The trajectory of a golf ball hit from a tee on the ground at an angle of 40 degrees with an initial speed of 50 meters per second can be modeled by the parabola f(x) = 0.84x − 0.0033x^2, where the x-axis is the ground. Find the height of the highest point of the trajectory and the horizontal distance the golf ball travels before hitting the ground.

Answer: 3.5

Step-by-step explanation: i got it right on the quiz

b. f(x) = x + 5, which represents a vertical shift of 5 units upwards.  f(x-a) = (x-a)^2, where a is a constant.

9) The function f(x) = x represents a linear function with a slope of 1 and y-intercept of 0. To shift the graph vertically, we need to add or subtract a constant from the function. Thus, the function that represents a vertical shift of f(x) = x would be of the form f(x) = x + b, where b is a constant.

Out of the given options, the correct answer is b. f(x) = x + 5, which represents a vertical shift of 5 units upwards.

10) To shift the graph of f(x) = x^2 horizontally, we need to add or subtract a constant inside the function, affecting the position of the vertex of the parabola. Thus, the function that represents a horizontal shift of f(x) = x^2 would be of the form f(x-a) = (x-a)^2, where a is a constant.

Out of the given options, the correct answer is a. f(x) = (x+2)^2, which represents a horizontal shift of 2 units to the left.

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You have to invest $15,506.08

PV = FV / (1 + r)^n

where:

PV = present value (amount of money you need to invest today)

FV = future value (amount of money you want to have in 5 years, which is $25,000)

r = interest rate (10% or 0.1)

n = number of periods (5 years)

Plugging in the values into the formula:

PV = $25,000 / (1 + 0.1)^5

PV = $25,000 / 1.61051

PV = $15,506.08

Therefore, you need to invest approximately $15,506.08 today at a 10% interest rate in order to have $25,000 in 5 years to purchase a car in cash.

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Answer:

35 pages per minute

Step-by-step explanation:

175/5= 35

Check

35 x 5 = 175

175/35= 5

Answer:

Step-by-step explanation:

1/3 is greater.

Step-by-step explanation:

| Equation | Solution |

| 6+x=15 | x = 9 |

| 9x = 18 | x = 2 |

The table would look like:

| Equation | Solution |

| 6+x=15 | X |

| 9x = 18 | X |

The calculated values of the angle measures when converted to radians are 1.31π rad and 3.34π rad

To convert angles from degrees to radians, we multiply the number of degrees by π/180.

This means that

Angle = Degree measure * π/180

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

Angle 236 = 236 * π/180

Evaluate the products

Angle 236 = 1.31π rad

Next, we repeat the same process for the second angle 601 degrees

Angle 601 = 601 * π/180

Evaluate the products

Angle 601 = 3.34π rad

Hence, the angles are 1.31π rad and 3.34π rad

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Answer:

1

Step-by-step explanation:

7+10+1/5

7/10 = 0.7

1/5 = 0.2

0.7+0.2=0.9

Therefore it would be closest to 1.

Answer: 1

Step-by-step explanation:

To find an estimate, you need to round your fractions. Let's start with 7/10. First let's look at the numerator, 7. 7 is a number greater than 5, so we'll round it to 10 and you keep your denominator. so now we have 10/10, or 1. Then round 1/5. 1/5 is lower than 5, so we'll round it to 0. Now, for the final step add them. 1 + 0 = 1, so 1 is the answer

The probability of choosing a ball numbered 29 is among the 28 balls numbered 1 through 28 is 0

From the question, we are to calculate the probability of choosing a ball numbered 29

From the formula for probability

P(A) = Number of favorable outcomes to A / Total number of possible outcomes

From the given information,

"A lottery game contains 28 balls numbered 1 through 28"

This means there are only 28 balls and they are numbered from 1, 2, 3, up until 28.

Now,

We are to determine the probability of choosing a ball numbered 29. Since there is no ball numbered 29,

Number of favorable outcomes = 0

Total number of possible outcomes = 28

Thus,

Probability of choosing a ball numbered 29 = 0/28

Probability of choosing a ball numbered 29 = 0

Hence,

Probability of choosing a ball numbered 29 is 0

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Answer:

√75 =8.66.

Step-by-step explanation:

The square root of 75 is an irrational number where the numbers after the decimal point go up to infinity. √75 = 8.660.√75 cannot be written in the form of p/q, hence it is an irrational number. irrational with never-ending digits.

Let's see how to find the square root of 75 by the long division method.

Step 1: Express 75 as 75.000000. We take the number in pairs from the right. Take 75 as the dividend.

Step 2: Now find a quotient which is the same as the divisor. Multiply quotient and the divisor and subtract the result from 75.

Step 3: Now double the quotient obtained in step 2. Here is 2 × 8 = 16. 160 becomes the new divisor.

Step 4: Apply decimal after quotient '8' and bring down two zeros. We have 1100 as the dividend now.

Step 5: We need to choose a number that while adding to 160 and multiplying the sum with the same number we get a number less than 1100. 160+ 6 = 166 and 166 × 6 = 996. Subtract 996 from 1100. We get 104

Step 6: Bring down two zeros again and place it after 104, so that it becomes 10400 which is the new dividend. Now multiply the number in the quotient by 2. Here it is 86. We get 172. Have it as 1720. Now find a number at the unit's place of 1720 multiplied by itself gives 10400 or less. We find that  1726  × 6 = = 10356. Find the remainder.

Step 7 : Repeat the process until we get the remainder equal to zero. The square root of 75 up to two places is obtained by the long division method. Thus √75 = 8.66

Answer:

[tex]\large\boxed{\tt No.}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to determine if the equation has a solution given a value.}[/tex]

[tex]\textsf{Since x is given to us, we can use the \underline{Substitution Property of Equality} to evaluate}[/tex]

[tex]\textsf{the equation.}[/tex]

[tex]\large\underline{\textsf{What is the Substitution Property of Equality?}}[/tex]

[tex]\textsf{The Substitution Property of Equality is a Property that allows us to substitute}[/tex]

[tex]\textsf{a known term, or expression for an unknown variable, or some kind of placeholder.}[/tex]

[tex]\textsf{After Substitution, we can prove that the expressions are still equal with this}[/tex]

[tex]\textsf{property.}[/tex]

[tex]\large\underline{\textsf{Solving;}}[/tex]

[tex]\tt \frac{1}{4} x + 3 = " 3 = " 4x+1[/tex]

[tex]\textsf{There's likely a typo in your equation given, hence I will fix it.}[/tex]

[tex]\tt \frac{1}{4} x + 3 = 4x+1[/tex]

[tex]\textsf{Substitute 8 for x in both sides of the equation using our property.}[/tex]

[tex]\underline{\textsf{Use the Substitution Property of Equality;}}[/tex]

[tex]\tt \frac{1}{4} (8) + 3 = 4(8)+1[/tex]

[tex]\underline{\textsf{Follow PEMDAS, multiply first;}}[/tex]

[tex]\tt 2 + 3 = 32+1[/tex]

[tex]\underline{\textsf{Evaluate;}}[/tex]

[tex]\tt 5 \neq 33[/tex]

[tex]\textsf{If the "typo" was the actual equation;}[/tex]

[tex]\tt 5 \neq 3 \neq 33[/tex]

[tex]\large\boxed{\tt No.}[/tex]

Answer:

1, -9

Step-by-step explanation:

xy = -9

x + y = -8    solve this for x and substitute into the 1st equation

x = -8 - y

(-8 - y)y = -9

-y² - 8y + 9 = 0

y² + 8y -9 = 0

Solve for y by factoring:

(y - 1)(y + 9) = 0

y = 1, -9

x(1) = -9

x = -9

x(-9) = -9

x = -9/-9 = 1

The set of coordinates that satisfy the equation are as follows:

(2, 3)

The equation given is as follows:

x - 2y = -1

2x + 3y = 12

Therefore, let's find the set of coordinates that satisfies the equation. Hence,

x - 2y = -1

2x + 3y = 12

multiply equation(i) by 2

Hence,

2x - 4y = -2

2x + 3y = 12

Therefore, subtract the equations

7y = 14

divide both sides of the equation by 7

y = 14 / 7

y = 2

Let's find x as follows

x - 2y = -1

x = -1 + 2(2)

x = -1 + 4

x = 3

Therefore, the solution is (2, 3)

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The new matrix from an elementary row operation to get a 1, in row 1 column 1 will have:

R₁ = [1 -10 2] and R₂ = [-12 7 -13]

Row operations are a set of operations that can be performed on the rows of a matrix in order to transform it into a row equivalent matrix, which has the same solution set as the original matrix.

The row operation R₁ - 6 — R₁ will be carried out as follows:

7 - 6 = 1 {row 1 column 1}

-4 - 6 = 5 {row column 2}

8 - 6 = -8 {row column 3}

Therefore, the resulting matrix from an elementary row operation to get a 1, in row 1 column 1 will have:

R₁ = [1 -10 2] and R₂ = [-12 7 -13]

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Answer:

[tex]100( {1.05}^{5} ) = 127.63[/tex]

[tex]127.63 - 100 = 27.63[/tex]

The closest answer here is B. $25

Answer:

B is the answer of the given above question

Answer:

Option D.   [tex]g(x)=5(0.8)^{x}+2[/tex]

Step-by-step explanation:

Main concepts

Concept 1: identifying horizontal asymptote

Concept 2: assuring decreasing exponential function

Concept 1. identifying horizontal asymptote

Any exponential function of the form [tex]y=a*b^x[/tex] has a horizontal asymptote on the x-axis.  A constant (positive or negative) added to the end of the exponential expression will shift the graph of the exponential function up (if positive) or down (if negative) the number of units equal to the magnitude of the number.  Since the original function f(x) has a "+2" at the end, it has been shifted up 2 units.  Thus, we can eliminate answers A and C from feasible answers since they each shift the exponential function up 3 units, not 2.

Concept 2. assuring decreasing exponential function

Exponential functions of the form [tex]y=a*b^x[/tex] increase or decrease based on the value of "b".

Observe that the graph of the function f(x) is decreasing, and the value of b=0.5.

To ensure that g(x) also decreases, the b-value must be between 0 and 1, which eliminates option B.

Option D is the correct answer because the value of "b" is between 0 and 1 (making the graph of the function a decreasing exponential), and the number added at the end is "+2", causing the horizontal asymptote to be at a height of positive 2.

Answer:

Step-by-step explanation:

[tex]\left \{ {{x+y=0} \atop {-3x+4y=14}} \right.[/tex] ⇔ [tex]\left \{ {{y=-x} \atop {y=\frac{3}{4} x+ \frac{7}{2} }} \right.[/tex]

46. There are 9 complete doses available from the bottle. 47. There are 8 full doses available in the 120 mL bottle.

Although weight and mass are frequently used interchangeably, they have distinct meanings in the study of physics. Weight is a measurement of the force of gravity acting on an item, whereas mass is a measure of the amount of matter that makes up an object. Weight is typically expressed in newtons (N) or pounds, while mass is typically expressed in kilogrammes (kg) (lb). While an object's mass remains constant, its weight can change depending on how strongly gravity is pulling on it.

46. We know that,

1 fluid ounce = 29.5735 mL

4 fluid ounces = 4 x 29.5735 = 118.294 mL

Each dose is 12.5 mL:

118.294 / 12.5 = 9.46

So there are 9 complete doses available from the bottle.

47. Given, 1 tablespoon is equal to 15 mL.

Thus, doses of 15 mL are in a 120 mL bottle:

120 / 15 = 8

So there are 8 full doses available in the 120 mL bottle.

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The percentage increase in the number of water bottles the company manufactured from February to April is 19%.

In March, the company manufactured 7% more water bottles than in February:

Number of water bottles in March = 4,100 + 7% of 4,100

Number of water bottles in March = 4,387

In April, the company manufactured 500 more water bottles than in March:

Number of water bottles in April = 4,387 + 500

Number of water bottles in April = 4,887

To find the percent increase from February to April, we can use the following formula:

percent increase = (new value - old value) / old value x 100%

percent increase = (4,887 - 4,100) / 4,100 * 100%

percent increase = 787 / 4,100 x 100%

percent increase = 19%

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Answer:

Step-by-step explanation:

We can use the formula for continuous compounding to determine how long it will take each account to reach $1,800.

For Michael's account, the formula is:

A = P*e^(rt)

where:

A is the amount in the account after t years

P is the principal

r is the annual interest rate

t is the time in years

Plugging in the values given, we get:

1,800 = 1,000*e^(0.0475t)

Taking the natural logarithm of both sides, we get:

ln(1,800/1,000) = 0.0475t

t = ln(1,800/1,000)/0.0475

t ≈ 8.55 years

So it will take approximately 8.55 years for Michael's account to reach $1,800.

Similarly, for Peter's account, the formula is:

A = P*e^(rt)

where:

A is the amount in the account after t years

P is the principal

r is the annual interest rate

t is the time in years

Plugging in the values given, we get:

1,800 = 1,200*e^(0.0425t)

Taking the natural logarithm of both sides, we get:

ln(1,800/1,200) = 0.0425t

t = ln(1,800/1,200)/0.0425

t ≈ 9.03 years

So it will take approximately 9.03 years for Peter's account to reach $1,800.

Therefore, Michael's account will grow to $1,800 first as it will take less time (8.55 years) compared to Peter's account (9.03 years).

Answer:31.42

Step-by-step explanation:

C=2πr=2·π·5≈31.41593

The rectangular block of wax can make approximately 2 candles.

To calculate the number of candles, we use the formula

V of wax = l x w x h = 10 cm x 9 cm x 20 cm = 1800 cubic cm

V of candle = l x w x h = 9 cm x 9 cm x 12 cm = 972 cubic cm

1800 / 972 = 1.85

The above answer is based on the full question below;

you are melting a rectangular block of wax to make candles. how many candles of the given shape can be made using a block that measures 10 cm by 9cm by 20 cm.

The height of the candle is 12cm and the base width is 9cm

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40(2.25)ˣ function equation is represented by the graph transformation.

What do graph transformations mean?

Changes to the graph of a parent function are referred to as transformations. Transformations may be divided into three categories: translations, reflections, and dilations. There are two types of transformations that may be done to a function: vertical (which affects the y-values) and horizontal.

                               (affects the x-values). The following guidelines apply to the function translation and transformation: The function is moved up b units by f (x) + b. The function is moved downward by the notation f (x) b. The function is moved left by the value of f (x + b).

Let the function be of the form

  f(X ) = a(b)ˣ

Then the point (0,40) lies on the graph of this function. This point must satisfy the equation of the function.

We substitute the point to get,

  40 = a(b)⁰

This implies that,

   40 = a(1)

    40 = a

We substitute a=40 into the function equation to get,

         f(x) = 40(b)ˣ

The point (1,90) also lies on the graph of the function. This gives us,

       90 = 40(b)¹

       90 = 40b

      b = 90/40

       b = 2.25

We substitute the value of b also into function to get,

    f(X) = 40(2.25)ˣ

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Hence, 8 and 14 are the two positive integers as Y must be 8 because we are seeking for positive integers.

All entire numbers (optimistic, negative, and zero) as well as their opposites are included in the category of integers. These can be visualised as evenly spaced-apart points with zero in the middle on a number line. The following numbers are part of the set of integers, which is represented by the symbol Z . The numbers of pupils in an educational setting, the weather in degrees Celsius, or the location of an object in relation to a reference point are all examples of quantities that can be represented by integers and are counted or measured in whole units. They adhere to specific arithmetic laws and can be added, deducted, multiplied, and divided.

given

Assume that x and y are the two positive integers, with x being the greater of the two. Finally, we may convert the provided data into equations:

In order to remove x, we can replace the first equation with the second equation as follows:

[tex](2y-2)^2 + y^2 = 260[/tex]

Adding and subtracting:

[tex]4y^2 - 8y + 4 + y^2 = 260[/tex]

combining comparable phrases

[tex]5y^2 - 8y - 256 = 0[/tex]

Using the quadratic formula, we can solve this quadratic equation:

y = [8 ± sqrt(8^2 - 45(-256))] / (2*5)

y = [8 ± sqrt(3368)] / 10

y ≈ 8.6 or y ≈ -9.4

Y must be 8 because we are seeking for positive integers. The first equation can then be used to determine x:

x = 2y - 2 = 2(8) - 2 = 14

Hence, 8 and 14 are the two positive integers as Y must be 8 because we are seeking for positive integers.

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The solutions to the rational equations are

The rational equations can be solved as follows

(1)

(x - 2)/(2x + 4) = 1/5

This gives

5x - 10 = 2x + 4

So, we have

3x = 14

x = 14/3

(2)

For equation (2), we have

(x + 3)/2 - x/4 = 4/3

So, we have

[2(x + 3) - x]/4 = 4/3

[x + 6]/4 = 4/3

So, we have

3x + 18 = 16

x = -2/3

(3)

For equation (3), we have

3/(x + 1) - 2/(x - 1) = 1/(x² - 1)

So, we have

3(x - 1) - 2(x + 1) = 1

This gives

3x - 3 - 2x - 2 = 1

x = 4

(4)

For equation (4), we have

18/(x² - 3x) = 2x/(x - 3) - 6/x

So, we have

18 = 2x² - 6(x - 3)

This gives

x = 0 or x = 3

(5)

For equation (5), we have

3x/(x + 2) + 6/x + 4 = 12/(x² + 2x)

Multiiply through by x² + 2x

3x² + 6(x + 2) + 4(x² + 2x) = 12

Evaluate

x = 0 or x = -2

(6)

For equation (6), we have

1/(x - 2) + 4/(x + 9) = 3/(x² + 7x - 18)

Multiiply through by (x² + 7x - 18)

x - 9 + 4x + 8 = 3

So, we have

5x = 4

Evaluate

x = 4/5

(7)

For equation (7), we have

3/5x² - 1/5 = 2/25x²

Multiiply through by 25x²

15 - 5x² = 2

So, we have

5x² = 17

Evaluate

x = √(17/5)

(8)

For equation (8), we have

9/(x + 1) = 2/(x² - 1)

Multiiply through by 25x²

9x - 9 = 2

So, we have

9x = 11

Evaluate

x = 11/9

(9)

For equation (9), we have

3/(x³ - 8) = 1/(x - 2)

Cross multiiply

(x³ - 8) = 3(x - 2)

Evaluate

x = -1 and x = 2

(10)

For equation (10), we have

x²/2 - 3x/2 + 1 = 0

Multiiply through by 2

x² - 3x + 2 = 0

Factoize

(x - 1)(x - 2) = 0

So, we have

x = 1 and x = 2

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A conclusion on the null hypothesis is C. Reject H_{0} because the P-value is less than or equal to a.

Stated in the initial description is the null hypothesis, establishing that adults who possess a desire to eliminate all personal information available online would equate to or exceed 53%, while the alternative conjecture rests on this percentage being under 53%.

The statistical significance level at hand designated as alpha equals 0.05 indicates that a P-Value having less than or equal value of 0.05 is necessary for declining the null hypothesis. As provided by the task's question, the computed P-value registers a score of 0.0059 which falls below the established significance level of 0.50 and thus resulting in null hypothesis rejection.

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The probability of picking a senator from at least one out of Georgia, South Carolina, or Florida is equal to 3/50 or 0.06.

Determining the probability of selecting a senator from either Georgia, South Carolina, or Florida is merely a summation of the individual probabilities of drawing one from each state.

There are 100 senators in all and two representatives from each region, thus resulting in an addition of 2 x 50 which equals to 100 senators altogether.

Subsequently, selecting a senator from Georgia has a chance of 1/50,

1/50 + 1/50 + 1/50 = 3/50

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Answer:

To answer these, we can use the standard normal distribution & z-scores. A z-score represents the number of standard deviations a value is from the mean. The formula to calculate a z-score is: z = (x - μ) / σ, where x is the value, μ is the mean and σ is the standard deviation.

A) To find the proportion of pregnancies that last more than 278 days, we first calculate the z-score for 278 days: z = (278 - 272) / 12 = 0.5. Using a standard normal distribution table, we find that the proportion of values above a z-score of 0.5 is approximately 0.3085. So, about 30.85% of pregnancies last more than 278 days.

B) To find the proportion of pregnancies that last between 257 and 275 days, we first calculate the z-scores for both values: z1 = (257 - 272) / 12 = -1.25 and z2 = (275 - 272) / 12 = 0.25. Using a standard normal distribution table, we find that the proportion of values between z-scores of -1.25 and 0.25 is approximately 0.3944. So, about 39.44% of pregnancies last between 257 and 275 days.

C) To find the probability that a randomly selected pregnancy lasts no more than 266 days, we first calculate the z-score for 266 days: z = (266 - 272) / 12 = -0.5. Using a standard normal distribution table, we find that the proportion of values below a z-score of -0.5 is approximately 0.3085. So, there is about a 30.85% chance that a randomly selected pregnancy lasts no more than 266 days.

D) To determine if very preterm babies are unusual, we first calculate the z-score for 242 days: z = (242 - 272) / 12 = -2.5. Using a standard normal distribution table, we find that the proportion of values below a z-score of -2.5 is approximately 0.0062. Since this value is less than 0.05, we can conclude that very preterm babies are unusual.