Please Help!!
(use the figure to answer questions 8,9 and 10)

The height ( in feet) of a ball thrown by a child is given by

= −^2 + 6 + 7,

where is the horizontal distance ( in feet) from where the ball is thrown ( see figure).

8. How high is the ball when it leaves the child’s hand? (Justify your answer)

9. What is the maximum height of the ball? ( must show work)

10. How far from the child does the ball strike the ground? ( must show work)

Between the time interval 0 to 1 hour, the greatest average rate of change is 700. Therefore, the option (1) is the correct answer.

The slope or rate of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).

Here,

1) 0 to 1 hour

Consider the coordinate points (0, 0) and (1, 700)

Now, rate = (700-0)/(1-0)

= 700

2) 1 hour to 1.5 hours

Consider the coordinate points (1, 700) and (1.5, 900)

Now, rate = (900-700)/(1.5-1)

= 200/0.5

= 400

3) 2.5 hours to 5 hours

Consider the coordinate points (2.5, 1000) and (5, 1640)

Now, rate = (1640-1000)/(5-2.5)

= 640/2.5

= 256

4) 5 hours to 8 hours

Consider the coordinate points (5, 1640) and (8, 1800)

Now, rate = (1800-1640)/(8-5)

= 160/3

= 53.33

Therefore, the option (1) is the correct answer.

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The statement "F(x) > 0 over the interval (-∞, -4)" is true.

A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is usual to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2. The addition, subtraction, multiplication, and division of functions are discussed in function algebra. We just perform the same operation for individual functions at the same input for every arithmetic operation of two functions at an input.

Here,

For any value of x less than -4, substituting it into the expression f(x) = x² + 4 will result in a positive value since x² is always positive. For example, if x = -5, then f(x) = (-5)² + 4 = 9 + 4 = 13, which is positive.

So, for all values of x that are less than -4, the function f(x) will have a positive value, making the statement "F(x) > 0 over the interval (-∞, -4)" true.

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$615.9 is the spending per person per year on the internet in 2007.

percentage, a relative value indicating hundredth parts of any quantity.

Consumer spending per person per year or the internet was $13.24. t

The spending increased by about 36% per person per year from 1996 to 2002.

36% of 13.24

36/100×13.24

0.36×13.24

4.7664

[tex]A=Pe^{rt}[/tex]

[tex]A=13.24e^{0.34(6)}[/tex]

[tex]A=13.24e^{2.04}[/tex]

A=101.82

Now the total amount is 101.82

From 2002 to 2007, the number of years are 5.

[tex]A=101.82e^{0.36(5)}[/tex]

[tex]A=101.82e^{1.8}[/tex]

A=101.82×6.049

A=615.9

Hence, $615.9 is the spending per person per year on the internet in 2007.

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Answer: Area = 4x^2 + 24x + 32

Step-by-step explanation:

Area = length x width

Length = x + 6 + x + 2 = 2x + 8

Width = x + 4 + x = 2x + 4

area = 2x + 8 * 2x + 4

multiply each term by each term

Area = 4x^2 + 24x + 32

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Answer:

see below

Step-by-step explanation:

90 x, y, z

x pennies =1/2y

y nickels

z quarters = 3 1/2 y

so 1/2y+y+3 1/2 y =90

total 5y =90

y =18

x=9

z = 63

The perimeter of this 19-sided regular polygon is equal to 152 cm.

The side length of this 19-sided regular polygon is equal to 8 cm.

Mathematically, the area of a regular polygon can be calculated by using this formula:

Area = (n × s × a)/2

Where:

Substituting the parameters into the area of a regular polygon formula, we have;

1,816.4 = (19 × s × 23.9)/2

3632.8 = 454.1s

Side length, s = 3632.8/454.1

Side length, s = 8 cm.

In Mathematics, perimeter of a regular polygon can be calculated by using this formula:

Perimeter of regular polygon = number of sides × side length

Perimeter of regular polygon = 19 × 8

Perimeter of regular polygon = 152 cm.

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Complete Question:

Find the perimeter and side length of a 19-sided regular polygon with an apothem of 23.9 cm and an area of 1,816.4 cm.

pr(z < 2.3) is =NORMSDIST(2.3) which equals 0.9893 or a probability of 0.9893 that a standard normal random variable is less than 2.3.

The probability that a standard normal random variable is less than 2.3 can be calculated using the cumulative distribution function (CDF) of the standard normal distribution. This function gives us the probability that a standard normal random variable is less than or equal to a given value.

In Excel, you can use the NORMSDIST function to calculate the CDF of the standard normal distribution. The syntax for this function is:

=NORMSDIST(x)

where x is the value for which you want to calculate the CDF.

