Suppose Paul kicks a soccer ball straight up into the air with an initial velocity of 96 feet per second. The function f(x) = -16t2 + 96t gives the height, in feet, of the soccer ball after t seconds. This function is shown in the graph below.



What do the x-intercepts represent in this real life situation in regards to the height of the soccer ball at that time?

We have been given that Lucia is making invisibility potions. Each potion requires 2 eyes of newt. We are asked to find the number of invisibility potions that Lucia can make with 16 eyes of newt.

We will use proportions to find the number of potions that Lucia can make with 16 eyes of newt as:

[tex]\frac{\text{Invisibility potions}}{\text{Number of Newt eyes}}=\frac{1}{2}[/tex]

[tex]\frac{\text{Invisibility potions}}{16}=\frac{1}{2}[/tex]

[tex]\frac{\text{Invisibility potions}}{16}\times 16=\frac{1}{2}\times 16[/tex]

[tex]\text{Invisibility potions}=8[/tex]

Therefore, Lucia can make 8 invisibility potions with 16 eyes of newt.

Answer:

z=10 because 3x5=15 and you do the same to the other number.

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

To get from 3 to 15 you multiply by 5 so if you multiply 2 by 5 you get 10

Answer:

(m,n)

Step-by-step explanation:

Since O is at the origin, we can take the coordinates of point A and divide them by 2 to find the midpoint

( 2m/2,2n/2)

The midpoint is at (m,n)

Answer:

There are 20 color strips in the blanket.

Step-by-step explanation:

We are given the following in the question:

Length of blanket = 6 meter

A new color strip is added every 3 decimetres

We have to find the number of color strips in the blanket.

1 decimetre = 0.1 meter

Number of color strips =

[tex]=\dfrac{\text{Length of blanket}}{\text{Color strip every 3 decimeter}}\\\\=\dfrac{6}{3\times 0.1}\\\\=20[/tex]

Thus, there are 20 color strips in the blanket.

Answer:

The time that the boys need to beat in order to earn a certificate of recognition from the fitness association is 511.264 seconds.

Step-by-step explanation:

We are given that the time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a standard deviation of 40 seconds.

The fitness association wants to recognize the fastest 10% of the boys with certificates of recognition.

Let X = time for this event for boys in secondary school

SO, X ~ Normal([tex]\mu=460,\sigma^{2} =40^{2}[/tex])

The z-score probability distribution for normal distribution is given by;

                               Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)

where, [tex]\mu[/tex] = mean time = 460 seconds

            [tex]\sigma[/tex] = standard deviation = 40 seconds

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, it is given that the fitness association wants to recognize the fastest 10% of the boys with certificates of recognition, which means;

       P(X > x) = 0.10   {where x is the required time which boy need to beat}

       P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{x-460}{40}[/tex] ) = 0.10

        P(Z > [tex]\frac{x-460}{40}[/tex] ) = 0.10

So, the critical value of x in the z table which represents the top 10% of the area is given as 1.2816, that is;

                       [tex]\frac{x-460}{40} =1.2816[/tex]

                         [tex]{x-460}{} =1.2816\times 40[/tex]

                          [tex]x[/tex] = 460 + 51.264 = 511.264 seconds

Hence, the time that the boys need to beat in order to earn a certificate of recognition from the fitness association is 511.264 seconds.

Stacey made 26 small bags of nuts.

To solve this problem, let's first convert all measurements to the same unit, ounces, so we can compare them easily.

Stacey bought 7 pounds of nuts. Since 1 pound is equal to 16 ounces, 7 pounds would be 7×16=112 ounces.

She used 8 ounces of nuts in a recipe.

So, the amount of nuts she had left after using them in the recipe would be 112−8=104 ounces.

Now, if each small bag contains 4 ounces of nuts, we can find out how many small bags she made by dividing the remaining nuts by the amount in each bag:

[tex]\begin{aligned}& \text { Number of small bags }=\frac{\text { Remaining nuts }}{\text { Nuts per bag }}=\frac{104 \text { ounces }}{4 \text { ounces per bag }} \\& =\frac{104}{4} \\& =26\end{aligned}[/tex]

So, Stacey made 26 small bags of nuts.

Answer: It will take the pump 20 min

Step-by-step explanation: Please see the attachments below

Answer:

A= It takes Solomon 16 minutes to print each chess piece.

Step-by-step explanation: Its the first one

The number 16 in this scenario signifies the amount of 3D printed chess pieces. The number indicates the quantity Solomon can print within a particular span of time.

In this given context, 16 refers to the number of 3D printed chess pieces. This is a common type of mathematical problem dealing with ratios or rates. Here, the table suggests a ratio that compares the number of pieces printed to the time it takes to print them. Therefore, 16 essentially represents the quantity of chess pieces that Solomon can print using his 3D printer within a certain amount of time.

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Answer:

14

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

So we know that triangle ABC and QRS are similar.

There is a theorem that states that corresponding sides of similar triangles are proportional.

This means that we can set up a proportion to find the missing side of the triangle.

3/7=6/n

Cross multiply.

3*n=7*6

3n=42

Divide both sides by 3.

n=14

We can find a and b using inverse trig functions,

[tex]

\cos(a)=\frac{4}{5}\implies a=\arccos\Big(\frac{4}{5}\Big)\approx36.87 \\

\sin(b)=-\frac{5}{13}\implies b=\arcsin\Big(-\frac{5}{13}\Big)\approx-22.62

[/tex]

[tex]\tan(36.87-(-22.62))\approx1.7[/tex]

Hope this helps.

I think it's $16.432 but I'm not sure.

The price per cap yielding demand of 330 caps when advertising is increased to $3250 is 16.51 per cap.

What is algebra ?

Algebra is a branch of mathematics that deals with various symbols and the arithmetic operations such as division , multiplication , etc.

It is given that at $15 per cap , $2750 is spent each week on ads , and demand is 330 caps.

So , we can find how much money earn if cost is $15 per cap.

As 330 is the demand , then total earning is :

= 330 × 15

= $ 4950

Out of this , $2750 is spent per week on ads. So , total profit is :

= 4950 - 2750

= $ 2200

Now , If advertising is increased to $3250 then , money more spent on ads is :

= 3250 - 2750

= 500

So , total earning will be :

= 3250 + 2200

= 5450

And price per cap for demand of 330 caps will be :

= 5450 ÷ 330

= 16.51 per cap

Therefore , the price per cap yielding demand of 330 caps when advertising is increased to $3250 is 16.51 per cap.

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Answer:

$480

Step-by-step explanation:

Perry makes 15% commission for each TV he sells.

How much would he have to sell a TV to get $72

First of all, let's call the unknown variable x

So 15% of x= $72

Mathematically, this would be represented as 15/100 * x= 72

15/100x= 72

Breaking down further,

15/100 can be broken down to 3/20

3/20x= 72

So to find the value of x, we divide both sides by 3/20

x= 72 ÷ 3/20

x= 72 * 20/3 (using the law of indices)

x= 1440/3

x= $480 dollars.

So, Perry would have to sell a TV for $480 to make a $72 commission.

Answer:

Diameter = 7cm

Radius = 3.5cm

Step-by-step explanation:

The diameter is the distance across the circle; shown as 7cm.

The radius is half the distance of the diameter, or half the distance across the circle.

Answer:

Radius = 3.5

Diameter = 7

Step-by-step explanation:

Radius = half of diameter

Diameter is the 7 cm you see on the image.

Answer:

The answer is..

A) 45 black cubes

B) 20 yellow cubes

E) 35 white cubes

Step-by-step explanation:

Final answer:

To estimate the total number of a certain cube in the bag, we can use the proportion of the selected cubes to the total number of cubes. The estimates for the total number of a certain cube in the bag are 45 black cubes and 20 yellow cubes.

Explanation:

To estimate the total number of a certain cube in the bag, we can use the proportion of the selected cubes to the total number of cubes. In this case, the proportion of black cubes to the total number of cubes is 9/20. So, if there are 100 cubes in total, we can estimate that there are approximately 45 black cubes in the bag. Similarly, the proportion of yellow cubes to the total number of cubes is 4/20, so we can estimate that there are approximately 20 yellow cubes in the bag. However, the proportion of white cubes to the total number of cubes is 7/20, which is less than the proportion of yellow cubes. Therefore, we cannot estimate that there are 70 white cubes in the bag. The estimates for the total number of a certain cube in the bag are A) 45 black cubes and B) 20 yellow cubes.

Answer:

[tex]240^\circ[/tex]

Step-by-step explanation:

See the attached picture. One possible angle measure is [tex]60^\circ+180^\circ=240^\circ[/tex]

The possible measure of an angle with terminal side in 3rd quadrant and making an angle of 60°with the X-axis is 240°.

When the vertex of an angle is at the origin and one ray is on the positive x-axis, it is said to be in standard position. The ray on the x-axis is known as the starting side, while the ray on the y-axis is known as the terminal side.

The question is shown in the figure below:

The angle made with X - axis = 60°

Angle is lying in 3rd quadrant

If we start moving in the anticlockwise direction then the measure of the total angle will be 180° + 60° = 240°.

Hence, the total angle for an angle lying in 3rd quadrant is 240°.

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Hey there,

The question given is as follows:

When we add polynomials we add like terms (e.x. we add 3x² with -x²) and combine the two to make one polynomial. When we add the two polynomials given above:

So our answer to the problem would be 2x² - 6x.

Hope I helped,

Amna

Answer: the probability that exactly two of the next five people who apply to that university get accepted is 0.23

Step-by-step explanation:

We would number of people that applies for admission at the university and gets accepted. The formula is expressed as

P(x = r) = nCr × p^r × q^(n - r)

Where

x represent the number of successes.

p represents the probability of success.

q = (1 - p) represents the probability of failure.

n represents the number of trials or sample.

From the information given,

p = 0.6

q = 1 - p = 1 - 0.6

q = 0.4

n = 5

the probability that exactly two of the next five people who apply to that university get accepted is

P(x = 2) = 5C2 × 0.6^2 × 0.4^(5 - 2)

P(x = 2) = 10 × 0.36 × 0.064

P(x = 2) = 0.23

Answer:

0.2304 or 23.04%

Step-by-step explanation:

Please kindly check the attached files for explanation

Step-by-step explanation:

Lily goes to gym once every 8 days.

Such that she will visit on 8, 16 , 24, 32 , 40, 48th days

Ann goes once every 12 days

Such that she will visit on 12, 24, 36, 48, 60th days ....

Taylor comes once every 16 days

Such that she will visit on 16, 32, 48, 64th days....

Comparing the common days on which they will visit again after wednesday,

it will be after 48 days, (i.e) after 6 weeks and 5 days, it will be tuesday

Answer:

48 days

Step-by-step explanation:

LCM of 8, 12, 16 is 48.

Answer:

A. Stock XYZ shows the best performance. The scale of Stock ABC makes the graph appear to be rising more slowly.

Step-by-step explanation:

Answer:

7.7833 × 108

Step-by-step explanation:

Answer:

7.78×10∧8

Step-by-step explanation:

Answer:

1.83 units

Step-by-step explanation:

To find we rest the width from the lenght. It would be 4.5 - 2.67 = 1.83, so the lenght was 1.83 units longer than the width.

The length of the rectangle is 1.83 units longer than its width. This value is calculated by subtracting the width (2.67 units) from the length (4.5 units).

The student asked how much longer the length of a rectangle was compared to its width. The length of the rectangle is 4.5 units and the width is 2.67 units. To find how much longer the length is than the width, we subtract the width from the length.

To calculate it:  4.5 - 2.67 = 1.83

So, the length is 1.83 units longer than the width of the rectangle.

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i believe the answer is independant.

if i'm wrong, please tell me so i can fix my mistake =)

Final answer:

The probability of a spinner, with equal chances of landing on any of its six regions, landing on Region 1 first and then on Region 3 in a second spin is 1/36, reflecting independent events.

Explanation:

The question concerns the concept of dependent probability, which involves calculating the likelihood of a sequence of events where the outcome of one event affects the outcome of another.

Since the spinner has an equal chance of landing on each of its six numbered regions, the probability of the first spin landing in region one is 1/6.

However, the second spin is independent of the first, making the probability of landing in region three also 1/6. Since these are independent events, the combined probability of both events happening in sequence is the product of their probabilities, which is 1/6 x 1/6 = 1/36.

Answer:

96%

because if you add all of them up then add 96 then divid by 5 you get 93 which is the average.

hope this helps :)

Answer:

58.077 cubic cm

Step-by-step explanation:

Given that:

As we know that, the volume of a conical perfume bottle is as following:

V = (1/3) * π * r² * h

So perfume can the bottle hold is:

V = (1/3) * 3.14 * 3.4² * 4.8 = 58.077 cubic cm

Hope it will find you well

Answer:

[tex]V \approx 58.107\,cm^{3}[/tex]

Step-by-step explanation:

The volume of a cone is:

[tex]V = \frac{1}{3}\pi\cdot r^{2}\cdot h[/tex]

Where:

[tex]r[/tex] - Radius, in centimeters.

[tex]h[/tex] - Height, in centimeters.

The volume of liquid that bottle can hold is:

[tex]V = \frac{1}{3}\pi \cdot (3.4\,in)^{2}\cdot (4.8\,cm)[/tex]

[tex]V \approx 58.107\,cm^{3}[/tex]

Answer:

[tex]m\angle ABC=46^o[/tex]

Step-by-step explanation:

step 1

we know that

The inscribed angle is half that of the arc it comprises.

so

[tex]m\angle ADC=\frac{1}{2}(arc\ AC)[/tex]

we have

[tex]m\angle ADC=23^o[/tex]

so

[tex]23^o=\frac{1}{2}(arc\ AC)\\arc\ AC=46^o[/tex]

step 2

we know that

Central angle is the angle that has its vertex in the center of the circumference and the sides are radii of it

so

[tex]m\angle ABC=arc\ AC[/tex] ----> by central angle

therefore

[tex]m\angle ABC=46^o[/tex]

The mean point of the each group can be calculated using midpoint and mean formula. The mean is sum of all the term divided by number of term.

The mean height of a plant is 30.5.

Given:

The height of plant and frequency is given in table.

Refer the attached table for the calculation of mid point and frequency of midpoint.

Now we have ,

[tex]\rm {Sum \:of\: frequencies} = 20[/tex]

[tex]{\rm Sum \:of\: frequency\: \times midpoint\: product} = 610[/tex]

Calculate the mean of height of a plant.

[tex]\rm Mean=\dfrac{610}{20}\\\rm Mean=30.5[/tex]

Thus, the mean height of a plant is 30.5.

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To estimate the mean height of 20 plants, using midpoints and frequencies, the calculation yields approximately 13.89 cm. This provides a representative value based on the distribution of heights within specified intervals.

To estimate the mean height of the plants using the midpoints of each group, we'll calculate the midpoints for each interval and then find the weighted average.

1. Midpoint for 0 < h < 10:

  - Midpoint = (0 + 10)/2 = 5

2. Midpoint for 10 < h < 20:

  - Midpoint = (10 + 20)/2 = 15

3. Midpoint for 20 < h < 30:

  - Midpoint = (20 + 30)/2 = 25

4. Midpoint for 30 < h < 40:

  - Midpoint = (30 + 40)/2 = 35

5. Midpoint for 40 < h < 50:

  - Midpoint = (40 + 50)/2 = 45\)

6. Midpoint for 50 < h < 60:

  - Midpoint = (50 + 60)/2 = 55

Now, calculate the weighted average using the frequencies:

[tex]\[ \text{Mean height} = \frac{\sum (\text{Midpoint} \times \text{Frequency})}{\sum \text{Frequency}} \]\[ \text{Mean height} = \frac{(5 \times 4) + (15 \times 2) + (25 \times 3) + (35 \times 0) + (45 \times 0) + (55 \times 0)}{4 + 2 + 3 + 0 + 0 + 0} \]\[ \text{Mean height} = \frac{20 + 30 + 75}{9} \]\[ \text{Mean height} = \frac{125}{9} \][/tex]

Therefore, the estimate for the mean height of a plant is approximately 13.89 cm.

Answer:

58

Step-by-step explanation:

Order of operations.

Additions and subtractions, in the order they appear, from left to right.

30 + 30 - 2 =

= 60 - 2

= 58

Step 1: Simplify both sides of the equation.

28 =  −7 /2 x

Step 2: Flip the equation.

−7 /2 x = 28

Step 3: Multiply both sides by 2/(-7).

( 2 /−7 )*( −7 /2 x) = (  2 /−7 )*(28)

x=−8

Answer:

x=−8

[tex]28 = - \frac{7}{2} x \\ x = 28 \div ( - \frac{7}{2} ) \\ x = 28 \times ( - \frac{ 2 }{7} ) \\ x = - 8[/tex]

Let's chek

[tex] - 8 \times ( - \frac{7}{2} ) = \frac{8 \times 7}{2} \\ = 28[/tex]

Answer:

[tex]x = - 8[/tex]

Answer:

a= 20

Step-by-step explanation:

We can use the Pythagorean theorem to solve

a^2+b^2 = c^2  where a and b are the legs and c is the hypotenuse

The diagonal is the hypotenuse  and the length and width are the legs

a^2 + 15^2 =25^2

a^2 +225 = 625

Subtract 225 from each side

a^2+225-255=625-225

a^2 = 400

Take the square root of each side

sqrt(a^2) =sqrt(400)

a = 20

Answer:

7.5 Quarts

Step-by-step explanation:

D'Naisa mixed the following:

We are to determine in total, the number of quarts of paint that she mixed. this is done by converting each of the volume to quart.

1 gallon of orange paint

3 pints of red paint.

Therefore,

Total Volume of Paint Mixed in quart= Volume of Orange+Yellow+Red

=4+2+1.5

=7.5 Quarts