The following system of linear equations has how many solutions?

3y = x + 6

6y - 2x = 12

Answer: the equation have two solutions: 0.25 and 0.75

[tex]x=\frac{1}{4}[/tex]  or  [tex]x=\frac{3}{4}[/tex]

Step-by-step explanation:

Notice the terms [tex]x+x^2+x^3+x^4+...+x^n[/tex] is just a geometric series (since -1<x<1)

A geometric series is given by the form

[tex]1+x+x^2+x^3+x^4+...+x^n = \frac{1}{1-x}[/tex]
This is
[tex]x+x^2+x^3+x^4+...+x^n = \frac{1}{1-x} -1[/tex]
plugging in in the equation

[tex]-1+\frac{1}{x} +\frac{1}{1-x} -1=\frac{10}{3}[/tex]

grouping terms

[tex]\frac{1}{x} +\frac{1}{1-x} =\frac{16}{3}[/tex]
groupings the fractions

[tex]\frac{1-x+x}{(x)(1-x)}=\frac{1}{(x)(1-x)} =\frac{16}{3}[/tex]

this leads to an simplified quadratic equation since X cannot be zero (notice the initial 1/x term)

[tex]3=16(x^2-x)[/tex]
the solution for this quadratic equation is just

[tex]x=\frac{1}{4}[/tex]  or  [tex]x=\frac{3}{4}[/tex]

Answer:

  1/4 or 3/4

Step-by-step explanation:

You want the value of x in the infinite sum ...

  -1 +1/x +x +x² +x³ +...  = 10/3

for |x| < 1.

After the 2nd term, this looks like a geometric series with a common ratio of x. If we define the series sum as ...

  S = 1/x +1 +x +x² +x³ +...

we see that the equation of interest is ...

  S -2 = 10/3

The series sum is that of a geometric series with first term 1/x and common ratio x:

  S = (1/x)(1/(1 -x)) = 1/(x(1-x))

Substituting for S in the above, we have the equation ...

  1/(x(1-x)) -2 = 10/3

This resolves to a quadratic that will have 2 real roots:

  1/(x(1 -x)) = 16/3 . . . . add 2

  x(1 -x) = 3/16 . . . . . . . invert both sides

  x² -x +3/16 = 0 . . . . . .  subtract the left side expression

  (x -3/4)(x -1/4) = 0 . . . . . factor

Solutions are the values of x that make these factors zero:

  x = 1/4 or x = 3/4

Answer:

The cost of a specialty pizza is $19.49.

Step-by-step explanation:

To write a subtraction equation that could be used to find the cost c of a specialty pizza, we need to set up an equation that represents the relationship between the cost of a one-topping pizza and the cost of a specialty pizza.

The problem states that a one-topping pizza costs $6.50 less than a specialty pizza. Therefore, we can subtract $6.50 from the cost of a specialty pizza to get the cost of a one-topping pizza:

Cost of specialty pizza - $6.50 = Cost of one-topping pizza

We can rearrange this equation to solve for the cost of the specialty pizza:

Cost of specialty pizza = Cost of one-topping pizza + $6.50

Now, we can substitute the given value for the cost of a one-topping pizza:

Cost of specialty pizza = $12.99 + $6.50

Simplifying the expression, we get:

Cost of specialty pizza = $19.49

Therefore, the cost c of a specialty pizza is $19.49.

Hope this helps! I'm sorry if it doesn't. If you need more help, ask me! :]

Tt would take Maurice and Olinda approximately 47.37 minutes

What is work done?

Work done in physics is the dot product of force and displacement. When a force applied on an object results in a displacement, it is said to be work is done on the object.

Let's denote the time it takes both Maurice and Olinda working together to weed the garden as t.

