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The Acme Company manufactures widgets. The distribution of widget weights is bell-
shaped. The widget weights have a mean of 56 ounces and a standard deviation of 10
ounces.
a) 95% of the widget weights lie between 36
o and
76
OF
b) What percentage of the widget weights lie between 26 and 76 ounces?
99.7
X%
c) What percentage of the widget weights lie above 46 ?
%
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The exponents a and b in the simplified expression are:

a = 1

b = 7

Remember the rules for exponents:

\(a^x*a^y = a^{x + y}\\\\a^x/a^y = a^{x - y}\\\\(a^x)^y = a^{x*y}\)

Now we need to use these rules to simplify our expression:

\(\frac{x^2(y^3)^4}{x*y^5}\)

We can rewrite that as:

\(\frac{x^2(y^3)^4}{x*y^5} = \frac{x^2}{x} *\frac{(y^3)^4}{y^5} = x^{2 - 1}\frac{y^{3*4}}{y^5} \\\\= x*y^{12 - 5} = x*y^7\)

Then the values of a and b are:

a = 1

b = 7

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Answer:

tan y°

Step-by-step explanation:

by using the Sine Rule (See attached), we can form the equation:

\(\frac{r}{sin (y)} = \frac{p}{sin (x)}\)

rearranging this, we get:

\(\frac{r}{p} =\frac{sin(y)}{sin(x)}\)   ---------------------eq 1

Recall that all internal angles of a triangle must sum to 180°. we observe that we have a right triangle where one of the angles is 90°. It then follows that the sum of the other two angles must sum to 90°

i.e x + y = 90°

with a little rearranging, we get

x = (90° - y)

Substituting this into eq 1 above, we get:

\(\frac{r}{p} =\frac{sin(y)}{sin(90- y)}\)  ---------eq 2

recall that from the trigonometric co-function identities,

sin (90°- y) = cos y

substituting this into eq 2 gives :

\(\frac{r}{p} =\frac{sin(y)}{cos(y)} = tan(y)\)   (answer)

The equivalent expressions are;

The correct answer choice is option B, C and E

-2/5(15 - 20d + 5c)

open parenthesis

= -30/5 + 40/5d - 10/5c

= - 6 + 8d - 2c

Check:

-6+8d-2c

True

-2c+8d-6

rearrange

= -6 + 8d - 2c

-2(3-4d+c)

open parenthesis

= -6 + 8d - 2c

Hence, the equivalent expression to -2/5(15 - 20d + 5c) are -6+8d-2c, -2c+8d-6 and -2(3-4d+c)

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The input is x while the output is y = f(x). If we multiply both sides of y = f(x) by 2/3, then we'll get (2/3)y = (2/3)f(x) = (2/3)x^2

We see that the new outputs are 2/3 the size of the original. So the graph is shorter and has been vertically squished or compressed. If we multiplied both sides by some number larger than 1, then the graph will be vertically stretched.

No reflection has been done because that only happens if we multiplied both sides by a negative value. The negative flips things around (from positive to negative or vice versa).

SOLUTION

From the diagram in the picture, the point (2, -3) is the point for Lake.

Hence the answer is Lake

Metric prefix for the base units.

1. 0.001 = milli
2. 0.000001 = micro
3. 0.01 = centi
4. 1000 = kilo

What are Metric prefixes? Explain your answer in detail?

Metric prefixes are used in the International System of Units (SI) to indicate the size or multiple of a standard unit of measurement. The metric prefix milli-, for example, indicates that the standard unit is divided into one thousand pieces. On the other hand, the metric prefix kilo- implies that the standard unit is multiplied by one thousand.

To represent measurements in terms of standard units, metric prefixes are placed before the standard units.

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The number of individuals who are homozygous dominant (VV) is 160 individuals, and the number of individuals who are heterozygous (Vv) is 320 individuals.

The population of Drosophila has 1000 individuals, 360 of which display the recessive phenotype. Homozygous dominant and heterozygous for this trait in Drosophila would be expected to be found in how many individuals?

