Answer:6 bookcases, 12 TV stands.
Step-by-step explanation:
We can model this using a system of equations. Let b represent how many bookcases he makes, and t how many TV stands he makes. He can make at most 18 pieces, so let's say that b+t <=18. The cost of the bookcases are 20, and the TV stands are 40, so 20b+40t gives us our total cost. We have 600 to spend, so 20b+40t <=600. We want to maximize the equation for profit, which is 60b+100t=P. We have three values we care about, where our inequalities intersect, if we have only TVs, and if we only have bookcases. But, if b=0 and t=18, then our cost is 720, which is too big. So if we only have tv stands, then we can have at most 15 (40*15=600). So our three cases are: (b=0, t=15), (t=0, b=18), and the intersection, which is where the inequalities are equal. To solve that, b=18-t, 20(18-t)+40t=600, 360-20t+40t=600, 360+20t=600, 20t=240, t=12. b=18-t, b=18-12, b=6. So our final case is (b=6, t=12). Now simply plug those three cases into our equation to maximize, 60*0+15*100=1500. 18*60+0*100=1080. 6*60+12*100=1560. So, our third case yields us the highest profit, and Andrew should make 6 bookcases and 12 TV stands.
6.
Write the equation of a line through points (5, 5) and (1, 0) in point-slope form.
Answer: \(y=\frac{5}{4} x-\frac{5}{4}\)
The graph shows the distribution of the lengths (in seconds) of videos on a popular video-streaming site. The distribution is approximately Normal, with a mean of 264 seconds and a standard deviation of 75 seconds.
A graph titled Streaming Videos has length (seconds) on the x-axis, going from negative 36 to 564. The highest point of the curve is at 264.
What percentage of videos on the streaming site are between 264 and 489 seconds?
0.15%
49.85%
95%
99.7%
According to the properties of the standard normal distribution, approximately 99.7% of the values lie within three standard deviations of the mean. Therefore, the answer is 99.7%.
To determine the percentage of videos on the streaming site that are between 264 and 489 seconds, we need to calculate the area under the normal curve within that range. Since the distribution is approximately normal with a mean of 264 seconds and a standard deviation of 75 seconds, we can use the properties of the standard normal distribution to find the desired percentage.
First, we need to convert the values 264 and 489 to z-scores, which represent the number of standard deviations a particular value is away from the mean. The z-score formula is given by:
z = (x - μ) / σ
where x is the value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get:
z1 = (264 - 264) / 75 = 0
z2 = (489 - 264) / 75 = 3
Next, we can use a standard normal distribution table or a calculator to find the area under the curve between z = 0 and z = 3. The area represents the percentage of videos falling within that range. The answer is 99.7% .
For more such questions on normal distribution
https://brainly.com/question/4079902
#SPJ8
what is the absolute value of -11 2/3
Answer:
112
Step-by-step explanation:
State the name of the property illustrated.
4(-8+5)= - 32 + 20
The property illustrated in equation 4(-8+5) = -32 + 20 is the Distributive Property.
The Distributive Property states that when a number is multiplied by a sum or difference in parentheses, it can be distributed or multiplied by each term inside the parentheses separately, and then the results can be added or subtracted.
In this case, the number 4 is multiplied by the sum (-8 + 5). By applying the Distributive Property, we distribute the 4 to each term inside the parentheses:
4(-8 + 5) = (4 * -8) + (4 * 5)
This simplifies to:
4(-8 + 5) = -32 + 20
Finally, we can perform the addition:
-32 + 20 = -12
Therefore, the equation demonstrates the application of the Distributive Property.
know more about Distributive Property here:
https://brainly.com/question/2807928
#SPJ8
Answer of question 3 pls
The highest point for the quadratic function for the height of the object, h(t) = -16·t² + 224·t + 816, indicates that the interval over which the height of the object is increasing is; (-∞, 7]
What is the shape of the graph of a quadratic function?The shape of the graph of a quadratic function is a parabola.
The function for the height of the object in question 3 is; h(t) = -16·t² + 224·t + 816
Where;
t = The time in seconds
The height of the object is increasing in the interval to the left of the highest point, which can be found as follows;
The x-coordinate of the highest point of the quadratic function, f(x) = a·x² + b·x + c is; x = -b/(2·a)
Therefore, the x-coordinates of the highest point of the object is; -224/(2 × (-16)) = 7
Therefore, the height of the object is increasing in the interval; -∞ < t ≤ 7
Learn more on quadratic functions here: https://brainly.com/question/27920694
#SPJ1
It takes Colton 14 minutes to decorate 4 cookies. It takes
David 20 minutes to decorate 6 cookies. Who decorates
at a faster rate? Explain how you know
Answer:
David decorated the cookies at a faster rate than Colton.
Step-by-step explanation:
David decorated one cookie every 3 and 1/3 minutes. Colton decorated one cookie every 3.5 minutes. The way to find the answer to your question is by dividing the number of minutes by the number of cookies decorated.
Help! Quadratic Word Problems!
Answer:
Step-by-step explanation:
Makayla is a botanist studying production of coconuts by two different groups of her coconut palms. She notices that Group 1 trees produce 25 percent more coconuts than Group 2. based on Makayla's observation, if Group 1 produced 150 coconuts, how many coconuts did group 2 produce?
If Group 1 trees produce 25 percent more coconuts than Group 2, proportionately, Group 2 trees produce 120 coconuts.
What is proportion?Proportion refers to the two ratios equated to each other.
Proportion shows how much quantity or value is contained in another.
We depict proportions using fractional values, such as fractions, decimals, and percentages.
The number of coconuts produced by Group 1 trees = 150
The percentage by which Group 1 trees produce more than Group 2 = 25%
Let Group 1's production compared to Group 2's = 1.25 (100% + 25%)
Let Group 2's production = 100% = 150/125 x 100
= 120 coconuts
Thus, Group 2 trees would produce 120 coconuts compared to Group 1 trees that produced 150, which was proportionately, 25% more.
Learn more about proportions at https://brainly.com/question/1496357
#SPJ1
Consider ∠A such that cos A = 12/13.
a) In which quadrant(s) is this angle? Explain.
b) If the sine of the angle is negative, in which quadrant is the angle? Explain.
c) Sketch a diagram to represent the angle in standard position, given that the condition in part b) is true.
d) Find the coordinates of a point on the terminal arm of the angle.
e) Write exact expressions for the other two primary trigonometric ratios for the angle.
A)
Using the unit circle, for the cos function to be positive, angle A must lie in either quadrant I or quadrant IV
B)
Using the unit circle, If the sine is negative, angle A must lie in either quadrant III or quadrant IV. Since we know that the cosine is positive, this only leaves quadrant IV
D)
cos = adj/hyp
Using Pythagorean theorem,
\(12^{2} +b^{2} = 13^{2}\)
b = ±5 (we know its -5 since we know sinA is negative)
this means that the x coord is 12, and the y coord is -5
any proportion of these two numbers would work as an answer
e.g. (12, -5), (24,-10), (12/13, -5/13), are all valid answers
E)
sinA = opp/hyp
sinA = -5/13
tanA = opp/adj
tanA = -5/12
how do you write 31.4 in scientific notation?
Answer:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the
10
. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
3.14
×
10
1
Step-by-step explanation:
Brandon buys a radio for $45.09 in a state where the sales tax is 7%. How much does he pay in taxes? If necessary round to the nearest cent
What is the total Brandon pays for the radio?
Answer:
Step-by-step explanation:
tax = 7% of $45.09 = 0.07×$45.09 ≅ $3.16
Total cost = $45.09 + $3.16 = $48.25
Which statement is the best definition of an angle
Answer:
In geometry, an angle can be defined as the figure formed by two rays meeting at a common end point. An angle is represented by the symbol ∠. ... Angles are measured in degrees, using a protractor.
