The water level in a spherical bowl has a diameter of 30 cm. If the horizontal diameter of the bowl is 10 cm below the water level, calculate the radius of the bowl and the depth of the water in the bowl.​

The restriction of the given equation is [tex]cos^{2}x =cos^{2} x[/tex],  other than 0≤x≤2π.

What is restriction of equation?

Restriction of the equation is the value of domain where the value is limited.

Given,

[tex]sin^{2} xcos^{2}x +cos^4x =(1-sinx)(1+sinx)[/tex]

taking [tex]cos^2x[/tex] common, we get

[tex]cos^2x(sin^2x+cos^2x)=1+sinx-sinx-sin^2x[/tex]

we know

[tex]sin^2x+cos^2x=1\\cos^2x=1-sin^2x[/tex]

we get,

[tex]cos^2x=cos^2x[/tex]

and the restriction is 0≤x≤2π.

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Answer:

[tex]34532x = 5647\\\\x=\frac{5647}{34532} = 0.16352947[/tex]

Answer: 4 - 0.75x = 0.83333333333

Step-by-step explanation:

3/4 = 0.75

5/6 = 0.83333333

So 4 - 0.75x = 0.83333333

Check the picture below on the left side.

now, let's notice on that table when y = 0, namely the points in red in the table, those are "zeros", well obviously, or solutions of the quadratic, and those occur when x = -9 and when x = -3, now, let's use another point hmmmm we also know that the quadratic goes through (-7 , 8) so let's use those fellows

[tex]\begin{cases} x=-9\implies &x+9=0\\\\ x=-3\implies &x+3=0 \end{cases}\hspace{5em}a(x+9)(x+3)=\stackrel{0}{y} \\\\\\ \textit{we know that} \begin{cases} x=-7\\ y=8 \end{cases}\implies a(-7+9)(-7+3)=8\implies a(2)(-4)=8 \\\\\\ -8a=8\implies a=\cfrac{8}{-8}\implies \boxed{a=-1} \\\\\\ -(x+9)(x+3)=y\implies -(x^2+12x+27)=y\implies \boxed{-x^2-12x-27=y}[/tex]

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Answer: $290

Step-by-step explanation:

Cost per bracelet = $10

5 bracelets sold x $10/bracelet = $50 cash earned already

x = number of bracelets sold

Money made = (x )($10/bracelet)

Total money made if Autumn sells 24 more bracelets:

$50 + (24)($10) = $290

The other diagonal is $70 long.

Given:

Rhombus $abcd$ has perimeter $148$, and one of its diagonals has length $24$.

P = 148 and d = 24

Area [tex]= 1/4 d \sqrt{P^2-4d^2}[/tex]

= 1/4(24)[tex]\sqrt{148^2 - 4*24^2}[/tex]

= 6 [tex]\sqrt{21904-4*576}[/tex]

= 6*[tex]\sqrt{21904-2304}[/tex]

= 6*[tex]\sqrt{19600}[/tex]

= 6*140

= 840

Area = d*d1 / 2

840 = 24 * d1 / 2

840 * 2 = 24 * d1

1680/24 = d1

d1 = $70

Therefore The other diagonal is $70 long.

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Answer:

70

Step-by-step explanation:

The four sides of a rhombus all have equal length, so if the perimeter is 148, then each side has length 148/4 = 37. Also, the diagonals of a rhombus bisect each other at right angles, so the diagonal of length 24 is cut into two pieces of length 12. We can show this information in a diagram (shown below.)

Applying the Pythagorean Theorem to any of the four right triangles in our diagram, we have

12² + x² = 37².

Solving this equation for positive x, we get x = √37² - 12² = √1369 - 144 = √1225 = 35. The length of the long diagonal is x + x = 70.

Explanation:

We simplify the square root of 64 to get 8

[tex]\sqrt{64} = \sqrt{8^2} = 8[/tex]

Then we'll have the plus minus out front to say

[tex]x = \pm \sqrt{64} = \pm 8[/tex]

That breaks down into x = 8 or x = -8

As a check

x^2 = (8)^2 = 8*8 = 64

x^2 = (-8)^2 = (-8)*(-8) = 64

Both values lead to 64 when squaring.

Answer:

Line of symmetry: -b/2a = 0 because b is 0 and a is 1

y-intercept is when x=0, therefore it is at 8.

x-intercept is when y=0, and you would get sqrt(-8), therefore there are no real zeros for this equation.

Vertex: (0,8)

Step-by-step explanation:

To find the vertex, plug in the x-value from the line of symmetry because the vertex happens at the line of symmetry. When you set x=0, then the y-value of the vertex is 8, therefore, the vertex is at (0,8).

The function to show the amount of tiles laid as a function of time is

The reasonable domain is 0 ≤ t ≤ 9.6

Information gotten from the question include

Jeremy and Travis are placing 1200 tiles in a building

hey have already place 200 tiles, and they are able to place 125 tiles every hour.

The relationship is expressed in the form.

y = mt + c

Definition of variables to suit the problem to be solved

y = Total number of tiles laid

m = tiles laid per hour = 125

t = number of time

c = tiles already placed

200 = 1200 - 125t

The reasonable domain is the range between zero tiles to laying up the 1200 tiles

0 = 1200 - 125t

1200 = 125t

t = 9.6

1200 = 1200 - 125t

0 = -125t

t = 0

the domain is 0 ≤ t ≤ 9.6

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The probability of filling a cup between 22 and 33 ounces is 0.9371

The variable here is the machine's output which is normally distributed.

The normal distribution is defined by two parameters, namely, the mean and the standard deviation.  

The population mean for this normal distribution is μ = 25 ounces per cup, and a population standard deviation of σ = 4 ounces (per cup).

calculate the z-score using this formula:

z = x-μ/σ

z is the z-score.

x is the raw score.

μ is the population mean.

σ is the population standard deviation.

The probability of filling a cup between 18 and 33 ounces

z = 18-25/4

z = -7/4

z = -1.75

P(Z< - 1.75) = 1 - P(Z > -1.75)

                  = 1 - 0.9599

                  = 0.0400

We can proceed in the same way to obtain the z-score and the associated probability with the raw score x = 33. We can see that this value is above the mean (positive).

z = 33-25/4

z = 8/4

z = 2

P(z<2) = 0.9772

P(18<x<33) = 0.9772 - 0.0400

P(18<x<33) = 0.9371  

the probability of filling a cup between 22 and 33 ounces is 0.9371

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The dimensions and area of the parts of the composite figure are as follows;

A composite figure is a figure that consists of two or more simpler figures.

The width of the whole figure of length 14 consists of the the missing dimension and the expression (x - 3)

Therefore;

14 = Missing dimension + (x - 3)

Missing dimension = 14 - (x - 3) = 17 - x

The expression for the missing dimension is = 17 - x

The area of the large rectangle = 14 × 12 = 168

Area of the smaller unshaded rectangle = (x - 3) × 12 = 12·x - 36

Area of the shaded figure = Area of the whole figure less the area of the unshaded figure

Therefore;

Area of the shaded figure = 168 - (12·x - 36) = 204 - 12·x

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The equation of the straight line which makes intercepts 3 and "-4" on the axes is 4x - 3y =12 and the point (1, 2) not lie on the line.

When you know the slope of the line to be investigated and the provided point is also the y intercept, you may utilize the slope intercept formula, y = mx + b. (0, b). The intercept form of a line's equation is written as [tex]\frac{x}{a} +\frac{y}{b} = 1[/tex], where a is the x- intercept and b is the y-intercepts, respectively. The x-intercept is the point on the x-axis that is closest to the origin where the line crosses the x-axis, and the y-intercept is the point on the y-axis that is closest to the origin where the line crosses the y-axis.

Now, finding the equation of line by putting the value of intercepts,

[tex]\frac{x}{a} +\frac{y}{b} = 1\\\frac{x}{3} +\frac{y}{-4} = 1\\-4x+3y=-12\\4x-3y=12[/tex]

so, the equation is 4x-3y=12.

Now, putting x=1 and y=2 to find whether (1,2) lie on the line or not,

4(1)-3(2)=12

4-6=12

-2≠12

So, the point (1, 2) not lie on the line.

Therefore, the equation of the straight line which makes intercepts 3 and "-4" on the axes is 4x - 3y =12 and the point (1, 2) not lie on the line.

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Answer:

Step-by-step explanation:

8x2 = 16

8x4= 32 (since its the 2nd one meaning its in the tenth place add 1 Zero, 10) making it 320

8x3 =24 (since its hundredths place add 2 Zeros 100) making 2400

2400+ 320+ 16= 2736

The answer is 2737

Answer:

To find the domain and range, we simply solve the equation y = f(x) to determine the values of the independent variable x and obtain the domain. To calculate the range of the function, we simply express x as x=g(y) and then find the domain of g(y)

Step-by-step explanation:

Thats basically it I think

Answer:

  128°

Step-by-step explanation:

You want the missing angle in the octagon with interior angles x, 106°, 144°, 129°, and 70°; exterior acute angles of 45° and 31°; and exterior obtuse angle 141°.

The sum of angles in the n = 8-sided polygon will be 180°(n -2) = 1080°

The interior angles are the supplement of exterior acute angles. The interior reflex angle is the difference between 360° and the exterior obtuse angle. This means we have ...

  x +(180 -45) +106 +144 +(180 -31) +129 +(360 -141) +70 = 1080

  x -45 +106 +144 -31 +129 -141 +70 = 360 . . . . . . subtract 720

  x + 232 = 360

  x = 128

The missing angle is 128°.

As the test's p-value above the 0.05 level of significance, we cannot reject the hypothesis.

X=97.77 is the mean on the PDI.

a )

The population standard deviation of the PDI:S = 14-69

The PDI sample size is n=70.

The test statistic value is

=X -μ/б-√n

97.77 - 100/14.69√70

Z = - 1.27

The test's p-value is 1.

Value of p = 2p (z - 1.27).

=2 ( = NORMSDIST (-1.27) )

= - 2 (0.1020 )

p-value = 0.2041

Since , the p -value of the test is greater the the 0.05 level of significance, so we fail to reject hypothesis

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The expression for double the product of 8 and a number is 16 + 2n.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

Let the number be n.

Double the product of 8 and a number will be:

= 2(8 + n)

= 16 + 2n

The expression is 16 + 2n.

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The value of the same input x is  -7

What is linear equation?

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.

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.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Let output A = A

And output B = B

According to the question,

5x - 4 = A

3x + 8 = B

And A = 3B

from the above equations,

5x - 4 = 3(3x + 8)

5x - 4 = 9x + 24

4x = -28

x = -7

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Answer:

37500

Step-by-step explanation:

100-80 = 20 percent of original price

Therefore 20 percent of selling price = 7500

[tex]\frac{20x}{100}=7500\\ 20x = 750000\\x = 37500[/tex]

Answer:

20 percent * 37500 =

(20:100)* 37500 =

(20* 37500):100 =

750000:100 = 7500

1. Everyone has a carrying capacity

     carrying capacity means is the total frequency of individuals within a    community a habitat can sustain.

2. Limiting factor are biotic or abiotic factors which limit the carrying capacity.

complete question:

When living conditions in an area are good, a population will generally grow. But eventually some environmental factors will cause the population to stop growing. A limiting factor is an environmental factor that causes a population to decrease. Some limiting factors for populations are food and water, space, and weather conditions.

1. Everyone has _____________

2.What is a limiting factor? please answer in a complete sentence by restating the question​

Answer:  

    1. Everyone has a carrying capacity

     carrying capacity means is the total frequency of individuals within a    community a habitat can sustain.

2. Limiting factor are biotic or abiotic factors which limit the carrying capacity.

The maximum population size that an ecosystem can support is called carrying capacity. Limiting factors determine carrying capacity. The availability of abiotic factors (such as water, oxygen, and space) and biotic factors (such as food) dictates how many organisms can live in an ecosystem. Carrying capacity is also impacted by the availability of decomposers. Decomposers breakdown and recycle dead organisms and organic matter. They prevent dead matter from accumulating and taking up space in an ecosystem.

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set A is equal to set B which was found by comparing both the sets. So, you have to choose set A = set B.

Given sets are :

A = {4, 7, 10, 15}

B = {10, 4, 15,7}

The elements in set A and set B are 4,7,10 and 15. So, we can say that both the sets are equal.

Therefore, set A is equal to set B which was found by comparing both the sets. So, you have to choose set A = set B.

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By making use of permutation, the number of possible orders for ways to get to school for three days is 6.

Permutation: An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are arranged in a linear or sequential order.

On the 1st day, the child goes to school either by walking or biking,

So, the number of possible ways for day one is 2.

Similarly, for Day 2 and Day 3, the number of possible ways is 2 each.

Thus, the number of ways in which it can be ordered is 2 +2+2 = 6.

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Answer: [tex]x > \frac{16}{3}[/tex]

Step-by-step explanation:

[tex]16(\frac{1}{4}x -\frac{1}{2} ) > 24-2x\\ 4x-8 > 24-2x\\6x > 32\\x > 32/6\\x > \frac{16}{3}[/tex]

By chain rule, the first derivative of the composite function f(x) = [tex]4^{5\cdot x - 9}[/tex] is equal to  [tex]4^{u}[/tex] · 5 · ㏑ 4.

Herein we have the case of a composite function, that is, a function of the form f[u(x)]. Chain rule is a derivative rule used to find the derivative of composite functions, which is now defined:

df / dx = (df / du) · (du / dx)

If we know that u(x) = 5 · x - 9 and f(u) = [tex]4^{u}[/tex], then the derivative of the compond function is:

df / du = [tex]4^{u}[/tex] · ㏑ 4

du / dx = 5

Then, by chain rule:

df / dx = [tex]4^{u}[/tex] · 5 · ㏑ 4

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8x + 5y ≥ 50

This is from the inequality 16x + 10y ≥ 100.

The other three inequalities are:

x + y ≤ 8

x ≥ 1

y ≥ 3

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

Total number of students = 100

Type A minibus = x

Type B minibus = y

Number of students type A carry = 16

Number of student type B carry = 10

We can write an inequality from the above situation as,

16x + 10y ≥ 100

Taking out the common factor.

2 (8x + 5y) ≥ 2 x 50

8x + 5y ≥ 50

The school wishes to use no more than eight minibusses.

This can be written as

x + y ≤ 8

The school wishes to use at least one type A minibus.

This can be written as

x ≥ 1

The school wishes to use at least three type B minibusses.

This can be written as

y ≥ 3

Thus,

8x + 5y ≥ 50

This is from the inequality 16x + 10y ≥ 100.

The other three inequalities are:

x + y ≤ 8

x ≥ 1

y ≥ 3

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Answer:

E = mc²

Step-by-step explanation:

Answer:

E =mc^2

Step-by-step explanation:

This equation meant (E)energy equals mass (m) times the speed of light (c) squared. (^2).

Answer:

  A: 8750(0.88^x)

  B: 9995(0.82^x)

Step-by-step explanation:

You want an exponential decay function for cars A and B given their cost and their "decay factor."

In general, an exponential function has the form ...

  value = (initial value)·(growth factor)^x

The growth factor is usually defined as ...

  growth factor = 1 + growth rate

where the "growth rate" is often expressed as a percentage or a fraction.

Your form for f(x) has a=(initial value) and b=(growth factor).

The value of x will be zero at the point where the initial value applies. It will increase by 1 unit for each interval in which the growth factor applies.

Car A

The initial value is presumed to be the Cost. What is called the "growth rate" above is the opposite of what is called the "Decay Factor" in this problem. That is ...

The exponential function is then ...

  f(x) = 8750·(0.88^x)

Car B

For this car, we have ...

The exponential function is then ...

  f(x) = 9995·(0.82^x)