By setting up a system of equations and solving them, we find that the cost per pound of almonds is $1.50, and the cost per pound of jelly beans is $2.00.
To find the cost for each pound of almonds and each pound of jelly beans, we can set up two equations to solve the problem algebraically. Let's denote the cost per pound of almonds as a and the cost per pound of jelly beans as b. We have two scenarios provided:
8 pounds of almonds and 3 pounds of jelly beans cost a total of $18.
2 pounds of almonds and 5 pounds of jelly beans cost a total of $13.
We can translate these scenarios into two algebraic equations:
8a + 3b = 18
2a + 5b = 13
Now, we will solve this system of equations to find the values of a and b.
Step 1: Multiply Equation (2) by 4
8a + 20b = 52 (We multiplied all terms by 4 to match the coefficient of a in Equation (1))
Step 2: Subtract Equation (1) from the new equation
8a + 20b - (8a + 3b) = 52 - 18
17b = 34
Step 3: Solve for b
b = 34 / 17
b = 2
Now we know each pound of jelly beans costs $2.
Step 4: Substitute b back into Equation (1) to solve for a
8a + 3(2) = 18
8a + 6 = 18
8a = 12
a = 12 / 8
a = 1.5
So, each pound of almonds costs $1.50.
Therefore, the cost per pound of almonds is $1.50, and the cost per pound of jelly beans is $2.00.
what is the square root of 61 to the nearest integer?
1. Graph the system of inequalities.
–2x + 3y ≥ –12
x + y < 3
how do i graph on a word doc?
see attached picture of how graph should look.
search through word for a graph icon, you should be able to do this in Word.
What is 12/7 written as a mixed number in simplest form
The floor of a conference hall can be covered completly with tiles.Its length is 36ft. longer than its width.The area of the floor is less than 2040square ft.How would you represent the with of the floor?How about its lenght?What mathematical sentence would represent the given situation?What are the possible dimensions of the floor?How about the possible areas of the floor?Would it be realistic for the floor to have an area of 144sq.ft?Explain your answer.
W<30; The width of the floor will be less than 30feet
The possible area of the floor is 1885 sq. ftSince 144 sq.ft ≠ 1885feet², hence it would not be realistic for the floor to have an area of 144sq.ft
The formula for calculating the area of the conference floor is expressed as:
A = LW
L is the length
W is the width
If the length is 36ft. longer than its width, hence;
L = W+36
Since the area of the floor is less than 2040 square feet, hence;
A < 2040
LW < 2040
(W+36)W < 2040
W² + 38W < 2040
W² + 38W - 2040 < 0
W² + 68W - 30W - 2040 < 0
W(W+68)- 30(W+68)< 0
(W-30)(W+68) < 0
W - 30 < 0 and W < -68
W < 30
Since the width cannot be negative, hence the width of the floor will be less than 30feet
Since L = 36 + W
L < 36 + 30
L < 66feet
The length of the floor will be less than 66feet
The possible dimensions area 29feet by 65feet since the width is less than 30 and the length is less than 66feet.
Get the possible area:
Possible area = 29 × 65
Possible area = 1885feet²
Since 144 sq.ft ≠ 1885feet², hence it would not be realistic for the floor to have an area of 144sq.ft
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A coin is tossed 6 times. what is the probability of getting at least one head? express your answer as a fraction or a decimal number rounded to four decimal places.
Final answer:
The probability of getting at least one head in six coin tosses is 1 minus the probability of getting tails on all tosses, resulting in a probability of 98.44% when rounded to four decimal places.
Explanation:
The question is about calculating the probability of getting at least one head when a coin is tossed six times. Rather than calculating the probability of at least one head directly, it's simpler to calculate the probability of the opposite event—getting no heads—which is the same as getting tails on all six tosses. Since the probability of flipping a tail on each toss is 0.5, the probability of flipping six tails in a row is (0.5)⁶, which equals 0.015625. Therefore, the probability of getting at least one head is 1 minus the probability of getting no heads, which is 1 - 0.015625, resulting in 0.984375 or 98.44% when rounded to four decimal places.
PLEASE HELP!!
(x-7)^3 (x+2)^2 (x-13) <0
solve the equation c²=4
Answer:
c = 2, c = -2
Step-by-step explanation:
The question is asking us to solve the equation [tex]\sf{c^2=4}[/tex].
To solve it, we take the square root of each side. Note that once we do this, we will have 2 solutions.
[tex]\sf{\sqrt{c^2}=\sqrt{4}}[/tex]
[tex]\sf{c=2,c=-2}[/tex]
Therefore, this equation has two solutions, which are c = 2 and c = -2.
When one thing is ten times as large as another, it is said to be "an order of magnitude" larger. a hundred times larger is two orders of magnitude. a thousand is three orders of magnitude. by how many orders of magnitude is the empire state building taller than a chair seat?
Does adding zero to a number ever change its value? what is this property called?
What are the coordinates of the point (2, −3) after a counterclockwise rotation of 90° about the origin?
(3, 2)
(−3, −2)
(−2, 3)
(−3, 2)
Answer:
(2,-3) changes to (3,2)
A is correct.
Step-by-step explanation:
Given: The point (2, −3) after a counterclockwise rotation of 90° about the origin.
[tex]R_{90\circ}(x,y)\rightarrow (-y,x)[/tex]
Rotation is counterclockwise about origin.
[tex](x,y)\rightarrow (-y,x)[/tex]
We are given coordinate
[tex](2,-3)\rightarrow (3,2)[/tex]
We can see in diagram also. Please see the attachment for rotation.
Hence, (2,-3) changes to (3,2)
Answer:
Point would be (3,2).
Step-by-step explanation:
Given: point (2, −3) after a counterclockwise rotation of 90° about the origin.
To find: What are the coordinates after rotation.
Solution: We have given that point (2, −3).
By transformation rotation 90° (x,y)→→→(-y,x).
Then point (2, −3) would be (-(-3),2) .
Then (3 ,2)
Therefore, Point would be (3,2).
Jennifer and Margaret have to make brownies for a bake sale. Jennifer can bake a dozen brownies in 20 minutes and Margaret can bake 15 brownies every half hour. Jennifer bakes for 1 hour and 40 minutes and Margaret bakes for 2 hours. How many brownies do the girls have for the sale altogether?
How long will it take to have R30 000 for a trip to Europe if I invest R20 000 now at 15% per year, compounded quarterly?
Compound interest formula
[tex]A=P(1+ \frac{r}{n} )^{nt} [/tex]
Where
A= Future value
P =
the Principal (the initial amount of money)
r = annual interest rate
t = time
n= number of times compounded in one tA= 30 000
P =20 000
r = 15%=0.15
time = t = ?
n= 4What is the sum of 2.5 × 10^4 and 3.4 × 10^4?
If the highest score in a distribution is x = 16 and the lowest is x = 4, then the range is 12 or 13 points.
a. True
b. False
The range in the given scenario is only 12 points, not 12 or 13 points as mentioned.
False
Range = Highest score - Lowest score
Range = 16 - 4 = 12
Therefore, the range can only be 12 points.
Evaluate the function at the given value of the independent variable and simplify f(x)= x^2 + 1
What is the solution of 7<5-2x<17
The standard recommendation for fluid needs is 30 ml/kg body weight. parker weighs 67 kg. how many cups of fluid will he need? (give your answer to the nearest tenth. give only the value. do not write the word cup or its abbreviation.)
what is the midpoint coordinates of segment HX H(13,8) X(-6,-6)
If 3.485 ÷ 5.1 is written in long division form as so that the divisor is written as a whole number, where should the decimal point be placed in the dividend
Can somebody help me with this one?
What is 60% of 7?????
60% = 0.60
7*0.6 = 4.2
Evaluate. 62+(3⋅4)−24 Enter your answer in the box. plz help mehh someone out there ty
The value of expression 62+(3⋅4)−24 is 50
What is PEMDAS ?
A rule of operations explains the correct order in which math expressions should be evaluated, and we can remember those steps using PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Here, the expression is given as 62+(3⋅4)−24 now using PEMDAS rule to solve this expression first by solving under bracket terms 3x4 = 12 and then adding 62 and 12, then subtract it by 24 to get the final answer.
62+(3⋅4)−24
62 + 12 -24
74 - 24
50
Therefore, the value of expression 62+(3⋅4)−24 is 50
Read more about additive identity at:
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Gth of a square tile is 8.0cm what is the approximatenlength of the tile in inches
S=p-0.2t solve for p
Answer:
The required equation is [tex]S+0.2t=p[/tex]
Step-by-step explanation:
Consider the provided equation.
[tex]S=p-0.2t[/tex]
We need to solve the equation for p.
Isolate the variable as shown.
Add 0.2t from both sides.
[tex]S+0.2t=p-0.2t+0.2t[/tex]
[tex]S+0.2t=p[/tex]
Hence, the required equation is [tex]S+0.2t=p[/tex]
I need help 2/3 - 4/10
A 0.5-kg ball accelerated at 50 m/s2 . What force was applied?
To make the bowling team. Jacques needs a three-game average of 160. If he bowled 141 and 162 for the first two games, what score S must be obtained in the third game so that his average is at least 160?
What is the domain of 2x+5
Examine the work shown. Explain the error and find the correct result.
2(4 – 16) – (–30)
2(–12) – (–30)
24 – (–30)
54
The error is in third step where 2(–12) is -24 and not 24 thus the correct result is 6.
What is an expression?An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.
Now the given expression is,
2(4 – 16) – (–30)
solving the bracket,
2(–12) – (–30)
expanding the bracket we get,
-24 – (–30)
this is the error in the given work where 2(–12)– (–30) = 24– (–30)
Thus open the bracket,
-24 + 30
solving we get,
6
which is the correct answer.
Thus, the error is in third step where 2(–12) is -24 and not 24 thus the correct result is 6.
To learn more about expressions:
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What is the conclusion in this conditional statement?
If a square has a perimeter of 8 units, then its sides have a length of 2 units each.
the square has a perimeter of 8 units
the sides of the square have a length of 2 units each
Submit
The conclusion in the given conditional statement is that the sides of the square have a length of 2 units each. This is deduced from the formula for the perimeter of a square (P = 4 × side length), and the given perimeter of 8 units.
Explanation:The conclusion in the conditional statement "If a square has a perimeter of 8 units, then its sides have a length of 2 units each" is the sides of the square have a length of 2 units each.
In a conditional statement, the "if" part is known as the hypothesis and the "then" part is the conclusion. Given that a square's perimeter is the sum of the lengths of all four sides, we can show this through an equation: P = 4 × s, where P represents the perimeter and s the length of one side. Since the perimeter is given as 8 units, we can solve for s by dividing the perimeter by 4: 8 units = 4 × s, which simplifies to s = 2 units. Therefore, each side of the square must be 2 units long.
Final answer:
The conclusion in this conditional statement is that the sides of the square have a length of 2 units each.
Explanation:
The conclusion in this conditional statement is:
The sides of the square have a length of 2 units each.
In a conditional statement of the form 'if A, then B', the conclusion (B) is the statement that follows 'then'. In this case, the conclusion states that the sides of the square have a length of 2 units each.