In 2015, there were roughly 1 x 10° high school football players and 2x 10° professional football players in the United States. About how many times more high school football players were there?​

Answer:

Step-by-step explanation:

To predict the number of bacteria after 10 hours using the formula P = Aekt, where P is the final population, A is the initial population, k is the growth rate, and t is the time elapsed, we need to first find the value of k.

dw

We know that after 4 hours, the population grew from 3,000 bacteria to 3,600 bacteria. So we can set up an equation:

3,600 = 3,000e^(4k)

Dividing both sides by 3,000 gives:

1.2 = e^(4k)

Taking the natural logarithm of both sides gives:

ln(1.2) = 4k

Solving for k, we get:

k = ln(1.2)/4

k ≈ 0.051

Now that we have the value of k, we can use the formula to predict the number of bacteria after 10 hours:

P = 3,000e^(0.051*10)

P ≈ 5,426

Therefore, we predict that after 10 hours, there will be approximately 5,426 bacteria present in the culture.

"The line has a positive slope and passes through the x-axis at -2. Additionally, it crosses through point (2, 1).

The formula in this case is 2x-y = -4. When we set the value of y to 0, we can use this equation to calculate the x-intercept: 2x0=42x=4. When we multiply both sides by 2, we obtain 2x2=42x=2. The x-intercept is therefore -2.

We may use the slope-intercept version of the equation, y = mx + b, where m is the slope and b is the y-intercept, to graph the line y = 4x - 2.

We can observe that the slope is m = 4 and the y-intercept is b = -2 by comparing y = 4x - 2 to y = mx + b.

Starting with the y-intercept of -2 on the y-axis, we can graph line by finding other points on it using the slope of 4.

To get to the point, if we move two units to the right, we must move up eight units. (2, 6). To get to the point, if we move two units to the left, we must move down eight units. (-2, -10).

According to the description and choices given, "The line has a positive slope and passes through the x-axis at -2" is the option that most closely matches our graph. Additionally, it crosses through point (2, 1).

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Answer:

Step-by-step explanation:

m = [tex]\frac{y2-y1}{x2-x1}[/tex]

m = [tex]\frac{-1-0}{0+3}[/tex]

m = [tex]\frac{-1}{3}[/tex]

Answer: -[tex]\frac{1}{3}[/tex]

The correct choice is: B. The statement is false because the reference values for the decrease and increase are not the same. The true improvement over the past two years is 8.56%.

In Mathematics, a percentage can be defined as any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.

Mathematically, percentage increase can be calculated by using this mathematical equation (formula):

Percentage increase = [Final value - Initial value]/Initial value × 100

Based on the information provided about the high school test scores, we have the following:

True improvement = (100% - 8%) × (100 + 18)

True improvement = (92%) × (100 + 18)

True improvement = (0.92) × (118)

True improvement = 108.56 ⇒ 8.56%.

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Answer:

well 10^4 is 10000, and 4x10^2 is 1600 and if we divide 10000 by 1600 we can find out how many times greater 10000 is than 1600, and the anwser is 6.25

Step-by-step explanation:

x = 3.6 units

First, some definitions before working the problem:

The three standard trigonometric functions, cosine, tangent, and sine, are defined as follows for right triangles:

[tex]sin(\theta)=\dfrac{opposite}{hypotenuse}[/tex]

[tex]cos(\theta)=\dfrac{adjacent}{hypotenuse}[/tex]

[tex]tan(\theta)=\dfrac{opposite}{adjacent}[/tex]

One memorization tactic is "Soh Cah Toa" where the first capital letter represents one of those three trigonometric functions, and the "o" "a" and "h" represent the "opposite" "adjacent" and "hypotenuse" respectively.

The triangle must be a right triangle, or there wouldn't be a "hypotenuse", because the hypotenuse is always across from the right angle.

Working the problem

For the given triangle, the right angle is in the top right, so the side on the bottom left is the hypotenuse.

We know the angle in the lower right corner (angle S), so the side touching it (side ST) with unknown length is the adjacent side.  (notice that the points that form the side include the vertex of the angle -- so, it's the adjacent side).

For this triangle, the "adjacent" leg is unknown, our "goal to find" side.  Additionally, the "hypotenuse" is known.

Therefore, the two sides of the triangle that are known or are a "goal to find" are the "adjacent" & "hypotenuse".