In Drosophila, the dominant allele for normal-length wings is denoted as 'V' and the recessive allele for vestigial wings is denoted as 'v.'To determine the number of individuals who are homozygous dominant or heterozygous for this trait, we'll first determine the number of individuals who are homozygous recessive:

Homozygous recessive individuals in the population = number of individuals displaying the recessive phenotype = 360

This indicate that there are 360 individuals with the genotype vv (homozygous recessive), which will be used to determine the remaining genotypes via the Punnett square. To get the number of individuals who are heterozygous (Vv), we first need to identify the number of individuals with the dominant V allele (VV and Vv). The sum of these two genotypes equals the total number of individuals minus the homozygous recessive individuals, as follows:

Total number of individuals - homozygous recessive individuals = (VV + Vv) individuals+ (vv) individuals = 1000 individuals

Hence, VV + Vv = 1000 - 360 = 640 individuals.Now that we know VV + Vv = 640, we can use the expected genotypic ratio of 1:2:1 to calculate the number of homozygous dominant (VV) and heterozygous (Vv) individuals.1:2:1 represents the expected genotypic ratio in the progeny derived from a cross involving two heterozygotes of the same gene. The first "1" represents the proportion of dominant homozygotes, the second class, or class "2", the heterozygotes, and the second "1" the recessive homozygotes.

Therefore, homozygous dominant (VV) and heterozygous (Vv) individuals in the population would be expected in the following ratio:VV:Vv:vv = 1:2:1. Therefore, the number of individuals who are homozygous dominant (VV) is 1/4 of the total individuals (VV + Vv + vv):

Number of individuals who are homozygous dominant (VV) = 1/4 (VV + Vv + vv)= 1/4 (640) = 160 individuals

And the number of individuals who are heterozygous (Vv) is 2/4 of the total individuals (VV + Vv + vv):

Number of individuals who are heterozygous (Vv) = 2/4 (VV + Vv + vv)= 2/4 (640) = 320 individuals

Therefore, the number of individuals who are homozygous dominant (VV) is 160 individuals, and the number of individuals who are heterozygous (Vv) is 320 individuals.

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Answer:

(-inf, 5)

Step-by-step explanation:

just the previous answer, in anothe r form

Answer:

1 and 7/10 pounds?

Step-by-step explanation:

because if its 4/10 more you add 3/10 and 4/10 im pretty sure

Answer:

PLEASE MARK BRAInliest

Step-by-step explanation:

tweety weighed 17/10 pounds last year.

Answer:

Angela's mistake is in step 1, she failed to change the sign when subtracting from both sides

Step-by-step explanation:

Equation given :

The correct solution should be :

3/4 - 3/4 + m = 5/4 - 3/4

m = 2/ 4

m = 1/2

Therefore failure to change the sign will result in a obtaining a wrong answer for the exercise.

m=1/2

hope this helps!

We now have three equations, so we can solve them.

Let's define the length of the 3 boards in terms of x:

F=x

S=2x-3

T=2

F+S+T =26

x+2x-3+2 =26

3x =26+1=27

x =27/3 = 9 feet for First section

2x-3 =18-3 = 16 feet = Second

2 = Third

9+16+2 = 27

27 is the length of the shortest piece.

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Answer:

23°

Step-by-step explanation:

