1. A box without a top is to be made from a rectangular piece of cardboard, with dimensions 3 in. b)
in., by cutting out square corners with side length x and folding up the sides.
Answer:
a) The volume of the box is represented by [tex]V = 21\cdot x - 20\cdot x^{2}+4\cdot x^{3}[/tex].
b) A side length of 0.653 inches leads to the maximum volume of the box: 6.299 inches.
Step-by-step explanation:
a) The volume of the box ([tex]V[/tex]), in cubic inches, is modelled by the equation for the cuboid:
[tex]V = (3-2\cdot x) \cdot (7-2\cdot x) \cdot x[/tex] (1)
Where [tex]x[/tex] is the side length of the cutted square corners, in inches.
[tex]V = (21 - 20\cdot x + 4\cdot x^{2})\cdot x[/tex]
[tex]V = 21\cdot x - 20\cdot x^{2}+4\cdot x^{3}[/tex]
The volume of the box is represented by [tex]V = 21\cdot x - 20\cdot x^{2}+4\cdot x^{3}[/tex].
b) The method consist in graphing the polynomial and looking for a relative maximum. We graph the equation found in a) by means of a graphic tool. We present the outcome in the image attached below. According to this, a side length of 0.653 inches leads to the maximum volume of the box: 6.299 inches.
Can someone help me please
What type of function is represented by the table, and for what reason?
A.
linear, because the X values increase at a constant rate
B. Linear, because the graph of the points makes a line
C.
exponential, because the Y values for success of Integer values of eggs have a common ratio of four
D.
exponential, because the Y values for successive Integer values of X have a common ratio of 16
Answer:
D.
Step-by-step explanation:
Based on the attached picture we can say that function representing these values would be exponential because the Y values for successive Integer values of X have a common ratio of 16. This can be proven by multiplying each one of the y values by 16, which would give us the next y value in the successive set. For example,
2.5 * 16 = 40
40 * 16 = 640
640 * 16 = 10,240
Meaning that the values have a common ratio of 16, and are increasing exponentially.
If f(n) = 3n^2-7, then f(-2) equals___.
Answer:
5
Step-by-step explanation:
f(n)=3n^2-7
f(-2)=3(-2)^2-7
f(-2)=3(-2)(-2)-7
f(-2)=3(4)-7
f(-2)=12-7
f(-2)=5
Help me with this question pls
Answer:
24
Step-by-step explanation:
The question is asking how many blueberries per day and in ounces, so we divide 3 by 2
3/2 = 1.5
Then, convert 1.5 pounds into ounces
1 pound = 16 ounces
1.5 * 16 - 24
divide the sum of 15 and 16 by 5
Answer:
6.2
Step-by-step explanation:
15+16=31
31/5=6.2
Step-by-step explanation:
[tex]15 + 16 \div 5 \\ calculate \: the \: sum \: of \: 15 \: and \: 16 \\ 31 \div 5 = 6 \frac{1}{5} \\ or \: 6.2[/tex]
If the mean of the data set shown below is 11, find x.
x, 12, 8, 15
11.5
10
9
Answer:9
Step-by-step explanation:
You have to add it together
FIND THE ANSWER AND I WILL GIVE BRAINLIEST AND 50 POINTS
Answer:
Paul needs to work for 50 weeks.
Step-by-step explanation:
1,500+200= 1700
14,200-1,700= 12,500
12,500/125= 100
100/2= 50
let me know if this is wrong.
ILL BRAINLIEST YOU
PLEASE HELP ME
if 100 students surveyed, 25 said they would vote for Jen for class president. If 2,000 students voted in the school's election, about how many votes should Jen receive?
A 25
B 100
C 500
D 1,900
Answer:
500 Votes
Step-by-step explanation:
25/100 = 0.25
500/2000 = 0.25
Therefore 500 students would vote for Jen.
Taylor is building doghouses to sell. Each doghouse requires 3 full sheets of plywood which Taylor cuts into new shapes. The plywood is shipped in bundles of 14 full sheets. How many doghouses can Taylor make from 12 bundles of plywood?
Answer:
Step-by-step explanation:
taylor is building doghouses to sell. each doghouse requires 3 full sheets of plywood which taylor cuts into new shapes. the plywood is shipped in bundles of 14 full sheets. how many doghouses can taylor make from 12 bundles of plywood?
Describe all the x-values at a distance of 20 or less from the number 12. Enter your answer in interval notation.
