A ball is thrown directly upward from a height of 5 ft with an initial velocity of 24 ​ft/sec. The function ​s(t)=−16t2+24t+5 gives the height of the​ ball, in​ feet, t seconds after it has been thrown. Determine the time at which the ball reaches its maximum height and find the maximum height.

Answer:

Y= -1/9x-9 that's the answer, you're welcome

The equation of line which is perpendicular to the line q is given by

y = ( -1/9 )x - 9

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

The point is P ( 9 , -10 )

Let the equation of line q be  y + 7 = 9 ( x + 4 )

Now , on simplifying the equation , we get

y + 7 = 9x + 36

Subtracting 7 on both sides of the equation , we get

y = 9x + 29

Now , the slope of the equation q is m₁ = 9

Now , since the line r is perpendicular to line q

The product of the slope is -1

So , m₁ x m₂ = -1

Substituting the values in the equation , we get

9 x m₂ = -1

Divide by 9 on both sides of the equation , we get

m₂ = -1/9

So , the slope of the line r m₂ = -1/9

The equation of line is given by y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - ( -10 ) = -1/9 ( x - 9 )

On simplifying the equation , we get

y + 10 = -1/9 ( x - 9 )

y + 10 =  ( -1/9 )x + 1

Subtracting 10 on both sides of the equation , we get

y = ( -1/9 )x - 9

Therefore , the value of A is y = ( -1/9 )x - 9

Hence , the equation of line r is y = ( -1/9 )x - 9

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The probability that two cards will be drawn at random, without replacement, is 13/18.

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.

The probability of an event can be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

In order to better grasp probability, let's look at a straightforward application.

Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.

There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.

According to our answer-

P(at least 1 green) = 1 - P(no green)

P(no green) = draw yellow on both draws

= P(draw yellow on 1st draw) * P( draw yellow on 2nd draw, given draw yellow on 1st draw)

= 5/9 * 4/8 = 20/72 = 5/18

P(at least 1 green) = 1 - 5/18

= 13/18

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The linear functions in this problem are given as follows:

1. y = 1/3x + 3.

2. y = 2.

3. y = 3x - 1.

4. x = 1.

The slope-intercept definition of a linear function is presented as follows:

y = mx + b.

In which the coefficients are given as follows:

For item 1, the points are given as follows:

(-6, 1) and (-3,2).

When x increases by 3, increases by 1, hence the slope is given as follows:

m = 1/3.

Then:

y = 1/3x + b.

When x = -3, y = 2, then the intercept b is calculated as follows:

2 = 1/3(-3) + b

b = 3.

Thus the function is:

y = 1/3x + 3.

Then items 2 and 4 are given as follows:

For item 3, we have an intercept of -1, hence:

y = mx - 1.

When x = 3, y = 8, hence the slope m is calculated as follows:

8 = 3m - 1

3m = 9

m = 3.

Hence the function is:

y = 3x - 1.

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The percentage change in the number of visitors = 42.30%.  

The prior value's increase or reduction is indicated by the percentage change. The percentage increase may be used to calculate how much it has increased if the present value exceeds the previous value.

The percentage decline may be used to calculate how much it has reduced if the current value is smaller than the prior value.

The formula for Percentage change in case of increase is given by

Percentage Increase = ( Increase/Original Number) × 100

Here we have

On Monday a museum had 150 visitors

On Tuesday it had 260 visitors

The number of visitors increased from Monday to Tuesday

= 260 - 150 = 110  

By the given formula percentage of change can be calculated as given below

Percentage Increase = (110/260) × 100

= 42.30%

Therefore,  

The percentage change in the number of visitors = 42.30%.  

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The given statement:

"the sum of a number and 10.7 is at most −3.2"

Is equivalent to the following inequality:

x + 10.7 ≤ -3.2

Here we have the following statement:

"the sum of a number and 10.7 is at most −3.2"

So let's define the variable "x" as "the number", we know that the sum between x and 10.7 is at most -3.2, we can say that the sum is equal to or smaller than -3.2

In that case, the symbol we need to use is: ≤

Then the inequality is:

sum ≤ -3.2

x + 10.7 ≤ -3.2

That is the statement written as an inequality.

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Yes, the point (2,4) is a solution to the system of inequalities in the graph.

How to solve inequalities?

By definition, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

The given parameters include

Points (4,2)

y<2x+3

y≥-4x+1

Solving these inequalities

y<2x+3

Let y<0

0<2x+3

-3<2x

x<-3/2

(-3/2,0)

when x<0

y<2(0)+3

y<3

(0,3)

From equation 2

y≥-4x+1

x≥0

y≥0+1

y≥1

(0,1)

y≥0

0≥-4x+1

x≥-1/4

(-1/4,0)

Using the coordinates to draw the graphs the lines cut each other at points where (4,2)

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The expressions that could represent how much snowfall Delphine had at her house in March will be:

1.4f

f + 0.4f

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

Since Delphine's house had 40 percent more snowfall than in February. Delphine's house had f centimeters of snowfall in February.

The expression will be:

f + (40% × f)

f + 0.4f

= 1.4f

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a) The break-even point under the old situation is 680000.

b) The break-even point under the proposed situation is 806451.

c) Birr sales volume must be obtained under the proposed plan to make as much profit as last year is 1129032.

a) The break-even point under the old situation:

100000 * a - 170000 = 1000000 * 8%

a = 25% (Profit rate)

x.a = 170000

x = 680000

b) The break-even point under the proposed situation:

1250000 * b - 170000 -30000 = 80000 + 30000

b = 24.8%

x.b = 20000

x = 806451

c) Birr sales volume must be obtained under the proposed plan to make as much profit as last year :

x.b - 200000 = 80000

x.b = 28000

x = 1129032

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Answer:

375

Step-by-step explanation:

let a garben table cost x

a bench cost x+47

x+x+47=703

2x=703-47

2x=656

x=656÷2=328

bench: 328+47=375

Reciprocal of a = [tex]\frac{1}{a}[/tex]

What is Reciprocal ?

In Mathematics , reciprocal is simply defined as the inverse of a value or a number. If n is a real number, then its reciprocal will be 1/n.

What are real numbers ?

In mathematics, a real number is a quantity that may be represented by an endless number of decimal expansions .

According to the given information

a ≠ 0

a is a real number

By the definition of reciprocal

Reciprocal of a will be the inverse of a = [tex]\frac{1}{a}[/tex]

Reciprocal of a = [tex]\frac{1}{a}[/tex]

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The length of the wrench handle 8.4 inches.

What is length?

Distance is measured in length. Length has the dimension of distance in the International System of Quantities. The majority of measurement systems choose a base unit for length from which all other units are derived. The metre serves as the foundational unit of length in the International System of Units.

f = k/l

35 = k/6        

k = 210

f = 210/l

25 =210/l      

l = 8.4 inches

The length "L" (in inches) of a wrench handle has an inverse relationship with the force "F" (in pounds) required to remove a certain bolt. In the case of a handle that is 6 inches long, 35 pounds of power is required. The length of the wrench handle if the bolt needs to be loosened with 25 pounds of force is 8.4 .

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The law for all large numbers with the central limit-theorem will tell us about how standard deviations doesn't as increase with medians. So b). false is correct.

The Law for all Large Number states that once pattern length has a tendency to infinity, the pattern imply equals to populace imply. The statements aren't contradictory. The Central Limit Theorem inform us that because the pattern length has a tendency to infinity, the of the distribution of pattern method methods the ordinary distribution.

The regulation of huge numbers has a completely vital position in possibility and statistics. It states that in case you repeat an test independently a huge variety of instances and common the result, what you got must be near the predicted value.

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The true proportion of the figure based on the triangle proportionality theorem is Option (A).

What is the basic proportionality theorem?

According to the Basic Proportionality Theorem (BPT), if a line is parallel to a triangle's side that divides the other sides into two separate points, the line will divide those sides proportionately.

Given that TU is parallel to QR, by the proportionality theorem, we get

[tex]\frac{ST}{TQ} = \frac{SU}{UR}[/tex]

or, [tex]\frac{k}{j} = \frac{h}{i}[/tex]

or, [tex]\frac{i}{j} = \frac{h}{k}[/tex]

Ans:  [tex]\frac{i}{j} = \frac{h}{k}[/tex]

Hence, a true proportion of the figure based on the triangle proportionality theorem is (A)  [tex]\frac{i}{j} = \frac{h}{k}[/tex]

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Answer: 16

Step-by-step explanation: 16 people can share the pizzas.

The equation of the quadratic function that models the height of the ball h(t) at time t is h(t) = −3(t − 4)² + 42

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

The above parameters mean that

h(1) = 15

h(7) = 15

h max = 42

This also means that the leading coefficient of the function is negative

So, the possible equations from the options are

h(t) = −2(t − 4)² + 42

h(t) = −3(t − 4)² + 42

Calculate h(1) and h(7)

h(t) = −2(t − 4)² + 42

h(1) = −2(1 − 4)² + 42 = 24

h(7) = −2(7 − 4)² + 42 = 24

h(t) = −3(t − 4)² + 42

h(1) = −3(1 − 4)² + 42 = 15

h(7) = −3(7 − 4)² + 42 = 15

Hence, the function is h(t) = −3(t − 4)² + 42

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Answer: Answer is C

Step-by-step explanation:

I took the test and it gave me credit for this question

what do you mean by &?

if its multiplication than

2 × 1/4 = 0.50 or 1/2

4+ (-2) = 2

so the answer is:

2 = 1/2

false

Answer:

Step-by-step explanation:

i need help on that too

Answer:

96

Step-by-step explanation:

21+75

The average change in the height of the rainwater is 1.25 inches per day

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

The initial height of the rainwater measured = y₁

The value of y₁ = 24.83 inches

The final height of the rainwater measured = y₂

The value of y₂ = 12.08

The change in height = y₁ - y₂

Substituting the values in the equation , we get

The change in height = 6.75

The number of days = 5 2/5 days

The number of days = 27/5 days = 5.4 days

So , the equation will be

The average change in the height of the rainwater = change in height / number of days

Substituting the values in the equation , we get

The average change in the height of the rainwater = 6.75 / 5.4

The average change in the height of the rainwater = 1.25 inches per day

Hence , the average change is 1.25 inches per day

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The statement "Δ ABD = Δ ACB by SSS" is true about the diagram.

The statement "Δ ABD = Δ ACB by SSS" is true about the diagram. SSS stands for Side-Side-Side, which is a congruence postulate stating that if three sides of one triangle are congruent to the corresponding sides of another triangle, then the triangles are congruent. In the given diagram, Δ ABD and Δ ACB are congruent because their corresponding sides AB, BD, and AC are equal in length.

This means that the triangles have the same shape and size, but they may be oriented differently. The SSS congruence allows us to conclude that all corresponding angles and other corresponding sides of the two triangles are also congruent. Therefore, we can say that Δ ABD is congruent to Δ ACB based on the Side-Side-Side congruence.

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The fourth degree Taylor polynomial of f(x) centered at 2 the [tex]T_4(2.4) = 11.0225[/tex].

What is Taylor polynomial?

The Taylor series or Taylor expansion of a function in mathematics is the infinite sum of terms expressed in terms of the function's derivatives at one particular point. The function and the sum of its Taylor series are roughly equal for the majority of common functions at this point.

Given:

[tex]f(x) = e^x[/tex]  centered at 2.

[tex]f(2) = e^2[/tex]

[tex]f'(x) = \frac{d}{dx}e^x = e^x , f'(2) = e^2\\f"(x) = \frac{d^2}{dx}(e^x) = e^x, f"(2) = e^2\\ f^3(x) = \frac{d^3}{dx}(e^x) = e^x, f^3(2) = e^2\\ f^4(x) = \frac{d^4}{dx}(e^x) = e^x, f^4(2) = e^2[/tex]

Therefore,

[tex]T_4(x) = f(2) + \frac{f'(2)(x-2)}{1!} + \frac{f"(2)(x-2)^2}{2!} + \frac{f^3(2)(x-2)^3}{3!} + \frac{f^4(2)(x-2)^4}{4!} \\T_4(x) = e^2 [1 + (x - 2) + \frac{(x-2)^2}{2}+\frac{(x-2)^3}{6}+ \frac{(x-2)^4}{24} \\ T_4(2.4) = e^2[1 + (2.4-2) + \frac{(2.4-2)^2}{2}+ \frac{(2.4-2)^3}{6}+\frac{(2.4-2)^4}{24}]\\ T_4(2.4) = 11.0225[/tex]

Hence, the fourth degree Taylor polynomial of f(x) centered at 2 the [tex]T_4(2.4) = 11.0225[/tex].

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By using the concept of fraction, it can be calculated that

Jamal has the better record

What is a fraction?

Suppose there is a collection of objects and a part of the collection has to be taken. The part which is taken is called fraction. In other words, part of a whole is called fraction.

The upper part of the fraction is called numerator and the lower part of the fraction is called denominator.

This is a word problem on fraction

Portion of free throws Jamal made in the last ten games = [tex]\frac{7}{9}[/tex]

Portion of free throws Brian made in the last ten games = [tex]\frac{5}{8}[/tex]

To compare between [tex]\frac{7}{9}[/tex] and [tex]\frac{5}{8}[/tex]

LCM of 9 and 8 = 72

[tex]\frac{7}{9} = \frac{7 \times 8}{9 \times 8} = \frac{63}{72}[/tex]

[tex]\frac{5}{8} = \frac{5 \times 9}{8 \times 9} = \frac{45}{72}[/tex]

As [tex]\frac{63}{72} > \frac{45}{72},[/tex]

So [tex]\frac{7}{9} > \frac{5}{8}[/tex]

So, Jamal has the better record

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Answer:

Step-by-step explanation:

199/4

The zero's of the polynomial p(x) = x(x² - 9) are -3, 0 and 3.

The zero's of a polynomial p(x) are all the x-values that make the polynomial equal to zero.

In other words, zeros of a polynomial can be defined as the points where the polynomial becomes zero as a whole.

Therefore, let's find the zero's of the polynomial .

p(x) = x(x² - 9)

p(x) = x³ - 9x

0 = x³ - 9x

x³ = 9x

x² = 9

x = √9

Therefore, x = -3 or 3

x  = 0

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Since the lemonade recipe calls for the juice of 5 lemons, 2 cups of water, and 2 tablespoons of honey we can use mathematical operations to make different lemonades with the following recipes:

1) To make more lemonade taste the same as the original, we can use the multiplication operation on the above recipe as follows:

Lemons = 10

Cups of water = 4

Tablespoons of honey = 4

2) To make less lemonade taste the same as the original recipe, we can use the division operation as follows:

Lemons = 2.5

Cups of water = 1

Tablespoons of honey = 1

3) To make lemonade that has a stronger lemon taste than the original recipe, we can use the subtraction operation as follows:

Lemons = 4

Cups of water 1

Tablespoons of honey

4) To make lemonade that has a weaker lemon taste than the original recipe, we can use the addition operation as follows:

Lemons = 6

Cups of water 3

Tablespoons of honey = 3

Lemons = 5

Cups of water = 2

Tablespoons of honey = 2

1) Using the multiplication operation to make more lemonade taste the same as the original:

Lemons = 10 (5 x 2)

Cups of water = 4 (2 x 2)

Tablespoons of honey = 4 (2 x 2)

2) Using the division operation to make less lemonade taste the same as the original recipe:

Lemons = 2.5 (5 ÷ 2)

Cups of water = 1 (2 ÷ 2)

Tablespoons of honey = 1 (2 ÷ 2)

3) Using the subtraction operation to make lemonade that has a stronger lemon taste than the original recipe:

Lemons = 4 (5 - 1)

Cups of water 1 (2 - 1)

Tablespoons of honey = 1 (2 - 1)

4) Using the addition operation to make lemonade that has a weaker lemon taste than the original recipe:

Lemons = 6 (5 + 1)

Cups of water 3 (2 + 1)

Tablespoons of honey = 3 (2 + 1)

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10% of the time, the population mean will go below $1,500 or exceed $2,100.

Given that,

Assume that we have data on the annual spending on apparel of a sample of families. The probability that the population mean will fall below $1,500 or rise over $2,100 is ________% if we are 90% positive that the genuine population mean will be between $1,500 and $2,100.

We have to fill the blank.

We know that,

90% of the time, the real population mean will fall in the range of $1,500 and $2,100.

The genuine population mean will therefore most likely fall between $1,500 and $2,100, with a 90% probability.

So, the probability that it will fall outside of this range (i.e., be either less than $1,500 or beyond $2,100) is 100-90, or 10%.

Therefore, 10% of the time, the population mean will go below $1,500 or exceed $2,100.

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Answer: 3/2

Step-by-step explanation:

3x - 2y = 14

-2y = 14-3x

y = 3/2x-7  divide both sides by -2

The total area of the Sea of Japan and the Southern Ocean is 2.1334 × 10⁷ km². The correct option is the first option 2.1334 × 10⁷ km²

From the question, we are to calculate the total area of the sea and ocean

From the given information,

"The area of the Sea of Japan is 1.007 × 106 km²"

and

"The area of the Southern Ocean is 2.0327 × 107 km²"

Thus,

The total area of the sea and ocean = 1.007 × 10⁶ km² + 2.0327 × 10⁷ km²

The total area of the sea and ocean = 0.1007 × 10⁷ km² + 2.0327 × 10⁷ km²

The total area of the sea and ocean = 2.1334 × 10⁷ km²

Hence, the total area is 2.1334 × 10⁷ km²

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The equation to determine the number of miles, m, you must run per day is B. 5m + 5.6 = 20; m = 2.88

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. An equation is not the same as a mathematical expression. The equal (=) operator is always used to join two mathematical expressions in an equation.

In mathematics, an equation is a relationship between two expressions that is expressed as an equality on either side of the equal to sign. An equation would be 3y = 16, for instance. Equations can be categorized into one of the following three categories depending on their degree:

In this scenario, the person must run a total of 20 miles per week and ran 5.6 miles in the first two days of the week.

Let the number of miles for the remaining 5 days be m.

This will be:

5m + 5.6 = 20;

Solving for m = will give 2.88.

In conclusion, the correct option is B.

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The number of sweets left in the box after giving 35% is 325.

There were 500 sweets in a box and Mrs. Miller has given out 35% as prizes. The number of sweets left in the box can be calculated as follows:

Therefore, the number of sweet left in the box = 500 - 35% of 500

number of sweet left in the box = 500 - 35 / 100 × 500

number of sweet left in the box = 500 - 17500 / 100

number of sweets left in the box = 500 - 175

= 325

Therefore, the number of sweets left in the box will be 325

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