Work out the volume of this sphere.
Give your answer to 1 decimal place.
1
1
I
4.7 cm
Spheres
Vol = ²

Answer:

8,000^0.0625=5

Step-by-step explanation:

Lol I was doing my homework rn and I wasn't 100% sure of my answer so I looked it up on brainly. So an exponential equation should look like this e^a=b so with the three values $8,000 , 6.25% , and 5 years I kind of just mixed around the numbers a bit in the exponential equation till one worked. So yeah...

Answer:

f(t)=8000e^(0.0625)(5)

Step-by-step explanation:

exponential growth function is f(t)=Pe^(rt)

where P is starting value, or price

e is the e on you calculator

r is rate of increase, in this case 6.25/100 is 0.0625, which is the rate

t is the time given

Hope this helps, also had this on my math hw today lol :)

Answer:

1.5 OR 1 1/2

Step-by-step explanation:

Convert the fractions into decimals.

9/10 = 0.9

3/5 = 6/10 = 0.6

Divide the decimals.

0.9/0.6 = 1.5

Convert back to fraction.

1.5 = 1 1/2

Answer:

(- 3, 1 )

Step-by-step explanation:

Given the 2 equations

2x - 2y = - 8 → (1)

x + 2y = - 1 → (2)

Adding the 2 equations will eliminate the y- term, that is

3x = - 9 ( divide both sides by 3 )

x = - 3

Substitute x = - 3 into either of the 2 equations and evaluate for y

Substituting into (2)

- 3 + 2y = - 1 ( add 3 to both sides )

2y = 2 ( divide both sides by 2 )

y = 1

Solution is (- 3, 1 )

Answer:

-3,1

Step-by-step explanation:

The total surface area is π[(4/3)x]² + π(4/3)x². The area of the base is greater than the lateral area.

An equation is an expression that shows how numbers and variables are related using mathematical operations. Equations can be linear, quadratic, cubic and so on.

Given the cone. The surface area (SA) is given by the equation:

SA = πr² + πrs

where r is the radius of the cone and s is the slant height.

Given that the slant height is x and the radius of the cone is 4/3 the slant height = (4/3)x

Hence:

SA = πr² + πrs

The base area =  πr²; Lateral area = πrs

substituting:

The base area = π[(4/3)x]², the lateral area =  π(4/3)x²

Hence:

SA = π[(4/3)x]² + π(4/3)x²

The area of the base is greater than the lateral area.

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Answer: 68.98 mph

Step-by-step explanation:

the rate at which something moves, or the speed multiplied by the amount of time at which it moved equals the distance it went. in this case,

(average speed) * 51 = 3518.
average speed          = 3518 / 51
average speed          = 68.98

The number of combination 6-letter words using five vowels in alphabetical order,

5*4*3*2*1*21=2520

Permutation and combination are methods for representing a collection of objects by selecting them from a set and forming subsets. It specifies the various ways to arrange a specific set of data. Permutations are when we select data or objects from a specific group, whereas combinations are the order in which they are represented.

The combination is a way of selecting items from a collection, such that (unlike permutations) the order of selection does not matter. In smaller cases, it is possible to count the number of combinations. Combination refers to the combination of n things taken k at a time without repetition. To refer to combinations in which repetition is allowed, the terms k-selection or k-combination with repetition are often used.

We have five vowels: a, i, e,0, and u.

make the 6-letter word using five vowels in alphabetical order,

5*4*3*2*1*21=2520

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The answer choice which is correct and represents a true statement about the function given; f(x) is; Choice A; The domain is; -9 < x -2, -2 < x < 1, 1 < x < 7.

It follows from the task content that the answer choice which correctly represents a true statement about the function given f(x) be determined.

Since the domain of a function (continuous or discontinuous) is the set of all possible x values for which such function is defined; it follows that the domain of the piece-wise function given in the task content is; as described in answer choice A.

Consequently, answer choice A is correct.

The range of the piecewise function does not include all values in the interval defined by; (-26, 1).

Also, the function is not decreasing in the interval; (-2, 1) as the function itself is constant in this interval.

The rate of change over the interval (-9, 1] is not certain to be 3 because, the rate of change is only constant (=3) for the interval; (-9, -2].

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Answer:

graphs that pass the vertical line test and is a function

bottom one on the left has only one y output and doesn't pass through xy twice

Step-by-step explanation:

Answer: x = 1/2

Step-by-step explanation: Set it equal to zero by subtracting 4x from both sides:

4x² - 4x + 1 = 0

Now, factor it:

(2x - 1)(2x - 1)

Set each one equal to zero, but since they’re the same, you only need to do it once:

2x - 1 = 0

Add 1 to both sides:

2x = 1

Divide both sides by 2:

x = 1/2

Hope this helps!

Answer:

x=1/2

Step-by-step explanation:

4x^2+1=4x

or,4x^2-4x+1=0

or,(2x)^2 - 2*2*x+(1)^2 =0

or,(2x-1)^2 =0

or,2x-1 =0

or,2x=1

Therefore, x=1/2

Answer:

The percent change is 30%. It is an increase.

Step-by-step explanation:

Based on the formula of the quadratic function y=-x^2+6x-5, we know that its graph is a downward-facing parabola that opens wide, with a vertex at (3,-14), and an axis of symmetry at x=3.

Based on the formula of the quadratic function y=-x^2+6x-5, we can determine several properties of its graph, including its shape, vertex, and axis of symmetry.

First, the negative coefficient of the x-squared term (-1) tells us that the graph will be a downward-facing parabola. The leading coefficient also tells us whether the parabola is narrow or wide. Since the coefficient is -1, the parabola will be wide.

Next, we can find the vertex using the formula:

Vertex = (-b/2a, f(-b/2a))

where a is the coefficient of the x-squared term, b is the coefficient of the x term, and f(x) is the quadratic function. Plugging in the values for our function, we get:

Vertex = (-b/2a, f(-b/2a))

= (-6/(2*-1), f(6/(2*-1)))

= (3, -14)

So the vertex of the parabola is at the point (3,-14).

Finally, we know that the axis of symmetry is a vertical line passing through the vertex. In this case, it is the line x=3.

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To determine when the particle is at rest, we need to find the values of t for which the velocity of the particle, given by the derivative of the position function x(t), is equal to zero.

Taking the derivative of x(t) = t^3 - 12t + 36t, we get x'(t) = 3t^2 - 12 + 36.

Setting x'(t) equal to zero and solving for t, we have:

3t^2 - 12t + 36 = 0.

Factoring out 3, we get:

3(t^2 - 4t + 12) = 0.

Simplifying further, we have:

t^2 - 4t + 12 = 0.

Now we can solve this quadratic equation using the quadratic formula:

t = (-b ± sqrt(b^2 - 4ac)) / 2a.

Plugging in the values of a = 1, b = -4, and c = 12, we have:

t = (-(-4) ± sqrt((-4)^2 - 4(1)(12))) / (2(1)).

Simplifying, we get:

t = (4 ± sqrt(16 - 48)) / 2.

t = (4 ± sqrt(-32)) / 2.

Since the discriminant (-32) is negative, there are no real solutions for t. Therefore, the particle is never at rest. The answer is (A) No values.

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The temperature at the point where the clouds begin to form is 77.65 °F

Given: The starting point is 1234 feet and air temperature is 79.4°F

You climb to where you notice clouds beginning to form.It can be observed that the temperature decreases by 3.5°F per 1000 feet as we go up.

Using this information, we can calculate the temperature at the point where the clouds start forming.

Let the height of the point where clouds begin to form be x feet above the starting point. As per the question, the temperature decreases by 3.5°F per 1000 feet as we go up.

Therefore, the temperature at the height of x feet can be calculated as:

T(x) = T(1234) - 3.5/1000 * (x - 1234)°F , where

T(1234) = 79.4°F

Substituting the value of x = 1234 + 500, (as we need to know the temperature at the point where clouds begin to form) we get:

T(1734) = T(1234) - 3.5/1000 * (1734 - 1234) °F

= 79.4 - 3.5/1000 * 500 °F

= 79.4 - 1.75 °F

= 77.65 °F

Therefore, the temperature at the point where the clouds begin to form is 77.65 °F

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The measure of the central angle of the circle BC = 176°

The central angle is an angle with two arms and a vertex in the middle of a circle. The two arms of the circle's two radii intersect the circle's arc at two separate locations. It is an angle whose vertex is the center of a circle with the two radii lines as its arms, that intersect at two different points on the circle.

The central angle of a circle formula is as follows.

Central Angle = ( s x 360° ) / 2πr

where s is the length of the arc

r is the radius of the circle

Central Angle = 2 x Angle in other segment

Given data ,

Let the three points be represented as A, B and C

Now , the measure of angle ∠BAC = 88°

And , the measure of the central angle is given by

Central Angle = 2 x Angle in other segment

On simplifying the equation , we get

The measure of central angle BC = 2 x 88°

The measure of central angle BC = 176°

Hence , the measure of central angle is 176°

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Step-by-step explanation:

2 equations with 2 variables.

either we use 1 equation to express 1 variable by the other and bring this into the second equation to solve for the second variable.

or we do equation arithmetic (subtract one equation from the other so that one variable disorders in the result, and solve for the remaining variable).

since the factors and constants don't seem to be multiples or share nice factors with each other, I suggest the second way.

7x - 4y = 37

6x + 3y = 51

multiply the first equating by 3, and the second one by 4, and then add both equations :

21x - 12y = 111

24x + 12y = 204

------------------------------

45x + 0 = 315

x = 7

then we use one of the original equations to get y :

7×7 - 4y = 37

49 - 4y = 37

12 = 4y

y = 3

Answer:

k = -3/4

Step-by-step explanation:

The lines will be parallel if their slopes are equal.  To find the slope of each line, write its equation in slope-intercept form (y = mx + b).  In other words, solve each equation for y and look at the coefficient of x.

2x + 3y = 4k

3y = -2x + 4k

y = (-2/3)x + 4k/3

The slope of the first line is -2/3.

x - 2ky = 7

-2ky = -x + 7

y = [1/(2k)]x - 7/(2k)

The slope of the second line is 1/(2k).

If the slopes are equal, then

1/(2k) = -2/3

Multiply by 2k.

1 = (-2/3)(2k) = (-4/3)k

1 = (-4/3)k

k = -3/4

The standard form of the equation of a line perpendicular to the line (3x + 6y = 5) and passing through the point (1, 3) is (2x - y = -1)

To determine the equation of a line perpendicular to the line (3x + 6y = 5) and passing through the point (1, 3), we can follow these steps:

1. Obtain the slope of the provided line.

To do this, we rearrange the equation (3x + 6y = 5) into slope-intercept form (y = mx + b):

6y = -3x + 5

y =\(-\frac{1}{2}x + \frac{5}{6}\)

The slope of the line is the coefficient of x, which is \(\(-\frac{1}{2}\)\).

2. Determine the slope of the line perpendicular to the provided line.

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the provided line.

So, the slope of the perpendicular line is \(\(\frac{2}{1}\)\) or simply 2.

3. Use the slope and the provided point to obtain the equation of the perpendicular line.

We can use the point-slope form of a line to determine the equation:

y - y1 = m(x - x1)

where x1, y1 is the provided point and m is the slope.

Substituting the provided point (1, 3) and the slope 2 into the equation, we have:

y - 3 = 2(x - 1)

4. Convert the equation to standard form.

To convert the equation to standard form, we expand the expression:

y - 3 = 2x - 2

2x - y = -1

Rearranging the equation in the form (Ax + By = C), where A, B, and C are constants, we obtain the standard form:

2x - y = -1

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Answer:

4.81 divided by 0.74=6.5       61.32 divided by 1.4= 43.8

Step-by-step explanation:

Answer:

The final amount  if 784 is decreased by 1% followed by a 4% increase is 807.52.

Step-by-step explanation:

General Formula

A way to solve this problem is as follows:

The general formula for this is taking into account that:

\( \\ percent\;change = \frac{change}{starting\;point}\)

The starting point is number 784.

The most important key is the solution for this answer is that:

\( \\ change = starting\;point - x\)

Where x is a number that we need to find. Then

\( \\ percent\;change = \frac{starting\;point - x}{starting\;point}\) [1]

Is 784 increased or decreased after all?

We also need to evaluate the following: if a quantity decreases a percentage, and then increases in another percentage, what is the final percentage? In this case, we have first that 784 decreases by 1% and then increases by 4%. As a result 784 will +4% - 1% = +3%, that is, 784 will increase in 3%.

Finding the result

If 784 increases by 3%, we have:

\( \\ 3\% = \frac{784 - x}{784}\)

Which is equal to

\( \\ 0.03 = \frac{784 - x}{784}\)

Solving for x, we first multiply by 784 to both sides of the previous formula:

\( \\ 0.03 * 784 = \frac{784 - x}{784}*784\)

\( \\ 0.03 * 784 = (784 - x)*\frac{784}{784}\)

\( \\ 0.03 * 784 = (784 - x)*1\)

\( \\ 0.03 * 784 = (784 - x)\)

Remember that if we add, subtract, multiply, divide... to both sides of the equation, we do not "alter" this equation.

Subtracting 784 to both sides:

\( \\ (0.03 * 784) - 784 = (784 - 784 - x)\)

\( \\ (0.03 * 784) - 784 = (0 - x)\)

\( \\ (0.03 * 784) - 784 = - x\)

\( \\ 23.52 - 784 = - x\)

\( \\ -760.48 = - x\)

Multiplying by -1 to both sides:

\( \\ -1 * (-760.48) = -1 * (-x)\)

We have to remember that:

\( \\ +*+ = +; - * - = +; - * + = -; + * - = -\)

\( \\ 760.48 = x\)

Then

\( \\ x = 760.48\)

Therefore, using formula [1], an increase of 3% is

\( \\ 3\% = \frac{784 - 760.48}{784}\)

\( \\ change = 784 - 760.48\)

\( \\ change = 23.52\)

Since an increase of 3% is 23.52, we have to add this to the starting point 784, and finally the amount is 784 + 23.52 = 807.52.

As a result, the final amount if 784 is decreased by 1% followed by a 4% increase is 807.52.  

In a more terse way of solving this problem, we can say that:

Increase of 4% = 784 * 0.04 = 31.36.

Decrease of 1% = 784 * 0.01 = 7.84.

Difference = 31.36 - 7.84 = 23.52.

Then, we need to add this value to 784, and 784 + 23.52 = 807.52 (the same result).

A directional hypothesis is a hypothesis that reflects the difference between groups and specifies the direction of the difference.

In contrast to a null hypothesis, which suggests there is no significant relationship between the variables being studied, a directional hypothesis makes a specific prediction about the direction of the relationship. A nondirectional hypothesis, on the other hand, predicts a relationship between the variables but does not specify the direction of that relationship.

Directional hypotheses are useful in research when there is a theoretical or empirical basis to expect a particular outcome. They can help researchers to better focus their investigation and narrow down possible outcomes, thus allowing for more robust statistical analyses. However, directional hypotheses also carry the risk of confirmation bias, as researchers might be more likely to interpret data in a way that supports their hypothesis.

In summary, a directional hypothesis predicts the difference between groups and specifies the direction of that difference, providing a more focused approach to analyzing research data compared to a null hypothesis or a nondirectional hypothesis.

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Answer:

q²-13q-30

Step-by-step explanation:

..............

Answer:

Let's assume that the distance between Chicago and Hoopertown is represented by 'x' miles.

According to the given information:

Raymond lives 23 miles from Chicago, so the distance between Amanda and Chicago is 23 - 15 = 8 miles.

Since Amanda lives halfway between Charlie and Chicago, the distance between Charlie and Chicago is also 8 miles.

Therefore, the distance between Charlie and Hoopertown is x - 8 miles.

Since Charlie lives halfway between Chicago and Hoopertown, the distance between Raymond and Charlie is (x - 8) / 2 miles.

Given that Raymond lives 15 miles from Amanda, we can set up the following equation:

(x - 8) / 2 = 15

To solve for x, we can multiply both sides of the equation by 2:

x - 8 = 30

Next, we can isolate x by adding 8 to both sides of the equation:

x = 38

Answer:

Step-by-step explanation:

its 2.82, a little further forward, 82% of the way to number 3

Check the picture below.

The value of pi is known to over 31 trillion decimal places, thanks to the use of powerful computers and sophisticated algorithms.

The history of pi dates back thousands of years, and over time, various civilizations have attempted to calculate its value with varying degrees of accuracy. One of the most inaccurate versions of pi was recorded by the ancient Babylonians around 2000 BC.

The Babylonians calculated the value of pi as 3.125, which is off by more than 6% from the actual value. It is believed that the Babylonians arrived at this value by using a rough approximation of a circle as a hexagon. They measured the perimeter of the hexagon and divided it by the diameter to get their approximation of pi.

This value was later refined by the ancient Egyptians and Greeks, who were able to calculate pi with greater accuracy. The Greek mathematician Archimedes, for instance, was able to calculate pi to within 1% accuracy by using a method of exhaustion.

It wasn't until the development of calculus in the 17th century that mathematicians were able to derive an exact formula for pi. Today, the value of pi is known to over 31 trillion decimal places, thanks to the use of powerful computers and sophisticated algorithms.

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Answer:

no it the other way around

Step-by-step explanation:

The correct answer would be the last option, D. If you graph it, then reflect it, it will be correct. When it is asking you to reflect over the x axis, you make the y coordinates negative and vise versa!

Hope this helps!

Answer:

y = 2x - 41

Step-by-step explanation:

\((x1 \: \: y1) = (13 \: \: \: 1) \\ (x2 \: \: y2) = (17 \: \: - 7) \\ now \\ slope = change \: in \: y \: over \: change \: in \: x \\ slope \: = y2 - y1 \div x2 - x1 \\ slope = - 7 - 1 \div 17 - 13 \\ - 8 \div 4 \\ slope = - 2\)

equation of the line

y=mx +c

\( slope = y - yo \ \: over \: x - xo \\ slope = - 7 - y \: over \: 17 - x \\ 2 = - 7 - y \: over \: 17 - x\)

\(1( - 7 - y) = 2(17 - x) \\ - 7 - y = 34 - 2x \\ - y = 34 + 7 - 2x \\ - y = 41 - 2x \\ - y = 41 - 2x\)

-y=41-2x/-y

y=2x+41

Answer:

12.75feet (12¾)

Step-by-step explanation:

7t+1+5t+8=162feet

12t+9=162feet

12t=162-9

=153

t = 153÷9

=12.75feet (12¾feet)

Answer:

3rd quadrant.

Step-by-step explanation:

We know that

4x + 7 < -3

5 - 3*y ≥ 11

We should isolate both of the variables in these inequalities:

for the first one we get:

4x + 7 < - 3

4x < -3 - 7

4x < -10

x < -10/4

So x is smaller than a negative number, then we know that x is negative, from this we already know that the point will be on quadrants 2 or 3.

For the other inequality we get:

5 - 3*y ≥ 11

5 - 11 ≥ 3y

-6 ≥ 3y

-6/3 ≥ y

-2 ≥  y

So we can see that y is equal to or smaller than a negative number, then y is a negative number.

So both values, x and y, are negatives.

This means that the point P(x, y) is in the 3rd quadrant.

Answer:

+ 2

Step-by-step explanation:

+ 3 + (- 1) = + 2