Step-by-step explanation:
hurray
There are 20 books in 4 boxes. How many books are there in 1 box?
Answer:
There are 5 books in 1 box
Step-by-step explanation:
It is quite easy to solve. You have to use division to figure out how many books go in each box. Our division equation will be: 20 ÷ 4 = ?
We will divide 20 by 4 and our answer is 5.
We can double-check our answer by doing multiplication. 5 x 4 = 20, leading us back to the original 20 books that are in boxes.
So, there are 5 books in each box.
Hope this helps! <3
Multiplying rational expressions (16x/4).(20/3x^5)
Given:
\(\frac{16x}{4}\cdot\frac{20}{3x^5}\)Required:
To multiply the given rational expression.
Explanation:
Consider the given expression,
\(\frac{16x}{4}\cdot\frac{20}{3x^5}\)Now
\(\begin{gathered} =\frac{4x}{1}\cdot\frac{20}{3x^5} \\ \\ =4\cdot\frac{20}{3x^4} \\ \\ =\frac{80}{3x^4} \end{gathered}\)Final Answer:
\(\frac{16x}{4}\frac{20}{3x^{5}}=\frac{80}{3x^4}\)A skyscraper casts a shadow 200 ft long. If the angle of elevation of the Sun is 38 degrees, then the height of the skyscraper is approximately _____.
A. 200 ft
B. 173.34 ft
D. 156.26 ft
The height of the skyscraper is D. 156.26 ft
How to determine the valueTo determine the height of the skyscraper, we need to consider the following trigonometric identities listed thus;
sinecosinetangentcotangentsecantcosecantFrom the information given, we have that;
Angle, θ = 38 degrees
The shadow casted is the adjacent side of the angle and is 200 ft
The height off the skyscraper is the opposite side
Now, using the tangent identity, we have that;
tan θ = opposite/adjacent
tan 38 = h/200
cross multiply the values, we get;
h = 200(0.7812)
Multiply the values
h = 156. 26 ft
Learn more about trigonometric identities at: https://brainly.com/question/7331447
#SPJ1
Violet bakes 7 dozen cookies.
She ate 2 cookies.
She gave 2 dozen cookies to her brother.
She gave 9 cookies to her mother.
How many cookies did Violet have left?
Show your work.
Answer: 49 cookies
Step-by-step explanation: 7 dozen= 84 , so subtract 84 by the 2 cookies she ate and you'll get 82, now 2 dozen= 24, so now subtract the 24 cookies that she gave to her brother by 82 and you'll get 58, then subtract the nine cookies she gave to her mom by 58 and you'll get 49 cookies.
so basically,, 84-2= 82 -2 = 58 -9= 49
I hope this helped :)
use the given frequency distribution to find the class width, class midpoint, and class boundaries
Based on the table attached, the class boundaries are as follows: 43.5, 49.5, 53.5, 59.5, 63.5, 69.5, 73.5, 79.5.
What is the frequency distribution about?Temperature (°F) Frequency
40-44 1
45-49 3
50-54 5
55-59 11
60-64 7
65-69 7
70-74 1
A. Viewing at the frequency table, we find that the lower class limits of two consecutive classes are 40 and 44, respectively. Thus the class width is:
Class width = 44 − 40= 4
B: One can find the class midpoints by putting the average of the lower and upper class limits. So the midpoint of the first class is seen below:
= 40 - 44 = \(\frac{40 + 44}{2}\) = 42. In a similar way, we find the rest.
C. The Class boundaries is known to be that which separate the classes removing the class limits. The class boundaries are as follows:
43.5, 49.5, 53.5, 59.5, 63.5, 69.5, 73.5, 79.5
Therefore, Based on the table attached, the class boundaries are as follows: 43.5, 49.5, 53.5, 59.5, 63.5, 69.5, 73.5, 79.5.
Learn more about frequency distribution from
https://brainly.com/question/1094036
#SPJ1
What type of Solution is the product of 2x+1=2x+2
Answer: no solution
Step-by-step explanation:
Aiden leans a 30-foot ladder against a wall so that it forms an angle of 78^{\circ} ∘ with the ground. What’s the horizontal distance between the base of the ladder and the wall? Round your answer to the nearest hundredth of a foot if necessary.
Answer:
6.2 approx i believe
Step-by-step explanation:
What are the new coordinates of the figure above if it is dilated by a scale factor of , with the origin as the center of dilation?
Answer:
could you show a picture and repost thx
Step-by-step explanation:
The picture of milk shown is a prism. The base has an area of 40 cm² and the height of the pitcher is
26 cm. Will the pitcher hold 1 Liter of milk?
Yes, the pitcher hold 1 Liter of milk.
We have to given that;
The picture of milk is a prism.
And, The base has an area of 40 cm² and the height of the pitcher is 26 cm.
Since, We know that;
Volume of prism is,
V = base area x Height
Now, Substitute all the values, we get;
V = 40 x 26
V = 1040 cm³
Since, 1 liter = 1000 cubic centimeters
Hence, the pitcher hold 1 Liter of milk.
To learn more about the volume visit:
brainly.com/question/24372707
#SPJ1
A sports trophy is in the shape of a cup
30 cm high. The winners are each given
copies of the cup, 7 cm high. One of the
copies holds 100 ml. What is the capacity of the trophy in liters?
The capacity of the trophy that us 30 cm high is 0.4286 liter
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
7 cm height cup holds 100 ml. Therefore:
7 cm = 100 ml
For a 30 cm height trophy:
30 cm = 30 cm * 100 ml per 7 cm = 428.57 ml
1000 ml = 1 l
428.57 ml = 428.57 ml * 1 liter per 1000 ml = 0.4286 liter
The capacity of the trophy is 0.4286 liter
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
At the supermarket 5 aplples cost $4. What is the cost of 25 apples
If 5 apples cost $4. How many times do you multiple 5x5 to get 25? The answer would be 5 times.
So 5apples x 5= 25 apples.
4x5=$20.
The answer would be $20
Express the division expression as a fraction in simplest form. Then, rewrite the fraction as a mixed number.
14 ÷ 4
Step-by-step explanation:
14 ÷ 4 is the same as the corresponding fraction (because a fraction is nothing else than a mini-division) :
14/4 = 7/2
and 7 divided by 2 is 3 with a remainder of 1. that means 1 time 1/2 remains as fraction.
so, the mixed number is
3 1/2
What is the solution for x in the equation?
-3x+7x-8 = 34+9x-2
OA =
8
OB.
OC. * = -8
OD. = 8
*
118
Answer:
10
Step-by-step explanation:
-3x+7x-8=34+9x-2
(Combine like terms)
4x-8=32
(Add 8 to each side)
4x=40
(Divide by 4)
X=10
A segment bisector is a line, ray or segment that divides a line segment into two equal parts. in the triangle formed by points A(-1,7), B(1,2), C(7,6) what is the slope of the line that goes through point A and bisects BC?
In decimal form, this is equivalent to -0.6
=================================================
Explanation:
This segment bisector is cutting side BC in half. So we have a point D such that it is between B and C. Also, we can say BD = DC. Refer to the diagram below.
To find the location of D, we'll apply the midpoint formula to points B and C.
B(1,2) and C(7,6) have x coordinates of 1 and 7 respectively. Average those x values to get (1+7)/2 = 8/2 = 4. This is the x coordinate of point D.
Repeat this idea for the y coordinates. We'll get (2+6)/2 = 8/2 = 4 which is the y coordinate of D.
Point D is located at (4,4)
---------------------
The takeaway from that last section, if we were to summarize it in one sentence, is that D is located at (4,4).
Now focus on the points A(-1,7) and D(4,4)
We'll apply the slope formula
m = (y2-y1)/(x2-x1)
m = (4-7)/(4-(-1))
m = (4-7)/(4+1)
m = -3/5 is the slope
Notice that to go from A to D, we can drop down by 3 units and move to the right 5 units. We can say rise = -3 and run = 5; therefore, slope = rise/run = -3/5
A piece of art is in the shape of a rectangular pyramid like the figure shown.
A rectangular pyramid with a base of dimensions 7 feet by 6 feet. The two large triangular faces have a height of 7.79 feet. The two small triangular faces have a height of 8 feet.
How much glass is needed to cover the entire pyramid?
After answering the provided question, we can state that As a result, 145.62 square feet of glass are required to cover the entire pyramid.
what is pyramid?A pyramid is a polygon formed by connecting points known as bases and polygonal vertices. For each hace and vertex, a triangle known as a face is formed. A cone with a polygonal shape. A pyramid with a floor and n pyramids has n+1 vertices, n+1 vertices, and 2n edges. Every pyramid is dual in nature. A pyramid contains three dimensions. A pyramid is made up of a flat tri face and a polygonal base that come together at a single point known as the vertex. A pyramid is formed by connecting the base and peak. The base's edges form triangle faces known as sides that connect to the top.
To determine how much glass is required to cover the entire pyramid, we must first determine the total surface area of the pyramid, including the base.
The formula for calculating the surface area of each triangular face is:
(1/2) x width x height
27.31 square feet = (1/2) x 7 feet x 7.79 feet
24 square feet = (1/2) x 6 feet x 8 feet
Simply multiply the length and width to find the area of the rectangular base:
7 feet by 6 feet equals 42 square feet
As a result, the total surface area of the pyramid is:
145.62 square feet = 2 (27.31 square feet) + 2 (24 square feet) + 42 square feet
As a result, 145.62 square feet of glass are required to cover the entire pyramid.
To know more about pyramid visit:
https://brainly.com/question/17615619
#SPJ1
Answer: 102.53
Step-by-step explanation: I calculated all the numbers you gave me and then added them to get 102.53
a train travels forward at 20 m/s. A person on the train stands up and walks towards the back of the train at a velocity of 1 m/s. What is the resultant velocity of the persons motion ?
The resultant velocity of the person is 19 m/s which is in the opposite direction to the forward motion of the train
Speed of person in forward = 20m/s
Speed of person in backward = 1 m/s
If a person moves in the opposite direction of the train, then the velocity of the person's motion is relative to the ground motion. The difference between the velocity of a person and the velocity of a train is calculated as:
The velocity of the person relative to the ground = Velocity of the train - Velocity of the person's motion
Velocity of person relative to ground = 20 m/s - 1 m/s
The velocity of the person relative to the ground = 19 m/s
Therefore, we can infer that the resultant velocity of the person is 19 m/s.
To learn more about the resultant velocity
https://brainly.com/question/30829294
#SPJ1
Solve x^2+8x+22=0 by completing the square.
Answer: x = √-6 - 4
Step-by-step explanation:
x^2+8x+22=0
(x+4)^2 - 16 + 22 = 0
(x+4)^2 + 6 = 0
(x+4)^2 = -6
√(x+4)^2 = √-6
x = √-6 - 4
√6 = 2.449
Help please!
S = 180m
How many strides would a runner take during a 1-hour run (60 min)
The number of strides the runner will make during 1 hour run will be =
10,800.
How to calculate the total number of strides made by the runner in a hour?To calculate the distance or number of strides made by the runner in an
hour, the graph given above is considered as follows;
The y-axis which represents the number of strides is plotted against the x-axis which is the number of hours.
From the graph
20 minutes= 3600 strides
60 minutes = X strides
make X the subject of formula;
x= 3600×60/20
= 216000/20
= 10,800
Learn more about distance here:
https://brainly.com/question/30694816
#SPJ1