2. How can the term unit square help you to remember
that area is measured in square units?

After 13 hours the population of bacteria in the culture is approximately 5,905,820, rounded to the nearest whole number.

we can use the formula for exponential growth

P = P0 * 2^(t/k)

Where:

P = population at time t

P0 = initial population = 74000

t = time = 13 hours

k = time for population to double = 3 hours

Plugging in the values:

P = 74000 * 2^(13/3)

P = 74000 * 2^4.33

P = 74000 * 79.83

P = 5905820

Answer:

Step-by-step explanation:

Top problem:

A = πr² = (22/7)(21)² = 1386 ft²

Bottom problem:

r = D/2 = 20/2 = 10 in

A = (22/7)(10)² = 314 in²

In mathematics, a line is a set of points that extend indefinitely in two directions.

Points on the line: These are points that lie exactly on the line. They are equidistant from the two endpoints of the line and are considered to be part of the line itself.

Points above the line: Points that are vertically above the line are referred to as points above the line. These points are located higher than the line and have a greater y-coordinate than any point on the line.

Points below the line: Points that are vertically below the line are referred to as points below the line. These points are located lower than the line and have a smaller y-coordinate than any point on the line.

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The equation is y = (-0.5)x + 34 and it will take 16 days for the water level to be 26 feet.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

Let the number of days = x, and the water level = y.

Given that,

Water level of river = 34 ft (initial value/y-intercept)

Rate of change = -0.5 ft per day (slope)

The equation of the line is given as:

y = mx + c

where, m is the slope

c is the y-intercept.

Substituting the values we have:

y = (-0.5)x + 34

The number of days in which the water level will reduce to 26 ft is:

26 = (-0.5)x + 34

26 - 34 = -0.5x

x = 16 days.

Hence, it will take 16 days for the water level to be 26 feet.

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Answer:

The distance to the nearest exit door is at most 100 feet can be written as an inequality as:

d ≤ 100

The blood platelet count is an illustration of normal distribution Approximately 95% of the data lies within 2 standard deviations of the mean. There are approximately 99.7% of women with platelet count between 65.2 and 431.8

The given parameters are:

μ = 248.5

[tex]\sigma = 61.1\\[/tex]

(a) The percentage within 2 standard deviation of mean or between 126.3 and 370.7

Start by calculating the z-score, when x = 126.3 and x = 370.7

[tex]Z = \frac{(x-u)}{\sigma}[/tex]

So, we have:

x = -2

Also,

x = 2

The empirical rule states that:

Approximately 95% of the data lies within 2 standard deviations of the mean.

Hence, there are approximately 95% of women with platelet count within 2 standard deviations of the mean.

(b) The percentage with platelet count between 65.2 and 431.8

Start by calculating the z-score, when x = 65.2 and x = 431.8

So, we have:

Z =-3

Also:

Z = 3

The empirical rule states that:

Approximately 99.7% of the data lies within 3 standard deviations of the mean.

Hence, there are approximately 99.7% of women with platelet count between 65.2 and 431.8

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The area of the shaded region found using trigonometric ratios is about 86.6 square centimeters

Trigonometric ratios are expressions of the relationship between the interior angle of a right triangle and the ratio of two of the sides of the triangle.

Whereby, the inscribing figure of the quadrilateral is a regular hexagon, we get;

Interior angle of a regular hexagon = 120°

The 10 cm segment bisects the top vertex angle of the regular hexagon, which together with the 5·√3 cm side and trigonometric ratios, indicates that we get;

sin(60) = s/(5·√3) = (√3)/2

Where;

s = The side length of the regular hexagon

(5·√3)/s = (√3)/2

s = (5·√3)/((√3)/2) = 10

The side length of the regular hexagon, s = 10

The area of the regular hexagon, A = ((3·√3)/2) × s² = (1/2)×6 ×s ×a

Where;

a = The apothem = 5·√3

Therefore; A = ((3·√3)/2) × 10² = 150·√3

A  = (1/2)×6 ×10 × 5·√3 = 150·√3

Area of the quadrilateral = 4 × (1/2) × 5·√3 × 10 = 100·√3

Area of the shaded region = Area of the hexagon - Area of the quadrilateral

Therefore;

Area of the shaded region = 150·√3 - 100·√3 = 50·√3 ≈ 86.6

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The solution is, The value of N is 12 sq cm.

Area of a rectangle (A) is the product of its length (l) and width (w).

A= l. w

here, we have,

1. Find the greatest common factor of 35 and 42 to find the length (horizontal). The GCF is 7.

2. The horizontal length of the 35 and 42 sq cm is 7, and the heights are 5 and 6 respectively.

3. Moving on tot he 10 sq cm rectangle,

since the height of just that one rectangle is  and 10/5 is 2, the horizontal length is 2.

4. For n, the horizontal length is 2 and the height is 6.

2 X 6 is 12 sq cm.

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Raoul and Sven are at an angle of = cos1 (cos a cos 43° + sin a sin 43°). The sled is being moved by a force with a magnitude of [(105 cos a + 122 cos 43°)2 + (105 sin a + 122 sin 43°)2].

The outcome of two vectors is determined by the parallelogram law of vector addition. The resultant vector, R=(A2+B2+2ABcos), follows this law. A and B are the two vectors in this situation, and is the angle between them.

The component in the direction of the sled's path is:

105 cos a

The component perpendicular to the path is:

105 sin a

Similar to this, Sven's force may be broken down into two parts: one that is parallel to the sled's course and one that is perpendicular to it. The element pointing in the sled's direction is:

122 cos 43°

The component perpendicular to the path is:

122 sin 43°

The net force on the sled is the vector sum of these four components:

Net force = (105 cos a + 122 cos 43°) i + (105 sin a + 122 sin 43°) j

The magnitude of the net force is:

|Net force| = √[(105 cos a + 122 cos 43°)² + (105 sin a + 122 sin 43°)²]

To find the angle between Raoul and Sven, we can use the dot product of their forces:

Raoul · Sven = |Raoul| |Sven| cos θ

We can solve for θ as follows:

cos θ = (Raoul · Sven) / (|Raoul| |Sven|)

cos θ = [(105)(122) cos a cos 43° + (105)(122) sin a sin 43°] / (105)(122)

cos θ = cos a cos 43° + sin a sin 43°

θ = cos⁻¹(cos a cos 43° + sin a sin 43°)

a. The angle between Raoul and Sven is θ = cos⁻¹(cos a cos 43° + sin a sin 43°).

b. The magnitude of the force moving the sled is |Net force| = √[(105 cos a + 122 cos 43°)² + (105 sin a + 122 sin 43°)²].

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4 x 9 is a multiplication problem, which means 4 is being multiplied by 9. This can also be written as 4 x 9 = 36. 4 multiplied by 9 is equal to 36 because 4 is being added to itself 9 times, resulting in 36.

4 x 9 is a multiplication problem which means we are multiplying 4 and 9 together. This can also be written as 4 x 9 = 36. When multiplying two numbers together, you are adding the first number to itself the second number of times. In this case, 4 multiplied by 9 is equal to 36 because we are adding 4 to itself 9 times: 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 = 36. This can also be written as 4 x 9 = 36, which means that 4 times 9 equals 36.

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The denominator 6 in 3/6 is should not be changed when adding fractions if other fractions have a denominator of 6, to make the addition easy because 6 will be the lowest common multiple.

One of the reasons why the denominator will always stay the same when adding fraction is because the size of the equal pieces does not change when you combine the two fractions together.

For example say you want to add 3/6 + 1/6 + 2/6,

you will notice that all the fractions have equal denominator, so adding the fractions together will have the following result.

3/6 + 1/6 + 2/6 = (3 + 1 + 2 ) / 6

= 6/6

= 1

So the 6 in 3/6 should not be changed if all other fractions you wish to add to 3/6 have 6 as their denominator, because the 6 is lowest common multiple.

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The value of the equation is 35 = 15 + 2y , where y is the number of years and the y = 10 years

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let the initial height of the weeping willow be = 15 feet

Let the final height of the weeping willow be = 35 feet

The height in feet the weeping willow grows each year = 24 inches = 2 feet

Let the number of years be = y

On simplifying the equation , we get

35 = 15 + 2y

Subtracting 15 on both sides of the equation , we get

2y = 20

Divide by 2 on both sides of the equation , we get

y = 10 years

Hence , the equation is y = 10 years

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Given parallelogram points are (4,3),(-4 3), and (2, -3).

Let's say A= (4,3) , B=(-4 3) ,C=(2, -3) and D=(x, y)

Parallelogram defined as opposite sides are equal and parallel to each other.

From the properties of parallelogram :

We can say diagonals bisect each other.

From this we can easily find 4th point of parallelogram by using mid point concept.

Mid point formula

 (X,Y)=[tex](\frac{x_{1} +x_{2}}{2},\frac{y_{1} +y_{2}}{2})[/tex]

Find mid point between AC line

midpoint (X,Y)= [tex](\frac{4 +2}{2},\frac{3-3}{2})[/tex]

                (X,Y)=[tex](\frac{6}{2},\frac{0}{2})[/tex]

                 (X,Y)=(3,0)

Find mid point between BD Line

Mid point (X,Y)= [tex](\frac{-4 +x}{2},\frac{3+y}{2})[/tex]

Mid point of AC and BD are equal to each other

(3,0)=[tex](\frac{-4 +x}{2},\frac{3+y}{2})[/tex]

Equate x-coordinate and y-coordinate.

[tex]3=(\frac{-4 +x}{2})[/tex]        and      [tex]0=(\frac{3+y}{2})[/tex]

6=-4+x             and       0=3+y

x=10                 and        y=-3

Therefore ,the coordinates of the 4th point is D(x, y)=(10,-3)

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The coordinates of the fourth point that would complete the parallelogram are (10, -3).

A parallelogram is defined as a special type of quadrilateral that has both pairs of opposite sides parallel and equal.

We know A, B, and C, where A = (4, 3), B = (-4, 3), and C = (2, -3).

To determine the fourth point, which represents D.

First, we need to find the vector representing side AB.

Subtracting the coordinates of point B from the coordinates of point A. So:

AB = A - B = (4, 3) - (-4, 3) = (8, 0)

Next, we need to find a point that is on the line that is parallel to AB and passes through point C.

The vector CD (where D is the point) is equal to AB. So:

CD = AB = (8, 0)

We know that C = (2, -3),

We can start by adding CD to C to get D:

D = C + CD = (2, -3) + (8, 0) = (10, -3)

Therefore, the coordinates of the fourth point are (10, -3).

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Answer: this app should be freer

Step-by-step explanation:

The length of the rectangle given the area and width is 21 inches

Area of the rectangle = 357 square inches

Width of the rectangle = 17 inches

Length of the rectangle= l

Area of a rectangle = Length × width

357 = l × 17

357 = 17l

divide both sides by 17

l = 357 / 17

l = 21 inches

In conclusion, 21 inches is the length of the rectangle.

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The length of the rectangular classroom will be 8 inches on the scale drawing.

What is a rectangle defined as?

Rectangles are four-sided polygons having internal angles of 90 degrees. At each corner or vertex, two sides meet at right angles. The rectangle differs from the square in that its opposite sides are of equal length.

If one side of a rectangle is 20 cm long, the other side must be 20 cm long as well.

Two diagonals cross form a rectangle. Both diagonals are the same length.

P = 2 (Length + Width) defines the perimeter.

Rectangle Area=Length*Breadth

Now,

As total length of room =36 feet

and 9 feet = 2 inch on drawing scale

then length of classroom on  drawing scale is = 36/9*2

=8 inch

Hence,

            The length of the rectangular classroom will be 8 inches on the scale drawing.

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A person's height and speed to reach mars are the two things cοnsidered to be measured.

Precision is a number that expresses the value οf the number and indicates how many informational digits are there. Fοr instance, 3.14 is an approximation οf pi that is reasonable and accurate. Hοwever, the precision digit, which is 3.199, is less than the precise digit.

1. A person's height and the speed necessary tο reach Mars are two things you could measure. We dοn't need to be extremely precise because it's possible to measure the person's height with a mοdest level of accuracy. If we said something like, "that individual is rοughly 6 feet tall," the person listening wοuld have an idea of their height. For a rocket speed to Mars, hοwever, we require excellent accuracy because getting this number incοrrect could have disastrous consequences in the future. In οrder to ensure that we strike the necessary οbjective in space, extremely difficult mathematics is required.

2. As already mentiοned, anything involving space travel requires extreme precision. The spacecraft might sοmehow crash if the calculations are off. Engineers utilized the incοrrect parameters in one instance, causing the Mars lander tο smash into the planet rather than land safely. Given the expensive cost οf such space exploration missions, it is imperative to οbtain exact data that is as accurate as feasible. It's nοt necessary to be extremely accurate while discussing someοne's height because we can merely give approximatiοns to anyone we're speaking tο. Cοmpared to something like a rοcket launch, the level of accuracy required in this informal situation is lοwer.

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Answer:

Value of account after t years is
[tex]A = \boxed{190( 1.0178)^{4t}}[/tex]

Percentage of growth per year

CAGR = [tex]\boxed{7.31\%}[/tex]

Step-by-step explanation:

The generalized equation for the accrued value of an amount P(the principal) deposited at i% annual interest compounded n times a year for t years is

[tex]A = P\left(1 + \dfrac{r}{n}\right)^{nt}[/tex]

where r = i/100, the interest rate expressed as a decimal

Given P = $190
i = 7.1% ==> r = 7.1/100 = 0.071

Since the interest is compounded quarterly and there are 4 quarters in a year, the interest is compounded 4 times a year so n = 4

[tex]A = 190 \left(1 + \dfrac{0.071}{4}\right)^{4t}[/tex]

[tex]A = 190\left(1 + 0.01775\right)^{4t}}\\\\A = 190( 1.01775)^{4t}[/tex]\

Rounding the annual growth rate to 4 decimal places gives

[tex]A = P(1.0178)^{4t}[/tex]

In one year, the investment of $190 will grow to
[tex]A = 190(1.0178)^{4}[/tex]

[tex]A = $203.89[/tex]

Compound Annual Growth = = 203.89 - 190 = $13.89

Compound Annual Growth Rage(CAGR) = $13.89/$190 = 0.073105

As a percentage, CAGR Percent = 0.073105 x 100 = 7.3105% or rounded to nearest hundredth it would be 7.31%

Caleb can choose which 20 items to buy in 1140 ways if he wants all 3 cheeses.

To choose 20 items at the grocery store, Caleb has narrowed down his selections to 5 vegetables, 8 fruits, 3 cheeses, and 7 whole grain breads. Since he wants all 3 cheeses, he only needs to choose 17 more items.

The number of ways he can choose these 17 items from the remaining vegetables, fruits, and breads is given by the combination: C(5+8+7, 17) = C(20, 17) = 1140.

This formula means that there are 20 items to choose from, and Caleb wants to choose 17. The order doesn't matter, so we use a combination.

Therefore, Caleb can choose which 20 items to buy in 1140 ways if he wants all 3 cheeses.

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The volume of the sphere with a radius of 8.9 m is given as follows:

V = 2,951.5 m³.

The volume of a sphere of radius r is given by the equation presented as follows:

V = 4πr³/3.

The radius for this problem has the measure given as follows:

r = 8.9m.

Hence, considering that π is rounded to 3.14, the volume of the sphere is obtained as follows:

V = 4 x 3.14 x (8.9)³ x 1/3

V = 2,951.5 m³.

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The m values that allow the quadratic equation [tex]x^2 + mx + 4[/tex] to have two independent real roots are m in the open range (-∞ , -4) (4 , ∞). This may be expressed in interval notation as:

m ∈ (-∞, -4) ∪ (4, ∞).

