Answer:
i think 48,000
Step-by-step explanation:
Answer:
me to
Step-by-step explanation:
In your job at the container factory, you are asked to design a rectangular box with volume 500 cm3 . The material for the sides and bottom costs $0.05 per cm2 while the material for the top costs $0.15 per cm2 . What dimensions do you recommend to minimize the total material cost
Answer:
6.3 cm by 6.3 cm by 12.6cm
Step-by-step explanation:
Volume of the box=[tex]500 cm^3[/tex]
The minimal dimensions of a box always occur when the base is a square.
[tex]L^2H=[/tex][tex]500 cm^3[/tex]
[tex]H=\frac{500}{L^2}[/tex]
Surface Area of a cylinder=[tex]2(L^2+LH+LH)[/tex]
Surface Area of the sides and bottom= [tex]L^2+2(LH+LH)[/tex]
Surface Area for the top = [tex]L^2[/tex]
The material for the sides and bottom costs $0.05 per [tex]cm^2[/tex]
The material for the top costs $0.15 per [tex]cm^2[/tex]
Therefore Cost of the box
[tex]C=0.15L^2+0.05[L^2+4LH]\\C=0.2L^2+0.2LH[/tex]
Recall:[tex]H=\frac{500}{L^2}[/tex]
[tex]C=0.2L^2+0.2L(\frac{500}{L^2})\\=0.2L^2+\frac{100}{L}\\C=\frac{0.2L^3+100}{L}[/tex]
The minimum value of C is at the point where the derivative is zero.
[tex]C^{'}=\frac{2(L^3-250)}{5L^2}\\\frac{2(L^3-250)}{5L^2}=0\\2(L^3-250)=0\\L^3=250\\L=6.3cm[/tex]
[tex]H=\frac{500}{L^2}=\frac{500}{6.3^2}=12.6cm[/tex]
The dimensions that would minimize the cost are 6.3 cm by 6.3 cm by 12.6cm
A random sample of people was asked to report the age and distance driven of their primary car. A line was fit to the data to model the relationship.
Answer:
y= 12x + 5 for part A, part B is 89 thousand miles
Step-by-step explanation:
Just copy the answer you nerd.
3x+3=2x+1 what is the value of x
Answer:
Answer: 3x + 3 = 2x + 1
Answer: 3x + 3 = 2x + 1 <=>3x - 2x = 1 - 3
Answer: 3x + 3 = 2x + 1 <=>3x - 2x = 1 - 3 <=> x = -2
Chandni has 3 pieces of orange yarn that are 1.25 feet long each and 2 pieces of blue yarn that are 2.75 feet long each. She uses all 5 pieces of yarn for an art project. What is the total length of yarn, in feet, that Chandni uses for her art project
Answer:
9.25 feet.
Step-by-step explanation:
Given:
Chandni has 3 pieces of orange yarn that are 1.25 feet long each and 2 pieces of blue yarn that are 2.75 feet long each.
She uses all 5 pieces of yarn for an art project.
Question asked:
What is the total length of yarn, in feet, that Chandni uses for her art project ?
Solution:
By unitary method:
Length of 1 piece orange yarn = 1.25 feet
Length of 3 pieces orange yarn = 1.25 feet [tex]\times[/tex] 3 = 3.75 feet
Length of 1 piece blue yarn = 2.75 feet
Length of 2 piece blue yarn = 2.75 feet [tex]\times[/tex] 2 = 5.5 feet
As she uses all 5 pieces of yarn for an art project:-
Total length of yarn, she uses for her art project = 3.75 feet + 5.5 feet = 9.25 feet
Thus, the total length of yarn, she uses for her art project = 9.25 feet.
Rachel is investing $14,000 in a CD at a bank. If the bank uses simple interest and the bank pays 2.5% annually, how much will the CD be worth in total at the end of 7 years when the CD matures?
Answer:
Step-by-step explanation:
The formula for determining simple interest is expressed as
I = PRT/100
Where
I represents interest paid on the amount of money invested.
P represents the principal or amount of money invested.
R represents interest rate on the investment.
T represents the duration of the investment in years.
From the information given,
P = $14000
R = 2.5%
T = 7 years
Therefore,
I = (14000 × 2.5 × 7)/100
I = $2450
The total amount that the CD would be worth after 7 years is
14000 + 2450 = $16450
Answer:
Value of CD in total at the end of 7 years when the CD matures is $16646
Step-by-step explanation:
This is based on the formula A= P(1+r)^ n
where r = annual rate of interest,
P = Principal amount,
n = number of years
p = 14000
r = 2.5
n = 7
A = 14000 ( 1+ 0.025) ^ 7
= 14000 ( 1.025)^7
=14000 x 1.189
=16646
A = $16646
The reciprocal of 11/7
[tex]\Huge{\underline{\underline{\tt{\orange{Answer:}}}}}[/tex]
Reciprocal of 11/7 is 7/11.Reason :
Reciprocal is also known as multiplicative inverse which means the number is to be multiplied with the given number to give the result 1.If we flip 11/7 , it becomes 7/11 , and if 7/11 is multiplied with 11/7 ,the result is 1.Usage :Reciprocal is generally used for division in which the second number is reciprocated and the division sign is converted into the multiplication sign. Then the number is simplified and we obtain our answer.__________________________________________
The reciprocal of the given fraction 11/7 is 7/11.
What is the reciprocal property?The reciprocal of any quantity is, one divided by that quantity. For any number ‘a’, the reciprocal will be 1/a. If the given number is multiplied by its reciprocal, we get the value 1.
The given fraction is 11/7.
The reciprocal of the given fraction is the fraction that results from switching or reversing the numerator and denominator.
The reciprocal of the fraction is 7/11.
Therefore, the reciprocal of the fraction is 7/11.
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A store sells white scarves and red scarves.
• A white scarf costs $3.
• A red scarf costs $5.
On Monday, the store sold 12 scarves for a total of $50.
The store sold 7 red scarfs and 5 white Scarfs
5+5+5+5+5+5+5+3+3+3+3+3=50
This Maths question involves formation and solution of a system of equations, where equations are representing the number and total cost of scarves sold. The variables used are 'w' for white scarves and 'r' for red scarves, forming two equations: w + r = 12, and 3w + 5r = 50.
Explanation:This question can be approached by using a system of equations. A system of equations is a set of two or more equations that have the same variables. You can think of this problem as having two equations:
The total number of scarves (both white and red) sold is 12.The total amount made from selling all the scarves is $50.
Let's represent the number of white scarves sold as 'w' and the red scarves sold as 'r'. So, our first equation would become: w + r = 12
And knowing the cost of each scarf, the second equation would be: 3w + 5r = 50
Now with these two equations, one can solve for 'w' and 'r'. This type of problem is often seen in algebra and is an example of linear equations.
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a statistics professor finds that when she schedules an office hour for student help, an average of 2.4 students arrive. find the probability that in a randomly selected office hour, the number of student arrivals is 2
Answer:
P=0.2613
Step-by-step explanation:
-Notice that this is a poison probability distribution problem.
-The Poisson probability function is expressed as:
[tex]P(X=x)=\frac{\lambda^x e^{-\lambda}}{x!}[/tex]
where:
x=0,1,2,3[tex]e[/tex] Euler's constant[tex]\lambda[/tex] =mean number of occurrences.Given that x= 2 and [tex]\lambda=2.4[/tex], the probability is calculated as:
[tex]P(X=2)=\frac{\lambda^xe^{-\lambda}}{x!}\\\\=\frac{2.4^2e^{-2.4}}{2!}\\\\\\=0.2613[/tex]
Hence, the probability that in a randomly selected office hour, the number of student arrivals is 2 is 0.2613
Final answer:
To find the probability that in a randomly selected office hour, the number of student arrivals is 2, we can use the Poisson distribution. The average number of student arrivals is 2.4.
Explanation:
To find the probability that in a randomly selected office hour, the number of student arrivals is 2, we can use the Poisson distribution. The average number of student arrivals is 2.4, so the parameter λ for the Poisson distribution is 2.4.
The probability of getting exactly 2 student arrivals can be calculated using the formula:
P(X=k) = (e^-λ * λ^k) / k!, where X is the random variable representing the number of student arrivals, k is the desired value (2 in this case), and λ is the average number of student arrivals per office hour.
Calculate e^-λ: e is the base of the natural logarithm and λ is 2.4. e^-2.4 ≈ 0.0908.
Calculate λ^k: 2.4^2 ≈ 5.76.
Calculate k!: 2! = 2.
Plug in the calculated values into the formula: P(X=2) = (0.0908 * 5.76) / 2 ≈ 0.2613.
So, the probability that in a randomly selected office hour, the number of student arrivals is 2 is approximately 0.2613 or 26.13%.
LOTS OF POINTS IM DESPERATE! can someone please refresh my memory on a couple of log equations? Thank you!
Answer:
78. t=8.66yrs
79. r=23.10%
80. r=11.0975%
Step-by-step explanation:
78. Given the initial deposit is $1,000 and the 8% compounded continuously. The doubling time can be calculated using the formula;
[tex]A=Pe^{it}[/tex]
Given that A=2P, we substitute in the equation to solve for t:
[tex]A=Pe^{rt}\\\\2P=Pe^{rt}\\\\2=e^{0.08t}\\\\0.08t=\ In 2\\\\t=8.66\ years[/tex]
Hence, it takes 8.66 years for $1,000 to double in value.
79.
Given the initial deposit is $1,000 and the r% compounded continuously.
-The doubling rate can be calculated using the formula;
[tex]A=Pe^{rt}[/tex]
#We substitute our values in the equation to solve for r:
[tex]A=Pe^{rt}\\\\A=2P, t=3\\\\\therefore\\\\2P=Pe^{3r}\\\\2=e^{3r}\\\\r=\frac{In \ 2}{3}\\\\=0.23105\approx 23.10\%[/tex]
Hence, the deposit will double in 3 years at a rate of 23.10%
80.
Given the initial deposit is $30,000 and the future value is $2,540,689.
-Also, given t=40yrs, the rate of growth for continuous compounding is calculated as:
[tex]A=Pe^{rt}, \ \ \ r=r, t=40yrs\\\\2540689=30000e^{40r}\\\\\frac{2540689}{30000}=e^{40r}\\\\r=\frac{In \ (2540689/30000)}{40}\\\\\\=0.110975=11.0975\%[/tex]
Hence, the deposit will grow at a rate of approximately 11.0975%
-5x -4y = -15 and -x + 4y = -3
So the first thing you would want to do is rewrite the equation like so.
−x+4y=−3;−5x−4y=−15
once you done that you'll have to think about what variable are you trying to get be itself which in this case it'll be x. So now you'll be solving this equation.
−x+4y=−3
next you'll add -4y to both sides
Once you done so you should have this written down
-x over -1 = 4y- 3 over -1
divide -1 to both sides and you should end up with x= 4y+3
Now you have to substitute 4y+3 for x in -5x-4y=-15
So it should look like this now
−5(4y+3)−4y=−15
The next step is to simplify both sides with the following equation
−24y−15=−15
After simplifying add 15 to both sides, It then should look like this
−24y=0
Divide -24 to both sides and your answer should be this
y=0
hope this helps :)
Nancy spent half of her allowance going to the movies. She washed the family
car and earned 7 dollars. What is her weekly allowance if she ended with
16 dollars ?
Select the correct answer.
Which sequence of transformations proves that shape I is similar to shape II?
Answer:
c
Step-by-step explanation:
im not explaining im taking the test
Please I need help with the following question, How can you obtain the graph of ( + )from the graph of ?
Answer:
B) Translate the graph [tex] k [/tex] units to the left.
The quality control team of a company checked 800 digital cameras for defects. The team found that 20 cameras had lens defects, 25 cameras had charging defects, and 6 cameras had both defects. What is the probability that a camera has a lens defect given that it has a charging defect?
Answer:
6/25
Step-by-step explanation:
Given two events A and B, the conditional probability of event A is the probability that event A occurs given that event B has occurred. It is calculated as
[tex]p(A|B)=\frac{p(A\cap B)}{p(B)}[/tex]
where
[tex]p(A\cap B)[/tex] is the probability that both A and B occur at the same time
[tex]p(B)[/tex] is the probability that B occurs
In this problem, we call:
A = the camera has a lens defect
B = the camera has a charging defect
Here we have:
a = 20 is the number of cameras with lens defects
b = 25 is the number of cameras with charging defects
c = 6 is the number of cameras having both defects
n = 800 is the total number of cameras
So we have:
[tex]p(A\cap B)=\frac{c}{n}=\frac{6}{800}[/tex] is the probability that the camera has both lens and charging defect
[tex]p(B)=\frac{b}{n}=\frac{25}{800}[/tex] is the probability that the camera has a charging defect
So the conditional probability is
[tex]p(A|B)=\frac{6/100}{25/100}=\frac{6}{25}[/tex]
Find the missing value in the ratio table
Answer: y-value=36
Step-by-step explanation:
If you take the unit rate of these set of numbers, (it can be any set of the numbers on the table), let's use 2 and 12. To find the unit rate all you have to do is divide. 12 divided by 2 is 6. This also works for 4 and 24. 24 divided by 4 is 6. Therefore 6 times any number in the x column will give you the y-value.
Plugging in the unit rate would look look this 6(6)=y
36=y
Therefore your missing value, or the y-value that is not filled in would be 36.
What is the height of a cylinder with a base area of 12 cm squared and a volume of 144 cubic cm?
Answer:
12
Step-by-step explanation:
h = V / A
Height equals volume divided by (base) area.
144 / 12 = 12
The height of the cylinder is 12 cm.
To find the height of the cylinder, we can use the formula for the volume of a cylinder, which is given by:
[tex]\[ V = B \times h \][/tex]
where [tex]\( V \)[/tex] is the volume, [tex]\( B \)[/tex] is the base area, and [tex]\( h \)[/tex] is the height of the cylinder.
Given that the base area [tex]\( B \)[/tex] is 12 cm² and the volume [tex]\( V \)[/tex] is 144 cm³, we can solve for the height [tex]\( h \)[/tex] by rearranging the formula:
[tex]\[ h = \frac{V}{B} \][/tex]
Substituting the given values:
[tex]\[ h = \frac{144 \text{ cm}^3}{12 \text{ cm}^2} \][/tex]
[tex]\[ h = 12 \text{ cm} \][/tex]
Therefore, the height of the cylinder is 12 cm.
Jeremy is packaging a stew containers.There are 8 3/4 cups of stew that need to put into 5 to go containers equally.How many cups of stew will be in each container?
Answer:
1 3/4 cups
Step-by-step explanation:
In order to be able to equally divide the stew into 5 containers we need to turn everything into the same format, in this case it would be by multiplying the whole number and the denominator and then adding the numerator like so
(8 * 4) + 3 = [tex]\frac{35}{4}[/tex]
Now we can divide the numerator by 5 (container) in order to calculate how much stew each container will get.
[tex]\frac{35}{4} / 5 = \frac{7}{4}[/tex]
So each container will get 7/4 of the Stew or 1 3/4 cups
Answer:
Each container = 1 3/4 cups
Step-by-step explanation:
*** There are 8 3/4 cups of stew that MUST be put into five containers EQUALLY.
*** We are basically required to calculate the number of cups of stew that must be in each container.
Since 8 3/4 cups of stew needs to be equally distributed and placed in just about five containers, we will need to first convert 8 3/4 cups which is in mixed fraction into improper fraction in order to enable us to calculate successfully.
8 3/4 = [(4×8)+3]/4
= 35/4
We will now use a little bit of the principle of proportion to get through this:
If 8 3/4 cups must be equal in five containers, then one container will have ? number of cups:-
5 containers --------- 35/4 cups
1 container ---------- ? cups.
1/5 × 35/4
= 7/4 cups.
We will now convert it back to mixed fractions and we will have 1 3/4 cups.
Therefore, each container we will contain 1 3/4 cups
Compared with the rest of Europe, northern Italy had many
churches.
cities.
farms.
forests.
Step-by-step explanation:
compared with the rest of Europe northern Italy had many cities
When compared with the rest of Europe, one will notice that Northern Italy has a lot of cities.
The Northern part of Italy is much more developed than the South and is so developed that it has one of the highest rates of developments in all of Europe.
This is due to the high density of cities located there such as:
Milan Genoa Turin Venice etcThere are about 23 cities in Northern Italy alone which leads us to conclude that in Europe, Northern Italy has one of the highest number of cities.
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A newborn who weighs 2,500 g or less has a low birth weight. Use the information on the right to find the z-score of a 2,500 g baby. In the United notes, birth weights of newborn babies are approximately normally distributed with a mean of mu = 3,600 grams and a standard deviation of sigma = 500 grams. Z = StartFraction x minus mu Over sigma EndFraction
Answer:
[tex]Z = -2.2[/tex]
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 3600, \sigma = 500[/tex]
Use the information on the right to find the z-score of a 2,500 g baby.
This is Z when X = 2500. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2500 - 3600}{500}[/tex]
[tex]Z = -2.2[/tex]
Answer:
Step-by-step explanation:
-2
ur welcome ;)
Which pairs of angles are congruent because they are vertical angles? Check all that apply.
◽Angle 1 and Angle 4
◽Angle 14 and Angle 12
◽Angle 7 and Angle 8
◽Angle 10 and Angle 8
◽Angle 3 and Angle 5
◽Angle 8 and Angle 12
Answer:
◽Angle 14 and Angle 12
◽Angle 10 and Angle 8
Step-by-step explanation:
Vertical angles are opposite to each other on a pair of intersecting lines.
◽Angle 1 and Angle 4
These angles are not on the same two intersecting lines.
◽Angle 14 and Angle 12
These angles are on the same two intersecting lines. They are also opposite to each other.
◽Angle 7 and Angle 8
These angles are on the same intersecting lines, but they are not opposite to each other.
◽Angle 10 and Angle 8
They are on the same pair on lines, and opposite to each other.
◽Angle 3 and Angle 5
They are not on the same pair of intersecting lines.
◽Angle 8 and Angle 12
These angles are not on the same pair on intersecting lines. (However, they are also equal because they are corresponding, on the insides of an "F" pattern).
Answer:
A and D
Step-by-step explanation:
Edge 2020
You roll a 6-sided die. What is the probability of rolling a 4? Write it as a fraction. P(4)=
Answer:
P(4)= 1/6
Step-by-step explanation:
Lots of Love!! <3
Stay Safe! Stay at Home!! =)
Answer:
Step-by-step explanation:
no of sample space, n(s) = 6
no of favorable cases , n(e) = 1
Probability of getting 4,
P(e) = n(e) / n(s)
= 1 / 6
For each day that Sasha travels to work, the probability that she will experience a delay due to traffic is 0.2. Each day can be considered independent of the other days. What is the probability that Sasha's first delay due to traffic will occur after the fifth day of travel to work?
The probability that Sasha's first delay due to traffic will occur after the fifth day of travel to work is approximately 0.67232 or 67.232%.
The probability that Sasha will not experience a delay on any given day is 1 − 0.2 = 0.8, as the complement of the probability of experiencing a delay is the probability of not experiencing a delay.
Since each day is independent, the probability that Sasha will not experience a delay on the first day, second day, third day, fourth day, and fifth day is given by multiplying the probabilities for each day:
P(no delay on day 1 to day 5) = 0.8×0.8×0.8×0.8×0.8
Now, since we are looking for the probability that Sasha's first delay occurs after the fifth day, it means she did not experience a delay on the first five days. Therefore, the probability of the first delay occurring after the fifth day is the complement of the probability mentioned above:
P(first delay after the fifth day) = [tex]1 - 0.8^5[/tex]
Now, you can calculate this value:
P(first delay after the fifth day) = [tex]1 - 0.8^5[/tex]
P(first delay after the fifth day) = 1 − 0.32768
P(first delay after the fifth day) ≈ 0.67232
A certain television is advertised as a 17-inch TV(the diagonal length). If the width of the TV is 8 inches, how many inches tall is the Tv?
Answer:
15
Step-by-step explanation:
Find the requested value.
f(-6) for f(x) =
Select one:
A. 12
B. -12
C. 3
D. -9
Answer:
C
Step-by-step explanation:
Why is the value of x limited to 0 in. < x < 4.25 in.?
Answer:
Lengths can't be negative
Step-by-step explanation:
Dimensions of the base are:
(8.5-2x) × (11 - 2x)
Since length cannot be negative:
x > 0
8.5 - 2x > 0
2x < 8.5
x < 4.25
11 - 2x > 0
x < 5.5
The set of values of x which satisfies all is:
0 < x < 4.24
definicion de Funcion Polinomica
Answer:
Ejemplos de funciones polinómicas son: , la cual es de grado 3, ya que el exponente mayor es 3. , que es una función polinómica de grado 2, o sea cuadrática, cuya gráfica es una parábola. ... Muchas veces a partir de la gráfica de un polinomio se puede deducir la ecuación de la función.
Step-by-step explanation:
Una función polinómica es una expresión matemática compuesta por términos de variables elevadas a exponentes no negativos con coeficientes.
Una función polinómica es una función matemática definida por una expresión polinómica, que es una combinación lineal de variables elevadas a exponentes no negativos, multiplicadas por coeficientes constantes. Formalmente, una función polinómica [tex]\( f(x) \)[/tex]se expresa como:
[tex]\[ f(x) = a_n x^n + a_{n-1} x^{n-1} + \ldots + a_1 x + a_0 \][/tex]
Donde:
[tex]- \( n \)[/tex] es un número entero no negativo (grado del polinomio).