In this case, to calculate the probability that a standard normal random variable is less than 2.3, we would use the following formula in Excel:

=NORMSDIST(2.3)

This gives us the result of 0.9893 or a probability of 0.9893 that a standard normal random variable is less than 2.3.

Note: The cumulative distribution function can also be approximated using tables or calculators that have the function built in. The result obtained using these methods may have some slight differences compared to the result obtained using Excel.

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Charlie would consume 30 units of bananas if he chose the bundle that maximized his utility function subject to his budget constraint There for the answer is option A

Charlie's utility function is given by U(A, B) = AB, where A is the number of apples he consumes and B is the number of bananas he consumes. The price of apples is $1, and the price of bananas is $2.

If Charlie's income is $120, he has a budget constraint given by:

1A + 2B = 120

To maximize his utility subject to this budget constraint, Charlie must use his income to purchase the combination of apples and bananas that gives him the greatest value of U(A, B).

The solution to this problem can be found by using the method of Lagrange multipliers. From the budget constraint, we can solve for A in terms of B:

A = 120 - 2B

Substituting this into the utility function, we have:

U(B) = (120 - 2B)B = 120B - 2B^2

To maximize U(B), we must find the value of B that maximizes this expression. Taking the derivative of U(B) with respect to B and setting it equal to zero, we find that:

dU/dB = 120 - 4B = 0

Solving for B, we find that:

B = 30

Thus, if Charlie chose the bundle that maximizes his utility subject to his budget constraint, he would consume 30 units of bananas. The answer is therefore a. 30.

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Answer:

no

Step-by-step explanation:

A: 360 -150 = 210 * (1+7%) = 224.7

B: 360 * 1.07  -150 =385.2 -150 =235.2

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3600\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &18 \end{cases}[/tex]

[tex]A = 3600\left(1+\frac{0.02}{12}\right)^{12\cdot 18}\implies A=3600(\frac{601}{600})^{216} \implies A \approx 5158.44[/tex]

Answer:

50.1

Step-by-step explanation:

let the height = h

so because that angle is 62 so it's supplemental angle in left triangle is 28°

in any triangle, the tangent of an angle is opposite/adjacent

so height/28 = tan28° =0.53

so height = 14.8

in any triangle, the sine of an angle is opposite/hypotenuse

so height / x = sin 38°

so x = 14.8 / sin 38° = 14.8/0.296 =50.1

Answer: don't no

Step-by-step explanation:

If the Car drive 15, 000 miles then gas used is 315 galloons.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

for example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

In 16.8 galloons of gas the Car can travel 400 miles.

So, if they dive about 15,000 miles then the gas in galloons used

= 16.8/400 x 15000

= 2.1 x 150

= 315 galloons.

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F(x) = 4x & g(x) = 3x are the two functions which the (f o g)(x) was equal to "12x".

Legislation, a regulation, or a declaration that demonstrates the relationships between the independent and relationship between the factors (the dependent variable). Functions may be found everywhere in mathematics, and they are essential for building physical connections in the sciences.

The functions f(x) & g(x) are given, and the task is to determine (f o g) (x).

For the following two functions, (f o g)(x) was identical to "12x":

f(x) = 4x and g(x) = 3x.

Proof :

g(x) = 3x

(f o g)(x) = f(x = 3x) = 4(3x) = 12x

(f o g)(x) = 12x

Hence, f(x) = 4x or g(x) = 3x are the 2 type which the (f o g)(x) was equal to 12x.

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The values of p and q are p = 35 and q = 12

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

Intersecting chords in a circle

To solve this question, we make use of the intersecting chords theorem

This is represented as

q/12 = 35/p

Cross multiply

So, we have the following representation

pq = 35 * 12

From the circle, we have

p > q

So, we can rewrite the equation as

p = 35 and q =12

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B: no, bc the side lengths ans angles arent similar

Jayden is folding a paper strip of 66 cm into a 6 sided honeycomb. So the length of each side will be 11cm.

Jayden has a paper strip of length 66 cm. He had to make a honeycomb with it. It will have six equal sides. To calculate the length we have to formulate the equation.

Total length = number of sides × length of one side

 66 = 6 × x

Dividing by 6 on both sides,

66÷6 = 6x ÷ 6

11 = x

So the length of the side of honeycomb will be of 11 cm.

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The complete question is as below

Jayden folded a 66cm strip of paper into 6 equal parts to model a honeycomb cell's. Each part was one side of the model. What is the length of one side of the model?

The dimension of the rectangular prism will be x, x + 2, and x + 1.

Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as

V = L x W x H

The volume of the rectangular prism is given as,

V = x³ + 3x² + 2x

Factorize the equation, then we have

V = x³ + 3x² + 2x

V = x(x² + 3x + 2)

V = x(x² + 2x + x + 2)

V = x[x(x + 2) + 1(x + 2)]

V = x(x + 2)(x + 1)

The dimension of the rectangular prism will be x, x + 2, and x + 1.