We can use the formula: 1 / t = 1 / a + 1 / b

Plugging in the given values, we get: 1 / t = 1 / 45 + 1 / 50

1 / t = (50 + 45) / (50 * 45) = 95 / 2250

Then, we can invert both sides of the equation to get: t / 1 = 2250 / 95

Simplifying the right-hand side by dividing both the numerator and the denominator by 5, we get:

t = 2250 / 95 = 47.37 minutes (rounded to two decimal places)

Therefore, it would take Maurice and Olinda approximately 47.37 minutes to weed the garden if they work together.

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Okay so you want to make all of the fractions have a common denominator. Think of the lowest number that 3 and 5 go into, the answer you should get is 15. So 15 is the common denominator.

Now we're going to make 1/3 have a denominator of 15. 1/3 of 15 would be 5. You get that by figuring out what you have to multiply 3 by to get 15 which is 5. Then you multiply 5 and 1 and you get 5.  The answer you will get will be 5/15 which is equal to 1/3.

Next we're going to make 4/5 have a denominator of 15. 4/5 of 15 would be 12/15. You can get this by figuring out what you have to multiply 5 by to get 15 which is 3. Then you take 3 and multiply it by 4 to get that 12 in 12/15. The answer 12/15 is equal to 4/5 of 15.

So now you have 5/15 + a = 12/15.

The denominator of the fraction that "a" will be is 15 because that is what we made the common denominator.

So what we have is 5/15 + x/15 = 12/15.

Think of what you have to add to 5 to get 12. (The answer is 7)

So a is equal to 7/15

Your final answer should be 5/15 + 7/15 = 12/15

Let x be the number of text messages that your older sister sends per day. Then we can write an equation based on the given information:

x + 12 = 26

We can solve for x by subtracting 12 from both sides of the equation:

x = 26 - 12

x = 14

Therefore, your older sister sends about 14 text messages per day.

Answer: x=7 y=5

Step-by-step explanation:

I believe this is the answer to the question  

The time between the injections that is injected again when the dosage reaches 9 is solved to be 1.8 to the nearest tenth

The information given by the problem include the expression

D(h) = 20e^(-0.45h)

The expression is an exponential function that shows the relationship between time and the dosage in milligrams  

given that D = 9 we find h

D(h) = 20e^(-0.45h)

9 = 20e^(-0.45h)

9/20 = e^(-0.45h)

take ㏑ of both sides

㏑(9/20) = -0.45h

isolating h by dividing by -0.45

h = ㏑(9/20) / -0.45

h = 1.774

h = 1.8 to the nearest tenth

This shows that the time is 1.8 hours

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Answer: -1/2

Step-by-step explanation:

To find the slope: rise/run

starting from the point (0,2), you go up 1 to reach the line

Therefore 1 is your rise.

Then go right 2 units and you hit the line again.

Therefore the slope is 1/2.

But the linear line is going downwards, so it is a negative slope

Therefore your final answer is:

-1/2

Answer:

4+5/8

or

5/8+4

Step-by-step explanation:

"increased by" is adding, and "quotient" id dividing two numbers.

The mathematical expression '4 increased by the quotient of 5 and 8' is written as 4 + 5/8 in standard mathematical notation, meaning you first divide 5 by 8 and then add the result to 4.

The sequence of operations described can be converted into an expression in the following way: In terms of mathematics, the term 'increased by' refers to addition. The 'quotient of 5 and 8' refers to the result of dividing 5 by 8. Therefore, the expression can be written as '4 + 5/8'.

So, the mathematical expression '4 increased by the quotient of 5 and 8' becomes 4 + 5/8 in standard mathematical notation. This means you first divide 5 by 8 and then add the result to 4.

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Using set theory, the element in each of the set are, A - B = {3, 5}, (A - B)^c = {2, 4, 6, 7, 8, 9, 10, 11}, U - (A - B)^c = {3, 5}, (A \cup B)^c = {2, 4, 6} and (A^c U B^c)^c = {7, 9, 11}.

