Norma had 3/8 birthday cake left over from her party . She ate 3/4 of the leftover cake at lunch. How much of the whole cake did Norma have at lunch?

Answer:

L = 36  and  w = 14

Step-by-step explanation:

50 - L = (1/2)L - 4

⇔ 50 + 4 = (1/2)L + L

⇔  54 = (3/2)L

⇔  2 × 54 = 3L

⇔  108 = 3L

⇔  3L = 108

⇔  L = 108/3

⇔  L = 36

Calculating the width ‘w’ :

w = (1/2)L - 4

Then

w = (1/2)(36) - 4

Then

w = 18 - 4

Then

w = 14

(a) The missing value of y is 8

(b) The missing value of x is 144

Now, According to the question:

The ration table is:

X      Y

2      ?

4     16

5     20

?      36

We have to find the value of y

Now, According to the table :

The value of x is 2

So, value of y will be 8

x/y = 2/8 = 1/4

Next, x/y = 4/16 = 1/4

=> 5/20 = 1/4

Similarly, we are multiplying the first column by 1/4 to get the second column, we can set up the following equation for x.

1/4x = 36

x = 144

Hence,  the missing value of y is 8

(b) The missing value of x is 144.

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Answer:

I HOPE IT WILL HELP

EXPLANATION IS IN THE PHOTO .

one-sided limits of a function f(x) at x = 1 is  lim x → 2[f(x) - f(2)]/(x - 2) = 20

Since  function f(x) = 5(x² - 1) and we want to find its derivative, we can proceed thus.

Let x = h + 2

So,  

f(x) = 5(x² - 1)

f(2) = 5[(2)² - 1]

= 5[4 - 1]

= 5(3)

= 15

f(2 + h) = 5[(2 + h)² - 1)

= 5(4 + 4h + h² - 1)

= 5(3 + 4h + h²)

= 15 + 20h + 5h²

So, f(2 + h) - f(2) = 15 + 20h + 5h² - 15

= 20h + 5h²

So, we have that

[f(2 + h) - f(2)]/h = (20h + 5h²)/h

= 20 + 5h

Now, taking the limit as h → 0, we have

= 20 + 5(0)

= 20 + 0

= 20

So,  lim h → 0[f(2 + h) - f(x)]/h = lim x → 2[f(x) - f(2)]/(x - 2) = 20

So,  lim x → 2[f(x) - f(2)]/(x - 2) = 20

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To solve this problem, we need to use the formula for permutations, which is nPr = n! / (n - r)!, where n is the total number of objects and r is the number of objects we are choosing. In this case, we are choosing 5 digits from a set of 6 digits (since we can't repeat any digit), so we have:

6P5 = 6! / (6 - 5)! = 6 x 5 x 4 x 3 x 2 = 720

Therefore, there are 720 5-digit numbers that can be formed using only the digits 3, 8, 1, 2, 5, and 7, where no digit is used more than once.
To form a 5-digit number using the digits 3, 8, 1, 2, 5, and 7 without repetition, follow these steps:

1. Choose a digit for the first position: You have 6 options (3, 8, 1, 2, 5, or 7).
2. Choose a digit for the second position: You now have 5 remaining options (since you cannot repeat the digit chosen in step 1).
3. Choose a digit for the third position: You have 4 remaining options (excluding the digits chosen in steps 1 and 2).
4. Choose a digit for the fourth position: You have 3 remaining options (excluding the digits chosen in steps 1, 2, and 3).
5. Choose a digit for the fifth position: You have 2 remaining options (excluding the digits chosen in steps 1, 2, 3, and 4).

Now, multiply the number of options for each position: 6 × 5 × 4 × 3 × 2 = 720

So, there are 720 different 5-digit numbers that can be formed using the digits 3, 8, 1, 2, 5, and 7 without repetition.

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If a bloodstain is 1.5cm wide and 30cm long, then the angle of impact is 30°.

In forensic science, the angle of impact is the angle at which a blood droplet strikes a surface. It has a range of 0 to 90 degrees and is, by definition, an acute (or right) angle.

Police can partially reconstruct a crime scene by connecting the "strings" that lead from the spatter to an origin area and knowing the angle of contact.

If a bloodstain has a tail or pattern, the angle of impact can be used to forecast how the subsequent bloodstain would look.

So, bloodstain pattern analysis examines the patterns of bloodstains found at crime scenes in an effort to piece together the sequence of events that led to the bloodshed.

Mathematically, we will have:

The angle of impact = sin⁻¹ (wide stain/length stain)

The angle of impact = sin⁻¹ (1.5/3.0)

The angle of impact = 30°

Therefore, if a bloodstain is 1.5cm wide and 30cm long, then the angle of impact is 30°.

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Answer:

C

Step-by-step explanation:

C is the right one

The height of the rectangle is 16.6 millimeters.

To find the height of a rectangle, we can use the formula for the perimeter of a rectangle, which states that the perimeter is equal to twice the sum of its length and width. In this case, the base of the rectangle is given as 15.8 millimeters, and the perimeter is given as 64.8 millimeters.

Let's denote the height of the rectangle as h. Using the formula, we can express the given information as:

Perimeter = 2 × (Base + Height)

Substituting the given values, we have:

64.8 = 2 × (15.8 + h)

To solve for h, we first simplify the equation by multiplying the values inside the parentheses:

64.8 = 2 × 15.8 + 2 × h

Next, we simplify further:

64.8 = 31.6 + 2h

Subtracting 31.6 from both sides:

64.8 - 31.6 = 2h

33.2 = 2h

To isolate h, we divide both sides by 2:

33.2/2 = h

16.6 = h

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Answer: 60

Step-by-step explanation:

If you subtract how much money you already had(54.75) from what you spent(79.99) you get 25.24. You then add 25.24 to the koney you had left(34.76) to get you answer of 60

Answer:

second one

Step-by-step explanation:

Answer:

20 shirts = $445.00

40 shirts = $541.00

60 shirts = $637.00

Step-by-step explanation:

multiply 20, 40 and 60 by 4.8 then add 349.

20*4.8 = 96

96+349 = 445

40*4.8 = 192

192+349 = 551

60*4.8 = 288

288+349 = 637

Expression 5 + (12.8 ÷ 3.2) represents the phrase 5 + the quotient of 12. 8 and 3. 2 and option (a) is the correct answer.

Expressions refer to a phrase with at least two numbers or variables with any mathematical operations such as addition, exponents, etc. x - 6, 9 + 4y, and 6a are all examples of mathematical expressions.

Equations refer to a sentence when two expressions are equated with the help of '='. x - 6 = 6a is an example of an equation.

In phrase 5+ the quotient of 12. 8 and 3. 2

We divide the phrase into different mathematical operations.

The first operation is of addition with 5, we can write the beginning as 5 + ...

The next operation is division in the phrase the quotient of 12. 8 and 3. 2 which is added to the expression and we get 5 + (12.8 ÷ 3.2)

And we get our answer.

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The complete question might be :

Which expression represents the phrase 5+ the quotient of 12. 8 and 3. 2?

a. 5 + (12.8 ÷ 3.2)

b. 5 - (12.8 + 3.2)

c. 5 + (12.8 * 3.2)

d. none of the above

The solution for differential equati is given by y + c1 = x + c2

To solve the differential equation \(e^{(-y*cos(x))} * dydx * sin^2(x) = 0\) using separation of variables, we can rewrite the equation as:

\(e^{(-y*cos(x))} * dy = 0\)

Now, we can separate the variables by moving all terms involving y to one side and terms involving x to the other side:

\(e^{(-y*cos(x))} * dy = 0\)

dy = 0

Integrating both sides with respect to y, we obtain:

∫dy = ∫0 dx

Integrating the left side gives us y + c1, where c1 is the constant of integration. The right side simply integrates to x + c2, where c2 is another constant of integration.

Therefore, the general solution to the differential equation is:

y + c1 = x + c2

where c1 and c2 are arbitrary constants.

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Answer:

8 weeks

Step-by-step explanation:

m=12+0.5w

Replace the m with the 16 and solve

16=12+0.5w

4=0.5w

8=w

The derivative function is given as

and f(0) = - 1 and f'(0) = 3

To determine the function,

It is also given that f(0) = - 1.

Take the integral and find the function

Then the function is determined as

Hence the function is determined as

Check the picture below.

Answer:

-9

Step-by-step explanation:

Plug 5 into the equation in place of the x:

- x - 4 becomes -(5) - 4.

-5 - 4 = -9

:)

Answer:

g = j - 12

Step-by-step explanation:

We know that if g is Gus' number of engine quantity, then j is Jessie's number of engine quantity, from this statement we have that Jessie made 12 more than Gus, therefore:

j = g + 12

if we solve for g:

g = j - 12

which is the same as saying that Gus made 12 number of engine less than Jessie

Answer:

g = x - 12

where x is the number of axles installed by Jessie

Step-by-step explanation:

Using a simple analogy. If a man has 7 cars while his friend has 3 cars, The statement may be written as the man has 4 cars more than his friend. The 4 cars being the difference between the number of cars he has and the number his friend has.

As such, if the number of engine blocks installed by Gus is g and Jessie installed 12 more axles than the number of engine blocks Gus installed yesterday, where Jessie must have installed x axles,

x = g + 12

Such that

g = x - 12

Answer:

9.(A) y + 7 < −7 OR y + 7 > 7

12.(C) 10A=44+300

Step-by-step explanation:

Answer:

C.

If Carlos doesn’t study at all, his grade will be 50%.

Step-by-step explanation:

If Carlos doesn’t study at all, his grade will be 50%.

Check Answer

Correct. If Carlos spends 0 hours studying, his grade will be 50%.

Answer:

x = -1

Step-by-step explanation:

3/4x + 3 -2x = -1/4 + 1/2x + 5

3/4x + 3 -2x = 19/4 + 1/2x

3x + 12 - 8x = 19 + 2x

-5x + 12 = 19 + 2x

-5x - 2x + 12 = 19

-7x = 19 - 12

-7x = 7

x = -1

By solving the algebraic equation  \(\frac{3}{4}x+3-2x = -\frac{1}{4}+ \frac{1}{2}x + 5\), x = -1.

Algebraic equation is statement of the equality of two expressions formulated by applying to a set of variables the algebraic operations, namely, addition, subtraction, multiplication, division, raising to a power, and extraction of a root.

\(\frac{3}{4}x+3-2x = -\frac{1}{4}+ \frac{1}{2}x + 5\\\\\frac{3}{4}x-2x-\frac{1}{2}x = -\frac{1}{4}+5-3\\\\\frac{3x-8x-2x}{4} = \frac{-1+20 - 12}{4} \\\\-\frac{7x}{4} = \frac{7}{4}\\ \\ x = -1\)

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Answer:

Find the X and Y Intercepts 3x-5y=-20

Find the X and Y Intercepts 3x-5y=-20. 3x−5y=−20 3 x - 5 y = - 20. Find the x-intercepts. Tap for more steps

Step-by-step explanation:

Answer:

36 is what percent of 80? = 45.

Answer:

45

Step-by-step explanation:

46/80%

pretty simple I hope this helps you

Answer:

B) 78 feet

Step-by-step explanation:

Just took the test

Answer:

B

Step-by-step:

(✿◠‿◠)

Each puppy would weigh approximately 2.13 grams if all the puppies weighed the same amount.

To estimate the weight of each puppy, we need to subtract the weight of the basket from the total weight of the basket and puppies to find the total weight of the puppies.

Total weight of puppies = Total weight of basket and puppies - Weight of basket alone

= 2,977 - 1,077 = 1,900 grams

Then we divide the total weight of the puppies by the number of puppies to find the weight of each puppy:

Weight of each puppy = Total weight of puppies / Number of puppies

= 1,900 / 888

= approximately 2.13 grams

Each puppy would weigh approximately 2.13 grams if all the puppies weighed the same amount.

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Answer:

pair is

30 and 315

co-prime

The explicit formula for f^-1 is (x-3)^(1/4) and this is obtained by switching the roles of x and y and solving for y in terms of x.

To find the inverse function of f(x)=x^4+3, we need to switch the roles of x and y, and solve for y.
Let y = x^4+3
Subtract 3 from both sides to get:
y - 3 = x^4
Take the fourth root of both sides to isolate x:
(x^4)^(1/4) = (y-3)^(1/4)
Simplify:
x = (y-3)^(1/4)
So the inverse function of f(x) is:
f^-1 (x) = (x-3)^(1/4)
This is the explicit formula for the inverse function of f(x).
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The first- and second order partial derivatives of the function f(x,y) = 3xy - 2xy² - x²y are:

∂f/∂x = 3y - 4xy - x², ∂f/∂y = 3x - 4xy - x²∂²f/∂x² = -4y, ∂²f/∂y² = -4x and ∂²f/∂y∂x = -4y.

Given function:

f (x,y) = 3xy - 2xy² - x²y

Let's find the first order partial derivatives.

1. First order partial derivative with respect to x.

Keep y constant and differentiate with respect to x.∂f/∂x = 3y - 4xy - x²2.

First order partial derivative with respect to y

Keep x constant and differentiate with respect to y.

∂f/∂y = 3x - 4xy - x²

Let's find the second order partial derivatives.

1. Second order partial derivative with respect to x.

Keep y constant and differentiate ∂f/∂x with respect to x.∂²f/∂x² = -4y2. Second order partial derivative with respect to y.Keep x constant and differentiate ∂f/∂y with respect to y.∂²f/∂y² = -4x3. Second order partial derivative with respect to x and y.

Keep x and y constant and differentiate ∂f/∂y with respect to x.∂²f/∂y∂x = -4y

From the above steps, we can say that the first order partial derivatives are:∂f/∂x = 3y - 4xy - x²and ∂f/∂y = 3x - 4xy - x²The second order partial derivatives are:

∂²f/∂x² = -4y∂²f/∂y² = -4x

and ∂²f/∂y∂x = -4y

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