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Answer:

4.89

Step-by-step explanation:

6×4 and the root of that is 4.8989794

By rounding off, we can determine that Mike thought the difference would be 72 whereas it is actually 72.74.

When a number is rounded off, its value is maintained but is brought closer to the next number, simplifying the number.

For entire numbers as well as decimals at different places of hundreds, tens, tenths, etc., it is done.

The crucial figures are preserved when numbers are rounded off.

Look at the next digit in the correct position to determine how to round a number; if it is less than 5, round down, and if it is 5 or more, round up.

So, Mike calculated 79 as 79.44 and 7 as 6.7, so he calculated the difference as follows:

79 - 7 = 72

Actual figures that differ are:

79.44 - 6.7 = 72.74

Therefore, by rounding off, we can determine that Mike thought the difference would be 72 whereas it is actually 72.74.

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Correct question:

Mike estimated the difference of 79.44 and 6.7 by rounding each number to the nearest whole. What was Mike's estimate, and what is the actual difference of the numbers? Enter your answers in the boxes. Mike estimated the difference to be . The actual difference is .

Answer:

13/24

Step-by-step explanation:

First we create a common denominator by multiplying the denominators of 8 and 3 to get 24. Now we convert the two given fractions

[tex] \frac{1}{8} = \frac{3}{24} [/tex]

[tex] \frac{1}{3} = \frac{8}{24} [/tex]

A full circle is 24/24. Now all we do is subtract

[tex] \frac{24}{24} - \frac{8}{24} - \frac{3}{24} = \frac{13}{24} [/tex]

Answer:

13/24

Step-by-step explanation:

1-11/24

=

13/24

The USB stick contains 6 whole GB

Given is that the capacity of a USB stick is 49/8 GB.

Given is the expression as -

49/8

Dividing, we get -

6.125

6 + 0.125

where 6 is a whole number while 0.125 is a decimal.

Therefore, the USB stick contains 6 whole GB.

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{Question in english -

Aid:

The capacity of a USB stick is 49\8 GB. How many whole GB does it contain?}

Hi there, here's your answer:

We have -1 < x ≤ 2 and -2 ≤ x < 3

Let's first solve both the inequalities one at a time.

Case 1:

-1 < x ≤ 2

The solution set for this inequality is (-1 , 2]

Case 2:

-2 ≤ x < 3

The solution set for this inequality is [-2 , 3)

Now, the values that satisfy both these inequalities can be taken from the solution set of case 1.

Thus, we get a new solution set for the satisfactory values.

New solution set = (0,2]

The required integer values are:

0, 1 and 2.

Hope this helps!

Answer: 0, 1, 2

Step-by-step explanation:

0 is less then 2 and 3 and greater than -1 and -2

Same for 1 and 2, but for 2 in the first equation it is equal but look at these signs [tex]\leq \geq[/tex]

It means equal or less/greater than.

2 is = 2 so it satsifys the first equation.

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Answer:

7 miles

Step-by-step explanation:

Let's call the distance from point C to point D as "x".

We know that the distance from A to B is 8 miles, and the distance from A to D is 4 miles. To ensure that all three towers are equidistant from each other, the distance from C to B must be equal to 8 miles.

Using the Pythagorean Theorem, we can find the distance from C to D:

(x)^2 + (4)^2 = (8)^2

Expanding and simplifying the equation:

x^2 + 16 = 64

x^2 = 48

x = sqrt(48) = 6.928

So the distance from the third tower to point D is approximately 6.9 miles (rounded to the nearest tenth of a mile).

Answer:

6.9 miles

Step-by-step explanation:

Since the distance between points A and B is 8 miles, and point C is equidistant from points A and B, triangle ABC is an equilateral triangle with side lengths of 8 miles.

As point D is 4 miles from point A, point D is the midpoint of AB.

Therefore, the distance between point C and point D is the altitude of the triangle.

The formula for the altitude of an equilateral triangle is:

[tex]h=\dfrac{\sqrt{3}}{2}s[/tex]

where s is the the side length.

Therefore, the altitude of an equilateral triangle with side length 8 miles is:

[tex]\implies h=\dfrac{\sqrt{3}}{2} \cdot 8[/tex]

[tex]\implies h=4\sqrt{3}[/tex]

[tex]\implies h=6.9\; \sf miles\;(nearest\;tenth)[/tex]

Therefore, the distance from the third tower C to point D is 6.9 miles to the nearest tenth of a mile.

Answer:

Below

Step-by-step explanation:

From 10 am to 1 pm is three hours

  the boys covered distance =  68 miles in 3 hours  

x = rate1

x+3 = rate2

rate  X   time   = distance

(x   +    x+3)  X  3  = 68

6x+9 = 68

6x = 59

x = 9  5/6 mph     then the other rate is x+3 = 12  5/6 mph

Answer: 9.833...

Step-by-step explanation:

The boys traveled a combined 68 miles in 3 hours (difference between 10am and 1pm). This makes their combined speed equal to 68/3.

We can make this equation to model how that combined speed breaks down between them:

68 miles/3 hours = (3 + x) miles/1 hour + x miles/1 hour

To solve:

68/3 = (3 + x) + x

68 = (3 + 2x) * 3

68 = 9 + 6x

59/6 = x

9.833... = x

A square must be a rectangle because it's a four-sided geometric shape with four right angles and congruent sides, but a rectangle doesn't always have congruent sides.

In Mathematics and Geometry, a square can be defined as a type of quadrilateral in which the length of all its four (4) sides are equal in magnitude (congruent) and the sum of all its interior angles is equal to 360 degrees (360°) and it forms a right angle.

In Mathematics and Geometry, a rectangle can be defined as a type of quadrilateral in which its opposite sides are equal and all the angles that are formed are right angles.

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The required amount did she spend on Food is $528.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

We have given;

100% = $2400 which is monthly spend.

Then,

there is 22% spending in food

So,

100% = $2400

1% = $24

22% = $528

Thus, Required spend on Food is $528.

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Answer:

[tex]\displaystyle{52\sqrt{\dfrac{39}{\pi}} \ \: \text{cm}^3}[/tex]

Step-by-step explanation:

The surface area of the sphere has formula of [tex]\displaystyle{4\pi r^2}[/tex] where r is radius. Therefore, set the equation:

[tex]\displaystyle{4\pi r^2=156}[/tex]

Divide both sides by 156:

[tex]\displaystyle{\dfrac{4\pir^2}{4}=\dfrac{156}{4}}\\\\\displaystyle{\pi r^2=39}[/tex]

Then divide both sides by [tex]\displaystyle{\pi}[/tex]:

[tex]\displaystyle{\dfrac{\pi r^2}{\pi} = \dfrac{39}{\pi}}\\\\\displaystyle{r^2=\dfrac{39}{\pi}[/tex]

Square root both sides:

[tex]\displaystyle{\sqrt{r^2}=\sqrt{\dfrac{39}{\pi}}}\\\\\displaystyle{r=\pm\sqrt{\dfrac{39}{\pi}}}[/tex]

However, radius can only be positive. Therefore:

[tex]\displaystyle{r=\sqrt{\dfrac{39}{\pi}}}[/tex]

To find the volume, we have to know that the sphere's volume is:

[tex]\displaystyle{\dfrac{4}{3}\pi r^3}[/tex]

Thus, substitute the value of r in:

[tex]\displaystyle{\text{V} = \dfrac{4}{3}\pi \cdot \left(\sqrt{\dfrac{39}{\pi}}\right)^3}\\\\\displaystyle{\text{V} = \dfrac{4}{3}\pi \cdot \dfrac{39}{\pi}\sqrt{\dfrac{39}{\pi}}}\\\\\displaystyle{\text{V} = 52 \sqrt { \dfrac{39}{\pi}}}[/tex]

Therefore, the volume of sphere is:

[tex]\displaystyle{52\sqrt{\dfrac{39}{\pi}} \ \: \text{cm}^3}[/tex]

At the end of 24 hours, 48 cupcakes will have grown. Every 8 hours, two cupcakes are grown, so after 24 hours, 24 sets of two cupcakes have been grown. Therefore, 48 cupcakes have grown.

At the end of 24 hours, 48 cupcakes will have grown. This is because every 8 hours, two cupcakes are grown. After 24 hours, 24 sets of two cupcakes have been grown. This means that in the 24 hours, two cupcakes were grown a total of 24 times. When this total is multiplied by two, it results in 48 cupcakes being grown. Therefore, after 24 hours, 48 cupcakes have grown. It is important to note that this is only the number of cupcakes that have grown in the 24 hour period, and not the total number of cupcakes. This number includes any cupcakes that were already present at the beginning of the 24 hour period, so the total number of cupcakes at the end of the 24 hour period could be higher than 48.

1. Calculate the number of sets of cupcakes grown in 24 hours: 24 hours divided by 8 hours = 3 sets

2. Calculate the number of cupcakes grown in 24 hours: 3 sets multiplied by 2 cupcakes = 6 cupcakes

3. Calculate the total number of cupcakes grown in 24 hours: 6 cupcakes multiplied by 4 sets = 24 cupcakes

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