Answer:
The rate of change will be the number of bags Fred fills for 1 customer.
Write a ratio.
21 : 3
x : 1
To solve for x, cross multiply.
3x : 21
Divide both sides by 3.
x = 7
Fred’s average rate of change is 7 bags.
:)
Solve the problem using a system of equations: Donnette found a widescreen TV at a garage sale, but she isn't sure if it will fit in her entertainment center. The TV is 50". The size of a TV is measured on the diagonal of the screen, and a widescreen has a length that is larger than the width. The screen also has an area of 1,200 square inches. What are the length and width of the TV screen?
length=___inches, width=___ inches
Check the picture below.
[tex]\begin{cases} L^2+w^2=50^2\\ Lw = 1200\\[-0.5em] \hrulefill\\ L^2+w^2=2500\\ L=\sqrt{2500-w^2} \end{cases}\qquad \stackrel{\textit{substituting on the 2nd equation}}{\sqrt{2500-w^2}~w=1200} \\\\\\ \stackrel{\textit{squaring both sides}}{w^2(2500-w^2) = 1200^2}\implies 2500w^2-w^4=1440000 \\\\\\ 0=w^4-2500w^2+1440000\implies 0=\stackrel{\textit{tis a quadratic}}{(w^2)^2-2500w^2+1440000}[/tex]
[tex]0=(w^2-900)(w^2-1600)\implies \begin{cases} 0=w^2-900\\ 900=w^2\\ \sqrt{900}=w\\ \boxed{30=w}\\[-0.5em] \hrulefill\\ 0=w^2-1600\\ 1600=w^2\\ \sqrt{1600}=w\\ \boxed{40=w} \end{cases} \\\\\\ \stackrel{\textit{we know that}}{L = \sqrt{2500 - w^2}}\implies \begin{cases} L=\sqrt{2500-30^2}\\ \boxed{L=40}\\[-0.5em] \hrulefill\\ L=\sqrt{2500-40^2}\\ \boxed{L = 30} \end{cases}[/tex]
The length of the given TV is 40 inches and width of the given TV is 30 inches.
What is the area of a rectangle?The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.
The area of rectangular shape TV is 1,200 square inches.
The TV is 50".
Now, L²+W²=50² ----------(I)
L×W=1200 ----------(II)
L²+W²=2500
⇒ L²=2500-W²
⇒ L=√(2500-W²)
Substitute L=1200/W in L=√(2500-W²), we get
1200/W=√(2500-W²)
Squaring on both the sides we get
1440000/W² =2500-W²
⇒ 1440000=2500W²-[tex]W^4[/tex]
⇒ [tex]W^4[/tex]-2500W²+1440000=0
⇒ (W²)²-2500W²+1440000=0
⇒ (W²)²-900W²-1600W²+1440000=0
⇒ W²(W²-900)-1600(W²-1600)=0
⇒ (W²-1600)(W²-900)=0
⇒ W²-1600=0 and W²-900=0
⇒ W²=1600 and W²=900
⇒ W=±40 and W=±30
So, W=40, -40, 30, -30
Length =1200/W =40 or 30
Therefore, the length of the TV is 40 inches and width is 30 inches.
To learn more about the area of a rectangle visit:
https://brainly.com/question/20693059.
#SPJ2
examine the following sequence 1,4,9,16,25…why is 36 the next number in the sequence ? because the pattern is
Answer:
The pattern is adding by consecutive odds.
Step-by-step explanation:
The first odd you start with is 3:
1 + 3 = 4
4 + 5 = 9
9 + 7 = 16
16 + 9 = 25
25 + 11 = 36
...
Note that each time you add, it is by consecutive odds, meaning that after 36, you are adding 13, then 15, etc.
~
What is John and Linda paid each hour
Henry was granted a loan of £96.00. The interest rate was 24% per annum. Calculate the interest at the end of the year
Answer:
110.00
Step-by-step explanation:
Use technology to find the P-value for the hypothesis test described below
The claim is that for 12 AM body temperatures, the mean is > 98.6°F. The sample size is n = 3 and the test statistic is t=2.446
P-value = (Round to three decimal places as needed)
Answer: C
Step-by-step explanation:
Hope it help
distance from the point to 0, so it can never be
negative.
a. Coordinate plane
b. Opposite
c. Absolute value
d. Quadrant
distance from the point to O, so it can never be negative so answer is
b.oppsite
Mary was asleep from 9:pm to 5:am. How long was she asleep for?
Answer:
8 hours
Step-by-step explanation:
Answer:
8hours
Step-by-step explanation:
What is 024 rounded off to the nearest 100?
Answer:
0.24
Step-by-step explanation:
There is nothing, after the hundredths (4), to round it, So 0.24 is already rounded to the nearest hundredths.
The number 0.024 after rounded off to the nearest hundred its become 0.02.
What is rounding off?Rounding numbers refers to changing a number's digits such that it approximates a value. The provided number is more simply represented by this value. For instance, 700,000 rather than 698,869 could be used to express a town's population.
Given that;
The number is,
⇒ 0.024
Now, After rounding off to the nearest hundred, we get;
⇒ 0.024 ≈ 0.02
( Because 4 is less than 5. )
Learn more about the rounding number visit:
https://brainly.com/question/1620496
#SPJ2
*What is the perimeter of a square with side length 13.4 inches? Write the direct variation equation.
Answer:
53.6 inches
p = 4s
Step-by-step explanation:
The perimeter of a square is four times the side
The direct variation equation is
p = 4s
p = 4 * 13.4
p = 53.6 inches
Find the length of the missing leg in the following right triangle.
A) 35.5
B) 20
C) 8
D) 400
Please and thank you!
Work Shown:
[tex]a^2 + b^2 = c^2\\\\b^2 = c^2 - a^2\\\\b = \sqrt{c^2 - a^2}\\\\b = \sqrt{29^2 - 21^2}\\\\b = \sqrt{841-441}\\\\b = \sqrt{400}\\\\b = 20\\\\[/tex]
I applied the pythagorean theorem.
Solve for x:
Spam: WHSIYWsugwediywedw
Answer:
um whats m or y?
Step-by-step explanation:
Answer:
[tex]x=3m+y[/tex]
Step-by-step explanation:
Let's solve for [tex]x[/tex].
[tex]m=\frac{x-y}{3}[/tex]
Step 1: Flip the equation.
[tex]\frac{1}{3}x+\frac{-1}{3}y=m[/tex]
Step 2: Add [tex]\frac{1}{3}y[/tex] to both sides.
[tex]\frac{1}{3}x+\frac{-1}{3}y+\frac{1}{3}y=m+\frac{1}{3}y[/tex]
[tex]\frac{1}{3}x=m+\frac{1}{3}y[/tex]
Step 3: Divide both sides by [tex]\frac{1}{3}[/tex].
[tex]\frac{\frac{1}{3}x }{\frac{1}{3} } ={\frac{m+\frac{1}{3}y }{\frac{1}{3} }[/tex]
[tex]x=3m+y[/tex]
Answer:
[tex]x=3m+y[/tex]
George eat 3/8 a pizza and 1/4 of pizza
What fraction of pizza has George eaten
Answer: 5/8
Step-by-step explanation:
Answer:
5/8
Step-by-step explanation:
1/4=2/8
2/8+3/8=5/8
Ramon Escalante purchases a digital camera for $399.99 in Omaha Nebraska, where the sales tax rate is 5.75 percent
A. what is the sales tax?
B. what is the total purchase price?
Answer:
[tex] \: [/tex]
A. The sales tax will be $ 22.999425
so, the sales tax » $ 23
5.75 % of $ 399.99
B. The Total Purchase will be →
$ ( 399.99 + 22.999425 ) $ 422.989425or
$(23 + 399.99) $ 422.99If F=(-3)
Find: F(x)=4x^2-5
Answers:
-41
31
29
None of the Above
Answer:
31
Step-by-step explanation:
as we put the value of X in the function it gives 3
a company blends 1000 bushels of two types of apples to make a beverage that contains 12% real-juice content. One of the two types of apple contains 10% real-juice content and the other contains 15% real juice content. how many bushels of each type of apple are needed?
Answer:
400 bushels of the 15%
600 bushels of the 10%
Step-by-step explanation:
x bushels of the 15% plus the balance of 1000 bushels at 10% yield 1000 bushels at 12%
15x + 10(1000 - x) = 12(1000)
distribute
15x + 10000 - 10x = 12000
Combine like terms
5x = 2000
Divide both sides by 5
x = 400 bushels of the 15%
1000 - x = 600 bushels of the 10%
The number of bushels of the 15% is 400, and the number of bushels of the 10% is 600.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have:
A company blends 1000 bushels of two types of apples to make a beverage that contains 12% real-juice content.
Let x be the bushels.
One of the two types of an apple contains 10% real-juice content and the other contains 15% real juice content.
The linear equation can be framed:
15x + 10(1000 - x) = 12(1000)
By using the distributive property:
15x + 10000 - 10x = 12000
5x = 2000 (combine like terms)
x = 400 bushels of the 15%
= 1000 - x
= 1000 - 400
= 600 bushels of the 10%
Thus, the number of bushels of the 15% is 400, and the number of bushels of the 10% is 600.
Learn more about the linear equation here:
brainly.com/question/11897796
#SPJ2
Find the area (A) of the figure below: 166) 6cm A) 18 square cm B) 35 square cm 12cm C) 72 square cm D) 144 square cm 167) 12 in A) 37.68 square inches B) 72.52 square inches C) 108.12 square inches D) 113.09 square inches
Answer:
166) C. 72 square cm 167) D. 113.09 square inches
Step-by-step explanation:
166) Parallelogram area formula is A=Base x height
A= 6 x 12
A= 72
167) Circle area formula A=πr²
r= half of diameter (12)
A=π(6)²
A=112.09
According to sales records at a local coffee shop, 75% of all customers like hot coffee, 30% like iced coffee, and 22% like both hot and iced coffee. The Venn diagram displays the coffee preferences of the customers.
Using Venn probabilities, it is found that there is a 0.08 = 8% probability that the customer only likes iced coffee.
In this problem, the events are:
Event H: Liking hot coffee.Event I: Liking iced coffee.The probability of only liking iced coffee is:
[tex]P(I \cap H^c) = P(I) - P(I \cap H)[/tex]
30% like iced coffee, hence [tex]P(I) = 0.3[/tex].22% like both hot and iced coffee, hence [tex]P(I \cap H) = 0.22[/tex]Then:
[tex]P(I \cap H^c) = P(I) - P(I \cap H) = 0.3 - 0.22 = 0.08[/tex]
0.08 = 8% probability that the customer only likes iced coffee.
A similar problem is given at https://brainly.com/question/24707032
Anyone able to help?!
[tex]\cos \theta = \dfrac 12\\\\\implies \theta = 2n\pi \pm \dfrac{\pi}3\\\\\text{For n =0 ~ \text{and}~ n=1}\\\\\\\theta = \dfrac{\pi}3 , \dfrac{5\pi}{3}\\\\\text{In degrees,}\\\\\theta = 60^{\circ} , ~ 300^{\circ}[/tex]
Which of the following describes a similarity between a solid and a gas
Answer:
they are both states of matterthey are both made up of atoms, molecules and ionsthey both have volumeJames made $85.00 in 2 weeks mowing yards. He spent 20% of that buying new tools. How much did he spend on tools? *
10 points
A $15
B $20
C $17
D $14
Answer asap please!
Answer: c 17
Step-by-step explanation:
Easy
Answer:
C. $17
Step-by-step explanation:
85 x (1/5) = 17
Ms. April likes for the twenty students in her
class to have a carton of milk each day at break
time. She sends three of her students down to
the cafeteria to ask for the cartons of milk, but
she likes to mix things up a bit and wants to
send a different group of students down every
day. Will she have enough different groups of
three students in her class of twenty students to
send a different group every day of the school year? (There are 180 days in the school year)
9514 1404 393
Answer:
yes
Step-by-step explanation:
There are 20 ways to choose the first student, 19 ways to choose the second student, and 18 ways to choose the third student. Chosen this way, the same three students can be chosen 3×2×1 = 6 different ways. So, the number of different choices of 3 students will be ...
(20×19×18)/(3×2×1) = 1,140
There are easily enough different combinations of 3 students to have a different combination each day.
_____
Additional comment
The number found above is the number of combinations of 20 students taken 3 at a time: 20C3 or C(20, 3). The value can be computed from ...
nCk = n!/(k!(n-k)!)
Multiply (3x+2)(x-6)
What is the middle term of the simplified answer?
Answer:
16x
Step-by-step explanation:
(3x + 2) (x - 6)
Multiply 3x by x and -6
3x^2 - 18x
Multiply 2 by x and -6
2x - 12
Combine like terms
3x^2 - 16x - 12
The middle term is 16x
Only answer this if you know the answer.
Find The nth Term of this number sequence
18, 16, 14, 12
Answer:
The nth term of this number sequence 18, 16, 14, 12,... will be -2n + 20.
First term = 18
Second term = 16
Common difference = 16 - 18 = -2
It should be noted that the formula for finding the next term of an arithmetic sequence will be:
= a + (n - 1)d
= 18 + (n - 1) × -2
= 18 - 2n + 2
= -2n + 20
Therefore, the nth term of this number sequence 18, 16, 14, 12,... will be -2n + 20.
Step-by-step explanation:
C D
Given: r is inversely proportional to s. If r = 16 when s = 3, then write the formula for the relation between r and s.
a. r=s/48
C. r=s/16
b. r= 48/s
d. r= 16/s
Please select the best answer from the choices provided
A
B
ОООО
Submit
Next
Save and Exit
Mark this and retum
Answer:
You choose but it looks like what you have labeled B
Step-by-step explanation:
R = K / S INVERSE PROPORTION
16 = K / 3 VALUES GIVEN: MULTIPLY BY 3 ON BOTH SIDES
16*3 = k
K = 48
Answer: R = 48/S
Progressions A person borrowed a sum of Rs. 3400 from his provident fund account on the condition to repay in 22 monthly installment of Rs. 150 and last installment of Rs. 100. Calculate the S.I. at the rate of 4.5% pa, which he , has to pay as the 24th installment?
Solve the inequality. 53(2x + 2) – 10 ≥ 2x + 2(23x + 2) please help
A relationship between two expressions or values that are not equal to each other is called 'inequality. inequality 53(2x + 2) – 10 ≥ 2x + 2(23x + 2) is x≥-92/58.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
The given inequality is
53(2x + 2) – 10 ≥ 2x + 2(23x + 2)
Apply the distributive property
106x+106-10≥ 2x + 46x+4
Add the like terms
106x+96≥ 48x+4
Take all common variables on one side
106x-48x≥4-96
106x-48x is 58 and 4 minus 96 is minus 92.
58x≥-92
x≥-92/58
Hence inequality 53(2x + 2) – 10 ≥ 2x + 2(23x + 2) is x≥-92/58.
To learn more on Inequalities click:
https://brainly.com/question/28823603
#SPJ5
What is the area of the figure at the right explain how you found your answer
Answer:
You have a photo to show the work?
Step-by-step explanation:
Please help me :0
What is the order of this matrix?
============================================================
Explanation:
The order of a matrix is a way of describing its size. Specifically, the order is represented in the form [tex]m \times n[/tex], where,
m = number of rowsn = number of columnsThe rows are laid out horizontally, and the columns are vertical.
In this case, we have 5 rows and 3 columns. Therefore, the answer is 5 x 3. The order is important because a 5 x 3 matrix is different from a 3 x 5 matrix.
Four movie tickets cost $48. At this rate, what is the cost of...
a. 5 movie tickets? Show your work.
b. 11 movie tickets? Show your work.
Solve for u.
–
7u–u+2u+11u=10
u=