you leave a 20% tip on your $50 dinner bill . how much was the tip ?

She reportedly invested $6600 at 3% and $3400 at 2.5%, according to the statement.

Investing is a smart way to put your money to work and could make you richer. If you make smart investing choices, your money may increase in value as outpace inflation. The major factors contributing to investment's increased growth potential are the possibility of compounding and the trade-off amongst risk and return.

Simple interest is calculated as follows: deposit amount multiplied by time and interest rate.

Let "a" represent the money placed in the account earning 3% interest.

Let's use the symbol to represent the amount deposited into the account earning 2.5% interest (10,000 - a)

a * 0.03 plus (10,000 - a) * 0.025 = 283

0.03a + 250 - 0,025a = 283

Collect like terms

0.03a - 0.025a = 283 - 250

0.005a = 33

a = $ 6600

What was put into the 2.5% account = 1000 - 6600 = $ 3400

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Both equations are satisfied, so the solutions to the equations are correct.

Matrix is a system of data or numbers arranged in rows and columns that is used to solve mathematical problems. It is a mathematical representation of a real-world situation. The rows represent the elements or items in the situation, while the columns represent the attributes or characteristics of the elements. Matrix can be used to solve various types of problems, such as linear equations, calculus, and statistics. It can also be used to represent data in graphs, tables, and other visual formats.

The augmented matrix in Exercise 12 is:

\begin{bmatrix}
1 & 4 & 5 & -10 \\
2 & 8 & 6 & -20
\end{bmatrix}

The corresponding equations are:

1x + 4y = -10
2x + 8y = -20

To verify that the solutions obtained in Exercise 12 are correct, we can substitute x=5 and y=-2 back into the equations:

1(5) + 4(-2) = -10
2(5) + 8(-2) = -20

Both equations are satisfied, so the solutions to the equations are correct.

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Both equations are satisfied, so the solutions to the equations are correct. This can be solved using the concept of matrix.

Matrix is a system of data or numbers arranged in rows and columns that is used to solve mathematical problems. It is a mathematical representation of a real-world situation. The rows represent the elements or items in the situation, while the columns represent the attributes or characteristics of the elements. Matrix can be used to solve various types of problems, such as linear equations, calculus, and statistics. It can also be used to represent data in graphs, tables, and other visual formats.

The augmented matrix in Exercise 12 is:

[tex]\left[\begin{array}{cccc}1&4&5&-10\\2&8&6&-20\end{array}\right][/tex]

The corresponding equations are:

1x + 4y = -10

2x + 8y = -20

To verify that the solutions obtained in Exercise 12 are correct, we can substitute x=5 and y=-2 back into the equations:

1(5) + 4(-2) = -10

2(5) + 8(-2) = -20

Both equations are satisfied, so the solutions to the equations are correct.

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Answer:

46

Step-by-step explanation:

The type of angle below is called an alternate angle where the opposite angle is the equal size.

As the angle given is 46 the alternating angle would be 46!

Have a lovely day :)

Answer:

46 because 46 is alternative angle

Answer:

13 times

Step-by-step explanation:

lol, I actually did this right now. I got 13 times for both coins being heads, 9 times for each coin being tales, and exactly 30 times both were uneven. I hope this helps :)

6

Step-by-step explanation:

um7

1) The definition of function F(x) is: B. F(x) = -(x + 2)²(x - 2).

2) The standard definition of the cubic function is: A. F(x) = ax³ + bx² + cx + d.

4) The approximate solution to the system of equations is given as follows: A. (-3.43, 6.30).

The Factor Theorem states that a polynomial function with roots(also called zeros) [tex]x_1, x_2, \codts, x_n[/tex], is represented by the product of it's linear factors [tex]x - x_1, x - x_2, \cdots x - x_n[/tex], according to the rule the rule presented as follows:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

From the graph, the roots of the function are given as follows:

Meaning that the cubic function is defined as follows:

F(x) = a(x + 2)²(x - 2).

The y-intercept of the function, numerically, is given as follows:

F(0) = a(2² x (-2))

F(0) = -8a.

The y-intercept is positive, meaning that the leading coefficient is negative, and thus the option B is the correct option.

The general format of a cubic function, with leading coefficient a and constant d positive, is given as follows:

y = ax³ + bx² + cx + d.

Meaning that the correct option for item 2 is given by option A.

The solution to the system of equations is found through graphing, and is the point of intersection of the two functions.

From the graph given by the image presented at the end of the answer, using rounding, the approximate solution for item 4 is given by option A.

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Answer: The answer is 5x

Answer: x=1

Step-by-step explanation:

=3x-[tex]2x^{2}[/tex]-1+8x-3x+[tex]2x^{2}[/tex]-7

= -1+8x-7

= -8=-8x

X=1

Step-by-step explanation:

A no

n + 7 = 16

n + 7 - 7 = 16 - 7

n = 9

that is not n = 15

B yes

(2/3)v = 8

3×(2/3)v = 3×8

2v = 24

2v/2 = 24/2

v = 12

C no

6z = 84

6z/6 = 84/6

z = 14

that is not z = 8

The unit rate of the relationship between the amount of water pumped and time is the amount of water pumped in one minute for 14 hours.

To calculate unit price, you need to divide the first term (quantity) by the second term (unit). The resulting value is the unit price.

For example, if you want to calculate the unit price for a bag of 4 $3 apples, divide the total cost ($3) by the number of apples (4).

$3 / 4 apples = $0.75 / apple

In this example, the unit price is $0.75 per apple. So the price per apple is $0.75.

Given by the equation:

The unit rate of water pumped versus time is the amount of water pumped in one minute, so:

28/2=14

That means 14 gallons of water is being pumped every minute.

Now you can calculate the water pumped in 3/2 minutes like this

14*3/2=21

So in total, water pumped in 12 minutes plus 3/2 minutes gives water pumped in 15/2 minutes.

14*15/2=105

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The cost of pair of gloves is $8.5 and cost of hat is $6.5. The solution has been obtained by using linear equation.

What is a linear equation?

The equation with the biggest degree of one is one that is linear. The lack of variables in a linear equation with an exponent larger than one is demonstrated by this. A straight line is produced by such an equation on the graph.

Let the cost of pair of gloves be 'x' and cost of hat be 'y'.

We are given that Cody bought two pairs of gloves and four hats for $43.00.

This can be represented as 2x + 4y = $43.00

Tori bought two pairs of gloves and two hats for $30.00.

This can be represented as 2x + 2y = $30.00

On subtracting both the equations, we get

⇒ 2y = 13

⇒ y = 6.5

Substituting this value in the equation, we get

⇒2x + 2(6.5) = $30.00

⇒x + 6.5 = 15

⇒x = 8.5

Hence, the cost of pair of gloves is $8.5 and cost of hat is $6.5.

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Since, there are multiple questions, so the question answered above is attached below.

The five vectors in span {v1,v2} are we first multiply each vector component (x, y, and z) of v1 and v2 by a constant and then add them together.

1. v3 = (3v1 + 2v2) = (18 8 −16)

2. v4 = (2v1 + 3v2) = (−12 6 0)

3. v5 = (4v1 + v2) = (0 6 −32)

4. v6 = (−2v1 + 5v2) = (36 10 0)

5. v7 = (−v1 + 4v2) = (−36 8 0)

To calculate the vectors, we first multiply each vector component (x, y, and z) of v1 and v2 by a constant and then add them together. For example, for v3 we multiplied v1 by 3 and v2 by 2 and then added the components together to get the vector (18 8 −16). We performed similar calculations for the other vectors.

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Answer:

6x^2y

Solution

6x2 y

Step-by-step explanation:

hopefully this helped.bye:)

Using the trigonometric ratios the correct option is option a) 4.98.

We have a known hypotenuse, but an unknown opposite side. Use the sine ratio to tie the two together to be able to solve for x.

Trigonometric ratios are a set of ratios that relate the angles of a right triangle to the lengths of its sides. The most commonly used trigonometric ratios are sine, cosine, and tangent, which are abbreviated as sin, cos, and tan, respectively.

These ratios can be used to find missing side lengths or angle measures in a right triangle, and they have many applications in mathematics, physics, engineering, and other fields.

sin(angle) = opposite/hypotenuse

sin(50) = x/6.5

6.5*sin(50) = x

x = 6.5*sin(50)

x = 4.97928888027336, make sure your calculator is in degree mode

x = 4.98

Therefore, Using the trigonometric ratios the correct option is option a) 4.98.

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Answer: because the mean is 48

Step-by-step explanation:

the average (mean) is 48 so therefore its reasonable that half scored under half scored higher

The coating thickness distribution is normal and has a mean value of 1.245.

In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply put, the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally. The three most frequently employed measures of central tendency are the mean, median, and mode.

To calculate the data's coating thickness, sample mean is employed.

The following formula is used to determine the mean value's point estimate:

[tex]\bar x = \frac{1}{n} \sum x_i[/tex]

The typical probability plot shown there has a rather straight pattern. Assume right now that the coating thickness distribution is normal and has a mean value:

[tex]\bar x = \frac{19.92}{16}\\\\\bar x = 1.245[/tex]

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Answer:

Step-by-step explanation:

√2x + 5 = 5

       -5    - 5

√2x = 0

√2x^2=0^2

2x=0

2x/2 = 0/2

[tex]\huge\red{ANSWER}[/tex]

[tex]\sf \sqrt{2} x+5=5[/tex]

[tex]\sf \sqrt{2} x=5-5[/tex]

[tex]\sf \sqrt{2} x = 0[/tex]

[tex]\sf \frac{\sqrt{2} x }{2}=0[/tex]

[tex]\sf x=0[/tex]

________......

[tex]\pmb{ \orange{LearningLifeII}}[/tex]

The area of this hexagon is 374.4 in².

The area of the hexagon is calculated by applying the following formula.

total area of the regular hexagon = 6 x area of one face

Area of one face = ¹/₂bh

where;

Area of one face = ¹/₂ x ( 12 in ) x ( 10.4 in )

Area of one face = 62.4 in²

Total area of the hexagon = ( 6 ) x ( 62.4 in² ) = 374.4 in²

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It is simpler to compute the likelihood of the complement event when calculating probabilities since you can then just subtract it from 1 to determine the probability.

the variety of strategies for success. all events that could possibly occur.

Since 13% of people are lefties and 87% are righties, we'll assume that everyone is either a righty or a lefty, thus the decimal percentage of 0.87 divided by the total number of participants, 12, is the mean.

P(Right handed) = 1 - 0.13 = 0.87 where P(Left handed) = 0.13 and P(Right handed) = 0.13 12 people make up the nth number. The binomial probability distribution will be used in this case, and it can be computed using the formula P(X = n|N,p) = NCn*(pn)*(1-p) (N-n).

where p is the chance of success and n is the sample size, or 12, in this case. Additionally, q represents the 0.13 failure chance.

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P(Right handed) = 1 - 0.13 = 0.87 where P(Left handed) = 0.13 and P(Right handed) = 0.13 12 people make up the nth number. It is simpler to compute the likelihood of the complement event when calculating probabilities.

the variety of strategies for success. all events that could possibly occur.

Since 13% of people are lefties and 87% are righties, we'll assume that everyone is either a righty or a lefty, thus the decimal percentage of 0.87 divided by the total number of participants, 12, is the mean.

P(Right handed) = 1 - 0.13 = 0.87 where P(Left handed) = 0.13 and P(Right handed) = 0.13 12 people make up the nth number. The binomial probability distribution will be used in this case, and it can be computed using the formula P(X = n|N,p) = NCn*(pn)*(1-p) (N-n).

where p is the chance of success and n is the sample size, or 12, in this case. Additionally, q represents the 0.13 failure chance.

