A rocket is launched in the air. Its height in feet is given by h= -16t^2+112th=−16t 2 +112t where tt represents the time in seconds after launch. How many seconds have gone by when the rocket is at its highest point?

Answer:

To solve this problem, we can use the Pythagorean Theorem to solve for a.

For part (a), we know that P(2, 3) and Q(a, -1) are 4 units apart, so we can use the Pythagorean Theorem to calculate a:

(a - 2)² + (-1 - 3)² = 4²

Solving for a, we get:

a = 7

For part (b), we know that P(-1, 1) and Q(a, -2) are 5 units apart, so we can use the Pythagorean Theorem to calculate a:

(a + 1)² + (-2 - 1)² = 5²

Solving for a, we get:

a = 4

For part (c), we know that X(a, a) is √√8 units from the origin, so we can use the Pythagorean Theorem to calculate a:

a² + a² = 8

Solving for a, we get:

a = 2√2

For part (d), we know that A(0, a) is equidistant from P(3, -3) and Q(-2, 2), so we can use the Pythagorean Theorem to calculate a:

(3 - 0)² + (-3 - a)² = (-2 - 0)² + (2 - a)²

Solving for a, we get:

a = -1

Therefore, the value of a that satisfies all conditions is a = -1.

The solution of the given system of equation are  x = 9 and y = 2.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We are given that the system of equation as;

3x-2y=23

X-3y=3

x = 3 + 3y

Now using substitution method, we get;

3x-2y=23

3(3 + 3y)-2y=23

9 + 9y - 2y = 23

7y = 23 - 9

7y = 14

y = 2

So, x = 3 + 3(2) = 9

Therefore, the solution are x = 9 and y = 2.

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The equations are,

A: y = 3x and y = 2x + 7,

B: T = -2t and  T = 4t.

When a linear equation is graphed, it always produces a straight line since each term in the equation has an exponent of 1. It is called a "linear equation" for this reason.

Both linear equations with one variable and those with two variables exist.

Given,

A:  Jamal is three times as old as Maria. In seven years, he will be twice as old as she will be,

Let age of Maria be x and Jamal age be y,

acc. to condition

y = 3x

and after 7 years,

jamal age = y + 7

Maria age = x + 7

equation,

y + 7 = 2(x + 7)

y + 7 = 2x + 14

y = 2x + 7

B: One day, the temperature in one city drops at a constant rate from 2 °C to -6 °C in 4 h. Meanwhile in another city, the temperature rises at a constant rate from -8 °C to 4 °C in 3 h.

let Temperature be T and time be t

for city 1,

temp. drop at constant rate,  from 2 °C to -6 °C in 4 h

temp. drop = -8° in 4 hour

temp. drop in 1 hour = -8/4 = -2°C

equation is  T = -2t

where T is temperature and t is time,

for city 2,

temp. rise at constant rate, from -8° to 4° C in 3 hour

temp. rise = 12° in 3 hour

temp. rise in 1 hour = 12/3 = 4°C

equation is T = 4t

Hence the  equations for given condition are,

A: y = 3x and y = 2x + 7

B: T = -2t and  T = 4t.

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Answer:

To find P(E' U T), we need to find the probability that a randomly selected person from Ahmed's friends either only texted or did both.

To find P(En T'), we need to find the probability that a randomly selected person from Ahmed's friends neither texted nor emailed.

To solve these problems, we need to know more information about Ahmed's friends, such as how many of them texted, emailed, or did both. Without this information, it is not possible to find P(E' U T) or P(En T').

is it right?

Answer:

689.6

Step-by-step explanation:

Let's say n is the number of numbers being added (n=8).

The average of the sum of n numbers is sum/n.

For example, let's say the numbers are 4, 5, and 6.

There are 3 numbers: 4, 5, and 6

4 + 5 + 6 = 15 ==> the sum of the numbers.

15/3 = 5 ==> 5 is the average of the numbers

5 * 3 = 15

Now back to the problem:

Since the average is 86.2, multiply that with the total number of numbers    (which is 8) to get the total sum of all numbers:

86.2 * 8 = 689.6

Hence, the answer is 689.6.

Answer:

16

Step-by-step explanation:

6 = [tex]\sqrt{w}[/tex] + 4/2

[tex]\sqrt{w}[/tex] = 6 - 4/2 = 6-2 = 4

([tex]\sqrt{w}[/tex])² = 4²

w = 16

**the square root of any number squared is the number

Answer:

32[tex]q^{5}[/tex]

Step-by-step explanation:

2q × 2q × 2q× 2q × 2q

= 2 × 2 × 2 × 2 × 2 × q × q × q × q × q × q

= 32 × [tex]q^{5}[/tex]

= 32[tex]q^{5}[/tex]

a) The equation that you can use to find out how many times Carlos stirred the batter is given as follows: 3y + y = 100.

b) The number of times that Carlos hit the batter is given as follows: 25 times.

The number of times is obtained via a system of equations, for which the variables are given as follows:

They stirred the batter 100 times in total, hence:

x + y = 100.

Elena stirred three times as many times as Carlos, hence:

x = 3y.

Hence the equation to obtain how many times Carlos hit the batter is given as follows:

3y + y = 100.

4y = 100

y = 100/4

y = 25 times.

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The order is 5 (first term), 35 (second term), and 245 (third term), according to the equation get the next term by multiplying the previous term by 7 (first term).

A collection of numbers, or "terms," is referred to as a sequence. Examples of terms include 2, 5, and 8. Some sequences can be made endlessly long by taking advantage of a particular pattern they follow. Use the example of 2,5,8 and add 3 to continue the series. There are formulas that demonstrate where to look for words within a sequence. A collection of objects that are in some order is known as a sequence in mathematics (or events). It resembles a set in that it has pieces (also called elements or terms). The total, perhaps infinite number of ordered objects are referred to as the sequence's length. the act of placing two or more objects in a logical order

given

first term = 5

third term = 35 * 7 = 245

the sequence is  5 , 35 , 245 ........

so an = a(n-1) * 7

The order is 5 (first term), 35 (second term), and 245 (third term), according to the equation get the next term by multiplying the previous term by 7 (first term).

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According to the table, each point does not give the same number of tickets.

The predicted number of tickets for getting 10 points is 60 tickets.

Proportional relationships are relationships between two variables where their ratios are equivalent.

A proportional relationship is one in which two quantities vary directly with each other. Therefore, proportional relationship can be re[presented as follows:

y = kx

where

Therefore, the two variables in the this table are the tickets and points.  If they have a constant ratio, then each points appear to give the same number of tickets.

Therefore,

28 = 4k

k = 28 / 4 = 7

48 = 8k

k = 48 / 8

k = 6

54 = 9k

k = 54 / 9

k = 6

Therefore, each points does not give the same number of tickets.

The predicted number of ticket for getting 10 points is 10(6) b= 60 tickets.

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The proof of how a hexagon made of 6 equilateral triangles is explained below .

What is a Regular Hexagon ?

A hexagon is figure that is two dimensional and closed and made up of six equal line segments .

We know that the equilateral triangle is a regular polygon that 3 equal sides where each angle is 60° .

We also know that ; sum of interior angles of a hexagon is 720 degree .

So , each interior angle of a hexagon is =  120°

because  [tex]\frac{720}{6}[/tex] = 120 degree .

When the lines are connected by using the two opposite vertices, then the internal angles are bisected, and each angle is 60° in measure.

In hexagon , the angle at center is 360° which is being divided into 6 equal parts.

So , the value of each angle at center of hexagon is equal to 60°.

We see that all 3 angles of six triangles formed in given hexagon are equal to 60°.

Therefore , a hexagon made of 6 equilateral triangles .

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Answer:

Step-by-step explanation:

Use the distance formula of coordinate geometry.

Mark all the coordinates.

(-5, 5) , (-1, 7) , (4, -3) , (0, -5)

We need to find the length and width of the rectangle.

Lets pick, (4, -3) and (0, -5).

Distance formula,

√((x₁ - x₂)² + (y₁ - y₂)²)

or, √((4 + 0)² + (-3 + 5)² = √20 = 2√5 (width)

Again, we can take (-5, 5) and (0, -5)

√(25 + 100) = √125 = 5√5 (length)

Area of rectangle is length x width or 2√5 x 5√5 = 10 x 5 = 50 units²

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The function is y=3x-16 and the rate of change is 3 when a  table of values that models a linear function.

Given that,

We have a table of values that models a linear function.

We have to find the rate of change of the function.

We know that,

x     |       y

-3   |      -25

1     |     -13

3    |      -7

8    |      8
So,

The equation of the function is

y=mx+b

Taking two points

(1,-13) and (3,-7)

m = -7+13/3-1 = 6/2 = 3

Now,

-7= 3(3)+b

b=-7-9

b= -16

So, y= 3x-16

Therefore, The function is y=3x-16 and the rate of change is 3 when a  table of values that models a linear function.

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Answer:

2x^2+4x-5

Step-by-step explanation:

The expression equivalent to the given expression is [tex]-5 \frac{1}{4}x - \frac{1}{2}[/tex], hence the correct option is D.

What is mixed fraction?

A mixed fraction is one that is represented by both its quotient and remainder.

To covert a fraction into mixed fraction:

By denominator, divide the numerator. Take the quotient as a whole number and use the remaining amount as the proper fraction's numerator while maintaining the original denominator.

In the given expression solve the brackets and seperate the like terms as follows:

[tex]-\frac{1}{2}(-\frac{3}{2}x + 6x + 1 ) - 3x\\ \\\frac{3}{4}x - 3x - \frac{1}{2} - 3x\\ \\ \frac{3}{4}x - 6x - \frac{1}{2}\\\\-\frac{21}{4}x - \frac{1}{2}[/tex]

Convert the fraction into mixed fraction by dividing the numerator and denominator:

[tex]-\frac{21}{4}x - \frac{1}{2} \\ \\-5 \frac{1}{4}x - \frac{1}{2}[/tex]

Hence, the expression equivalent to the given expression is option D.

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The solution to the expression 8 * 3 / (4² - 13) + 5² + 4 * 3 is 45.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the equation:

8 * 3 / (4² - 13) + 5² + 4 * 3

To solve this question we use PEDMAS. That is parenthesis, then exponents, division, multiplication, addition and subtraction.

First solving the exponents to get:

= 8 * 3 / (16 - 13) + 25 + 4 * 3

Then solving the bracket:

= 8 * 3 / 3 + 25 + 4 * 3

Performing the division:

= 8 * 1 + 25 + 4 * 3

Performing the multiplication:

= 8 + 25 + 12

Performing the addition:

= 45

The solution to the expression is 45.

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Answer:

Slope= -9/0

Step-by-step explanation:

Slope= y2-y1/x2-x1

(-6,5) (-6, -4)

-4= y2

5= y1

-6= x2

-6= x1

-4-5/-6-(-6)= -9/0

The amount of green beans that CJ bought at the market, given the amount of potatoes he bought, is 3. 75 pounds of green beans.

The amount of green beans that CJ bought, is related to the amount of potatoes that CJ bought in the market such that CJ bought 2. 5 times as many green beans as pounds of potatoes.

This means that the amount of green beans that CJ bought was :

= pounds of potatoes bought x number of times more green beans bought

= 1. 5 x 2 . 5

= 3 .75 pounds of green beans

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The volume of the right circular cylinder is 126π m³.

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface.

Let's find the volume of the cylinder with a diameter of 6 meters and a height of 14 meters.

Therefore,

volume of a cylinder = πr²h

where

Therefore,

r = 6  /2= 3 meters

h = 14 metres

Hence,

volume of a cylinder = π × 3² × 14

volume of a cylinder = π × 9 × 14

volume of a cylinder = 126π m³

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We can apply a vertical line test to determine whether or not a graphical plot or drawing is a function.

Choose the output values. You should classify a connection as a function if each input value results in only one output value. Don't categorise the relationship as a function if any input value results in two or more outputs. However, a relation is not always a function and vice versa. An association between a student's roll number and their math test scores, for instance, can be made.

This allows us to have pairs like (A, B), (C, D), etc. Although there is a relationship, there may not be one. Functions need that the output be the same for the same input, and this is true. However, this is not a must for a relationship. Since two different students with two different Roll numbers could receive the same grades. Relations That Do Not Function.

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This answer provides number of instructions on how to create a new workbook using the Monthly Attendance Report template in Microsoft Excel.

1. Open Microsoft Excel.

2. Click the File tab at the top of the window.

3. Select “New” from the menu.

4. Select “Templates” from the list of options.

5. Type “Monthly Attendance Report” into the search box.

6. Select the Monthly Attendance Report template from the list of search results.

7. Click “Create” to create a new workbook using the template.

This answer provides number of instructions on how to create a new workbook using the Monthly Attendance Report template in Microsoft Excel.

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Answer:

14

Step-by-step explanation:

If 8 bucketfuls of the green one is used, that makes it 28 gallons (3.5×8)

It's asking you how many bucketfuls you need to obtain the same aount of water. And the amount of water is 28 gallons. So how will you know how many bucketfuls of the orange you need to obtain 28 gallons? Just maths

For orange:

2 gallon = 1 bucketful

1 gallon = ½ bucketful

28 gallons = 14 bucketful (28×½ which also equals 28÷2)

Tori's loss from the stock will be $28.29 and her rate of return will be -84.75%.

While a high share price discourages trading in the company's stock, it advertises its stellar performance to existing and potential investors.

A high share price also discourages corporate takeovers, assuring the jobs of senior management. Existing investors can realize some quick gains by selling their shares at high profits.

Since Tori bought one share of Macy's stock on Nov 1, 2016, for $33.38 and she sold it and the closing price for that day was $5.09, her loss will be;

= $5.09 - $33.38

= -$28.29

Her rate of return will be:

= -28.29/33.38 × 100

= -84.75%

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The probability of drawing 2 defective chips out of a lot of 100 semiconductor chips is 19/495.

Let us define the events first.

A1 = first selected chip is defective

A2 = second selective chip is defective.

Now, there are 100 semiconductor chips, out of which 20 are defective.

The probability of selecting and drawing one defective chip out of 100

[tex]= \frac{20}{100} = \frac{1}{5}[/tex]

The probability of drawing a second chip that is defective:

[tex]= \frac{19}{99}[/tex]

The probability of drawing 2 chips that are defective is:

[tex]\frac{1}{5} * \frac{19}{99} = \frac{19}{495}[/tex]

Thus, the probability of drawing 2 defective chips out of a lot of 100 semiconductor chips is 19/495.

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Rate of Change: $25 per banner.

Rate of change is the measure of how quickly one quantity changes in relation to another. It is the ratio of the change in one quantity to the change in another quantity over a specified time period. It is commonly used in mathematics, physics, economics, and other disciplines to measure the rate at which a process is occurring. Rate of change is also known as velocity, derivative, or slope.

Number of Banners  Set-up Fee  Cost Per Banner  Total Cost

1  $150.00  $25.00  $175.00
2  $150.00  $50.00  $250.00
3  $150.00  $75.00  $325.00
4  $150.00  $100.00  $400.00

Rate of Change: $25 per banner.

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According to the line plot, the measurement by Joseph of he difference between the longest and shortest lengths is 2 1/2 feet is correct

The correct measurement is gotten from the information from the line plot  

The two extremes that is the longest and the shortest lengths from the line plot are 12 and 9 1/2 respectively

comparing the distance between the two distances, using subtraction oration we have

= the longest length -  the shortest length

= 12 - 9 1/2

= 2 1/2

The distance between the longest and the shortest length is solved to be 2 /1/2 hence Joseph is correct

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The length of the triangle side CD is equal to 12.7 approximately to 3 significant figure using the trigonometric ratio of sine for the angle 55°

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

According to Pythagoras rule, considering the right triangle ABC;

CB² + 6² = 12²

CB² + 36 = 144

CB² = 144 - 36 {collect like terms}

CB² = 108

CB = √108 {take square root of both sides}

sin 55° = √108/CD {opposite/hypotenuse}

CD = √108/sin 55° {cross multiply}

CD = 12.6866

Therefore, the length of CD approximately to 3 significant figure is 12.7 using the trigonometric ratio of sine for the angle 55°.

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The following is one of the requirements for using a one-way, between-subjects Anova is the data must be measured on a continuous scale.

One of the requirements for using a one-way, between-subjects ANOVA is that the data must be measured on a continuous scale. This means that the variable being measured (such as time, weight, or temperature) should be able to take on any value within a certain range.

Another requirement for using a one-way, between-subjects ANOVA is that the data must be independent. This means that the observations for each group should not be related to one another in any way. For example, if the groups being compared are different treatment groups in a medical study, it would not be appropriate to use a one-way, between-subjects ANOVA if the patients in each group were related to one another (such as siblings or close friends).

The third requirement is that the data should be approximately normally distributed in each group. A normal distribution is a probability distribution that has a bell shape, which means that the data is symmetric and the mean, median, and mode are equal. The ANOVA assumes that the data is normally distributed and if the data is not normally distributed, the results may be unreliable. This requirement can be checked by using normality test such as Shapiro-Wilk test.

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Answer:

6.45kg

Step-by-step explanation:

there are 1000g in one kilogram

250g/1000g=0.25kg

4.2kg+2.25kg=6.45kg

Answer:

6.45kg

Step-by-step explanation:

First, let us convert all the values into grams.

Weight of a watermelon ⇒ 4.2 kg

Multiply by 1000 to convert it to grams.

Weight of a watermelon ⇒ 4200 g

Weight of a pumpkin ⇒ 2kg 250g

First, multiply 2kg by 1000 to convert it to grams and add it to 250 grams.

Weight of a pumpkin

⇒ ( 2 × 1000 ) + 250

⇒ 2000 + 250

⇒ 2250 g

Total Weight  :

To get the total weight, add the weights of the watermelon and pumpkin in grams.

Total weight ⇒ 4200g + 2250g

                     ⇒ 6450g

Now to convert the answer into kilograms, divide the answer by 1000.

⇒ 6450/1000 = 6.45kg

V(t) = 30 * e^(-0.012t) is the value of the car after t years.

The value of the car 2 years from now will be approximately $29,300.

Let's call the original value of the car V0, and the decay factor k. The exponential model representing the value of the car after t years is given by:

V(t) = V0 * e^(-kt)

To find the value of the car after 3 years, we can plug in t=3 into the equation:

V(3) = V0 * e^(-k*3) = 18

We can rearrange the equation to solve for the decay factor k:

k = -ln(V(3)/V0)/3

Plugging in the known values, we get:

k = -ln(18/V0)/3

Since the value of the car has decreased by 40%, V0 = 18 / (1 - 0.4) = 30. Therefore, k = -ln(18/30)/3 = -0.012.

Therefore, the exponential model representing the value of the car after t years is:

V(t) = 30 * e^(-0.012t)

V(2) = 30 * e^(-0.012*2) = 30 * e^(-0.024) = 30 * 0.977 = 29.3

This model represents the value of the car in thousands of dollars.

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According to the decreasing exponential value, the exponential function for the given situation is written as [tex]E(t) = 30 \times e^{-0.012t}[/tex] and the value of the car 2 years from now will be approximately $29,300.

Here we have given that  a new xar 3 years ago. Its value has decreased exponentially by 40 percent since I got it and it's now worth $18,000

Here let us consider that the original value of the car E0, and the decay factor k.

Then the exponential model representing the value of the car after t years is written as

=> [tex]E(t) = E0 \times e^{-kt}[/tex]

Here we need to find the value of the car after 3 years, then we have to  plug in t=3 into the equation, then we get,

[tex]E(3) = E0 \times e^{-k\times3}= 18[/tex]

Now, we have to rearrange the equation to solve for the decay factor k, then we get the value as,

=> k = [-ln(E(3)/E0)]/3

Now, we have to put the values on the equation then we get

=> k = [-ln(18/V0)]/3

Here we know that the value of the car has decreased by 40%,

Therefore, it can be written as,

=> E0 = 18 / (1 - 0.4) = 30.

Therefore, the value of

=> k = -ln(18/30)/3 = -0.012.

Now the exponential model representing the value of the car after t years is calculated as

[tex]E(t) = 30 \times e^{-0.012t}[/tex]

Apply the value of t as 2, then we get the value of E(T) as,

=> [tex]E(t) = 30 \times e^{-0.012\times 2}[/tex]

=> E(T) = 29.2

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