A recipe calls for 3 3/4 cups of flour. How many cups will you need if you are preparing 5 batches of the recipe?

Answer:

a) C) The system has no solutions only when h=3 and k is any real number.

b) D) The system has a unique solution when [tex]h=(-\infty,3)U(3,\infty)[/tex] and k is any real number.

c) The system has may solutions when h=3 and k=15

Step-by-step explanation:

a) In order to determine when the system will have no solution, we can start by solving the equation by substitution. We can solve the first equation for x1:

[tex]x_{1}+hx_{2}=3[/tex]

so

[tex]x_{1}=3-hx_{2}[/tex]

Next we can substitute this into the second equation so we get:

[tex]5(3-hx_{2})+15x_{2}=k[/tex]

We distribute the 5 into the first parenthesis so we get:

[tex]15-5hx_{2}+15x_{2}=k[/tex]

and group like terms:

[tex]-5hx_{2}+15x_{2}=k-15[/tex]

we factor x2 so we get:

[tex]x_{2}(-5h+15)=k-15[/tex]

and solve for x2:

[tex]x_{2}=\frac{k-15}{-5h+15}[/tex]

this final answer is important because it tells us what value the system of equations is not valid for. That answer will not ve vallid if the denominator is zero, so we can set the denominator equal to zero and solve for h, so we get:

[tex]-5h+15= 0[/tex]

and solve for h:

[tex]-5h= -15[/tex]

[tex]h=\frac{-15}{-5}[/tex]

[tex]h= 3[/tex]

so it doesn't really matter what value k gets since all that matters is that the denominator of the answer isn't zero.

b)

For part b we need to know when the system of equations will have infinitely many answers. Generally, this will happen when both equations are basically the same, so we need to make sure to simplify the second equation so it looks like the first equation, compare them and determine the respective coefficients.

So we take the second equation and factor it:

[tex]5x_{1}+15x_{2}=k[/tex]

we start by factoring a 5 from the left side of the equation so we get:

[tex]5(x_{1}+3x_{2})=k[/tex]

Next, we divide both sides of the equation into 5 so we get:

[tex]x_{1}+3x_{2}=\frac{k}{5}[/tex]

we now compare it to the first equation:

[tex]x_{1}+hx_{2}=3[/tex]

[tex]x_{1}+3x_{2}=\frac{k}{5}[/tex]

In this case, every coefficient of the two equations must be the same for us to get infinitely many answers, so we can see that h=3 and [tex]\frac{k}{5}=3[/tex]

when taking the second condition and solving for k we get that:

[tex]k=3(5)[/tex]

so

k=15

Anything else than the specific combination h=3 and k=15 will give us unique solutions, so for b, the answer is:

D) The system has a unique solution when and k is any real number.

c)

We have already solved part c on the previous part of the problem, so the answer is:

The system has many solutions when h=3 and k=15

Answer:

X=8

Step-by-step explanation:

JK would equal 28, since it basically is double the side of that triangle. So now we have the equation, 2x+12=28. Now we solve using inverse operation. 28-12=16 and then 16 divided by 2 is 8, so x=8.

The required simplified value of x is 8, for the given triangle.

A midpoint is a point on the line whose distance from both ends of the line is equal.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

Here,
The property of a triangle states that the line joining the midpoints of the two adjacent sides is equal to half of the third side.
So,
JK = 2NO
2x + 12 = 24
x = 16 / 2
x  = 8

Thus, the required simplified value of x is 8, for the given triangle.

Learn more about triangles here:

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Answer:

If the answer is north why did you post it?

Answer:

1,2,4,8

Step-by-step explanation:

Try 1x8=8, put on factor list.

Take 2.

Take 3 next.

Since there's no more, iss done.

Answer:

the initial value is 15 and it represents the y-intersect in the context of this problem

Step-by-step explanation:

Answer:

474$

Step-by-step explanation:

Answer:

first one

Step-by-step explanation:

it is what is it

Answer:

Survey data

Step-by-step explanation:

Survey data is defined as the resultant data that is collected from a sample of respondets that took a survey

The data obtained by conducting a survey is called as "survey data".