Answer: [tex]12< x \leq 20[/tex]
Step-by-step explanation:
Given
x is at a distance of 20 or less i.e. x can be 20 or less
[tex]x\leq20[/tex]
and it starts from the number 12 i.e.
[tex]12< x[/tex]
In interval notation it is
[tex]12< x \leq 20[/tex]
6. The swing set on the playgrounds is getting wobbly, and you have been asked to put outrigger boards to help stabilize it. If the crossbar of the swing is 10 feet off of the ground, the outrigger to be attached at a 40 degree angle, and you want to bury the outrigger boards 3 feet onto the ground, how long would the boards have to be? (Hint: the outrigger is the hypotenuse of a right triangle)
Answer:
[tex]X=18.6ft[/tex]
Step-by-step explanation:
From the question we are told that:
Height of swing's crossbar [tex]H=10ft[/tex]
Angle [tex]\theta=40 \textdegree[/tex]
Depth of outrigger [tex]d_=3ft[/tex]
Generally the equation for slant height l is mathematically given by
[tex]l=\frac{opposite}{sin\theta}[/tex]
Therefore
[tex]l=\frac{H}{sin\theta}[/tex]
[tex]l=\frac{10}{sin 40\textdegree}[/tex]
[tex]l=15.6ft[/tex]
Since the Depth of outrigger
[tex]d_=3ft[/tex]
Therefore Length of the board X
[tex]X=l+d[/tex]
[tex]X=15.6+3[/tex]
[tex]X=18.6ft[/tex]
What is the possible number of turns for a square
Answer: 5
Step-by-step explanation:
A bag with 10 marbles has 2 yellow marbles, 4 blue marbles, and 4 red marbles. A marble is chosen from the bag at random. What is the probability that it is yellow?
Answer:
P(Y) = 2/10 = 1/5
Step-by-step explanation:
From the above question:
Total number of marbles = 10 marbles
Number of yellow marbles = 2 yellow marbles
Number of blue marbles = 4 blue marbles
Number of red marbles = 4 red marbles.
The probability of choosing a marble that is yellow is calculated as:
= P(Y) = Number of yellow marbles/Total number of marbles
P(Y) = 2/10
P(Y) = 1/5
plz help me do this
Answer:
Data set doesn't go to 17
Step-by-step explanation:
None of the numbers go to 17
Answer:
1st option. the data set doesn't GO to seventeen
Step-by-step explanation:
look at the number line. I always had trouble with this so I get where your coming from first, look at where the line is touching don't pay attention to the box yet because it's confusing the entire point of this line is to show you that there MAY have been 1 or two people who where at 0 for this data and 1 or two people who were at 15
the point here is that the bulk of the data was 11-14, but because there were less people down lower, the mean of the data is at 13, and the data is bigger (skewed) to the left.
making everything lekse true except for the first option.
Fiona deposited $900 in the bank over 2 years. She earned $60 in
simple interest at the end of the 2 years. What was the annual
interest rate?
If Fiona deposited $900 in the bank over 2 years. She earned $60 in
simple interest at the end of the 2 years then 3.33% is the annual
interest rate.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that Fiona deposited $900 in the bank over 2 years.
She earned $60 in simple interest at the end of the 2 years.
We have to find the annual interest rate
I=PRT
60=900×2×T
60=1800T
Divide both sides by 1800
T=3.33%
Hence, the annual interest rate is 3.33%
To learn more on Percentage click:
https://brainly.com/question/28269290
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What shape will result when you make a vertical cross section through the picture below?
A) Circle
B) Cylinder
C) Rectangle
D) Sphere
Answer:
rectangle
Step-by-step explanation:
Convert 6.3 meters to millimeters.
Answer:6300mm
Step-by-step explanation:
whoever has the right answers for ALL will get brainiest and all points
Answer:
1st: Equal to
2nd: Greater than
3rd: Less than
Answer:
Step-by-step explanation:
So the second problem 325 x 1 2/3 is greater then 325
and the third problem 325 x 1/4 is equal to 325HELP ME PLSSS NO LINKSS I WILL REPORT
Answer:
I would say b as it's easier to group and find a common denominator
Step-by-step explanation:
can anybody help me with these?
simplify 2 × n × p × 4
Answer:
8np
Step-by-step explanation:
2 x 4 = 8
8 * n * p = 8np
Si 1 kg de naranjas cuesta 14 pesos y al final del día el dueño de la frutería cuenta 1124 pesos por venta de naranjas, a) ¿cuántos kilogramos vendió? b) ¿cuánto cuesta comprar 3⁄4 de kg de naranjas? Si una señora compra dos naranjas cuyo peso fue de 0.3 kg, c) ¿cuánto pagó? Si en la compra de 5 kg de naranja se hace un descuento del 10%, d) ¿cuánto se paga? e) ¿Cuántos tipos de números hay en el problema?
