Felipe used a 40 percent off coupon on a single item at the craft store which saved him $16.42. What would the item have cost if he had not used the coupon?
$22.99
$32.84
$41.05
$56.42

Answer:

a) A = p(1 + r)^t

b) A = 500(1 + 0.07)^2=572.45

Step-by-step explanation:

t=2 in b)

The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

for more such questions on sampling method

https://brainly.com/question/13219833

#SPJ8

Answer:

2y - 9x - 40 = 0

Step-by-step explanation: i already done the test

Answer:

answer is 0.1 ....................

Answer:

The coordinates are ( 4, -3).

Step-by-step explanation:

We can find the coordinates by solving the 2 equations

y =  1/4x-4

y = -1/2x-1

As both left sides of the equation are y we can say:

-1/2x-1 = 1/4x-4

-1/2x - 1/4x = -4 + 1

-3/4 x = -3

x = -3 * -4/3

x = 4.

- and y = 1/4(4) - 4 = -3.

Answer:

Step-by-step explanation:

See the attached graph.

The intersection of the lines gives us the solution:

Answer:

y=5

Step-by-step explanation:

Let me know if you need an explanation

1.5 or 50%

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

The amounts of each solution that he should use are given as follows:

The amounts of each solution are obtained by a system of equations, for which the variables are given as follows:

The total solution is of 18 liters, hence:

x + y = 18.

x = 18 - y.

The final concentration is of 80%, hence:

0.3x + 0.9y = 0.8 x 18

0.3x + 0.9y = 14.4.

As x = 18 - y, the value of y is obtained as follows:

0.3(18 - y) + 0.9y = 14.4

0.6y = 9

y = 9/0.6

y = 15.

Hence the value of x is obtained as follows:

x = 18 - y

x = 18 - 15

x = 3.

More can be learned about a system of equations at https://brainly.com/question/13729904

#SPJ1

ASA stands for "Angle-Side-Angle." Triangles classified as ASAs have two known angles and a common side. The ASA triangle ABC, with provided angles B and C and their common side a between them, is depicted below.

What does a congruence mean in mathematics?

If two numbers can be placed exactly over one another, they are said to be "congruent." When placed one on top of the other, the two bread slices are the same size and form. Things that are precisely the same size and shape are said to be congruent.

Describe ASA congruence through an example.

ASA (Angle-Side- Angle) 

According to the ASA rule, two triangles are said to be congruent if any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and side included between the angles of the second triangle.

More details about congruence

brainly.com/question/2938476

#SPJ4

To determine the equation of the line that has slope m=1/3 and passes through the point (3,2) you have to use the point-slope form:

Where

m is the slope of the line

(x₁,y₁) are the coordinates of one point of the line

Replace the formula above with the known information about the line:

Next is to write the equation in slope-intercept form, which means that you have to leave the y term alone on the left side of the equation and all other terms have to be on the right side.

-First, distribute the multiplication on the parentheses term:

-Second, pass "-2" to the right side of the equation by applying the opposite operation, "+2", to both sides of the equal sign:

So, the equation of the line with slope 1/3 that passes through the point (3,2), expressed in slope-intercept form is:

Answer:

Triangles A and B are acute, C is right, and I think D might be obtuse.

Step-by-step explanation:

Acute means that the angles are less than 90 degrees, and obtuse means that at least one angle is more than 90 degrees.

Answer:

Triangle A: Acute

Triangle B: Acute

Triangle C: Obtuse

Triangle D: Right

Step-by-step explanation:

Acute angle: 0°-90°

Right angle: 90°

Obtuse angle: 90°-180°

An acute triangle only has acute angles. A right triangle has one right angle. An obtuse triangle has one obtuse angle.

Answer:  A  129

Step-by-step explanation:

Because the 2 chords are the same (lines in the circle), the 2 arcs are the same  create an equation that makes them equal

3x+24 = 4x -11             >bring x to one side by subtracting both sides by 3x

24 = x -11                     > add both sides by 11

35 = x

Now that we have solved for x you need to plug that back into the equation for BC

BC= 4x-11

BC = 4(35) - 11

BC =  140 - 11

BC = 129                   >A

It will take 3.5 hours for the two cars to be 280 miles apart.

To determine the time it takes for the two cars to be 280 miles apart, we can use the concept of relative velocity.

Since the cars are traveling in opposite directions, their velocities can be added together to find their relative velocity:

Relative velocity = Velocity of car traveling east + Velocity of car traveling west

Relative velocity = 60 mph + 20 mph

Relative velocity = 80 mph

The relative velocity of the cars is 80 mph, which means that they are moving away from each other at a combined speed of 80 mph.

To find the time it takes for them to be 280 miles apart, we can use the formula:

Time = Distance / Speed

Plugging in the values, we have:

Time = 280 miles / 80 mph

Time = 3.5 hours

Therefore, it will take 3.5 hours for the two cars to be 280 miles apart.

During this time, the car traveling east would have covered a distance of 60 mph × 3.5 hours = 210 miles, while the car traveling west would have covered a distance of 20 mph × 3.5 hours = 70 miles.

The sum of these distances is indeed 280 miles, confirming the result.

For more questions on relative velocity.

https://brainly.com/question/11418015

#SPJ8

Answer:

(x-2)^2-2

Step-by-step explanation:

x^2-4x+2

take the x out

x(x-4) + 2

(x-2)^2-2

because (x-2)^2 is

x^2-4x+4

its like completing the square

Answer:

(x-2)² -2

Step-by-step explanation:

Consider that (a+b)² = a²+2ab+b²

To find the form (x-A)²+B compare  x²-4x+2 with a²+2ab+b²

x² - 4x +2

a² + 2 a b+ b², so a= x and b = (-2)

x²+ 2· x ·(-2)+ (-2)² -  2  = (x-2)² -2 is in the form (x-A)²+B

Check our answer:

(x-2)² -2= (x²-2·2x+4)-2 = x²-4x +2 ✅

Using the concept of perimeter of polygon, the perimeter of figure C is 27cm shorter than total perimeter of A and B

To solve this problem, we have to know the perimeter of the polygon C.

The perimeter of a polygon is the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

The perimeter of the figures are;

Using the concept of perimeter of a rectangle;

a. figure A = 2(4 + 11) = 30cm

b. figure B = 2(8 + 4) = 24cm

c figure C = 11 + 4 + 8 + 4 = 27cm

Now, we can add A and B and then subtract c from it.

30 + 24 - 27 = 27cm

Learn more perimeter of polygon here;

https://brainly.com/question/27083382

#SPJ1

Answer:

Adults = 167

Students = 256

Teachers = 85

Step-by-step explanation:

Let:

S represents Students

A represents Adults

T represents Teachers

From the instructions in the question, we have that:

\(A + S = 423\) -- (1)

\(8A + 5S = 2616\) -- (2)

Make A the subject in (1)

\(A + S = 423\)

\(A = 423 - S\)

Substitute \(423 - S\) for A in (2)

\(8A + 5S = 2616\)

\(8(423 - S) + 5S = 2616\)

Open Bracket

\(3384 - 8S + 5S = 2616\)

\(3384 -3S = 2616\)

Solve for S

\(-3S = 2616 - 3384\)

\(-3S = -768\)

\(S = -768/-3\)

\(S = 256\)

Recall that \(A = 423 - S\)

\(A = 423 - 256\)

\(A = 167\)

From the question, we understand that;

\(T = \frac{1}{3}S\)

\(T = \frac{1}{3} * 256\)

\(T = 85.333\)

\(T = 85\) (Approximated)

Answer:

E

Step-by-step explanation:

ab is sometimes rational

The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

From the figure, the area of triangles can be calculated using the:

Area = (1/2)height×base length

Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)

Area of three triangle = 1/2(24×3) = 36 square units

Area of the figure = area of three triangle + area of the rectangle

= 36 + 6×4

= 60 square units

Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

Learn more about the triangle here:

brainly.com/question/25813512

#SPJ1

Answer:

The approximate guest rating for the movie by all the guests is 0.

The factory must produce 6,400 parts  so that there is 1 ton of scrap aluminum for recycling.

It is given that For every part produced by a factory there are 5 ounces of scrap aluminum that can be recycled there are 16 ounces in 1 pound and 2,000 in 1 ton we need to find how many parts must the factory produce so that there is 1 ton of scrap aluminum for recycling

What is a Ratio?

A quantitative relation between two amounts showing the number of times one value contains in another

1 part produced  ⇒ 5 ounces scrap aluminium recycled.

So, the ratio of parts produced : Scrap of aluminium = 1   : 5  .... (a)

Let us assume for m parts produced ,  1 ton of scrap is recycled.

Also, 1 ton = 2, 000 pounds

and 1 pound = 16 ounces

⇒ 1 ton = 2000 x (16 ounces)  = 32,000 ounces

So, for m parts made in the  factory, 32,000 ounces scrap is recycled.

So, the ratio of parts produced : Scrap of aluminium =  m   : 32,000  .... (b)

From both the given ratio, we get

1   : 5  = m   : 32,000

m=32000/5

m=6400

To learn more about ratios click here : https://brainly.com/question/18956877

#SPJ1

\((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

We can use the rules of exponents and simplify the terms with the same base.

Dividing the coefficients: 21 / 7 = 3.

For the variables, you subtract the exponents: \(a^6 / a^3 = a^(^6^-^3^) = a^3.\)

Similarly,\(b^5 / b = b^(5-1) = b^4\).

Putting it all together, the simplified expression is:

\(3a^3b^4.\)

Therefore, \((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

Learn more about rules of exponents here : brainly.com/question/11975096

#SPJ1

Answer:

-5.87,-33,0.5,17/25

Answer:

-33, -5.87, 0.5, 17/25.

Step-by-step explanation:

Thanks for the points!

Have a great day!

Stay safe and healthy!

Happy holiday seasons!

May I please have brainliest?

(a) let number of miles Carol walked be e.

Patty walked 7 miles more than Carol.

Patty walked e + 7 miles.

Let total number of miles walked be T

that is how many miles Carol walked plus how many miles Patty walked

T = e + (e + 7)

(b) :Let number of miles patty walked be p.

p = e + 7

e = 9

P = 9 +7

P = 16

(c) T = e + (e + 7)

T = 11 + (11+7)

T = 11+18

T=29

Answer:

2x^3-5x^2-28x+15 -------------------------expanded

2x^3-5x^2-28x+15--------------------simplified

Step-by-step explanation:

\left(2x-1\right)\left(x+3\right)\left(x-5\right)

=2x^2x+2x^2\left(-5\right)+5xx+5x\left(-5\right)-3x-3\left(-5\right)

simplyfied

\left(2x^2+5x-3\right)\left(x-5\right)

=2x^2x+2x^2\left(-5\right)+5xx+5x\left(-5\right)-3x-3\left(-5\right)

=2x^3-5x^2-28x+15

Answer:

\(\cos\theta = \pm\frac{2\sqrt{2}}{3}\\\tan\theta=\pm\frac{\sqrt{2}}{4}\)

Step-by-step explanation:

sinθ = 1/3

\(\cos\theta=\pm\sqrt{1-\cos^2\theta} = \pm\sqrt{1-\frac{1}{9}}=\pm\sqrt\frac{8}{9}=\pm\frac{2\sqrt{2}}{3}\)

\(\tan\theta=\frac{\sin\theta}{\cos\theta}=\pm\frac{1}{2 \sqrt{2}}=\pm\frac{\sqrt{2}}{4}\)

Answer:

a = -8

Step-by-step explanation:

4/a + 4 = -1/a + 9

-1(a + 4) = 4(a + 9)

-1a - 4 = 4a + 36

-5a - 4 = 36

-5a = 40

a = -8

Answer:

A. P = 9x + 2

Step-by-step explanation:

Perimeter is all the sides lengths added together.

Step 1: Set up equation

P = 2x - 6+ 2x + 1 + 2x + 3x + 7

Step 2: Combine like terms

P = 9x + 2

The product of 5 × 5ab × 5, a, b is 125ab5 when written in its most Simple form

The expression 5 × 5ab × 5, a, b is equal to 125ab5. The reasoning is that when we multiply 5 by 5ab, we get 25ab, which we then multiply by 5 to get 125ab. Since a, b are variables, the product 125ab5 is the product of 5 × 5ab × 5, a, b, when written in its most simple form.

The expression 5 × 5ab × 5, a, b is an algebraic expression, which consists of numbers, variables, and operators. Variables are usually represented by letters or other symbols, while operators such as +, -, ×, ÷, ^ are used to indicate mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. In algebra, expressions can be simplified by combining like terms, expanding brackets, and applying other rules of arithmetic.

The most simple form of an expression is the one that cannot be further simplified.In the given expression, 5 × 5ab × 5, a, b, we can see that the number 5 appears three times, so we can simplify the expression by multiplying the numbers together.

Similarly, we can multiply the variables a and b together to get the term ab. Finally, we write the result as 125ab5, which is the product of 5 × 5ab × 5, a, b, in its most simple form.

Therefore, the product of 5 × 5ab × 5, a, b is 125ab5 when written in its most simple form.

For more questions on  Simple form.

https://brainly.com/question/27624273

#SPJ8

Answer: Section formula

Step-by-step explanation:

Given

The line segment AB with endpoints \(A(2,2)\) and \(B(14,14)\) is divided by a point X in the ratio 1:2

To verify that X divides the line segment in the ratio 1:2, we will use section formula. Section formula tells the coordinates of the point which divide the line segment in the certain ratio or vice-versa.

We will assume that X divides AB in k:1 and insert the values in the section formula. If the ratio k:1 comes out to be 1:2, then it verifies the claim.