________________________________

Answer:

Neil Armstrong and Buzz Aldrin

Step-by-step explanation:

Fifty years after Neil Armstrong, Buzz Aldrin and Michael Collins became etched in history, the Apollo 11 mission remains an iconic moment in broadcasting. It's estimated that between 600-650 million people tuned in around the world to Armstrong and Aldrin's broadcast from the lunar surface on July 20, 1969.

Answer:

-definition of cosine

-definition of sine

-Pythagorean Theorem

-Substitution

-laws of exponents

Step-by-step explanation:

The blanks are filled by the definition of cosine, the definition of sine,  Pythagorean Theorem, substitution, and laws of exponents respectively.

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

Given the right triangle shown below, prove cos²(θ) + sin²(θ) = 1.

A triangle with sides x, y, and hypotenuse r.

Angle θ is opposite to side y.

As per the Laws of Cosine,

cos(θ) = x/r, and

As per the Laws of Sine,

sin(θ) = y/r.

Multiplying both sides of the above equations by r,

x = r cos(θ) and

y = r sin(θ).

The Pythagorean Theorem states that x² + y² = r².

By Substitution method, we have [r cos(θ)]² + [r sin(θ)]²= r².

Applying the Laws of Exponents, the equation can be written as r² cos²(θ) + r² sin²(θ) = r².

Dividing both sides of the equation by r² results in cos²(θ) + sin²(θ) = 1.

Hence, the blanks are filled by the definition of cosine, the definition of sine,  pythagorean theorem, substitution, and laws of exponents respectively.

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Answer:

1671.58

Step-by-step explanation:

V=1/3(3.14)(9.75)squared(16.8)

The explicit rule for the nth month in the credit union savings club account is to multiply the balance of the previous month by 1.007. This rule represents the monthly interest rate of 0.7% or the annual interest rate of 8.4%.



To calculate the balance of the account for each month, we apply the monthly interest rate of 0.7% or the annual interest rate of 8.4%.

Starting with an initial deposit of $30, the balance for the first month is $30 * 1.007 = $30.21.

For the second month, we multiply the previous month's balance ($30.21) by 1.007, resulting in $30.21 * 1.007 = $30.42.

We continue this pattern for each subsequent month, multiplying the previous month's balance by 1.007. This can be represented by the explicit rule for the nth month: Balance(n) = Balance(n-1) * 1.007.

By following this rule, we can determine the balance of the credit union savings club account for any given month based on the initial deposit and the monthly interest rate.

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Answer:

  4.0 feet

Step-by-step explanation:

You want the diameter of a rubber ball that costs $1, if that cost is $0.02 per square foot.

The surface area of a sphere is given by ...

  A = 4πr²

In terms of diameter, this is ...

  A = 4π(d/2)² = πd²

The cost will be ...

  Cost = (cost/square foot)(area)

  1.00 = 0.02(πd²)

Solving for d, we have ...

  d² = 1.00/(0.02π) ≈ 15.915

  d ≈ √15.915 ≈ 3.989 ≈ 4.0 . . . . feet

The diameter of the ball is about 4.0 feet.

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Answer:

2340

Step-by-step explanation:

3 3/4=15/4            3 1/4=13/4    turn the mixed fractions into improper fractions

(15/4)(3)(13/4)=36.5625ft³        this is the volume of the shipping box

(1/4)(1/4)(1/4)=1/64ft³                  this is the volume of the fish food box

36.5625/(1/64)                          divide it to find out how much fish boxes can fit

36.5625×64                             flip the fraction and multiply

2340

Answer:

C is the correct answer

= ∂V∂t + (V⋅∇)V

In mathematics, the complete derivative of a function f at a point is the best linear approximation near that point of the function with respect to its arguments. Unlike partial derivatives, the total derivative approximates a function with respect to all of its arguments, not just one. Pressure is defined as force/area, and the derivatives of pressure physically correspond to the rate of change of this quantity. If the derivatives are with time, the derivatives will tell you how fast the pressure is changing with time, just like any function.a = dVdt = ∂V∂t + u∂V∂x+v∂V∂y+w∂V∂z = ∂V∂t + (V⋅∇)V

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It will take the town 21 years 4 months to reach 4600 in population

a rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate.

initial population = 3000

population increase every year = 2.5% of 3000

which is 2.5/100 x 3000 = 75

let the time taken to reach 4600 be d

increment for d number of years = 75d

Total population after d years is 75d + 3000

so 75d + 3000 = 4600

75d = 4600  - 3000

75d = 1600

d = 1600/75

d = 21.33 years which is 21 years 4 months

In conclusion 21 years 4 months is the time taken for the ton tto get tto 4600

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Answer:

The zero is at x=3.497

Step-by-step explanation:

This polynomial can be simplified by factoring by grouping. The groups for this polynomial are:

\((x^{5}-7x^{4})+(19x^{3}-37x^{2})+(60x-46)=0\)

For each group, factor out the common terms:

\((x^{5}-7x^{4})\) becomes \(x^{4}(x-7)\)

\((19x^{3}-37x^{2})\) becomes \(x^{2}(19x-37)\)

(60x-46) becomes 2(30x-23)

The original equation has factored into: \(x^{4}\left(x-7\right)+x^{2}\left(19x-37\right)+2\left(30x-23\right)\)

Since the factored equation does not have any common terms, it can't be factored anymore.

There are several ways to find the zeros of this function. The simplest way would be to graph the function and determine where it intersects the x-axis. Assuming you need to find the zeros without graphing the function, you can use synthetic division or approximate to find the zeros.

Using approximation and assuming the zeros are between 0 and 5:

\(x^{4}\left(x-7\right)+x^{2}\left(19x-37\right)+2\left(30x-23\right)=0\)

Testing x=0:

\(0(0-7)+0(0-37)+2(0-23)=2*-23=-46\)

Testing x=1:

\(1(1-7)+1(19*1-37)+2(30*1-23)=-6-18+14=-10\)

Testing x=2:

\(2^{4}(2-7)+2^{2}(19*2-37)+2(30*2-23)=-80+4+74=-2\)

Testing at x=3:

\(3^{4}(3-7)+3^{2}(19*3-37)+2(30*3-23)=-324+180+134=-10\)

There potentially is a zero between x=2 and x=3. For this function, there is not a zero there. This can be determined by testing more points between x=2 and x=3 or by graphing the function. The easiest extra points to test are x=1.9 and x=2.1. If both of these produce a value less than -2 then there is not a zero between x=2 and x=3 because x=2 would be part of the vertex of this graph segment.

Testing at x=4:

\(4^{4}(4-7)+4^{2}(19*4-37)+2(30*4-23)=-768+624+194=54\)

There is a potential zero between x=3 and x=4.

Testing at x=3.5:

\(3.5^{4}(3.5-7)+3.5^{2}(19*3.5-37)+2(30*3.5-23)=-525.2188+361.375+164=0.1562\)

This means that the function has a zero very close to 3.5. Additional points to test to approximate this zero are 3.4 and 3.6. You can continue to pick bracketing points to test until you are satisfied. When graphed, this zero is actually x=3.497. This is actually the only zero this function has when you look at its graph. There is no need to test any more of its points, and you can verify that this function is rapidly increasing once it passes through x=3.

Answer:

little bit messy but whatever

Step-by-step explanation:

if you haven't learned imaginary numbers just write (x²+4)(x-1)(x-3)²

Step-by-step explanation:

-26a-19-35=-84

-26a-19+(19)-35=-84+(19)

-26a-35=-65

-26a-35+(35)=-65+(35)

-26a=-30

-26a/26=-30/26

Answer:

x = 5

Step-by-step explanation:

1. Multiply 6 by x and 4 to have the first equation:

6x +24

2. Multiply 3 by 4x and -2 to have second equation:

12x-6

3. Set equations equal to each other:

6x+24=12x-6

4. Subtract 6x from 12x and add 6 to 24:

30=6x

5. Isolate 6x by dividing both sides by 6.

6. x = 5

Answer:

6x+24=12x-6

12x-6x=24+6

6x=30

x=30:6

x=5

Answer:

1. Ans;

\( \frac{1}{3} \times 1 \frac{1}{3} = \frac{1}{3} \times \frac{4}{3} = \frac{4}{9} = 0.4 \)

2. Ans ;

\(1 \frac{1}{5} \times \frac{3}{4} = \frac{6}{5} \times \frac{3}{4} = \frac{9}{10} = 0.9\)

3. Ans ;

\( \frac{2}{3} \times 1 \frac{3}{5} = \frac{2}{3} \times \frac{8}{5} = \frac{16}{15} = 1 \frac{1}{15} = 1.06\)

4. Ans ;

\(2 \frac{1}{2} \times 1 \frac{1}{3} = \frac{5}{2} \times \frac{4}{3} = \frac{10}{3} = 3 \frac{1}{3} = 3.3\)

5. Ans ;

\(2 \frac{1}{2} \div \frac{4}{5} = \frac{5}{2} \div \frac{4}{5} = \frac{5}{2} \times \frac{5}{4} = \frac{25}{8} = 3 \frac{1}{8} = 3.125\)

6. Ans ;

\(9 \div 1 \frac{1}{9} = 9 \div \frac{10}{9} = 9 \times \frac{9}{10} = \frac{81}{10} = 8 \frac{1}{10} = 8.1\)

7. Ans ;

\(2 \frac{1}{2} \div 3 \frac{1}{3} = \frac{5}{2} \div \frac{10}{3} = \frac{5}{2} \times \frac{3}{10} = \frac{3}{4} = 0.75\)

8. Ans ;

\(7 \frac{1}{2} \div 1 \frac{2}{3} = \frac{15}{2} \div \frac{5}{3} = \frac{15}{2} \times \frac{3}{5} = \frac{9}{2} = 4 \frac{1}{2} = 4.5\)

I hope I helped you^_^

7.08  is the probability, rounded to the nearest thousandth.

What does the math term "probability" mean?

The simple definition of probability is the likelihood that something will occur.

                   We can discuss the probabilities of various outcomes to determine how likely they are whenever we are uncertain about the result of an event. Statistics describes the examination of events subject to probability.

Probability of getting a six on rolling a dice = 1/3

Here ,

n = 4 , p = 1/3

So, For P(X <= 1) = P(X = 0) + P(x = 1)

4C0 * (1/6)^0 * (1 - 1/3)^(4-0) + 4C1 * (1/3)^1 * (1-1/3)^(4-1)

= 1 * 1 * (5/3)^4 + 4 * (1/3) *

= 5.75 + 1.33

=  7.08

= 7.08 (nearest thousandth)

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Answer:

From the General Equation of a straight line

Y=Mx + c

where M = Slope of the line

c= Intercept on Y axis

y=-4.2x-80

Comparing with the Eqn of a straight line

Slope = -4.2

From the Options the answers are in Fractions

You can easily convert this figure to fraction by Moving the decimal to the back once and then divide by 10

Then we have -42/10

Reducing Further

you have = -21/5.

Option D✅

Answer:

\(D. -\frac{21}{5}\)

Step-by-step explanation:

Hello!

Slope-Intercept Form: \(y = mx +b\)

Given our equation: \(y = -4.2x - 80\)

We basically have to find the fraction that represents -4.2.

Since the number is negative, we can narrow down three possibilities:

-80 is not -4.2, and -5/21 is less than 1. So the correct option is -21/5.

Based on the image, the figure appears to be a cube.

Faces: 6 Edges: 12 Vertices: 8

To find the number of edges in a cube, you need to count the number of line segments that make up the corners and sides of the cube. A cube has 12 edges.

The number of vertices, edges, and faces can vary greatly for different types of three-dimensional shapes. For example, a pyramid has one base and several triangular faces that meet at a single vertex, while a sphere has no faces or edges but has an infinite number of points on its surface.

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Answer:

there are 9 possibilities I think

Graphs and the correlation coefficients are mentioned below-

A scatter plot uses dots to represent values for two different numeric variables. There are three types of scatter plots or charts -

There are the three most important correlations as -

Given are the scatter plots and the associated correlation coefficient.

        \($r =\frac{\sum\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right)}{\sqrt{\sum\left(x_{i}-\bar{x}\right)^{2} \sum\left(y_{i}-\bar{y}\right)^{2}}}\)

        r = correlation coefficient

        \($x_{i}\) = values of the x-variable in a sample

        \($\bar x\) = mean of the values of the x-variable

        \($y_{i}\) = values of the y-variable in a sample

 \(\bar y\) = mean of the values of the y-variable

The graph and their corresponding values of [r] are mentioned below -

Therefore, graphs and the correlation coefficients are mentioned below-

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To complete the square for the equation x2 - 16x + 60 = -12, add 64 to each side of the equation. This will give us x2 - 16x + 124 = 52.

Then, factor out the coefficient of x2 (1) and the coefficient of x (16). This will give us (x - 8)2 = 52. Finally, subtract 52 from both sides to get (x - 8)2 = 0. Solving for x yields x = 8.

Equations are mathematical statements that express the equality of two expressions. They involve one or more unknowns that are represented by variables and involve numbers, constants, and operators. An equation states that the expressions on either side of the equal sign have the same value.

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Answer: x is doubled.

Step-by-step explanation:

A proportional relationship between x and y is written as:

y = k*x

where k is called the constant of proportionality.

In this case, we know that we have a proportional relationship between z and x^3

Then:

z = k*x^3

What will happen to x when z is 8 times greater?

Let's rewrite this equation for two new quantities, z' and x'

z' = k*(x')^3

Now we need to replace z' by 8*z, then:

8*z =  k*(x')^3

We want to find a relationship between x' and x.

And by the first relationship, we know that:

z =  k*x^3

Then we can replace this in the equation "8*z =  k*(x')^3" to get:

8*(k*x^3) =  k*(x')^3

8*k*x^3 = k*(x')^3

Now we can divide both sides by k, so we get:

8*x^3 = (x')^3

Now we can apply the cubic root to both sides, to get:

∛(8*x^3) = ∛(x')^3

∛(8)*x = x'

2*x = x'

Then when we increase the value of z 8 times, the value of x will be doubled.

To find the number of bicycles that must be manufactured to minimize the cost, we need to determine the value of x that corresponds to the minimum point of the cost function C(x).

We can find this by taking the derivative of C(x) with respect to x and setting it equal to zero. Let's differentiate C(x):

C'(x) = 6x - 1500

Now we set C'(x) = 0 and solve for x:

6x - 1500 = 0

6x = 1500

x = 250

Therefore, the number of bicycles that must be manufactured to minimize the cost is 250 bicycles.

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Answer:

C. The price of a standard ticket is $11. The price of a matinee ticket is $9. The price of a senior ticket is $8.

Answer:

The answer is C

Step-by-step explanation:

The volume of the cone is V = 381.15 cu.cm

The curved surface area of the cone is given by

A = πrl

The slant height given in the question is

l = 10.5 cm

A = 115.5 sq.cm

radius = ?

Height = ?

Volume = ?

Using the Curved Surface Area Formula

115.5 = π * r * 10.5

taking π = 22/7

r = 3.5 cm

The slant height is given by

\(\rm l = \sqrt{ r^2 + h^2}\)

Therefore the height is

\(\rm h = \sqrt{ 10.5^2 -3.5^2}\)

h = 9.9 cm

The volume of the cone is

V = π r²h

V = (22/7) * 3.5 * 3.5 * 9.9

V = 381.15 cu.cm

The volume of the cone is V = 381.15 cu.cm

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Answer:

the answer is 5 got it right on quiz

Answer:  E

Reason:

The tip of the right whisker is the max value. This is assuming there aren't any large outliers.

Fraction 12 over 2 can be used to calculate the rate per second at which the machine launches the balls

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The x axis label is Time in seconds, and the x axis values are from 0 to 10 in increments of 2 for each grid line.

The y axis label is Number of Balls, and the y axis values from 0 to 60 in increments of 12 for each grid line

A line is shown connecting points on ordered pair (2, 12) and (4, 24) and (6, 36) and (8, 48)

m=24-12/4-2

m=12/2

Hence,  fraction 12 over 2 can be used to calculate the rate per second at which the machine launches the balls

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The surface area can be obtained by integrating the square root of the sum of the squares of the partial derivatives of f(x, y) with respect to x and y over the region r.

To find the surface area, we need to calculate the square root of the sum of the squares of the partial derivatives of f(x, y) with respect to x and y. In this case,

√(1 + (∂f/∂x)^2 + (∂f/∂y)^2) becomes √(1 + 16x^2 + 4y^2).

Then, we integrate this expression over the region r, which is the disk of radius 3 centered at the origin.

Using polar coordinates, we can rewrite the integral as

∫∫r √(1 + 16r^2 cos^2 θ + 4r^2 sin^2 θ) r dr dθ, where 0 ≤ r ≤ 3 and 0 ≤ θ ≤ 2π. By evaluating this integral, we can determine the area of the given surface.

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If 18,793 is multiplied by 1000, then the product of this arithmetic equation will be equal to 18,793,000.

The arithmetic equations are the mathematical problems which includes simple functions such as addition (summation), subtraction, multiplication and division. The function of multiplication is also called as repeated addition. In the given question, the multiplicand is 18,793 and the multiplier is 1000 and the result which we get that is 18,793,000 is called as product.

The multiplicand is always written first. When the multiple of 10 is multiplied to any number, the general rule says that there is simple addition of zeroes in the right hand side of the number if is not in decimal form. If the number is in decimal form, the decimal point shift to the right hand side as many times as there are zeroes in the multiplier.

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All of the actions listed would have the effect of changing the direction (sign) of the Pearson r value. However, only options (a) and (b) would change the size of the Pearson r value.

a. Adding or subtracting a constant value to each X and Y score would change the location of the data points but not the shape or scatter of the data. This would affect both the means and the standard deviations of X and Y, which are used to compute Pearson r, and thus would change the size of the r value.

b. Same as (a), subtracting a constant value from each X and Y score would also change the size of the r value.

c. Multiplying each X and Y score by a negative constant value would reverse the direction of either X or Y axis, effectively flipping the scatterplot horizontally or vertically. This would only change the sign (positive or negative) of the r value, but not the size.

d. Dividing each X and Y score by a positive constant value would scale the scatterplot along the X and Y axes, effectively changing the units of measurement. This would not change the shape or scatter of the data, and the correlation coefficient would be unchanged.

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