Answer:
La respuesta a cada una de las preguntas es:
a) Se vendieron 562/7 kilogramos de naranjas.b) Comprar 3/4 de kg de naranjas cuesta 10.5 pesos.c) La señora pagó 4.2 pesos.d) Se paga 63 pesos por 5 kg de anaranja con el descuento.e) Se utilizan números racionales y números naturales.Step-by-step explanation:
a) Para calcular los kilogramos de naranjas vendidos durante el día, al tener el costo por kilogramo (14 pesos/kg) y la venta total (1124 pesos), puedes calcular de la siguiente forma:
Kilogramos vendidos = venta total / costo por kilogramoKilogramos vendidos = 1124 pesos / (14 pesos/kg)Kilogramos vendidos = 562/7 kg de naranjas.b) Para identificar el costo de 3/4 de naranja, debes multiplicar 3/4 por el valor del kg de naranja (14 pesos/kg):
Costo de 3/4 kg = (3/4 kg) * (14 pesos/kg)Costo de 3/4 kg = 10.5 pesos.c) Si la señora compra un peso total de 0.3 kg de naranja, para obtener el costo debes realizar la misma operación del ejercicio anterior, es decir, multiplicar los kilos comprados (0.3 kg) por el costo de cada kilogramo de naranja (14 pesos/kg):
Costo de 0.3 kg = 0.3 kg * (14 pesos/kg)Costo de 0.3 kg = 4.2 pesosd) Para calcular el costo de 5 kg de naranja con un descuento del 10%, debemos multiplicar el costo por kilogramo (14 pesos/kg), por el número de kilogramos comprados (5 kg), y luego por el porcentaje restante tras el descuento (90%), puesto que el total es el 100% y le restamos el 10% de descuento, nos queda el 90%:
Precio total de 5 kg de naranja tras descuento = (14 pesos/kg * 5 kg) *90%Precio total de 5 kg de naranja tras descuento = 70 pesos * 90%Precio total de 5 kg de naranja tras descuento = 63 pesos.e) De entre todos los tipos de números que hay, dentro de los ejercicios resueltos se hace uso de los números racionales (por el uso de fraccionarios) y de los números naturales (por el uso de los números enteros positivos).
solve for x
can somebody please help
Answer:
15
Step-by-step explanation:
you can easily use this for it a^2 + b^2 = c^2 where x would be c. after you plug everything in, take the square root of what you got for a^2 + b^2, that will give you x
Which of the following is equivalent to ( 16 3/2) 1/2
Answer:16 ^ 1.5 (or 3/2) = 64
64 ^ 0.5 (or 1/2) = 8
8 should be your answer
Step-by-step explanation:
hey can someone tell me why 132 is wrong? and help me with the right answer pls
Answer:
∠CBA = 132
Step-by-step explanation:
Bisectors split up an angle into two identical angles
Thus, 7x - 11 = 2x + 44
This is the equation we will use to solve for x
7x - 11 = 2x + 44
step 1 add 44 to each side
44 + 11 = 55
-11 + 11 cancels out
we now have 7x = 2x + 55
step 2 subtract 2x from each side
7x - 2x = 5x
2x - 2x cancels out
we now have 5x = 55
step 3 divide each side by 5
5x / 5 = x
55 / 5 = 11
we're left with x = 11
The question is asking for the measure of ∠CBA
To find the measure of ∠CBA we plug in 11 for x in one of the given expressions and multiply that by 2 ( this is because the two angles are identical so there is no need to find the measures of both because ∠CBD≅∠ABD )
7(11) - 11
7 * 11 = 77
77 - 11 = 66
66 * 2 = 132
Please help me with this
Answer:
216in
Step-by-step explanation:
6 + 8 + 10 = 24
24 * 9 = 216
Pls help! First correct answer gets brainliest!!
Answer:
3 and -(-2)
Step-by-step explanation:
14. A normal distribution has a mean of 700 and a standard deviation of 35. What is the
probability that a value selected at random is at most 630?
Answer: 0.025
Step-by-step explanation: