The formula h = rt – 16t ^2 gives a good approximation of the height h in feet that an object will reach in t seconds, when it is projected upward with an initial speed of r feet per second. Write a model for each of the following situations in problem. Solve each equation, and then use your graphing calculator to sketch the function and verify your answer.
An object is thrown upward from the ground with an initial velocity of 32 ft/sec. Find the number of seconds it takes the object to reach the ground. What is the maximum height obtained by this object?

Answer:

3<2*x=5

Step-by-step explanation:

Hope this helped, Have a Wonderful Day/Night!!

( btw the astric means multiplication )

The unknown number will be equal to 4.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that three is less than the product of 2 and a number is equal to 5. The unknown number will be calculated as:-

2x - 3 = 5

2x = 5 + 3

2x = 8

x = 8 / 2 = 4

Therefore, the unknown number will be equal to 4.

The complete question is given below:-

Three less than the product of 2 and a number is equal to 5. Calculate the unknown number.

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The center of mass (centroid) of the triangular region is located at (\(x_0 / 3, y / 3\)). This represents the point where the mass of the region is evenly distributed.

The triangular region in the first quadrant bounded by the y-axis, the x-axis, and the line \(2x + y = 4\) is a right-angled triangle. To find the center of mass of this region, we need to determine the coordinates of its centroid. The centroid represents the point at which the mass is evenly distributed in the region.

The centroid of a triangle can be found by taking the average of the coordinates of its vertices. In this case, since one vertex is at the origin (0, 0) and the other two vertices are on the x-axis and y-axis, the coordinates of the centroid can be found as follows:

x-coordinate of centroid = (0 + x-coordinate of second vertex + x-coordinate of third vertex) / 3

y-coordinate of centroid = (0 + y-coordinate of second vertex + y-coordinate of third vertex) / 3

Since the second vertex lies on the x-axis, its coordinates are (x0, 0). Similarly, the third vertex lies on the y-axis, so its coordinates are (0, y).

Substituting these values into the formulas, we have:

x-coordinate of centroid = \((0 + x_0 + 0) / 3 = x_0 / 3\)

y-coordinate of centroid = \((0 + 0 + y) / 3 = y / 3\)

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Answer:

2/3 =x

Step-by-step explanation:

2/x = 6/2

Simplify 6/2 =3

2/x = 3

Multiply each side by x

2/x *x = 3*x

2 = 3x

Divide each side by 3

2/3 = 3x/3

2/3 =x

Answer:

\(\frac{7}{5}\)

Step-by-step explanation:

1 \(\frac{2}{5}\)

= 1 + \(\frac{2}{5}\)

= \(\frac{5}{5}\) + \(\frac{2}{5}\)

= \(\frac{5+2}{5}\)

= \(\frac{7}{5}\)

The fraction is:

7/5

Step-by-step explanation:

The number we're given is:

\(\large\pmb{1\dfrac{2}{5}}\)

To convert it into an improper fraction, we first multiply the whole number part (1) times the denominator (5). Then, we add 2, the numerator. We get 7.

That is the numerator of the improper fraction. As for the denominator, we just copy it.

\(\pmb{\dfrac{7}{5}}\)

Therefore, the answer is 7/5.

Answer:

The car will use 9 3/8 or 9.375(simple form) gallons of gasoline on the highway

Step-by-step explanation:

if a car uses 3 1/8 gollon per one hour

Multiply the gallon usage of the car by the hours the car will travel on the road

3 1/8(gallons) x 3(hours on the road)

9 3/8 or if you change it to simple form it will be equal to 9.375

Answer:

Step-by-step explanation:

2/9 + x = 11/18

x = 11/18 - 2/9

x = 63/162

x = 7/18

2/9 + 7/18 = 11/18

11/18 = 11/18

The maximum and minimum possible values for P(A|B) in this scenario are both 0.4.

To determine the maximum and minimum possible values for P(A|B), we need to consider the relationship between events A and B.

The maximum possible value for P(A|B) occurs when A and B are perfectly dependent, meaning that if B occurs, then A must also occur. In this case, the maximum value for P(A|B) is equal to P(A), which is 0.4.

The minimum possible value for P(A|B) occurs when A and B are perfectly independent, meaning that the occurrence of B has no impact on the probability of A. In this case, the minimum value for P(A|B) is equal to P(A), which is again 0.4.

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The exponential model that calculates the concentration of bacteria after x weeks can be represented by the equation B(x) = 2.1 million * (3^x), the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

This equation assumes that the concentration triples each week, starting from the initial concentration of 2.1 million bacteria per milliliter.

To estimate the concentration after 1.6 weeks, we can substitute x = 1.6 into the exponential model. B(1.6) = 2.1 million * (3^1.6) ≈ 14.87 million bacteria per milliliter. Therefore, after 1.6 weeks, the estimated concentration of bacteria in the river would be approximately 14.87 million bacteria per milliliter.

The exponential model B(x) = 2.1 million * (3^x) represents the concentration of bacteria after x weeks, where the concentration triples each week. By substituting x = 1.6 into the equation, we estimate that the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

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Answer:

I got 105°

Step-by-step explanation:

Triangle ABC is an isosceles triangle so base angles are equal. <A = 30° (given)

180 - 30 = 150°

150/2 = 75°

the little triangle is also isosceles. the original base angles have been bisected so the base angles are 37.5.

37.5 X 2 = 75°

180-75 = 105°

D = 105°

P(X = 7), λ = 6: The Poisson probability of X = 7, with a parameter (λ) value of 6, is 0.1446. P(X = 11), λ = 12: The Poisson probability of X = 11, with a parameter (λ) value of 12, is 0.0946. P(X = 6), λ = 8: The Poisson probability of X = 6, with a parameter (λ) value of 8, is 0.1206.

The Poisson probability is used to calculate the probability of a certain number of events occurring in a fixed interval of time or space, given the average rate of occurrence (parameter λ). The formula for Poisson probability is P(X = k) = (e^-λ * λ^k) / k!, where X is the random variable representing the number of events and k is the desired number of events.

To calculate the Poisson probabilities in this case, we substitute the given values of λ and k into the formula. For example, for the first case (a), we have λ = 6 and k = 7: P(X = 7) = (e^-6 * 6^7) / 7!

Using a calculator, we can evaluate this expression to find that the probability is approximately 0.1446. Similarly, for case (b) with λ = 12 and k = 11, and for case (c) with λ = 8 and k = 6, we can apply the same formula to find the respective Poisson probabilities.

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flips a fair coin five times, 5/16 is the probability that there are 3 heads in a row somewhere in the sequence of five flips.

The number of positive outcomes to all possible outcomes of an event is the ratio, which is known as probability.

The number of positive outcomes may be expressed by x for an experiment with n number of outcomes.

The following equation can be used to determine an event's probability:

Probability(Event) = Favorable outcomes / Total Outcomes = x/n

Considering a fair coin, after 5 flips, there are \(2^5\) = 32 different arrangements of heads and tails.

To get exactly 3 heads,

\(^5C_3\) = 5! / (5 - 3)! 3!

     = 5!/ 3! 2!

     = 10 ways

P(exactly 3 heads) = 10/32 = 5/16

Therefore, the probability of exactly 3 heads is 5/16.

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True, the links in the blockchain are created using an algorithm.

What is blockchain?                                                                                                                                                                                                                       Blockchain is a decentralized ledger technology that enables the secure exchange of digital assets across a network of participants without the need for a centralized authority or intermediary. The blockchain is created using an algorithm to secure the network and ensure that all transactions are transparent and verifiable.

In a blockchain, each block contains a cryptographic hash of the previous block, forming a chain of blocks (hence the name "blockchain"). The algorithm used to create the blockchain is a consensus algorithm, which ensures that all participants on the network agree on the same state of the ledger.

This consensus algorithm also ensures that no single participant can manipulate the ledger or change the contents of a block without being detected.

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Answer:$15.95

Step-by-step explanation:

You have to Add to get your answer I'll show you how I got $15.93:

1.29+1.29=$2.58

2.58+1.35=$3.93

3.93+12=$15.93

Your answer is:$15.93

hope this was helpful:)

Quantitative type of variable is the number of robberies reported in your city.

The number of robberies reported in your city is a quantitative variable because it represents a numerical measurement or quantity.

It involves the collection of numeric data that quantifies the frequency or amount of a specific event (in this case, the number of robberies) occurring in your city.

More specifically, it is a continuous variable. Continuous variables are characterized by being able to take on any value within a certain range. In the case of the number of robberies reported, it can have decimal or fractional values.

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The true statements for the given function f(x) are:

The value of g(1) is 3 and the y- intercept of g(x) is at the point (0, 1) .

The function g(x) = f( x - 3 )

g (1) = f (1 -3 )

       = f (-2 )

       = 3

g (-1) = f (-1 -3)

       = f (-4)

       = - 1

Substituting , x = 0 to find the y intercept of g(x)

g ( 0 ) = f ( 0 - 3)

          =f (-3)

          =1

The y intercept of g(x) is at the point (0, 1)

Thus, options 1 and 4 are the true statements for the given function.

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Answer:

the additive inverse of 12 is -12

Step-by-step explanation:

To form a triangle, the set of line segments must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, we need to check if the given line segments 8 cm, 4 cm, and 3 cm meet this requirement.

We can start by checking if the sum of the two smaller sides (3 cm and 4 cm) is greater than the largest side (8 cm). 3 cm + 4 cm = 7 cm, which is less than 8 cm. Therefore, these three line segments cannot form a triangle.

In general, for a set of line segments to form a triangle, the largest side must be smaller than the sum of the other two sides. In this case, the line segment of 8 cm is too long compared to the other two sides, which makes it impossible to form a triangle.

In conclusion, there are no line segments that meet the requirements to form a triangle with lengths of 8 cm, 4 cm, and 3 cm.

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Answer:

(a+b)^2-2ab= a^2+b^2+2ab-2ab=a^2+b^2= 3^2+2^2= 9+4= 13

hope it helps

Answer

y= 3/2 x  - 2

Step-by-step explanation:

so you have to find the slope which would be

m =  

y2 - y1

x2 - x1

then you find you points that you are using (2, 1) and (0, -2)

when you plug it in it is

m=

-2-1

0-2

you simplify the numbers and get rid of the negatives to get m=3/2 x

then your y intercept is where your line meets the y axis or wherever x=0

so your y intercept is (0, -2) so the b = -2

Answer:

d is the correct answer to your question

Answer:

9.2 units

Step-by-step explanation:

cause the last guy is right...

Using a t-table or statistical software, the critical t-value for a 90% confidence interval with 70 degrees of freedom is approximately 1.667.

To find the critical T-value for a 90% confidence interval, we need to determine the degrees of freedom (df) and use a T-table or a T-distribution calculator. Assuming that the sample size is n = 72, the degrees of freedom for a 90% confidence interval would be:

df = n - 1 = 72 - 1 = 71

Using a T-table or a T-distribution calculator, we can find the critical T-value for a two-tailed test at a 90% confidence level with 71 degrees of freedom. The result is approximately 1.667. Therefore, the critical T-value for this 90% confidence interval is 1.667.

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Answer:

Area of DEABC = 30100 m²

Step-by-step explanation:

Area of the given composite figure will be the sum of areas of 5 different figures.

Area of figure (1) = Area of right triangle ΔEGD

                           = \(\frac{1}{2}(EG)(GD)\)

                           = \(\frac{1}{2}(120)(100+80)\)

                           = \(60\times 180\)

                           = 10800 m²

Area of figure (2) = Area right triangle AGE

                            = \(\frac{1}{2}(EG)(AG)\)

                            = \(\frac{1}{2}(120)(30+50)\)

                            = 60 × 80

                            = 4800 m²

Area of figure (3) = area of triangle AHB

                            = \(\frac{1}{2}(AH)(HB)\)

                            = \(\frac{1}{2}(50)(50)\)

                            = 1250 m²

Area of figure (4) = Area of trapezoid BCFH

                             = \(\frac{1}{2}(b_1+b_2)h\)

                             = \(\frac{1}{2}(HB+FC)(HF)\)

                             = \(\frac{1}{2}(50+100)(30+80)\)

                             = \(\frac{1}{2}(150)(110)\)

                             = 8250 m²

Area of figure (5) = Area of right ΔDFC

                             = \(\frac{1}{2}(DF)(FC)\)

                             = \(\frac{1}{2}(100)(100)\)

                             = 5000 m²

Therefore, area of composite figure = Area of (1) + Area of (2) + Area of (3) + Area of (4) + Area of (5)

= 10800 + 4800 + 1250 + 8250 + 5000

= 30100 m²

Answer:

7.49

Step-by-step explanation:

Well first you have to find how much the bike lock cost.

8.75 x 0.2

1.75 = how much 20% of 8.75 is

8.75-1.75

7 = the cost of the bike lock with the 20% markdown

Now you have to find the sales tax.

7 x 0.07

0.49

7 + 0.49

7.49 = total cost with all the stuff

Hopefully this was helpful. There is a shorter method too tho.

Answer:

y=-3.6+3x

Step-by-step explanation:

The solution of the following equation is y = 15.

The equation is -2y + 17 = -13.

The goal is to isolate y on one side of the equation and solve for it.

We'll go through the steps to achieve this.

Step 1: Move the constant to the right side of the equation by subtracting 17 from both sides of the equation.

We get: -2y = -30

Step 2: To isolate y, we have to get rid of the coefficient -2 on it by dividing both sides of the equation by -2.

So we have: y = -30/-2.

Step 3: Simplifying the right side of the equation, we get y = 15.

The answer is y = 15.

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Step-by-step explanation:

S°R can be seen as exercising the relation R first, and then using the result of R to exercise the relation S.

the x values of R therefore drive the composition :

1, 2, 3

let's start with x = 1.

when x = 1, then R gives us the possible y values of 2 and 3.

that means we can go with x = 2 and x = 3 into S.

x = 2 gives us y = 1 in S.

x = 3 gives us y = 1 or 2 in S.

therefore S°R(x = 1) = {(1, 1), (1, 2)}

when x = 2, then R gives us the possible y values of 3 and 4.

that means we can go with x = 3 and x = 4 into S.

x = 4 gives us y = 2 in S.

x = 3 gives us y = 1 or 2 in S.

S°R(x = 2) = {(2, 1), (2, 2)}

when x = 3, then R gives us the possible y value of 1.

that means we can go with x = 1 into S.

x = 1 gives us y = nothing in S.

S°R(x = 3) = {}

S°R in general is then the union of all 3 sets :

{(1, 1), (1, 2), (2, 1), (2, 2)}

The solution is: 1) rate = 80 km/h and, 2.) rate = 15 km/h.

Here, we have,

given that,

1.) distance = 280 km

   time = 3.5 hours.

2.) distance = 7.5 km

   time = 30 mints.

now, we have to find the rate i.e. speed.

we know that,

Speed = Distance/ Time.

so, we get,

1.) distance = 280 km

   time = 3.5 hours.

so, rate = 280/3.5 = 80 km/h

2.) distance = 7.5 km

   time = 30 mints. = 1/2 hours

so, rate = 7.5/ 1/2 = 15 km/h

Hence, The solution is: 1) rate = 80 km/h and, 2.) rate = 15 km/h.

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The yield to maturity of a ten-year, $1000 bond with a 5.2% coupon rate and semi-annual coupons, if the =bond is currently trading for a price of $884, is 6.23%. Thus, option a and option b is correct

Yield to maturity (YTM) is the anticipated overall return on a bond if it is held until maturity, considering all interest payments. To calculate YTM, you need to know the bond's price, coupon rate, face value, and the number of years until maturity.

The formula for calculating YTM is as follows:

YTM = (C + (F-P)/n) / ((F+P)/2) x 100

Where:

C = Interest payment

F = Face value

P = Market price

n = Number of coupon payments

Given that the bond has a coupon rate of 5.2%, a face value of $1000, a maturity of ten years, semi-annual coupon payments, and is currently trading at a price of $884, we can calculate the yield to maturity.

First, let's calculate the semi-annual coupon payment:

Semi-annual coupon rate = 5.2% / 2 = 2.6%

Face value = $1000

Market price = $884

Number of years remaining until maturity = 10 years

Number of semi-annual coupon payments = 2 x 10 = 20

Semi-annual coupon payment = Semi-annual coupon rate x Face value

Semi-annual coupon payment = 2.6% x $1000 = $26

Now, we can calculate the yield to maturity using the formula:

YTM = (C + (F-P)/n) / ((F+P)/2) x 100

YTM = (2 x $26 + ($1000-$884)/20) / (($1000+$884)/2) x 100

YTM = 6.23%

Therefore, If a ten-year, $1000 bond with a 5.2% coupon rate and semi-annual coupons is now selling at $884, the yield to maturity is 6.23%.

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