A certain brand of laundry detergent is manufactured for $4.40 and then marked up 25% by the local store before selling. The store offers a 30% discount with the purchase of three or more bottles of the detergent. Showing all work, determine the total cost, before tax, of three bottles of detergent. (10 points)

From the computation done, it can be denoted that the total price that will be paid will be $12.90.

1 Krispy Kosmos at $2.89 = $2.89

2 Chewy Chocos at $3.19 each = 2 × $3.19 = $6.38

1 Gooey Globs at $2.99 = $2.99

Total = $2.89 + $6.38 + $2.99 = $12.26

We'll then add the sales tax of 5.2%, therefore, the total value will be:

= $12.26 + (5.2% × $12.26)

= $12.26 + $0.638

= $12.90

In conclusion, the correct option is $12.90.

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Answer:

C

Step-by-step explanation:

Edg 2022

In 1940, John Atanasoff, a physicist from Iowa State University, wanted to solve a 29 x 29 linear system of equations. To solve this system using Gaussian elimination, it would have required approximately 29^3/3 = 24389 arithmetic operations.

In 1940, John Atanasoff developed the Atanasoff-Berry Computer (ABC), which was the first electronic computer. Atanasoff wanted to use the ABC to solve a 29 x 29 linear system of equations.

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Answer:

Answer on a graph

Answer:

29x-41y-11z

Step-by-step explanation:

Answer:

29 x − 41 y- 11 z

Step-by-step explanation:

The bones at the time they were​ discovered when the radioactive element​ carbon-14 has a​ half-life of total 5750 years are 10062.5-year-old.

Half lives is the time interval which is need to decay the atomic nuclei of a radioactive sample.

There is a scientist who determined that the bones from a mastodon had lost 70.3​% of their​ carbon-14.  Thus, the fraction remaining is,

f=1-(70.3/100)=1-0.703

f=1-(70.3/100)=0.297

Now the fraction remaining can be given as,

f=(1/2)ⁿ

Here, n is the half life elapsed. Put the value of fraction remaining.

0.297=(1/2)ⁿ

n=1.75

The radioactive element​ carbon-14 has a​ half-life of total 5750 years. Thus,

Years=1.75*5750

Years=10062.5

Thus, the bones at the time they were​ discovered when the radioactive element​ carbon-14 has a​ half-life of total 5750 years are 10062.5-year-old.

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Answer:

n  ⩽ 30

Step-by-step explanation:

then the sum of the areas of the two smaller squares will be equal to the area of the largest square.

if three squares have sides that make an acute triangle, then the sum of the areas of the two small squares is equal to the area of the largest square. This is known as the Pythagorean Theorem, which states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side (the hypotenuse). However, in an acute triangle, there is no side that is longer than the other two sides, and so the three squares cannot form a right triangle. Therefore, the sum of the areas of the two smaller squares cannot be determined from the information given.

If three squares have sides that make an obtuse triangle, then the sum of the areas of the two small squares is less than the area of the largest square. In an obtuse triangle, one of the angles is greater than 90 degrees, which means that the square with its side opposite the obtuse angle will have a larger area than the other two squares. Therefore, the sum of the areas of the two smaller squares will be less than the area of the largest square.

If three squares have sides that make a right triangle, then the sum of the areas of the two small squares is equal to the area of the largest square. This is the Pythagorean Theorem, as mentioned in the first answer. In a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. Therefore, if the squares are constructed with their sides equal to the lengths of the sides of the right triangle, then the sum of the areas of the two smaller squares will be equal to the area of the largest square.

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Answer:

C

Step-by-step explanation:

y=kx or xy=k are true such that k=0.3

in C, 1.2=4*0.3, 2.4=8*0.3, and 3.9=13*0.3, so C follows this rule

All the zeros of the polynomial function p(x) = (x + 2)(2x - 3)(x − 3) are

The zeros of the polynomial function is solved by equating each term in parenthesis to zero.

for the function, p(x) = (x + 2)(2x - 3)(x − 3)

firstly, x + 2 = 0

x = -2

secondly, (2x - 3)

2x - 3 = 0

2x = 3

x = 3/2

thirdly, (x + 3)

x + 3 = 0

x = -3

the zeros are x = -2, x = 2/3 and x = -3

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Your answer would be 230,000

Check the picture below.

Answer:

The first one

Step-by-step explanation:

The dots are the farthest away from the line in that one.

(a) a = 9, 3, b = -2, 6 are orthogonal

(b) a = 4, 7, -2, b = 3, -1, 7 are neither parallel nor orthogonal

(c) a = -6i + 9j + 3k, b = 4i - 6j - 2k are neither parallel nor orthogonal

(d) a = 3i - j + 3k, b = 3i + 3j - 2k are orthogonal

(a) To determine if vectors a = (9, 3) and b = (-2, 6) are orthogonal, parallel, or neither, first check if their dot product is 0. If it is, they are orthogonal.

a · b = (9 * -2) + (3 * 6) = -18 + 18 = 0, so a and b are orthogonal.

(b) For vectors a = (4, 7, -2) and b = (3, -1, 7), calculate the dot product.

a · b = (4 * 3) + (7 * -1) + (-2 * 7) = 12 - 7 - 14 = -9, which is not 0, so they are not orthogonal. Since the vectors are not scalar multiples of each other, they are neither parallel nor orthogonal.

(c) For vectors a = (-6i + 9j + 3k) and b = (4i - 6j - 2k), check the dot product:

a · b = (-6 * 4) + (9 * -6) + (3 * -2) = -24 - 54 - 6 = -84, which is not 0, so they are not orthogonal. Since the vectors are not scalar multiples of each other, they are neither parallel nor orthogonal.

(d) For vectors a = (3i - j + 3k) and b = (3i + 3j - 2k), calculate the dot product:

a · b = (3 * 3) + (-1 * 3) + (3 * -2) = 9 - 3 - 6 = 0, so a and b are orthogonal.

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According to the slope, the angle 3 also has a measure of 143 degrees.

To find the measure of angle 3, we first need to understand how angles 2 and 3 are related.

In other words, angles 2 and 3 are congruent (have the same measure). Therefore, if we can find the measure of angle 2, we can determine the measure of angle 3.

We know that angle 2 has a measure of 143 degrees. We also know that angles 2 and 3 are alternate interior angles, which means they are congruent.

Now, let's justify why this is true using the concept of slopes. Since the power lines are parallel, they have the same slope. This means that the angle between each power line and the horizontal is the same.

Since angle 2 is the angle between one of the power lines and the horizontal, we know that angle 3 must also have the same measure because it is the angle between the other power line and the horizontal.

Therefore, we can confidently say that the measure of angle 3 is also 143 degrees.

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Complete Question:

A pair of parallel power lines in Mohamed Bin Zayed City is installed on a slope. Find m∠3 if m∠2= 143 degrees . Justify your answer

The x-component of the total electric field due to the two charges at a point on the x-axis a distance 3d from the origin, at the point (x = 3d, y = 0) is 3.962 N/C.

The electric field at point P which is located on the x-axis a distance 3d from the origin due to two charges Q1 and Q2 is a vector sum of the individual electric fields created by the two charges.

Electric field due to point charge Q at a distance r from the point charge Q can be calculated using Coulomb's law as:

                                     E = k Q / r^2where k = 9 x 10^9 Nm^2/C^2 is the Coulomb's constant

Now, the electric field created by Q1 at point P isE1 = k Q1 / r^2where r is the distance between Q1 and P.

Here, Q1 is at a distance d from P on the y-axis and the distance between Q1 and P is given as:

                                             r1 = sqrt[(3d)^2 + d^2] = sqrt(10) * d

We know that, Q1 = 6.80 x 10^-9 CE1 = 9 x 10^9 * 6.80 x 10^-9 / [sqrt(10) d]^2= 4.628 N/C

Again, the electric field created by Q2 at point P isE2 = k Q2 / r^2where r is the distance between Q2 and P.

Here, Q2 is at a distance d from P on the y-axis and the distance between Q2 and P is given as:

                                                  r2 = sqrt[(3d)^2 + d^2] = sqrt(10) * d

We know that, Q2 = 6.20 x 10^-9 CE2 = 9 x 10^9 * 6.20 x 10^-9 / [sqrt(10) d]^2= 4.208 N/C

The x-component of the electric field E1 along the x-axis will be zero, since it is perpendicular to the x-axis.

The x-component of the electric field E2 is directed towards the origin and is given as:

                              Ex2 = E2 cos θ = E2 (x / r2) = E2 [3d / sqrt(10) d]= 0.9407 * E2

Therefore, the x-component of the total electric field at point P due to the two charges is:

                                       Ex = Ex1 + Ex2= 0 + 0.9407 * E2= 3.962 N/C (approx.)

Hence, the x-component of the total electric field due to the two charges at a point on the x-axis a distance 3d from the origin, at the point (x = 3d, y = 0) is 3.962 N/C.

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Answer:

its 90°

Step-by-step explanation:

because its a right angle triangle

To compare a confidence interval obtained from a sample to a worldwide result, you would typically check if the worldwide result falls within the confidence interval.

A confidence interval is an estimate of the range within which a population parameter, such as a mean or proportion, is likely to fall. It is computed based on the data from a sample. The confidence interval provides a range of plausible values for the population parameter, taking into account the uncertainty associated with sampling variability.

To compare the confidence interval to a worldwide result, you would first determine the population parameter value that represents the worldwide result. For example, if you are comparing means, you would identify the mean value from the worldwide data.

Next, you check if the population parameter value falls within the confidence interval. If the population parameter value is within the confidence interval, it suggests that the sample result is consistent with the worldwide result. If the population parameter value is outside the confidence interval, it suggests that there may be a difference between the sample and the worldwide result.

It's important to note that the comparison between the confidence interval and the worldwide result is an inference based on probability. The confidence interval provides a range of values within which the population parameter is likely to fall, but it does not provide an absolute statement about whether the sample result is significantly different from the worldwide result. For a more conclusive comparison, further statistical tests may be required.

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Answer:

k=75

Step-by-step explanation:

\(\frac{k}{5}\)+8=23

(subtract 8 from both sides of the equation)

\(\frac{k}{5}\)+8-8 = 23-8

(simplify)

\(\frac{k}{5}\) = 15

(multiple all terms by the same value to eliminate fractional denominators)

5. \(\frac{k}{5}\) = 5.15

(cancel multiplied terms that are in the denominator, multiply the numbers)

k=75

Answer:

60

Step-by-step explanation:

you add what he needs to make in total up ten dollars for the cupcake tin and the thirty five dollars for the profit he wants to make then I used the guess and check strategy knowing that 100 cupcakes would make him 75 dollars I worked my way down multiplying 0.75 times 90, 80, 70 and then landed on the answer 60

The given vector field f(x,y) = 39x^2y^2i + 26x^3yj is conservative.

The vector field f(x,y) is given by:
f(x,y) = 39x^2y^2i + 26x^3yj

To check if the vector field is conservative, we need to verify if the curl of the vector field is zero. The curl of a 2D vector field is defined as:

Curl(f) = (∂(26x^3y) / ∂x) - (∂(39x^2y^2) / ∂y)

Calculate the partial derivative with respect to x for the second component (j):

∂(26x^3y) / ∂x = 78x^2y

Calculate the partial derivative with respect to y for the first component (i):

∂(39x^2y^2) / ∂y = 78x^2y

Subtract the second derivative from the first derivative:

Curl(f) = 78x^2y - 78x^2y = 0

Since the curl of the vector field f(x,y) is 0, the vector field is conservative.

The correct question should be :

Determine whether or not the vector field given below is conservative.

f(x,y) = 39x^2y^2i + 26x^3yj

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Answer:

x^2 + 2x + 1

Step-by-step explanation:

(x + 1)(x + 1) = x^1 + x + x + 1 = x^2 + 2x + 1

Answer:

x² + 2x + 1

Step-by-step explanation:

(x+1)(x+1)

x² + 1x + 1x + 1

Step-by-step explanation:

remember, when 2 signs collide (like a mathematical operation and the sign of an operand of that operation), the following is always true (for additions/subtractions and multiplications/divisions) :

+ + = +

+ - = -

- + = -

- - = +

and don't forget : when a number or term is positive, we usually don't write the sign. only the mathematical operation.

1. 2 - 3 = -1

2. 11 - 10 = 1

3. 3 - 5 = -2

4. 22 - 21 = 1

5. -8 + 44 = 36

6. -12 + 6 + 3 = -3

7. 16 + 12 = 28

8. -36 + 36 = 0

9. -4 × 10 = -40

10. -1 × -1 = 1

11. 7 × -7 = -49

12. -4 / 4 = -1

13. -7 × -5 = 35

14. -10 × 8 = -80

15. -2 × -7 = 14

The expression as a number in scientific notation is 4.2 * 10^5

The expression is given as:

quantity 7 times 10 cubed end quantity times quantity 5.4 times 10 to the fourth power end quantity all divided by quantity 9 times 10 squared

Rewrite properly as:

[7 * 10^3 * 5.4 * 10^4]/[9 * 10^2]

Evaluate the product of 7 and 5.4

So, we have:

[37.8* 10^3 * 10^4]/[9 * 10^2]

Evaluate the product of 10^3 and 10^4

So, we have:

[37.8* 10^7]/[9 * 10^2]

Evaluate the quotient of 37.8 and 9

So, we have:

[4.2 * 10^7]/[10^2]

Evaluate the quotient of 10^7 and 10^2

So, we have:

4.2 * 10^5

Hence, the expression as a number in scientific notation is 4.2 * 10^5

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Answer:

f(x)-h(x) = 6x - 12

Explanation:

Given the functions f(x) and h(x) defined as follows:

We want to find: f(x)-h(x)

The equation of the line passing through point P(-1,-4) that is parallel to y = -6x + 8 is y = -6x - 10.

A straight line is made up of an infinite number of points connected at their ends.

Any straight line's slope, "m," is determined by:

\(\rm m =\dfrac{y_2-y_1}{x_2-x_1}\)

The slope of the line y = -6x + 8

m = -6

The slope of the line passing point P (-1,-4)

M = -6

y - (-4) = -6(x - (-1))

y + 4 = -6(x + 1)

y = -6x - 10

Thus, the equation of the line passing through point P(-1,-4) that is parallel to y = -6x + 8 is y = -6x - 10.

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Answer:

-1/2

Step-by-step explanation:

slope is  \(\frac{y_{2}- y_{1}}{x_{2}-x_{1}}\)

so:

\(\frac{6-8}{12-8} = -\frac{2}{4} = -\frac{1}{2}\)

The ONE DIGIT NUMBER that best describes the linear program is unbounded feasible region and unique optimal solution.

The given linear program states "MINIMIZE 1x + 3y subject to x, y ≥ 0." In this case, we have a bounded feasible region since the constraints restrict both x and y to be greater than or equal to zero. The feasible region is limited to the positive quadrant of the coordinate plane.

As for the objective function, 1x + 3y, it forms a linear equation with a positive slope. The objective function represents a family of parallel lines with a steeper slope of 3 compared to the slope of 1 for the x-axis. As we move away from the origin, the objective function increases.

Since the feasible region is unbounded, there are infinitely many points that satisfy the constraints. However, since the objective function is linear and the feasible region is unbounded, there exists a unique optimal solution. The optimal solution is the point in the feasible region that minimizes the objective function. Therefore, the linear program is best described as having an unbounded feasible region with a unique optimal solution, which corresponds to the digit.

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Answer:

50 questions

Step-by-step explanation:

Given the following question:

92% of 50

To find the answer we have to use the formula to calculate percentage.

\(\frac{p\times n}{100}\)
\(\frac{92\times50}{100} =92\times50=4600\div100=46\)
\(=46\)

Which means in total there was "50 questions" on the test.

Hope this helps.

The length of the QR is 16 cm when PQR ~MNO

In the given question, it is given that two similar triangles as PQR ~MNO

Then, the corresponding sides will be in equal proportion to each other as follows

PQ / MN = PR / MO = QR / NO

We need to find the length of the side QR

As above relations are given,

\(\frac{PQ}{MN}\) = \(\frac{PR}{MO}\) = \(\frac{QR}{NO}\)

\(\frac{30}{10}\) = \(\frac{5x + 7}{x+5}\) = \(\frac{4x}{\frac{16}{3} }\)

Equating all the fractions, equal to each we'll find

\(\frac{5x + 7}{x+5}\) = \(\frac{30}{10}\)

5x + 7 = 3(x +5)

5x + 7 = 3x + 15

2x = 8

x = 4

We know that, the length of the QR = 4x cm = 4 x 4 cm = 16 cm

Therefore, the length of the QR is 16 cm when PQR ~MNO

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The weight of the Avery's lunch box using given weights is equal to 0.92 pounds (rounded to two decimal places).

Total weight of the backpack= 2 2/3 pounds

                                                = 8/3 pounds

The weight of the each book =7/8 pounds.

Let x be the weight of the lunch box in pounds.

An equation that represents the total weight in Avery's backpack,

2(7/8) + x = 8/3

To solve for x, simplify and solve for x,

⇒14/8 + x = 8/3

Multiplying both sides by 24 the least common multiple of 8 and 3 to clear the fractions,

⇒42 + 24x = 64

Subtracting 42 from both sides,

⇒24x = 22

Dividing both sides by 24,

⇒x = 22/24

Simplifying the fraction,

⇒x = 11/12

     =  0.92 pounds (rounded to two decimal places).

Therefore, the  weight of the lunch box is equal to 0.92 pounds (rounded to two decimal places).

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