The given sets are:

U = {2,3,4,5,6,7,8,9,10,11}

A = {3,5,7,9,11}

B = {7,8,9,10,11}

We can use these sets to find the following:

1. A - B: The elements in set A that are not in set B are {3, 5}.

2. (A - B)^c: The complement of set A - B in U contains all the elements in U that are not in A - B. These elements are {2, 4, 6, 7, 8, 9, 10, 11}.

3. U - (A - B)^c: This set contains all the elements in U that are not in the complement of A - B. These elements are {3, 5}.

4. (A U B)^c: This set contains all the elements in U that are not in the union of sets A and B. The union of A and B is {3, 5, 7, 8, 9, 10, 11}, so the complement is {2, 4, 6}.

5. (A^c U B^c)^c: This set contains all the elements in U that are in neither the complement of set A nor the complement of set B. The complement of set A is {2, 4, 6, 8, 10} and the complement of set B is {2, 3, 4, 5, 6}. The union of these two sets is {2, 3, 4, 5, 6, 8, 10}, so the complement of this set in U is {7, 9, 11}.

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Therefore, the value of hydraulic conductivity using the Thiem equation is approximately 10.67 ft/day.

An equation is a mathematical statement that indicates that two expressions are equal. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The expressions on both sides of the equation are separated by an equal sign "=" which means that the two expressions have the same value. Equations are used to model relationships between variables, solve problems, and make predictions in various fields of science, engineering, economics, and mathematics. They are an essential tool in algebra, calculus, and other branches of mathematics.

Here,

To compute the value of hydraulic conductivity using the Thiem equation, we need to substitute the given values into the equation:

K = (Q / π) * ((h2 - h1) / log(r2/r1))

where:

Q = pumping rate = 78,000 ft³/d

h1 = head at the pumping well = 260 ft ASL

h2 = head at the observation well 385 ft away = 291 ft ASL

r1 = distance from the pumping well to the observation well 125 ft away = 125 ft

r2 = distance from the pumping well to the observation well 385 ft away = 385 ft

Substituting the values, we get:

K = (78,000 / π) * ((291 - 260) / log(385/125))

K = 10.67 ft/day

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Answer:

Step-by-step explanation:

[tex]S=40R+20[/tex]

We can rewrite 3.1672 × 10¹² as 3.1672 × 10² The correct option is A

First we first express it as a number between 1 and 10 multiplied by a power of 10. In this case, 316.72 can be expressed as:

3.1672 × 10¹² (since we move the decimal point 2 places to the right to get to 31672)

However, in scientific notation, the exponent should represent the number of places the decimal point is moved. Since we moved the decimal point to the right, the exponent should be negative.

Therefore, we can rewrite 3.1672 × 10¹² as:

3.1672 × 10²

So, the answer is (A).

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The point in which f(x) have a horizontal tangent are (-7 + √46)/3, (-7 - √46)/3

To find the values of x where the graph of f(x) has a horizontal tangent, we need to find where the derivative of f(x) is equal to zero (since the derivative gives the slope of the tangent line).

First, we find the derivative of f(x):

f'(x) = 3x² + 14x + 1

Next, we set f'(x) equal to zero and solve for x:

3x² + 14x + 1 = 0

Using the quadratic formula, we get:

x = (-14 ± √(14² - 431)) / (2*3)

x = (-14 ± √(184)) / 6

x = (-14 ± 2√46) / 6

Simplifying:

x = (-7 ± √46) / 3

Therefore, the values of x where the graph of f(x) has a horizontal tangent are (-7 + √46)/3 and (-7 - √46)/3.

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Answer:

w = 6in, l = 10in

Step-by-step explanation:

Area of a rectangle is [tex]A=l*w[/tex]

and [tex]l = 4 + w[/tex]

We can solve for length and width by substituting these values for the equation.

[tex]60in^2=(4+w)*w[/tex]

[tex]60in^2=4w+w^2[/tex]

[tex]0 = w^2 + 4w + 60in^2[/tex]

factor out the equation.

[tex]0= (w+10)(w-6)[/tex]

therefore w = 6in (tossing out the negative solution)

which means

[tex]l = 4 + w[/tex]

[tex]l = 6in + 4[/tex]

l = [tex]10in[/tex]

Hope this helps!
Brainliest is much appreciated!

To adjust the recipe to make 30 rolls instead of 12, we need to multiply the amount of each ingredient by a factor of 30/12 = 2.5.

A factor is a number or expression that divides another number or expression evenly without a remainder.

To adjust the recipe to make 30 rolls instead of 12, we need to multiply the amount of each ingredient by a factor of 30/12 = 2.5.

To determine this factor, we divide the desired number of rolls (30) by the original number of rolls (12):

2.5 = 30/12

To find the amounts of each ingredient needed to make 30 rolls, we multiply the original amounts by 2.5:

Yeast: 1/4 oz x 2.5 = 0.625 oz (or about 0.63 oz)

Warm water: 1 cup x 2.5 = 2.5 cups

Molasses: 3 tbsp x 2.5 = 7.5 tbsp (or about 1/2 cup + 1 tbsp)

Powdered milk: 1/3 cup x 2.5 = 0.83 cups (or about 3/4 cup + 1 tbsp)

Egg yolk: 1 beaten yolk x 2.5 = 2.5 beaten yolks (or about 2 yolks)

Egg white: 1 beaten white x 2.5 = 2.5 beaten whites (or about 2 whites)

Bread flour: 3 1/2 cups x 2.5 = 8.75 cups (or about 8 3/4 cups)

Butter: 6 tbsp x 2.5 = 15 tbsp (or about 1 cup - 1 tbsp)

Salt: 1 tsp x 2.5 = 2.5 tsp (or about 2 1/2 tsp)

Whole wheat flour: 1/2 cup x 2.5 = 1.25 cups (or about 1 1/4 cups)

Raisins: 1/3 cup x 2.5 = 0.83 cups (or about 3/4 cup + 1 tbsp)

To make 30 rolls, you will need 0.625 oz (or about 0.63 oz) of yeast.

To make 30 rolls, you will need 0.83 cups (or about 3/4 cup + 1 tbsp) of powdered milk.

To make 30 rolls, you will need 15 tbsp (or about 1 cup - 1 tbsp) of butter.

To make 30 rolls, you will need 8.75 cups (or about 8 3/4 cups) of bread flour, which is 8.75 - 1.25 = 7.5 cups more than the 1.25 cups of whole wheat flour needed.

If you put in 3/8 cup of water instead of the 1/4 cup called for in the original recipe, you have added an extra 3/8 - 1/4 = 1/8 cup of water, or 2 tablespoons of water.

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Answer:

A equals 13.5 centimeters

Answer:

Step-by-step explanation:

[tex]V=\pi r^2 h[/tex]

Substitute [tex]h=l,r=2,V=150,[/tex] we get

[tex]150=\pi \times 2^2 \times l[/tex]

[tex]150=4\pi l[/tex]

[tex]l=\frac{150}{4\pi}=11.94cm[/tex]

Answer:

a

Step-by-step explanation:

The formula to calculate simple interest is:

I = P * r * t

Where:

I = Interest

P = Principal amount

r = Rate of interest

t = Time period

Given:

Principal amount (P) = $1,700

Rate of interest (r) = 8% per annum

Time period (t) = 4 years

Using the formula of simple interest:

I = P * r * t

I = 1,700 * 0.08 * 4

I = $544

Therefore, the total interest on a 4-year term loan of $1,700 with a simple annual interest rate of 8% is $544.

Answer: A. $544

Applying the definition of variation, we have:

1. When x = 36, y = 6.

2. When x = 1, y = 27.

3. It takes 3 seconds for the object to fall 144 feet.

4. Length of a string that vibrates 64 times per second is 48 inches.

Inverse variation is a type of relationship between two variables in which one variable increases while the other decreases, or vice versa, in a way that the product of the two variables remains constant.

In other words, if we have two variables x and y that are inversely proportional, we can write:

x × y = k, where k is a constant.

1. We are given that y varies directly as the square root of x. This means that we can write:

y = k√x

where k is a constant of proportionality. To find the value of k, we can use the given information that when x = 16, y = 4:

4 = k√16

4 = 4k

k = 1

Now we can use this value of k to find y when x = 36:

y = 1√36

y = 6

Therefore, when x = 36, y = 6.

2. We are given that y varies inversely with the cube of x. This means that we can write:

y = k/x³

where k is a constant of proportionality. To find the value of k, we can use the given information that when x = 3, y = 1:

1 = k/3³

1 = k/27

k = 27

Now we can use this value of k to find y when x = 1:

y = 27/1³

y = 27

Therefore, when x = 1, y = 27.

3. We are given that the distance that an object falls varies directly with the square of the time, t, of the fall. This means that we can write:

d = kt²

where d is the distance, k is a constant of proportionality, and t is the time. To find the value of k, we can use the given information that when t = 1, d = 16:

16 = k(1)²

16 = k

k = 16

Now we can use this value of k to find the time it takes for the object to fall 144 feet:

144 = 16t²

9 = t²

t = 3

Therefore, it takes 3 seconds for the object to fall 144 feet.

4. We are given that the rate of vibration of a string under constant tension varies inversely with the length of the string. This means that we can write:

r = k/L

where r is the rate of vibration, L is the length of the string, and k is a constant of proportionality.

To find the value of k, we can use the given information that when L = 24 inches, r = 128 vibrations per second:

128 = k/24

k = 3072

Now we can use this value of k to find the length of a string that vibrates 64 times per second:

64 = 3072/L

L = 48 inches

Therefore, the length of a string that vibrates 64 times per second is 48 inches.

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Answer: 14 dollars.

Step-by-step explanation:

You (1) + your four friends (4) is 5.

5 times a number is 70.

5x=70

70/5=14

x=14

Answer:

No solution

Step-by-step explanation:

y = 2x + 1 _____(equ 1)

2x - y = 3 _____(equ 2)

from equ 1

y = 2x + 1

2x + 1 = y

2x = y - 1

x = (y - 1)/2

substitute x = (y - 1)/2 into equ 2

2x - y = 3

2((y-1)/2) - y = 3

(2y - 2)/2 - y = 3

y - 1 - y = 3

y - y = 3 + 1

0 = 4

Hello and best regards sanungapatricio1985

This equation has no solution, since -1 cannot be equal to 3. Therefore, the system has no solution.

We have the following equations:

                ⇒ y = 2x + 1

                ⇒ 2x - y = 3

The substitution method is a common method for solving systems of linear equations. It consists of isolating one of the variables from one of the equations and substituting the expression obtained in the other equation to eliminate that variable and obtain an equation with a single variable, which can be solved to find the value of that variable. Then, the found solution can be substituted into any of the original equations to find the value of the other variable.

From the first equation we have a good substitution candidate:

                ⇒ y = 2x + 1

Now we have to plug y = 2x + 1 found from the first equation, into the second equation 2x - y = 3, to find that:

                ⇒ 2x - y = 3

                ⇒ 2x - (2x + 1) = 3

                ⇒ 2x - 2x - 1 = 3

Based on the previous results, the system has no solution.

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Answer:

??

Step-by-step explanation:

is there a picture or something?

The percent of the bottle of apple juice is 40%.

An element of a whole number is a fraction. There are many different kinds of fractions. Three-quarters, for instance, is a fraction.

A decimal point separates a fractional component from an integral component to form a decimal. In the decimal 2.5, for instance, the fractional portion comes after the decimal point and is followed by the integer 2, which is put before it.