Out of "Soh Cah Toa," the part that uses "a" & "h" is "Cah".  So, the desired function to use for this triangle is the Cosine function.

[tex]cos(\theta)=\dfrac{adjacent}{hypotenuse}[/tex]

[tex]cos(69^o)=\dfrac{x}{10}[/tex]

To isolate "x", multiply both sides by 10...

[tex]10*cos(69^o)=x[/tex]

Make sure your calculator is set to degree mode, and calculate:

[tex]10*(0.3583679495453...)=x[/tex]

[tex]x=3.583679495453...[/tex] units

Rounded to the nearest tenth...

x = 3.6 units

Answer:

Step-by-step explanation:

To write the standard equation of a circle with its center in the fourth quadrant tangent to x=7, y=-4 and x=17, we can first find the center of the circle.

Since the center is in the fourth quadrant and tangent to x=7, y=-4 and x=17, the center must lie on the line x=12 (the midpoint between 7 and 17) and y=-4 (the point of tangency).

So the center of the circle is (12, -4).

Next, we need to find the radius of the circle. Since the circle is tangent to x=7 and x=17, the radius is the distance from the center to either x=7 or x=17.

The radius is thus 12 (the difference between 12 and 7) or 5 (the difference between 12 and 17).

So the standard equation of the circle is:

(x - 12)^2 + (y + 4)^2 = 25

If x + 5 is a factor of the given polynomial, then (x + 5) must divide the polynomial evenly, meaning that the remainder is 0 when the polynomial is divided by x + 5.

We can use polynomial long division or synthetic division to find the quotient and remainder, but it's easier to use the fact that if x + 5 is a factor, then (-5) must be a root of the polynomial.

So, we can substitute x = -5 into the polynomial and set it equal to 0 to find m:

-3(-5)^4 - 10(-5)^3 + 20(-5)^2 - 22(-5) + m = 0

Simplifying and solving for m:

-3(625) + 10(125) + 20(25) + 110 + m = 0

-1875 + 1250 + 500 + 110 + m = 0

m = 1015

Therefore, m = 1015 so that x + 5 is a factor of - 3x^4 - 10x^3 + 20x^2 - 22x + m.

Answer:

x = 4√3

y = 8√3

Step-by-step explanation:

The interior angles of the given right triangle are 30°, 60° and 90°.

Therefore, the triangle is a special 30-60-90 triangle.

In a 30-60-90 triangle, the measures of its sides are in the ratio 1 : √3 : 2.  

Therefore, the formula for the ratio of the sides is b : b√3 : 2b where:

From inspection of the given triangle, the side opposite the 60° angle is 12 units in length. Therefore:

[tex]b\sqrt{3} = 12[/tex]

Solve the equation for b:

[tex]\begin{aligned}b&=\dfrac{12}{\sqrt{3}}\\\\b&=\dfrac{12 \cdot \sqrt{3}}{\sqrt{3} \cdot \sqrt{3}}\\\\b&=\dfrac{12\sqrt{3}}{3}\\\\b&=4\sqrt{3}\end{aligned}[/tex]

"x" is the side opposite the 30° angle. Therefore:

[tex]\begin{aligned}x& = b\\x& = 4\sqrt{3}\end{aligned}[/tex]

"y" is the side opposite the right angle. Therefore:

[tex]\begin{aligned}y&=2b\\y&=2 \cdot 4\sqrt{3}\\y&=8 \sqrt{3}\end{aligned}[/tex]

Therefore, the values of x and y are:

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The airplane weigh if it is carrying 52 gallons of fuel will be, 2338 pounds

Let,

Weight of airplane = y

Amount of fuel = x

The general linear equation can be written as, y=mx + c, where, (m) is slope, and (c) is a constant.

It is given,

2091 = 14m + c ..... (1)

2312 = 48m + c ..... (2)

On subtracting, (1) with (2), we get

221 = 34m

m= (221/34)= 6.5

Now, on putting the value of (m) in (1), we get,

2091 = 14(6.5) + c

So,

c = 2000

Therefore, the linear equation can be written as,

y = (6.5)mx + 2000

Now to find the airplane weight at 52 gallons of fuel, we put x = 52, to find y.

That is,

y = (6.5)(52) + 2000

y = 2338

So, the airplane weigh if it is carrying 52 gallons of fuel will be, 2338 pounds.

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The number of flowers needed is 226

The circumference is the perimeter of a circle or ellipse. The circumference is the outer body of a circle and it can also be called perimeter of a circle.

The circumference of a circle is expressed as!

C = 2πr , where r is the radius.

the radius of the garden is 18ft

C = 2 × 3.14 × 18

C = 113.04

This means the perimeter of the garden is 113.04

For a space of 6 inches, the flower needed is calculated as;

113.04 × 12/6 ( since 1 foot is 12 inches)

= 113.04 × 2

= 226 flowers ( nearest whole number)

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Here is the truth table for the statement (~ p V q) → q:

```

p     q     ~p    ~p V q   (~p V q) → q

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

T     T     F      T           T

T     F     F      F           T

F     T     T      T           T

F     F     T      F           T

```

In the table, `p` and `q` represent the truth values of the propositions `p` and `q`, respectively. The symbol `~` represents negation (i.e., "not"). The symbol `V` represents the logical connective "or" (i.e., "inclusive or"). The symbol `→` represents the conditional connective "implies" (i.e., "if...then").

To fill in the truth table, we first evaluate `~p` and `~p V q` for each combination of truth values for `p` and `q`. Then, we evaluate `(~p V q) → q` for each combination of truth values.

We can see that the statement is always true, regardless of the truth values of `p` and `q`, except for the case where `p` is true and `q` is false.

Answer:

D. its a two dimensional object

Answer:

A. It is a polygon

C. It is a one-dimensional object

The shape is a polygon in two dimensions since a polygon must have at least three straight sides.

The equation of the line parallel is y = mx + (1 + 2m).

We have,

The equation of the line.

y = mx + c

Slope = m

And,

(-2, 1) = (x, y)

So,

1 = m x -2 + c

c = 1 + 2m

Now,

y = mx + c

y = mx + (1 + 2m)

Thus,

The equation of the line parallel is y = mx + (1 + 2m).

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Area of the base of the pyramid is 16 square centimeters

Area of one lateral face of the pyramid  is  14 square centimeters

The lateral surface area of the pyramid is  56 square centimeters

The total surface area of the pyramid is 72  square centimeters

Area of the base of the pyramid = length x length

= 4 x 4

=16 square centimeters

Area of one lateral face of the pyramid = area of a triangle

=1/2×base×height

=1/2×4×7

=14 square centimeters

The lateral surface area of the pyramid =  4 x area of one lateral face

= 4 x 14

= 56square centimeters

The total surface area of the pyramid = lateral surface area of the pyramid +  area of the base

=56+16

=72 square centimeters

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the value of 4% as a fraction is 1/25

4/100 is the fraction, but when 4 is divided into 100, it gives you 1/25 in simplest form.

Is this compound interest or simple interest? I'll just do it by the simple interest method. The answer is 9 months!

Answer:

Step-by-step explanation:

y=-3x-1

format for formula:

y=mx+b

b=1  that is your y-intercept.  where it hits the y-axis

m= -3    this is your slope    [tex]\frac{rise}{run} =\frac{-3}{1}[/tex]  

from a point you have, the y-intercept, you go down 3 (because of the negative in front of it), this is your rise,
and to the right 1, this is your run

Answer:

2 1/3

Step-by-step explanation:

add then multiplying to the nearest one.

The quadratic equation is solved and discriminant is 5, so it has two real solutions

Given data ,

The given equation is a quadratic equation in the standard form ax² + bx + c = 0, where a = 1, b = -1, and c = -1

The discriminant of a quadratic equation is given by b² - 4ac. So, the discriminant of the given equation is

(-1)² - 4(1)(-1) = 1 + 4 = 5

Since the discriminant is positive (not zero or negative), the equation has two real solutions.

Hence , its discriminant is 5, so it has two real solutions

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5 seconds.

In a function expressing altitute (h) in terms of time (t), finding the vertex will provide the time and altitute when the object reaches the maximum height. Therefore, let's use the vertex formula to see exactly when this happens:

"x" vertex value: [tex]-\dfrac{-b}{2a}[/tex]

a) For using that equation, first write the given equation on its standard form.

Standard form of quadratic equations: [tex]ax^{2} +bx+c=0[/tex]

b) You can substitute h(t) by 0 on the origina equation:

[tex]-0.2t^{2} +2t=0[/tex]

c) Idenfity the coefficients.

a= -0.2, beacuse "t²" is being multiplied by -0.2.

b= 2, beacuse "t" is being multiplied by 2.

d) Substitute in the formula and calculate.

[tex]\sf X\,value_{Vertex} =-\dfrac{-b}{2a}=-\dfrac{-(2)}{2(-0.2)}=-\dfrac{-(2)}{-0.4}=5[/tex]

So the "x" value of this h(t) equation is located on x= 5, therefore, the maximum point happens at x= 5. Since this is an equation that expresses altitute in terms of time, this means that 5 seconds after the object starts its movement it reaches its maximum altitute.

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a. The dependent variable is the number of unit sold. The independent variable is price.

b. The value of r is -0.9965

c. ŷ = -0.68688X + 56.95837

X Values

∑ = 301

Mean = 50.167

∑(X - Mx)2 = SSx = 920.833

Y Values

∑ = 135

Mean = 22.5

∑(Y - My)2 = SSy = 437.5

X and Y Combined

N = 6

∑(X - Mx)(Y - My) = -632.5

R Calculation

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -632.5 / √((920.833)(437.5)) = -0.9965

Meta Numerics (cross-check)

r = -0.9965

c. Regression line calculation

Sum of X = 301

Sum of Y = 135

Mean X = 50.1667

Mean Y = 22.5

Sum of squares (SSX) = 920.8333

Sum of products (SP) = -632.5

Regression Equation = ŷ = bX + a

b = SP/SSX = -632.5/920.83 = -0.68688

a = MY - bMX = 22.5 - (-0.69*50.17) = 56.95837

ŷ = -0.68688X + 56.95837

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Comparing each pair of expressions using >, <, or = is given below:

-32 < |-32| (because -32 is negative and |-32| is positive)

5 - 5 = 0 (because subtracting the same number results in zero)

15 > |___15| (because |___15| is equal to 15)

|5| = |___|-5|| (because both expressions are equal to 5)

2 - 17 < ▾ (because 2 - 17 equals -15, which is less than the square root symbol)

2 > |____|-17|| (because 2 is positive and |-17| is also positive)

|-27| > ||-45|| (because |-27| is 27 and ||-45|| is 45)

-27 > -45 (because -27 is closer to zero than -45)

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The speed limit for the highway in rounded to the nearest whole is 33 mi/h.

The speed is the ratio of the distance in a given time interval. The distance is represented by a unit of length and the time is represented by a unit of time.

There are different units for the length or distance. In the International System Units (SI), the standard unit of distance is the meter (m) and the standard unit of time is the second (s). Nonetheless, there are others units, for example: inches (in), miles (mi) and  yards (yd).

For solving this exercise, you need to know the relation between the given units for distance and time.

The question gives - 100 km/h. The kilometer (km) is a multiple of the  standard unit of distance -  the meter (m) and the hour is a submultiple of the  standard unit of time  - the second (s)

For solving this question, it is necessary that you know the relation between km/h and mi/h. See  below.

[tex]\text{1 km/h}= 0.6213712 \ \text{mi/h}[/tex]

Now you can solve the question from a math tool - Rule of three. Thus,

[tex]\text{1 km/h}= 0.6213712 \ \text{mi/h}[/tex]

[tex]100 \ \text{km/h}= \text{x mi/h}[/tex]

[tex]\text{x}= 100 \times 0.6[/tex]

[tex]\text{x}=33 \ \text{mi/h}[/tex]

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a) Based on the first derivative test, h(x) has a relative minimum at x = -2 and a relative maximum at x = 0.

b)  For x = -2: h''(-2) = 6(-2) + 6 = -6 < 0, so h(x) has a relative maximum at x = -2.

For x = 0: h''(0) = 6(0) + 6 = 6 > 0, so h(x) has a relative minimum at x = 0.

Calculus is a branch of mathematics that deals with the study of rates of change, accumulation, and the properties and behavior of functions.

(a) First derivative test:

The first derivative test involves finding the critical points of the function, where the first derivative is equal to zero or undefined, and then checking the sign of the first derivative in the intervals between the critical points to determine whether the function has relative extrema at those points.

Find the first derivative of h(x):

h'(x) = 3x² + 6x

Set h'(x) = 0 and solve for x to find the critical points:

3x² + 6x = 0

x(x + 2) = 0

x = 0 or x = -2

Test the intervals between the critical points using the sign of the first derivative:

For x < -2: Choose x = -3, h'(-3) = 27 + (-18) = 9 > 0, so h(x) is increasing.

For -2 < x < 0: Choose x = -1, h'(-1) = 3 - 6 = -3 < 0, so h(x) is decreasing.

For x > 0: Choose x = 1, h'(1) = 3 + 6 = 9 > 0, so h(x) is increasing.

Based on the first derivative test, h(x) has a relative minimum at x = -2 and a relative maximum at x = 0.

(b) Second derivative test:

The second derivative test involves finding the critical points of the function using the first derivative, and then checking the sign of the second derivative at those points to determine whether the function has relative extrema at those points.

Find the second derivative of h(x):

h''(x) = 6x + 6

Evaluate the second derivative at the critical points found in step 2 of the first derivative test:

For x = -2: h''(-2) = 6(-2) + 6 = -6 < 0, so h(x) has a relative maximum at x = -2.

For x = 0: h''(0) = 6(0) + 6 = 6 > 0, so h(x) has a relative minimum at x = 0.

Hence, the ease of a test may vary for different individuals and their familiarity with calculus concepts.

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Adding -4(row 1) to row 3 in the matrix will produce: 0, -9, 2, and 12 respectively.

A rectangular array of numbers or mathematical objects which are arranged in rows and columns is called a matrix. Each row of a matrix is a horizontal sequence of numbers or objects that are separated by commas and enclosed within square brackets, and it represents a vector in the row space of the matrix.

row 1 of the given matrix are: 1, 2, 1, and -5, multiplying -4(row1) will gives;

-4 × 1 = -4

-4 × 2 = -8

-4 × 1 = -4

-4 × -5 = 20

-4(row 1) + row 3 will result to:

-4 + 4 = 0

-8 + (-1) = -9

-4 + 6 = 2

20 + (-8) = 12

Therefore, adding -4(row 1) to row 3 in the matrix will produce: 0, -9, 2, and 12 respectively.

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Answer:

70.7°

350 feet

Im not too sure about the last one

Answer:

Based on the hypothesis test conducted with a significance level of 5%, we fail to reject the null hypothesis that the proportion of smokers in the city is 20%. This means that we do not have sufficient evidence to conclude that the proportion of smokers is less than 20%. The p-value of 0.828 suggests that there is a high probability that the observed proportion of smokers in the sample is due to chance and not a true difference in the proportion of smokers in the population. Therefore, we cannot conclude that the city has a lower proportion of smokers than 20%.

In this hypothesis test set up by the researcher, the p-value is 0.828, which is greater than the significance level (0.05). Therefore, we do not reject the null hypothesis, meaning there is not enough statistical evidence to validate the researcher's claim that the proportion of smokers is less than 20%

A hypothesis test in statistics uses test statistics based on sample data to accept or reject a null hypothesis. In this scenario, the null hypothesis (H0) states that the proportion of smokers (p) is 20%. The alternative hypothesis (Ha) claims that the proportion of smokers is less than 20%. The p-value is a measure of the probability that the observed data could occur under the null hypothesis. In our case, a p-value of 0.828 means that there is an 82.8% chance of observing the data if the true proportion of smokers is 20%, or higher.

Usually a threshold known as the significance level (in this case 5% or 0.05) is used to determine whether the null hypothesis should be rejected or not. If the p-value is less than or equal to the significance level, it suggests that the observed data is inconsistent with the null hypothesis, and the null is usually rejected. However, since our p-value is greater (0.828 > 0.05), we would not reject the null hypothesis, suggesting that there is not enough evidence to support the researcher's claim that the proportion of smokers is less than 20%.

Therefore, the conclusion is that the researcher's claim cannot be validated using the provided data.

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Answer:

A

Step-by-step explanation:

To calculate the percentage of questions Danielle got correct on her math test, we can divide the number of questions she got correct by the total number of questions on the test and then multiply by 100. In this case, Danielle got 23 out of 25 questions correct, so we can calculate her percentage as follows: (23/25) * 100 = 92%. Therefore, Danielle got 92% of the questions correct on her math test.

Percent = amount per 100

23/25 = amount per 25

25 x 4 = 100

23 x 4 = 92

92/100 = 92%

Answer = 92%

Hope this helps!