A town doubles its size every 64 years. If the population is currently 1700, what will the population be in 128 years.

Answer:

D. all real numbers where x ≤ –1 or x ≥ 1.

Step-by-step explanation:

The graph of the function  f(x) = (1/x)cos √(x² - 1) is continuous for all real numbers, where - 1 ≤ x ≤ 1. The correct is option C.

A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.

Given:

f(x) = (1/x)cos √(x² - 1)

To prove continuous function:

At that value, the limit must exist.

At that value, the function must be defined, and.

And at that point, both the limit and the function must have equal values.

In mathematics, a continuous function is one where a continuous variation of the argument results in a continuous variation of the function's value (i.e., a change without a leap).

As you can see in the attached image.

Function is not defined in between (-1, 1)

And function have a leap in between (-1, 1).

Therefore, the function is continuous for all real numbers, where - 1 ≤ x ≤ 1.

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Complete question is:

Seventy million pounds of trout are grown in the U.S. every year. Farm-raised trout contain an average of 32 grams of fat per pound, with a standard deviation of 7 grams of fat per pound. A random sample of 34 farm-raised trout is selected. The mean fat content for the sample is 29.7 grams per pound. Find the probability of observing a sample mean of 29.7 grams of fat per pound or less in a random sample of 34 farm-raised trout. Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

Answer:

Probability = 0.0277

Step-by-step explanation:

We are given;

Mean: μ = 32

Standard deviation;σ = 7

Random sample number; n = 34

To solve this question, we would use the equation z = (x - μ)/(σ/√n) to find the z value that corresponds to 29.7 grams of fat.

Thus;

z = (29.7 - 32)/(7/√34)

Thus, z = -2.3/1.200490096

z = -1.9159

From the standard z table and confirming with z-calculator, the probability is 0.0277

Thus, the probability to select 34 fish whose average grams of fat per pound is less than 29.7 = 0.0277

Answer:

Step-by-step explanation:

\(\frac{-3+7i}{-6-7i} \times \frac{-6+7i}{-6+7i} =\frac{18-21i-42i-49i^2}{(-6)^2-(7i)^2} \\=\frac{18-63i -49(-1)}{36-49i^2} \\=\frac{18+49-63 i}{36-49(-1)} \\=\frac{67-63i}{36+49} \\=\frac{67-63i}{85} \\=\frac{67}{85} +(\frac{-63}{85} )i\\\)

\(a=\frac{67}{85} \\b=\frac{-63}{85}\)

The correct representations of the inequality are  -6x + 15 < 10 - 5x and x <-5. Options C and D

Inequalities are described as mathematical relations that makes a non-equal comparison between two elements, variables, numbers or mathematical expressions.

They are often used to compare two numbers on the number line based their sizes.

From the information given, we have the inequality;

–3(2x – 5) < 5(2 – x)

expand the bracket

-6x + 15 < 10 - 5x

collect like terms

-6x + 5x < 10 - 15

add or subtract the like terms

-x < -5

Make 'x' the subject of formula

x < 5

Hence, the value is -6x + 15 < 10 - 5x

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The complete question:

Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.

Answer:

B.)The new pyramid has a volume that is One-half the volume of the original pyramid.

Step-by-step explanation:

got it right on test.

Answer:

B

Step-by-step explanation:

I got it correct

Step-by-step explanation:

Solve the inequality for b

-15b <= 45 divide both sides by -15, since you're dividing by a negative number switch the direction of the sign.

b >= -3

So, your number line is all values of b greater than or equal to -3. Since it is including -3, the circle will be filled and increase to the positive.

a. The  slope of the curve at the point (4,16)   is approximately 1.165, and at the point (16,4)  is approximately -0.496.

b. The   curve has a horizontal tangent line at the points(0,0) and (3,27).

c. The   curve has a vertical tangent lineat the points (0,0) and (65/2, (65/2)³).

a. To find the   slope of the curve given by the equation x³ + y³ - 65xy = 0 at the points (4,16) and (16,4),we can differentiate the equation implicitly with respect to x and solve for dy/dx.

Differentiating the equation with respect to x, we have  -

3x² + 3y²(dy/dx) - 65y - 65x(dy/dx) = 0

To find the slope at a specific point, substitute the x and y coordinates into the equation and solve for dy/dx.

For the point (4,16)  -

3(4)² + 3(16)²(dy/dx) - 65(16) - 65(4)(dy/dx) = 0

48 + 768(dy/dx) - 1040 - 260(dy/dx) = 0

508(dy/dx) = 592

(dy/dx) = 592/508

(dy/dx) ≈ 1.165

For the point (16,4)  -

3(16)² + 3(4)²(dy/dx) - 65(4) - 65(16)(dy/dx) = 0

768 + 48(dy/dx) - 260 - 1040(dy/dx) = 0

(-992)(dy/dx) = 492

(dy/dx) = 492/(-992)

(dy/dx) ≈ -0.496

Thus, the slope of the   curve at the point (4,16) isapproximately 1.165, and at the point (16,4) is approximately -0.496.

b. To find the point where the curve has   a horizontal tangent line, we need to find the x-coordinate(s)where dy/dx equals zero.

This means   the slope is zero and the tangent line is horizontal.

From the derivative we obtained earlier  -

3x² + 3y²(dy/dx) - 65y - 65x(dy/dx) = 0

Setting dy/dx equal to zero  -

3x² - 65y = 0

Substituting y = x³/65 into the equation  -

3x² - 65(x³/65) = 0

3x² - x³ = 0

Factoring out an x²  -

x²(3 - x) = 0

This equation has two solutions  -  x = 0 and x = 3.

hence, the curve has a horizontal   tangent line at the points(0,0) and (3,27).

c. To find the point where the curve has a vertical tangent line, we need to find the x-coordinate(s)   where the derivative is undefinedor approaches infinity.

From the derivative  -

3x² + 3y²(dy/dx) - 65y - 65x(dy/dx) = 0

To find the vertical tangent line, dy/dx should be undefined or infinite. This occurs when the denominator of dy/dx is zero.

Setting the denominator equal to zero:  -

65x = 65y

x = y

Substituting this condition back into the original equation  -

x³ + x³ - 65x² = 0

2x³ - 65x² = 0

x²(2x - 65) = 0

This equation has two solutions  - x = 0 and x = 65/2.

Therefore, the curve has a vertical tangent line   at the points (0,0)

and(65/2, (65/2)³).

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\(\boxed{ \mathrm{ \% \: error = \dfrac{error}{assumed \: value} \times 100}}\)

_____________________________

\(\mathrm{ \#TeeNForeveR}\)

Answer:

Well 30 minutes as seconds is 1800 already so it would be 10,800 seconds

Step-by-step explanation:

i hope this helps you

Answer:

Here is the desmos graph

Step-by-step explanation:

Based οn the true statements (i) and (ii), we can cοnclude that △ ABC is nοt cοngruent tο △ DEF.

Statement (i) tells us that if twο triangles are cοngruent, then they are similar. This means that cοngruence implies similarity. Hοwever, statement (ii) tells us that △ ABC is nοt similar tο △ DEF. This means that there is nο similarity between the twο triangles.

Therefοre, we cannοt cοnclude that the twο triangles are cοngruent, because cοngruence implies similarity and we have been given that there is nο similarity between them. In οther wοrds, the fact that △ ABC is nοt similar tο △ DEF means that we cannοt cοnclude anything abοut their cοngruence, because we dο nοt have enοugh infοrmatiοn tο determine whether they are cοngruent οr nοt.

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The volume of the composite figure is 6,330.24 in^3

We know that the volume of half a sphere of radius R is:

V = (2/3)*pi*R^3

Here we know that pi = 3.14 and R = 12 inches, then the volume is:

V = (2/3)*3.14*(12 in)^3 = 3,617.28 in^3

And the volume of a cone of height H and radius R is:

v = (1/3)*pi*R^2*H

So here the volume is:

v = (1/3)*3.14*(12in)^2*18in = 2,712.96 in^3

Then the total volume is:

3,617.28 in^3 +  2,712.96 in^3 = 6,330.24 in^3

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The probability of getting 14 successes out of 19 trials with a probability of success of 0.8 is approximately 0.0572.

Using the binomial probability formula, we have:

P(X=14) = (n choose x) * pˣ . (1-p)⁽ⁿ⁻ˣ⁾

Plugging in the values, we get:

P(X=14) = (19 choose 14) x 0.8¹⁴ x 0.2⁵

P(X=14) ≈ 0.0572

Therefore, the probability of getting 14 successes out of 19 trials with a probability of success of 0.8 is approximately 0.0572.

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Answer:

x = 9    if there is any confusion, please ask questions

Step-by-step explanation:

so in math, a complementary angle is when two angles add up to 90 degrees.

to find this, you have to do 90-81

90 - 81 = 9

3.1.1 The basic property of operations used is the commutative property of multiplication.

3.1.2 The basic property of operations used is the additive inverse property.

3.1.3 The basic property of operations used is the associative property of addition.

3.1.1 The basic property of operations used in this calculation is the commutative property of multiplication. It states that the order of the factors in a multiplication problem can be rearranged without changing the product. In this case, the numbers 25 and 4 were swapped, resulting in the same product of 100.

3.1.2 The basic property of operations used in this calculation is the additive inverse property. It states that for any number, there exists an additive inverse such that when the number and its additive inverse are added together, the result is zero. In this case, adding 412 and its additive inverse (-412) results in zero.

3.1.3 The basic property of operations used in this calculation is the associative property of addition. It states that the grouping of numbers being added does not affect the sum. In this case, the numbers 25, 37, 20, 5, 30, and 7 were regrouped to facilitate easier mental addition. By grouping 25 and 37, and then grouping 20, 5, 30, and 7, the final sum of 62 is obtained, which is the same as adding all the numbers together in the original order.

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Answer: b. Yes

Step-by-step explanation: Confidence Interval for a population proportion is calculated as:

p ± \(z\sqrt{\frac{p(1-p)}{n} }\)

where

p is the sample proportion

n is sample size

z is z-score, in this case, as it is 95%, z-score=1.96

Calculating confidence interval:

\(p=\frac{152}{468}\)

p = 0.3248

0.3248 ± \(1.96\sqrt{\frac{0.3248(0.6752)}{468} }\)

0.3248 ± \(1.96\sqrt{0.000468}\)

0.3248 ± 0.0425

Interval: 0.2823 < μ < 0.3673

The interval means we are 95% sure the true mean is between 0.2823 and 0.3673. As the campaign claims a proportion of no more than 0.32 of the voters wants to see Mayor Waffleskate defeated and the number is in the confidence interval, the claim is supported.

Answer:

i depends of degre of triangle it can be three 14-11

it can also be 16

The domain and range of the graph above in interval notation include the following:

Domain = [-6, 3]

Range = [-3, 3]

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-6, 3] or -6 ≤ x < 3.

Range = [-3, 3] or -3 < y < 3

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Answer:

gradient: 1.5

Explanation:

Take two points from the graph: (2, 0), (0, -3)

\(\sf gradient : \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points\)

So here given:

Inserting values

\(\rightarrow \sf gradient : \dfrac{-3-0}{0-2} = \dfrac{-3}{-2} = 1.5\)

Answer:

170.87 or 10.875 is u round it then its 170.88

Answer:

2.75

Step-by-step explanation:

The amplitude is half of the difference between the highest and lowest y-coordinates.

amplitude = 0.5|6.75 - 1.25| = 0.5(5.5) = 2.75

Answer:

Hello

Midpoint of (-8,6) and (5,-7)

P(a,b)=(x1+x2/2),(y1+y2/2)

        =(-8+5/2),(6+-7/2)

        =(-3/2),(-1/2)

Midpoint of (-8,6) and (5,-7) is (-3/2),(-1/2)

Hope it helps you.....

Answer:

Before a variable there is no coefficient.

There is an invisible 1 infront bc there is no real number. so the 1 appears.

Answer:

(a) The function has a minimum value

(b) The minimum value is 2

Step-by-step explanation:

(a)Currently y = x^2 + 4x + 6 is in standard form, whose general equation is

y = ax^2 + bx + c.  

We know that for our function a = 1.

Thus, y = x^2 + 4x + 6 must have a minimum value.

(b) Whenever a problem asks for the minimum value, it's asking for the y-coordinate of the minimum.

Step 1:  First we can find the x-coordinate of the minimum using the equation -b/2a from the quadratic formula.  

Plugging in 4 for b and 1 for a, we get:

x-coordinate of minimum = -4 / 2(1)

x-coordinate of minimum = -4 / 2

x-coordinate of minimum = -2

Step 2:  Now we can plug in -2 for x in the quadratic function.  The result will be our minimum value:

f(-2) = (-2)^2 + 4(-2) + 6

f(-2) = 4 - 8 + 6

f(-2) = -4 + 6

f(-2) = 2

Thus, the minimum value of the quadratic function is 2.

The number 91.470 is the rational number.

For the given number.

91.470 can be written in the fraction as;

91470/1000

Or 914/100

As, the form is p/q where q ≠ 0.

Thus, the number 91.470 is the rational number.

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Answer:

210

Step-by-step explanation:

you have to multiple 15 by 14

Answer:

DO NOT MULTIPLY 15x14! THAT IS WRONG

Step-by-step explanation:

To find the area of a triangle the formula is 1/2 x b x h
If 15 and 14 is the base and height just do half of 15 x 14
so 15 x 14= 210/ divided by 2= 105  


Formula for area of a circle= 1/2*b*h

The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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Answer:

The formula for finding the area of a circle using its radius is:

The formula for finding the area of a circle using its radius is:A = πr²

The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.

The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:

The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²

The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²where A is the area of the circle and d is its diameter.

The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²where A is the area of the circle and d is its diameter.Note that π (pi) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter and is approximately equal to 3.14

Step-by-step explanation:

Hope it Helps

The formula for finding the area of a circle using its radius is π * r².

The formula for finding the area of a circle using its diameter is (π/4) * d².

The formula for finding the area of a circle using its radius is:

A = π * r²

where:

A represents the area of the circle,

π (pi) is a mathematical constant approximately equal to 3.14159, and

r represents the radius of the circle.

If you have the diameter of the circle instead of the radius, you can use the following formula:

A = (π/4) * d²

where:

A represents the area of the circle,

π (pi) is a mathematical constant approximately equal to 3.14159, and

d is the diameter of the circle.

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