Hello! :) Pls help me with this math question :)) I want 5 halves of a cupcake for myself, 2 halves for my friend and 1 half for our other friend, FrostingTower would be great. Pls help!!! Ty :>

Answer:

Step-by-step explanation:

Δy=v-0.32 and dy = -0.32 .Δy and dy are both used to represent changes in the dependent variable y based on changes in the independent variable x.

Δy represents the change in y (the dependent variable) resulting from a specific change in x (the independent variable). In this case, y = x^4 + 7, x = -2, and Δx = dx = 0.01. Therefore, we need to calculate Δy and dy based on these values.

To calculate Δy, we substitute the given values into the derivative of the function and multiply it by Δx. The derivative of y = x^4 + 7 is dy/dx = 4x^3. Plugging in x = -2, we have dy/dx = 4(-2)^3 = -32. Now, we can calculate Δy by multiplying dy/dx with Δx: Δy = dy/dx * Δx = -32 * 0.01 = -0.32.

On the other hand, dy represents an infinitesimally small change in y due to an infinitesimally small change in x. It is calculated using the derivative of the function with respect to x. In this case, dy = dy/dx * dx = 4x^3 * dx = 4(-2)^3 * 0.01 = -0.32.

Therefore, both Δy and dy in this context have the same value of -0.32. They represent the change in y corresponding to the change in x, but Δy considers a specific change (Δx), while dy represents an infinitesimally small change (dx) based on the derivative of the function.

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The function f(x,y) = x^2/2 + 5y^3 + 6y^2 − 7x has a global maximum at (7,-4/5) and no global minimum.

To determine if the function has a global maximum or minimum, we need to check its critical points and boundary points.

Taking partial derivatives with respect to x and y and setting them equal to 0, we have:

∂f/∂x = x - 7 = 0

∂f/∂y = 15y^2 + 12y = 0

From the first equation, we get x = 7. Substituting this into the second equation, we get:

15y^2 + 12y = 0

3y(5y + 4) = 0

This gives us two critical points: (7, 0) and (7, -4/5).

To check if these critical points are local maxima or minima, we need to use the second partial derivative test. Taking second partial derivatives, we have:

∂^2f/∂x^2 = 1, ∂^2f/∂y^2 = 30y + 12

∂^2f/∂x∂y = 0 = ∂^2f/∂y∂x

At (7,0), we have ∂^2f/∂x^2 = 1 and ∂^2f/∂y^2 = 0, which indicates a saddle point.

At (7,-4/5), we have ∂^2f/∂x^2 = 1 and ∂^2f/∂y^2 = -12, which indicates a local maximum.

To check for global extrema, we also need to consider the boundary of the domain. However, the function is defined for all values of x and y, so there is no boundary to consider.

Therefore, the function has a global maximum at (7,-4/5) and no global minimum.

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\(\boxed{\boxed{\pink{\bf \leadsto Perimeter\ of \ cross\ shaped \ pattern \ is \ 128cm. }}} \)

Given that a cross shaped pattern is made by arranging four identical rectangles around the side of the square . The area of square is 64cm².

So , let's find the side of the square :-

\(\bf\implies\orange{Area_{square}=(side)^2}\\\\\bf\implies a\times a = 64cm^2\:\:\bigg\lgroup \red{\sf Assuming \ side \ to \ be \ a }\bigg\rgroup \\\\\bf\implies a^2 = 64cm^2 \\\\\bf\implies a=\sqrt{64cm^2} \\\\\implies\boxed{\purple{\bf a = 8cm }}\)

Hence the side of square is 8cm .

Now , breadth of rectangle will be 8cm.

Now its given that the area of rectangle is 1½ times the area of square. So ,

\(\bf\implies Area_{rec.} = \dfrac{3}{2} \times Area_{square} \\\\\bf\implies Area_{rec.} = \dfrac{3}{2} \times 64 cm^2 \\\\\bf\implies \boxed{\red{\bf Area_{rectangle}= 96cm^2}}\)

Hence side will be :-

\(\bf\implies lenght \times breadth = 96cm^2\\\\\bf\implies 8cm \times l = 96cm^2\\\\\bf\implies l =\dfrac{96cm^2}{8cm}\\\\\bf\implies \boxed{\red{\bf lenght = 12cm }}\)

Hence the lenght of rectange is 12cm .

Now , the perimeter of the given figure will be ,

\(\bf\implies Perimeter_{cross} = 8(lenght) + 4(breadth) \\\\\bf\implies Perimeter_{cross} = 8\times 12cm + 4\times 8cm \\\\\bf\implies Perimeter_{cross} = 96cm + 32cm \\\\\bf\implies \boxed{\red{\bf Perimeter_{cross} = 128cm }}\)

Note that based on probabilities,

The expected number of Democrats on the committee is 5.

The expected number of states represented on the committee is 26.

The expected number of states such that both of the state's senators are on the committee is 9.09.

a)  The probability that a randomly chosen senator is a Democrat is 50/100 = 1/2.

So, the expected number of Democrats on a committee of size 10 is

1/2 * 10 = 5.

b) The minimum number of   states that can be represented on a committee of size 10 is 2, and the maximum numberis 50.

The expected number of states representedon the committee is the average of these two values, which is (2 + 50)/  2 = 26.

c)  There are 50 states, and each state has 2 senators. So, there are a total of 100 pairs of senators.

The probability that a randomly chosen pair of senators both belong to the same state is 50/100 * 49/99

= 1/11.

The expected number of states such that both of the state's senators are on the committee is 100 * 1/11 = 9.09.

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Therefore, the minimum ratio of the number of female employees to the number of male employees proposed by the management is 112:1.

To determine the minimum ratio of female employees to male employees proposed by the management, we can set up an inequality based on the given condition. Let's assume the number of male employees is represented by the variable "m" and the number of female employees is represented by the variable "f". According to the management's proposal, the number of female employees (f) must be at least 112 times the number of male employees (m). Mathematically, we can express this as:

f ≥ 112m

To find the minimum ratio, we need to determine the smallest possible value of f/m. Dividing both sides of the inequality by "m" (assuming m > 0), we get:

f/m ≥ 112

This inequality tells us that the ratio of f/m must be greater than or equal to 112.

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The null and alternative hypotheses for testing the claim that the proportion of people who own cats is significantly different from 90% at the 0.02 significance level are:

H0: p = 0.9 (proportion of cat owners is 90%)

H1: p ≠ 0.9 (proportion of cat owners is not equal to 90%)

Based on a sample of 500 people, where 82% owned cats, we can conduct a hypothesis test to determine the p-value at the 0.02 significance level. The p-value is the probability of obtaining a sample proportion as extreme as the observed proportion (82%) assuming the null hypothesis is true.

The p-value for this test is the probability of observing a sample proportion as different from 90% as 82%. Since the p-value is not provided in the question, it needs to be calculated based on the sample data and the assumed null distribution.

If the p-value is less than 0.02, we would reject the null hypothesis and conclude that the proportion of cat owners is significantly different from 90%. However, if the p-value is greater than or equal to 0.02, we would fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a significant difference in the proportion of cat owners from 90%.

Without the calculated p-value, we cannot make a definitive conclusion about rejecting or failing to reject the null hypothesis.


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The approximate noon Sun angle at 41°N latitude (on Long Island) on February 14th is 61°. None of the provided answer choices match the correct answer.

To calculate the approximate noon Sun angle at 41°N latitude (on Long Island) on February 14th, we can use the analemma.

The analemma is a figure-8 shaped curve that represents the position of the Sun in the sky at the same time each day over the course of a year. It accounts for the Earth's axial tilt and elliptical orbit around the Sun.

To find the approximate noon Sun angle, we need to consider the declination of the Sun on February 14th and the latitude of Long Island.

On February 14th, the Sun's declination is approximately -12°.

The Sun angle at noon can be calculated using the following formula:

Sun angle = 90° - (latitude - declination)

Substituting the values, we have:

Sun angle = 90° - (41° - (-12°))

Simplifying this equation, we get:

Sun angle = 90° - 41° + 12°

Sun angle = 61°

Therefore, the approximate noon Sun angle at 41°N latitude (on Long Island) on February 14th is 61°.

None of the provided answer choices match the correct answer.

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Answer:

are you sure the question isn't f(x)= -x²+62x-2?

In general, there are five kinds of task analyses:

Task analysis is the process of learning about ordinary users by observing them in action to understand in detail how they perform their tasks and achieve their intended goals. Tasks analysis helps identify the tasks that your website and applications must support and can also help you refine or re-define your site’s navigation or search by determining the appropriate content scope.

In their book User and Task Analysis for Interface Design, JoAnn Hackos and Janice Redish note that performing a task analysis helps you understand:

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The solution of the system of equations f(x) = 2^x + 1 and g(x) = 3^x is x = 1

From the question, we have the following parameters that can be used in our computation:

f(x) = 2^x + 1

g(x) = 3^x

The above expression is a system of exponential equations

We are required to solve by graph

That implies that we graph the equations in the system on the same plane and write out ordered pairs from the point of intersection of the equations in the system

Next, we plot the graph

See attachment for the graph of the equations

The ordered pairs of the intersection point is (1, 3)

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Answer:

Les trois nombres sont 5, 6 et 7.

Step-by-step explanation:

Soit x le premier nombre.

x + 1 sera le second et x + 2 sera le troisième.

On pose l'équation :

2x + 3(x + 1) = 4(x + 2)

2x + 3x + 3 = 4x + 8

5x - 4x = 8 - 3

x = 5

We would reach our office by 7:34 a.m.

The average speed is given as 30 miles per hour.

Let us convert this into miles per minute.

30 miles/1 hour = 30 miles/60 minutes

= 0.5 miles per minute

The distance between the house and the office is 12 miles.

Therefore, we can find what it would take to reach the office by dividing the distance by the average speed:

Time taken = distance/average speed

= 12 miles/0.5 miles per minute

= 24 minutes

The time is given to be 7:10 a.m. Therefore we would reach our office by 7:34 a.m.

Therefore, we would reach our office by 7:34 a.m.

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The amount in the account after the given time if compounded semiannually is $1104.2

Interest is any amount added on a sum of money over a period of time. The formula for calculating the compound interest is:

A = P(1+r/n)^nt

Given

P = $1000

rate r = 0.05

time =3years

n = 2

Substitute

A = 1000(1 + 0.05/3)^3(2)
A= 1000(1.1042)
A = $1104.2

Hence the amount in the account after the given time if compounded semianually is $1104.2

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(a) Expected number of repairs per year is 0.33 (b) Standard deviation of number of repairs per year is 0.749, (c) The mean and standard deviation of annual expense are $136.55 and $26.217 respectively.

Standard deviation is a measure in statistics which measures the amount of deviation a set of data has with respect to their mean.

(a) Expected number of repairs for the freezer per year is the sum of the product of number of repairs to their probability.

E(Repairs) = (0 × 0.80) + (1 × 0.11) + (2 × 0.05) + (3 × 0.04)

                 = 0.33

(b) Standard deviation of number of repairs per year can be calculated as,

SD(Repairs) = \(\sqrt{[(0 - 0.33)^{2}(0.8)]+[(1-0.33)^{2}(0.11)] + [(2-0.33)^{2}(0.05)]+[(3-0.33)^{2}(0.04)] }\)

= √ (0.5611)

= 0.749

(c) Mean of the restaurant's annual expense with service contract is,

Mean = Expected cost = $125 + ($35 × 0.33) = $136.55

Standard deviation of the restaurant's annual expense with service contract is,

SD = \(\sqrt{35^{2}(0.5611) }\) = 35 × 0.759 = 26.217

Hence the expected number of repairs is 0.33, standard deviation of number of repairs is 0.749, mean and standard deviation of annual expense is $136.55 and $26.217 respectively.

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Answer:

13866.66

Step-by-step explanation:

you divide

Brainliest please

Answer:

  6.83 units

Step-by-step explanation:

Let the height of the original pyramid be represented by h. Then the cut off top has a height of (h -2). The scale factor for the area is the square of the scale factor for height, so we have ...