It is given that we are conducting a survey.

what will we call the data which is obtained through the survey.

What is a survey ?

Survey is a research method of gathering information or collecting the data.

Survey data is defined as the resultant data that is collected from a sample of respondents that took a survey.

The survey data is generally precise and enclosed within the topic of survey.

Thus, the data obtained by conducting the survey is called "survey data".

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Answer:

0.705

Step-by-step explanation:

Answer: the answer is .705

Step-by-step explanation:

the numbers 0.25 and 0.33 are technically 0.250 and 0.330

so just line them up and add. 0.250+0.125+0.330=0.705

Answer:

1.8 x 71 = 127.8, just 18 x 71 = 1278, then count the the decimal place from the right, i.e 127.8

same for 2.6 x 83 = 215.8

.......ok try 5.52 x 5

Answer:

27,579.24 OR 343.6

Step-by-step explanation:

I don't know if this is what you mean but 1.8x71x2.6x83=27,579.24

Also, (if that was not what you meant), 1.8x71=127.8, 2.6x83=215.8, 127.8+215.8=343.6

Answer:

Correct mean = 32 grams

Correct Standard deviation = observed S.D = 2 grams

Step-by-step explanation:

We are told in the question above :

A scientist is weighing each of 30 fish. She obtains a mean of 30 g and a standard deviation of 2 g. After completing the weighing, she finds that the scale was misaligned and always under reported every weight by 2 g that is

The mean after correcting the error in the scale is :

= observed mean + 2g

= 30g + 2g = 32g

The standard deviation after correcting the error in the scale remains the same as the difference of 2g has no significant effect on the Standard deviation.

This standard deviation = 2g

Answer:

25 and 18

Step-by-step explanation:

Answer:

A function is a relationship that maps the elements of a set, the domain, into elements of another set, the range.

The restriction that we have for functions is: The elements on the domain can be mapped into only one element in the range.

Then if:

f(x1) = y1

and

f(x1) = y2

where y1 is different than y2

f(x) is not a function.

Now, in the graph you can see a region where both lines overlap, then for some values of x we have two possible values of y, this means that the graph does not represent a function.

Then:

Ed: He is incorrect because we can have different values in the domain mapped into the same value in the range (like in the case of a line y = b, where we have all the elements in the domain mapped into the same element in the range, b)

Debra: There is something called piecewise functions, that are functions of this type, formed by different pieces.

Alejandro: He is correct.

Antoine: Not because you can write an equation means that the relation is a function. You can write an equation for a circle, but it will not be a function.

Answer:

The answer is 23

Answer:

t = 23

Step-by-step explanation:

Answer: 65

Step 1: Multiply and add until you get 49.

11 x 4 = 44.

44 + 5 = 49.

Step 2: Multiply and add until you get 26, because 7:11 to 49 boys is 26,       26 : 49.

7 x 3 = 21.

21 + 5 = 26.

Step 3: Add 26 and 49.

26 + 49 = 65

Answer:

126 students

Step-by-step explanation:

Boys : Girls

7 : 11

How do you get from 7 to 49?

49 ÷ 7 = 7

Therefore, you should multiply the number of boys by 7.

Multiply:

7 : 11

7 × 7 = 49

49 : 11

Remember that whatever we do to the left, do to the right.

Multiply:

49 : 11

11 × 7 = 77

49 : 77

Now, let's add the number of boys and girls in the class to find the total number of students.

Add:

49 + 77 = 126

Therefore, there are 126 students in all.

Answer:

2.4x - 4.4

Step-by-step explanation:

0.3(4x – 8) – 0.5(–2.4x + 4)

1.2x - 2.4 + 1.2x -2

2.4x - 4.4

Answer:

Step-by-step explanation:

9. Alternative exterior

10. Alternate interior

11. Complementary

12. Corresponding

13. Corresponding

14. Alternate exterior

15. Vertical

16. Linear Pair

Answer:

The Answer is D

Step-by-step explanation:

Do what answer D tells you to do. Obviously.

Answer:

.4625

Step-by-step explanation:

To find the mean, add up all the numbers, then divide by the number of terms

(0.2 +0.4+ 1+ 0.25) /4

1.85/4

.4625

Answer:

i think its C

Step-by-step explanation:

sorry if i get it wrong

Answer:

a) C(2000)=1915

C(2014)=1915

b) [tex]C'(2000)=-\frac{275}{14}[/tex]

[tex]C'(2014)=-\frac{275}{14}[/tex]

c) [tex]C(t)=-\frac{275}{14}t+\frac{288405}{7}[/tex]

d) t=2021

e) too early

Step-by-step explanation:

a)

Since C(t) is the concentration of CFCs in ppt in year t, all we need to do to solve this part is determine what the concentration of CFCs is in years 2000 and 2014. Luckily for us, the problem already gives us those values, so:

C(2000)=1915    concentration in year 2000

C(2014)=1915      concentration in year 2014

b)

By definition, the derivative of a function at a given point is interpreted as the slope of the tangent line to the point of interest, so in order to find this answer, we need to find the slope of the line. Since the problem specifies that the behavior is linear, this means that the slope will always be the same no matter the year, so we get:

[tex]m=C'(t)=\frac{C'(t_{2})-C'(t_{1})}{t_2-t_1}[/tex]

so:

[tex]C'(t)=\frac{1640-1915}{2014-2000}=-\frac{275}{14}\approx -19.64[/tex]

therefore:

[tex]C'(2000)=-\frac{275}{14}[/tex]

[tex]C'(2014)=-\frac{275}{14}[/tex]

c)

Since the behavior is linear, we can calculate it with the point-slope form of the line which is:

[tex]y-y_{1}=m(x-x_{1})[/tex]

in this case:

[tex]C(t)-C(t_1)=C'(t)(t-t_{1})[/tex]

so we get:

[tex]C(t)-1915=-\frac{275}{14}(t-2000)[/tex]

and we can now solve for C(t) so we get:

[tex]C(t)=-\frac{275}{14}t+\frac{275000}{t}+1915[/tex]

for a final answer of:

[tex]C(t)=-\frac{275}{14}t+\frac{288405}{7}[/tex]

d)

So next we solve the equation for C(t)=1500 so we get:

[tex]1500=-\frac{275}{14}t+\frac{288405}{7}[/tex]

[tex]1500-\frac{288405}{7}=-\frac{275}{14}t[/tex]

[tex]-\frac{277905}{7}=-\frac{275}{14}t[/tex]

[tex]t=2021 \frac{7}{55}[/tex]

so we will reach that concentration level at the year 2021 approximately.

e)

Since the second derivative of the concentration function is greater than zero, this means that the original function might be a function in the form: .

This means that the decrease of the concentration levels is slower than that of a linear equation. So the projected date will be too early than the real date.

Answer:

13

Step-by-step explanation:

Step 1:

EF + FG = EG        Equation

Step 2:

7 + 6 = EG        input values

AnsweR:

13 = EG            Add

Hope This Helps :)

Answer:

4/16

Step-by-step explanation:

Answer:

(-2,-4) or (2,4) depending on which one you start on.

Step-by-step explanation:

if you start from the highest point it is (-2,-4)

And if you start from the lowest point (2,4)

Answer:

subtract from the maximum load the 1500 of the loading equipment and you have 6500 pounds of capacity for the containers you divide this by 300 which is what each of the containers weighs gives you 21,666 which tells us that the maximum of containers is 21

8000-1500 = 6500

6500/300 = 21.66

Step-by-step explanation:

Answer:

X<1 or X>3/2

Step-by-step explanation: