Simplify and write the answer as product of powers of prime numbers:

The group needs to sell at least 104 granola bars and any number of bottles of water in order to make a profit of at least $150.

The correct inequality is B. 1.4x + 0.75y ≥ 150. This inequality states that the group must sell at least $150 worth of items in order to make a profit. The cost of a granola bar is $1.40, and the cost of a bottle of water is $0.75. Therefore, the total cost of the items must be greater than or equal to $150. The formula for this inequality is 1.4x + 0.75y ≥ 150, where x represents the number of granola bars sold and y represents the number of bottles of water sold.

To solve this inequality, we can first multiply both sides of the inequality by 100. This will give us 140x + 75y ≥ 15000. Next, we can subtract 75y from both sides to get 140x ≥ 14250. Finally, we can divide both sides of the equation by 140 to get x ≥ 102.86. This means that the group needs to sell at least 103 granola bars in order to make a profit of at least $150. This can be further simplified by rounding up the granola bars sold to 104. Therefore, the group needs to sell at least 104 granola bars and any number of bottles of water in order to make a profit of at least $150.

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Answer:

its 67...... ...........

Answer:

it's 67°

Step-by-step explanation:

48°+90°=(2x+4). reason is vertically opposite angles are equal

The measure of angle DAB in the given quadrilateral can be calculated as: 109°.

To find the measure of an angle in a quadrilateral, you need to use the fact that the sum of all angles in a quadrilateral is always equal to 360 degrees.

Using the above fact stated, we can add up the three known angles in the given quadrilateral and then subtract it from 360 degrees to find the measure of angle DAB.

Thus, we have:

m<DAB = 360 - (90 + 97 + 64)

m<DAB = 360 - 251

m<DAB = 109°

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Answer:

$12 per hour multiplied by 22 hours = $264

Step-by-step explanation:

Dont overthink it... The question basically is: What is the total pay for someone working 22 hours (straight time) at $12. per hour?

Answer: Cindy is 7

Step-by-step explanation:

Alice is 21

Barbie is 16

Some acceptable board lengths are: 15.8 ft, 16.20 ft and 16.10 feet

Now, According to the question:

Board lengths that should be accepted

From the question, we have the following parameters that can be used in our computation:

Length = 16 ft

Percent error = 1.5%

This means that the acceptable lengths are

Acceptable = Length ± Percent error * Length

Substitute the known values in the above equation, so, we have the following representation

Acceptable = 16 ± 1.5% * 16

So, we have

Acceptable = 16 ± 0.24

Evaluate

Acceptable = 15.76 to 16.24

Some board lengths that should be accepted are 15.8 ft, 16.20 ft and 16.10 feet

Board lengths that should be rejected

In (a), we have

Acceptable = 15.76 to 16.24

Some board lengths that should be rejected are 14.8 ft, 17.20 ft and 12.10 feet

The intended lengths of the boards

Here, we have

Lengths = 10, 12 and 14 feet

Length too long = 2.3 inches

Convert to inches

Length too long = 0.19

So, we have

Intended lengths = (10, 12 and 14 feet) + 0.19

Evaluate

Intended lengths = 10.19, 12.19 and 14.19 feet

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Answer:

16 months

Step-by-step explanation:

Hey there!

This would be the correct answer because first you need to subtract the amount she paid from the amount she owes.

\(4500-2740\)

\(=1760\)

After that divide that answer from 110

This is because she will be paying 110 each month

\(1760/110\)

Once you calculate that you will get 16.

Answer:

As shown in picture:

A(-4, 1)

Z(-2, 3)

P(3, -4)

The length of AZ is calculated by:  

L = sqrt((-4 - -2)^2 + (1 - 3)^2) = 2.83

The length of AP is calculated by:

L = sqrt((3 - -4)^2 + (-4 - 1)^2) = 8.60

THe length of ZP is calculated by:

L = sqrt((3 - -2)^2 + (-4 - 3)^2) = 8.60

=>Perimeter of triangle AZP is calculated by:

P = AZ + AP + ZP = 2.83 + 8.60 + 8.60 = 20.3

Hope this helps!

:)

a. The simultaneous linear equations for the given scenario in the form of ax + by = c are:

Demand equation: 5x + 3y = 30

Supply equation: 52x - 30y = -45

b. To solve the simultaneous equations using the matrix method, we can rewrite the equations in matrix form as AX = B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.

The coefficient matrix A:

| 5  3 |

| 52 -30 |

The variable matrix X:

| x |

| y |

The constant matrix B:

| 30 |

| -45 |

To find the equilibrium quantity and price, we can solve the system of equations AX = B by finding the inverse of matrix A and multiplying it with the matrix B. The solution is given by X = A^(-1) * B.

After performing the matrix calculations, we find that the equilibrium quantity (x) is approximately 0.66 thousand units, and the equilibrium price (y) is approximately $3.70 per unit.

Therefore, the equilibrium quantity is 0.66 thousand units, and the equilibrium price is $3.70 per unit.

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Answer:

Area = 54 cm

Step-by-step explanation:

Using the formulas

A=6a2

V=a3

Solving forA

A=6V⅔=6·27⅔≈54

Answer:

-15

Step-by-step explanation:

0)(2)+(2)(0)−15

=−15

Answer:

x ≈ 9.6

Step-by-step explanation:

Using Pythagoras' identity in the right triangle, that is

x² + 14² = 17²

x² + 196 = 289 ( subtract 196 from both sides )

x² = 93 ( take the square root of both sides )

x = \(\sqrt{93}\) ≈ 9.6 (to the nearest tenth )

Answer:

if you mean 8 divided by 5 then use long division which will result in 1 with a remainder or 3 or 1.6

Answer:

8/5=1.6

Step-by-step explanation:

There's no step by step for explaining this answer. Or nothing that I can think of

The partial fraction decomposition of the function is\(\\& \Rightarrow \frac{1}{x^2+x^4}=\frac{A}{x}+\frac{B}{x^2}+\frac{C x+D}{x^2+1}\end{aligned}\)

In algebra, a rational fraction—that is, a fraction where the numerator and denominator are both polynomials—can be partially decomposed or expanded by adding a polynomial (potentially zero) and one or more fractions with a lower denominator to the original fraction.

In symbols, the partial fraction decomposition of a rational fraction of the \({\textstyle {\frac {f(x)}{g(x)}},}\)

\({\displaystyle {\frac {f(x)}{g(x)}}=p(x)+\sum _{j}{\frac {f_{j}(x)}{g_{j}(x)}}}\)

Where p(x) is a polynomial, \(g_{j}\) for each j is a power of an irreducible polynomial (which cannot be factored into polynomials of positive degrees), and \(f_{j}\) for each j is a polynomial with a smaller degree than this irreducible polynomial's degree.

The numerical values of the coefficients is \(\frac{1}{x^2+x^4}$\).

Now,

\($\begin{aligned} x^2+x^4 & x^2+x^4 \\ = & x^2\left(1+x^2\right)\end{aligned}$\)

Therefore, the form of the partial fraction decomposition is

\(\begin{aligned}& \frac{1}{x^2\left(1+x^2\right)}=\frac{A}{x}+\frac{B}{x^2}+\frac{C x+D}{x^2+1} \\& \Rightarrow \frac{1}{x^2+x^4}=\frac{A}{x}+\frac{B}{x^2}+\frac{C x+D}{x^2+1}\end{aligned}\)

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The feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

To determine whether the feasible set for each system of constraints is convex, we need to analyze the constraints individually and examine their intersection.

a) (x1)² + (x2)² > 9

This constraint represents points outside the circle with a radius of √9 = 3. The feasible set includes all points outside this circle.

b) x1 + x2 ≤ 10

This constraint represents points that lie on or below the line x1 + x2 = 10. The feasible set includes all points on or below this line.

c) x1, x2 > 0

This constraint represents points in the positive quadrant, where both x1 and x2 are greater than zero.

Now, let's analyze the intersection of these constraints:

Considering the first two constraints (a and b), we can see that the feasible set consists of all points outside the circle (constraint a) and below or on the line x1 + x2 = 10 (constraint b).

To determine whether the feasible set is convex, we need to check if any two points within the set create a line segment that lies entirely within the set.

If we consider the points (5, 5) and (3, 7), both points satisfy the individual constraints (a) and (b). However, the line segment connecting these two points, which is the line segment between (5, 5) and (3, 7), exits the feasible set since it passes through the circle (constraint a) and above the line x1 + x2 = 10 (constraint b).

Therefore, the feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

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\( \sqrt{25} = 5 \\ \sqrt{16 } = 4 \\ \sqrt{49} = 7\)

5+4-7 = 9-7 = 2

Our Answer 2

Answer:

The answer is 2

Step-by-step explanation:

√25 = 5

√16 = 4

√49 = 7

Now,

√25 + √16 - √49

5 + 4 - 7

9 - 7 = 2

Thus, The answer is 2

-TheUnknownScientist

Answer:

c. The mapping represents y as a function of x, because each x-value is related to exactly one y-value.

Step-by-step explanation:

A mapping can be considered to be a function if any of the following conditions met:

1. Every x-value has exactly only 1 possible y-value mapped to it.

2. Two or more x-values can be mapped to the same y-value provided each x-value is not having more than 1 y-value. That is, provided condition 1 is maintained.

Now looking at the mapping given, every x-value you see there is mapped to exactly just 1 y-value. No x-value is mapped to more than 1 y-value.

However, 3 different x-values, -3, 0, and 8, have the same y-values, 4. This also fulfills the condition for a mapping to be regarded as a function, as a y-value of a function can have more than 1 possible x-value mapped to it.

Therefore the mapping represents y as a function of x.

The mapping represents y as a function of x, because each x-value is related to exactly one y-value.

A mapping can be considered to be a function if any of the following conditions met:

Condition : Mapping denotes the relation from Set A to Set B. Relation from A to B is the subsets A\(\times\)B. Mapping the oval on the left-hand side denotes the values of Domain and the oval on the right-hand side denotes the values of Range.

Now looking at the mapping given, every x-value you see there is mapped to exactly just 1 y-value. No x-value is mapped to more than 1 y-value.

However, 3 different x-values, -3, 0, and 8, have the same y-values, 4. This also fulfills the condition for a mapping to be regarded as a function, as a y-value of a function can have more than 1 possible x-value mapped to it.

Therefore the mapping represent y as a function of x.

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The percent decrease for the given numbers is 25%.

A percentage is a value that indicates 100th part of any quantity.

A percentage can be converted into a fraction or a decimal by dividing it by 100.

Given that,

The number is decreasing from 40 to 30.

The difference is 40 - 30 = 10.

The percent decrease can be found by multiplying the ratio of the difference to the initial value by 100 as follows,

Percent decrease = 10/40 × 100

                              = 25%

Hence, the percent decrease from 40 to 30 is 25%.

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Answer:

The weight in kilograms of a 150 pound person is 68.039 kg

Step-by-step explanation:

Weight = 150 pounds.

We need to convert this to kg,

Now, 1 pound = 0.453592 kg.

Then, 150 pounds will be,

150 pounds = 150(0.453592) kg

So, 150 pounds = 68.039 kg

The weight of a 150 pound person is approximately 68.04 kilograms.

To convert the weight of a person from pounds to kilograms, we can use the conversion factor of 1 pound = 0.4536 kilograms.

Given that the person weighs 150 pounds, we can multiply this value by the conversion factor to find the weight in kilograms:

Weight in kilograms = 150 pounds * 0.4536 kilograms/pound

Weight in kilograms = 68.04 kilograms

Therefore, the weight of a 150 pound person is approximately 68.04 kilograms.

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The study conducted by Consumer Reports does not provide a clear answer as to whether the anti-wrinkle cream or the plain moisturizer is more effective in reducing wrinkles

Based on the study conducted by Consumer Reports, it is not clear whether the anti-wrinkle cream or the plain moisturizer is more effective in reducing the appearance of wrinkles.


- The study enrolled 79 subjects with moderate to marked wrinkles and instructed them to use both products, one on each side of their face, every morning for 12 weeks.
- The subjects didn't know which product they were using, and at the end of the study, panelists examined before and after photos of the subjects to assess wrinkle appearance.
- The panelists did not know which product the subjects had used.
- The study did not reveal any significant difference between the effectiveness of the anti-wrinkle cream and the plain moisturizer in reducing the appearance of wrinkles.
- Therefore, it is not clear which product is more effective in reducing wrinkles based on this study.

n conclusion, the study conducted by Consumer Reports does not provide a clear answer as to whether the anti-wrinkle cream or the plain moisturizer is more effective in reducing wrinkles. Further research may be needed to determine the effectiveness of these products in reducing the appearance of wrinkles.

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Please find the photograph for the square root of 3.

4√3

= 4 × 1.732

= 6.928

6.928

Hope it helps

To write 1/16 as a decimal, you must divide the numerator by the denominator of the fraction.

We now divide 1 by 16 which we write as 1/16 and we get 0.0625

1/16 to decimal is equal to 0.0625

Answer:

a rise of 20 degrees

Step-by-step explanation:

since it started at -2 degrees, you have to add enough to get out of the negatives.

-2 + 2= 0, then 0+18 to get to the 18°

-2 + 20 = 18

Answer:

slope is undefined

Step-by-step explanation:

We have 2 coordinates (-4,0) and (-4,1)

Slope m = (y2 - y1)/(x2 - x1) = (1 - 0)/(-4 - -4) = 1/0 or undefined

The undefined slope is the slope of a vertical line

Given:

\(\sin (x)=-\dfrac{1}{2}\)

\(\cos (y)=-\dfrac{1}{3}\)

x is an angle in quadrant III, and y is an angle in quadrant II.

To find:

The value of sin(x+y).

Solution:

We know that, only sin and cosec are positive in II quadrant. Only tan and cot are positive in III quadrant.

x is an angle in quadrant III,

\(\cos x=-\sqrt{1-\sin^2 x}\)

\(\cos x=-\sqrt{1-(-\dfrac{1}{2})^2}\)

\(\cos x=-\sqrt{1-\dfrac{1}{4}}\)

\(\cos x=-\sqrt{\dfrac{4-1}{4}}\)

\(\cos x=-\dfrac{\sqrt{3}}{2}\)

y is an angle in quadrant II.

\(\sin y=\sqrt{1-\cos^2x}\)

\(\sin y=\sqrt{1-(-\dfrac{1}{3})^2}\)

\(\sin y=\sqrt{1-\dfrac{1}{9}}\)

\(\sin y=\sqrt{\dfrac{9-1}{9}}\)

\(\sin y=\sqrt{\dfrac{8}{9}}\)

\(\sin y=\dfrac{2\sqrt{2}}{3}\)

Now,

\(\sin(x+y)=\sin x\cos y+\cos x\sin y\)

\(\sin(x+y)=(-\dfrac{1}{2})\times (-\dfrac{1}{3})+(-\dfrac{\sqrt{3}}{2})\times (\dfrac{2\sqrt{2}}{3})\)

\(\sin(x+y)=\dfrac{1}{6}-\dfrac{2\sqrt{6}}{6}\)

\(\sin(x+y)=\dfrac{1-2\sqrt{6}}{6}\)

Therefore, the correct option is B.

Answer:

Choice B

Step-by-step explanation:

Answer: 2x - y = 1 this should be it

The equation in standard form, y = 2x -1

The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system.

Given an equation, y = 2x-1

The standard form is given as - y = mx+c

The given equation is already in standard form, where, m = 2, c = -1

Hence, The equation in standard form, y = 2x -1

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There are 144 ways to arrange the letters in UNIVERSALLY so that no two vowels occur consecutively and the consonants appear in alphabetical order

To solve this problem, we can break it down into two parts:

Part 1: Arranging the consonants in alphabetical order
The consonants in UNIVERSALLY are N, R, S, V, and Y. Since we want them to appear in alphabetical order, there is only one way to arrange them: NRSVY.

Part 2: Arranging the vowels so that no two occur consecutively
There are four vowels in UNIVERSALLY: E, I, U, and A. To arrange them so that no two occur consecutively, we can use the following strategy:

1. Start with the two consonants N and R. There are three spaces between them where we can place the vowels: _N_R_. We can place the vowels in these spaces in 4! = 24 ways.

2. Next, we add the consonant S to the left of N. There are now four spaces between S and R: S _ N _ R _. We can place the vowels in these spaces in 3! = 6 ways.

3. We continue adding consonants in alphabetical order and placing the remaining vowels in the available spaces. After adding V and Y, we end up with the following arrangement:

S U N I V E R S A L L Y R

There are 24 ways to arrange the vowels between the consonants at step 1, 6 ways to arrange them at step 2, and only 1 way to arrange them after all the consonants have been added. Therefore, the total number of arrangements that satisfy both conditions is:
24 x 6 x 1 = 144

So there are 144 ways to arrange the letters in UNIVERSALLY so that no two vowels occur consecutively and the consonants appear in alphabetical order.

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Answer:

2, 3, 4, 9, 32, 279, 8928, 2,491,833, 22,236,502,176.

Step-by-step explanation:

To find the first 9 terms of the sequence defined recursively by S_n = S_{n-2} * (S_{n-1} - 1), with S(1) = 2 and S(2) = 3, we can use the recursive formula to calculate each term step by step. Here are the first 9 terms:

S(1) = 2 (given)

S(2) = 3 (given)

S(3) = S(1) * (S(2) - 1) = 2 * (3 - 1) = 2 * 2 = 4

S(4) = S(2) * (S(3) - 1) = 3 * (4 - 1) = 3 * 3 = 9

S(5) = S(3) * (S(4) - 1) = 4 * (9 - 1) = 4 * 8 = 32

S(6) = S(4) * (S(5) - 1) = 9 * (32 - 1) = 9 * 31 = 279

S(7) = S(5) * (S(6) - 1) = 32 * (279 - 1) = 32 * 278 = 8928

S(8) = S(6) * (S(7) - 1) = 279 * (8928 - 1) = 279 * 8927 = 2,491,833

S(9) = S(7) * (S(8) - 1) = 8928 * (2,491,833 - 1) = 8928 * 2,491,832 = 22,236,502,176