Per cent simply means one in a hundred. Hence, it is a number with a fractional representation that has a denominator of 100. As a result, fractions of a whole number are also described using percentages.

Given that, 80-ounce bottle of apple juice contains 32 ounces of water.

Thus,

% of water = (32 / 80) * 100 = 40%

Hence, the percent of the bottle of apple juice is 40%.

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To determine the distance of the foot of the ladder from the wall, we can use trigonometry. Let's call the distance we want to find "x".

First, let's draw a diagram:

          |\

          | \

   20   |  \ x

          |   \

          |____\

           40°

In this diagram, the ladder is the hypotenuse of a right triangle, and the distance we want to find ("x") is one of the legs. The other leg is the height of the ladder on the wall, which we don't need to know in order to solve the problem.

We can use the trigonometric function for the sine of an angle to relate the angle of elevation to the distance "x" and the length of the ladder:

sin(40°) = x / 20

To solve for "x", we can multiply both sides by 20:

20 sin(40°) = x

Using a calculator, we can evaluate the sine of 40 degrees to get:

20 sin(40°) ≈ 12.85

So the distance of the foot of the ladder from the wall is approximately 12.85 meters, rounded to two decimal places.

Answer:

y= -x - 3 is correct

Step-by-step explanation:

The median shows that the average number of students per middle school classroom in both districts is 24, while the mean shows that the average number of students per middle school classroom in one district is 24 and the other is 25.  

Median is the middle value of a set of data. It is the value that divides the data set into two equal halves. It is an important measure of central tendency and is used to compare sets of data.  

The difference between the mean number of students per middle school classroom in each school district is 2 students. The difference between the median number of students per middle school classroom in each school district is 0 students.

Based on the number of students shown for each school district, the median would provide the most accurate picture of the number of students in a middle school classroom, as there are some extreme values that would affect the mean but not the median.

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Answer:

Rounding to the nearest hundredth, the area of the shaded region is approximately 167.91 square yards.

Step-by-step explanation:

To find the area of the shaded region between two circles with the same center, we need to subtract the area of the smaller circle from the area of the larger circle.

The area of the larger circle is:

A_outer = πr_outer^2

= π(11.9 yd)^2

≈ 445.03 yd^2

The area of the smaller circle is:

A_inner = πr_inner^2

= π(9.4 yd)^2

≈ 277.12 yd^2

Therefore, the area of the shaded region is:

A_shaded = A_outer - A_inner

≈ 445.03 yd^2 - 277.12 yd^2

≈ 167.91 yd^2

Hope this helps! Sorry if it doesn't. If you need more help, ask me! :]

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{\underline{annually}, thus once} \end{array}\dotfill &1\\ t=years\dotfill &6 \end{cases} \\\\\\ A = 3000\left(1+\frac{0.04}{1}\right)^{1\cdot 6} \implies A \approx 3795.96 \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{\underline{quarterly}, thus four} \end{array}\dotfill &4\\ t=years\dotfill &6 \end{cases} \\\\\\ A = 3000\left(1+\frac{0.04}{4}\right)^{4\cdot 6} \implies A \approx 3809.20 \\\\[-0.35em] ~\dotfill[/tex][tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{\underline{monthly}, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &6 \end{cases} \\\\\\ A = 3000\left(1+\frac{0.04}{12}\right)^{12\cdot 6} \implies A \approx 3812.23 \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$3000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &6 \end{cases} \\\\\\ A = 3000e^{0.04\cdot 6} \implies A \approx 3813.75[/tex]

Answer: -5 1/4

Step-by-step explanation:

After answering the final question incorrectly, Sandra's score will be -5 1/4 in fraction form, and -5.25 in decimal form. This is because every time Sandra gets a question wrong her grade goes down by -3/4 points. And -4 1/2 minus -3/4 is -5 1/4. I hope this helped. If not, let me know and I can try to reword it.

Answer: b

Step-by-step explanation: