In a laboratory experiment, the population of bacteria in a petri dish started off at
4900 and is growing exponentially at 8% per hour. Write a function to represent the
population of bacteria after t hours, where the rate of change per minute can be
found from a constant in the function. Round all coefficients in the function to four
decimal places. Also, determine the percentage rate of change per minute, to the
nearest hundredth of a percent.

Answer:

Answers following the rounding instructions:  see below for details

BC = 5.1

m∠B = 23°

m∠V = 116°

Step-by-step explanation:

Givens:

AC = 3

AB = 7

m∠A = 41°

Unknowns:

BC = ?

m∠B = ?

m∠C = ?

Find side BC using the law of cosines:  c² = a² + b² - 2ab cos(C)

a² = 3² + 7² - 2(3)(7)(cos41)

a = √9 + 49 - 42(cos41)

a = 5.128 ≈ 5.13

side BC = 5.13

Use the law of sines to find m∠B:  sin(A) / a = sin(B) / b = sin(C) / c

m∠B = sin⁻¹[sin41/5.13 x 3] = sin⁻¹(0.3837) = 22.56 ≈ 22.6°

Sum of interior angles of a triangle is 180, so now you can find m∠C:

m∠C = 180 - 22.6 - 41 = 116.44 ≈ 116.4°

Rounding side BC to nearest tenth: BC = 5.1

Rounding angles to nearest whole degree:

m∠B = 23°

m∠V = 116°

Answer:

5:52

Step-by-step explanation:

Answer: 5:52

Step-by-step explanation:

Answer:

A. 11.2

Step-by-step explanation:

But this has nothing to do with 5.6 × 2. Erase that! Lol.

You have a right triangle here. The only thing to do with the circle is that there are two radii (plural of radius) shown. So they have to be the same measure.

The unmarked "bottom" of the triangle, the short leg, is a radius, so it too, is 8.4.

The hypotenuse of the right triangle, the side on the right, the longest side is 5.6 + 8.4.

The hypotenuse is 14.

Let's do some Pythagorean Theorem.

Leg^2+ leg^2=hypotenuse^2

you know,

a^2 + b^2 = c^2

fill in what we know.

8.4^2 + b^2 = 14^2

simplify.

70.56 + b^2 = 196

subtract 70.56

b^2 = 125.44

squareroot both sides

b = 11.2

Sin(2x) = 20 x cos²(x), cos(2x) = -99 x cos²(x), and tan(2x) = -20/99.

To find the values of sin(2x), cos(2x), and tan(2x) using the given information, use trigonometric identities to express them in terms of tan(x) and sin(x).

Given that tan(x) = 10 and sin(x) is negative. Since tan(x) = sin(x)/cos(x), find cos(x) using the given information.

Let's solve for cos(x) first:

tan(x) = sin(x)/cos(x)

10 = sin(x)/cos(x)

Now, let's find sin(x) using the given information that sin(x) is negative:

Since tan(x) = sin(x)/cos(x) and tan(x) = 10, substitute 10 for sin(x)/cos(x):

10 = sin(x)/cos(x)

Multiplying both sides by cos(x):

10 x cos(x) = sin(x)

Now, sin(x) = 10 x cos(x).

Since sin(x) is negative, conclude that cos(x) must be positive.

Now, let's use the double-angle identities to find sin(2x), cos(2x), and tan(2x):

sin(2x) = 2 x sin(x) x cos(x)

cos(2x) = cos²(x) - sin²(x)

tan(2x) = sin(2x) / cos(2x)

Substituting sin(x) = 10 x cos(x) into the above formulas, express sin(2x), cos(2x), and tan(2x) in terms of cos(x):

sin(2x) = 2 x (10 x cos(x)) x cos(x) = 20 x cos²(x)

cos(2x) = cos²(x) - (10 x cos(x))² = cos²(x) - 100 x cos²(x) = -99 x cos²(x)

tan(2x) = sin(2x) / cos(2x) = (20 x cos²(x)) / (-99 x cos²(x)) = -20/99

Therefore, sin(2x) = 20 x cos²(x), cos(2x) = -99 x cos²(x), and tan(2x) = -20/99.

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Answer:

Step-by-step explanation:

Answer:The max volume of Purple berry paint is 85

Step-by-step explanation:

Purple = Red + Blue

P = 5 : 2

Simplify 5 : 2 which is 2.5 : 1

P = 30L : 10L

P = (30 x 2.5 ) + (10 x 1)

P = 75 + 10

P = 85 L

The type of sytudy that we have here is the observational study.

In an observational study, the researcher observes and analyzes data from individuals without actively intervening or manipulating any variables.

In this case, the researcher is observing and comparing the health outcomes of two groups of individuals: those who have eaten a vegan diet for the past five years and those who have not.

The participants are not randomly assigned to the groups, and the researcher does not actively control or manipulate the diet of the individuals.

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The total value of her liquid assets would be = $3,980. That is option B.

An asset is said to be a liquid asset because it can easily be converted into cash in a short period of time.

Examples of liquid assets include the following:

Therefore, the total value of liquid assets = $580+$3400 = $3980

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Answer:

15

Step-by-step explanation:

Answer:

B Mean: 17.5  | W Mean: 20.5 | B Mode: 15 | W Mode: 20.5 | B Mode: 14 & 15 | W Mode: 20 & 21 | B Range: 17 | W Range: 3

Step-by-step explanation:

The value of x is approximately 34.02.

Given that in a rectangle with length 31 and width is 14 and the diagonal length is x.

To find the value of x using the Pythagorean Theorem, we can consider the rectangle as a right triangle, where the length and width of the rectangle form the two sides of the triangle, and the diagonal length (x) is the hypotenuse.

According to the Pythagorean Theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Applying the given data gives,

[tex]x^2 = length^2 + width^2[/tex]

Substituting the given values into the equation:

diagonal length [tex]x^2 = 31^2 + 14^2[/tex]

diagonal length [tex]x^2[/tex] = 961 + 196

diagonal length [tex]x^2[/tex] = 1157

To find x, we take the square root of both sides:

diagonal length x = [tex]\sqrt{1157}[/tex]

diagonal length x = 34.02

Therefore, the value of x is approximately 34.02.

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Answer:

626.71 cm^2

Step-by-step explanation:

Area of figure = area of half circle + Area of half circle + area of a rectangle

here, diameter=15 cm

radius = 15/2=7.5 cm

length=30cm

breadth=15cm

Now

Area of figure = 1/2*π*radius^2+ 1/2*π*radius^2+length*breadth

=1/2* 1/2*π*7.5^2+1/2* 1/2*π*7.5^2+30*15

=626.71 cm^2

To find the height of the square pyramid, we can use the Pythagorean theorem. The slant height of the pyramid (s) is the hypotenuse of a right triangle formed by the height (h), half the length of the base (b/2), and the slant height.

Using the Pythagorean theorem:

s^2 = (b/2)^2 + h^2

We are given that the length of one of the base sides (b) is 23.8 and the slant height (s) is 89.3.

Plugging in the values:

89.3^2 = (23.8/2)^2 + h^2

Simplifying:

h^2 = 89.3^2 - (23.8/2)^2

h^2 = 7950.49 - 141.64

h^2 = 7808.85

Taking the square root of both sides:

h = √7808.85

h ≈ 88.37

Therefore, the height of the square pyramid is approximately 88.37 inches.[tex]\huge{\mathcal{\colorbox{black}{\textcolor{lime}{\textsf{I hope this helps !}}}}}[/tex]

♥️ [tex]\large{\textcolor{red}{\underline{\texttt{SUMIT ROY (:}}}}[/tex]

Answer: 18

Step-by-step explanation:

Multiply number of each item possible

3*2*3=18

The expression for the total number of packets of crisps that Jane buys is given as follows:

p + c.

The amounts of packets of crisps purchased are given as follows:

The expression for the total number of packets of crisps that Jane buys is given by the addition of these two amounts.

Hence the expression for the total number of packets of crisps that Jane buys is given as follows:

p + c.

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The quadratic equation in standard form that corresponds to the given graph is [tex]f(x) = (-4/9)(x + 2)^2 + 4[/tex]

To determine the quadratic equation in standard form that corresponds to the given graph, we need to identify the key features of the parabola. From the graph, we can see that the parabola opens upwards and intersects the y-axis at the point (0, c). We can also observe that the vertex of the parabola lies at the point (h, k).

The standard form of a quadratic equation is given as follows:

[tex]f(x) = a(x - h)^2 + k[/tex]

Where (h, k) represents the coordinates of the vertex, and 'a' is a constant that determines the shape and direction of the parabola.

Looking at the graph, we can determine the vertex by identifying the x-coordinate where the parabola reaches its highest or lowest point. Let's assume the vertex is located at the point (h, k).

From the graph, it appears that the vertex lies at (-2, 4). Therefore, we have h = -2 and k = 4.

Now we can rewrite the equation as:

[tex]f(x) = a(x + 2)^2 + 4[/tex]

Next, we need to determine the value of 'a'. To do this, we can use another point on the graph. Let's consider the point (1, 0).

Plugging in the coordinates (1, 0) into the equation, we get:

[tex]0 = a(1 + 2)^2 + 4[/tex]

0 = 9a + 4

9a = -4

a = -4/9

Now we have the value of 'a'. Substituting it back into the equation, we get:

[tex]f(x) = (-4/9)(x + 2)^2 + 4[/tex]

Thus, the quadratic equation in standard form that corresponds to the given graph is:

[tex]f(x) = (-4/9)(x + 2)^2 + 4[/tex]

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1. There is no relationship

2. Two cities have an average snowfall of nearly 100 inches.

A scatter plot, also known as a scatter diagram or scatter graph, displays the relationship between two variables. It is particularly beneficial for identifying any patterns or trends in the data and showing how one variable might be related to another.

In a scatter plot, each data point is represented on the graph by a dot or marker. The horizontal axis (x-axis) is frequently used to represent the independent variable or predictor, while the vertical axis (y-axis) is frequently used to represent the dependent variable or reaction. Each dot's locations on the graph correspond to the values of the two variables for that particular data point.

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Answer:  A.   x=3     y= -1         z=4

Step-by-step explanation:

I plugged it into my graphing calculator.

>2nd Matrix

>Edit >A

>choose 3x3

>Enter all coefficients as they look

>2nd Matrix

>Edit >B

>Choose 3x1

>Enter answers as they look

Go to main page

[tex][A]^{-1} [B]\\[/tex]

Answers end up being 3, -1,  4

Answer: $1.50 for every 1 pound

Step-by-step explanation:

If 2 pounds equal to $3.00 divide $3.00 by 2 and you end up with $1.50, you can also keep adding $1.50 to get the other prices.

The factored expression of n² - 11n + 10 is (n - 10)(n - 1)

From the question, we have the following parameters that can be used in our computation:

n² - 11n + 10

To determine the pair of factors to factor the expression, we find two expressions

using the above as a guide, we have the following:

The expressions are -10n and -n

So, we have

n² - 11n + 10 = n² - 10n - n + 10

When factored, we have

n² - 11n + 10 = (n - 10)(n - 1)

Hence, the factored expression of n² - 11n + 10 is (n - 10)(n - 1)

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Answer:

The area of the rectangle is 168 ft².

Step-by-step explanation:

Formula: A = lw

where l and w are the length and width of the rectangle respectively.

We're given with the length and the width as

a = 12 ft

b = 14 ft

Let's solve for the area using the formula above.

A = lw

A =  12ft(14ft)

A = 168 ft²

Answer:

a. 73°

b. 98°

Step-by-step explanation:

In quadrilateral EFGH

∡E+∡G=180° sum of opposite angle of quadrilateral inside the circle is 180°

substituting value

11x+8+8x+1=180°

19x+9=180°

19x=180=9

19x=171

x=171/19

x=9°

similarly,

∡H+∡F=180° sum of opposite angle of quadrilateral inside the circle is 180°

substituting value

6y-4+5y-3=180°

11y-7=180°

11y=180°+7

11y=187°

y=187/11

y=17°

Now

a. m∡G=8x+1=8*9+1=73°

b. m∡H=6y-4=6*17-4=98°

The degrees of freedom is 21, the critical values correspond to the points where the chi-square distribution curve separates the rejection and non-rejection areas and chi-square test statistic is 27.

The null and alternative hypotheses can be stated as follows:

Null Hypothesis (H0): The population variance is equal to 14.

Alternative Hypothesis (Ha): The population variance differs from 14.

To find the critical values of χ2 with α = 0.05, we need to determine the degrees of freedom first.

For a sample variance, the degrees of freedom (df) is given by (n - 1), where n is the sample size.

In this case, n = 22, so the degrees of freedom is 21.

Using a chi-square table or statistical software, we can find the critical values for a chi-square distribution with 21 degrees of freedom and α = 0.05.

The critical values correspond to the points where the chi-square distribution curve separates the rejection and non-rejection areas.

To determine the test statistic χ2 value, we need to calculate the chi-square test statistic using the given information.

The chi-square test statistic is calculated as:

χ2 = (n - 1) ×(sample variance) / (population variance)

Plugging in the values, we have:

χ2 = (22 - 1) × 18 / 14

=27

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The calculated inches from end to end on the bed is 72 inches

From the question, we have the following parameters that can be used in our computation:

Length = 6 feet long

By conversion of units, we have

1 feet = 12 inches

using the above as a guide, we have the following:

Length = 6 * 12 inches long

Evaluate the products

Length = 72 inches long

Hence, the inches from end to end on the bed is 72

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Answer:

[tex]x\approx0.39,-3.89[/tex]

Step-by-step explanation:

[tex]\displaystyle 2x^2+7x=3\\2x^2+7x-3=0\\\\x=\frac{-7\pm\sqrt{7^2-4(2)(-3)}}{2(2)}\\\\x=\frac{-7\pm\sqrt{49+24}}{4}\\\\x=\frac{-7\pm\sqrt{73}}{4}\\\\x\approx0.39,-3.89[/tex]

Container #1 is the only one large enough to hold the contents of a one liter bottle of soft drink.

Container #1: The volume formula for a cylinder is V = πr²h, where r is the radius and h is the height.

Radius (r) = 8 cm / 2 = 4 cm

Height (h) = 19 cm

So, V1 = π(4 cm)²(19 cm)

≈ 3032.07 cm³

Container #2:

Radius (r) = 5 cm

Height (h) = 12 cm

Using the formula:

V2 = π(5 cm)²(12 cm)

≈ 942.48 cm³

Container #3:

Diameter (d) = 12 cm

Radius (r) = 12 cm / 2 = 6 cm

Height (h) = 10 cm

V3 = π(6 cm)²(10 cm)

≈ 1130.97 cm³

Now, Comparing the volumes:

V1 ≈ 3032 cm³

V2 ≈ 942 cm³

V3 ≈ 1131 cm³

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Answer:

please see answers below

Step-by-step explanation:

Volume of sphere = (4/3) X π X r ³

volume of hemisphere = (2/3)X π X r ³

12) volume of hemisphere = (2/3)X π X r ³

= (2/3) X π X (5)³

= (250/3)π

= 261.80 km³ to nearest hundredth

13) 18 foot is the diameter. radius = 1/2 X diameter = 9.

volume of hemisphere = (2/3)X π X r ³

= (2/3) X π X (9) ³

=  1526.81 ft³ to nearest hundredth

Answer:

  38.9 in²

Step-by-step explanation:

You want the area of the composite figure that is an 8-inch square with a semicircle removed.

The missing semicircle has a diameter of 8 in, so a radius of 4 in. The area of that half-circle is ...

  A = 1/2πr² = (π/2)(4 in)² = 8π in² ≈ 25.1 in²

The area of the square without the semicircle removed is ...

  A = s² = (8 in)² = 64 in²

After removing the semicircle from the square, the remaining area is ...

  A = square area - semicircle area

  A = 64 in² -25.1 in² = 38.9 in²

The area of the figure is about 38.9 square inches.

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The Burj Khalifa, located in Dubai in the United Arab Emirates, is the tallest building in the world as of 2022, there are approximately 148 floors in the Burj Khalifa.

We can make use of the data given to determine the Burj Khalifa's floor count.

Andre is known to have stood 1,000 metres away from the structure and turned his head to look up at a 39.62 degree angle.

Let's write "h" for the Burj Khalifa's height and "d" for Andre's distance from the building's base.

tan(39.62°) = h / d

h = d * tan(39.62°)

h = 1000 * tan(39.62°) ≈ 753.7 meters

So, as per this, Number of floors = h / floor height

Number of floors = 753.7 meters / 5.079 meters

Number of floors ≈ 148.4 floors or 148 floors.

Thus, 148 floors are there in Burj Khalifa.

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