (the average number of hours of sleep)
Critical Value: t-value corresponding to a 90% confidence level with 100 degrees of freedom (101 students - 1)
Standard Error: Standard Deviation / Square Root of Sample Size
Let's plug in the values and calculate the confidence interval:
Standard Error = 2.14 / √101 ≈ 0.2139
Confidence Interval = 6.5 ± (1.660 x 0.2139)
Confidence Interval = 6.5 ± 0.3546
Lower Bound = 6.5 - 0.3546 ≈ 6.1454
Upper Bound = 6.5 + 0.3546 ≈ 6.8546
Rounding to the hundredths place, the 90% confidence interval for the average number of hours of sleep for working college students is between 6.15 and 6.85 hours.
Therefore, the answer is option (a) 6.15 and 6.85 hours.
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What is the surface area?
5 yd
6 yd
5 yd
5 yd
4 yd
Answers
Find the area of the triangle.
Answers
Answer: 5 units^2
Step-by-step explanation:
You can deduce that the height of the triangle is 5. You use the pythagoreon theorem to find the missing distance. 5^2+x^2=7^2
X=sqrt24.
Using that info you find the area of the missing triangle. Getting 2.5sqrt24. Find the area of the combined triangles, (5*(2+sqrt25))/2.
you should get 5+2.5sqrt24. Then subtract the missing triangle to get 5.
5. Solve the following problems. Note: In those problems the geometric multiplicity is less than algebraic multiplicity. (a)d/ dx = ( 1 −44 −7) x2−30
Answers
Answer:
-130
Step-by-step explanation:
On a cold winter day, Joel and Duncan brought a container of hot chocolate with them to go sledding. There were 15 ounces of hot chocolate, and they split it evenly. How much hot chocolate did each boy get?
Answers
If Joel and Duncan split the 15 ounces of hot chocolate evenly, then they each got half of the container.
To find out how much hot chocolate each boy got, we need to divide the total amount of hot chocolate by the number of people sharing it. Since there are two boys, we can divide 15 by 2 to get the amount of hot chocolate each boy received: 15 ÷ 2 = 7.5
Therefore, each boy got 7.5 ounces of hot chocolate to drink while they went sledding.It's important to note that when dividing something equally between two people, we divide by two since there are two individuals.
In this case, each boy received half of the container, or half of the total amount of hot chocolate. This type of division is known as "fair" or "equal" sharing, as both parties receive an equal portion.
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