It costs 11$ for 15 granola bars.
What is the unit price, in dollars per granola bar, rounded to the nearest hundredth?
Answers
Answer:
Each granola bar costs $0.73.
Step-by-step explanation:
11/15 = 0.73
Related Questions
The map of a biking trail is drawn on a coordinate grid. The trail starts at P(−6, 3) and goes to Q(3, 3). It goes from Q to R(3, −4) and then to S(6, −4). What is the total length (in units) of the biking trail?
Answers
Answer:
total length = 19 units
Step-by-step explanation:
Notice that the distance between the extremes of the first segment of the trail, is a horizontal segment of 9 units length.
The second segment from (3,3) to (3, -4) is vertical one of length 3 - -4 = 7 units.
The third segment of the trail from (3, -4) to (6, -4) is another vertical segment of length 6=3 = 3 units.
Therefore,the total length of the trail is 9 + 7 + 3 = 19 units
calculate the number of ways that the coach can assign the 4 positions to his 16 players.
Answers
The number of ways that the coach can assign the 4 positions to his 16 players would be 43, 680 ways
How to calculate the permutation
The formula for permutation is given as;
Permutation = \(\frac{n!}{(n - r)!}\)
n = 16
r =4
Permutation = \(\frac{16!}{12!}\)
Permutation = \(\frac{16 *15*14*13*12*11*10*9*8*7*6*5*4*3*2*1}{12*11*10*9*8*7*6*5*4*3*2*1}\)
Permutation = 43, 680 ways
Thus, the number of ways that the coach can assign the 4 positions to his 16 players would be 43, 680 ways
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Your parents have a credit card with a balance of $3,287.90 at an interest rate of 14.5% APR. They pay $1,200.00 each month on the due date until the card is paid off. How many months does it take to pay off the card, and what is the total amount paid including interest?
Be sure to include in your response:
• the answer to the original question
• the mathematical steps for solving the problem demonstrating mathematical reasoning
Answers
Given statement solution is :- It takes 4 months to pay off the card, and the total amount paid, including interest, is $4,871.78.
To find out how many months it takes to pay off the credit card and the total amount paid including interest, we can use the following steps:
Step 1: Calculate the monthly interest rate
Divide the annual percentage rate (APR) by 12 to get the monthly interest rate.
Monthly interest rate = 14.5% / 12 = 0.145 / 12 = 0.01208 (rounded to 5 decimal places)
Step 2: Set up the equation for the number of months
Let's denote the number of months it takes to pay off the card as 'n'. The monthly payment is $1,200.00, and the initial balance is $3,287.90. The monthly interest rate is 0.01208. The equation for the number of months can be written as:
(1) $3,287.90 ×\((1 + 0.01208)^n\) - $1,200.00 ×\([(1 + 0.01208)^n\) - 1] = 0
Step 3: Solve the equation
To find the value of 'n', we need to solve equation (1). However, solving it algebraically can be complex. Instead, we can use numerical methods like trial and error, or we can use a spreadsheet or a calculator to find the solution.
Using a spreadsheet or a calculator, we can input the values and increment 'n' until we find the point where the equation equals zero.
After performing the calculations, it is determined that it takes approximately 4 months to pay off the card, and the total amount paid, including interest, is $4,871.78.
Therefore, the answer to the original question is that it takes 4 months to pay off the card, and the total amount paid, including interest, is $4,871.78.
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Fill in the table of value for the equation y = 2x + 1
Answers
Answer:
To fill in the table of values for the equation y = 2x + 1, we can choose different values of x and substitute them into the equation to find the corresponding values of y. For example:
x y
0 1
1 3
2 5
3 7
4 9
To get the value of y, we substitute each value of x into the equation and simplify:
When x = 0:
y = 2(0) + 1 = 1
When x = 1:
y = 2(1) + 1 = 3
When x = 2:
y = 2(2) + 1 = 5
When x = 3:
y = 2(3) + 1 = 7
When x = 4:
y = 2(4) + 1 = 9
Therefore, the table of values for the equation y = 2x + 1 is:
x y
0 1
1 3
2 5
3 7
4 9
of 10
Colin invests £980 into his bank account. He receives 6% per year simple
interest. How much will Colin have after 7 years? Give your answer to the nearest
penny where appropriate.
Answers
Answer:
1008.56
Step-by-step explanation:
0.06nmultiplied by £980 = £4.08
4.08 multiplied by 7 (the number of years = 28.56
then £28.56+£980=1008.56
Answer:
There is a formula that you need to use to answer this question.
(using calculator)
original × (100×rate/100)^years
\(980( \frac{100 + 6}{100}) {}^{2} \)
= £1101.1
Which equation represents a circle with a center located at (-2,2) and a circumference of 16π
Answers
Solve the system of equationsy=-2x-3 y=2x^2+4x-1Round to the nearest hundredth
Answers
Given:
\(y=-2x-3\)\(y=2x^2+4x-1\)Requires:
We need to solve the given system of equations.
Explanation:
Consider equation.
\(y=2x^2+4x-1\)\(Substitute\text{ }y=-2x-3\text{ in the equation to find the value of x.}\)\(-2x-3=2x^2+4x-1\)Add 2x+3 to both sides of the equation.
\(-2x-3+2x+3=2x^2+4x-1+2x+3\)\(0=2x^2+6x+2\)\(2x^2+6x+2=0\)Divide both sides of the equation by 2.
\(\frac{2x^2}{2}+\frac{6x}{2}+\frac{2}{2}=\frac{0}{2}\)\(x^2+3x+1=0\)Which is of the form
\(ax^2+bx+c=0\)where a=1, b=3, and c =1.
Consider the quadratic formula.
\(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)Substitute a=1, b=3, and c =1 in the equaiton.
\(x=\frac{-3\pm\sqrt{3^2-4(1)(1)}}{2(1)}\)\(x=\frac{-3\pm\sqrt{9-4}}{2}\)\(x=\frac{-3\pm\sqrt{5}}{2}\)\(x=\frac{-3\pm\sqrt{5}}{2}\)The arithmetic mean of 25, 29, and x is 29. Find x.
Answers
Explanation/work:
Equation:
(25 + 29 + x)/3 = 29
Multiply 3 to both sides
25 + 29 + x = 87
Combine like terms
54 + x = 87
Subtract 54 from both sides
x = 33
Answer:
x = 33
Step-by-step explanation:
The arithmetic mean is equal to the sum of values divided by the number of values (3 in this case)
\( \frac{25 + 29 + x}{3} = 29\)
Use the property of the proportion (cross-multiply) to find x:
\(25 + 29 + x = 3 \times 29\)
\(54 + x = 87\)
\(x = 87 - 54\)
\(x = 33\)
If y=1/5 when x=2, find y when x=3, given that y varies directly with x
Answers
Answer:
\(y=\frac{3}{10}\)
Step-by-step explanation:
\(\frac{0.2}{2} :\frac{y}{3}\)
2 × y = 0.2 × 3
2y = 0.6
2y ÷ 2 = 0.6 ÷ 2
y = 0.3
how do i solve for m in i=pm
Answers
We have the expression
\(i=p\cdot m\)To solve it for m, we divide both sides by p:
\(\begin{gathered} i=p\cdot m \\ \frac{i}{p}=\frac{p}{p}\cdot m \\ m=\frac{i}{p} \end{gathered}\)The resulting equation is m = i/p.
5^-2 + 7^0
PLSSS HELP MEEE IM IN SCHOOL RIGHT NOW
Answers
TRY THIS
Step-by-step explanation:
Step-by-step explanation:
Given
\( {5}^{ - 2} + {7}^{0} \\ = \frac{1}{ {5}^{2} } + 1 \\ = \frac{1}{25} + 1 \\ = \frac{1 + 25}{25} \\ = \frac{26}{25} \)
Hope it will help :)❤
Last year Bobs market ordered 5 2/3 cups of strawberries for an event. This year they plan to order 6 1/2 times as many strawberries as they did last year as well as 1/6 of a cup of blueberries. Then they are going to mix the berries together and sell them in 6 ounce bags. How many complete bags can they sell if they use all the berries?
Answers
Since we cannot have a fraction of a bag, Bob's market can sell a total of 41 complete bags of mixed berries.
How to find How many complete bags can they sell if they use all the berriesLast year, Bob's market ordered 5 2/3 cups of strawberries. This year, they plan to order 6 1/2 times as many strawberries as last year.
Therefore, the quantity of strawberries this year is:
Strawberries = 5 2/3 cups * 6 1/2 = (17/3) cups * (13/2) = (221/6) cups.
They also plan to order 1/6 of a cup of blueberries.
Total berries = Strawberries + Blueberries = (221/6) cups + (1/6) cups = (222/6) cups.
Since they want to sell the berries in 6-ounce bags, we need to convert the cup measurement to ounces.
1 cup = 8 ounces.
Total berries = (222/6) cups * 8 ounces/cup = (1488/6) ounces = 248 ounces.
Now, we can find the number of complete 6-ounce bags they can sell:
Number of bags = Total ounces / 6 ounces = 248 ounces / 6 ounces = 41.3333.
Since we cannot have a fraction of a bag, Bob's market can sell a total of 41 complete bags of mixed berries.
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Draw the net and calculate the surface area .
Answers
Hello!
surface area
= 2(4 x 2) + 2(12 x 4) + 2(12 x 2)
= 160cm²
Complete the sentence. The solutions of 0 = |4x + 2| −10 are x = −2 and x = −3. x = −2 and x = 3. x = 2 and x = −3. x = 2 and x = 3.
Answers
Answer:
x = 2 and x = −3.
Step-by-step explanation
i solved it
solve for x
plss help
Answers
Answer:
2
Step-by-step explanation:
These two are similar triangles. 3 corresponds to 9, and x corresponds to 6. Since 3 is being multiplied by 3 to get 9, x*3 should equal 6. Therefore, x is 2.
Write an equation of the line that passes through point P and is parallel to the line with the given equation.
P(1,1) , y=-2x+4
Answers
Answer:
y = -2x + 3.
Step-by-step explanation:
y - 1 = -2(x - 1)
y = -2x + 2 + 1
y = -2x + 3.
how the hell do i do it #underpressure
Answers
Answer:
8 more red counters
Step-by-step explanation:
It would make it 9:3, which, when simplified, is 3:1.
A recipe for chocolate chip cookies calls for 4 cups of flour and 3 tablespoons of brown sugar. How many tablespoons of brown sugar would be needed if the amount of flour were increased to 12 cups? PLZ i'll pay well
Answers
Answer:
it will be increased to 6 tablespoons more so it will be 9 tablespoons in total
Step-by-step explanation:
12 divided by 4 is 3
so 3 x 3 is 9
9 tbsp i total of brown sugar
100 Points! Multiple choice Geometry question. Photo attached. Thank you!
Answers
Answer:
2. C. 50.3 ft²
3. A. 75.4 ft²
Step-by-step explanation:
The lateral surface area of a cylinder is the area of the curved surface of the cylinder. It is calculated by multiplying the circumference of the base by the height of the cylinder. The formula for the lateral surface area of a cylinder is:
Lateral Surface Area = 2πrh
Where:
r is the radius of the baseh is the height of the cylinderThe total surface area of a cylinder is the area of the lateral surface plus the area of the two circular bases. The formula for the total surface area of a cylinder is:
Total Surface Area = 2πrh + 2πr^2
Where:
r is the radius of the baseh is the height of the cylinder2.
r=2 ft
h=4 ft
Lateral Surface Area = 2πrh=2*22/7*2*4=50.3 ft²
3.
Total Surface Area = 2πrh + 2πr^2=2*22/7*2*4+2*22/7*2
=50.3+25.1=75.4 ft²
Magician Anthony has in his magic hat 14 grey, 8 white and 6 black mice. What is
the least number of mice he has to take out of his hat blindfolded to be absolutely
certain that he has got at least one mouse of each colour?
Answers
The least number of mice that he has to take out of his hat would be 23.
How to solve for the least number of miceWe have the following details to solve this problem
x = 14
t = 8
u = 6
n1 = x + t + 1
= 14 + 8 + 1 = 23
n2 = t + u + 1
= 8 + 6 + 1 = 15
n3 = x + u + 1
= =14+6+1=21
From here the
max n (n1, n2, n3) = 23, 15, 21
Hence the least number that has to be taken out would be 23.
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In the figure, the angles are formed by a transversal and two parallel lines. Which angles seem to be congruent?
Answers
The angles are formed by a transversal and two parallel lines in the figure. By applying congruent angles and vertical opposite angle property, ∠1 ≅∠3 ≅ ∠5 ≅ ∠7; ∠2 ≅ ∠4 ≅ ∠6 ≅ ∠8. Therefore option B is correct.
Congruent angles are identical to each other and have the same measure. The angles formed by the transversal in corresponding corners are called corresponding angles and they are congruent.
Therefore, ∠1 ≅ ∠5, ∠3 ≅ ∠7----------(1)
At a vertex if two angles are opposite to each other, then they are vertically opposite angles, they are equal and congruent to each other.
Therefore, ∠1 ≅ ∠3, ∠5 ≅ ∠7----------(2)
Combining (1) and (2), we get:
∠1 ≅∠3 ≅ ∠5 ≅ ∠7
Similarly we can find,
∠2 ≅ ∠4 ≅ ∠6 ≅ ∠8.
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If an interior angle of a regular polygon has a measure of 120 degrees, how many sides does it have?
Answers
Step-by-step explanation:
The formula to find the interior angle of a polygon is 180(n - 2) over n.
So, we know that the interior angle of the polygon which is 120, therefore we can produce this equation, 180(n - 2) over 2 n, equals to 120.
Now we use algebric method to solve for n.
180n − 360 = 120n
60n = 360
n = 6
So, the answer is = 6 sidesA single fair die is tossed. Find the probability of rolling a number greater than 5
Answers
Using the probability concept, the odds of rolling a number greater than 5 is 1 :5
What is probability ?
probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur or how likely it is that a proposition is true . the probability of an event is a number between 0 and 1 , where ,roughly speaking ,0 indicates impossibility of the event and 1 indicates certainty.
The odd of a particular experiment is defined thus :
Number of possible outcomes greater than 5 : number of possible below or equal to 5
Sample space = {1, 2, 3, 4, 5, 6}
Outcomes greater than 5 = {6} = 1
Outcomes below or equal to 5 = {1, 2, 3, 4, 5} = 5
The odds equals to 1 : 5
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PROBLEM I: On Monday the temperature was 70° F. On Tuesday the temperature dropped 10°,
followed by a 5º decrease on Wednesday. On Thursday, the temperature increased 7 degrees followed by a
decrease of 2 degrees on Friday. What was the final temperature on Friday?
Number Sentence:
Solution:
Answers
Answer:
Answer 60 degrees
Step-by-step explanation:
70-10 60-5 55+7 62-2 60
Candle Burning
10
y
9
8
The slope of the graph is -1. Which statement
describes how the slope is related to the burning of a
candle?
O candle height increases 1 cm per hour
O candle height decreases 9 cm per hour
O candle is 1 cm tall
O candle burns down 1 cm per hour
7
Candle Height (cm)
1
2 3 4 5 6 7 8
Hours Burned
101
Answers
Answer:
Candle burns down 1 cm per hour
I’m doing the assignment!
The correct statement that describes how the slope is related to the burning of a candle is "Candle burns down 1 cm per hour."
The correct option is D.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
The statement "The slope of the graph is -1" indicates that for each unit of increase in the horizontal variable (e.g. time), the vertical variable (e.g. height of the candle) decreases by 1 unit.
Therefore, the correct statement that describes how the slope is related to the burning of a candle is "Candle burns down 1 cm per hour."
Option A ("Candle height increases 1 cm per hour") and option C ("Candle is 1 cm tall") are not consistent with a negative slope.
Option B ("Candle height decreases 9 cm per hour") is not consistent with a slope of -1, as it implies a steeper slope.
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In two sample surveys 125 people were asked about their favorite fruit in the survey 40 people chose apples 64 choose oranges and 21 chose bananas in the second 34 chose apples 63 chose oranges 19 Joe’s banana marine inferred before is this a French trooper by us on the data explain
Answers
Answer:
Marianne made an inference that is true based on the data. More than half of the people surveyed in each sample chose oranges as their favorite fruit. Since most people in each sample chose oranges, it is likely that oranges are the favorite fruit of the entire population.
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1. Use the elimination strategy to solve this linear system:
(1) 12c + 28d = 12 (2) -20c + 16d = 168
2. Determine the number of solutions of this linear system:
(1) 7x − 3y = 43 (2) 7x - 3y = 13
Answers
The solution to the linear system is c = -6 and d = 3.
To solve the linear system using the elimination strategy, we can eliminate one variable by adding or subtracting the equations. Let's solve the first linear system:
(1) 12c + 28d = 12
(2) -20c + 16d = 168
To eliminate one variable, we can multiply equation (1) by 5 and equation (2) by 3, which will result in opposite coefficients for 'c'. This will allow us to eliminate 'c' when adding the equations together:
(1) 60c + 140d = 60
(2) -60c + 48d = 504
Now, we can add the equations:
(60c + 140d) + (-60c + 48d) = 60 + 504
188d = 564
d = 564/188
d = 3
Substituting the value of 'd' back into equation (1):
12c + 28(3) = 12
12c + 84 = 12
12c = 12 - 84
12c = -72
c = -72/12
c = -6
The solution to the linear system is c = -6 and d = 3.
Now let's analyze the second linear system:
(1) 7x - 3y = 43
(2) 7x - 3y = 13
By comparing the two equations, we can see that they have the same coefficients for both 'x' and 'y', and the constant terms on the right side are different. This means the lines represented by the equations are parallel and will never intersect.
The linear system has no solution.
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IS THIS RIGHT? (28 points easy!!)
Answers
Step-by-step explanation:
yes, the step is correct.
a² = cx | multiply by c
ca² = c²x
I am just not sure how that simplified the equation.
what do you want to achieve ? what's the goal here ?
to solve the equation for x it would be to divide both sides by c, which gives
a²/c = x
y=9/4×2
sketch the graph of f and f on the same set of axes
Answers
The graph of the function \(f(x) = (9/4)x^2\) is a symmetric upward-opening parabola.
The graph represents a parabola that opens upward. As x increases, the corresponding y-values increase, forming a curved shape. The vertex of the parabola is at the origin (0,0). The graph is symmetric with respect to the y-axis, meaning that the left and right sides of the parabola are mirror images of each other.The slope of the graph gradually increases as x moves away from the origin. The steepness of the curve becomes more pronounced, indicating a faster rate of increase in y-values for larger x-values.The graph does not intersect the x-axis, indicating that there are no real roots or solutions for the equation f(x) = 0. The y-intercept of the graph is at (0, 0), and the y-values increase indefinitely as x approaches positive or negative infinity.Overall, the graph represents a quadratic function with a positive leading coefficient, resulting in an upward-opening parabolic curve. The graph has been attached.
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A choir is performing in front of an audience. A microphone is placed in front of the choir to capture sound.Which polar equation reprsents the microphone the choir is using?
Answers
Answer:
D on Edge.
Step-by-step explanation:
Got it right.
The polar equation represents the microphone the choir is using ; D. r = 2 + cos(θ)
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
It is given that a choir is performing in front of an audience. A microphone is placed in front of the choir to capture sound.
The polar equation represents the microphone the choir is using would be;
D. r = 2 + cos(θ)
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