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The evaluation of the piecewise function gives:

when x = -3, f(x) = -4; when x = 2, f(x) = 0; and when x = 4, f(x) =  2.

when x = -3, w(x) = 2; when x = 2, f(x) = 5; and when x = 4, f(x) = 5

A piecewise function is a function that is defined by multiple sub-functions, each of which applies to a certain range of the input (or domain) values.

We want to evaluate the piecewise function when x = -3, x =2 and x = 4:

        { -4,   x < 2

f(x) = { x-2, -2 ≤ x≤ 4

         {0      x > 4

when x = -3:

f(x) = -4 because x < 2 (i.e. -3 < 2)

when x = 2:

f(x) = x-2

f(2) = 2-2 = 0

when x = 4:

f(x) = x-2

f(2) = 4-2 = 2

        { -x - 1,       x ≤ -3

w(x) = { 2x + 2,  -3 < x < 2

         {5,            x ≥ 2

when x = -3:

w(x) = -x - 1

w(-3) = -(-3) - 1 = 2

when x = 2:

f(x) = 5

when x = 4:

f(x) = 5

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The speed of the current is 1 mile per hour.

To calculate we can start by using the formula: distance = speed x time.

Let's call the speed of the current "c" and the speed of Sarah's rowing "r".

When Sarah rows down the river with the current, her speed is the sum of her rowing speed and the current speed: distance = (r + c) * time

When she rows back against the current, her speed is the difference between her rowing speed and the current speed: distance = (r - c) * time

We know that the distance is four miles in both cases, and the time is one hour and two hours respectively.

So we can set up the following two equations:

(r + c) * 1 = 4

(r - c) * 2 = 4

Solving the first equation:

r + c = 4

Solving the second equation:

r - c = 2

Adding the two equations:

r = 3

We know that Sarah is rowing at a constant speed, so we can substitute this value back into one of the original equations:

(3 + c) * 1 = 4

c = 1

So the speed of the current is 1 mile per hour.

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Answer: 6x - 5

Step-by-step explanation:

    Given:

1/6 (12x - 30) + 4x

    Distribute:

2x - 5 + 4x

    Combine like terms with addition:

6x - 5

Answer:

6x - 5

Step-by-step explanation:

Given expression,

→ (1/6)(12x - 30) + 4x

Let's simplify the expression,

→ (1/6)(12x - 30) + 4x

→ ((12x - 30)/6) + 4x

→ 2x - 5 + 4x

→ (2x + 4x) - 5

→ 6x - 5

Hence, the answer is 6x - 5.

On solving the provided question, we can say that length of the rectangle pool is  is = 17.58

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

[tex](30+2x)(40+2x)-1200=3696\\1200+60x+80x+4x^2 -1200=3696\\4x^2 +140x-3696=0\\x=17.58 or -52.58\\[/tex]

length is = 17.58

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So, the probability of selecting a menu from a Japanese restaurant is 4/18, which can also be simplified as 2/9.

The probability of selecting a Japanese restaurant menu from Zach's collection of 18 menus is found by taking the number of Japanese restaurant menus (4) and dividing it by the total number of menus in the collection (18). This can be written mathematically as:

p(japanese) = 4/18

So the probability of selecting a menu from a Japanese restaurant is 4/18, which can also be simplified as 2/9.

In other words, if Zach selects a menu at random from his collection, there is a 2/9 chance that it will be from a Japanese restaurant.

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The rate of change of the perimeter of the square is 11.2 cm/min when the side length is 6 cm.

Step 1: The area of a square is A = s2, where s is the side length.

Step 2: The rate of change of the area of the square is 28 cm2/min.

Step 3: The perimeter of the square is

P = 4s.

Step 4: Substitute s = 6 into the equation for P to get

P = 24 cm.

Step 5: Differentiate P with respect to time to get the rate of change of

the perimeter:

dP/dt = 4ds/dt.

Step 6: Substitute the rate of change of the area (dA/dt = 28 cm2/min) into the equation for dP/dt to get dP/dt = 4(28 cm2/min)/dt.

Step 7: Simplify the equation to get

dP/dt = 112 cm/min.

Conclusion: The rate of change of the perimeter of the square is 112 cm/min when the side length is 6 cm

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Answer:

12

Step-by-step explanation:

Draw a horizontal line that splits the hexagon in half

x = 180 - measure of a angle in the pentagon - half of the angle in the hexagon

x = 180 - 540/5 - 1/2*(720/6)

x = 180 - 108 - 60 = 180 - 168 = 12

Hope this helps :)

Have a great day

The probability that the card is a face card (i.e., a jack, queen, or king) or a heart is 8/13

In the given question, suppose that you draw a card from a standard deck of cards.

We have to find the probability that the card is a face card (i.e., a jack, queen, or king) or a heart.

As we know that in a deck of cards have total 52 cards.

In which 26 cards are in heart shape.

Every different type of card have 3 face cards and have total four different type of cards. That means there are total 12 face cards.

In 26 cards of heart have total 6 face cards.

So, the probability that the card is a face card (i.e., a jack, queen, or king) or a heart

P = (Total face cards + total heart shape card - 6 face cards)/Total cards in a deck

P = (12 + 26 - 6)/52

P = (38 - 6)/52

P = 32/52

P = 8/13

Hence, the probability that the card is a face card (i.e., a jack, queen, or king) or a heart is 8/13.

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The perimeter of the triangle is 96, rounded to the nearest hundredth.

To calculate the perimeter of the triangle, we need to first calculate the length of the hypotenuse.

The hypotenuse of a right triangle is calculated using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the two sides.

Therefore, for this triangle, we have:

(Hypotenuse)² = (24)² + (32)²

Therefore, the Hypotenuse = √(24² + 32²)

Hypotenuse = √(576 + 1024)

Hypotenuse = √1600

Hypotenuse = 40

To calculate the perimeter, we need to add up all three sides of the triangle.

the perimeter = 24 + 32 + 40

the perimeter = 96

Therefore, the perimeter of the triangle is 96, rounded to the nearest hundredth.

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Answer: a. in the step by step explanation.  b. 20x - 15

Step-by-step explanation:

I think that Denise thought that the 5 only appplied to 4x since they were closer and since she multiplied them both, she thought there would be no use of it.

Example - 2 (3x+2)

                 2 x 3x = 6x

                 6x + 2

Of course this is wrong since the real answer should be 6x + 12 but someoneone like Denise may see it that way, only multiplying the ones closest and not opening it fully.

It must be less effective than 100%. Any time you switch from one source of energy to another, especially if there is effort involved, there is a cost.

An enzyme is a protein that must retain its three-dimensional structure in order for it to function as a "lock and key." A little alteration to the enzyme structure might render it inoperative.

Denaturation of proteins is common. The protein's structure can change as a result of environmental factors including pH and temperature. An increase in temperature should hasten the process, but an excessive increase might harm the enzyme. Therefore, the situation in which there is no change to the enzyme structure would be the "ideal" one.

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Note : The complete question could be as bellow,

A second set of measurements were taken, and the efficiency was found to be greater than 100%. What reasons most likely explain why the second set had a different efficiency? Select all that apply:

Used the reciprocal of the efficiency formula

Raised the resistance force in a shorter amount of time

Used the incorrect conversion factor from pounds to Newtons for force Incorrect values for the resistance distance

Inaccurate readings from force sensor for effort force

Increase efficiency from reduced friction

Answer:

There are 4 quarts in a gallon, so 3 1/2 gallons is equal to 3.5 x 4 = 14 quarts.

Since the shop packages its ice-cream in 1-quart containers, the shop will need 14 containers to fulfill the order.

Step-by-step explanation: