A store is having a sale on jelly beans and trail mix. For 5 pounds of jelly beans and 3 pounds of trail mix, the total cost is $20. For 7 pounds of jelly beans and
9 pounds of trail mix, the total cost is $46. Find the cost for each pound of jelly beans and each pound of trail mix.
Cost for each pound of jelly beans:
Cost for each pound of trail mix:
Answers
Answer:
1 pound of jelly beans cost $1.75 , 1 pound of trail mix cost $3.75
Step-by-step explanation:
let j represent 1 pound of jelly beans and t represent 1 pound of trail mix , then
5j + 3t = 20 → (1)
7j + 9t = 46 → (2)
multiplying (1) by - 3 and adding to (2) will eliminate t
- 15j - 9t = - 60 → (3)
add (2) and (3) term by term to eliminate t
(7j - 15j) + (9t - 9t) = 46 - 60
- 8j + 0 = - 14
- 8j = - 14 ( divide both sides by - 8 )
j = \(\frac{-14}{-8}\) = 1.75
substitute j = 1.75 into either of the 2 equations and solve for t
substituting into (1)
5(1.75) + 3t = 20
8.75 + 3t = 20 ( subtract 8.75 from both sides )
3t = 11.25 ( divide both sides by 3 )
t = 3.75
then
cost of 1 pound of jelly beans = $1.75
cost of 1 pound of trail mix = $3.75
Answer:
Cost for each pound of jelly beans: $1.75
Cost for each pound of trail mix: $3.75
Step-by-step explanation:
Define the variables:
Let J be the cost of one pound of jelly beans.Let T be the cost of one pound of trail mix.Using the given information and defined variables, create a system of equations:
\(\begin{cases}5J+3T=20\\7J+9T=46\end{cases}\)
To solve the system of equations, multiply the first equation by 3 to create a third equation:
\(5J \cdot 3+3T \cdot 3=20\cdot 3\)
\(15J+9T=60\)
Subtract the second equation from the third equation to eliminate the term in T:
\(\begin{array}{crcrcl}&15J & + & 9T & = & 60\\\vphantom{\dfrac12}- & (7J & + & 9T & = & 46)\\\cline{2-6}\vphantom{\dfrac12} &8J&&&=&14\end{array}\)
Solve the equation for J by dividing both sides by 8:
\(\dfrac{8J}{8}=\dfrac{14}{8}\)
\(J=1.75\)
Therefore, the cost of each pound of jelly beans is $1.75.
To find the cost of one pound of trail mix, substitute the found value of J into one of the original equations and solve for T.
Using the second equation:
\(7(1.75)+9T=46\)
\(12.25+9T=46\)
\(12.25+9T-12.25=46-12.25\)
\(9T=33.75\)
\(\dfrac{9T}{9}=\dfrac{33.75}{9}\)
\(T=3.75\)
Therefore, the cost of each pound of jelly beans is $3.75.
Related Questions
when the sum of 1 and twice a negative number is subtracted from twice the square of the number, 0 results. Find the number.
Answers
Okay, here we have this:
Considering the provided information, we obtain the following equation:
\(\begin{gathered} 2x^2-\mleft(1+2x\mright)=0 \\ 2x^2-1-2x=0 \end{gathered}\)Let's solve it to find the number:
\(\begin{gathered} x_{1,\: 2}=\frac{-\left(-2\right)\pm\sqrt{\left(-2\right)^2-4\cdot\:2\left(-1\right)}}{2\cdot\:2} \\ x_{1,\: 2}=\frac{-\left(-2\right)\pm\:2\sqrt{3}}{2\cdot\:2} \\ x_1=\frac{-\left(-2\right)+2\sqrt{3}}{2\cdot\:2},\: x_2=\frac{-\left(-2\right)-2\sqrt{3}}{2\cdot\:2} \\ x=\frac{1+\sqrt{3}}{2},\: x=\frac{1-\sqrt{3}}{2} \end{gathered}\)Since the number is negative, then we are left with the second result, so finally we find that the number is:
\(x=\frac{1-\sqrt[]{3}}{2}\)How to convert 6/15 into a decimal
Answers
Answer:
0.4
Step-by-step explanation:
6 / 15 is the same as 6 ÷ 15 which is 0.4
hope this helps...
Answer: 0.4
Step-by-step explanation:
In fractions, the numerator is the number above the line and the denominator is the number below.
The line in a fraction that separates the numerator and the denominator represents division.
To convert a fraction to a decimal, divide the numerator by the denominator.
Find the percent of decrease from $60 to $48. Round the percent to the nearest tenth if necessary.
Answers
Answer: 20%
Step-by-step explanation: Basically you find the difference which is twelve, and put it over the original amount which is 60. You get 1/5 which in percent form is 20%
The percent of decrease from $60 to $48 is 20%.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Let n be the percent of decrease.
60 - 48 = 12
60n = 12
n = 12/60
n = 0.2
n = 20%
Therefore, the percent in decrease is 20%.
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The table shows a pattern of exponents. Powers of 5 Value 5 cubed 125 5 squared 25 5 Superscript 1 5 5 Superscript 0 1 5 Superscript negative 1 One-fifth 5 Superscript negative 2 StartFraction 1 Over 25 EndFraction What is the pattern as the exponents decrease? subtract 5 from the previous value subtract 100 from the previous value divide the previous value by 5 divide the previous value by 25
Answers
Answer:
C
Step-by-step explanation:
ege 2020
Answer:
divide the previous value by 5
Step-by-step explanation:
is the prime factorization of what composite number? 91 point
Answers
Answer: The question isn't clarified, what are you looking for?
Step-by-step explanation:
Answer:
The Prime Factors of 91 are 1, 7, 13, 91
Step-by-step explanation:
Please can you find the gradient of this line.
Answers
Answer:
So, gradient is 2.
Step-by-step explanation:
Here Let's take points (3,4) and (4,6)
so
gradient(m) = (y2-y1)/(x2-x1)
= (6-4)/(4-3)
= 2/1
If there are initially 5000 bacteria in a culture, and the number of bacteria triple each hour, the number of bacteria after t hours can be found using the formula y = 5000(3)^t. How long will it take the culture to grow to 80,000? Round to the nearest tenths.
Answers
Then it will take approximately 6.3 hours for the culture to grow to 80,000 bacteria
The given formula for the number of bacteria in a culture after t hours is:y = 5000(3)^tWe are required to find the number of hours it will take the culture to grow to 80,000.
This can be done by setting y equal to 80,000 and then solving for t.5000(3)^t = 80,000
Divide both sides by 5000:3^t = 16Now, we need to solve for t by taking the logarithm of both sides.
However, it is easier to use logarithmic properties to simplify the equation first.3^t = 2^4
Raise both sides to the power of (1/log3):log3(3^t) = log3(2^4)t = 4/log3(2)Using a calculator, log3(2) ≈ 0.631, so:t ≈ 4/0.631 ≈ 6.3.
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bao mom is picking him up from the ice rink she is at home which is located at the origin (0,0) how many total units is the ice rink away from the origin explain
Answers
The total units of length for the ice rink away from the origin is 14.42 units.
How to determine the distance between the coordinates for each points?In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represent the data points (coordinates) on a cartesian coordinate.
Note: Ice rink is located at point (12, 8).
By substituting the given end points into the distance formula, we have the following;
Distance = √[(12 - 0)² + (8 - 0)²]
Distance = √[(12)² + (8)²]
Distance = √[144 + 64]
Distance = √208
Distance = 14.42 units.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
is it true that George Washington LOVED political parties?
Answers
Answer:
No, It's false.
Step-by-step explanation:
In the long history of the United States, only one president, George Washington, did not represent a political party.
The central angle in a circle of radius 6 meters has an intercepted arc length of 10 meters. Find the measure of the angle in radians and in degrees
Answers
Answer:
The central angle is 5/3 radians or approximately 95.4930°.
Step-by-step explanation:
Recall that arc-length is given by the formula:
\(\displaystyle s = r\theta\)
Where s is the arc-length, r is the radius of the circle, and θ is the measure of the central angle, in radians.
Since the intercepted arc-length is 10 meters and the radius is 6 meters:
\(\displaystyle (10) = (6)\theta\)
Solve for θ:
\(\displaystyle \theta = \frac{5}{3}\text{ rad}\)
The central angle measures 5/3 radians.