13x + 154 = 180

13x = 26

x =2

~~~~~~~~~~~~

6(2) + 11

12+11 =23

the maximum height of a quadratic equation can be find Use the formula: x = -b / (2a) then Substitute the value of x back into the quadratic equation to find the corresponding maximum height.

To find the maximum height of a quadratic equation, you need to determine the vertex of the parabolic curve. The vertex represents the highest or lowest point of the quadratic function, depending on whether it opens upward or downward.

A quadratic equation is generally written in the form of y = ax² + bx + c, where "a," "b," and "c" are coefficients.

The x-coordinate of the vertex can be found using the formula: x = -b / (2a). This formula gives you the line of symmetry of the parabola.

Once you have the x-coordinate of the vertex, substitute it back into the original equation to find the corresponding y-coordinate.

The resulting y-coordinate represents the maximum height (if the parabola opens downward) or the minimum height (if the parabola opens upward) of the quadratic equation.

Here's an example:

Consider the quadratic equation y = 2x² - 4x + 3.

1. Identify the coefficients:

a = 2

b = -4

c = 3

2. Find the x-coordinate of the vertex:

x = -(-4) / (2 * 2) = 4 / 4 = 1

3. Substitute x = 1 back into the equation to find the y-coordinate:

y = 2(1)² - 4(1) + 3 = 2 - 4 + 3 = 1

Therefore, the maximum height of the quadratic equation y = 2x² - 4x + 3 is 1.

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The maximum height of a quadratic equation can be found by determining the vertex of the parabolic shape represented by the equation. The x-coordinate of the vertex can be found using the formula x = -b / (2a), and the corresponding y-coordinate represents the maximum height.

To find the maximum height of a quadratic equation, we need to determine the vertex of the parabolic shape represented by the equation. The vertex is the point where the parabola reaches its highest or lowest point.

The general form of a quadratic equation is ax^2 + bx + c, where a, b, and c are constants. To find the x-coordinate of the vertex, we can use the formula x = -b / (2a).

Once we have the x-coordinate, we can substitute it back into the equation to find the corresponding y-coordinate, which represents the maximum or minimum height of the quadratic equation.

Let's take an example to illustrate this process:

Suppose we have the quadratic equation y = 2x^2 + 3x + 1. To find the maximum height, we first need to find the x-coordinate of the vertex.

Using the formula x = -b / (2a), we can substitute the values from our equation: x = -(3) / (2 * 2) = -3/4.

Now, we substitute this x-coordinate back into the equation to find the y-coordinate: y = 2(-3/4)^2 + 3(-3/4) + 1 = 2(9/16) - 9/4 + 1 = 9/8 - 9/4 + 1 = 9/8 - 18/8 + 8/8 = -1/8.

Therefore, the maximum height of the quadratic equation y = 2x^2 + 3x + 1 is -1/8.

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The 25th percentile of the data is therefore found in the 0 to 1-hour range.

A percentile score is one that evaluates an individual's performance in relation to that of the other group members. It shows the percentage of scores that a certain score exceeded

There are 48 speakers present, or around 25% of the total 192 speakers.

The graph shows that 60 speakers delivered talks that lasted between 0 and 1 hour.

This signifies that the number 48 is between 0 and 1.

A percentile is a score that assesses a certain score in relation to the scores of the other group members. It displays the proportion of other scores that a given score exceeded.

The percentile calculation is used to compare an individual's performance to that of others in order to assess it. The percentile method is used to compare a student's test score to that of other candidates.

The 25th percentile of the data is therefore found in the 0 to 1-hour range.

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The complete question is:

Since the triangle is scalene, then every side must have diferent size. The options are

Then, all the options can be the perimeter of the triangle

The x- and y-coordinates of the center of mass are; (20, 0)

The center of mass is the location where the sum of the relative position of the masses in a mass distribution is zero. It is the point where force can be applied on the distributed mass without causing a rotation of the system.

The mas of the steel plate = 800 g = 0.8 kg

The base length of the isosceles triangular plate = 20 cm = 0.2 m

The height of the isosceles triangular plate = 30 cm = 0.3 m

Considering a small strip of height, dx and width, I, we get

Area of small strip, dA = I·dx

Density of the plate for a unit thickness, ρ = M/A

Density of the small strip of mass dm = dm/dA

Considering the density of the plate as uniform, we get;

\(\displaystyle {\frac{dm}{dA} =\frac{M}{A}\)

Therefore;

\(\displaystyle {dm=\frac{M}{A}\times dA}\)

The area of the triangular plate, A = (1/2) × 0.2 m × 0.3 m = 0.03 m²

Mass of the plate, M = 0.8 kg

Therefore;

\(\displaystyle {dm=\frac{0.8}{0.03}\times I\cdot dx}\)

The width of the small strip, I, located at a distance x from the vertex of the triangular plate, using similar triangles, indicates;

\(\dfrac{I}{20} = \dfrac{x}{30}\)

\(I=20\times \dfrac{x}{30} = \dfrac{2}{3} \cdot x\)

Therefore;

\(\displaystyle {dm=\frac{0.8}{0.03}\times I\cdot dx} = \frac{0.8}{0.03}\times \dfrac{2}{3} \cdot x\cdot dx}\)

The center of mass, \(x_{cm}\), can be obtained with the formula; \(\displaystyle {x_{cm} = \dfrac{1}{M} \cdot \int\limits {x} \, dm }\)

Therefore; \(\displaystyle {x_{cm} = \dfrac{1}{0.8} \cdot \int\limits {x} \cdot \frac{0.8}{0.03} \cdot \frac{2}{3}\cdot x\, dx }\)

\(\displaystyle {x_{cm} = \dfrac{1}{0.8} \cdot \int\limits {x} \cdot \frac{0.8}{0.03} \cdot \frac{2}{3}\cdot x\, dx } = \dfrac{1}{0.8} \times \frac{0.8}{0.03} \times \frac{2}{3}\cdot \int\limits^3_0 {x^2} \, dx\)

\(\displaystyle {x_{cm} = \dfrac{1}{0.8} \times \frac{0.8}{0.03} \times \frac{2}{3}\cdot \int\limits^3_0 {x^2} \, dx = \frac{200}{9} \cdot \left[\frac{x^3}{3} \right]^{0.3}_0\)

\(\displaystyle {x_{cm} = \frac{200}{9} \cdot \left[\frac{x^3}{3} \right]^{0.3}_0=\frac{200}{9} \times \frac{0.027}{3} =0.2\)

The location of the x-coordinate center of mass, \(x_{cm}\) = 0.2 m = 20 cm from the vertex, which is the same location as the x-coordinate of the centroid of the plate of uniform density.

The plate is symmetrical about the x-axis, therefore, the y-coordinate of the center of mass is along the x-axis, which is \(y_{cm}\) = 0

The coordinate of the center of mass = (0.2, 0)

Part of the question requires the location of the coordinate of the center of mass of the triangular plate

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To determine which differential equation(s) are linear, we need to examine the form of each equation. A linear differential equation is one that can be written in the form a(x)y" + b(x)y' + c(x)y = g(x), where a(x), b(x), c(x), and g(x) are functions of x.

The differential equation 2xy" - 5xy' + y = sin(3x) is linear. It can be written in the form a(x)y" + b(x)y' + c(x)y = g(x), where a(x) = 2x, b(x) = -5x, c(x) = 1, and g(x) = sin(3x).
The differential equation (v)² + xy = In(x) is not linear. It does not follow the form a(x)y" + b(x)y' + c(x)y = g(x) because it contains a term with (v)², where v represents the derivative of y with respect to x. This term does not have a linear coefficient.
The differential equation y' + sin(y) = e^(3x) is linear. It can be written in the form a(x)y' + b(x)y = g(x), where a(x) = 1, b(x) = sin(y), and g(x) = e^(3x).
The differential equation (x²+1)y" - 3y - 2x³y = -x - 9 is not linear. It does not follow the form a(x)y" + b(x)y' + c(x)y = g(x) because it contains a term with (x²+1)y", where the coefficient is a function of x.
The differential equation y' + xy = y" is linear. It can be written in the form a(x)y' + b(x)y = g(x), where a(x) = 1, b(x) = x, and g(x) = y".

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Answer:

x = 3 for the point of intersection of these two lines

Step-by-step explanation:

Please, label these functions:  y = 2x + 3 and y = 4x - 3.

Solve this system by equating the left function to the right one:

2x + 3 = 4x - 3

Combining like terms results in:

6 = 2x

Therefore, x = 3 for the point of intersection of these two lines.

let's say for a second that that angle is θ, so we can say that

\(sin^{-1}\left(\cfrac{\sqrt{7}}{7} \right)=\theta \qquad therefore\qquad tan\left[ sin^{-1}\left(\cfrac{\sqrt{7}}{7} \right) \right]\implies tan(\theta ) \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{this really means}}{sin^{-1}\left(\cfrac{\sqrt{7}}{7} \right)=\theta}\implies \cfrac{\stackrel{opposite}{\sqrt{7}}}{\underset{hypotenuse}{7}}=sin(\theta )\)

let us notice something, the opposite side is positive, that means either the I or II Quadrant, however the sin⁻¹ function has a range constrained to π/2 to -π/2, which excludes the II Quadrant, so that means that θ must be on the I Quadrant, where the adjacent side or cosine or "x" is positive too.

now, let's use the pythagorean theorem to get the adjacent side for θ

\(\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=\stackrel{hypotenuse}{7}\\ a=adjacent\\ b=\stackrel{opposite}{\sqrt{7}}\\ \end{cases} \\\\\\ \pm\sqrt{7^2-(\sqrt{7})^2}=a\implies \pm\sqrt{42}=a\implies \stackrel{I~Quadrant}{+\sqrt{42}=a} \\\\[-0.35em] \rule{34em}{0.25pt}\)

\(tan(\theta )\implies \cfrac{\stackrel{opposite}{\sqrt{7}}}{\underset{adjacent}{\sqrt{42}}}\implies \cfrac{\sqrt{7}\cdot \sqrt{42}}{\sqrt{42}\cdot \sqrt{42}}\implies \cfrac{\sqrt{294}}{42}\implies \cfrac{7\sqrt{6}}{42}\implies \cfrac{\sqrt{6}}{6}\)

Answer:

a: 00:45

b: 7:30 PM

Step-by-step explanation:

Hope this is right

Answer:

\(\frac{-2}{3}\)

Step-by-step explanation:

\(\frac{-8}{3}\) x \(\frac{1}{4}\) = \(\frac{-8}{12}\)  A negative times a positive is a negative.

\(\frac{-8}{12}\) ÷ \(\frac{4}{4}\) = \(\frac{-2}{3}\)  Divide the numerator and denominator by 4 to simplify.

Each of the equations of parabolas should be matched with the x-intercepts of the parabolas as follows;

In Mathematics and Geometry, the x-intercept of any function refers to the point at which the graph of a function crosses the x-coordinate and the y-value of "f(x)" is equal to zero (0).

Next, we would determine the x-intercept of each of the equations of parabolas (quadratic functions) as follows;

y = x² + x - 12

0 = x² + x - 12

0 = x² + 4x - 3x - 12

0 = (x + 4)(x - 3)

Therefore, the x-intercept are (-4, 0) and (3, 0).

y = x² + 5x + 4

0 = x² + 5x + 4

0 = x² + 4x + x + 4

0 = (x + 4)(x + 1)

Therefore, the x-intercept are (-4, 0) and (-1, 0).

y = x² - 5x - 24

0 = x² - 5x - 24

0 = x² - 8x + 3x - 24

0 = (x - 8)(x + 3)

Therefore, the x-intercept are (-3, 0) and (8, 0).

y = -x² - 5x + 14

0 = -x² - 5x + 14

0 = -x² - 7x + 2x + 14

0 = (x - 7)(x + 2)

Therefore, the x-intercept are (-2, 0) and (7, 0).

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

Option D, 4

Step-by-step explanation:

2 pizzas x 6 slices per pizza = 12 slices of pizza

12 slices of pizza divided by 3 friends eating equal slices = 4 slices per friend

Option D, 4, is your answer

The correct answer is:

**C) 0.28**

The sum of deviations refers to the sum of the differences between individual data points and the mean of the dataset. In any dataset, the sum of deviations from the mean will always equal 0.

This is because, when calculating the mean, you sum all the data points and then divide by the number of data points. The mean represents the "middle" or "balance" point of the dataset. When you add up the differences between each data point and the mean, the positive and negative deviations will cancel each other out, resulting in a sum of 0.

So, any non-zero value for the sum of deviations is impossible. In this case, 0.28 is the only non-zero value.

Therefore, the degree of the resulting polynomial is m + n when two polynomials of degree m and n are multiplied together.

What is polynomial?

A polynomial is a mathematical expression consisting of variables and coefficients, which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. Polynomials can have one or more variables and can be of different degrees, which is the highest power of the variable in the polynomial.

Here,

When two polynomials are multiplied, the degree of the resulting polynomial is the sum of the degrees of the original polynomials. In other words, if the degree of the first polynomial is m and the degree of the second polynomial is n, then the degree of their product is m + n.

This can be understood by looking at the product of two terms in each polynomial. Each term in the first polynomial will multiply each term in the second polynomial, so the degree of the resulting term will be the sum of the degrees of the two terms. Since each term in each polynomial has a degree equal to the degree of the polynomial itself, the degree of the resulting term will be the sum of the degrees of the two polynomials, which is m + n.

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Gastronomy is a way of promoting understanding among different cultures, and of bringing people and traditions closer together.

The practise of choosing, preparing, presenting, and consuming exquisite cuisine. The foundation of gastronomy lies in the connections between food, culture, and tradition. Gastronomy has emerged through time as a more potent cultural force than language or other influences among the peoples of the world.

Molecular gastronomy is a relatively recent branch of science that studies the physical and chemical changes that take place during cooking. Molecular cuisine is the name of the new culinary movement based on this emerging discipline.

Nowadays, the world may be broken down into separate gastronomic zones, where different cuisines are popular and similar cooking techniques are used. Throughout much of Southeast Asia, rice is the main food. The abundant and creative use of spices to give meals an extra flavour is what makes Indian and Indonesian cuisine unique. The prevalent ingredient in Mediterranean recipes is olive oil.

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Complete question:

How can gastronomy help us live harmoniously?

The working class was unable to achieve much, despite valiant efforts, due to their lack of solidarity and the capitalist's willingness to use violence against them.The middle class responded to the struggle between labor and capital, as well as the changes that American society underwent during the late nineteenth century, by supporting a variety of social reform movements.

After the Civil War, Reconstruction failed to establish racial equality and black freedom in the United States. The rapid industrialization of the United States under the system of "free labor" in the years following the Civil War contributed to a social crisis by the end of the nineteenth century. This crisis seemed to be causing the disappearance of traditional American values of democracy, equality, and opportunity, and class conflict was threatening to tear society apart.In their struggle against each other, capitalists and working classes attempted to enhance their own power and interests. Capitalists attempted to enhance their power by instituting new labor policies, cutting wages, and lowering working conditions.

The working class was unable to achieve much, despite valiant efforts, due to their lack of solidarity and the capitalist's willingness to use violence against them.The middle class responded to the struggle between labor and capital, as well as the changes that American society underwent during the late nineteenth century, by supporting a variety of social reform movements. They sought to provide relief for the urban poor and to reform politics by promoting women's suffrage and demanding the elimination of political corruption.In conclusion, Reconstruction failed to establish racial equality and black freedom in the United States. The rapid industrialization of the United States under the system of "free labor" in the years following the Civil War contributed to a social crisis by the end of the nineteenth century. Capitalists and working classes attempted to enhance their power and interests in their struggle with each other. The working class was unable to achieve much, despite valiant efforts. The middle class responded to the struggle between labor and capital, as well as the changes that American society underwent during the late nineteenth century, by supporting a variety of social reform movements.

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Answer:

My theory is that the cold war was so cold that it turned him to ice, so in honor of him the soldiers turned him into an ice sculpture, which is how he was shaped by the cold war

Step-by-step explanation:

here's the real reason, lol:

I honestly don't know

Answer:

15.6

Step-by-step explanation: