What is the sum of 18+516+38 1 8 + 5 16 + 3 8 ?

The area of the parallelogram can be found out by using the equation:

A = 4 × 9 = 36m².

By multiplying the base with the altitude, one can determine the area of a parallelogram. A parallelogram's base and height are perpendicular to each another.

Area of parallelogram = b × h square units

Now in the question,

Height of parallelogram, h = 4m

base of parallelogram, b = 9m

Area of parallelogram = b × h

= 4 × 9

=36m²

Therefore, the equation A = 4 × 9 can be used to find the area of the parallelogram.

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(a) The relative rate of growth of the bacterium population is 15% per unit time; (b) the initial population of the culture is 90 bacteria; (c) the culture will contain approximately 239 bacteria at time t=5.

(a) The relative rate of growth of the bacterium population can be calculated by taking the derivative of the function n(t) with respect to t and then dividing it by the value of n(t) at that point, which gives:

relative rate of growth = (dn/dt) / n(t)

= (0.15 * 90[tex]e^0.15t[/tex]) / (90[tex]e^0.15t[/tex])

= 0.15

Therefore, the relative rate of growth is 15%.

(b) The initial population of the culture at t=0 is given by plugging in t=0 in the function n(t):

n(0) = 90[tex]e^0.15[/tex]*0

= 90

Therefore, the initial population of the culture is 90.

(c) The number of bacteria in the culture at time t=5 can be found by plugging in t=5 in the function n(t):

n(5) = 90[tex]e^0.15[/tex]*5

= 385.97 (rounded to two decimal places)

Therefore, the culture will contain approximately 385.97 bacteria at time t=5.

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Answer:

5x+4=19

5x=19-4

5x=15

5x÷5=15÷5

x=3

The 3rd graph is the correct one representing the open sentence.

Inequalities is defined as the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values or data. The equal sign in between can be replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

-5≤n-2≤2

First you need to get n by itself, so add 2 to all 3 terms:

-5 +2 ≤ n-2+2 ≤ 2+2

Simplify:

-3 ≤ n ≤ 4

The less than or equal to signs (≤) mean the dots on the line graph are solid.

And n is between -3 and positive 4, the 3rd graph is the correct one.

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Answer:

It will be same as angle x because they are on the same line and are alternative angles

So, measurement of angle u will be u=152

Step-by-step explanation:

Hope this helps:)

Good luck

Answer: 3.3= .033 percentage. .033 times 34000=1112 times (t) time (10 years) equals 11120

Step-by-step explanation:

Answer:

Step-by-step explanation:

(1\2, 4) = (0.5, 4)

The quadratic equation in the given graph can be written in the vertex-form as:

y = -2(x - 1)² + 4

We can see the graph of a quadratic equation. Remember that a quadratic equation with a vertex (h, k) and a leading coefficient a can be written as:

y = a*(x - h)² + k

in the graph we can see that the vertex is (1, 4), replacing that we will get:

y = a*(x - 1)² + 4

In the graph we also can see that the curve passes through the point (0, 2), replacing thesevalues in the equation we will get:

2 = a*(0 - 1)² + 4

2 = a + 4

-2 = a

Then the quadratic is:

y = -2(x - 1)² + 4

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The standard form of the quadratic functions can be analyzed, by finding the specified coordinates as follows;

1. Vertex; (2, -3)

Axis of symmetry; x = 2

Minimum value; -3

Range; y ≥ -3

2. Vertex; (1, 4)

Axis of symmetry; x = 1

Maximum value; 4

Range; y ≤ 4

3. Vertex; (-3, -1)

Axis of symmetry; x = -3

Maximum value; -1

Range; y ≤ -1

4. Vertex; (-3, 5)

Axis of symmetry; x = -3

Maximum value; 5

Range; y ≤ 5

5. Vertex; (-0.75. -6.125)

Axis of symmetry; x = -0.75

Minimum value; -6.125

Range; y ≥ -6.125

6. Vertex; (2/3, 4/3)

Axis of symmetry; x = 2/3

Maximum value; 4/3

Range; y ≤ 4/3

The standard form of a quadratic function is the form; f(x) = a·x² + b·x + c, a, b, and c are constants and a ≠ 0.

1. The x-value of the vertex point of the quadratic equation; y = ax² + bx + c is; x = -b/(2·a)

Therefore, the x-value of the vertex point of the equation, y = x² - 4·x + 1 is; x = 4/2 = 2

The y-value of the vertex point is; y = 2² - 4×(2) + 1 = -3

The vertex is; (2, -3)

The axis of symmetry if the x-value of the vertex point, therefore;

The axis of symmetry is; x = 2

The minimum value is the y-value of the vertex point, therefore;

The minimum value is; y = -3

The range is the set of the possible y-values

The positive leading coefficient of the function, indicates that the range of the function is the set of values larger than the minimum value.

Therefore, the range is; y ≥ -3

2. The x-value of the vertex point of the equation, y = -x² + 2·x + 3, therefore is; x = -2/(-2) = 1

The y-value at the vertex point is; y = -1² + 2×1 + 3 = 4

The vertex is; (1, 4)

The axis of symmetry is; x = 1

The maximum value is; y = 4

The range is; y ≤ 4

3. The x-value of the vertex is; x = -(-6)/(2 × (-1)) = -3

The y-value at the vertex is; y = -(-3)² × -6 × (-3) - 10 = -1

The vertex is; (-3, -1)

The axis of symmetry is; x = -3

The maximum value is; y = -1

The range is; y ≤ -1

4. The x-value of the vertex is; x = -18/(2×3) = -3

The y-value of the vertex is; y = 3 × (-3)² + 18 × (-3) + 32 = 5

The vertex is; (-3, 5)

The axis of symmetry is; x = -3

The minimum value is; y = 5

The range is; y ≥ 5

5. The x-value of the vertex is; x = -3/(2 × 2) = -3/4

The y-value of the vertex is; y = 2 × (-3/4)² + 3 × (-3/4) - 5 = -6.125

The vertex is; (-3/4, -6.125)

The axis of symmetry is; x = -3/4

The minimum value is; -6.125

The range is; y ≤ -6.125

6. The x-value of the vertex is; -4/(2 × (-3)) = 2/3

Y-value at the vertex is; y = -3 × (2/3)² + 4 × (2/3) = 4/3

The vertex point is; (2/3, 4/3)

The axis of symmetry is; x = 2/3

The maximum value is; 4/3

The range is; y ≤ 4/3

7. The graphs of the quadratic equations can be obtained by finding the coordinates of the vertex, the y-intercept and the x-intercepts and joining the points using a curve symmetrical about the vertex as follows;

The following values are obtained using an online tool.

7. The graph of the equation; y = x² + 2·x - 5, can be obtained using the following points;

The vertex is; (-1, -4)

The y-intercept is; (0, -5)

The x-intercepts are; (-1 + √6, 0), and (-1 - √6, 0)

8. The graph of the equation; y = -x² + 3·x + 1, can be obtained using the following points;

The vertex is; (3/2, 5/4)

The y-intercept is; (0, 1)

The x-intercepts are; (-0.30, 0), and (3.30, 0)

9. The graph of the equation; y = 2·x² + 4·x - 4, can be obtained using the following points;

The vertex is; (-1, -6)

The y-intercept is; (0, -4)

The x-intercepts are; (-1 + √3, 0), and (-1 - √3, 0)

10. The graph of the equation; y = (-1/2)·x² - 3·x + 3, can be obtained using the following points;

The vertex is; (-3, 7.5)

The y-intercept is; (0, 3)

The x-intercepts are; (-3 + √(15), 0), and (-1 - √(15), 0)

Please find attached the graphs of the quadratic equations created with MS Excel

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The calculated value mean of the sampling distribution for this population is 56

The mean of the sampling distribution for a population with a normal distribution is equal to the population mean.

Therefore, in this case, the mean of the sampling distribution is also 56.

To understand why this is the case, we can consider the central limit theorem, which states that the sampling distribution of the mean of a random sample from a population with any distribution will be approximately normal if the sample size is large enough.

This means that as the sample size increases, the mean of the sampling distribution approaches the population mean.

Therefore, the mean of the sampling distribution for this population is 56.

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The missing component in this equation is an alpha particle (He), which has a mass number of 4 and an atomic number of 2. Therefore, the balanced nuclear equation for this alpha decay would be:

^45/20Ca -> ^45/21Sc + ^4/2He

Answer: ^45/20Ca -> ^45/21Sc + ^4/2He

Answer: a) We know that the Revenue equation is a polynomial of order 1, so we can write it in the form:

R(x) = ax + b

where a and b are constants to be determined. We also know that R(1) = 1 and R(5) = 9, so we have two equations:

a(1) + b = 1

a(5) + b = 9

Solving these equations simultaneously, we get:

a = 2, b = -1

Therefore, the Revenue equation is:

R(x) = 2x - 1

Similarly, the Cost equation is a polynomial of order 2, so we can write it in the form:

C(x) = ax^2 + bx + c

where a, b, and c are constants to be determined. We know that C(1) = R(1) = 1 and C(5) = R(5) = 9, so we have two equations:

a(1)^2 + b(1) + c = 1

a(5)^2 + b(5) + c = 9

We also know that C(2) = 0, so we have a third equation:

a(2)^2 + b(2) + c = 0

Solving these equations simultaneously, we get:

a = 1, b = -4, c = 4

Therefore, the Cost equation is:

C(x) = x^2 - 4x + 4

b) The common solutions to the Revenue and Cost equations represent the production level(s) at which the company makes a profit, since the Revenue equation represents the amount of money the company earns and the Cost equation represents the amount of money the company spends. In other words, the common solutions are the values of x for which R(x) - C(x) > 0. At these production levels, the company's revenue is greater than its cost, resulting in a profit. At production levels where R(x) - C(x) < 0, the company is making a loss. At production levels where R(x) - C(x) = 0, the company is breaking even. Therefore, the common solutions to the two equations signify the production levels at which the company makes a profit or breaks even.

Step-by-step explanation:

Therefore , the solution of the given problem of interest comes out to be Offer 1 should be selected by the new homeowner since it has a reduced overall cost.

Divide the sum by the funding cost, the remaining time, and other factors to determine the simple interest rate. Principal loan repayment hours is the marketing plan with the simplest return. The simplest way to determine involvement is through this technique. In most instances, income is calculated as a percentage of the starting sum.

Here,

Part A: To start, we must divide the yearly interest rate by 12 to determine the monthly interest rate:

Monthly interest rate equals 24.90% divided by 12 equals 0.0249 per month.

=> Monthly payment = (P * r) / (1 - (1 + r)⁻ⁿ

=> Monthly payment = $104.23 per month

=>  (2784 * 0.0249 / (1 - (1 + 0.0249)(-36)).

Taking the entire number of months (36) into account, we get:

Cost of the whole deal 1 = 36 * $104.23 = $3,751.28

As a result, offer 1's overall price is $3,751.28.

Part B:

First, we figure out the interest rate per month:

Monthly interest rate = 22.90% / 12 = 0.0229 / month.

=> Monthly payment = (P * r) / (1 - (1 + r)⁻ⁿ

=> Monthly payout

=> (1 - (1 + 0.0229)(-48)) / (2784 * 0.0229) ≈ $82.12/month

Using the entire number of months (48) as a multiplier, we obtain:

Cost of the whole deal 2 = 48 * $82.12 = $3,938.56

Part C:

Offer 1 costs $3,751.28 in total, while Offer 2 costs $3,938.56 in total.

Offer 1 should be selected by the new homeowner since it has a reduced overall cost.

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The resulting number is 12/5

Arithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.

Given that we need to, increase the number 15/16 by 3/5 of it, then increase the resulting number by 3/5 of it

So, performing the operations,

15/16+15/16×3/5

= 15/16(1+3/5)

= 15/16(8/5)

= 120/80

= 3/2

Now,

3/2+3/2×3/5

= 3/2(1+3/5)

= 3/2(8/5)

= 24/10

= 12/5

Hence, the resulting number is 12/5

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Answer:

Step-by-step explanation:

The area of the track is closely 1017.36 square feet.

The rectangle has dimensions of 84 ft by 36 ft,

we then find the area by:

Area of rectangle = length x width = 84 ft x 36 ft = 3,024 square feet

A_semicircle = (1/2)πr^2 = (1/2) x 3.14 x 18^2 = 508.68 square feet

The total area of the two semicircles is:

2 x A_semicircle = 2 x 508.68 = 1017.36 square feet

The area of the rectangle plus the area of the two semicircles is:

A_track_outer = A_rectangle + 2 x A_semicircle

= 3024 + 1017.36

= 4041.36 square feet

The area of the rectangle (the field) is:

A_field = length x width = 84 ft x 36 ft = 3024 square feet

We will subtract the area of the field from the area of the track to find the area of the track itself:

Area of track = A_track_outer - A_field

= 4041.36 - 3024

= 1017.36 square feet

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Answer:

Step-by-step explanation:

yes since they are both divisible by their denominators and equal the same thing

Answer:

yes, they are equivalent

Step-by-step explanation:

2/2 = (2/2)x(4/4) = 8/8 = 1

The graph of the function y = -|x| is the graph of the function y = |x| reflected across the x-axis

The function given in the question is

y = -|x|

The above function is an absolute value function graph

And the parent function of an absolute graph is

y = |x|

When y = |x| and y = -|x| compared, we have the transformation to be

A reflection across the x-axis

This means that the graph of y = |x| is reflected across the x-axis to create y = -|x|

See attachment for the graph of the function

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we input the value 2 into the function, it will output the value 4.

Each element of X is given precisely one element of Y by the function from a set X to a set Y. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively. Initially, functions represented the idealized relationship between two variable quantities.

The function F(x) = x^2 represents a quadratic function, where the input value (x) is squared to produce the output value (F(x)).

To find the value of F(2), we simply need to substitute 2 in place of x in the equation:

F(2) = (2)^2 = 4

This means that when we input the value 2 into the function, it will output the value 4.

In other words, F(2) represents the value of the quadratic function at the point where x is equal to 2.

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Complete question:

If F(x)=x^2 then what is f(2).

Answer:

The temperature on the eighth day is 80.

Step-by-step explanation:

Let t = temperature on the eighth day.

[tex] \frac{71 + 80 + 69 + 80 + 73 +77+ 70 + t}{8} = 75[/tex]

[tex] \frac{520 + t}{8} = 75[/tex]

[tex]520 + t = 600[/tex]

[tex]t = 80[/tex]

Answer:

To find the number of bags of rice in 2850kg, we need to divide the total weight of rice by the weight of each bag. In this case, each bag weighs 50kg, so:

Number of bags = 2850 kg / 50 kg per bag

Simplifying this expression, we get:

Number of bags = 57 bags

Therefore, there are 57 bags of rice in 2850kg.

To find the value, we need to know the price per bag of rice. If we know this price, we can simply multiply the number of bags by the price per bag to get the total value. Without knowing the price, we cannot determine the value.

Answer:

57

Step-by-step explanation:

Answer:

There are 2.2 fans per employee.

Step-by-step explanation:

19812/8900 = 2.2 Rounded.

Helping in the name of Jesus.

The correct graph would be the one with a normal distribution curve centered at 0, with two tails shaded on either side, representing the lowest and highest 4% of scores So option C is correct.

What is standard normal distribution ?

The standard normal distribution is a special case of the normal distribution in which the mean is 0 and the standard deviation is 1. It is also known as the "Z-distribution" because the scores are expressed in terms of their z-scores, which are the number of standard deviations above or below the mean.

The standard normal distribution is a bell-shaped curve that is symmetric around the mean of 0. It is used in statistics as a reference distribution for calculating probabilities and making statistical inferences.

To convert a normal distribution with a given mean and standard deviation to a standard normal distribution, we use the formula:

z = (x - μ) / σ

According to the question:
To find the bone density test scores that can be used as cutoff values separating the lowest 4% and highest 4%, we need to find the z-scores that correspond to the 4th and 96th percentiles of the standard normal distribution.

Using a standard normal table, we find that the z-score corresponding to the 4th percentile is approximately -1.75, and the z-score corresponding to the 96th percentile is approximately 1.75.

Therefore, the bone density test scores that can be used as cutoff values separating the lowest 4% and highest 4% are approximately -1.75 and 1.75, respectively.

To sketch the region containing the lowest 4% and highest 4%, we need to shade the area under the normal curve to the left of -1.75 and to the right of 1.75.

The shaded regions represent the lowest 4% and highest 4% of bone density test scores, respectively. The correct graph would be the one with a normal distribution curve centered at 0, with two tails shaded on either side, representing the lowest and highest 4% of scores.


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The polynomial function f(x) which produced the graph shown is f(x) = -6(x - 1/2)²(x + 1)²(x - 2).

In Mathematics and Geometry, a polynomial graph touches the x-axis at zeros, roots, solutions, x-intercepts, and factors with even multiplicities.

By critically observing the graph of the polynomial function shown above, we can logically deduce that its x-intercepts include the following;

x = -1 ⇒ x + 1 = 0.

x = 2 ⇒ x - 2 = 0.

Also, the graph has a zero of multiplicity 2 at x = 1/2;

x = 1/2 ⇒ x - 1/2 = 0.

(x - 1/2)²

In this context, an equation that represent the polynomial function is given by:

f(x) = a(x - 1/2)²(x + 1)²(x - 2)

By evaluating and solving for the leading coefficient "a" in this polynomial function based on the y-intercept (0, 3), we have;

3 = a(0 - 1/2)²(0 + 1)²(0 - 2)

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

3 = -a/2

a = -6.

Therefore, the required polynomial function is given by:

f(x) = -6(x - 1/2)²(x + 1)²(x - 2)

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Reason:

We cannot divide by zero. This means the denominator cannot equal zero. If it was zero, then,

2x+10 = 0

2x = -10

x = -10/2

x = -5

Follow that chain in reverse to see that x = -5 causes the denominator 2x+10 to be zero. This is why we kick -5 out of the domain. Any other x value is valid.

The maximum height reached after the 13th bοunce is 6.14 cm.

The height οf bοunce is the height tο which an οbject rebοunds after cοIIiding with a surface, such as a baII bοuncing οn the grοund οr a diver bοuncing οff a diving bοard. The height οf the bοunce depends οn severaI factοrs, incIuding the initiaI height οf the οbject, the surface it cοIIides with, the eIasticity οf the οbject and the surface, and the angIe οf incidence.

Tο sοIve this prοbIem, we need tο use the fοrmuIa fοr the height οf each bοunce:

[tex]h = (3/4)^{{n}} \times H[/tex]

where h is the height οf the nth bοunce, H is the initiaI height (in this case, 187.00 cm), and n is the number οf bοunces.

We want tο find the maximum height reached after the 13th bοunce, which means we need tο find the height οf the 13th bοunce and then muItipIy it by 3/4 tο get the maximum height.

Using the fοrmuIa abοve, we can find the height οf the 13th bοunce:

[tex]h = (3/4)^{{13}} \times 187.00[/tex]

h ≈ 8.18 cm

Nοw we can find the maximum height:

maximum height = (3/4) × h

maximum height = (3/4) ×8.18

maximum height ≈ 6.14 cm

Therefοre, the maximum height reached after the 13th bοunce is apprοximateIy 6.14 cm.

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Answer:

147

Step-by-step explanation:

A= h^b b=21*14= 147

Answer:

We can use the formula for average rate of change to find the rate at which the gas is being used:

average rate of change = (change in y) / (change in x)

where y is the number of gallons left in the tank and x is the number of hours driven.

Substituting the given values, we get:

average rate of change = (5 - 14) / (5 - 0)

Simplifying, we get:

average rate of change = -9/5

Therefore, the rate at which the gas is being used is -9/5 gallons per hour, or -1.8 gallons per hour. This means that the gas in the tank is decreasing at a rate of 1.8 gallons per hour.

Answer:

Step-by-step explanation:

This question's answer is 'c'. In the first function here we put the value of x=0, then y =3 but in the second function if we put the value of x=0 then y  =2. so c is the correct answer.