[tex]- \( a_n, a_{n-1}[/tex], [tex]\ldots, a_1, a_0 \)[/tex] son coeficientes constantes.
[tex]- \( x \)[/tex] es la variable independiente.
Por ejemplo, [tex]\( f(x) = 2x^3 - 3x^2 + 5x - 7 \)[/tex] es una función polinómica de grado 3. Las funciones polinómicas son un tipo importante de funciones en matemáticas y se utilizan en una variedad de campos, incluyendo álgebra, cálculo, estadística y física.
There are only chickens and pigs in Henry's Barn Henry counted a total of Sixteen animal heads and a total of 50 animal feet.How many pigs does Henry have?
Answer:
9 pigs
Step-by-step explanation:
We have the following numbers of heads:
pigs (p) + chickens (c) = 16 animal heads (1)
And the following numbers of feet:
4p + 2c = 50 animal feet (2)
From equation (1):
p = 16 - c (3)
By entering equation (3) into (2) we have:
4(16 - c) + 2c = 50
64 - 4c + 2c = 50
c = 7
Now, entering the value of c into equation (3) we have the next value of p:
p = 16 - c
p = 16 - 7
p = 9
Therefore, the number of pigs that Henry has is 9.
I hope it helps you!
Two sides and an angle are given below. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any triangle(s) that results. b equals 6 comma c equals 8 comma Upper B equals 30 degrees
The information given results in one triangle. By applying the law of sines and trigonometric relation, we find the angles A=107.52, B=30, C=42.48 degrees for a triangle with sides b=6, c=8.
Explanation:The problem deals with the Law of Sines which can be used to determine if a triangle exists given two sides and a non-included angle. According to the law of sines, ratio of the length of a side to the sine of the opposite angle is the same for all three sides of a triangle. Using this, we can determine whether the given conditions lead to a valid triangle.
Given: b = 6, c = 8, B = 30 degrees
1. Compute the value of sin(B) = sin(30) = 0.5 (using standard angle values).
2. Apply the law of sines to compute the missing angle. You get sin(C) = c*sin(B)/b = 8*0.5/6 = 0.67
3. Check sin(C): if sin(C) is greater than 1 or less than -1, no triangle exists. If sin(C) = 0.67, we get C = arcSin(0.67) = 42.48 degrees.
4. To find the third angle A, use the relationship 'Sum of angles in a triangle' equals 180. Hence, A = 180 - B - C = 180 - 30 - 42.48 = 107.52 degrees. We know that in a triangle, no angle can exceed 180 degrees, hence A=107.52 degrees confirms that the triangle is possible.
Hence given information results in one triangle with sides b=6, c=8 and angles A=107.52, B=30 and C=42.48
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The given information results in one triangle. To solve the triangle, we can use the Law of Sines.
Explanation:The given information of b=6, c=8, and B=30 degrees results in one triangle.
To solve the triangle, we can use the Law of Sines.
By plugging in the values, we can find the length of side a using the formula: a = (b * sin(A)) / sin(B).
After substituting the values, we find that the length of side a is approximately 3.464 units.
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Eight pounds of peanuts cost $24.00. Six pounds of walnuts cost half as much.
Which is more expensive and by how much?
Answer:
24 is more expensive by $18.00
Step-by-step explanation:
Answer:
The eight pounds of peanuts are more expensive, by $1.
Step-by-step explanation:
If eight pounds of peanuts cost $24.00, then one pound of peanuts costs $24.00/8 = $3.00.
If six pounds of walnuts cost $12.00 (half as much), then one pound of walnuts costs $12.00/6 = $2.00.
Mia says that two adjacent angles are supplementary and drew the figure on the left.
Ethan says that adjacent angles are not supplementary and drew the figure on the right.
Who is correct?
Explain your answer.
Answer:
Ethan
Step-by-step explanation:
Supplementary angles are angles which add up to 180 degrees.Two or more angles are Adjacent when they have a common side and a common vertex.In the scenario presented, Ethan is right to say that adjacent angles are not supplementary. This is as a result of the fact that no other condition was attached.
Adjacent angles are only supplementary "if they are all on a straight line" as in Mia's case. This is a special case and an extra condition has been imposed.