Carole used 3 3/4cups of butter for baking. The
amount of sugar she used was 1/3 of the amount of
butter she used. How much sugar, in cups, did
she use?
1 1/4cups
1 1/3cups
2 1/2 cups
3 5/12cups

To show that the function f(x) = x³ for x < 0 and f(x) = x²sin(x) for x > 0 is differentiable, we need to demonstrate that the function has a derivative at every point in its domain.

Let's consider the function f(x) separately for x < 0 and x > 0.

For x < 0

In this case, f(x) = x³. The power rule tells us that the derivative of xⁿ with respect to x is nxⁿ⁻¹. Applying this rule, we find that the derivative of f(x) = x³ is f'(x) = 3x².

For x > 0

In this case, f(x) = x²sin(x). The product rule is used when we have a function that is the product of two other functions. The derivative of f(x) can be calculated as follows

f'(x) = (x²)' sin(x) + x² (sin(x))'

To find the derivative of x² sin(x), we use the product rule again

(f(x)g(x))' = f'(x)g(x) + f(x)g'(x)

Let f(x) = x² and g(x) = sin(x). We have

f'(x) = 2x

g'(x) = cos(x)

Substituting these values back into the product rule equation

f'(x) = (x²)' sin(x) + x² (sin(x))'

= (2x) sin(x) + x^2 cos(x)

Therefore, the derivative of f(x) = x²sin(x) is f'(x) = (2x) sin(x) + x²cos(x).

Now, we have found the derivatives of f(x) for both x < 0 and x > 0. To show that f(x) is differentiable, we need to verify that the derivatives from both cases match at x = 0.

As x approaches 0 from the left side (x < 0), we have

lim(x → 0⁻) f'(x) = lim(x → 0⁻) 3x² = 0

As x approaches 0 from the right side (x > 0), we have

lim(x → 0⁺) f'(x) = lim(x → 0⁺) (2x) sin(x) + x²cos(x) = 0

Since the limits of the derivatives from both cases are equal at x = 0, we can conclude that f(x) = x³ for x < 0 and f(x) = x²sin(x) for x > 0 is differentiable at every point in its domain.

To know more about function here

https://brainly.com/question/30721594

#SPJ4

Answer:

The value of x is 5 that represents the searched number

Step-by-step explanation:

Let us assume x be the number [^ 2] i.e. squared.

Now  

x^2  -10 = 3x

This is a quadratic equation

x^ 2 - 3x - 10 = 0

x^2 - 5x + 2x - 10

x (x - 5) + 2(x - 5)

(x-5) (x + 2) = 0  

x - 5 = 0 where x = 5 positive.

x + 2 = 0 where x = -2 negative.

Here we considered the positive  

The value of x is 5 that represents the searched number

Answer: Figure B is 2x bigger on all sides

Explanation: You can see that each of the numbers times 2 would equal all of the numbers on B.

Answer:

each rope should be 1 1/7 yard long

Step-by-step explanation:

9 1/7 ÷8

1 1/7

Answer:

8/7 yd per piece

Step-by-step explanation:

To answer this, divide the total rope length 9 1/7 yd by 8 pieces:

 64 yd

------------------ = 8/7 yd per piece

7(8 pieces)

Check:  does 8 times (8/7 yd/piece) come out to 64/7 yd, or 9 1/7 yd?  YES

y = mx+b

(5-8)/(9-0) = -1/3 which is m

solve point slope to find slope intercept by using one of the points (0,8)

y-y1=m(x-x1)

y-8 = -1/3(x-0)

y-8 = -1/3x

Answer: y = -1/3x + 8

(a) The unit vector normal to the surface at point P is n = (-2/3, -2/3, 1/3).

(b) The gradient vector ∇f = (-2x, -2y, 0.5z).

(c) The curl of the gradient vector, ∇ × ∇f, is not applicable in this case since ∇f is not a vector field, but a surface normal.

To find a unit vector normal to the surface at point P(1, 1, 2) given the equation 0.25z² - x² - y² = 0, we can follow these steps:

Step 1: Define the Surface Function

Let's define the surface function f(x, y, z) based on the given equation:

f(x, y, z) = 0.25z² - x² - y²

Step 2: Calculate the Gradient Vector (∇f)

The gradient vector (∇f) represents the vector of partial derivatives of the surface function. Calculate ∇f(x, y, z) by taking the partial derivatives of f(x, y, z) with respect to each variable:

∂f/∂x = -2x

∂f/∂y = -2y

∂f/∂z = 0.5z

Thus, the gradient vector (∇f) is (∇f) = (-2x, -2y, 0.5z).

Step 3: Evaluate ∇f at Point P

Evaluate the gradient vector (∇f) at point P(1, 1, 2) by substituting the coordinates into (∇f):

∇f(P) = (-2(1), -2(1), 0.5(2))

= (-2, -2, 1)

Step 4: Normalize the Normal Vector

To obtain a unit vector normal to the surface at point P, we need to normalize (∇f(P)) by dividing it by its magnitude.

Magnitude of ∇f(P) = √((-2)² + (-2)² + 1²)

= √(4 + 4 + 1)

= √9

= 3

The unit vector normal to the surface at point P is then:

n = (∇f(P)) / |∇f(P)|

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

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

So, the unit vector normal to the surface at point P(1, 1, 2) is n = (-2/3, -2/3, 1/3).

Learn more about the unit vector normal at

https://brainly.com/question/29752499

#SPJ4

The question is -

Find a unit vector normal to the surface at Point P: (1,1,2):

0.25z² - x² - y² = 0

(a) n = ?

(b) ∇f = ?

(c) ∇ × ∇f = ?

Answer:A and b

Step-by-step explanation:

The dimensions of cylinders that have a volume under 220 cubic inches per serving are:

3-inch radius and 4-inch height
4-inch diameter and 4-inch height
4-inch diameter and 9-inch height

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

Here,
We can use the formula V = πr²h to find the volume of each cylinder.

For a cylinder with a 3-inch radius and 4-inch height:

V = π(3)²(4) ≈ 113.1 cubic inches

For a cylinder with a 4-inch radius and 4-inch height:

V = π(4)²(4) ≈ 200.96 cubic inches

For a cylinder with a 9-inch radius and 9-inch height:

V = π(9)²(9) ≈ 2289.0 cubic inches

For a cylinder with a 4-inch diameter and 9-inch height (radius is 2 inches):

V = π(2)²(9) ≈ 113.04 cubic inches

For a cylinder with a 6-inch diameter and 9-inch height (radius is 3 inches):

V = π(3)²(9) ≈ 254.5 cubic inches

For a cylinder with a 9-inch diameter and 4-inch height (radius is 4.5 inches):

V = π(4.5)²(4) ≈ 254.5 cubic inches

Therefore, the dimensions of cylinders that have a volume under 220 cubic inches per serving are:

3-inch radius and 4-inch height
4-inch diameter and 4-inch height
4-inch diameter and 9-inch height

Learn more about Volume here:
https://brainly.com/question/1578538

#SPJ3

The set has a size of 1, which is the largest possible size for a subset that is common to A and B.

To find a set of largest possible size that is a subset of both A and B, we need to find the common elements of A and B.

The common element of A and B is 10. Therefore, any subset of A and B that is of largest possible size must include 10.

One possible set of largest possible size that is a subset of both A and B is:

{10}

This set has a size of 1, which is the largest possible size for a subset that is common to A and B.

Learn more about Sets and Subsets : https://brainly.com/question/2000547

#SPJ11

Answer:

tangent x = 12/9

Step-by-step explanation:

Hello There!

Once again these are the Trigonometric Ratios

SOH CAH TOA

Sine = Opposite over Hypotenuse (SOH)

Cosine = Adjacent over Hypotenuse (CAH)

Tan = Opposite over Adjacent (TOA)

And for this one we are asked to find the tangent of angle x

Remember tangent = opposite over adjacent

opposite - the side length that is opposite of the angle (so the angle will be facing that side length)

adjacent - the side length that is not the opposite nor the hypotenuse

The opposite of angle x is 12 and the adjacent of angle x is 9

so tangent x = 12/9

Answer:

q = -10

Step-by-step explanation:

If the slope is undefined, then there is no change in x. Therefore, since -10-(-10) = 0, then q=-10.

Answer:

16

Step-by-step explanation:

If each game is $1.50 we would divide the 24 by 1.50, or multiple 1.50 to find 24. So 24 divided by 1.50 is 16.

So she could play 16 games.

Answer:

It can be calculated by finding the difference between the two angles. Half of this difference will be the angle that is required.

Therefore

236 - 124 = 112

Tanget-tanget angle = 112 / 2 = 56 degrees

Answer:

I would say C or B

Step-by-step explanation:

⚠ warning, there are multiple bots that spam links, that are usually written in a link shortening form (eg, c u t . l y , b i t . l y) do NOT click on those links, as they usually contain trojan viruses, and/or adult content. please copy + paste this message so other users can be aware and stop these bots. thank you, and be safe! :) #waronbitlybots

Answer:

c is your answer

Step-by-step explanation:

The number of ways in which 52 cards can be distributed such that Sara receives 17 cards, Jacob receives 17 cards, and their mother receives 18 cards is given by the following expression:52!/17!17!18!

Explanation: The number of ways to distribute k objects among n persons in which the order does not matter and each person receives at least one object is given by the following expression: ((k - n) choose (n - 1)). This can be extended to the case where each person is required to receive a specific number of objects. For example, if we have k objects and want to distribute them to persons A, B, and C such that A receives a objects, B receives b objects, and C receives c objects, where a + b + c = k, then the number of ways to do this is given by the expression: ((k - a - b - c) choose (2))This can be simplified as follows: ((k - a - b - c)!)/((2!)(k - a - b - c - 2)!)), which can be further simplified as follows: (k - a - b - c)(k - a - b - c - 1)/2!.

Therefore, the number of ways in which 52 cards can be distributed such that Sara receives 17 cards, Jacob receives 17 cards, and their mother receives 18 cards is given by: ((52 - 17 - 17 - 18) choose (2))= ((52 - 52) choose (2))= (0 choose 2)=0. Therefore, the required number of ways is 52!/17!17!18!.

To know more about Combination, click here:

https://brainly.com/question/20211959

#SPJ11

The circumference is:

14.6 x 3.14 = 45.844 (m)

Answer:

c = 45.8 m

Step-by-step explanation:

The diameter of this circle is 14.6 m.  The formula for the circumference of a circle of diameter d is πd.  Here, using 3.14 for π, C = (3.14)(14.6 m), or

C = 45.8 m

The instrument uncertainty in e/m for each data point is calculated using error propagation.

e/m = 3.125x10^6 V/r^2I^2

From the given equation above, the formula for error propagation required in experiment step 8 can be derived. The error propagation formula is given as;Δe/m = (e/m)(ΔV/V + 2Δr/r + 2ΔI/I)

The voltage is changed to 400 V for the third dataset. The instrument uncertainties in V, I, and r are to be estimated.

The last digit place read from the power supplies is used as the uncertainties V and I. The uncertainty in r should be estimated from the thickness of the beam path.

Estimation of instrument uncertainties in V, I, and r:For V, the reading is up to 0.1 V.

Hence, the uncertainty in V isΔV = 0.1 VFor I, the reading is up to 0.01 A.

Hence, the uncertainty in I isΔI = 0.01 AFor r, the thickness of the beam path is given as 0.25 cm. Hence, the uncertainty in r isΔr = 0.25 cm

The instrument uncertainty in e/m for each data point is to be calculated using error propagation.

Data for three datasets are given below;

Data Set 1: V = 200 V, r = 0.56 cm, I = 0.2 AData Set 2: V = 300 V, r = 0.56 cm, I = 0.2 AData Set 3: V = 400 V, r = 0.56 cm, I = 0.2 A

For Data Set 1;e/m = 3.125 x 106 × 200/ (0.56)2 (0.2)2= 1.75867 × 1011 C/kgΔe/m = (1.75867 × 1011)(0.1/200 + 2(0.25/0.56) + 2(0.01/0.2))= 1.78853 × 1010 C/kg

For Data Set 2;e/m = 3.125 x 106 × 300/ (0.56)2 (0.2)2= 2.63800 × 1011 C/kgΔe/m = (2.63800 × 1011)(0.1/300 + 2(0.25/0.56) + 2(0.01/0.2))= 1.70314 × 1010 C/kg

For Data Set 3;e/m = 3.125 x 106 × 400/ (0.56)2 (0.2)2= 3.51733 × 1011 C/kgΔe/m = (3.51733 × 1011)(0.1/400 + 2(0.25/0.56) + 2(0.01/0.2))= 1.61057 × 1010 C/kg

Hence, the instrument uncertainty in e/m for each data point is calculated as;

For Data Set 1, Δe/m = 1.78853 × 1010 C/kg

For Data Set 2, Δe/m = 1.70314 × 1010 C/kg

For Data Set 3, Δe/m = 1.61057 × 1010 C/kg

Therefore, the instrument uncertainty in e/m for each data point is calculated using error propagation.

Know more about error propagation here,

https://brainly.com/question/31841713

#SPJ11

Answer:

18

Step-by-step explanation:

she needs 18 boxes divide 144 by 8 then u get ur answer

Answer:  

The second box  

Step-by-step explanation:

The volume of a pyramid can be given by the formula:  V=31​Ah. Where.  A:  Area of the V=(1/3)(B)(h)

multiply both sides by 3

3V=Bh

divide both sides by B

3V/B=h

Therefore, If it is wider it has more space to carry more items such as macaroni.

The ratio of students who wish they had x-ray vision to all students: 2:9

The ratio of students who wish for flight to all students: 3:1

The ratio of students who wish for flight to those who wish for invisibility: 6:1

1. The ratio of students who wish they had x-ray vision to all students: 2:9

This means that out of a group of students, there are 2 students who wish they had x-ray vision for every 9 students in total.

2. The ratio of students who wish for flight to all students: 2:3

This ratio indicates that out of a group of students, there are 2 students who wish for the ability to fly for every 3 students in total.

3. The ratio of students who wish for flight to those who wish for invisibility: 1:6

This ratio compares the number of students who wish for flight to the number of students who wish for invisibility. It states that for every student who wishes for flight, there are 6 students who wish for invisibility.

Learn more about ratios at https://brainly.com/question/12024093

#SPJ1

1- True: Linear programming can be used to identify the critical path for a PERT network.

2- False: The probabilistic approach characterized by PERT does not use median activity times.

3- False: The critical path is the sequential path of activities from the first to the last, defined by activities with zero slack.

4- False: Linear programming can be used for both profit and nonprofit organizations.

Linear programming can indeed be used to identify the critical path for a PERT network. The critical path represents the sequential path of activities from the first activity to the last, and it is defined by activities with zero slack. By analyzing the dependencies and constraints between activities, linear programming techniques can be applied to determine the optimal schedule and identify the critical path.

The probabilistic approach characterised by PERT does not use median activity times. Instead, it utilises three time estimates for each activity: optimistic, most likely, and pessimistic activity times. These estimates are used to calculate the expected duration and variability of the project.

Regarding the statement about linear programming and profit optimization, it is incorrect to say that linear programming cannot be used for nonprofit organizations. Linear programming can be applied to various optimisation problems, including those related to resource allocation, cost minimisation, and efficiency improvement, which are relevant to both for-profit and nonprofit organisations.

Learn more about linear programming here, https://brainly.com/question/14309521

#SPJ11

Answer:

B)All the real numbers

Step-by-step explanation:

the given Graph is Parabola

so the function has to be quadratic

we know that the domain of a quadratic function is always [tex]x\in\mathbb{R}[/tex]

hence, our answer is B

Answer:

three thirds is one whole

Step-by-step explanation:

The answer is 18 because three thirds is one whole which in this case is 18! Have a nice day!

Answer:

Measure of angle A = 100°

Measure of angle B = 80°

Measure of angle C = 65°

Step-by-step explanation:

From the given picture,

Angle A and angle B are the linear pair of angles, and linear pair of angles are supplementary angles,

m(∠A) + m(∠B) = 180°

(3x - 20)° + (2x)° = 180°

5x - 20 = 180

5x = 200

x = 40

By substituting the value of x in the measures of each angle,

m(∠A) = (3x - 20)°

          = 3(40) - 20

          = 120 - 20

          = 100°

m(∠B) = 2x°

          = 2(40)

          = 80°

m(∠C) = (2x - 15)°

          = 2(40) - 15

          = 80 - 15

          = 65°

Answer:

-14

Step-by-step explanation:

Hello,

Let's have a look at this figure and think about how are these two angles related to each other. These two angles are vertically opposite angles, and any two vertically opposite angles should be equal to each other.

Because the two angles should be equal to each other, we can equate the two equations together and solve for x.

9x + 184 = 7x + 156

9x - 7x = 156 - 184

2x = -28

x = -14

The critical value for the [tex]X^{2}[/tex] goodness-of-fit test with 4 categories and α = 0.05 is approximately 7.815.

In a chi-square goodness-of-fit test, we compare the observed frequencies of a nominal variable across different categories with the expected frequencies under the null hypothesis. The test statistic, [tex]X^{2}[/tex], measures the discrepancy between the observed and expected frequencies.

To determine if the observed frequencies significantly differ from the expected frequencies, we compare the test statistic with the critical value at the specified significance level (α). The critical value is determined based on the degrees of freedom, which is the number of categories minus 1.

In this scenario, the nominal variable has 4 categories. Degrees of freedom is (4 - 1) = 3. Using the degrees of freedom and the significance level of α = 0.05, we can consult the chi-square distribution table or use statistical software to find the critical value.

The critical value for the [tex]X^{2}[/tex] goodness-of-fit test with 4 categories and α = 0.05 is approximately 7.815.

Since the test statistic [tex]X^{2}[/tex] = 6.432 is less than the critical value of 7.815, we fail to reject the null hypothesis. This means that there is not enough evidence to suggest a significant difference between the observed and expected frequencies.

Learn more about hypothesis here:

brainly.com/question/17099835

#SPJ11

Answer:

Alfredo está en lo correcto porque los números negativos se encuentran a la izquierda del cero y mientras más a la izquierda se encuentra un número negativo, más pequeño será y a medida que te desplazas hacia la derecha mayor será el número. Puedes representar los dos números en una recta numérica de la siguiente forma:

___________________________________________________________

-14   -13    -12    -11    -10    -9    -8    -7    -6    -5    -4    -3    -2    -1    0    1    2    3

Como se ve aquí, -14 se encuentra a la izquierda de -10 y esto significa que es menor. Por esto, Alfredo está en lo correcto al decir que -14 es menor.

Answer:

Your answer will be x= -1

Step-by-step explanation:

have a nice day:)