  (height ratio)^2 = 1/2

  ((h -2)/h)^2 = 1/2

  (h -2)√2 = h . . . . . . square root; multiply by h√2

  h(√2 -1) = 2√2 . . . . add 2√2 -h

  h = (2√2)/(√2 -1) ≈ 6.8284 . . . units

The altitude of the original pyramid is about 6.83 units.

So the scale used was

Step-by-step explanation:

Given;

Length of library on drawing = 13 inches

Actual length of library = 78 feet

In order to find the scale we divide the actual length by the length of library on drawing.

So, scale = 1 inch = 6 feet

Keywords: Scale, Maps

Answer:

C

Step-by-step explanation:

78 feet/13 inches=6 inches/foot

The flow rate of 5 MGD is equivalent to 7.73615 cfs

To convert million gallons per day (MGD) to cubic feet per second (cfs), we need to use the conversion factor between the two units. The conversion factor is 1 MGD = 1.54723 cfs.

Therefore, to convert MGD to cfs, we can multiply the given value of MGD by the conversion factor. For example, if we have a flow rate of 5 MGD, we can convert it to cfs as follows:

5 MGD x 1.54723 cfs/MGD = 7.73615 cfs

So, the flow rate of 5 MGD is equivalent to 7.73615 cfs. Similarly, we can convert any given flow rate in MGD to cfs by using the same conversion factor.

It is important to note that these units are commonly used in the context of water supply and distribution systems, where flow rates are a crucial factor in the design and operation of such systems. Therefore, knowing how to convert between different flow rate units is essential for engineers and technicians working in this field.

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Answer:

∠ LOE = 20°

Step-by-step explanation:

since OJ is perpendicular to OE then ∠ JOE = 90°

from the diagram

∠ JOL + ∠ LOE = ∠ JOE ( substitute values )

6x + 10 + x + 10 = 90

7x + 20 = 90 ( subtract 20 from both sides )

7x = 70 ( divide both sides by 7 )

x = 10

Then

∠ JOE = x + 10 = 10 + 10 = 20°

In observational studies, the variable of interest is not controlled.

The correct answer is D.

Observational studies are a type of research design used to investigate the relationship between variables. In an observational study, the researcher observes and records data without manipulating any variables. The variable of interest is the one that the researcher wants to investigate and understand its relationship with other variables.

Numerical variables are those that can be measured and expressed as numbers. Examples of numerical variables include age, weight, height, temperature, and income. These variables are important in observational studies because they can be analyzed quantitatively and compared to other variables of interest.

In contrast, categorical variables are not numerical, and they cannot be measured or expressed as numbers. Examples of categorical variables include gender, race, occupation, and marital status. These variables are not appropriate as the variable of interest in observational studies because they cannot be analyzed quantitatively.

In observational studies, the variable of interest is not controlled, meaning the researcher does not manipulate or control it. Instead, the researcher observes and records data on the variable and its relationship with other variables. This is in contrast to experimental studies, where the researcher manipulates one or more variables to observe their effect on another variable. Therefore the answer is D) is not controlled.

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Answer:

Plug the following equation in your calculator and this will be your result

7.247 x 10^6

The value of the exponential equation in scientific notation A = 7.247 x 10⁶

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the exponential equation be represented as A

Let the first number be p = 7.26 x 10⁶

Let the second number be q = 1.3 x 10⁴

Now , the equation is A = p - q

A in the scientific notation is

Substituting the values in the equation , we get

A = 7.26 x 10⁶ - 1.3 x 10⁴

On simplifying the equation , we get

Taking the common factor as 10⁴ , we get

A = 10⁴ ( 7.26 x 10² - 1.3 )

A = 10⁴ ( 726 - 1.3 )

On further simplification , we get

A = 10⁴ ( 724.7 )

And , the value of A in scientific notation is A = 7.247 x 10⁶

Hence , the exponential equation is A = 7.247 x 10⁶

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Fraction of the area of the circle is the area of the shaded region is 5/18.

From the figure:

The shaded region has angle = 100

In the circle the total angle is 360.

Fraction = 100/360

= 50/180

= 25/90

= 5/18

Therefore fraction of the area of the circle is the area of the shaded region is 5/18.

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The conditions on the constants a, b, c, and d for the differential equation to be exact are a = d and b = c.

And, Once we have established the given differential equation is exact, we can find its general solution by using the following formula:

∫Mdx + ∫(N - ∂∫M/∂y dy)dy = C,

where C is the constant of integration.

Now, For find the conditions on the constants a, b, c, and d such that the given differential equation is exact, we need to use the following theorem:

A necessary and sufficient condition for the differential equation

M dx + N dy = 0 to be exact is that,

⇒  ∂M/∂y = ∂N/∂x.

Hence, Using this theorem, we can find the conditions on a, b, c, and d as follows:

∂M/∂y = a, and ∂N/∂x = d.

Therefore, for the differential equation to be exact, we need;

⇒ a = d.

Similarly, ∂M/∂x = b, and ∂N/∂y = c.

Therefore, for the differential equation to be exact, we need,

⇒ b = c.

Hence, the conditions on the constants a, b, c, and d for the differential equation to be exact are a = d and b = c.

And, Once we have established the given differential equation is exact, we can find its general solution by using the following formula:

∫Mdx + ∫(N - ∂∫M/∂y dy)dy = C,

where C is the constant of integration.

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The new odds that the box picked is a special one is 4

Since, there are four boxes that look the same. in one box (the special one), half of the marbles are blue. but only 1/8 of the marbles in the other boxes are blue.

We will have this hypothesis:

The box the blue marble was picked from is the special box.

Prior confidence we had:

Ratio of special boxes to non special boxes=1:3

Now P(blue &special)=1/2, given that a box is selected from the special box, there is 1/2 chance that it is blue

And P(blue & not special)=1/8, given that a box is selected from a non-special box, there is 1/8 chance that it is blue

According to  Baye's factor ,we get:

P(B & S)/P(B & NS)=(1/2)/(1/8)

                               =4

Thus, 4 is the new odds that the box picked is the special one.

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Answer:

60 problems correct so b is correct

The linear equation for the coordinate points given is obtained as y = -3/2x + 19.5.

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

The coordinate points for the lines are (11,3) and (7,9).

The slope-intercept form of an equation/function is - y = mx + b

To find the slope m use the formula -

(y2 - y1)/(x2 - x1)

Substituting the values in the equation -

[9 - 3]/[7 - 11]

(6)/(-4)

3/-2

So, the slope point is obtained as m = 3/-2.

The equation becomes - y = -3/2x + b

To find the value of b substitute the values of x and y in the equation -

3 = -3/2(11) + b

3 = -33/2 + b

b = 3 + 33/2

b = (6 + 33)/2

b = 39/2

b = 19.5

So, the value for b is 19.5.

Now, the equation becomes -

y = -3/2x + 19.5

The graph for the equation is plotted.

Therefore, the equation is obtained as y = -3/2x + 19.5.

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The maximum possible number of elements in set B is 62.

A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets. A set is the mathematical model for a collection of various things.

The universal set is A consisting of the primary one hundred positive integers.

Now, Set B is a subset of A.

Set B might be made up of the first 62 positive numbers, for example.

Only then is 123 the largest number that can be formed by adding all the components of set B.

Set B contains 62 items altogether.

Additionally, we can carefully swap out one or more pieces from set B and add them to its complement.

In the majority of these cases, set B may have 62 elements.

Therefore, we get the number of elements in set B will be 62.

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Answer:

x = -1/4

x = 3

The solutions of the given quadratic equation 8x² = 6 + 22x will be x = -1/4 and x = 3 thus, option (B) and (C) is correct.

An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, and a must not be zero.

For example, 3x² + 6x + 8 = 0 here x has the highest term as 2 and the coefficient of x² is not zero.

As per the given quadratic equation,

8x² = 6 + 22x

The roots must satisfy the above equation,

8(-3)² = 6 + 22(3)

72 = 72

And,

8(-1/4)² = 6 + 22(-1/4)

8/16 = 6 - 11/2

1/2 = 1/2

Hence "The solutions of the given quadratic equation 8x² = 6 + 22x will be x = -1/4 and x = 3"

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