Recall that to convert from radians to degrees, we can multiply by 180°/π. Hence:
\(\displaystyle \frac{5\text{ rad}}{3} \cdot \frac{180^\circ}{\pi \text{ rad}} = \frac{300}{\pi}^\circ\approx 95.4930^\circ\)
So, the central angle is approximately 95.4930°
hi gibing broonlist please please
Answers
Answer:
what??
Step-by-step explanation:
Need help!
Please explain your answer
Answers
k = (2,2)
L=(4,5)
first see the x-axis and then y-axis
Write the equation of the line below. Please help
Answers
Step-by-step explanation:
The line is a vertical line of the form x = a, where a is a real constant.
Sincw the line passes through the point (-5, 0), the line equation is x = -5.
Chris has $145.80 in his checking account. He deposits a $252.95 check in his account. The following day he fills his car with gas $44.32 and uses his debit card. He pays some bills by writing checks for $150.00 and for $84.75. What is the balance in his checking account?
Answers
Answer:
$254.68
Step-by-step explanation:
145.80+252.95-44.32-15-84.75=$254.68
A computer designer has to build a computer which can executes 300 instructions and represents integers in
\( - {10}^{14} \)
to
\( {10}^{14} \)
lf one instruction is stored in the entire memory word, what is the maximum memory capacity this computer can occupy?
Answers
The computer can occupy a maximum of 1200 bytes of memory.
To determine the maximum memory capacity of a computer that can execute 300 instructions, we need to consider the representation of integers and the storage requirements for instructions.
If each instruction is stored in the entire memory word, it implies that each instruction occupies one memory word. Therefore, the number of instructions executed (300) directly corresponds to the number of memory words required.
The memory capacity of a computer is typically measured in bytes. However, since we are assuming each instruction occupies one memory word, we can consider the memory capacity in terms of memory words.
Hence, the maximum memory capacity this computer can occupy would be 300 memory words.
To convert this capacity into bytes, we need to know the size of a memory word. If we assume the computer uses a 32-bit word size, which is common in many systems, each memory word would consist of 4 bytes (32 bits / 8 bits per byte). Therefore, the maximum memory capacity in bytes would be:
300 memory words * 4 bytes per word = 1200 bytes.
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In 2021 a 30-second commercial during the Super Bowl cost $5.6 million and the CPI was approximately 271.4. Assuming that price changes are simply due to inflation, what would the same 30 second commercial have cost during the first Super Bowl in 1967, when the CPI was 33.4? Round your answer to the nearest hundred dollars.
Answers
In 2021 a 30-second commercial during the Super Bowl cost $5.6 million and the CPI was approximately 271.4. Assuming that price changes are simply due to inflation, when the CPI was 33.4 the estimated cost of a 30-second commercial during the first Super Bowl in 1967 would be approximately $68,900.
To calculate the cost of the 30-second commercial during the first Super Bowl in 1967, we can use the concept of inflation and the Consumer Price Index (CPI).
The CPI measures the average price change of a basket of goods and services over time. By comparing the CPI values of two different years, we can estimate the relative increase in prices due to inflation.
Given data:
Cost of a 30-second commercial in 2021 = $5.6 million
CPI in 2021 = 271.4
CPI in 1967 = 33.4
To calculate the cost in 1967, we need to adjust the 2021 cost for inflation using the CPI ratio:
Cost in 1967 = (Cost in 2021) * (CPI in 1967 / CPI in 2021)
Cost in 1967 = ($5.6 million) * (33.4 / 271.4)
Cost in 1967 ≈ $0.689 million
To round the cost to the nearest hundred dollars, we can multiply the cost by 100 and round it to the nearest whole number:
Cost in 1967 ≈ $68,900
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Find the surface area
Answers
Answer: 120 yds
Step-by-step explanation:
48+30+24+18+120 yds
Multiply. Write your answer as a fraction in simplest form.
Answers
Answer: 9/11
Step-by-step explanation:
Answer:
9/11
Step-by-step explanation:
3/22 * 6/1= 18/22
18/22 divided by 2 = 9/11
Mathematical
8. PRACTICE Model Math Sarah has
32 crackers. She eats 2 and throws away 2 that
she dropped. Sarah puts the rest of the crackers
into 4 equal groups. How many crackers are
in each group?
Answers
Answer:
7
Step-by-step explanation:
32 - 2 = 30
30 - 2 = 28
From those 28 left that Sarah has left, divide by 4 to get 7 in each group remaining.
Answer:
I think 7 in each
Step-by-step explanation:
add 2 +2 Subtract 32 and 4 then divided by 4
35% percent of a number is what fraction of that number?
Answers
Answer:
The answer is 7/20 because 35% as a fraction of 7/20
The triangle above is a right triangle with side lengths a = 7 in., b = 24 in., and c = 25 in. Which statement is true? A. The sum of the squares of the two smaller sides is equal to the third side. B. The difference between the squares of the two smaller sides is equal to the square of the third side. C. The difference between the squares of the two smaller sides is equal to the third side. D. The sum of the squares of the two smaller sides is equal to the square of the third side.
Answers
Answer: D is the correct answer.
Step-by-step explanation:
The pythagoras theorum states that in a right angled triangle, the sum of the squares of the two smaller sides is equal to the square of the hypotenuse ( the largest side.)
Can someone help me with this!:)
Answers
Answer:
A-60 students
...........
Answer:
a)60 students
Step-by-step explanation:
10=X.....(eq.1st)
25=150.....(eq.2nd)
10 out of 25 were carrying lunchbox
Now,
as we compared eq. 1st and 2nd to 150student's
multiplying 150 by 10.
we have,
1,500....( eq 3rd)
25_/1,500 =60.....(divideding 1st and 3rd)
Hence,60 students have brought lunchbox
Evaluate |x - y| + 4 if x = -1, y = 3, and z = -4.
Answers
Answer:
8
Step-by-step explanation:
Substitute the values in the expression, we have:
\(\displaystyle{|-1-3|+4}\)
Evaluate:
\(\displaystyle{|-4|+4}\)
Any real numbers in the absolute sign will always be evaluated as positive values. Thus:
\(\displaystyle{|-4|+4 = 4+4}\\\\\displaystyle{=8}\)
Hence, the answer is 8. A quick note that z-value is not used due to lack of z-term in the expression.
Integrated Potato Chips paid a $2 per share dividend yesterday. You expect the dividend to grow steadily at a rate of 4 percent per year. a. What is the expected dividend in each of the next 3 years? b. If the discount rate for the stock is 12 percent, at what price will the stock sell? c. What is the expected stock price 3 years from now? d. If you buy the stock and plan to hold it for 3 years, what payments will you receive? What is the present value of those payments? Compare your answer to (b).
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
Given that:
Dividend paid (D) = $2
Growth rate (g) = 4% per annum = 0.04
Expected Dividend in each of the next 3 years :
1st year : $2 * 1.04 = $2.08
2nd year : $2.08 * 1.04 = $2.16
3rd year: $2.16 * 1.04 = 2.2464 = $2.25
B) If the discount rate for the stock is 12 percent, at what price will the stock sell?
Discount rate (r) = 12% = 0.12
Price of stock = Dividend / (r - g)
Price of stock = 2 / (0.12 - 0.04)
Price = 2 / 0.08 = $25
c. What is the expected stock price 3 years from now?
(2.25 * 1.04) / 0.08
2.34 / 0.08 = $29.25
D) If you buy the stock and plan to hold it for 3 years, what payments will you receive? What is the present value of those payments?
Dividend to be received from year 1 to 3
2.08, 2.16, 2.25
Stock price in 3rd year = 29.25
Present value :
(29.25/1.12^3) + (2.25/1.12^3) + (2.16/1.12^2) + (2.08 / 1.12^1) = 26.00
For year 1 :
D = 2.08
Stock price = 2.16/0.08 = 27
Present value (PV) = (27/1.12) + (2.08/1.12) = 25.96
Year 2 :
D = 2.16
Stock price = 2.25/0.08 = 28.125
cashflow = (2.16 + 28.125) = 30.285
PV = (28.125/1.12^2) + (2.16/1.12^2) + (2.08/1.12^1) = 26.00
Year 3:
D = 2.25
STOCK PRICE = 29.25
Total Cashflow = (2.25 + 29.25) = 31.5
PV = (31.5/1.12^3) + (2.25/1.12^3) + (2.16/1.12^2) + (2.08/1.12^1) = $27.60
The graph of the function f(x) = (x - 3)(x + 1) is shown.
Ty
-10-8-6
10
8
6
-6
8
-10-
6
10
X
Which describes all of the values for which the graph is
positive and decreasing?
O all real values of x where x < -1
O all real values of x where x < 1
O all real values of x where 1
O all real values of x where x > 3
Answers
Answer:
all real values of x where x < -1
The correct statement is all real values of x where x < -1.
Option A is the correct answer.
We have,
To determine the values for which the graph of the function
f(x) = (x - 3)(x + 1) is positive and decreasing, we need to analyze the behavior of the function.
Let's consider the factors individually:
(x - 3): This factor is positive for x > 3 and negative for x < 3.
(x + 1): This factor is positive for x > -1 and negative for x < -1.
To determine the overall sign of the function, we need to consider the signs of both factors together.
When both factors are positive or both factors are negative, the function is positive.
When the factors have opposite signs, the function is negative.
From the above analysis, we can conclude the following:
When x > 3, both factors are positive, so the function is positive.
When -1 < x < 3, the factor (x - 3) is negative, while the factor (x + 1) is positive. Therefore, the function is negative.
When x < -1, both factors are negative, so the function is positive again.
Since we are looking for values where the function is positive and decreasing, we can eliminate the options that include positive and increasing regions (such as x > 3).
Thus,
The correct statement is all real values of x where x < -1.
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Show all steps necessary to verify the trigonometric identity:
1 - 2cos^2x = 2sin^2x - 1
Answers
Step-by-step explanation:
please mark me as brainlest
Using trigonometric identity sin²θ+cos²θ=1, the given identity is proved.
The given trigonometric identity is 1-2cos²x = 2sin²x-1.
What are trigonometric identities?Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation. There are various distinct trigonometric identities involving the side length as well as the angle of a triangle.
Using trigonometric identity sin²θ+cos²θ=1
Here, 1-2cos²x = 2sin²x-1
⇒ 1+1=2sin²x+2cos²x
⇒ 2=2(sin²x+cos²x)
⇒ 2=2(1)
⇒ 2=2
LHS=RHS
Therefore, using trigonometric identity sin²θ+cos²θ=1, the given identity is proved.
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If the variance for a set of data equals 8.1, find the standard deviation.
Answers
The standard deviation for this set of data is approximately 2.85.
To find the standard deviation, we first need to take the square root of the variance. Therefore, the standard deviation for the given data set is the square root of 8.1, which is approximately 2.846.
To find the standard deviation of a set of data when the variance is given, you simply need to take the square root of the variance. In this case, the variance equals 8.1.
Step 1: Identify the variance, which is 8.1.
Step 2: Take the square root of the variance.
Standard Deviation = √(Variance) = √(8.1)
Step 3: Calculate the square root of 8.1.
Standard Deviation ≈ 2.85
So, the standard deviation for this set of data is approximately 2.85.
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Write an equivalent expression by distributing the "
"sign outside the parentheses:
-(0.3h + 4k –3
Answers
Hi there!
»»————- ★ ————-««
I believe your answer is:
\(-0.3h-4k+3\)
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
\(-(0.3h+4k-3)\\------------\\-1 * 0.3h = -0.3h\\\\-1 * 4k = -4k\\\\-1 * -3 = 3\\\\\\-(0.3h+4k - 3) \rightarrow \boxed{-0.3h-4k +3}\)
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Using Company A's calling plan, the cost of an overseas phone call is a $0.85 connection fee plus 28 cents per minute. If the total cost of the call is $14.85, how long is the phone call?
Answers
Answer:
50 minutes
Step-by-step explanation:
28 cents = $0.28
Let the call be for x minutes
Total cost = connection fee + x*cost per minute
14.85 = 0.85 + 0.28x
14.85 - 0.85 = 0.28x
0.28x = 14
x = 14/0.28
x = 50
Answer:
50 min
Step-by-step explanation:
Let the call be for x minutes
14.85 = 0.85 + 0.28x
0.28x = 14
x = 14/0.28 = 50
What is 2x2 + 1000 x 1000
Answers
Answer: 2x2 + 1000 x 1000 = 1000004
Step-by-step explanation: you add on 5 0's to the one and 2x2 = 4 so add on the 4 also
Answer:
1000004
Step-by-step explanation:
First we do can separate it into the parentheses: (2*2) + (1000*1000)
= 4 + 1000000
= 1000004