The quadratic formula tells us that the quadratic equation's roots

[tex]x^2 + mx + 4 = 0[/tex]

are provided by:

[tex]x = (-m[/tex] ± [tex]sqrt(m^2 - 16))/2[/tex]

The discriminant [tex](m^2- 16)[/tex]must be positive, i.e., [tex]m^2[/tex] > 16, for the quadratic to have two separate real roots. As a result, we have two instances to consider:

Case 1: m > 4. Because [tex](-m + sqrt(m^2 - 16)/2[/tex]and[tex](-m - sqrt(m^2 - 16)/2[/tex]are both real and unique in this case, the quadratic has two separate real roots.

Case 2: m < -4. In this situation, [tex](-m + sqrt(m^2 - 16)/2[/tex] is negative, whereas[tex](-m - sqrt(m^2 - 16)/2[/tex] is positive, indicating that the quadratic has two separate real roots.

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The table is

x = 0            5         8            10           30.

y = 300       250    220        200         0

The height of the airplane decreases with time. Thus airplane landed in the time interval.

What is an equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.

Given equation is y = -10x + 300.

Putting x = 0 in the equation:

y = -10×0 + 300

y = 300

Putting x = 5 in the equation:

y = -10×5 + 300

y = -50 + 300

y = 250

Putting x = 8 in the equation:

y = -10×8 + 300

y = -80 + 300

y = 220

Putting x = 10 in the equation:

y = -10×10 + 300

y = -100 + 300

y = 200

Putting x = 30 in the equation:

y = -10×30 + 300

y = -300 + 300

y = 0

The height of the airplane after 5 minutes is 250 feet.

The height of the airplane after 30 minutes is 0 feet.

The altitude of the airplane decreases with time. The altitude of the airplane decreases with time. The airplane is landing in the time interval.

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Answer:

x = 4

Step-by-step explanation:

Move the x to the left-hand side and change its sign

2x - x = 9 - 5

x = 9 - 5

Answer:

x=4

Step-by-step explanation:

Subtract 1x from both sides

Subtract 5 from both sides to isolate the variable

x=4

In mathematical terms, each point (x, y) on Shape A is mapped to a point (2 + (2 - x), y) on Shape B as reflected line equation and explained as

When a shape is reflected in a line, it means that each point on the original shape is mapped to a corresponding point on the reflected shape that is symmetrical with respect to the reflecting line.

The line of reflection can be any straight line, and in this case, the line of reflection is given by the equation x = 2. To understand how the reflection works, imagine holding a mirror along the line x = 2 and placing Shape A on the mirror. The reflected shape, Shape B, would be the image that you see in the mirror. In mathematical terms, each point (x, y) on Shape A is mapped to a point (2 + (2 - x), y) on Shape B. This means that for each point on Shape A, we take its x-coordinate, subtract it from 2 to find the distance from the line of reflection, and then add that distance to 2 to find the x-coordinate of the corresponding point on Shape B. The y-coordinate remains the same.

The line of reflection acts as a dividing line between Shape A and Shape B, and the points on Shape B are exactly the same distance from the line of reflection as the points on Shape A, but on the opposite side. This means that Shape B is a perfect mirror image of Shape A, reflected across the line x = 2.

In summary, the reflection of Shape A in the line x = 2 maps each point on Shape A to a corresponding point on Shape B that is symmetrical with respect to the line of reflection. The result is a perfect mirror image of the original shape, reflected across the line.

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Step-by-step explanation:

2y+57=180

2y=180-57

2y=123

y=123/2=61.5°

y=61.5

Answer:

61.5

Step-by-step explanation:

As the lines are parallel you can use the alternate angle rule.

So within the triangle you have 57 + x + x ( y is equal to the other angle because the lines are the same length and angle highlighted by the double lines )

And so...

180 - 57 = 123

123/2 = 61.5

The set X ∪ Y is the union of sets X and Y, which is the set of all elements that are in either X or Y. In this case, X ∪ Y = X = {1, 2, 4, 8, 16, 32}.

Answer:

I don't have a way to explain, but it is an Equilateral and Isosceles :)

Hope it helps!